Engineering of Crystalline Materials Properties: State of the Art in Modeling, Design and Applications

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Engineering of Crystalline Materials Properties

NATO Science for Peace and Security Series This Series presents the results of scientific meetings supported under the NATO Programme: Science for Peace and Security (SPS). The NATO SPS Programme supports meetings in the following Key Priority areas: (1) Defence Against Terrorism; (2) Countering other Threats to Security and (3) NATO, Partner and Mediterranean Dialogue Country Priorities. The types of meeting supported are generally "Advanced Study Institutes" and "Advanced Research Workshops". The NATO SPS Series collects together the results of these meetings. The meetings are coorganized by scientists from NATO countries and scientists from NATO's "Partner" or "Mediterranean Dialogue" countries. The observations and recommendations made at the meetings, as well as the contents of the volumes in the Series, reflect those of participants and contributors only; they should not necessarily be regarded as reflecting NATO views or policy. Advanced Study Institutes (ASI) are high-level tutorial courses intended to convey the latest developments in a subject to an advanced-level audience Advanced Research Workshops (ARW) are expert meetings where an intense but informal exchange of views at the frontiers of a subject aims at identifying directions for future action Following a transformation of the programme in 2006 the Series has been re-named and re-organised. Recent volumes on topics not related to security, which result from meetings supported under the programme earlier, may be found in the NATO Science Series. The Series is published by IOS Press, Amsterdam, and Springer, Dordrecht, in conjunction with the NATO Public Diplomacy Division. Sub-Series A. B. C. D. E.

Chemistry and Biology Physics and Biophysics Environmental Security Information and Communication Security Human and Societal Dynamics

http://www.nato.int/science http://www.springer.com http://www.iospress.nl

Series B: Physics and Biophysics

Springer Springer Springer IOS Press IOS Press

Engineering of Crystalline Materials Properties State of the Art in Modeling, Design and Applications edited by

Juan J. Novoa University of Barcelona, Barcelona, Spain

Dario Braga University of Bologna, Bologna, Italy and

Lia Addadi Weizmann Institute of Science, Rehovot, Israel

Published in cooperation with NATO Public Diplomacy Division

Proceedings of the NATO Advanced Study Institute on Engineering of Crystalline Materials Properties: State of the Art in Modeling, Design and Applications. New Materials for better Defence and Security Erice, Italy 7– 17 June 2007

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-1-4020-6824- 9 (PB) ISBN 978-1-4020-6822-5 (HB) ISBN 978-1-4020-6823-2 (e-book)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com

Printed on acid-free paper

All Rights Reserved © 2008 Springer Science+Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

TABLE OF CONTENTS PREFACE

vii

LIST OF CONTRIBUTORS

ix

Biomineralization Design Strategies and Mechanisms of Mineral Formation: Operating at the Edge of Instability Lia Addadi, Yael Politi, Fabio Nudelman, Steve Weiner

1

Self-Assembled Monolayers as Templates for Inorganic Crystallization: A Bio-Inspired Approach Joanna Aizenberg

17

Databases in Crystal Engineering Alessia Bacchi

33

Case Studies on Intermolecular Interactions in Crystalline Metals Patrick Batail

59

Crystal Polymorphism Joel Bernstein

87

Complementarity: Correlating Structural Features with Physical Properties in Supramolecular Systems Susan A. Bourne Making Crystals from Crystals: A Solid-State Route to the Engineering of Crystalline Materials, Polymorphs, Solvates and Co-Crystals; Considerations on the Future of Crystal Engineering Dario Braga, Marco Curzi, Elena Dichiarante, Stefano Luca Giaffreda, Fabrizia Grepioni, Lucia Maini, Giuseppe Palladino, Anna Pettersen, Marco Polito

111

131

Nanostructured Frameworks for Materials Applications Neil R. Champness

157

Crystal Engineering of Multifunctional Molecular Materials Eugenio Coronado, Carlos Giménez-Saiz, Carlos Martí-Gastaldo

173

Topological Approaches to the Structure of Crystalline and Amorphous Atom Assemblies Linn W. Hobbs Hydrogen-Bonded Crystals of Exceptional Dielectric Properties Andrzej Katrusiak v

193

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Chirality in Crystals Reiko Kuroda Design, Characterization and Use of Crystalline Thin Film Architectures at the Air-Liquid Interface Leslie Leiserowitz, Isabelle Weissbuch, Meir Lahav Design, Synthesis, and Characterization of Molecule-Based Magnets Joel S. Miller From Bonds to Packing: An Energy-Based Crystal Packing Analysis for Molecular Crystals Juan J. Novoa, Emiliana D’Oria On the Calculation and Interpretation of Crystal Energy Landscapes Sarah L. Price NMR Crystallography and the Elucidation of Structure-Property Relationships in Crystalline Solids Susan M. Reutzel-Edens

251

271

291

307

333

351

Organic Materials for Nonlinear Optics M. Blanca Ros

375

Building Conducting Materials from Design to Devices Concepció Rovira

391

Hydrogen Bonding and Concurrent Interactions Urszula Rychlewska

407

Signalling by Modulation of Intermolecular Interactions Janet L. Scott, Koichi Tanaka

429

Biomineralization of Organic Phases Associated with Human Diseases Jennifer A. Swift

449

Crystal Structure Determination from X-ray Powder Diffraction Data Maryjane Tremayne

477

Surface Properties of the Binary Alloy Thin Films Ilona Zasada

495

SUBJECT INDEX

515

PREFACE

This volume collects the lecture notes (ordered alphabetically according to the first author surname) of the talks delivered by the main speakers at the Erice 2007 International School of Crystallography, generously selected by NATO as an Advanced Study Institute (# 982582). The aim of the school was to discuss the state-of-the-art in molecular materials design, that is, the rational analysis and fabrication of crystalline solids showing a predefined structural organization of their component molecules and ions, which results in the manifestation of a specific collective property of technological interest. The School was held on June 7–17, 2007, in Erice (an old town, over 3000 years, located on the top of a Sicilian hill that oversees the sea near Trapani). The school developed following two parallel lines. First we established “where we are” in terms of modelling, design, synthesis and applications of crystalline solids with predefined properties. Second, we attempted to define current and possible futuristic lines of development in the quest for novel molecule-based materials with potential applications in magnetism, conductivity and superconductivity, non-lineal optics (NLO), drug delivery, and nanotechnology. In recent years, solid state chemistry and crystal engineering have evolved at the intersection between the top-down and bottom-up approaches towards materials design and fabrication. An ever-increasing number of scientists are learning how to control self-assembly, molecular recognition, and other fundamental processes on the way to achieving ‘tailor-made’ materials, such as crystal nucleation, crystal growth, and polymorphism. And yet, only in a limited manner and in a limited number of cases, chemists have been able to design collective properties of crystalline materials. In order to push forward this ambitious project we need to develop a synergistic interaction across a wide variety of disciplines. Trying to facilitate such interaction, this school brought together scientists from different areas of interest in the field of “Molecular Materials by Design”, ranging from the theoretical evaluation of crystal and molecular properties, to the preparation, crystallization and characterization of molecular and covalent crystalline materials, covering also other relevant issues such as biomaterials, bio-inspired crystallization, and crystal polymorphism. We concluded in the school that we are starting to understand many of the key issues needed for a rational design and fabrication of crystals having a desired packing. We are also getting better at predicting what factors control the presence/absence of some macroscopic properties. We are learning how to rationalize already known crystal structures, and are getting a handle on complex issues such as polymorphism, nucleation and vii

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growth, in some cases thanks to the study of biogenic materials. All of these conclusions are properly described in the lecture notes that follow these lines. However, we are still far from being able to perform a proper crystal packing prediction and growth of crystals presenting a specific property. In the meantime, we can look for new approaches by educated serendipity, supplemented by close inspection of the new structures and their properties. We hope that the school not only provided an opportunity to further develop interdisciplinary approaches in crystal engineering, but also will assist in the dissemination of new ideas and results. We also hope that the school and the lecture notes here collected will help to attract young and energetic scientist to this exciting field of science. Finally, we would like to thank all the institutions that made possible the event. First of all, NATO Science for Peace Division for a generous grant that made possible the organization of the Advanced Study Institute. We would also like to thank the economical support provided by the International Union of Crystallography. Substantial economical support was also provided by the US National Science Foundation, the company PolyCrystalLine (Bologna, Italy), and by CrystEngComm and the New Journal of Chemistry (two of the journals of the U.K. Royal Society of Chemistry). Last but not least, we want to thank all the members of the local organization, starting from Prof. Lodovico Riva di Sanseverino and Prof. Paola Spadon, and on to all the members of the “orange scarves” (in alphabetical order, G. Falini, L. Fonso, J. Irwin, M. Lusi, G. Palladino, E. Papinutto, M. Polito, M. Pota). Thanks to them organizing the school was easy, and running it was a pleasure. Juan J. Novoa Dario Braga Lia Addadi

LIST OF CONTRIBUTORS

Lia Addadi Dept of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel Joanna Aizenberg Harvard University, School of Engineering and Applied Sciences, 29 Oxford Street, Cambridge, MA 02138, USA Alessia Bacchi Dipartimento di Chimica Generale ed Inorganica, Chimica Analitica, Chimica Fisica, University of Parma, Italy Patrick Batail CNRS, Université d’Angers, 49045 Angers, France Joel Bernstein Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, Israel 84105 Susan A. Bourne Department of Chemistry, University of Cape Town, Rondebosch 7701, South Africa Dario Braga Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Neil R. Champness School of Chemistry, The University of Nottingham, University Park, Nottingham NG7 2RD, U.K. Eugenio Coronado Instituto de Ciencia Molecular, Universitat de Valencia Polígono de la Coma, s/n, 46980 Paterna, Spain Marco Curzi PolyCrystalLine s.r.l. Via Stradelli Guelfi 40/c, 40138 Bologna, Italy

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Elena Dichiarante PolyCrystalLine s.r.l. Via Stradelli Guelfi 40/c, 40138 Bologna, Italy Emiliana D’Oria Departament de Química Física, Fac. Química & CERQT, Parc Cientìfic de Barcelona, Universitat de Barcelona, Av. Diagonal, 647, 08028-Barcelona, Spain Stefano Luca Giaffreda PolyCrystalLine s.r.l. Via Stradelli Guelfi 40/c, 40138 Bologna, Italy Carlos Giménez-Saiz Instituto de Ciencia Molecular, Universitat de Valencia Polígono de la Coma, s/n, 46980 Paterna, Spain Fabrizia Grepioni Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Linn W. Hobbs Department of Materials Science & Engineering Department of Nuclear Science & Engineering Massachusetts Institute of Technology Room 13-4054, 77 Massachusetts Avenue Cambridge, MA 02139-4307, USA Andrzej Katrusiak Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Pozna , Poland Reiko Kuroda Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo, 153-8902 Japan & JST ERATO-SORST Kuroda Chiromorphology Team, 4-7-6, Komaba, Meguro-ku, Tokyo, 153-0041 Japan Meir Lahav Dept. Materials & Interfaces, The Weizmann Institute of Science, Rehovot, Israel

LIST OF CONTRIBUTORS

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Leslie Leiserowitz Dept. Materials & Interfaces, The Weizmann Institute of Science, Rehovot, Israel Lucia Maini Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Carlos Martí-Gastaldo Instituto de Ciencia Molecular, Universitat de Valencia Polígono de la Coma, s/n, 46980 Paterna, Spain Joel S. Miller Department of Chemistry, University of Utah, 315 S. 1400 E. Room 2120, Salt Lake City, UT 84112-0850 Juan J. Novoa Departament de Química Física, Fac. Química & CERQT, Parc Cientìfic de Barcelona, Universitat de Barcelona, Av. Diagonal, 647, 08028-Barcelona, Spain Fabio Nudelman Dept of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel Giuseppe Palladino Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Anna Pettersen Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy Yael Politi Dept of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel Marco Polito Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy

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Sarah L. Price Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK Susan M. Reutzel-Edens Lilly Research Laboratories, Eli Lilly and Company Indianapolis, IN, 46285 USA M. Blanca Ros Química Orgánica, Facultad de Ciencias, Universidad de Zaragoza-Instituto de Ciencia de Materiales de Aragón, 50009-Zaragoza, Spain Concepció Rovira Departament de Nanociència Molecular i Materials Orgànics, Institut de Ciència de Materials de Barcelona (CSIC), Campus Universitari de Bellaterra, 08193 Cerdanyola, Barcelona, Spain Urszula Rychlewska Dept. of Chemistry Adam Mickiewicz University 60-780 Pozna , Poland Janet L. Scott School of Chemistry, Monash University, Wellington Road, Clayton, Victoria 3800, Australia Jennifer A. Swift Department of Chemistry, Georgetown University, 37th and O Sts NW, Washington, DC 20057-1227, USA Koichi Tanaka Department of Applied Chemistry, Faculty of Engineering & High Technology Research Center, Kansai University, Suita, Osaka 564-8680, Japan Maryjane Tremayne School of Chemistry, University of Birmingham, Edgbaston, Birmingham, United Kingdom, B15 2TT

LIST OF CONTRIBUTORS

Steve Weiner Dept of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel Isabelle Weissbuch Dept. Materials & Interfaces, The Weizmann Institute of Science, Rehovot, Israel Ilona Zasada Solid State Physics Department, University of Lodz, ul. Pomorska 149/153, 90263 Lodz, Poland

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BIOMINERALIZATION DESIGN STRATEGIES AND MECHANISMS OF MINERAL FORMATION: OPERATING AT THE EDGE OF INSTABILITY LIA ADDADI*, YAEL POLITI, FABIO NUDELMAN AND STEVE WEINER Dept of Structural Biology, Weizmann Institute of Science, Rehovot 76100, Israel

Abstract. The biological approach to forming crystals is proving to be most surprising. Three strategies evolved by organisms to build their mineralized materials will be discussed. These are: 1) Building mineralized structures with stable amorphous phases; 2) building mineralized structures with single crystals; 3) building mineralized structures with polycrystalline organized arrays. Interestingly, all appear to involve at some stage the use of an amorphous mineral phase.

Keywords: Biomineralization, biogenic minerals, amorphous calcium carbonate, spicules, sea urchin, mollusk shell, ascidians

1. Introduction The process of mineral formation by organisms – biomineralization – is an intriguing interplay between the biological and the inorganic worlds. A variety of mineralized hard parts are built by organisms, using more than 60 different minerals in crystalline and/or amorphous forms.1 Many biogenic materials fulfill mechanical support functions, such as sponge spicules, coral and vertebrate skeletons, provide protection, such as mollusk shells, crustacean carapaces or echinoderm spines and tests and are used for food grinding, such as echinoderm, mollusk and vertebrate teeth. Some have more specialized functions, such as navigation control in fish otoliths or magnetotactic bacteria2 and optical photonic effects in fish skin and

______ *

To whom correspondence should be addressed.

1 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 1–15. © 2008 Springer.

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insect elytra.3,4 The functions of many other mineralized deposits, such as the calcium oxalate crystals and cystoliths in some plant leaves, are as yet unknown. Organisms have been building skeletal materials for more than 550 millions years.5 Nature has thus had the advantage of hundreds of millions of years to evolve strategies for building materials that are optimally adapted to their function and have advantageous properties, such as being light-weight and often with amazing mechanical properties even though production occurs at ambient temperatures and pressures. Furthermore, the starting materials are often not suited for such functions, and ingenious solutions have been found. The formation of many mineralized materials thus involves the use of unconventional strategies. The control over their construction encompasses all length scales, from Ångstroms to centimeters.1 Thus much of the focus in biomineralization research is on understanding the strategies that evolved for exercising control. One group of organisms belonging to the Chordata, the phylum that includes the Vertebrata, shows astounding abilities to control crystal properties. These are the ascidians or tunicates, colloquially known as sea squirts. They produce spicules to presumably stiffen their outer walls or tunics, which are composed of cellulose.6 The spicules adopt some amazing shapes and are formed from a variety of different calcium carbonate polymorphs and amorphous calcium phosphate. Calcite (Fig 1A), aragonite (Fig 1B), vaterite (Fig 1C), amorphous calcium carbonate (Fig 1D) and amorphous calcium phosphate (Fig 2B) spicules are produced by different species with consistent control over all parameters, which indicates that they are genetically controlled.7 Control is thus exerted over nucleation and growth, crystal polymorphism, morphology, size, as well as location, orientation and organization in the tissue. The shapes of the spicules in figures 1A and D are not similar to any calcium carbonate crystals grown in non-biogenic environments, raising the first fundamental question: how can shape control be achieved with a mineral that is solid and often crystalline, so as to produce objects with complex morphologies? The problem is that crystals tend to grow preferentially along the directions in which interactions are stronger, and they terminate with sharp defined faces. In fact these can be seen in the ascidian spicules shown in figures 1B and C. Some organisms achieve what appears to be almost total control over shape, completely overruling the preferred crystal growth directions, whereas others incorporate the natural tendencies of crystals to adopt certain shapes into complex structures. There are six known phases of calcium carbonate: at ambient temperatures calcite (Fig 1E) is the most stable phase, followed by aragonite (Fig 1F), vaterite (Fig 1G), monohydrocalcite (Fig 3B), calcium carbonate hexahydrate and finally amorphous calcium carbonate (ACC). The phases are listed here in order of sharply decreasing stability.8

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Amorphous calcium carbonate is very rare in non-biogenic environments, because of its instability.9 Several taxa, however, deposit stable ACC (see below).

Figure 1. A–D. Examples of spicules produced by different species of ascidians (tunicates). Within each species, the mineral, the shape and the size of the spicules are consistently reproduced, showing that these properties are genetically controlled. The spicules in this figure are all composed of different polymorphs of calcium carbonate. A. Calcitic spicule from Bathypera ovoidea (1E); B. Aragonitic spicules from Didemnidum sp. (1F); C. Part of a spicule composed of vaterite from Herdmania momus (1G); D. Body spicule from Pyura pachydermatina: the mineral is amorphous calcium carbonate; E. Crystal structure of calcite: Ca, white; C, black; O, gray; F. Crystal structure of aragonite; G. Crystal structure of vaterite. Photographs A–C were taken from the collection of Heinz A Lowenstam. Scale bars are 10 m.

Here we discuss 3 different strategies that organisms use to produce mineralized materials. Interestingly, all appear to involve the use of an amorphous mineral phase. These are: 1) building mineralized structures with stable amorphous phases; 2) building mineralized structures with

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single crystals; 3) building mineralized structures with polycrystalline organized arrays. 2. Building Mineralized Structures with Stable Amorphous Phases One advantage of building skeletal parts of complex shapes out of amorphous minerals is obviously related to their being isotropic.10 This property is suitable for the formation of complex shapes, in a manner analogous to the ways in which waxes or glasses can be molded by the geometrical constraints of the containing vessel. Amorphous minerals are not rare in biomineralization: in fact, one of the most abundant minerals produced is opal, amorphous hydrated silica.11 Siliceous skeletons are particularly widespread in the kingdoms of Protoctista (diatoms (Fig 2A), radiolarians), in the Plantae (phytoliths), and in the animal kingdom by the Porifera (sponges). Silica is amorphous and stable because it is composed essentially of a 3-dimensional disordered polymeric network of (SiO2)n. The amorphous phases of other minerals, however, are relatively unstable, yet quite a few different groups of organisms use them for building their skeletal parts. In addition to the ascidians that form spicules composed of amorphous calcium carbonate (Fig 1D) and amorphous calcium phosphate (Fig 2B), this includes plant cystoliths (Fig 2C),12 crustacean carapaces and various calcium storage granules.13 An organism that uses amorphous calcium carbonate to build its mineralized parts, must invest energy to stabilize it. The stabilization of the amorphous mineral becomes then part of the strategies used for controlling mineralization. How is this achieved? In most known biogenic skeletal parts stable ACC contains other ions, such as Mg or phosphate,14 which presumably contribute to the stabilization of the amorphous phase. All biogenic ACCs contain proteins, although in minute amounts, typically 0.05wt%.15 The proteins from Pyura pachydermatina ACC body spicules were shown in vitro, to be able to stabilize the amorphous phase without any other additives in solution.16 Not much is known about these proteins, besides the fact that they are rich in Glu/Gln, Ser and Gly. Only one protein associated with stable ACC has been sequenced to date: it contains 16 repeats of glutamic acid and glutamine.17 Specialized proteins appear thus to be crucial in the strategy evolved by organisms to stabilize amorphous calcium carbonate. How this is achieved with such a minute amount of protein additive, is still not clear. There are just too few macromolecules for them to function through active inhibition of each and every critical nucleus of crystallization that may not be larger than a few tens of ions.

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Figure 2. Examples of biogenic skeletal parts composed of stable amorphous minerals. A. Diatom cell wall: diatoms are a major group of unicellular algae. Their cells are encased within a unique cell wall made of silica. B. Spicule from the ascidian Culeolus murrayi: the mineral is amorphous calcium phosphate (photograph H.A. Lowenstam). C. Cystolith from Ficus microcarpa: cystoliths are irregular-shaped objects, a few tens of μm in length, which are found in the epidermis of leaves from plants of various families. They are composed entirely of ACC.

TGA-DTA analyses of stable biogenic ACCs show that they all contain water in proportions of one molecule of water/calcium carbonate.18 Raman, infrared spectroscopy, X-ray absorption spectroscopy (XAS)19 and theoretical DFT calculations20 have been used to characterize these peculiar phases of hydrated ACC. XAS in particular provides structural information about the neighborhood of absorbing atoms, which cannot be obtained from diffraction as these are amorphous materials. XAS studies show that stable biogenic ACCs possess different degrees of short range order in their coordination spheres around the calcium ions. In agreement with their composition (one mole of water for one mole of calcium carbonate), their structures are closest to monohydrocalcite (Fig 3A, B). They are however all different from each other in the amount of disorder, ranging from the ascidian spicules, which are partially ordered only at the level of the first oxygen atoms around the calcium ions, to the plant cystoliths, which are the closest to a crystalline structure (Fig 3A).19 The water clearly contributes to the biogenic ACC stability. The macromolecules presumably stabilize kinetically the amorphous hydrated form, in such a manner that critical nuclei for crystallization do not form. As noted, how this is achieved is not yet clear.

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Figure 3. A. Schematic representation of the information obtained from XAS measurements performed on skeletal parts composed of stable (top row) and transient (bottom row) amorphous calcium carbonate, together with the equivalent representations of monohydrocalcite and calcite. The circles represent the coordination shells, for which the number of atoms in the shell is reported. The fact that the XAS spectra of Pyura pachydermatina spicules and of the sea urchin larva 1 do not provide information beyond the carbon and oxygen atom shells, respectively, indicates that these structures are more disordered. The coordination patterns and the amount of order are different in each sample. The stable biogenic ACC has a coordination sphere similar to monohydrocalcite, whereas the transient ACC has a structure practically identical to calcite, even though the spicules are still >70% ACC. B. The structure of the Ca1 coordination sphere in monohydrocalcite. The structure comprises 3 independent Ca atoms. C. The structure of the Ca coordination sphere in calcite. Ca, white; C, black; O, light gray; H2O, dark gray.

3. Building Mineralized Structures Composed of Single Crystals The advantages of building large and complex skeletal parts out of single crystals are not completely obvious. On the one side, using a single crystal provides a continuity and homogeneity of the solid medium that could hardly be achieved with a less ordered polycrystalline material. Crystalline phases in most cases do not have to be stabilized, and are thus preferable to amorphous unstable phases (see above). Single crystals may also have useful optical or magnetic properties that could be exploited by organisms.2,21 Mechanically, single crystals are tougher than their amorphous counterparts, but are often brittle because of the intrinsic anisotropy of the structure. This is particularly true for calcite, whose typical {104} cleavage plane dominates the mechanical behavior of the crystals, making it very brittle. Sponges and echinoderms in particular evolved strategies that allow them to build large skeletal parts with convoluted morphologies, using large

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calcite single crystals (Fig 4). Paradoxically, the biogenic calcite fracture surfaces are conchoidal, resembling the manner in which glass fractures rather than single calcite crystals.22 High-resolution X-ray diffraction measurements of the crystal coherence lengths in different crystallographic directions, combined with crystal growth experiments in vitro, provided part of the answer to this paradox. The intrinsic brittleness of calcite is overcome by the intercalation of specialized proteins along specific crystal planes oblique to the {104} cleavage plane, thus effectively blocking cleavage at a scale of hundreds of nanometers.23 The intercalated proteins generate imperfections that limit the coherence length of perfect crystal domains anisotropically. Interestingly, this anisotropy is often independent of the crystallographic symmetry rules and closely reproduces the convoluted crystal morphology.24 This raises the fundamental question of whether protein intercalation determines crystal growth morphology in different directions or rather the morphology induced by the mineral-depositing cells determines the location and partly the direction of intercalation of the macromolecules. How are the single crystals molded into their complex morphologies? Analysis of the sea urchin larval spicule formation process provides an answer to this question.25 This system has the enormous advantage that it can be followed in real time during its development. The setting up of the microenvironment and the development of mineralization can be monitored using live specimens. Sea urchin larvae have an endoskeleton composed of two spicules, each behaving under polarized light as if it were a single crystal of calcite.26 During spicule development, the first deposit has the shape of a crystal of calcite. This first deposit develops into a triradiate spicule, with three arms in the directions of the a* axes of calcite. The spicule then curves through 90 degrees and grows along the c direction of the final calcite crystal, developing into the complex mature morphology (Fig 4C).27 The spicule forms in a privileged compartment inside a specialized membrane, the syncitium. The syncitium is connected to cells which secrete into the membrane-delimited space the mineral precursors and macromolecules needed for spicule development. After the initial deposition, the spicule grows into a single crystal via a phase of amorphous calcium carbonate that is introduced directly into the syncitium through vesicles produced in the cells.28 The strategy thus consists of molding the object out of an isotropic transient amorphous phase, and then transforming it in a controlled manner into a crystalline material. What is the ‘structure’ of the transient ACC? How does the transformation work out? Analysis of spicules at different stages of development, using both XAS and IR spectroscopy provides a structural description of the mineral development in time.29 Initially the forming triradiate spicules are

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composed of >70% ACC, while the more mature stages reach up to >80% ACC. Intermediate stages occasionally produce spectra that both in IR and in XAS appear to be 100% amorphous (Fig 3A, sea urchin larva 1).

Figure 4. Examples of biogenic skeletal parts composed of calcite single crystals. A. Vertebra from the brittle star Ophiocoma vendtii. Brittle stars (Ophiuroidea) are echinoderms, closely related to sea stars and sea urchins. Their bodies have typical five-fold symmetry; the five jointed arms have several types of ossicles, each formed by one or two calcite single crystals. The vertebrae are formed of two crystals, fused along the middle mirror-symmetry line. B. Quadriradiate spicules extracted from the calcareous sponge Kebira uteoides. Each spicule is composed of one single crystal of calcite; the crystallographic orientation of the spicule arms is preserved in all spicules, but their morphological symmetry does not follow the crystallographic symmetry of calcite.24 C. Larval spicule from the sea urchin Lytechinus pictus. The mature spicule diffracts X-rays as a calcite single crystal, with the c-axis parallel to the long spicule body rod. The central part has a typical triradiate shape, with each of the radii oriented along the a* axis of the crystal: this is the location where the spicule growth starts. D. Five days old regenerated sea-urchin spine (left), growing on the original broken spine (right). Sea urchin spines are living structures, and thus may be regenerated when broken. The regenerated part grows seamlessly fused to the broken stump, such that the two parts together form one single calcite crystal. The fenestrated stereom structure, typical of young spines, is subsequently filled in resulting in the solid sectors of the mature spine.

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Figure 5. Schematic representation of the evolution of a hypothetical structure from an amorphous, completely disordered state characterized by distorted coordination spheres, to an amorphous state with short range order and finally to an organized lattice. The short range ordered structure has local order around the central atom, but the different coordination spheres are not oriented relative to each other.

Interestingly, XAS structural fitting shows that the coordination sphere around the calcium ions is practically identical to calcite (Fig 3A, sea urchin larva 2), even though the bulk of the mineral is still amorphous. We conclude that this form of transient ACC has short-range order and atomic coordination similar to that of calcite, but the individual coordination spheres are not correlated in the medium and long range with each other. The crystallization process would than consist of long range ordering of the lattice (Figure 5). 4. Building Mineralized Structures with Polycrystalline Organized Arrays The fundamental strategy underlying this type of construction consists of laying down a preformed organic matrix, which is then progressively filled in with arrays of oriented crystals. The matrix provides the framework for mineralization and directly controls the polymorph type, shape, orientation and organization of the crystals.1 In the bone-type materials, nanometer size oriented crystals of carbonated apatite are initially deposited inside the grooves within the collagen fibers.30,31 In tooth enamel, tens of micrometers long carbonated apatite ribbon-shaped crystals form bundles that interweave in three dimensions.32 Specialized proteins, the amelogenins, form the envelopes within which each crystal is deposited.33 Mollusks use seven basic structures for forming their shells.34,35 An individual shell is usually

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composed of two or three different structures. Two of these structures, the nacreous and simple prismatic structures, will be compared and contrasted here. Nacre constitutes the ‘mother of pearl’ internal layer of many shells and is composed of layers of polygonal crystal tablets growing inside a predeposited framework composed of -chitin, silk and acidic proteins (Fig 6 A, B, C; Fig 7A).36–38 Each tablet is a single crystal of aragonite (Fig 1B).39 The -Chitin is organized in sheets that form the scaffold onto which unusually acidic proteins are adsorbed and inside which the crystals grow.40,41 The silk-fibroin-like proteins are in a hydro-gel state that fills the space between two layers of chitin, and probably also have the function of inhibiting non-specific crystallization.42–44 After the mineral grows, the silklike proteins end up compressed between the nacre tablets and the chitin scaffold. Some of the acidic proteins are located in a nucleation site, where they are actively involved in the induction of nucleation.45,46 The crystal nucleates and grows on the chitin sheets, and in fact the orientation of the chitin fibers dictates the orientation of the crystals on the ab plane.47 Extrapolating from the fact that mollusk larvae form their shells via a transient ACC phase, and from other circumstantial evidence, we suggest that mineral deposition also occurs through amorphous calcium carbonate particles, secreted by the cells into the silk fibroin hydro-gel. These particles would eventually nucleate on the acidic proteins adsorbed on the chitin fibers, and grow into the mature crystals, filling the space between the chitin sheets. In contrast to nacre, the prismatic layer of the bivalve Atrina rigida is composed of calcite crystals 50–100 μm wide and hundreds of μm long, oriented with their c-axes parallel to the direction of elongation of the prisms (Fig 6D, E). Each crystal is enclosed in an organic envelope (Fig 6F), composed mainly of hydrophobic glycine-rich macromolecules. The crystals are of exceptional quality, with coherence lengths of close to half a micron.48 Astoundingly, these high-quality crystals occlude a dense meshwork of chitin fibers (Fig 7B, C) that extends throughout the whole volume of the crystal, with a mesh size of hundreds of nanometers.49 This is yet another proof of calcite’s ability to occlude all kinds of macromolecules and over-grow them without substantially changing its properties. The crystals also contain a family of acidic proteins with composition >75% aspartic and glutamic acids. A sub-group of these proteins, called Asprich, have been sequenced.50 Asprich proteins are associated with 50 nm particles that are observed at the prism surface, where active growth occurs. Growth is in the form of layers of mineral deposited roughly parallel to the (001) calcite surface. Based on observations of the crystal growth cycles at the growing edge, we believe that growth along the c axis starts by the deposition of the dense meshwork of chitin fibers on top of a previously formed layer of mineral. Mineral particles are subsequently deposited on

BIOMINERALIZATION DESIGN STRATEGIES AND MECHANISMS

11

top of the chitin fibers, to which they bind possibly through Asprich. An explanation which can coherently accommodate the crystal growth by finite

Figure 6. Organization of nacreous (left, A–C) and prismatic (right, D–F) layers of mollusk shells. A. Fractured cross-section of the nacreous septum of a shell from the cephalopod Nautilus pompilius. B. Isolated tablets extracted from nacre after removal of the organic matrix: Each tablet is a single crystal of aragonite, oriented perpendicular to the crystallographic c-axis. C. Mineral dissolution reveals the layers of organic matrix, consisting of chitin and silk fibroinlike proteins. D. Fractured cross-section of the prismatic layer of Atrina rigida. E. Isolated prisms extracted after removal of the organic matrix. Each prism is a single crystal of calcite, elongated parallel to the c crystallographic axis. F. Mineral dissolution reveals the organic matrix envelopes, consisting mainly, if not exclusively, of hydrophobic Gly-rich proteins.

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particles with the high-quality single crystal end-product is to assume that these particles are composed of amorphous calcium carbonate, stabilized by Asprich. Epitaxial nucleation would then be induced by the underlying crystalline layer, resulting in a single crystal. No hydrogel was detected in the prismatic layer. There must be a nucleation site for each individual prism, which may be composed by acidic proteins. The majority of these proteins do not, however, appear to be involved in nucleation, but rather related to the stabilization of the amorphous phase, or involved in crystal growth.

Figure 7. A. Nacre after etching with acetic acid: The only exposed matrix consists of layers that separate between the crystal tablets: there is no intra-crystalline matrix preserved. B. Etched single prism revealing a dense meshwork of chitin fibers. C. Higher magnification view of the meshwork.

In conclusion, the formation of nacre and prismatic layers, coexisting in the same shell, follows common general concepts that are, however, significantly different in the individual solutions adopted. 5. Concluding Remarks The hallmark of the biological strategy for fabricating many skeletal parts in desired shapes is producing the first-formed solid deposits as disordered phases that with time may or may not transform into a stable crystalline deposit.

BIOMINERALIZATION DESIGN STRATEGIES AND MECHANISMS 13

If all the examples of beautifully sculpted carbonate minerals in biology are formed by way of an amorphous calcium carbonate precursor phase, the strategy is most certainly widespread. This approach also requires the involvement of a designed nucleation substrate, and of different specialized macromolecules, inhibiting or modulating crystal growth. The microenvironment in which mineralization takes place is complex, involving both structured and gel-like domains, hydrophobic and hydrophilic surfaces, spatial differentiation of functionalized domains on the matrix surface and the participation of amorphous colloids as precursor phases for the mature crystals. There are still many gaps, some of them large, in our knowledge of the processes involved in controlling mineral formation. Where we have some insight, unexpected and yet conceptually simple and efficient solutions to problems in crystal growth have been identified. We now realize that biology can overcome the strong forces that dictate crystal properties in the inorganic world. There is still a lot to learn. 6. Acknowledgements We thank the Minerva Foundation and the Kimmelman Center for Biomolecular Structure and Assembly, Weizmann Institute, for financial support. L.A. is the incumbent of the Dorothy-and-Patrick-Gorman professorial chair of Biological Ultrastructure, and S.W. is the incumbent of the Dr.-Trude Burchardt professorial chair of Structural Biology.

References 1.

H. A. Lowenstam, S. Weiner, On Biomineralization, New York, Oxford University Press, 1989. 2. R. P. Blakemore, Science 190, 377–379 (1975). 3. E. J. Denton, Phil. Trans. R. Soc. Lond. B 258, 285–313 (1970). 4. P. Vukusic, B. Hallam, J. Noyes, Science 315, 348 (2007). 5. A. H. Knoll, Reviews in Mineralogy Geochemistry: Biomineralization, Vol. 54 (Eds.: P. M. Dove, J. J. De Yoreo, S. Weiner), Washington D.C., Mineralogical Society of America, 2003, pp. 329–356. 6. G. Lambert, C. C. Lambert, H. A. Lowenstam, Protochordate biomineralization., Vol. I, New York. Van Nostrand Reinhold, 1990. 7. H. Lowenstam, Science 211, 1126–1131 (1981). 8. F. Lippmann, Sedimentary Carbonate Minerals, Berlin, Springer Verlag, 1973. 9. N. Koga, Y. Nakagoe, H. Tanaka, Thermochim. Acta 318, 239–244 (1998). 10. S. Weiner, L. Addadi, H. Wagner, Mat. Sci. Engn. C 11, 1–8 (2000). 11. S. Mann, C. C. Perry, R. J. P. Williams, C. A. Fyfe, G. C. Gobbi, G. J. Kennedy, J. Chem. Soc., Chem. Commun., 168–170 (1983).

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12. M. G. Taylor, K. Simkiss, G. N. Greaves, M. Okazaki, S. Mann, Proc. R. Soc. Lond., B, Biol. Sci. B 252, 75–80 (1993). 13. D. Travis, Ann. N.Y. Acad. Sci. 109, 177–245 (1963). 14. A. P. Vinogradov, The Elementary Chemical Composition of Marine Organisms, New Haven, Sears Foundation for Marine Research II. Yale University, 1953. 15. L. Addadi, S. Raz, S. Weiner, Adv. Mat. 15, 959–970 (2003). 16. J. Aizenberg, G. Lambert, L. Addadi, S. Weiner, Adv. Mat. 8, 222–226 (1996). 17. N. Tsutsui, K. Ishii, Y. Takagi, T. Watanabe, H. Nagasawa, Zoo. Sci. 16, 619–628 (1999). 18. Y. Levi-Kalisman, S. Raz, S. Weiner, L. Addadi, I. Sagi, Journal of the Chemical Society-Dalton Transactions, 3977–3982 (2000). 19. Y. Levi-Kalisman, S. Raz, S. Weiner, L. Addadi, I. Sagi, Adv. Funct. Mat. 12, 43–48 (2002). 20. R. Gueta, A. Natan, L. Addadi, S. Weiner, K. Refson, L. Kronik, Ang. Chem. 119, 295–298 (2006). 21. J. Aizenberg, A. Tkachenko, S. Weiner, L. Addadi, G. Hendler, Nature 412, 819–822 (2001). 22. G. Donnay, D. L. Pawson, Science 166, 1147 (1969). 23. A. Berman, L. Addadi, A. Kvick, L. Leiserowitz, M. Nelson, S. Weiner, Science 250, 664–667 (1990). 24. J. Aizenberg, J. Hanson, T. F. Koetzle, L. Leiserowitz, S. Weiner, L. Addadi, Chem. Eur. J 1, 414–422 (1995). 25. E. Beniash, J. Aizenberg, L. Addadi, S. Weiner, Proc. R. Soc. London B Ser. 264, 461–465 (1997). 26. H. Theel, Nova Acta Res. Soc. Sci. Upsala 15, 1–57 (1892). 27. K. Okazaki, Embryologia 5, 283–329 (1960). 28. E. Beniash, L. Addadi, S. Weiner, J. Struct. Biol. 125, 50–62 (1999). 29. Y. Politi, Y. Levi-Kalisman, S. Raz, F. Wilt, L. Addadi, S. Weiner, I. Sagi, Adv. Funct. Mat. 16, 1289–1298 (2006). 30. A. J. Hodge, J. A. Petruska, Aspects of Protein Structure (Ed.: G. N. Ramachandran), New York, Academic Press, 1963, pp. 289–300. 31. S. Weiner, Crc Critical Reviews in Biochemistry 20, 365–408 (1986). 32. G. Daculsi, J. Menanteau, L. M. Kerebel, D. Mitre, Calcif Tissue Int 36, 550–555 (1984). 33. A. G. Fincham, J. Moradian-Oldak, J. P. Simmer, Journal of Structural Biology 126, 270–299 (1999). 34. J. G. Carter, G. R. Clark, Mollusks. Notes for a Short Course (Ed.: T. W. Broadhead), University of Tennessee. Dept Geological Science Studies, 1985, pp. 50–71. 35. J. G. Carter, (Eds.: D. C. Rhoads, R. A. Lutz), 1980. 36. N. Watabe, Journal of Ultrastructural Research 12, 351–370 (1965). 37. C. Gregoire, J. Biophys. Biochem. Cytol. 3, 797–808 (1957). 38. H. Nakahara, The Japanese Journal of Malacology 38, 205–211 (1979). 39. M. E. Marsh, R. L. Sass, Science 208, 1262–1263 (1980). 40. S. Weiner, W. Traub, FEBS Lett. 111, 311–316 (1980). 41. C. Jeunieux, Chitine et Chitinolyse, Paris, Masson, 1963. 42. Y. Levi-Kalisman, G. Falini, L. Addadi, S. Weiner, J. Struct. Biol. 135, 8–17 (2001). 43. L. Addadi, D. Joester, F. Nudelman, S. Weiner, Chemistry 12, 980–987 (2006). 44. O. Cohen, Weizmann Institute of Science (Rehovot, Israel), 2003. 45. M. A. Crenshaw, H. Ristedt, The Mechanisms of Mineralization in the Invertebrates and Plants (Eds.: N. Watabe, K. M. Wilbur), Colombia, University of South Carolina Press, 1976, pp. 355–367. 46. F. Nudelman, B. A. Gotliv, L. Addadi, S. Weiner, Journal of Structural Biology 153, 176–187 (2006).

BIOMINERALIZATION DESIGN STRATEGIES AND MECHANISMS 15 47. S. Weiner, W. Traub, Phil. Trans. R. Soc. London Ser. B 304, 421–438 (1984). 48. A. Berman, J. Hanson, L. Leiserowitz, T. F. Koetzle, S. Weiner, L. Addadi, Science 259, 776–779 (1993). 49. F. Nudelman, H. H. Chen, H. A. Goldberg, S. Weiner, L. Addadi, Faraday Discuss. in press (2007). 50. B. Gotliv, N. Kessler, J. L. Sumerel, D. E. Morse, N. Tuross, L. Addadi, S. Weiner, Chembiochem 6, 304–314 (2005).

SELF-ASSEMBLED MONOLAYERS AS TEMPLATES FOR INORGANIC CRYSTALLIZATION: A BIO-INSPIRED APPROACH

JOANNA AIZENBERG Harvard University, School of Engineering and Applied Sciences, 29 Oxford Street, Cambridge, MA 02138, USA

Abstract. Nature produces a wide variety of exquisite mineralized tissues fulfilling diverse functions, and often from simple inorganic salts. Organisms exercise a level of molecular control over the physico-chemical properties of inorganic crystals that is unparalleled in today’s technology. This reflects directly or indirectly the controlling activity of biological organic surfaces that are involved in the formation of these materials. Biological materials are intrinsically nano-scale. Biomineralization occurs within specific nanoenvironments, which implies stimulation of crystal formation at certain interfacial sites and relative inhibition of the process at all other sites. Our approach to artificial crystallization is based on the combination of the two latter concepts: that is, the use of organized organic surfaces patterned with specific initiation domains on a nano-scale to study and orchestrate the crystallization process. This bio-inspired engineering effort made it possible to achieve a remarkable level of control over various aspects of the crystal nucleation and growth, including the precise localization of particles, nucleation density, crystal sizes, morphology, crystallographic orientation, arbitrary shapes, nanostructure, stability and architecture. The ability to construct large, defect-free, patterned single crystals with controlled nanoporosity; periodic arrays of uniform, oriented nanocrystals or films presenting patterns of nanocrystals offers a new, bioinspired nanotechnology route to materials engineering.

1. Introduction Crystallization is a key process in the synthesis of many technologically important materials [1–5]. Our knowledge of basic crystallization mechanisms, e.g. what defines the location and density of nucleation, polymorph selectivity or face-selective nucleation and, after the specific nucleus is formed, what determines crystal sizes, shapes, and architecture of the formed crystals and their stability is, however, extremely limited. Better 17 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 17–32. © 2008 Springer.

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understanding of these processes is essential in engineering advanced materials with controlled properties. In contrast, the formation of crystalline materials in nature is highly regulated [6–8]. Different organisms, irrespective of their systematic position, exercise a level of molecular control over the physico-chemical properties of minerals that is almost unthinkable in artificial processes. It is achieved by means of organized assemblies of specialized biological macromolecules. Recently, new synthetic strategies that mimic biomineralization have been developed [9–16]. These promising approaches utilize processes involving molecular recognition at the organic-inorganic interfaces. A number of elegant studies demonstrate the use of simplified molecular assemblies that resemble biological membranes, such as Langmuir monolayers [9,10,17–21], self-assembled monolayers (SAMs) [22–26], biological macromolecules [11–13] and surfactant aggregates [27–29], as the nucleation templates. Most of these studies, however, address only one “crystallization problem” at a time, e.g. oriented nucleation, polymorph specificity, or shapes of the growing crystals. The present paper describes our approach to govern crystallization [30– 31] based on engineering the nucleation site and on controlling mass transport to the surface at the micron scale, using micropatterned SAMs of alkanethiols supported on metal films. This method, which we apply to crystallization of calcium carbonate, makes it possible, for the first time, to achieve nanoscale control over many of the crucial aspects of nucleation and crystal growth – oriented nucleation, location and density of nucleation, crystal sizes and patterns – in one experiment. 2. Experimental 2.1. SUBSTRATES

Silicon wafers were coated with 2 nm of Ti, to promote adhesion, and then with 50 nm of metal (Ag or Au) using an electron beam evaporator. 2.2. SAMs

SAMs of HS(CH2)15CO2H, HS(CH2)11OH, HS(CH2)11SO3H, HS(CH2)11 PO3H2, HS(CH2)11N(CH3)3Cl and HS(CH2)15CH3 were formed on metal substrates by exposing the surfaces to a 10 mM solution of the thiol in ethanol for 24 hours, followed by washing with ethanol [32]. Patterned SAMs were formed using microcontact printing (μCP) [33–34]: elastomeric stamps with different relief structures were “inked” with a 10 mM solution of HS(CH2)nX in ethanol and brought into conformal contact with gold for 10 s; the non-contact areas were then derivatized with a 10 mM solution of HS(CH2)nY in ethanol by immersion for 1 min.

CRYSTALLIZATION ON SAMs

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2.3. CRYSTALLIZATION

The substrates were placed upside-down (to ensure that only particles grown on the SAM would be bound to the surface) in 10 mM calcium chloride solution in a closed desiccator containing vials of ammonium carbonate [12, 30–31, 35–36]. All experiments were carried out at room temperature for 1 h. Precipitation of calcium carbonate results from the diffusion of carbon dioxide vapor into the CaCl2 solution, according to the following reactions: (NH4)2CO3 (s) → 2NH3 (g) + CO2 (g) + H2O; CO2 + Ca2+ + H2O → CaCO3 (s) + 2H+; 2NH3 + 2H+ → 2NH4+. 2.4. ANALYSIS

The crystals, once formed, were examined using optical microscopy to determine the densities of nucleation and crystal sizes. The specific crystallographic orientations of the crystals relative to the interface between the SAM and the solution were analyzed using XRD in the θ−2θ scan mode. A detailed morphological analysis was undertaken to confirm the assignment of each specific crystallographic orientation and to estimate the deviation in angle of the crystals from these directions of growth (see text for details). 3. Oriented Nucleation We have chosen the crystallization of calcite on SAMs of alkanethiols HS(CH2)nX bearing negatively charged headgroups (X = CO2–, SO3–, OH) as a model system for three reasons (Fig. 1): i) calcite has a simple structure, its crystallization is relatively easy to perform and there is an extensive background information describing this process [6, 12, 13, 19, 20, 26, 35, 37–39]; ii) formation of crystallographically oriented, exquisitely shaped calcite crystals with unique materials properties is common in biological environments [7, 8], and is believed to be controlled by acidic macromolecules, conceivably by virtue of a match between the structures of the organic surface and that of a particular crystal plane [11, 12, 35, 36]; iii) alkanethiols self-assemble on metal substrates into highly ordered, crystalline monolayers with various structural parameters [40–44] and present, therefore, an attractive candidate for an organized organic surface to mediate crystallization [22–26, 30, 31]. Alkanethiols terminated in different functional groups assemble on Au(111) in a hexagonal overlayer characterized by the interchain distance a = 4.97 Å, the tilt of the chain α = 28– 32°, and the twist angle around the axis of the chain β = 50–55° [42]. On Ag(111), X-terminated alkanethiols self-assemble in a hexagonal array with

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a = 4.77 Å, α = 8–12°, β = 42–45° [43]. The presence of counterions, such as Cd2+ and Ca2+, has been shown to induce an additional ordering of terminal acidic headgroups in SAMs [31, 45–48]. We anticipated that different SAMs – those terminated in different functional groups and even those bearing the same terminal group but supported on different metals – would induce oriented nucleation of calcite in different crystallographic directions. Indeed, crystallization experiments with CO2-, SO3- and OHterminated SAMs supported on Au and Ag produced arrays of highly oriented calcite crystals [31], nucleated from crystallographic planes specific to each surface type (Fig. 1).

Figure 1. Scanning electron micrographs showing the face-selective nucleation of calcite crystals mediated by SAMs. The inserts present computer generated simulations of the regular calcite rhombohedra viewed down perpendicular to the corresponding average nucleating face (shadowed). (a) CO2–/Au; (b) OH/Au; (c) SO3–/Au; (d) CO2–/Ag; (e) OH/Ag; (f) SO3–/Ag.

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21

The predominant nucleating planes (NP) of the calcite crystals were first determined from the XRD profiles [31]. To confirm the assignment of each specific crystallographic orientation and to estimate the angular deviation from these directions of growth, a detailed morphological analysis was performed. For each surface type, a population of 40 crystals was used in statistics. The crystals were viewed down the surface normal in a scanning electron microscope. We measured the angles between the crystal edges meeting at the upper corner of the crystal. These angles can be unequivocally related to the orientation of the regular {104} calcite rhombohedra visà-vis the interface, using structural relationships in the calcite unit cell [6, 37]. The morphological results were visualized using the sphere of reflection (Fig. 2, top). The nucleating planes for each surface type were plotted as circles on the sphere with a 5% gray scale; the intensity of the gray scale of the final circles is proportional to the number of crystals in the corresponding orientation [31]. The example shown in figure 2(top) corresponds to the morphological measurements of a set of 40 crystals in which one crystal nucleated from the (101) plane, two from the (110), three from the (100), four from the (113), five from the (104), six from the (012), eight from the (018) and 11 from the (001) plane. A significant clustering of the data was observed for each surface type, indicative of a high degree of orientational specificity induced by SAMs. The positions of the average nucleating planes estimated from the morphological analysis (NP MA) were compared to the predominant orientations observed in the corresponding X-ray diffraction profiles (NPXRD) (indicated by arrows). Table 1 summarizes the results of oriented crystal growth on CO2– , SO3– and OH-terminated SAMs supported on Ag and Au. We believe that the orientational uniformity of crystals formed on each surface is controlled by the specific interfacial structure of the oriented, homogeneous SAM. It is noteworthy that for each pair X/Au and X/Ag, the difference in crystallographic orientations of calcite crystals (~15–20°) corresponds to the difference in the tilt of the alkanethiol molecules (a) in the SAMs on Au and Ag. This relationship is illustrated in Fig. 3, which presents the example of oriented nucleation of calcite from the (015) and (012) crystallographic planes induced by SAMs of HS(CH2)15CO2H/Au and HS(CH2)15CO2H/Ag. It is also important to note that in most cases, we did not observe a satisfactory match between the lattices of the SAMs and crystal planes they nucleate. On the other hand, there always existed a certain orientation of the functional groups in the SAM that precisely matched the orientation of the carbonate ions in the nucleated crystal (Fig. 3). Careful study of this relationship showed that the orientation of inorganic crystals at the organic interface is governed by the orientation of the functional groups [49–50].

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Figure 2. Pole figure presentation of morphological data for the orientations of calcite crystals grown on different SAMs (see text for description). The indices of the crystallographic planes are indicated. (a) CO2–/Au; (b) OH/Au; (c) SO3–/Au; (d) CO2–/Ag; (e) OH/Ag; (f) SO3–/Ag.

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TABLE 1. Average nucleation plane and percentage of oriented calcite crystals grown on SAMs supported on gold and silver

Nucle- DiheS ation dral A plane, angle, M NPMA δ a b CO2 (015)

41°

Au Ang- Percentage of oriented ular crystals devi- From mor- From ation phological XRD c analysis analysis 4.3°

97

73

Ag Nucle- Dihe- Ang- Percentage of oriented crystals ation dral ular plane, angle, devi- From mor- From NPMA δ ation phological XRD c analysis b analysis a (012)

60°

3.6°

97

82

OH (104) 43° 3.6° 100 91 (103) 56° 5.1° 97 81 (1 0 78 56 (107) 35° 2.7° 78 63 SO3 21° 3.4° 12) a Average nucleation plane NP corresponds to the highest density in Figure 2 (open MA circles). b Average dihedral angle between the NP and (001) plane. MA c Standard angular deviation from the NP . MA

HS(CH2)15CO2H/Au Surf ace normal -axis Δδ ≅ Δα

δ = 41°

HS(CH2)15CO2H/Ag Surface normal -axis δ = 60°

(012) (015) α = 8-12°

α = 28-32°

(a )

Au

Ag

(b )

Figure 3. Schematic presentation (to scale) of the geometrical relationship between the structure of the SAMs of HS(CH2)15CO2H supported on gold (left) and silver (right) and the oriented calcite crystal they nucleate. (a) Relative orientations of the SAM and the nucleated crystals. Note the possible co-alignment of the CO2-groups in the SAM and of the carbonates in the nucleated face; (b) Mismatch between the lattices of the CO2-groups in the undistorted SAM (large open circles) and the Ca ions in the nucleated face (small solid circles).

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4. Growing Crystals in Ordered Arrays Another important advantage of using SAMs of alkanethiols as nucleation templates compared to alternative supramolecular assemblies is that they can be easily patterned on a micron scale [33–34]. We used this property to control area-selective crystallization. The analysis of the nucleation activity of various SAMs showed the induction time of calcite nucleation to increase and the density of nucleation to decrease in the following sequence: –

–

+

SO3 – CO2 – OH – CH3 – N(CH3)3 . Patterned SAMs of ω-terminated alkanethiols with a controlled distribution of more active nucleation sites within a less active background were formed by µCP (Fig. 4a). Crystallization of calcite on these substrates resulted in the formation of large-area, high-resolution inorganic replicas of the underlying organic patterns [30]. The observed patterned crystallization can be explained in terms of diffusion-limited, island-specific nucleation [30, 51]. Figure 4b describes the mechanism of the process. After the nucleation begins at rapidly nucleating SAMs, the ion flux into these regions depletes calcium carbonate concentration over slowly nucleating zones. In the region ld where the effective concentration of the solution is below saturation (csat), nucleation does not occur. Nucleation on slowly nucleating regions is allowed only for distances from the rapidly nucleating region x > ld, where c > csat. This mechanism was confirmed in the experiment, in which calcite crystals were grown on a methyl-terminated surface with one isolated carboxylic acid terminated region: the halo pattern clearly seen in the SEM (Fig. 4b) corresponds to the depletion region ld. Therefore, if we keep the distance between rapidly nucleating regions below 2ld, crystallization will be entirely restricted to the rapidly nucleating regions (Fig. 4b). By adjusting various parameters of our experimental setup (concentration of the crystallizing solution, density and sizes of features in the stamp and functionality of the surface of the SAM), we can exert further control over the crystallization process: in addition to precise localization of nucleation, we can define the density of the active nucleating regions on the surface (N), the number of crystals that nucleate within each region (n), as well as their crystallographic orientation. The general algorithm that we used to control crystallization is presented below: 1) We choose a specific X-terminated alkanethiol/metal combination to induce the desired oriented crystallization. 2) For a given N, we determine the corresponding distance between the features in the stamp: p = N –1/2.

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3) By varying the concentration of the crystallizing solution, we define the range of concentrations for which ld > p/2, so that inhibition of nucleation occurs over the entire slowly nucleating regions due to the mass transport to the regions of crystal growth. For example, for patterned crystallization on a SAM supported on Ag and consisted of circles of HS(CH2)15CO2H (d = 35 µm, p = 100 µm) in the field of HS(CH2)15CH3, the required concentrations for the CaCl2 solution are below 100 mM (for higher concentrations, sporadic formation of crystals on the CH3-terminated regions remote from the CO2H-terminated sites occurred). 4) At constant concentration, the number of crystals, n, within each active nucleation region appears to depend linearly upon its area [30]. This relation makes it possible to determine the optimum size, d, of the raised features in the stamp for any chosen n.

Figure 4. (a) Schematic presentation of the experimental design of crystallization on patterned SAMs; (b) Mechanism of diffusion-limited, localized nucleation [30, 49] (see text for details).

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Using this algorithm, we have been able to determine the necessary experimental conditions – concentration of the crystallizing solution, geometric characteristics and functionality of the micropatterned SAM, supporting metal – to fabricate arbitrary nanopatterns of oriented calcite nanocrystals (Fig. 5). The crystals can be grown in dense, oriented islands (Fig. 5a) or in highly ordered two-dimensional arrays of single calcite crystals of uniform size and orientation (Fig. 5b); we can reverse the crystallization pattern and fabricate interconnected, oriented films of calcite crystals with the edge resolution of <50 nm (Fig. 5c); patterned growth of calcite in different crystallographic directions can be achieved by using substrates patterned with SAMs that have similar nucleating activity, but induce nucleation from different crystallographic planes (Fig. 5d).

Figure 5. Scanning electron micrographs showing the controlled crystallization of calcite on patterned SAMs. (a) A square array of densely nucleated calcite crystals; (b) A square array of discrete, oriented calcite crystals; (c) Complex pattern of an interconnected, oriented calcitic film; (d) Simultaneous patterned growth of calcite in two crystallographic directions.

5. Bottom-Up Synthesis of Large Micropatterned Single Crystals Fabrication of crystallographically oriented single crystals with regular micro- and nano-features presents another materials challenge. These crystals are broadly used in technology as components of various electronic, optical and sensory devices. Learning from nature and introducing biological crystal growth techniques could potentially improve the complex

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technological processing routes currently used for patterning single crystals. An inspirational biological system is single crystals of calcite formed by echinoderms [7]. Figure 6a shows a brittlestar arm plate: the entire element with its micrometer feature sizes is a unique, intricately shaped, singlecrystalline, 3D meshwork (so-called stereom) bearing an array of highly efficient microlenses with controlled orientation of the optical axis of the constituent calcite [52]. This structure represents a fascinating example of a multifunctional biomaterial that effectively fulfills mechanical and optical function. The mechanism of the formation of such structures is still a mystery. It has been shown, however, that in certain biological systems, crystallization takes place through the transformation of a transient metastable amorphous calcium carbonate (ACC) phase triggered by regiospecific, oriented nucleation [53–56]. Figure 6b depicts such an amorphous-to-crystalline transition in a sea urchin larval spicule.

Figure 6. Scanning electron micrographs of biogenic calcium carbonate structures: a) Dorsal arm plate of the brittle star Ophiocoma wendti with the external array of microlenses. The entire elaborate structure is a single calcite crystal. The lenses are oriented in the optic axis direction of the constituent birefringent calcite. Inset: Epitaxial overgrowth of synthetic calcite crystals on a brittlestar stereom. Note that the nucleation of the newly formed calcite crystals is not homogeneous and occurs at specific, locally activated nucleation sites on the surface. b) Sea urchin Paracentrotus lividus larval spicule (25 h embryo). Triradiate spicule is first deposited in an ACC form within a membrane-delineated compartment, inside a syncitium formed by specialized mesodermal cells. Within 20 h, an oriented calcite with the crystallographic a-axes parallel to the three radii nucleates in the center of a spicule (see a rhombohedral-shaped crystal). The subsequent amorphous-to-crystalline transition results in the formation of a single crystal of calcite that has the predetermined triradiate shape and constant crystallographic orientation [53, 54].

For the purposes of bio-inspired crystal engineering, we identified two major elements of the sea urchin larval spicule formation and used them in our synthetic effort: (i) Amorphous calcium carbonate stabilized by specialized macromolecules is deposited in a preformed space and adopts its shape; (ii) Oriented nucleation then occurs at a well-defined, chemically modified intracellular site and the crystallization front propagates through

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the amorphous phase, resulting in the formation of a single crystal with controlled orientation and predetermined microstructure [53]. We have shown that biogenic ACC is stabilized by means of specialized macromolecules rich in hydroxyamino acids, glycine, glutamate, phosphate and polysaccharides [57]. These macromolecules extracted from the biological ACC tissue and introduced as an additive into saturated calcium carbonate solution induced the formation of stabilized ACC in vitro. The stabilization of ACC can also be achieved using surface-mediated processes. Our results show that significantly disordered organic substrates bearing phosphate and hydroxyl groups, suppress the nucleation of calcite and induce the formation of a metastable ACC layer from highly saturated solutions [50]. The deposited ACC layer is stabilized for 1–2 hrs and then transforms into a polycrystalline film [58]. Figure 7a,b shows the experimental procedures that were designed on the basis of the above biomineralization principles are shown in Figure 7 [50]. The micropatterned 3D substrate was primed with a disordered phosphate-, methyl- and hydroxy-terminated monolayer that induces the formation of amorphous CaCO3. One nanoregion of the SAM of HS(CH2)nA (A = OH, CO2H, SO3H) serving as calcite nucleation site was integrated into each template (Fig. 7a). When placed in a supersaturated solution of calcium carbonate, these organically modified templates induced the deposition of the ACC mesh in the interstices of the framework (Fig. 7b). Oriented nucleation of calcite then occurred at the SAM nanoregion, followed by the propagation of the crystallization front through the ACC film. This new bio-inspired crystal engineering strategy made it possible to directly fabricate millimeter-size single crystals with a predetermined sub10-micron pattern and crystallographic orientation (Fig. 7c,d). In order to elucidate the mechanism of the amorphous-to-crystalline transition, we performed control experiments using 3D templates engineered with or without nucleation sites, with varied feature sizes and using impurities in the solution. These experiments suggested that organically modified 3D templates with the feature sizes smaller than 10 μm, in addition to stabilizing the ACC and to controlling the oriented crystal nucleation and the micropattern of the single crystal, also act as stress release sites and discharge sumps for excess water and impurities during crystallization. Interestingly, the achievable size range of the mesh in synthetic calcite crystals is comparable with the stereom sizes in their biologically formed counterparts. This observation suggests that the described mechanisms of the amorphous-to-crystalline transition may also have direct biological relevance. It is conceivable that a 3D array of selfassembling biological macromolecules and/or cells serving as structural templates will provide sites for stress relaxation and impurity discharge, thus giving rise to the formation of a large microporous single crystal.

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The use of the concept of the amorphous-to-crystalline transition within functionalized micropatterned templates may have important generic implications in materials science. The possible applications of the engineered 3D frameworks may include the direct growth of defect-free micropatterned crystals, the relaxation of stresses encountered during amorphous-tocrystalline transitions in existing materials, controlled solvent release during polycondensation reactions, etc.

Figure 7. Formation of a “microperforated” single crystal using the concept of controlled amorphous-to-crystalline transition in confined 3D spaces: a) Structural and chemical features of the engineered 3D templates. b) Deposition of the ACC mesh from the CaCO3 solution, followed by the oriented nucleation at the imprinted nucleation site and the amorphous-to-crystalline transition of the ACC film. c) Polarized light micrograph, showing the perforated single crystal of calcite with the feature sizes of ~10 μm and the polycrystalline background. d) Magnified scanning electron micrograph of the crystal, showing its regular microstructure. Inset: large-area transmission electron diffraction, confirming that the section is a single crystal of calcite oriented along the optic axis.

6. Conclusions Diffusion-controlled growth of calcite in nature is a well-known phenomenon [6–8]. Formation of intricate biogenic calcitic structures usually occurs from organized macromolecules in specific microenvironments that provide the directional flux of ions towards the growing crystals [7, 8]. The power of the presented bio-inspired approach to artificial crystallization is, therefore, based on our ability to govern mass transport to different regions of the surface at a micron scale and to control the molecular structure and microenvironment of the nucleation site, by patterning ω-terminated SAMs

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into regions with different nucleating activity. Using crystallization of calcite as an example, we demonstrate that we can regulate the precise location, density and area of the regions active for nucleation, and thereby the number, size and crystallographic orientation of the crystals that nucleate in each part of the surface. We conclude, therefore, that the combination of three major ideas – (i) the ability of SAMs to nucleate growth from a single crystallographic plane, (ii) patterning SAMs with nano/micro-regions having different nucleating activity, and (iii) taking advantage of mass transport and the proper size of the nanopattern, so that the ion flux into the regions of crystal growth keeps the concentration of the crystallizing solution over slowly nucleating regions low enough that nucleation effectively never happens, – provides a simple and convenient route to control nucleation. We believe that this method could find applications in engineering of oriented inorganic nanomaterials with complex form, such as ceramics or semiconductors whose mechanical, optical and electrical performance can be regulated by controlling the sizes, distribution, and morphology of the constituent crystals. 7. Acknowledgments I would like to thank Lia Addadi, Steve Weiner, George Whitesides, Yong Han, Boaz Pokroy, for their contribution to this work.

References 1.

A. H. Heuer, D. J. Fink, V. J. Laraia, J. L. Arias, P. D. Calvert, K. Kendall, G. L. Messing, J. Blackwell, P. C. Rieke, D. H. Thompson, A. P. Wheeler, A. Veis and A. I. Caplan, Science, 255, 1098 (1992). 2. C. B. Murray, C. R. Kagan and M. G. Bawendi, ibid., 270, 1335 (1995). 3. S. I. Stupp and P. V. Braun, ibid., 277, 1242 (1997). 4. B. J. J. Zelinsky, C. J. Brinker, D. E. Clark and D. R. Ulrich, Eds., Better Ceramics Through Chemistry (Materials Research Society, Pittsburgh, 1990). 5. S. Mann and G. A. Ozin, Nature, 382, 313 (1996). 6. F. Lippmann, Sedimentary Carbonate Minerals (Springer-Verlag, Berlin, 1973). 7. H. A. Lowenstam and S. Weiner, On Biomineralization (Oxford Univ. Press, 1989). 8. S. Mann, J. Webb and R. J. P. Williams, Eds., Biomineralization. Chemical and Biological Perspectives (VCH, Weinheim, 1989). 9. E. M. Landau, M. Levanon, L. Leiserowitz, M. Lahav and J. Sagiv, Nature, 318, 353 (1985). 10. E. M. Landau, S. G. Wolf, M. Levanon, L. Leiserowitz, M. Lahav and J. Sagiv, J. Am. Chem. Soc., 111, 1436 (1989). 11. L. Addadi and S. Weiner, Proc. Natl. Acad. Sci. USA, 82, 4110 (1985). 12. L. Addadi, J. Moradian, E. Shay, N. G. Maroudas and S. Weiner, ibid., 84, 2732 (1987).

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13. A. M. Belcher, R. J. Christensen, P. K. Hansma, G. D. Stucky and D. E. Morse, Nature, 381, 56 (1996). 14. M. Alper, P. D. Calvert, R. Frankel, P. C. Rieke and D. A. Tirrell, Eds., Materials Synthesis Based on Biological Processes (Materials Research Society, Pittsburgh, 1991). 15. S. Mann, Nature, 365, 499–505 (1993). 16. S. Mann, D. D. Archibald, J. M. Didymus, T. Douglas, B. R. Heywood, F. C. Meldrum and N. J. Reeves, Science, 261, 1286 (1993). 17. X. K. Zhao and J. H. Fendler, J. Phys. Chem., 95, 3716–3723 (1991). 18. B. R. Heywood and S. Mann, J. Am. Chem. Soc., 114, 4681 (1992). 19. S. Mann, B. R. Heywood, S. Rajam and J. D. Birchall, Nature, 334, 692 (1988). 20. P. W. Carter and M. D. Ward, J. Am. Chem. Soc., 115, 11521 (1993). 21. L. M. Frostman and M. D. Ward, Langmuir, 13, 330 (1997). 22. B. C. Bunker, P. C. Rieke, B. J. Tarasevich, A. A. Campbell, G. E. Fryxell, G. L. Graff, L. Song, J. Liu, J. W. Virden and G. L. McVay, Science, 264, 48 (1994). 23. S. Feng and T. Bein, Nature, 368, 834 (1994). 24. L. M. Frostman, M. M. Bader and M. D. Ward, Langmuir, 10, 576 (1994). 25. V. K. Gupta and N. L. Abbott, Science, 276, 1533 (1997). 26. A. Berman, D. J. Ahn, A. Lio, M. Salmeron, A. Reichert and D. Charych, Science, 269, 515 (1995). 27. D. D. Archibald and S. Mann, Nature, 364, 430 (1993). 28. D. Walsh, J. D. Hopwood and S. Mann, Science, 264, 1576 (1994). 29. T. Douglas, D. P. E. Dickson, S. Betteridge, J. Charnock, C. D. Garner and S. Mann, ibid, 269, 54 (1995). 30. J. Aizenberg, A. J. Black and G. M. Whitesides, Nature, 398, 495 (1999). 31. J. Aizenberg, A. J. Black and G. M. Whitesides, J. Am. Chem. Soc., 121, 4500 (1999). 32. N. B. Larsen, H. Biebuyck, E. Delamarche and B. Michel, J. Am. Chem. Soc., 119, 3017 (1997). 33. A. Kumar, H. A. Biebuyck and G. M. Whitesides, Langmuir, 10, 1498 (1994). 34. A. Kumar, N. A. Abbott, E. Kim, H. A. Biebuyck and G. M. Whitesides, Acc. Chem. Res., 28, 219 (1995). 35. A. Berman, L. Addadi and S. Weiner, Nature, 331, 546 (1988). 36. S. Albeck, J. Aizenberg, L. Addadi and S. Weiner, J. Am. Chem. Soc., 115, 11691 (1993). 37. D. D. Archibald, S. B. Qadri and B. P. Gaber, Langmuir, 12, 538 (1996). 38. G. Falini, S. Albeck, S. Weiner and L. Addadi, Science, 271, 67–69 (1996). 39. H. H. Teng, P. M. Dove, C. A. Orme and J. J. De Yoreo, Science, 282, 724 (1998). 40. A. Ulman, An Introduction to Ultrathin Organic Films: From Langmuir-Blodgett to Self-Assembly (Academic Press, San Diego, 1991). 41. P. E. Laibinis and G. M. Whitesides, J. Am. Chem. Soc., 114, 1990 (1992). 42. R. G. Nuzzo, L. H. Dubois and D. L. Allara, J. Am. Chem. Soc., 112, 558 (1990). 43. P. E. Laibinis, G. M. Whitesides, D. L. Allara, Y. T. Tao, A. N. Parikh and R. G. Nuzzo, J. Am. Chem. Soc., 113, 7152 (1991). 44. N. Camillone, C. E. D. Chidsey, G. Liu and G. Scoles, J. Chem. Phys., 98, 4234 (1993). 45. F. Leveiller, D. Jacquemain, M. Lahav, L. Leiserowitz, M. Deutsch, K. Kjaer and J. Alsnielsen, Science, 252, 1532 (1991). 46. J. A. Zasadzinski, R. Viswanathan, L. Madsen, J. Garnaes and D. K. Schwartz, Science, 263, 1726 (1994). 47. C. Böhm, F. Leveiller, D. Jacquemain, H. Mohwald, K. Kjaer, J. Alsnielsen, I. Weissbuch and L. Leiserowitz, Langmuir, 10, 830 (1994). 48. J. Li, K. S. Liang, G. Scoles and A. Ulman, Langmuir, 11, 4418 (1995). 49. Y.-J. Han and J. Aizenberg, Angew. Chem. Int. Ed. 42, 3668–3670 (2003).

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50. J. Aizenberg, D. A. Muller, J. L. Grazul and D. R. Hamann, Science 299, 1205–1208 (2003). 51. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, 1995). 52. J. Aizenberg, A. Tkachenko, S. Weiner, L. Addadi, and G. Hendler, Nature, 412, 819 (2001). 53. E. Beniash, J. Aizenberg, L. Addadi, and S. Weiner, Proc. R. Soc. Lond. Ser. B-Biol. Sci., 264, 461 (1997). 54. E. Beniash, L. Addadi, and S. Weiner, J. Struct. Biol., 125, 50 (1999). 55. I. M. Weiss, N. Tuross, L. Addadi, and S. Weiner, J. Exp. Zool., 293, 478 (2002). 56. Y. Politi, T. Arad, E. Klein, S. Weiner, and L. Addadi, Science 306, 1161–1164 (2004). 57. J. Aizenberg, G. Lambert, S. Weiner, L. Addadi, J. Am. Chem. Soc., 124, 32 (2002). 58. J. Aizenberg, Adv. Mater. 16, 1295–1302 (2004).

DATABASES IN CRYSTAL ENGINEERING

ALESSIA BACCHI Dipartimento di Chimica Generale ed Inorganica, Chimica Analitica, Chimica Fisica, University of Parma, Italy

Abstract. Crystallographic databases are a growing gold mine in the field of crystal engineering (CE), since they contain information precious in many aspects for solid state chemistry. In this contribution we will first enumerate and briefly describe the most relevant crystallographic databases (DB); then we will illustrate some problems that can be addressed by an educated use of DB; in this context we will present examples of remarkable results obtained with the aid of DB. A section will be devoted to the introductory illustration of statistical methods involved in expert use of DB. Knowledge-based applications will be also outlined.

1. Crystallographic Databases A database is an organized body of related information, consisting in one or more large structured sets of persistent data, usually associated with software to update and query the data. One way of classifying databases is by the programming model associated with the database. The flat model consists of a two-dimensional table of data elements, where all members of a given column are values of the same parameter expressed on different objects, and all members of a row are different parameters related to one object. For instance, covalent radius, first ionization potential and electronegativity could be columns in a database where each chemical element would occupy one row. This model is the basis of the spreadsheet. The network model consists of multiple tables that are linked together by the use of pointers. Some columns contain pointers to different tables instead of data. Thus, the tables are related by references in a network structure. Relational databases also consist of multiple database tables but they do not contain explicit pointers. Any column may be used to set a relationship between two or more tables by writing queries that were not anticipated by the database designer. 33 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 33–58. © 2008 Springer.

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Databases must ensure data integrity, meaning consistency, accuracy, and correctness of stored data. Crystallographic data submitted directly by authors or retrieved from scientific literature are generally checked and validated before being stored and made accessible.1 The remarkable progress in computing and information technology of the last decades has revolutionized the importance of DB in crystallographic researches due to two factors: the communication of data between authors, journals and the databases has been tremendously speeded up by the introduction of the Crystallographic Information File format and by electronic interchange of information. Secondly, software applications for data retrieval and processing have been constantly upgraded and refined, allowing more and more users to access sophisticated data elaborations by using standard packages. There are a number of major crystallographic and solid state properties databases continuously maintained and updated (as of February 2007). An exhaustive overview of crystallographic DB can be found in the special issues B58 and D58 of Acta Crystallographica Sections B and D (2002), and in other recent reviews.2–5 Biological Macromolecule Crystallization Database (http://xpdb.nist. gov:8060/BMCD4/) contains crystal data and the crystallization conditions compiled from the published literature of biological macromolecules for which diffraction quality crystals have been obtained. BMCD also contains the NASA Protein Crystal Growth Archive, which includes the crystallization data generated from studies carried out in a microgravity environment. Cambridge Structural Database (http://www.ccdc.cam.ac.uk/) contains information on over 400,000 experimentally determined (x-ray or neutron diffraction) crystal structures of organic and organometallic compounds, compiled since 1923. Each crystallographic entry in the CSD provides bibliographic information, chemical connectivity, and numeric data. Crystal Data File (http://www.nist.gov/srd/nist3.htm) contains chemical, physical, and crystallographic information useful to characterize inorganic, organic, organometallic, metal, intermetallic and mineral compounds. The data include the standard cell parameters, cell volume, space group number and symbol, calculated density, chemical formula, chemical name, and classification by chemical type. Crystal Lattice Structures (http://cst-www.nrl.navy.mil/lattice/) offers a concise index of common crystal lattice structures. CRYSTMET (http://www.tothcanada.com/databases.htm) is a relational database of critically evaluated crystallographic data for metals, alloys, intermetallics, and minerals, accompanied by pertinent physical, chemical, and bibliographic information since 1913.

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Electron Diffraction Database (http://www.nist.gov/srd/nist15.htm) contains crystallographic and chemical information on crystalline materials for application to electron diffracton. Each entry contains space group data, unit cell data, chemical formula and name, and literature references. Inorganic Crystal Structure Database (http://icsd.ill.fr/icsd/) is a comprehensive compilation of crystal structure data of inorganic compounds. All information has been obtained from the original sources and checked to assure high quality. The literature is covered back to 1915. The database is now updated by direct scanning of major journals. Nucleic Acids Database (http://ndbserver.rutgers.edu//) contains threedimensional structural information on RNA and DNA oligonucleotides that have been obtained from x-ray crystallographic experiments. The NDB allows retrieval of coordinates, of information about the conditions used to derive the coordinates, and of the structural information derived from the coordinates. Powder Diffraction File (http://www.icdd.com/) is the most comprehensive database for single phase X-ray powder diffraction patterns, updated every year. The primary use of the PDF is to identify “fingerprints” of unknown materials by matching the spacings of the unknown material’s diffraction patterns with the spacings of known substances. Protein Data Bank (http://www.rcsb.org/pdb/) is an electronic archive of experimentally determined 3-dimensional structures of proteins, nucleic acids, and other biological macromolecules. It contains atomic coordinates, bibliographic citations, primary and secondary structure information, as well as crystallographic structure factors and nuclear magnetic resonance (NMR) experimental data of proteins, nucleic-acids, and viruses. PDB is the single global archive of such data. Structural Classification of Proteins (http://scop.mrc-lmb.cam.ac.uk/ scop/) provides a detailed and comprehensive description of the structural and evolutionary relationships between all proteins whose structure is known. It provides a broad survey of all known protein folds, detailed information about the close relatives of any particular protein, and a framework for future research and classification. Surface Structure Database (http://www.nist.gov/srd/nist42.htm) is a complete critical compilation of reliable crystallographic information on surfaces and interfaces, associated to three-dimensional graphics to allow researchers to visualize the structures of crystal surfaces on the atomic scale. Thermochemical and Physical Properties Database (http://www.esmsoftware.com/tapp/) lists properties of over 13,000 solids including: crystal structure, phase transformations, density, thermal expansion, elastic moduli, thermal conductivity, electrical resistivity, diffusivity, dielectric constant,

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magnetic properties, cryogenic properties, and optical properties. TAPP also lists properties of more than 15,000 fluid phases, including density, dielectric constant, surface energy, as well as properties of over 10,000 compound phases and solutions. NIST Chemistry WebBook (http://webbook.nist.gov/chemistry/) provides access to chemical and physical property data for chemical species through the internet. Particularly interest in CE are the Condensed Phase Thermochemistry Data and the Phase Change Data. These DB cover different fields of solid state chemistry; CSD is the most relevant for researches dealing with CE because it collects exhaustively all the known experimental structural data both in organic and in organometallic systems, among which: molecular crystals and co-crystals, polymorphs, solvates, nanostructrures, metallo-organic-frameworks (MOF), coordination polymers. The use of DB in addressing crucial problems in CE will be now outlined. 2. Databases and Crystal Engineering Crystal engineering deals with the design of solid materials whose functional characteristics are a direct and predetermined consequence of the way in which arrays of molecules are assembled in the solid state.6,7 A totally deliberate design would require an ‘a priori’ complete knowledge of (i) the relations between structure and function and (ii) the physics of selfassembly and crystallization. This approach is rarely successful mainly because the factors which rule self-assembly in the solid state are still obscure to a large extent, and molecules cannot be easily convinced to line up according to a predetermined scheme.8 Much bulk experimental work in CE still relies upon heuristic, trial and error, or even serendipitous protocols.9 Currently the most useful approaches to the intricate task of relating molecular structure to the final crystal architecture are based on two complementary views of the problem. On the one hand, crystal structure prediction (CSP) theoretical methods are oriented to look at the molecule as a continuous distribution of charge density, and at intermolecular cohesion as the integration of many point-topoint electrostatic interactions, attractive and repulsive, plus the repulsion due to Pauli exclusion principle.10–11 The final actual structure will be the outcome of a delicate balance between many elusive factors, and the differences in energy for different alternative assemblies of a given molecule often are within the uncertainty limits of the computational methods themselves. This picture accounts for the hard life that chemists have in designing and actually obtaining a desired three-dimensional network.12

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On the other hand, with the growth of the structural data available in the literature, it has been evidenced that several functional groups tend to generate recurrent patterns whenever they associate in the solid state.13 These patterns, designated by the term ‘supramolecular synthons’, can be considered as a starting point for the solid state chemist who wishes to find operative ways to deliberately build a predefined crystal network. According to molecular tectonics, crystal design may be considered as the convolution of molecular properties into three-dimensional networks whose structure depends on the presence of groups giving robust supramolecular self-association patterns capable to achieve close packing with the help of symmetry operators.14,15 This practical approach requires a thorough knowledge of the most popular modes of association for the functional groups present on the molecular constituents and of their most probable three-dimensional distribution in the crystal. The DB offer a precious mine of rough data collecting all the known cases. It must be noted that the outcome of the crystallization process is under kinetic control, so that there may be discrepancies between the CSP results, which consider only thermodynamic stability as a rule for finding the most stable form, and observed structures, which may be the easiest to obtain. In this sense, information collected in the DB represents an experimental picture of the relative influence of thermodynamics and kinetics on the crystallization.16 DB offer a view of the molecule in their ‘natural surroundings’, thus providing operative information on the behaviour of interacting groups inside the organized environment determined by molecular replicas repeated by symmetry. 3. Bias, Pitfalls and Cautions “Databases are socially biased.” A. Gavezzotti 8 Crystallographic databases do not contain a random statistical sample of possible crystal structures, but rather contain those structures that are most interesting to chemists, or easier to solve, or easier to crystallize, as concisely expressed by the well-known sentence17 ‘the number of forms known for a given compound is proportional to the time and money spent in research on that compound’. Following the same line, the apparent higher density and stability of racemic crystals compared to their chiral counterparts claimed by Wallach was successively attributed by a bias in the data that he considered for the analysis: when the racemic crystals are more stable than their chiral counterparts the latter can be obtained by resolution prior to crystallization, while spontaneous resolution forbids the crystallization of racemic crystals if they are less stable than their chiral

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counterparts. The overall result is that the cases when racemic crystals are less dense than chiral counterparts do not appear in the DB18. Structures with Z’ > 1 are almost certainly more frequent in reality than in the CSD, due to difficulties in structure solution and refinement of crystals with many atoms in the asymmetric unit, although their frequency in the CSD has been almost unchanged since 1970, meaning that the improvements in data collection and computing resources has not influenced significantly their occurrence.19 Disordered, modulated, and incommensurate structures are probably underrepresented for the same reasons.20 Crystallographic DB contain errors such as wrong spaceA groups assignements,21 abnormally low θ density due to missing included solvent, multiple inclusion of the same structure D H under different identification codes.22 A' Usually the majority of the outliers in distributions obtained from crystallographic DB result from wrong data rather than from novel and unexpected properFigure 1. Cone correction for evaluating the angular distribution of ties. Structural data are affected by D-H…A hydrogen bonds. The uncertainties, and some standard cautions difference in solid angle sweep of the are normally practised in database work. donor hydrogen related to A and A’ is Crystal structures are conventionally shown. considered only if they respond to the criteria:23 R factor <0.1 (although this point could introduce a bias against ‘problematic’ compounds, as discussed above8), atomic coordinates present, chemical/crystallographic connectivity match, no errors, no disorder. Hydrogen atoms positions must be normalised to the neutron diffraction value (HNORM). In analyzing angular distributions of D-H…A systems the so-called cone correction must be applied for the difference in solid angle sweep of the donor hydrogen as a function of θ with the weighting factor 1/sin θ (Figure 1). 4. Databases Applications The first applications of DB in systematic structural studies date back to 1970’s, and regard the determination of average molecular bond lengths and angles observed in the solid state, for comparison with the values reported by theoretical studies on the geometry of isolated molecules in vacuo.24 Lists of expected values for commonly found bond distances and angles have been compiled, both for organic and inorganic systems. These represent a valuable tool for building reliable starting geometries in molecular modelling, and for validation of structural results, especially in

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macromolecular crystallography.25–27 Soon researchers began to point their attention on correlations between intramolecular bonding parameters, deriving models of dynamic behaviour, conformational preferences and chemical reactivity from the examination of large numbers of similar crystal structures, by the structure correlation principle.28,29 Parallely, statistical studies aiming to categorize intermolecular bonding began to search for geometrical criteria to define the role of hydrogen bonding in molecular recognition.30–32 A powerful arsenal of statistical tools was optimized for handling structural descriptors, e.g. circular statistics to deal with torsion angles, univariate tests to assess the relative importance of experimental error and crystal packing effects, the use of parametric or non-parametric tests to evaluate significant differences of mean values, chi-square tests to probe non-normal spatial distributions in intermolecular contacts, regression analysis to estimate linear correlations between parameters, principal compo nent analysis and cluster analysis to recognize patterns in structureproperties relationships studies.29 With the advent of CE more and more effort is being put in the analysis of intermolecular aggregation as a design tool, for rationalizing polymorphism, co-crystallization, inclusion compounds. These systematic studies embrace many aspects of crystal aggregation: the analysis of correlations between global descriptors such molecular volume, density, packing coefficient, calculated lattice energy, the analysis of crystal symmetry, the individuation and characterization of particularly robust interaction patterns between functional groups. In the last decade databases developers have also conceived several applications which pre-elaborate DB contents and present the information at a higher level of organization, the so-called knowledge-based applications. For an exhaustive and updated compilation of scientific papers concerning databases use, one can refer to the free service WebCite provided on the web by the CCDC: http://www.ccdc.cam. ac.uk/free_services/webcite/. A survey of relevant examples of the use of DB in CE is now presented. These certainly do not cover exhaustively the vast literature on the subject, but have been chosen both for their historical value and because they illustrate well the methods of data mining and elaboration of results. 4.1. RELEVANCE OF MOLECULAR SIZE AND SHAPE ON PACKING

The first element to consider in the study of condensed matter is the occupation of available space by molecular objects. The principle of close packing formulated by Kitaigorodski in 196133 states that maximum space

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occupation confers stability to crystals. It is quite natural to relate the ability of a molecule to realize close packed arrangements with its size and shape. Molecular size and shape can be characterized by a variety of quantitative descriptors8. Van der Waals radii: The most basilar geometrical parameters for the definition of intermolecular interactions are certainly the van der Waals (vdw) radii, firstly introduced by Pauling, and whose values were collected in a compilation assembled from many sources by Bondi back in 1964.34 Thirty years later these values were confirmed by analyzing the average non-bonding distances found in the CSD for common non-metallic elements.35 In this paper for a given (Å) element pair, all intermolecular disFigure 2. Histogram of nonbonded tances were tabulated in histograms contact distances for Cl…Cl atom pairs in the CSD (ver. 5.28, Nov. (number of contacts vs distance, in 0.1 2006), according to the procedure Å bins) out to a value equivalent to the followed in Ref. 35. sum of Bondi’s vdw radii plus a large tolerance of 1.5 Å, to ensure that no bias was introduced by the cut-off. For a random distribution of intermolecular contacts one would expect that the number of contacts would rise with the cube of the distance, while many actual histograms showed a clearly defined maximum (Figure 2), meaning that those pairs of atoms pack in close contact according to a preferential distance. This non-bonding preferential sepaNumber of observations rations have been characterized for each atom pair on the corresponding histonk gram by the value d of the distance at which the contact number reaches half nk/2 of the maximum height (Figure 3). It must be noted that d does not correspond to the vdw contact, but it is has Distance been chosen as the most representative d(Å) statistic parameter for the histograms Figure 3. Schematic representation because of its numerical stability. The of the definition of d according to Ref. 35. nk represents the height at extraction of vdw radii Ri from dij the maximum of the histogram. values involves two steps: first, a set of non-bonded radii ri was generated by least-squares minimization of the function: f=Σij(dij-[ri+rj])2, where the summation is over all pairs of atom types (H, C, N, O, F, S, Cl, Br, I). The

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Crystal density

resulting ri values were scaled to represent the actual best representative non-bonding distance by comparison with Bondi’s vdw radii (Bi): Ri=c Bi, c=Σiri/ΣiBi. Overall, the results confirm that these new Ri values correlate well with Bondi’s vdw radii, are reliably transferable, give satisfactory predictions of experimental interatomic distances. It is concluded that the use of Bondi’s values, obtained long ago mainly from gas kinetic collision cross sections, critical densities, liquid state properties, is justified also from a solid-sate point of view, with the only exception is for hydrogen, whose radius should be reduced by 0.1 Å. From atomic positions, cell dimensions, atomic masses and vdw radii one can derive descriptors for molecular shape and for packing characteristics: molecular volume, molecular surface, inertial axes, molecular self-density, self-occupation coefficient, molar volume, packing coefficient.8 Density: a consequence of the close packing principle is that crystal density is mainly determined by molecular self-density (defined as the ratio of molecular mass to molecular volume), whilst shape has in general a marginal effect on space occupation8. However, density variations may highlight subtle differences in the comparison of closely related compounds. (i) With this aim, a statistical study of density and packing Molecular self-density variations among crystalline isoFigure 4. Crystal density versus molecular mers has been performed.36 Crystal self-density for hydrocarbon crystals. structures of groups of isomeric hydrocarbons, oxahydrocarbons and azahydrocarbons have been retrieΔNB ved from the CSD. The slope of the regression line correlating crystal density with molecular self-density represents the average packing coefficient for the compounds under %ΔD exam (Figure 4), which in this case is Ck=0.72(2), only slightly less Figure 5. Scatterplot of differences in than 0.74, meaning that these organumber of non-C-H links ΔNB as a function of percent density difference %ΔD nic molecules have roughly the for hydrocarbons. The upward trends same packing efficiency as a close means that a higher density is related to a packed assembly of spheres. The higher number of links. number of links NB between nonhydrogen atoms in the molecules was taken as an indicator of molecular shape, since high NB means a more compact molecule. The scatterplot of the difference of NB vs the difference of density between hydrocarbon isomers shows a trend implying that more compact molecules are generally

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denser (Figure 5), because they concentrate more molecular mass in a smaller volume. (ii) A comparison between density of close related compounds has been carried out to test the validity of Wallach’s rule (1895), stating that racemic crystals tend to be denser than their chiral counterparts.18 To test the rule, 129 pairs of corresponding racemic and chiral crystals were identified in the CSD. The quantity Δ(%) = 100[(V/Z)C – (V/Z)R]/{0.5[(V/Z)C + (V/Z)R]} (C and R refer to the chiral and racemic crystals and V/Z is the volume available to each molecule in the crystal – inversely related to crystal density) is +0.56(22)%, an inconclusive result. When the sample is divided into two subpopulations according to the rates of racemization, group I containing 64 pairs of achiral molecules and rapidly interconverting enantiomers and group II containing 65 pairs of enantiomers that can be resolved, Δ(%) is reduced to +0.20(34)% for group I and increased to +0.92(29)% for group II. This difference in behavior was attributed to statistical bias in group II population, since this shouold contain pairs in which the racemic crystal is markedly more stable than the chiral one (obtainable by crystallizing resolved material) but no pairs in which the racemic crystal is markedly less stable. (iii) A correlation between stability and density has also been sought for pairs of polymorphs,37 by searching the CSD for complete X-ray crystallographic structural determinations of more than one polymorphic form containing C, H, N, O, F, Cl, S in any combination and connectivity, at room temperature and with comparable refinement accuracy. Packing energy E was calculated for each structures by an empirical force field using “6-exp”atom-atom potentials, and differences in density and packing energies for polymorphic pairs where plotted. The ΔD vs ΔE Figure 6. Scatterplot of differences scatter plot (Figure 6) shows that in in density (ΔD, %) and in packing most cases a higher packing energy energy (ΔE, %) between polymorph corresponds to a higher density. Shape: pairs. An extreme parameterization and simplification of packing patterns in terms of molecular shape has been attempted by describing molecules as boxes with three unequal dimensions.38 In this model, unit cells are containers which accommodate a number of boxes equal to Z, and cell edges (Dcell) are expressed in terms of multiples of molecular dimensions (Dmol) ranked as long, medium, short (L, M, S). Depending on Z, there is a limited number of boxes arrangements to fill a cell, indicated by the pattern coefficients CL,M,S, where Ci=Di(cell)/ Di(molecule) (i=L,M,S). For instance, Z = 4 structures belong to two packing pattern families, namely, 221 and 114 (Figure 7). Thus, a histogram of

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Figure 7. Left: Model of 221 and 114 packing patterns for four boxes of dimensions l >m>s. Right: Histogram showing the frequency of occurrence of pattern coefficients (cell length/molecular dimension) calculated for Z = 4 structures belonging to space group P21 /c.

pattern coefficients would be expected to show large peaks at approximately 1 and 2, and a smaller peak at 4. This is in close agreement with the histogram obtained from analysis of CSD structures, although the most frequently observed pattern coefficients for experimental structures do not have integer values, because of molecular interdigitation. In general, it is found that most crystal structures are represented by packing patterns which have low surface area to volume ratio. 4.2. A GRAMMAR OF CRYSTAL PACKING

The elucidation of rules by which molecules are put together in periodic ordered arrays would be of great help as guides to the synthesis of designed molecular materials. Many researches have tried to decipher a so-called grammar of crystal packing by looking for frequency and regularities in the operations by which symmetry elements arrange the molecules in the structures observed in the CSD. This has been pursued by analyzing spacegroup frequencies, Z’ distribution, relationships between molecular and crystal symmetry. Space groups: the abundance of space group occurrence in molecular crystal structures has been related to the presence of symmetry elements which facilitate the close packing (inversion centres, screw axes, glide planes), and to the concomitant absence of those elements that disfavour close packed arrangements (proper rotation axes, mirror planes).33 (i) The experimental space groups frequency in the CSD has been analyzed to test the effective efficiency of symmetry elements in filling the space.39–41 Study of 34730 organic molecules retrieved from the CSD reported 75 space groups for which no example of typical organic molecular crystal has ever been found. The rarity of these space groups was attributed to mirror planes

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and rotation axes, their inhibiting effect being mitigated by the simultaneous presence of glide planes or screw axes or both. To a first approximation the number of structures in each space group of a given crystal class is given by Nsg = Acc exp (– Bcc[2]sg – Ccc[m]sg), where [2]sg is the number of twofold axes and [m]sg is the number of reflexion planes in the primitive cell, Bcc and Ccc are parameters characteristic of the crystal class in question, and Acc is a normalizing factor, proportional to the total number of structures in the crystal class. The current top ten list of space groups in the CSD (1 January 2007) is reTABLE 1. CSD top ten most frequent space groups ported in Table 1. (ii) It has been shown that Rank Space Group N in CSD % of CSD some space groups occur pre1. P21/c 139 603 35.1 dominantly, or even almost 2. P-1 89 628 22.6 exclusively, when symmetric 3. P212121 32 236 8.1 molecules occupy special 4. C2/c 31 558 7.9 positions in the cell.42 Some 5. P21 21 995 5.5 rules have been enunciated: 6. Pbca 14 047 3.5 (1) inversion centres are fa7. Pna21 5 753 1.4 vourable; unoccupied inver8. Pnma 5 107 1.3 sion centres are not a penalty for crystal packing, while 9. Cc 4 281 1.1 centrosymmetric molecules 10. P1 3 850 1.0 usually occupy crystallographic inversion centres. (2) Mirror planes are always occupied; unoccupied mirror planes require unfavourable like-like intermolecular contacts, and generate a sheet of forbidden space in the packing. (3) Space groups with 3-, 4-, and 6-fold axes do not usually occur unless the molecules are located on the axes; exception to this rules are structures in which particular supramolecular motifs are formed, such as hydrogen bonded rings among bulky molecules,43 or aggregation of MAr4 molecules around empty -4 sites,44 or phenyl embraces.45 (4) Z is relatively constant across the crystal systems, i.e. space groups with a low number of symmetry operations allow for more than one independent molecules (Z’>1) more easily than space groups with high symmetry, where fractional Z’ (molecule occupying a special position) are more frequent. (iii) A critical analysis of monolayers observed by scanning tunneling microscopy at the liquid-solid interface was conducted and the data were assembled into a two-dimensional analogue of the CSD. Plane-goups frequencies were determined, showing that the most populated 2D plane groups are p2 (58%), p1 (17%) and p2gg (9.7%). It was also observed that achiral molecules tend to give chiral 2D aggregates, and racemic mixtures give resolved enantiomeric 2D domains.46 Occurrence of Z’≠ 1: The absolute frequencies of Z’ values in organic and organometallic crystal structures appearing in the CSD have been studied.47 51 different values of Z’, ranging from 1/96 to 32 are present.

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Remarkable differences are seen between the Z’ frequencies in different chemical classes. In porphyrins, which often have internal symmetry, Z’ values < 1 occur very frequently (41.2%), whereas Z’ > 1 is rare (3.5%). In chiral organic compounds, where no inversion centres, mirror and glide planes are allowed, the situation is reversed. There are strong substance dependencies in the occurrence of Z’ > 1. In organic compounds, Z’ > 1 occurs with a frequency of 10.8% on average. For steroids, it is strongly elevated to 18.8%, and for nucleosides and nucleotides it even reaches 20.8%. In a further classification, the frequency of Z’ values <1 continuously increases with increasing crystal symmetry, being smallest in the triclinic (19.7%) and largest in the cubic systems (98.2%), while the tendency for Z’ to be >1 is reversed. Molecular vs crystal symmetry: The distribution of molecules over Wyckoff positions and the occupancy of Wyckoff positions in crystal structures has been studied by using CSDSymmetry,48 a relational database containing information pertaining to the symmetry of molecules and the crystal structures that host them. It was found that molecules that possess an inversion centre retain this symmetry element in their crystal structures in more than 80% of cases. Similarly high degrees of retention were observed for S4 and S6. These symmetry elements can, like an inversion centre (which is equivalent to an S2 axis), be described as ‘point-acting’, since all atoms are transposed through the inversion point of the improper rotation axis. Proper rotation axes were retained by molecules in approximately 50% of cases and mirror planes were usually retained in less than 30% of cases. Figure 8 shows the distribution of molecules with point group symmetry C(2) and S(4) on Wyckoff positions across different space groups. Thus, symmetry elements described by an axis or a plane are retained to a lesser extent than point-acting symmetry elements.

Figure 8. Histograms showing the top six locations in crystal structures for molecules of C(2) and S(4) point groups The Wyckoff positions occupied within the space group is indicated.

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4.3. INTERMOLECULAR INTERACTIONS

The CSD is a major source of knowledge on intermolecular interactions of all types. The typical protocol used to study the geometry of intermolecular interactions is (a) define the fragments involved in the interaction that is being studied; (b) define one or more descriptors that give information on the geometry of approach between the fragments; (c) select appropriate thresholds that identify the real occurrence of the interaction; (d) perform a query to retrieve all the instances of the interaction under exam; (e) choose appropriate statistics and graphic representations to describe the distribution of the geometric parameters through the dataset. Search queries may involve chemical substructures linked via non-bonded interactions that are defined in terms of distances, or relative to sums of van der Waals radii. Other geometrical limitations may also be used in query definitions. Statistical analyses of the occurrence of several types of interactions in the CSD have been used to elucidate energetic and geometric aspects of supramolecular recognition and aggregation. Hydrogen bond geometry: Hydrogen bonds and their environment have a well-defined geometry in the crystalline state. CSD provides a vast amount of experimental data that allows hydrogen bond geometries to be analyzed at a high statistical level.49 The CSD has been used extensively in studies of common strong hydrogen bonds having N or O as donors and acceptors. Several studies have examined distribution of H-bond distances and angles,30 H-bond lone-pair directionality at the acceptor,50 resonance assisted and resonance-induced H-bonds.32 A major contribution of CSD analysis has been to support the existence of a wide range of weaker hydrogen bonds involving weak donors and strong acceptors (e.g. C–H…O, C–H…N), strong donors and weak acceptors (e.g. O,N–H…Cl, O,N–H…π), weak donors and weak acceptors (e.g. C–H…Cl, C–H…π). A relevant success was the identification of short C–H…O and C–H…N contacts as hydrogen bonds.31 (i) The hydrogen bond preference for linearity in the O-H…O case has been assessed by analyzing the distribution of angles θ in carbohydrates49 (Figure 9): after the cone correction, θ shows a clear peak at linear values between 170 Figure 9. Directionality of O-H…O hydrogen and 180°. Angular preferences bonds in carbohydrates before (left) and after (right) cone-correction. (Reproduced with have been further analyzed30 by permission from Angew. Chem. Int. Ed., 41, scatter plots of angles θ against 48–76, 200249 © 2002 Wiley-VCH) distances d. The plot includes all

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contacts found in crystal structures with dH…O<5.0 Å at any angle and each point in these clusters represents a hydrogen bond. The scatter within the clusters is considerable, and their borders are diffuse.51 There is a highly populated cluster of data points at short distances and fairly linear angles, while other clusters indicate minor components of bifurcated bonds, non-bonding next-neighbours contacts, randomly scattered non-bonding second-neighbour contacts, and a stereochemically forbidden region due to limited O…O approach. (ii) Another study52 has shown that the degree of directionality depends on the polarity of the donor (Figure 10). For OFigure 10. Directionality of X-H…O=C H… O=C, C-H…O=C, and Cinteractions with X-H groups of different polarities (cone-corrected angular histogramH…H-C interactions, the degree ms). The degree of directionality decreases of directionality decreases in gradually from (a) to (d), and interaction (e) parallel with the polarity of the is isotropic within a broad angular range. (Reproduced with permission from Angew. X-H group, namely, O-H> C CChem. Int. Ed., 41, 48–76, 200249© 2002 H> C=CH2 >-CH3. (iii) The Wiley-VCH) acceptor directionality (represented for instance by the C=O…H angle Φ in the above cases) in general corresponds to the orientation of electron lone pairs. Angular histograms representing Φ for N/O-H…O/S=C hydrogen bonds50 (Figure 11), show that the oxygen lone pair lobes are in the R2C=O plane and Figure 11. Acceptor directionality of C=O (right) and C=S form angles of about (left) in N/O-H…O/S=C hydrogen bonds. (Reproduced with 120° with the C=O permission from Angew. Chem. Int. Ed., 41, 48–76, 200249© bond. The acceptor 2002 Wiley-VCH)

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directionality is much more pronounced for thiocarbonyl groups, as seen by the higher concentration of occurrences at the lobes, that are located at about 105°. (iv) The CSD was used to investigate the hydrogen-bond accepting capabilities of the M-Cl unit,53 by searching for structures containing O/N-H and M-Cl, C-Cl, or Cl-. The percentage of short H…Cl interactions found in these three classes of compounds was taken as an indicator of the strength of the corresponding D-H…Cl interaction. The sequence of acceptor strength is Cl- > M-Cl >> C-Cl. Other interactions: a wide range of attractive non-bonded interactions other than hydrogen bonds contributes to supramolecular aggregation in the solid state. The CSD plays a central role in identifying and characterizing such interactions. Some examples follow. (i) A database study has given insight into the role of the Figure 12. Scatterplot showing linear dependence CH/π(C6 aromatic) in the cryof the C–H…π access angle α on the CH/π plane stal packing.54,55 It has been distance for CCl3H…π contacts (acidic proton). found that a CH/π short distance (<3.05 A°) occurs in 54% of organic compounds containing at least a YCH3 and an aromatic group, while short OH/π interactions are observed only in 4% of cases. The approach between CH and the aromatic ring has been analyzed by retrieving from CSD the values of several geometric descriptors and examining the corresponding mono- and bivariate statistics. An area correction similar to the cone correction has been suggested51 to account for the fact that the acceptor is a multi-atom entity. Monovariate statistics on distances show that the mean CH/π distance decreases as the proton acidity increases; scatterplots of the C–H…π access angle on the CH/π plane distance55 (Figure 12) show that

Figure 13. Correlation between the displacement angle (n–CC) (calculated between the normal to the pyridine plane n and the CC vector connecting the ring centroids C) and the centroid–centroid distance (CC) for pyridines coordinated to transition metals (M).

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the more acidic the proton, the more linear is the correlation, as already observed for CH/n hydrogen bonds.52 (ii) Similar geometric descriptors have been used to characterize the geometry of π…π interaction between metal-coordinate pyridines.56 In the CSD centroid–centroid contacts between two pyridine fragments start slightly below 3.4 Å and a relative maximum in the number of examples is found around 3.8 Å. In the vast majority of cases the interplane angle is near zero, but the angle formed between the ring-centroid vector (CC) and the ring normal to one of the pyridine planes averages 27°. A correlation between the displacement angle and the centroid–centroid distance (Figure 13) reveals a slightly smaller tendency for parallel displacement at shorter distance. (iii) The marked tendency of the halogens X = Cl, Br, I to form short contacts to each other and to electronegative N and O atoms is shown by a CSD analysis of C-X…O=C< systems.57 The shortest X…O interactions present a marked preference to form along the extension of the C–X bond. By contrast C–Cl…Cl–C interactions tend to form with C–Cl…Cl angles close to 90°.58 4.4. INTERACTION PATTERNS

The scope of crystal engineering is to establish relations between molecular and supramolecular structure on the basis of intermolecular interactions. Particularly recurrent intermolecular patterns, the so-called supramolecular synthons, may be exploited to design crystal structures.13 Patterns of interactions can be obtained by manual inspection or more rigorously with the use of crystallographic databases. (i) The CSD developers have implemented a method for characterising hydrogen-bonded ring motifs formed between two organic molecules without any prior knowledge of the topology or chemical constitution of the motifs.59 All intermolecular ring motifs comprising ≤20 atoms formed with N—H···N, N—H···O, O—H···N and O—H···O hydrogen bonds in organic structures in the CSD have been classified. 75 bimolecular motifs occurring in >12 structures in the CSD were ranked according to their frequency of occurrence and according to their probabilities of formation, i.e. their frequency relative to the number of possible motifs which could have formed. These probabilities provide insights into the relative robustness of known and potential supramolecular synthons. (ii) Recently interaction motifs between carboxylic acids and carboxylic acids or amides have been classified by using clustering and multivariate analysis.60,61 Structural fragments mined from the CSD have been grouped into similar motifs based on intermolecular contacts: a matrix containing the differences between all the interatomic distances and angles of acid-acid fragments extracted from the CSD has been used to generate

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dendograms for the cluster analysis (Figure 14). The majority of the contacts in the acid fragments occur “in front” of the central contact group, group A. Hydrogen bonds to the “exo-” position occur in only 7% of cases (group C). A number of weaker hydrogen bonds are included in group E. A number of non hydrogen bonded contacts just inside the defined van der Waals distance (particularly groups B and D) is also observed. Group F consists of structural outliers due to errors in the output coordinates. (iii) A CSD analysis has shown62 that –PPh3 groups frequently aggregate by forming six-fold phenyl embraces based on six concerted edge-to-face interactions between phenyl groups. The relevance of 6PE to crystal packing ha been assessed by retrieving all structures containing at least one M-PPh3 fragment (M=transition metal). The geometry of the aggregation between PPh3 groups was represented by the P…P separation and by the M-P…P-M colinearity (θ=half the sum of the M-P…P and P…P-M angles); all interactions with P…P in the range 5.5–8.0 Å and θ in the range 120–180° were considered. The scatterplot of these two parameters shows a preponderance of interactions with P…P=6.4–7.4 Å and θ=160–180°, corresponding to regular 6PE. These values have been taken as a reference to describe 6PE in the successive literature.

Figure 14. Similarity dendogram (left) from the cluster analysis of acid…acid contacts, and Isostar plot (right) of the spatial distribution of the clusters around the central fragment

4.5. POLYMORPHISM

The Cambridge Structural Database release of October 2001 contained only less than 2% of entries recognized as polymorphic. However, the flag ‘polymorph’ depends mainly on the original publication. All pairs of polymorphs in the CSD were identified by a method devised to automatically compare two crystal structures on the basis of simulated powder diffraction

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patterns, taking into account differences in unit-cell volumes caused by temperature or pressure.22 A total of 7300 pairs of polymorphs were identified, of which 154 previously were unknown, among the 325 000 crystal structures in the CSD, by comparison of 35 000 pairs of crystal structures of the same chemical compound. Polymorphs are usually contained in a narrow energy range; differences in density, static packing energy, latticevibrational entropy and other crystal properties for 204 pairs of CSD polymorphs have been discussed.37 4.6. SOLVATES AND CO-CRYSTALS

Solvates: (i) The occurrence of 20 common solvents that appear at least 50 times in organic crystal structures was retrieved from the CSD.63 These solvents were ranked in the order of their occurrence, Ocorr. The fact that different solvents are used to different extents by chemists for crystallisation was normalised by correcting for solvent usage through a manual inspection of Acta Crystallographica, Section C volumes of 1986 and 1996. Thus, a value of 1.00 for Ocorr indicates that the solvent is included in organic crystals commensurate with its usage. Values much greater and much less than unity mean that these solvents have greatly enhanced and greatly reduced tendency to form solvates, respectively. Dimethylformamide (DMF), dimethyl sulfoxide (DMSO) and dioxane are the top solvents (Ocorr 5.69, 4.73 and 4.70, respectively), and EtOH, Et2O and n-hexane are least likely to be included in crystals (Ocorr 0.46, 0.35, 0.11, respectively). (ii) Subsequently the frequency of occurrence in crystal structures of more than 300 different solvent molecules were calculated and reported as a function of the year of publication.64 The increased proportion of crystal structures which include cocrystallized solvent molecules in recent years is related to the increasing complexity of the molecules being synthesized, making a packing arrangement without cavities or channels less easily attainable. The relative prevalences of various cocrystallized solvents are different in organic and metallorganic structures. Several frequently used organic solvents are also common ligands for metal ions. The occurrence of heterosolvates has increased in recent years, and up to five different types of solvent molecules were found in a single crystal structure. (iii) The CSD has recently been used to study water affinity.65 A subset of CSD structures was analysed in terms of 36 chemical functional groups. The water affinity of those groups has been expressed as the ratio of the number of hydrated structures containing the group divided by the total number of structures containing the group. It can be seen that the highest affinities are exhibited by compounds containing charged species, while the lowest affinities are

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exhibited by compounds having terminally bound halogens. common functional groups. (iv) The effect of solvation on the packing metrics of a family of organic and metallorganic wheel-and-axle diols (waad) has been studied by defining simple packing descriptors (d=distance between the molecular axles, Δ=offset of the molecular centers) related to the interaction of pairs of waad molecules in the solvated and unsolvated compounds.66 The comparison of the distribution of d and Δ for the two classes has allowed to formulate a simple model of solid-solid conversion explaining the structural rearrangements occurring during reversible solvent uptake and release for inorganic waad.67 Co-crystals: (i) Supramolecular heterosynthons represent an opportunity for design of multi-component crystals (co-crystals). A CSD study of supramolecular synthons involving primary amides revealed that they tend to form supramolecular heterosynthons in the presence of chemically different but complementary functional groups, while in the absence of hydrogen bond competitors 84% of primary amides form amide-amide dimers, and 14% form catemers.68 These results facilitated the selection of components for seven new primary amide co-crystals. (ii) In the crystal structures of 5 hemiadducts and one 1:1 adduct of paracetamol, the drug molecules are linked in chains by OH…O=C and NH…O=C hydrogen bonds, depending on the guest. The co-crystal structural organization has been rationalized by comparing hydrogen-bond strengths with those in the CSD.69 The relational DB CSD symmetry has been used to investigate the role of both molecular and space group symmetry in co-crystal formation. 5. Statistical Methods The discipline of chemometrics is rooted in analytical chemistry, but with the increasing availability of crystallographic databases it has found many applications in structural chemistry. These databases contain important information hidden in the relations between all the data, such as similarities and dissimilarities, that may reveal important new chemical knowledge. Finding these hidden relations in databases is sometimes called data mining or knowledge discovery. An exhaustive review of statistical and numerical methods of data analysis is provided by R. Taylor and F. H. Allen,29 and theory and applications may be found in a series of paper.70–79 Of particular importance are: (a) descriptive statistics (mean, median and standard deviation) for a distribution of, for instance, a specific bond length observed in many crystal structures; (b) parametric and non-parametric tests to assess the significance of differences between means; (c) the use of covariance, correlation and regression to determine the extent and nature of any relationship between pairs of parameters; and (d) multivariate methods, such as

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principal components analysis (PCA) and cluster analysis (CA). PCA essentially searches for correlations among all variables simultaneously, extracting linear combinations of highly correlated variables that describe, in turn, the greatest amount of sample variance, the second greatest, and so on. Its main use therefore lies in dimensionality reduction. Cluster analysis represents a complementary technique that groups together similar points in the multidimensional data space, thereby yielding clusters or clouds of data points that are often useful in classifying the data. PCA and CA are appropriate for structural problems which require the analysis of three or more parameters for each substructure retrieved from the CSD, e.g. the analysis of conformational preferences of n-membered rings,78 where each conformer is described by n torsion angles, or the analysis of metal coordination spheres, where each sphere is characterised by the [n(n – 1)]/2 L–M–L valence angles in an MLn species.72 The application of factor analysis to analytical chemistry has been outlined by Malinowski and Howery,81 while Massart and Kaufman have described the use of cluster analysis.82 6. Knowledge Based Applications Some knowledge-based libraries provide easy access to a variety of structural information interesting in CE.83 Mogul is a library of intramolecular geometry data such bond lengths, valence angles and acyclic torsions. One particular geometric parameter of interest may be selected within a complete molecule or a substructural query generated in the Mogul graphical interface, and then the distribution of the corresponding CSD values may be obtained. IsoStar is a library of intermolecular interactions between pairs of groups A…B.84 One central group A and one probe group B are selected; all the A…B contacts observed in the CSD, PDB, and in some cases by theoretical calculations, are reported in a three-dimensional scatterplot by superimposing all the A moieties, showing the experimental distribution of B around A. The scatterplot can be converted to a contoured surface showing the density of contact groups around the central group. Isostar has been used to elucidate desolvation mechanism sites for organic and metallorganic inclusion compounds formed by wheel-and-axle diols (waad).66 User-defined scatterplots have shown that in the solid state waad present two preferential directions of coordination to guest molecules, related to two possible solvation sites within the waad solvated networks. Desolvation experiments67 showed that for some organic and inorganic waad the preferential way of escape of guests from the crystal bulk corresponds to a migration along the array of alternate guest sites evidenced by the Isostar analysis. CSDSymmetry is a relational database constructed

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using Microsoft Access. It contains information about space group, point group, Z, Z’, and symmetry of Wyckoff positions It contains information for each entries in the CSD. Auxiliary tables, linked to the main table, list the symmetry elements which belong to 38 common point groups, the symmetry operators, and Wyckoff positions of the 230 space groups. These tables allow selection of molecules by the symmetry elements that characterise them or by their membership of a space group with a particular symmetry operator.

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16. G. R. Desiraju, Cryptic Crystallography, Nature Materials, 1, 77–79 (2002) 17. W. C. McCrone, Polymorphism in Physics and Chemistry of the Organic Solid State, Edited by D. Fox, M. M. Labes and A. Weissberger (Wiley Interscience New York 1965), Vol. II, pp. 726–767 18. C. P. Brock, W. B. Schweizer and J. D. Dunitz, On the Validity of Wallach’s Rule: On the Density and Stability of Racemic Crystals Compared with Their Chiral Counterparts, J. Am. Chem. Soc., 113, 9811–9820 (1991) 19. T. Steiner, Frequency of Z’ values in organic and organo-metallic crystal structures, Acta Crysallogrt. Sect. B, B56, 673–676 (2000) 20. C. P. Brock, Investigations of the Systematics of Crystal Packing Using the Cambridge Structural Database, J. Res. Natl. Inst. Stand. Technol. 101, 321 (1996) 21. R. E. Marsh, Space group P1: an update, Acta Crystallogr., Sect. B, B61(3), 359 (2005) 22. J. Van de Streek and S. D. Motherwell, Searching the Cambridge Structural Database for Polymorphs, Acta Cryst. Sect. B, B61, 504–510 (2005) 23. A. Nangia, Database research in crystal engineering, CrystEngComm, 4(17), 93–101 (2002) 24. A. Domenicano and P. Murray-Rust, Geometrical Substituent Parameters for Benzene Derivatives: Inductive and Resonance Effects Tetrahed. Lett., 2283–2286 (1979) 25. F. H. Allen, O. Kennard, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor, Tables of bond lengths determined by X-ray and neutron diffraction. Part 1. Bond lengths in organic compounds, J. Chem. Soc., Perkin Trans. 2, S1–S19 (1987) 26. A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, Tables of bond lengths determined by X-ray and neutron diffraction. Part 2. Organometallic compounds and co-ordination complexes of the d- and f-block metals. J. Chem. Soc., Dalton Trans., S1–S83 (1989) 27. R. A. Engh and R. Huber, Accurate Bond and Angle Parameters for X-ray Protein Structure Refinement, Acta Crystallogr. Sect. A, 47, 392–398 (1991) 28. H. B. Buergi, J. D. Dunitz, From Crystal Statics to Chemical Dynamics, Acc. Chem. Res., 16, 153–161 (1983) 29. Structure Correlation, edited by H. -B. Buergi and J. D. Dunitz (VCH Publishers, Weinheim, 1994) 30. T. Steiner and W. Saenger, Geometric analysis of non-ionic O-H…O hydrogen bonds and non-bonding arrangements in neutron diffraction studies of carbohydrates, Acta Crystallogr. Sect. B, B48, 819-827 (1992) 31. R. Taylor and O. Kennard, Crystallographic Evidence for the Existence of C-H-O, C-HN, and C-H-Cl Hydrogen Bonds, J. Am. Chem. Soc., 104, 5063–5070 (1982) 32. G. Gilli, F, Bellucci, V. Ferretti and V. Bertolasi, Evidence for resonance-assisted hydrogen bonding from crystal-structure correlations on the enol form of the beta – diketone fragment, J. Am. Chem. Soc., 111, 1023–1030 (1989) 33. A. I. Kitaigorodski, Organic Chemical Crystallography (Consultants Bureau, New York, 1961) 34. A. Bondi, Van der Waals volumes and radii, J. Phys. Chem., 68, 441 (1964) 35. R. S. Rowland and R. Taylor, Intermolecular Nonbonded Contact Distances in Organic Crystal Structures: Comparison with Distances Expected from van der Waals Radii, J. Phys. Chem., 100, 7384–7391 (1996) 36. J. D. Dunitz, G. Filippini and A. Gavezzotti, A Statistical Study of Density and Packing Variations among Crystalline Isomers, Tetrahedron, 56(36), 6595–6601 (2000)

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37. A. Gavezzotti and G. Filippini, Polymorphic forms of organic crystals at room conditions: thermodynamic and structural implications, J. Am. Chem. Soc. 117, 12299– 12305 (1995) 38. E. Pidcock and W. D. S. Motherwell, A Novel Description of the Crystal Packing of Molecules, Crystal Growth & Design, 4, 611–620 (2004) 39. A. J. C. Wilson, Space groups rare for organic structures. I. Triclinic, monoclinic and orthorhombic crystal classes, Acta Crystallogr. Sect. A, A44, 715–724 (1988) 40. A. J. C. Wilson, Space groups rare for organic structures. II. Analysis by arithmetic crystal class Acta Crystallogr. Sect. A, A46, 742–754 (1990) 41. A. J. C. Wilson, Space groups rare for organic structures. III. Symmorphism and inherent molecular symmetry, Acta Crystallogr. Sect. A, A49, 795–806 (1993). 42. C. P. Brock and J. D. Dunitz, Towards a grammar of crystal packing, Chem. Mater., 6, 1118–1127 (1994) 43. C. P. Brock and L. L. Duncan, Anomalous Space-Group Frequencies for Monoalcohols CmHnOH, Chem. Mater. 6, 1307–1312 (1994). 44. M.A. Lloyd and C. P. Brock Retention of 4- Symmetry in Compounds Containing MAr4 Molecules and Ions, Acta Crystallogr. Sect. B, 53, 780–786 (1997) 45. T. Steiner, Multiple phenyl interactions. Part 1: relative frequencies of six-fold phenyl embraces (6PE) in crystalline compounds containing the fragment (X = any tetrahedral atom) XPh3, New J. Chem., 24, 137–142 (2000) 46. K. E. Plass, A. L. Grzesiak and A. J. Matzger, Molecular Packing and Symmetry of Two-Dimensional Crystals, Acc. Chem. Res., 40, 287–293 (2007) 47. T. Steiner, Frequency of Z’ values in organic and organo-metallic crystal structures, Acta Crystallogr. Sect. B, B56, 673–676 (2000) 48. J. W. Yao, J. C. Cole, E. Pidcock, F. H. Allen, J. A. K. Howard and W. D. S. Motherwell, CSDSymmetry: The definitive database of point-group and space-group symmetry relationships in small-molecule crystal structures, Acta Crystallogr. Sect. B, B58, 640–646 (2002) 49. T. Steiner, Reviews: The hydrogen bond in the solid state, Angew. Chem. Int. Ed., 41, 48–76 (2002) 50. F. H. Allen, C. M. Bird, R. S. Rowland, and P. R. Raithby, Resonance-induced hydrogen-bonding at sulphur acceptors in R1,R2C=S and R1CS2- systems, Acta Crystallogr. Sect. B, 53, 680–695 (1997) 51. G. R. Desiraju, Hydrogen Bridges in Crystal Engineering: Interactions without Borders, Acc. Chem. Res., 35, 565–573 (2002) 52. T. Steiner and G. R. Desiraju, Distinction between the weak hydrogen bond and the van der Waals interaction, Chem. Commun., 891–892 (1998) 53. G. Aullon, D. Bellamy, L. Brammer, E. A. Bruton and G. A. Orpen Metal-bound chlorine often accepts hydrogen bonds, Chemical Commun., 653–654 (1998) 54. Y. Umezawa, S. Tsuboyama, K. Honda, J. Uzawa, and M. Nishio, CH/π interaction in the crystal structure of organic compounds. A database study. Bull. Chem. Soc. Japan, 71(5), 1207–1213 (1998) 55. M. Nishio, CH/π hydrogen bonds in crystals, CrystEngComm, 6(27), 130–158 (2004) 56. C. Janiak, A critical account on π–π stacking in metal complexes with aromatic nitrogen-containing ligands, J. Chem. Soc., Dalton Trans., 3885–3896 (2000) 57. J. P. M. Lommerse, A. J. Stone, R. Taylor and F. H. Allen, The nature and geometry of intermolecular interactions between halogens and oxygen or nitrogen, J. Am. Chem. Soc., 118, 3108–3116 (1996) 58. S. L. Price, A. J. Stone, J. Lucas, R. S. Rowland and A. E. Thornley, The nature of -Cl...Cl- intermolecular interactions, J. Am. Chem. Soc, 116, 4910–4918 (1994)

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59. F. H. Allen, W. D. S. Motherwell, P. R. Raithby, G. P. Shieldsa and R. Taylor, Systematic analysis of the probabilities of formation of bimolecular hydrogen-bonded ring motifs in organic crystal structures, New J. Chem., 25–34 (1999) 60. A. Parkin, G. Barr, W. Dong, C. J. Gilmore and C. C. Wilson, Identifying structural motifs in inter-molecular contacts using cluster analysis Part 1. Interactions of carboxylic acids with primary amides and with other carboxylic acid groups, CrystEngComm, 8, 257–264 (2006) 61. A. Collins, A. Parkin, G. Barr, W. Dong, C. J. Gilmore and C. C. Wilson, Identifying structural motifs in intermolecular contacts using cluster analysis Part 2. Interactions of carboxylic acids with secondary amides, CrystEngComm, 9, 245–253 (2007) 62. I. Dance and M. Scudder, The sextuple phenyl embrace, a ubiquitous concerted supramolecular motif, J. Chem. Soc., Chem. Commun., 1039–1040 (1995) 63. A. Nangia and G.R. Desiraju, Pseudopolymorphism: occurrences of hydrogen bonding organic solvents in molecular crystals, Chem. Commun., 605–606 (1999) 64. C. H. Goerbitz and H. -P. Hersleth, On the inclusion of solvent molecules in the crystal structures of organic compounds, Acta Crystallogr. Sect. B, B56, 526–534 (2000) 65. L. Infantes, J. Chisholm and S. Motherwell, Extended motifs from water and chemical functional groups in organic molecular crystals, CrystEngComm, 5, 480–486 (2003) 66. A. Bacchi, Models, Mysteries, and Magic of Molecules, edited by J.C.A. Boeyens and J.F. Ogilvie, pp. 89–110 (Springer, 2007) 67. A. Bacchi, E. Bosetti, and M. Carcelli, Engineering organic/inorganic diols that reversibly capture and release volatile guests, CrystEngComm, 7, 527–537 (2005) 68. J. A. McMahon, J. A. Bis, P. Vishweshwar, T. R. Shattock, O. L. McLaughlin and M. J. Zaworotko, Crystal engineering of the composition of pharmaceutical phases. 3. Primary amide supramolecular heterosynthons and their role in the design of pharmaceutical cocrystals, Zeit. Kristall., 220(4), 340–350 (2005) 69. I. D. H. Oswald, W. D. S. Motherwell, S. Parsons, E. Pidcock and C. R. Pulham, Rationalisation of co-crystal formation through knowledge-mining, Crystallogr. Rev., 10, 57–66 (2004) 70. R. Taylor and O. Kennard, Cambridge Crystallographic Data Centre. 7. Estimating average molecular dimensions from the Cambridge Structural Database. J. Chem. Inf. Comput. Sci., 26, 28–32 (1986) 71. R. Taylor and O. Kennard, The estimation of average molecular dimensions. 2. Hypothesis testing with weighted and unweighted means. Acta Crystallogr. Sect. A., A41, 85 (1985) 72. T. Auf der Heyde, Determination of Reaction Paths for Pentacoordinate Metal Complexes with the Structure Correlation Method, Angew. Chem., Int. Ed. Eng., 33, 823–839 (1994) 73. F. H. Allen, M. J. Doyle and R. Taylor, Automated conformational analysis from crystallographic data. 1. A symmetry-modified single-linkage clustering algorithm for 3D pattern recognition, Acta Crystallogr. Sect. B, B47, 29–40 (1991) 74. F. H. Allen, M. J. Doyle and R. Taylor, Automated conformational analysis from crystallographic data. 2. Symmetry-modified Jarvis-Patrick and complete-linkage clustering algorithms for 3D pattern recognition, Acta Crystallogr. Sect. B, B47, 41–49, (1991) 75. F. H. Allen, M. J. Doyle and R. Taylor, Automated conformational analysis from crystallographic data. 3. 3D Pattern recognition within the Cambridge Structural Database System: Implementation and practical examples, Acta Crystallogr. Sect. B, B47, 50–61 (1991)

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76. F. H. Allen and O. Johnson, Automated conformational analysis from crystallographic data. 4. Statistical descriptors for a distribution of torsion angles, Acta Crystallogr. Sect. B, B47, 62–67 (1991) 77. F. H. Allen and R. Taylor, Automated conformational analysis from crystallographic data. 5. Recognition of special positions in conformational space in symmetry-modified clustering algorithms, Acta Crystallogr. Sect. B, B47, 404–412 (1991) 78. F. H. Allen, M. J. Doyle and T. P. E. Auf der Heyde, Automated conformational analysis from crystallographic data. 6. Principal component analysis for n-membered carbocyclic rings (n=4,5,6). Symmetry considerations and correlations with ringpuckering parameters, Acta Crystallogr. Sect. B, B47, 412–424 (1991) 79. L. M.C. Buydens, T. H. Reijmers, M. L. M. Beckers, and R. Wehrens, Molecular datamining: a challenge for chemometrics, Chemom. and Intell. Lab. Syst., 49, 121–133 (1999) 80. T. P. E. Auf der Heyde, Analyzing Chemical Data in More Than Two Dimensions-A Tutorial on Factor and Cluster Analysis, J. Chem. Ed., 67, 461–469 (1990) 81. E. R. Malinowski and D. G. Howery, D. G., Factor Analysis in Chemistry (Wiley, New York, 1980) 82. L. D. Massart and L. Kaufman, The Interpretation of Analytical Chemical Data by Cluster Analysis, (Wiley, New York, 1983) 83. J. Chisholm, E. Pidcock, J. van de Streek, L. Infantes, W. D. S. Motherwell and F. H. Allen, Knowledge-based approaches to crystal design, CrystEngComm., 8, 11–28 (2006) 84. I. J. Bruno, J. C. Cole, J. P.M. Lommerse, R. S. Rowland, R. Taylor and M. L. Verdonk, IsoStar: A library of information about nonbonded interactions, J. Comp.-Aid. Mol. Des., 11, 525–537 (1997)

CASE STUDIES ON INTERMOLECULAR INTERACTIONS IN CRYSTALLINE METALS

PATRICK BATAIL CNRS, Université d’Angers, 49045 Angers, France

Abstract. It is the purpose of this contribution to take the reader throughout a set of case studies which serve to illustrate an integrated approach which spans the design of functional π-conjugated precursors, their assembly into conducting crystalline solids of high purity, and the diversity and complexity of their crystal chemistry. This is accomplished by deciphering very many, entangled intermolecular interactions acting in unisson together with a rich low dimensional physics.

Keywords: hydrogen bonds, halogen bonds, crystal engineering, radical cations, band structures, Fermi surfaces, molecular metals, materials chemistry, Mott physics, Wigner crystals

1. Introduction One of the many faces of intermolecular interactions in complex, ordered conducting systems of high purity based on π-conjugated molecules1 is their inherent anisotropy. The embraces of such planar, rigid functional objects direct the topology of anisotropic, long range ordered metallic molecular constructs of great harmony. Such anisotropic large collections of intermolecular interactions, blessed with the periodicity and translational symmetry of the crystalline solid state, give rise, over in the momentum space, by virtue of the Bloch theorem, to low dimensional electronic band structures and Fermi surfaces.2,3 In these solids, electrons and holes travel long distances between molecular sites or, rather, become increasingly prevented to do so as electron correlations take over at low temperature. Strong electronic correlations are a distinctive, direct consequence of their low dimensional character and, accordingly, they are the strongest in 1D. When electronic localization sets 59 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 59–86. © 2008 Springer.

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in, charge disproportionation eventually occurs at some low temperature and results in the crystallization of a long range-ordered Wigner network of charges, the essence of Mott physics.4

1

2

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An approach is emerging throughout this research, revolving around the symmetry of the molecular precursors. This is true primarily for hybrid systems where anionic mononuclear or polynuclear metal complexes or clusters are prone to accept weak, electrostatic directional hydrogen and halogen bonds because of the Lewis base character of their halide or cyanide ligands. Hence, hydrogen bond and halogen bond-appended radical cations consistently coordinate to and thereby express over into the network topology the symmetry of inorganic nodes such as those shown in 1. This makes for beautiful architectures, illustrated in 2 by the early example, reported in 1989, of the layered structure of α-(BEDT-TTF)8 [SiW12O40],5 space group I2, whose noncentrosymmetric character originates in a set of interfacial C–H···O hydrogen bonds involving the top and bottom, closedpacked outer oxygen atom anion layers which are orthogonal to each other because of the tetrahedral symmetry of the Keggin polyoxometalate. The very molecular nature of such systems makes for small values of interactions energies between molecular sites; they typically amounts to 1 eV (24 kcal mole–1), and are a great deal smaller than the net dispersion of energy bands in inorganic metals where extensive covalent bonding is the rule.3,6 Thus, deep underneath, a subtle balance of intermolecular interacttions sets the scene for creative, materials discovery undertakings rooted in the crystal engineer and materials designer ability to modify, then modulate, such complex equilibrium by engaging molecular precursors suitably decorated like, for example, by hydrogen bond and halogen bond donor/acceptor functionalities. Hence, this research is interdisciplinary par excellence: the field of molecular conductors has developed into a singular, integrated culture where organic and inorganic chemists, materials scientists, quantum chemists join forces with condensed matter physicists, experimentalists and theoreticians alike, share concepts and cut across disciplinary barriers.7,8,9 2. A Subtle Balance of Intermolecular Iinteractions 2.1. INVENTORY OF INTERMOLULAR INTERACTIONS

The making of such molecular solids involves striking a balance between very many hydrogen and halogen bonding interactions, van der Waals interactions, quadrupole-quadrupole π-π stacking interactions, βHOMO-HOMO (respectively, LUMO-LUMO) energy interactions3 between radical cations (or anions).10 It is important to note that, when it comes to balance the former interactions at kT, none dominates the others; and that those interactions are weak11,12 (Table 1).

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TABLE 1. Compared order of magnitudes of hydrogen and halogen bonds O–H···O and N–H···O: normal hydrogen bonds NH4+···OH2 19 kcal mole–1 – HO–H···Cl 13.5 kcal mole–1 HO–H···OH2 5 kcal mole–1

0.8 eV 0.6 eV 0.2 eV

C–H···X: weaker hydrogen bonds H–C C–H···OH2 H2C=C–H···OH2

2.2 kcal mole–1 1 kcal mole–1

0.1 eV 0.04 eV

Halogen bonds: comparable to normal hydrogen bonds C–Cl···N C CF3–I···NH3

2.4 kcal mole–1 6 kcal mole–1

0.1 eV 0.3 eV

1 kcal mole–1 = 4.33641146 10–2 eV

As it is as strong and even more directional than hydrogen bonding, halogen bonding11,13,14 is currently the focus of an intense scrutiny by crystal engineers and deserves a special attention. Halogen bonding involves halogen atoms covalently attached to a carbon atom and finds its origin in the anisotropy of the electron density surrounding the halogen nucleus; a smaller effective atomic radius makes for a polar axis in the C– Hal direction, as illustrated in 3. Extensive surveys of the crystal structure databases demonstrate13 that either one of two ways are adopted to satisfy the demand of directional electrostatic interaction towards any Lewis base (4).

3

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4 For example, deciphering the crystal structure 15 of E–TTF–I2 reveals,11 5, that the whole solid is built in such a way as to satisfy two typical type II halogen bonds:

5 Likewise, note in 6 that two type II, C–Br···Br–C halogen bonds are identified and direct the formation of slabs in the structure of Br– thiophene(ethylenedioxothiophene)thiophene–Br (Br2–TET):16

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6 The fine crystal engineering ability of halogen bonds is illustrated further in the construction of [PPh4]2{[E-TTF–I2][Re6Se8(CN)6]},17 where a textbook example of a type I, C–I···N C–Re halogen bond (I···N, 2.79 Å; ∠C–I···N, 177°; ∠I···N C, 172°) directed towards the cyanide lone pairs serves to express into a 1D polymer an octahedral halogen-bond hexaacceptor nanonode isosteric to C60:

7

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2.2. ACTIVATED INTERMOLECULAR INTERACTIONS

Consider the 6:1 salt shown in 8 and formulated (EDT-TTF– CONHMe)6[Re6Se8(CN)6](CH3CN)2(CH2Cl2)2,18 where two fully oxidized (A•+ and B•+) and one neutral (C0) secondary amides, [(A•+)2(B•+)2(C0)2] [Re6Se8(CN)6]4–, are hydrogen bonded to cyanide ligands of the cluster anion, which act as strong hydrogen bond acceptor, Lewis bases.

8

9

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Both N–H···N and C–H··N hydrogen bond lengths are shorter with A•+ than with C0, an indication that the hydrogen bond donor character of A•+ is stronger than that of C0. Meanwhile, it is remarkable that the C=O’s of A•+ and B•+ are not involved in any hydrogen bond while the oxygen carbonyl of C0 is grasped within the recurrent seven-membered cyclic motif. Thus, as illustrated in 9, upon one-electron oxidation, an activation of the ortho N–H and Csp2–H hydrogen bond donor ability of the conjugated tetrathiafulvalene amide system is coupled to a deactivation of the hydrogen bond acceptor character of the oxygen carbonyl atom, as confirmed by calculations of electrostatic potential surfaces for A•+ and C0 shown in 8. 3. The Many Benefits of Electrocrystallization, an Invaluable Tool to Assemble Molecular Salts In the course of three decades, the electrocrystallization technique has developed has a suitable, invaluable tool to assemble radical cation salts,19 be they metallic, semiconducting (that is, the growing crystals have a finite resistivity) or electrical insulators even (infinite resistivity). The nucleation and crystal growth occur at or near room temperature, from very pure πdonor molecules in neat solvent or mixture of solvents. The latter are chosen such as the solution dissolves the molecular precursor and electrolyte (the source of counter anion) yet allowing the radical cation salt to crystallizes at the Pt electrode (here, 1 mm in diameter; crystals grown in 2006 by Cécile Mézière in our electrocrystallization laboratory):

10 Hence, single crystals of high purity are grown at low constant direct current (of the order of 1 μA) in the course of one to several weeks and delivered for extensive exploration of their phase diagram by transport measurements, high resolution solid state NMR on one single crystal, angular-resolved photolectron spectroscopy, photo-induced charge ordering

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phenomena, and the like. These smart molecular objects are all the more valuable as they become the focus of breathtaking and seemingly unabated creative experimental investigations by solid state physicists, down to low temperatures, high pressures, large magnetic fields. 4. An Hydrogen-Bonded Zwitterionic Metal in 2000 A significant crystal engineering milestone was met in 2000 with β”-(EDTTTF-CONHMe)2[Cl– H2O],20 an hydrogen-bonded zwitterionic solid which exhibit metallic conductivity down to very low temperatures. Today, there are yet only a few molecular metals based on hydrogen-bond appended πdonor molecules. These include Decurtins-Wallis et al.’s radical cation salt21 [EDT-PDT(CH2OH)2TTF]2I3 and Morita-Nakasuzi et al.’s designed mixed-valence charge transfer complex (TTF–Im)2(p-chloranil), both disclosed in 2004,22 and the metallic molecular Kagome system, (EDTTTF-CONH2)64(·+)[Re6Se8(CN)64–],22 reported in 2005. In β”-(EDT-TTF-CONHMe)2[Cl– H2O], the chloride and the water molecule are equally distributed on the same site and captured by the two strong N–H···Cl–/OH2 and C–H···Cl–/OH2 hydrogen bonds:

11 Note that the strength of the intra-zwitterion hydrogen-bond pair of tweezers illustrated in 11 is enhanced for the radical cation and that, conversely, the amide oxygen atoms appear not to be involved as they do

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not accept any hydrogen bond, as discussed earlier. Note also that the distribution of βHOMO–HOMO interactions energies is quite isotropic within the β”-type layer and that the calculated Fermi surface shown in Figure 1 has a pronounced 2D character.

Figure 1. (a) The rather homogenous distribution in the (a,b) plane of the βHOMO-HOMO interaction energies (11) translates into the quasi-2D Fermi surface in (a*,b*), that is sweeping across from M→X to M→Y in the momentum space; (b) The system is metallic down to very low temperatures where no superconducting transition is detected, perhaps because of the structural disorder inherent to the random distribution of equivalent amounts of chloride and water molecules.

Figure 2. In the triclinic P-1 Bechgaard salts, the molecule is symmetric and centers of symmetry in between the molecules along the stack allow for any, however small, amount of dimerization. Here, for (TMTSF)2PF6, separations of 3.63 and 3.66 Å between the molecular planes alternate along the chain.

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5. A Non-Dimerized, Quarter-filled Band Mott Insulator In contrast with the (TMTSF)2X and (TMTTF)2X series shown in Figure 2, there is no center of symmetry between the molecules along the stack in δ[EDT-TTF-CONMe2]2AsF6.24 Here, for the tertiary amide, the π-donor C1 symmetry, associated with the two hydrogen bond donor functions, Csp2– H···O and Csp3–H···O (Figure 3, top left and bottom, respectively), is expressed by a glide plane, that is, a ±c/2 repetition. Thus, the stacks are exactly uniform, i.e., non-dimerized, a salient difference with the Bechgaard and Fabre salts where the dimerization gap (Figure 2) splits the band in two S S S

O

S

S

N

S H

S S S

O

S

S

N

S H

S S S

O

S

S

N

S H

Figure 3. In the structure of δ-[EDT-TTF-CONMe2]2•+AsF6–, space group P21/c at 150 K, glide planes at ¼ and ¾ along b make the stacks uniform. Thus, for this non-dimerized system with two molecules and 1 hole per unit along the chain, the band is ¼-filled with holes. Note the criss-cross intermolecular interactions topology (top left), an expression of Csp2–H···O hydrogen bonds (top right) and the locking of the ethylene conformation along c, a manifestation of Csp3–H···O hydrogen bonds (bottom). The total bandwith is 0.31 eV with t|| = +71 meV and t⊥ = –25 meV; it is very similar to (TMTTF)2Br which, however, has a dimerization gap of 0.027 eV.

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and the upper band is half-filled, given the 2:1 stoichiometry. Thus, the complication inherent to the dimerization in the Bechgaard salts does not exist for δ-[EDT-TTF-CONMe2]2AsF6. Experiments, including transport and spin susceptibility data (Figure 4), demonstrate a strong Mott localization at ambient pressure. The latter vanishes under hydrostatic pressure up to the point where a metallic state appears above 15 kbar. These results are strong evidence that ¼-umklapp processes are efficient to impose the electron localization in such strongly correlated one-dimensional systems as long as the transverse coupling remains weaker than the Mott gap. The presence of a spin density wave and antiferromagnetic ground state, at variance with the spin-Peierls state commonly observed in ½-filled localized one-dimensional systems, suggest that the presence of a center of symmetry and the possibility of a dimerization are compulsory to promote the spin-Peierls ground state.

Figure 4. Transport, spin and static susceptibility data for δ-[EDT-TTF-CONMe2]2AsF6.

6. Hydrogen Bond Coordination Expresses Inorganic Node 3-fold Symmetry 6.1. AMIDE FUNCTIONALITY DISCRIMINATES OCTAHEDRAL FROM TETRAHEDRAL ANION SYMMETRY

6.1.1. Neutral Molecule Confinement Issue The 6:1 stoichiometry observed10 for (EDT-TTF-CONH2)6AsF6 is unusual, implying that the charge would be diluted to an unprecedented, somewhat irrealistic extend within the π-donor lattice. As illustrated in 12 (only onehalf molecules are represented here), a concerted set of redox activated N– H···F and C–H···F hydrogen bonds cooperate into the cyclic synthon {···X– ···Hδ+–N–C–C=C–Hδ+···} which serves to recognize one of the two independent AsF6– sites and acts as a robust motif of association:

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13

71

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Three crystallographically independent donor molecules form monooxidized centrosymmetric hexameric units (BCA•iACB)•+ wrapped around two independent three-fold symmetry sites both occupied by AsF6– anions. Note in 13 that the two AsF6– are selectively encapsulated either by hydrophobic CH2CH2 groups (darker shade of grey) or hydrophilic (lighter shade of grey) CONH2 functions, an illustration of the ambivalent character of fluorides which adjust to both environments:

14 The analysis of intramolecular bond lengths within the TTF cores allows to identify molecules B and C as neutral while A is partially oxidized, hence, the formulation of a pseudo-ternary system, [(A2)•+(B0)2(C0)2]AsF6–, where a large proportion of neutral π-donor molecules (removed in 14, also keeping with the anions on the hydrophilic sites only) are in effect confined within hexagonal channels. Engaging a tetrahedral anion yields very different stoichiometry and structure, as exemplified in (EDT-TTF–CONH2)2ReO4,10 15. Each partially oxidized molecule is hydrogen-bonded via the same, seven-membered cyclic synthon to ReO4– which acts as a stronger acceptor than the oxygen carbonyl atom, which turns out to be fully deactivated here:

15

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The partially oxidized donors form a layered, β-type structure which exhibits metallic conductivity down to 200 K where a weak localization leads to a semiconducting behavior with a small activation energy (0.3 eV). These striking differences of stoichiometries and structures between salts of octahedral and tetrahedral anions of the same radical cation demonstrate the efficiency of concerted hydrogen-bond intermolecular interactions at distinguishing between otherwise isosteric anions which typically affords isostructural salts with Me4TTF or Me4TSF, for example. 6.2. A METAL WITH A KAGOME TOPOLOGY

6.2.1. Express 3-fold Symmetry at the Organic-Inorganic Interface In this system,23 one strong N–H···N C hydrogen bond per radical cation (16) captures, as anticipated, each N C–Re cyanide acceptor to form the three-fold symmetry motif 17, a supramolecular expression of the cluster expanded octahedral coordination site. Hence, the 6:1 formulation, (EDTTTF-CONH2)64(·+)[Re6Se8(CN)64–].22 The self-complementary nano-scale supramolecular complexes click into each other to yield a Kagome topology, 18, where mixed valence dimers are located at each triangle vertices:

16 The analysis of the spin and static susceptibility, supplemented by the deconvolution of the g factor of the single hybrid resonance, demonstrates that a minute fraction of the carriers visit the cluster site in the metallic rhombohedral phase which experiences a structural and electronic transition at 190 K. The static and spin susceptibility data and proton spin-lattice relaxation rate data, 1/T1, below 200 K show that the paramagnetic state

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corresponds to a 1D Heisenberg chain in which the carriers are localized by the existence of strong correlations. They are also in agreement with the fit of the spin susceptibility data which models the magnetism of the low temperature phase in terms of a uniform chain of spins. Hence, the gap of ca. 1000 K derived from EPR and transport data can be ascribed to a Mott localization. 7. Hydrogen Bond Activity at the Organic-Inorganic Interface: From TTF-(p-chloranil) in 1980 to (TTF–Im)2(p-chloranil) in 2004 7.1. TTF–CHLORANIL AND TTF–BROMANIL

One important milestone qualifying the role of hydrogen bonding in the field of electroactive (charge transfer) solids is the early recognition that weak electrostatic C–H···O interactions, their structure-directing ability and their implication in a collective electronic response, play a significant role in TTF-(p-chloranil).25 It was discovered in 1980 in the course of a purposeful X-ray diffraction analysis of the thermal expansion tensor that a structural transition (19) parallels the electronic neutral-to-ionic phase transition which occurs in this material: An analysis of the anisotropy of the thermal contraction tensor above and below the transition demonstrates that the latter takes place at 84 K in synchronicity with the collective activation upon charge transfer of a twodimensional network of hydrogen bonds qualifying the transformation of a set of weak C–H···O interactions into a two-dimensional array (20) of two Csp2–Hδ+···Oδ– hydrogen bonds (thick dark lines) activated upon charge transfer.

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20 Note the striking difference in orientation of the largest principal axis of the thermal contraction tensors above and below the phase transition. Note also that no Cl···Cl halogen bond is identified in the high and low temperature structures of TTF-(p-chloranil). By contrast, a recent26 analysis of the structure of TTF–(p-bromanil) at 100 K reveals the occurrence of a typical type II halogen bond (Br···Br, 3.566 Å; ∠C–Br···Br, 170 ± 10° and 90 ± 10°) shown in 21 whose attractive character has been qualified by Lecomte et al. in the course of a recent experimental electron density determination:26

21 This stabilizing, type II halogen bond is perhaps of primary significance in imposing the quasi-orthogonal orientation of mixed-stacks running along a and b, 22, in shear contrast with TTF-(p-chloranil) where all stacks are parallel as no such stabilizing, type II halogen bond operates.

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7.2. MORITA-NAKASUZI’S TTF–IMIDAZOLE

7.2.1. A Neutral Monocomponent Solid with Stacks There is no ambiguity as to how the primary intermolecular hydrogenbonding interaction would occur in solid TTF–imidazole22 when applying Desiraju’s criteria:27 N–H, the stronger H-bond donor grasps the nitrogen atom of the Lewis base, the stronger H-bond acceptor (23).

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Remarkably, not only does this drive the formation of hydrogen-bonded 1D polymers, but the co-planar topology adopted by the hydrogen-bonded units (23) serves to enhance the resonance-conjugation within each individual component upon stabilization of long range electrostatic interactions. It is of interest to note that a similar, cooperative, extended electrostatic layering principle directs the formation of stacks shown in Figure 5, instead of an herringbone pattern of intermolecular association, in the monocomponent solid of the planar, rigid and polar π-conjugated molecule Me2TTF– (CONHMe)2, space group Cc, which presents extensive non linear optical responses. 28

Figure 5. In order to achieve the harmony of a molecular stack of π-conjugated molecules, one has to use a template in order to overcome the π-π quadrupole-quadrupole interactions29 which favor herringbone patterns of association; here, in Me2TTF–(CONHMe)2, the hydrogen-bonded, closed hydrophilic end of the rigid, polar ortho-diamides achieve upon stacking long range electrostatic interactions in the solid state.

7.2.2. A Mixed-Valence Complex by Design Now, taking into account the expected enhancement upon charge transfer of the Lewis base character of the carbonyl oxygen atoms of p-chloranil, and anticipating (24) its dominant strength over that of the imidazole nitrogen atom:

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S S

S Cl

S N

N

H

O

Cl

Cl

O Cl

24

25 Morita, Nakasuji and co-workers proceeded22 to the deliberate cocrystallization of two equivalents of TTF–Im for one equivalent of pchloranil, a π-acceptor molecule whose electron widthdrawing power is strong enough to oxidize TTF–Im. As anticipated, (TTF–Im)2(p-chloranil) is obtained (25), where a charge transfer of one-half is stabilized by design in the π-donor framework. Note that, in addition to this brilliant crystal engineering accomplishment, further rewarded by the observation of metallic conductivity, the very same principle also installs uniform stacks of fully reduced radical anions which act as uniform Heisenberg chains of spins ½ running parallel to the mixed-valence stacks, an unprecedented situation in this chemistry. Note also that the two significant hydrogen bonds in the system, that is the former N–H···O and the C–H···Cl shown in 26, are all essentially coplanar, which again emphasizes the cooperative, long range net electrostatic interaction energy as contributing significantly to the balance of intermolecular interactions in the solid state:

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26 Interestingly, halogen bonding is not a contributor to the panel of intermolecular interactions in this system. One rather long C–Cl···Cl–C contact is identified which do not fulfill the topological requirements for either one of type I or II halogen bonds. 8. Disorder Issues The issue of disorder, like from the point of view of its manifestations on the collective properties of functional molecular assemblies, pervades the whole of materials sciences; it is an issue of growing concern also in the life sciences, for example from the point of view of the consequences of polymorphism on phase formulation and drug delivery. These issues are all the more complex than little is known on the structural (microscopic) nature of defects, and that, in the physicist’s perception, disorder also encompass the concept of having to live with an extra potential to be reckon with in the balance of the energy map within a phase diagram. The two examples below are meant to illustrate this key issue from a crystal engineering perspective.

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8.1. PERTURBATION AND DISORDER AT THE ORGANIC-INORGANIC INTERFACE TOPOLOGY WITHIN 21 METALLIC PSEUDO-POLYMORPHS

Within the series β”-(BEDT-TTF)4·(host)n·[Re6Q6Cl8], (Q ) = S, Se),30 the transport properties are modulated by the nature of the incarcerated solvent molecules. Hence, for H2O, the system is metallic down to 4.2 K; for tetrahydrofuran and dioxane (28), a metal-insulator transition occurs at 80100 K; and the conductivity is activated for dimethylformamide. Electronic localization and structural disorder go hand-in-hand in these systems and this balance is determined by the nature of the solvent molecule selectively captured and installed on one single site at the OI interface, and expressed via C–H···O hydrogen bonds between the host and BEDT-TTF. The whole of this synergy goes down to how tiny structural modifications induced by changing the solvent molecule induce modifications of the Fermi surface topology in the series. The minute energy balance involved in each structural rearrangement is of the order of magnitude of a weak activation (by about 0.1 eV) of the HOMO of a fraction of the donor molecules within the conducting slab. Hence, subtle intermolecular interaction modifications among complex molecular assemblies translate into a comparatively large

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macroscopic electronic response of the system, here, for example, a metalinsulator transition. 8.2. RACEMIC CRYSTAL IS DISORDERED: CONDUCTIVITY OF CHIRAL ENANTIOPURE CRYSTAL IS HIGHER

An elegant perspective on the correlation between structural disorder and macroscopic, collective electronic response of a molecular object is that offered by engaging both the racemic and complete series of chiral oxazoline-appended ethylenedithiotetrathiafulvalenes31 (29) to yield a series of racemic and enantiopures single crystalline metals, (EDT-TTF- OX)2AsF6. The inherent disorder of the racemic crystal is wiped out in the enantiopure solids, here, [(R)-EDT-TTF-Me-OX]2AsF6, 30. O S

S

S

S

S

S

* N

R

EDT-TTF-OX * (+/-), (R), (S) R = Me, iPr, ...

29

30

31 Remarkably, the room temperature conductivity (31) of both enantiopure crystals is one order of magnitude larger than that observed for the racemic system.

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9. Ternary Systems 9.1. SELF-ASSEMBLED HALOGEN-BONDED INTERFACES

9.1.1. Yamamoto-Kato Seminal Ternary Systems One remarkable crystal engineering initiative in the field of organic metals is offered by the seminal work of Yamamoto, Kato and co-workers whose deliberate introduction of halogen bond multi-donor neutral linkages provides an entry into the phase diagram of ternary constructs while allowing for a modulation of their interface. This is illustrated in 32 with the example of the two-dimensional metal, β”-(BEDT-TTF)3•+[1,4-bis(iodoethynyl)benzene][Cl–]32:

32 Immense opportunities are thus offered for creative manipulation of symmetry, stoichiometry, band filling (electron count). 9.1.2. An Hybrid Ternary System with an Octahedral Halogen-Bond Hexa-Acceptor Nanonode, and Yet a Single Interface Engaging the octahedral, halogen-bond hexa-acceptor nanonode into the construction of ternary hybrid systems, [Radical cation]/[1,4-bis(iodoethynyl)benzene]/[Re6Se8(CN)6] has produced the semi-conducting phase [EDT-TTF]8[1,4-bis(iodoethynyl)benzene]/[Re6Se8(CN)6] with a 1D selfassembled halogen-bonded polymeric interface shown in 33.33 The topology of the hybrid interface, templated by the conducting radical cation slab, bears a striking resemblance with that described earlier (7) for [PPh4]2{[ETTF–I2][Re6Se8(CN)6]}.17

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33 Note that, in the context of framework solids, the use here of neutral linkages instead of E-TTF–I2•+ radical cations was expected to minimize charge densification and favor the stabilization of n:2:1 or n:3:1 phases, with 2 or 3D frameworks, respectively. 10. Outlook The series of selected case studies presented herein primarily offers a geometrical way to regard complex molecular constructs, which in turn often strongly influence the way the solid is described electronically.34 A complementary, entangled approach is that of the orbital structure, indeed tapped upon here, however briefly, along the way; it is the combination of both which allow to reveal which are those hidden structural details relevant to the electronic property, and physics, of any such complex system.3,10,23,29 11. Acknowledgements This work is supported by the program ANR CHIRASYM 2005-08 NT05– 2 42710. The contributions of the Ministry of Education and Research, the CNRS, the University of Angers, the Région Pays de la Loire to this research and to PhD and post-doctoral grants are gratefully acknowledged, as are the contributions and dedication of all students, post-docs and collaborators. I am grateful for the insights and contributions to this work of Enric Canadell, and our physicist partners at Orsay, Pascale Auban-Senzier, Claude Pasquier and Denis Jérome and Jean-Paul Pouget.

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References 1. 2. 3. 4. 5. 6. 7.

8. 9. 10. 11. 12. 13.

14. 15. 16. 17. 18. 19.

20. 21. 22. 23.

24. 25. 26. 27.

M. Bendikov, F. Wudl, D. F. Perepichka, Chem. Rev., 104, 4891–4846 (2004) R. Hoffmann, Angew. Chem. Int. Ed. 26, 846 (987) R. Rousseau, M. Gener, E. Canadell, Adv. Funct. Mater. 14, 201 (2004) T. Giamarchi, Chem. Rev. 104, 5037–5056 (2004); H. Seo, C. Hotta, H. Fukuyama, Chem. Rev. 104, 5005–5036 (2004) A. Davidson, K. Boubekeur, A. Pénicaud, P. Auban-Senzier, P. Batail, G. Hervé, Chem. Commun. 1373–1374 (1989) C. Bourbonnais, D. Jérome, Science 281(5380), 1155–1156 (1998); D. Jérome, Chem. Rev. 104, 5565–5592 (2004) P. Batail, E. Canadell, N. Dupuis, M. Fourmigué, D. Jérome, J.-P. Pouget, Eds., Proceedings ISCOM 2003 (2004) J. Phys. IV France 114, 3–678; S. Brazovskii, P. Monceau, N. Kirova, Eds., Proceedings ECRYST 2005 (2005) J. Phys. IV France 131, 3–366 P. Batail, Chem. Rev. 104, 4887–4890 (2004) See Special Issue on Molecular Conductors Chem. Rev. 104, 4887–5781 (2004) K. Heuzé, M. Fourmigué, P. Batail, E. Canadell, P. Auban-Senzier, Chem. Eur. J., 5, 2971–2976 (1999) M. Fourmigué, P. Batail, Chem. Rev. 104, 5379–5418 (2004) J. J. Novoa, M. C. Rovira, C. Rovira, J. Veciana, J. Tarrès, Adv. Mater. 7, 233 (1995) P. Metrangelo, H. Neukirch, T. Pilati, G. Resnati, Acc. Chem. Res. 38, 386–395 (2005); P. Metrangelo, G. Resnati, T. Pilati, R. Liantonio, F. Meyer, J. Polym. Sc. Part A: Polym. Chem. 45, 1–15 (2007) G. R. Desiraju, R. Parthasarathy, J. Am. Chem. Soc. 111, 8725 (1989) C. Wang, A. Ellern, V. Khodorkovsky, J. Bernstein, J. V. Becker, Chem. Commun. 983 (1994) P. Batail, F. Frère, et al. to be published A. Ranganathan, A. El-Ghayoury, C. Mézière, R. Harté, R. Clérac, P. Batail, P. Chem. Commun. 2878–2802 (2006) S. A. Baudron, P. Batail, C. Rovira, E. Canadell, R. Clérac, Chem. Commun. 1820– 1821 (2003) P. Batail, K. Boubekeur, M. Fourmigué, J.-C. Gabriel, Chem. Mater. 10, 3005–3015 (1998); A. Deluzet, S. Perruchas, H. Bengel, P. Batail, J. Molas, J. Fraxedas, Adv. Funt. Mater. 12, 123–128 (2002) K. Heuzé, C. Mézière, M. Fourmigué, P. Batail, C. Coulon, E. Canadell, P. AubanSenzier, D. Jérome, Chem. Mater. 12, 1898–1904 (2000) S.-X. Liu, A. Neels, H. Stoeckli-Evans, M. Pilkington, J. Wallis, S. Decurtins, Polyhedron 23, 1185–1189 (2004) T. Murata, Y. Morita, K. Fukui, G. Sato, D. Shiomi, T. Takui, M. Maesato, H. Yamochi, G. Saito, K. Nakasuji, Angew. Chem. Int. Ed., 43, 6343–6346 (2004) S. A. Baudron, P. Batail, C. Coulon, R. Clérac, E. Canadell, V. Laukhin, R. Melzi, P. Wzietek, D. Jérome, P. Auban-Senzier, S. Ravy, J. Am. Chem. Soc. 127, 11785–11797 (2005) K. Heuzé, M. Fourmigué, P. Batail, C. Coulon, R. Clérac, E. Canadell, P. AubanSenzier, D. Jérome, Adv. Mater. 15, 1251–1254 (2003) P. Batail, S. J. La Placa, J. J. Mayerle, J. B. Torrance, J. Am. Chem. Soc. 103, 951–953 (1981) P. Garcia, S. Dahaoui, C. Katan, M. Souhassou, C. Lecomte, Faraday Discuss. 135, 217–235 (2007) G. R. Desiraju, Crystal Engineering: The Design of Organic Solids (Elsevier, Amsterdam, 1989)

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28. C. Mézière, L. Zorina, P. Batail, C. Colin, C. Pasquier, Z. Essaïdi, I. Rau, B. Sahraouï, to be published 29. C. A. Hunter, J. K. M. Sanders, J. Am. Chem. Soc. 112, 5525 (1990) 30. A. Deluzet, R. Rousseau, C. Guilbaud, I. Granger, K. Boubekeur, P. Batail, E. Canadell, P. Auban-Senzier, D. Jérome, Chem. Eur. J. 8, 3884–3900 (2002) 31. Réthoré, C., Avarvari, N., Canadell, E., Auban-Senzier, P., Fourmigué, M. (2005) J. Am. Chem. Soc. 127, 5748 32. H. M. Yamamoto, J.-I. Yamaura, R. Kato, J. Am. Chem. Soc. 120, 5905 (1998); H. M. Yamamoto, R. Kato, Chem. Lett. 970–971 (2000) 33. A.-L. Barrès, A. El-Gharoury, E. Canadell, P. Auban-Senzier, E. Batail, to be published 34. J. K. Burdett, Chemical Bonding in Solids (Oxford University Press, Oxford, 1995)

CRYSTAL POLYMORPHISM

JOEL BERNSTEIN Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, Israel 84105

Abstract. The importance of understanding and considering the role of the existence of different crystal forms in the design and preparation of new materials is discussed.

Keywords: polymorphism; solvates; hydrates; concomitant polymorphism; conformational polymorphism; disappearing polymorphs; thermodynamic form; kinetic form; stability; growth conditions; structure-property relationships

1. Introduction The concept of engineering implies that a considerable measure of control has been achieved and maintained over some process or procedure. When that process is the engineering of crystalline materials properties, as in the title of this School, then the implication is that specific desired properties can be designed and built into materials, just as specific properties can be designed and built into a bridge or an electronic circuit. In the end, of course, the properties of the two latter examples depend intimately on the structure of the materials. Variations in structure can and do lead to variation in properties. Therefore, in the engineering of crystalline materials the desired properties must be designed into the material and in order to achieve those design goals control must be obtained over the structure. The existence of different crystal forms (polymorphs and solvates) of the same molecule or of aggregates of the same molecule with other molecules (co-crystals) can be an anathema to this engineering effort. Changes in structure are likely to be accompanied by undersigned and undesired changes in properties. On the other hand, changes in structure can also lead to improved properties, so that the search for, and preparation of a variety of crystal forms can be a crucial aspect of the whole engineering process. In 87 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 87–109. © 2008 Springer.

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fact the search for and characterization of crystal forms is one of the most active and challenging research areas of modern solid state chemistry. The effort is by no means theoretical or academic. In the pharmaceutical field, the existence of multiple crystal forms is relevant for the choice of the solid dosage form of an active pharmaceutical ingredient (API) most suitable for drug development and marketing and has important implications both in terms of the drug’s ultimate efficacy and in terms of the protection of the intellectual property rights associated with the pharmaceutical product. Similarly, the properties of pigments, explosives, electrically conducting organic materials, organic magnetic materials, etc. are all intimately related to their solid state structure, so that the understanding and control over that structure is one of the key aspects of engineering those materials for their desired properties. This chapter deals with some of the fundamental aspects of the variation of structure and properties of various crystal forms. Strictly speaking, the term “polymorphism” refers to but one aspect of this variation, but in the lingua franca among practitioners the term “polymorphism” is often used and meant to include all crystal forms of a material [e.g. Ref. 1]. 2. What is Polymorphism and the Multiplicity of Crystal Forms? Materials are traditionally classified in three states of matter: gases, liquids and solids and distinguished by their properties. In addition to different crystal structures, called polymorphs, which are characterized by long range order, a material may appear as an amorphous solid, characterized by the lack of long range order. The polymorphism of calcium carbonate (calcite, vaterite and aragonite) was identified more than 200 years ago by Klaproth in 1788,2 but formal recognition of the phenomenon is generally credited to Mitscherlich.3 Diamond, graphite, fullerenes and nanotubes are polymorphic forms (denoted as allotropes for elements) of carbon all exhibiting very different properties. Cocoa butter can crystallize in at least five different ways, the various crystal structures affecting the perception of the epicurean quality of the prepared chocolate, although all forms are chemically identical.4 In this chapter we discuss the different crystal forms of molecular crystals, in which a particular molecule crystallizes in different ways (polymorphs) and/or with a solvent molecules (solvates). When the solvent is water then they are referred to as hydrates. As we will attempt to show, although the subject has been widely investigated, mainly in the field of solid state organic chemistry, the polymorphism of molecular crystals is still a fascinating phenomenon, and it still represents a substantial scientific challenge to the very idea of rational design and construction of crystalline solids with

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predefined architectures and physical properties starting from the choice of the molecular components, which is the paradigm of molecular crystal engineering.5 Although some classic works still provide an excellent entry to the fundamental aspects of crystal forms,6–8 the last dozen years have witnessed an almost exponential increase in the interest in crystal forms and the number of publications and conferences devoted to the subject.1,5,9–16

Figure 1. Schematic representation of the structural relationship between “true” polymorphs, solvates, polymorphs of solvates and the amorphous phase.

3. Importance of Polymorphism – Concomitant and Disappearing Chemists who encounter polymorphism for the first time are often unaware of its existence and baffled by its manifestations. Experimental problems might include, for example, variable or diffuse melting point, crystal batches with inconsistent physical properties (electrical or thermal conductivity, filtering, drying, flow, tabletting, dissolution), two (or more) different colored or different shaped crystals in the same batch of (chemically) “pure” material, etc. (for example, see Brittain11). These problems result because the conditions of that particular crystallization have led to the production of a number of polymorphs, which are present in the crystallizing medium or vessel at the time of harvesting or collection of the crystals. The fact that polymorphs of a substance can appear concomitantly (accompanying each other or happening together) has long been recognized but has only recently been reviewed.17 Is the phenomenon of concomitant polymorphs a curse or a blessing? Both. It is a curse for the chemist seeking a pure substance and a robust procedure to repeatedly and consistently produce that pure material, and the

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existence of concomitant polymorphs corrupts that procedure. It is a blessing, however, because (the recognition of) the existence of polymorphs in general, and concomitant polymorphs in particular can provide the information and the opportunity to gain control over the crystallization process, and to achieve the desired specificity and robustness. On the other end of the spectrum of crystallization phenomena of polymorphs is that of disappearing polymorphs.18 There are many documented tales of difficulties in obtaining crystals of a particular known form or in reproducing results from another laboratory, or even ones own. There are cases where it was difficult to obtain a given polymorphic form even though this had previously been obtained routinely over long time periods. This phenomenon also suggests a loss of control over the crystallization process, so widely used by chemists for the purification of materials. The reasons for the sudden appearance of a new crystal modification are not always clear, even after the fact, but its presence may make the production of the previously obtained form particularly difficult, or apparently impossible. However, once a particular polymorph has been obtained it should always be possible to obtain it again; it is only a matter of finding the right experimental conditions. Both concomitant and disappearing polymorphs depend on the experimental conditions governing the crystallization process. Two of the fundamental ones (but certainly not the only ones) are the thermodynamics and kinetics of crystallization. An understanding of the competing thermodynamic and kinetic factors governing the crystallization of polymorphs in general, or of a particular substance in particular helps to facilitate the control over the production of the desired polymorph, at the exclusion of undesired ones. Such control has important implications in a variety of industrial applications, of which pharmaceutical production and formulation is but one important example. This next section deals with the essentials of the thermodynamics involved; more detailed accounts may be found elsewhere. 19–24 The following section deals with kinetic factors. 4. Thermodynamic and Kinetic Stability Amongst Polymorphs Thermodynamics tells us that crystallization must result in an overall decrease in the free energy of the system. This means that in general the crystal structures that appear will be those having the greater (negative) lattice (free) energies. In polymorphic systems there are evidently a number of possible structures that have similar lattice energies. This drive towards free energy minimization will be balanced, as in all chemical changes, by the kinetic tendency of the system to crystallize as quickly as possible so as to relieve the imposed supersaturation. From the

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molecular point of view the process of crystallization is one of a supramolecular assembly in which the building blocks of the crystal assemble through the utilization of molecular recognition forces involving an array of intermolecular interactions as well as stereochemical packing constraints. If some structures are able to form more quickly than others then the system may in the short term settle for less than the maximum energy decrease, providing such a situation can be achieved at speed. A secondary transformation to a lower energy state can subsequently take place. The distinction between thermodynamic and kinetic influences is often demonstrated using the example of the graphite and diamond forms of carbon. The former is the thermodynamically preferred crystalline form, but kinetic factors (in particular, a high activation barrier) make the rate of transformation from diamond to graphite infinitely slow.25 4.1. ENERGY VERSUS TEMPERATURE DIAGRAM

The energy versus temperature diagram was introduced into crystallography by Buerger26 without application to any specific example. The theoretical derivation and practical application of this diagram have been described and discussed by Burger and Ramberger22,23 and by Grunenberg et al.24 For simplicity we will limit the discussion to two polymorphic solids, although the extension to a larger number is based on the same principles. The relative stability of two polymorphs depends on their free energies, the more stable one having a lower free energy. The Gibbs free energy of a substance is expressed as G = H – TS

(1)

G and H are clearly functions of temperature and this variation may be plotted for one possible relationship between the two polymorphs and the melt (liquid) in Figure 2. Such diagrams contain a great deal of information in a compact form, and provide a visual and readily interpretable summary of the often complex relationships among polymorphs. At absolute zero TS vanishes so that the enthalpy is equal to the Gibbs free energy. As a consequence, at absolute zero the most stable polymorphic modification should have the lowest Gibbs free energy. Above absolute zero the entropy term will play a role which may differ for the two polymorphs so that the free energy as a function of the temperature follows a different trajectory for the two polymorphs, as represented by the GI and GII curves in Figure 2. The two G curves cross at the thermodynamic transition point Tp,I/II, but since the enthalpy of I is lower than that of II a quantity of

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energy ΔHt,I/II is required to be input for the phase transition.. The endothermic solid to liquid transitions at the melting points may be understood in the same way, with ΔHf,I and ΔHf,II denoting the respective enthalpies of fusion. Figure 2 represents an enantiotropic situation, since Tp,I/II lies at a temperature below the melting points for the two polymorphs. The monotropic situation is represented in Figure 3. In this case, there is no transition point below the melting points of the two polymorphs. The

Figure 2. Energy versus temperature (E/T) diagram of a dimorphic system. G is the Gibbs free energy and H is the enthalpy. This diagram represents the situation for an enantiotropic system, in which form I is the stable form below the transition point, and presumably at room temperature.

Figure 3. Energy versus temperature (E/T) diagram for a monotropic dimorphic system. The symbols have the same meaning as in Figure 1. Form I is more stable at all temperatures.

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phenomenological manifestation of enantiotropism is that there can be a reversible transition from one phase to another without going through the gas or liquid phase. If the thermodynamic relationship is one of monotropism the two modifications are not interconvertible. In the context of simultaneously crystallizing polymorphs the thermodynamics is clear. First, only at thermodynamic transition points can two forms have the same stability and hence coexist as mixtures at equilibrium. At any other temperature there will be a thermodynamic tendency to transform to the more stable structure. This implies that except at the thermodynamic transition point mixtures of polymorphs will have limited lifetimes, with transformation kinetics playing a role in those lifetimes. 4.2. VAPOR PRESSURE VERSUS TEMPERATURE DIAGRAM

Another common representation of phase relationships is the pressure versus temperature diagram. Figure 4 shows the prototypical plots of pressure versus temperature for the enantiotropic and monotropic cases. These are best understood by traversing along various curves, which represent equilibrium situations between two phases. The l./v. line in the high temperature region of Figure 4a is the boiling point curve for the (common) melt of the two polymorphs. Moving to lower temperatures along that line one encounters the II/v. line, which is the sublimation curve for form II. The intersection is the melting point for form II. Under

Figure 4. Pressure versus temperature (P/T) plots. I/v. and II/v. represent sublimation curves; l./v. is the boiling point curve. Broken lines represent regions which are thermodynamically unstable or inaccessible. (a) Enantiotropic system; (b) monotropic system. The labeling corresponds to Figures 1 and 2 to indicate that form I is stable at room temperature, which is below the transition point in the enantiotropic case.

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thermodynamic conditions form II would crystallize out at this point and the solid part of the II/v. line would govern the behavior. However, if kinetic conditions prevail (for example, if the temperature is lowered rapidly) the system may proceed along the broken l./v. line to the intersection with the I/v. line, at which point form I would crystallize. Continuing downward along the solid part of the II/v. curve, the crossing point with the I/v. sublimation curve is the transition point between the two polymorphic phases. Once again, if thermodynamic conditions prevail form II will be transformed to form I. Under kinetic conditions form II may continue to exist (even indefinitely in some cases) along the II/v. sublimation curve. Figure 4a represents the enantiotropic case because the transition point between the two phases is found at a temperature below the melting point of form II, while Figure 4b represents the monotropic situation, in which the transition point is above the melting points of both forms. 4.3. SOME PRACTICAL ASPECTS OF RELATIVE STABILITIES OF POLYMORPHS

A knowledge of the enantiotropic or monotropic nature of the relationship between polymorphs can be used to steer crystallization processes to obtain a desired polymorph at the exclusion of an undesired one. For a dimorphic system there are four possibilities: 1. the thermodynamically stable form in a monotropic system: no transformation can take place to another form, and no precautions need be taken to preserve that form or to prevent a transformation. 2. the thermodynamically stable form in an enantiotropic system: precautions must be taken to maintain the thermodynamic conditions (temperature, pressure, relative humidity, etc.) at which the G curve for the desired polymorph is below that for the undesired one. 3. the thermodynamically metastable form in a monotropic system: a kinetically controlled transformation may take place to the undesired thermodynamically stable form. To prevent such a transformation it may be necessary to employ drastic conditions to reduce kinetic effects (e.g. very low temperatures, very dry conditions, storage in the dark, etc.). 4. the thermodynamically metastable form in an enantiotropic system: the information for obtaining and maintaining this form is essentially found in the energy-temperature diagram. Therefore, it is of practical importance (e.g. preformulation studies of a drug substance24,25) to determine whether a system of polymorphs is monotropic or enantiotropic to enable the choice of and control over the desired polymorphic form. The combination of experience with polymorphic systems

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and the accumulation of sufficient thermodynamic and structural data have permitted the development of some useful “rules” for determining the relative positions of the G and H isobars, as well as the enantiotropic or monotropic nature of the relationship between polymorphs.22–24 4.4. KINETIC CONSIDERATIONS

4.4.1. Solubility and Dissolution Rates In addition to differences in melting points, heats of fusion, entropies of fusion, densities, heat capacities and virtually every chemical and physical property, different modifications can also exhibit different solubilities and dissolution rates. Since the solubility is directly proportional to the free energy of a modification, determination of solubility curves is the most reliable method of assessing the relative free energies of polymorphs. The difference in solubility of two polymorphs is a direct measure of the ΔG between them. It is important to note that although the absolute solubility (and hence the dissolution rate) of a polymorph will be solvent dependent, the relative solubility of different forms will not depend on the solvent used.27 The situations in which polymorphs concomitantly crystallize are determined by the experimental conditions in relation to both the free energy – temperature relationships and the relative kinetic factors. These situations may arise either because specific thermodynamic conditions prevail or because the kinetic processes have equivalent rates. In thermodynamic terms we have seen that polymorphs can only exist in true equilibrium at the thermodynamic transition temperature (where the G curves cross). The chance of carrying out a crystallization precisely at such a temperature must be small, with the inevitable conclusion that kinetics play at least some role in the overall process. The final consequence of this of course is that a system of concomitantly crystallizing polymorphs will be subject to change in the direction favoring the formation of the most stable structure. If the crystals have grown from and remain in contact with solution then the most likely route for this transformation is via solution by dissolution and recrystallization.21,28 If the crystals have formed from the melt or vapor phase or have been isolated from their mother phase, the solid state transformation is possible.29 4.4.2. Kinetic Factors The starting point for a discussion of the kinetic factors is the traditional energy – reaction coordinate diagram, Figure 5. This shows G0, the free energy per mole of a solute in a supersaturated fluid which transforms by crystallization into one of two crystalline products, I or II, in which I is the

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more stable (GII > GI). Associated with each reaction pathway is a transition state and an activation free energy which is implicated in the relative rates of formation of the two structures. Unlike a chemical reaction, crystallization is complicated by the nature of the activated state since it is not a simple bi- or trimolecular complex as would be expected for a process in which a covalent bond is formed; rather it relates to a collection of self assembled molecules having not only a precise packing arrangement but also existing as a new separate solid phase. It is the existence of the phase boundary that complicates matters since this is associated with an increase in free energy of the system that must be offset by the overall loss of free energy. For this reason the magnitudes of the activation barriers are dependent on the size (i.e. the surface to volume ratio of the new phase) of the supramolecular assembly (crystal nucleus). This was recognized in 1939 by Volmer in his development of the kinetic theory of nucleation from homogeneous solutions and remains our best guide today.30

Figure 5. Schematic diagram of the reaction coordinate for crystallization in a dimorphic system, showing the activation barriers for the formation of polymorphs I and II.

One of the key outcomes of this theory is the concept of critical size that an assembly of molecules must have in order to be stabilized by further growth. The higher the operating level of supersaturation the smaller this size is (typically a few tens of molecules). In Figure 5 the supersaturation with respect to I is simply G0-GI and is higher than G0-GII for structure II. However it can now be seen that if for a particular solution composition the critical size is lower for II than for I then the activation free energy for

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nucleation is lower and kinetics will favor form II. Ultimately form II will have to transform to form I, a process that we discuss later. Overall we can say that the probability that a particular form I will appear is given by P(i) = f(ΔG, R)

(2)

in which ΔG is the free energy for forming the n-th polymorph and R is the rate of some kinetic process associated with the formation of a crystal by molecular aggregation. Thus, for example, if we follow the above reasoning we could equate the rate process with J, the rate of nucleation of the form. If all polymorphs had the same rates of nucleation then their appearance probability would be dominated by the relative free energies of the possible crystal structures. The rates of nucleation as expressed by the classical expression of Volmer are related to various thermodynamic and physical properties of the system such as bulk and surface free energy (γ), temperature (T), degree of supersaturation (σ), solubility (hidden in the pre-exponential factor An) which will not be the same for each structure but will correctly reflect the balance between changes in bulk and surface free energies during nucleation. This is seen in equation 3 which relates the rate of nucleation to the above parameters (ν is the molecular volume): J = Anexp(–16πγ3ν2/3κ3T3σ2)

(3)

From this analysis it is clear that the tradeoff between kinetics and thermodynamics is not at all obvious. Consider a monotropic, dimorphic system (for simplicity) whose solubility diagram is shown schematically in Figure 5. It is quite clear that for the occurrence given by solution compositions and temperatures that lie between the form I and II solubility curves only polymorph II can crystallize. However, the outcome of an isothermal

Figure 6. chematic solubility diagram for a dimorphic system (polymorphs I and II) showing a hypothetical crystallization pathway (vertical arrow) at constant temperature.

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crystallization that follows the crystallization pathway indicated by the vector in Figure 6 s not so obvious since the initial solution is now supersaturated with respect to both polymorphic structures, with thermodynamics favoring form II and kinetics favoring form I. Experimentally, the reality of this overall scenario of kinetic versus thermodynamic control was known long before the development of nucleation theory and is encompassed by Ostwald in his Rule of Stages of 1897.31–33 The German scientific literature between 1870 and 1914 contains many organic and inorganic examples in which crystallization from melts and solutions yields an initial metastable form which is ultimately replaced by a stable structure and Ostwald was led to conclude that ‘when leaving a metastable state, a given chemical system does not seek out the most stable state, rather the nearest metastable one that can be reached without loss of free energy’. Of course this conclusion is significantly flawed: when a crystallization experiment yields only a single form there is no way of knowing whether it contradicts the rule or whether the material is simply not polymorphic. There is no way of answering this question. However, a sufficient number of cases of successively crystallizing polymorphic forms have been observed (see for instance Ciechanowicz et al.34) to warrant considering the principles behind Ostwald’s Rule as guidelines for understanding the phenomenon. By making use of Volmer’s equations some attempts have been made by Becker and Doering,35 Stranski and Totomanov,36 and Davey32 to explain the rule in kinetic terms. In it becomes apparent that the situation is by no means as clear cut as might be inferred from Ostwald’s Rule. Figure 7 shows the three possible simultaneous solutions of the nucleation equations that indicate that by careful control of the occurrence domain there may be conditions in which the nucleation rates of the two forms are equal and hence their appearance probabilities are nearly equal. Under such conditions we might expect the polymorphs to crystallize concomitantly. 4.5. EXAMPLES OF CONCOMITANT AND DISAPPEARING POLYMORPHS

Many additional aspects and examples of concomitant polymorphs have been reviewed.17 Those for disappearing polymorphs appeared in a slightly older review.18 As noted above, one of the challenges of disappearing polymorphs is to be able to prepare modifications that apparently vanished with the appearance of new forms. Some successful attempts have been surveyed37 and a detailed study has been reported.38 One recent example of a disappearing polymorph that had particularly important consequences in the pharmaceutical industry was that of ritonavir, a component of cocktail administered for treatment of AIDS.39

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Figure 7. The rates of nucleation as functions of supersaturation for the dimorphic system defined in Figure 6. The three diagrams a, b and c represent the three possible solutions for the simultaneous nucleation of two polymorphs each of which follows a rate equation of the form of equation 3. Note that solutions a and c both allow for simultaneous nucleation of the forms at supersaturations corresponding to the crossover of the curves.

5. Conformational Polymorphism The differences in energy between polymorphs (1–2 kcal/mol) are generally of the same order of magnitude as the energetics of rotations about single bonds. This similarity in energy allows for conformationally flexible molecules to adopt different conformations in different polymorphs, a phenomenon known as conformational polymorphism.40,41 For cases of conformational polymorphism one can ask the following questions: 1. What are the structural differences among the polymorphs? 2. What are the differences in energy, if any, in the molecular conformations observed in the various crystal forms? 3. How does the energetic environment of the molecule vary from one crystal form to another? To answer these questions, a typical study might proceed according to the following scenario: Determination of the existence of polymorphism in the system under study. Determination of the existence of conformational polymorphism by the appropriate physical measurements. Determination of the crystal structures to obtain the geometrical information – molecular geometries and packing motif – of the various polymorphs. Determination of the differences in molecular energetics, by appropriate computational techniques. Determinaton of differences in lattice energy and the energetic environment of the molecule by appropriate computational methods.

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Examples of conformational polymorphism, along with the application of this strategy have been given.40 The computational aspects of such investigations combine both molecular energetics and lattice energetics within rather limited energy ranges, and therefore provide quite demanding benchmarks for both the algorithms and the force fields used in such calculations. A minimum requirement would be the correct ordering of the relative stability of the polymorphs, without any regard for the differences in energy or the absolute value of the lattice energies (compared, say, to the sublimation energy). Increasingly stricter demands would require the differences in computed lattice energies to match those measured by thermal (e.g. differential scanning calorimetry) methods or for the absolute energies to match experimentally determined sublimation energies. 6. Phase Transformations and Conversions From thermodynamic principles, under specified conditions only one polymorph is the stable form (except at a transition point).42 In practice, however, due to kinetic considerations, metastable forms can exist or coexist in the presence of more stable forms. Such is the case for diamond, which is metastable with regard to graphite, the thermodynamically stable form of carbon under ambient conditions. In practice, the relative stability of the various crystal forms and the possibility of interconversion between crystal forms, between crystals with different degree of solvation and between an amorphous phase and a crystalline phase, can have very serious consequences on the life and effectiveness of a polymorphic product and the persistence over time of the desired properties (therapeutic effectiveness in the case of a drug, chromatic properties in the case of pigment, etc). Conversions between different crystal forms are possible and often take place. Among the many possibilities for conversion, depending on variables such as temperature, pressure, relative humidity, etc. specific examples are: a metastable form can convert to a thermodynamically more stable crystal form with very slow kinetics; an unsolvated crystal form can form solvates and co-crystals with other “innocent” molecules which will nonetheless alter significantly the physical properties with respect to the “homomolecular” crystals; an anhydrous crystalline form can be transformed into a crystal hydrate via vapor uptake from the atmosphere; a solvate can, in turn, be transformed into another crystal form with a different degree of solvation up to the anhydrous crystal via stepwise solvent/water loss;

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a (metastable) amorphous phase may transform into a stable crystalline phase over time. The variety of phenomena related to polymorphism (hydration, solvation, amorphicity and interconversions) demonstrates the importance of acquiring a thorough mapping of the “crystal space” of a substance that is ultimately intended for some specific application. 7. Why are Polymorphism and Multiple Crystal Forms Important? The example of the polymorphs (allotropes) of carbon point on the key messages of this chapter: different crystal forms of a substance can possess very different properties and behave as different materials. This concept has important implications in all fields of chemistry associated with the production and commercialization of molecules in the form of crystalline materials (drugs, pigments, agrochemicals and food additives, explosives, etc). The producer, in fact, needs to know not only the exact nature of the material in the production and marketing process, but also its stability with time, the variability of its chemical and physical properties as a function of the crystal form, etc. In some areas, e.g. the pharmaceutical industry, the search for and characterization of crystal forms of the API has become a crucial step for the choice of the best form for formulation, production, stability and for intellectual property protection. Table 1 summarizes some major possible differences in chemical and physical properties between crystal forms and solvates of the same substance. Different crystal forms are often recognized by differences in the color and TABLE 1. Examples of chemical and physical properties that can differ among crystal forms and solvates of the same substance PHYSICAL AND THERMODYNAMIC PROPERTIES

SPECTROSCOPIC PROPERTIES KINETIC PROPERTIES SURFACE PROPERTIES MECHANICAL PROPERTIES CHEMICAL PROPERTIES

density and refractive index, thermal and electrical conductivity, hygroscopicity, melting points, free energy and chemical potential, heat capacity, vapor pressure, solubility, thermal stability electronic, vibrational and rotational properties, nuclear magnetic resonance spectral features rate of dissolution, kinetics of solid state reactions, stability surface free energy, crystal habit, surface area, particle size distribution hardness, compression, thermal expansion chemical and photochemical reactivity

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shape of crystals. A striking example of these two properties is provided by the differences in color and form of the crystal forms of ROY (ROY = red, orange, yellow polymorphs of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophene carbonitrile)43 (color figure in original reference). 8. How do we Detect and Characterize Multiple Crystal Forms? In spite of the efforts of a great number of research groups worldwide, and of a familiarity with the experimental factors that can lead to multiple crystal forms, our ability to predict or control the occurrence of polymorphism is still embryonic. In many cases the crystallization of a new crystal form or of an amorphous phase of a given substance turns out to be the result of serendipity44 rather than a process under complete human control. The exploration of the “crystal form space” (polymorph screening) of a substance is the search of the polymorphs and solvates with a twofold purpose: 1) identification of the relative thermodynamic stability of the various forms including the existence of enantiotropic crystalline forms (that interconvert as a function of the temperature) or of monotropic forms (that do not interconvert) and of amorphous and solvate forms and 2) physical characterization of the crystal forms with as many analytical techniques as possible. The relationships between the various phases and commonly used industrial and research laboratory processes are schematically illustrated in Figure 8.

Figure 8. Some general relationships between polymorphs, solvates and amorphous phases and the type of research lab or industrial or process for preparation and interconversion. 1, Crystallization; 2, Desolvation; 3, Exposure to solvent/vapor uptake; 4, Freeze drying; 5, Heating; 6, Melting; 7, Precipitation; 8, Quench cooling; 9, Milling; 10, Spray drying; 11, Kneading; 12, Wet granulation. Analogous relationships apply to polymorphic modifications of solvate forms. Note that the figure represents general trends rather than every possible transformation; the presence or absence of an arrow or number does not represent the exclusive existence or absence of a transformation.

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Polymorph assessment, on the other hand, is part of the system of quality control. It is necessary to make sure that the scale-up from laboratory preparation to industrial production does not introduce variations in crystal form. Polymorph assessment also guarantees that the product conforms to the guidelines of the appropriate regulatory agencies and does not infringe the intellectual property protection that may cover other crystal forms. The polymorph pre-screening, screening and assessment are best achieved by the combined use of several solid-state techniques, among them (not exclusively or in any preferential order): microscopy and hot stage microscopy (HSM), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), infrared and Raman spectroscopy (IR and Raman), single crystal/powder X-ray diffraction (SCXD, PXD), solid state nuclear magnetic resonance spectroscopy (SSNMR).45 It is also important to mention in the context of this discussion the advantages offered by the possibility of determining the molecular and crystal structure of a crystal form by means of single crystal X-ray diffraction. This technique, although generally much more demanding than powder diffraction in terms of experiment duration and data processing, has the great advantage of providing detailed structural information on the molecular geometry, but more important for this discussion, it provides information on the packing of the molecules in the crystal and the nature and structural role of solvent molecules. Moreover, the knowledge of the single-crystal structure allows calculating the X-ray powder diffraction pattern that can be compared with the one measured on the polycrystalline sample as demonstrated in Figure 9. Importantly, the calculated diffraction pattern is not affected by the typical sources of errors or the experimental powder diffraction (preferential orientation, mixtures, presence of amorphous) that often complicate or render uncertain the interpretation of the measured powder diffractograms; hence the calculated powder pattern is often referred to as the “gold standard” pattern for a crystal form.

Figure 9. Comparison between measured and calculated X-ray diffraction patterns for form II of gabapentine (single crystal data from reference 46).

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The search for various crystal forms requires that the behavior of a solid phase is investigated as a function of the variables that can influence or determine the outcome of the crystallization process, e.g. temperature, choice of solvents, crystallization conditions, rate of precipitation, interconversion between solid forms (from solvate to un-solvate and vice versa), pressure and mechanical treatment, absorption and release of vapor, etc. The most effective way to search for crystal forms is to evaluate the effect of the changes of one variable at a time. There has been a recent burst of activity in developing crystallization techniques and variables for obtaining new crystal forms,47 some of which are described in the next section. The efficiency of screening protocols, whether high throughput automatic methods or manual procedures, can be considerably increased by carrying out preliminary HSM, DSC and variable temperature XPD investigations for initial detection of multiple phases and the temperature ranges of their existence, as well as transformations among them. These observations can then be summarized with a semiempirical energy-temperature diagram24,48 that can be helpful in designing protocols for screening for crystal forms. In particular, it is possible to determine if various phases are related enantiotropically (reversibly) or monotropically (non-reversibly). Once the thermodynamic screening of the crystalline product has been completed, the quest for new forms can extend to the investigation of the effect of changing the solvent or the mixture of solvents and/or to the temperature gradient, the presence of templates or seeds. Examples of the utilization of variable temperature diffraction methods (VTXPD) to investigate phase transitions between

Figure 10. VTXPD measurements applied to the investigation of phase transitions between Form I and Form II of anthranilic acid.49

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Figure 11. VTXPD measurements applied to the investigation of the de-hydration of barbituric acid dihydrate with formation of Form I of barbituric acid.50

enantiotropic systems (in the case of anthranilic acid49) and desolvation processes (water removal from barbituric acid dihydrate50) are shown in Figures 10 and 11, respectively. 9. New Developments in Detecting and Characterizing Multiple Crystal Forms The last decade has witnessed many developments in the generation and detection of new crystal forms. These have resulted from the increased awareness of the possibility of multiple crystal forms of a substance, the utility that may derived by preparing a crystal form with enhanced properties and the potential intellectual property implications of new crystal forms. These factors, combined with the development of new technology,51 the attempts to design and control crystal structure,52 combined with some spectacular encounters with new (and undesired) crystal forms53 and some high profile pharmaceutical patent litigations,9 have led to many new techniques for exploring the crystal form space of any particular substance. Some of these depend simply on an awareness of the older literature,54 the application of crystal engineering principles, based on hydrogen-bonding patterns, to the preparation of new multicomponent solids,55 the induction of crystal forms by incorporating a variety of functional groups onto a polymer backbone,56 the development of high throughput crystallization technology,57 the utilization of solid-solid and solid-gas reactions,58 solvent-free synthesis,59 the desolvation of solvated crystals60 and crystallization from a supercritical solvent.61

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R. Hilfiker, ed. Polymorphism in the Pharmaceutical Industry (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2006). M.H. Klaproth, Bergmannische J. I, 294–9 (1798) [cited in J.R. Partington, A History of Chemistry, Vol. 3, p. 203 (MacMillan & Co., London, 1964)]. E. Mitscherlich, Über die Körper, welche in zwei vershiedenen kristallisieren Formen [Considerering the materials which can crystallize in two different crystal forms]. Abhl. Akad. Berlin, 43-48 (1823). R. Peschar, M.M. Pop, D.J.A. De Ridder, J.B. Van Mechele, R.A.J. Driessen and H. Schenk, Crystal structures of 1,3-distearoyl-2-oleoylglycerol and cocoa butter in the (V) phase reveal the driving force behind the occurrence of fat bloom on chocolate. J. Phys. Chem. B. 108, 15450–15453 (2004), and references therein. D. Braga and F. Grepioni, eds. Making Crystals by Design: Methods, Techniques and Applications (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2006) W.C. McCrone, Polymorphism, in Physics and Chemistry of the Organic Solid State; edited by D. Fox, M. M. Labes and A. Weissenberg (Interscience, New York, 1965, vol. II, pp. 725–767. J. Haleblian and W.C. McCrone, Pharmaceutical Applications of Polymorphism, J. Pharm. Sci. 64, 1269–1288 (1969). W.C. McCrone, Fusion Methods in Chemical Microscopy (Interscience, New York, 1957). J. Bernstein, Polymorphism in Molecular Crystals (Oxford University Press, Oxford, 2002). S.R. Byrn, T.R. Pfeiffer and J.G. Stowell, Solid State Chemistry of Drugs, 2nd edition (SSCI, West Lafayette, Indiana, 1999). H.G. Brittain, ed., Drugs in the Pharmaceutical Sciences, J. Sarbrick, editor, Vol. 95, Polymorphism in Phamaceutical Solids (Marcel Dekker, New York, 1999). H.G. Brittain, ed., Physical Characterization of Pharmaceutical Solids (Marcel Dekker, New York, 1995). T. Threlfall, Analysis of Organic Polymorphs. A Review, The Analyst 120, 2435–2460 (1995). M.R. Caira, Crystalline Polymorphism of Organic Compounds, Top. in Curr. Chem. 198, 163–208 (1998). S. Datta and D.J.W. Grant, Crystal structures of drugs: Advances in determination, prediction and engineering. Nature Reviews/Drug Discovery 3, 42–57 (2004). D. Braga, Crystal engineering, where from? Where to? Chem. Commun. 2751–2754 (2003). J. Bernstein, R. Davey, and J.-O Henck, Concomitant Polymorphs. Angew. Chem. Int. Ed. Engl. 38, 3440–3461 (1999). J.D. Dunitz, and J. Bernstein, Disappearing Polymorphs. Acc. Chem. Res. 28, 193–200 (1995) A.F. Findlay, The Phase Rule and Its Applications, 9th ed. revised and rewritten by A.N. Campbell and N.O. Smith, (Dover Publications, New York, 1963). E.F. Westrum and J.P. McCullough, Thermodynamics of crystals. Chapter 1 in Fox, D., Labes, M.M. and Weissberger, A. (eds.) Physics and Chemistry of the Organic Solid State, Vol. 1, (Wiley Interscience, New York, 1963) pp. 1–178. A. Burger, Thermodynamic and other aspects of the polymorphism of drug substances. Pharm. Int. 3, 158–163(1982).

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22. A. Burger and R. Ramberger, On the polymorphism of pharmaceutical and other molecular crystals. I Theory of thermodynamic rules. Mikrochim. Acta [Wien] 259–271 (1979). 23. A. Burger and R. Ramberger, On the polymorphism of pharmaceutical and other molecular crystals. II Applicability of thermodynamic rules. Mikrochim. Acta [Wien] 273–316 (1979). 24. A. Grunenberg, J.-O. Henck and H.W. Siesler, Theoretical derivation and practical applications of energy/temperature diagrams as an instrument in preformulation studies of drug substances. Int. J. Pharm., 129, 147–158 (1996). 25. B.D. Sharma, Allotropes and polymorphs. J. Chem. Educ. 64, 404–407 (1987). 26. M.J.Buerger, M.J Crystallographic aspects of phase transitions. Chapter 6 in Smoluchowski, R., Mayer, J.E. and Weyl, W.A. (eds.) Phase Transformations in Solids, (John Wiley & Sons, New York, 1951) pp. 183–211. 27. S. Lindeman and S.E. McGraw, Pharm. Manuf. Jan. 27–30 (1985). See also Ref. 9, p. 111. 28. P.T. Cardew, and R.J. Davey, Kinetic factors in the appearance and transformation of metastable phases. J. Chem. Soc. Faraday Trans. 80, 659–668 (1984). 29. P.T. Cardew, and R.J. Davey, The kinetics of solvent-mediated phase transformations. Proc. Roy. Soc. London, A298, 415–428 (1985). 30. M. Volmer, Kinetik der Phasenbildung, (Steinkopf, Leipzig, 1939). 31. W. Ostwald, Studies on the formation and transformation of solid materials. Z. Phys. Chem. 289–330 (1897). 32. R.J. Davey, R.J. General discussion Faraday Disc. 95, 160–162 (1993). 33. P.T. Cardew and R. Davey, Tailoring of Crystal Growth, Institute of Chemical Engineers, North Western Branch, Symposium Papers, Number 2 (ISBN 090663623X) pp. 1.1–1.8 (1982). 34. M. Ciechanowicz, A.C. Skapski, and P.G.H. Troughton, The crystal structure of the orthorhombic form of hydridodicarbonylbis(triphenylphosphine)iridium(I): successful location of the hydride hydrogen atom from x-ray data.Acta Crystallogr. B32, 1673– 1679 (1976). 35. R. Becker, and W. Doering, The kinetic treatment of nuclear formation in supersaturated vapors. Ann. Phys., 719–752 (1935). 36. I.N. Stranski, and D. Totomanov, Rate of formation of (crystal) nuclei and the Ostwald step rule. Z. Phys. Chem. A163, 399–408 (1933). 37. J. Bernstein and J.-O. Henck, Disappearing and reappearing polymorphs – An anathema to crystal engineering? Crystal Engineering 1, 119–128 (1998). 38. J.-O. Henck, J. Bernstein, A. Ellern, and R. Boese, Disappearing and reappearing polymorphs. The case of benzocaine:picric acid. J. Am. Chem. Soc. 123, 1834–1841 (2001). 39. S.R. Chemburkar, J. Bauer, K. Deming, H. Spiwek, K. Patel, J. Morris, R. Henry, S. Spanton, W. Dziki, W. Porter, J. Quick, P. Bauer, J. Donaubauer, B.A. Narayanan, M. Soldani, D. Riley, D. and K. McFarland, Dealing with the impact of ritonavir polymorphs on the late stages of bulk drug process development. Org. Process Res. & Development 4, 413–417 (2000). 40. J. Bernstein, Conformational polymorphism. Chapter 14 in Desiraju, G.R. (ed.), Organic Solid State Chemistry, (Elsevier, Amsterdam, 1987) pp. 471–518. 41. J. Bernstein, and A.T. Hagler, Conformational polymorphism. The influence of crystal forces on molecular conformation. J. Am. Chem. Soc., 100, 673–681 (1978). 42. J.D. Dunitz, Phase changes and chemical reactions in molecular crystals. Acta Crystallogr. B51, 619–631 (1995).

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43. S. Chen, Guzei and L. Yu, New polymorphs of ROY and new record for coexisting polymorphs of solved structures J. Am. Chem. Soc. 127, 9881–9885 (2005); L. Yu, G.A. Stephenson, C.A. Mitchell, C.A. Bunnell, S.V. Snorek, J.J. Bowyer, T.B. Borchardt, J.G. Stowell and S.R. Byrn, Thermochemistry and conformational polymorphism of a hexamorphic crystal system. J. Am. Chem. Soc. 122, 585, 2000. 44. R.K. Merton and E. Barber, The travels and adventures of serendipity, (Princeton University Press: Princeton, 2004). 45. Many examples of the applications of these techniques can be found in references 1, 9–15. 46. J.A. Ibers, Gabapentin and gabapentin monohydrate, Acta Crystallogr. Sect. C, 57, 641–643 (2001). 47. J. Bernstein, Cultivating crystal forms, Chem. Commun., 5007–5012 (2005). 48. J.-O. Henck and M. Kuhnert-Brandstatter, Demonstration of the terms enantiotropy and monotropy in polymorphism research exemplified by flurbiprofen, J. Pharm. Sci. 88, 103–108 (1999). 49. C.J. Brown and M. Ehrenberg, Anthranilic acid I C7H7NO2 Acta Crystallogr. Sect. C. 41, 441–443 (1985); G.E. Hardy, W.C. Kaska, B.P. Chandra and J.I. Zink, Triboluminescencestructure relationships in polymorphs of hexaphenylcarbodiphosphorane and anthranilic acid, molecular crystals, and salts, J. Am. Chem. Soc. 103, 1074–1079 (1981); H. Takazawa, S. Ohba and Y. Saito, Structure of monoclinic o-aminobenzoic acid,Acta Crystallogr. Sect. C. 42, 1880–1 (1986); T.-H. Lu, P. Chattopadhyay, F.-L. Liao and J.-M. Lo, Crystal structure of 2-aminobenzoic acid Anal Sci. 17, 905–906 (2001). 50. T.C. Lewis, D.A. Tocher and S.L. Price, An experimental and theoretical search for polymorphs of barbituric acid: The challenges of even limited conformational flexibility Cryst. Growth & Des. 4, 979–987 (2004); W. Bolton, Acta Crystallogr. 16, 166–(1963); G.A. Jeffrey, S. Ghose and J.O.Warwicker, Acta Crystallogr. 14, 881–(1961); A.R. AlKaraghouli, B. Abdul-Wahab, E. Ajaj and S. Asaff, Neutron diffraction study of barbituricacid dihydrate, Acta Crystallogr. Sect. B. 33, 1655–1660 (1977); G.S. Nichol and W. Clegg, A variable-temperature study of a phase transition in barbituric acid dihydrate Acta Crystallogr. Sect. B. 61, 464–472 (2005) 51. S.L. Morissette, S. Soukasenem, D. Levinson, M.J. Cima and Ö. Almarsson, Elucidation of crystal form diversity of the HIV protease inhibitor ritonavir by highthroughput crystallization Proc. Natl. Acad. Sci. U. S. A., 100, 2180–21 84 (2003). 52. G.R. Desiraju, ed., Crystal Design: Structure and Function, (Wiley: Chichester, 2003). 53. J. Bauer, S. Spanton, R. Henry, J. Quick, W. Dziki, W. Porter and J. Morris, Ritonavir: An extraordinary example of conformational polymorphism, Pharm. Res. 18, 859-866 (2001). 54. W.I.F. David, K. Shankland, C.R. Pulham, N. Blagden, R. Davey and M. Song, Polymorphism in benzamide Angew. Chem., Int. Ed. 44, 7032–7035 (2005); N. Blagden, R. Davey, G. Dent, M. Song, W.I.F. David, C.R. Pulham and K. Shankland, Woehler and Liebig revisited: A small molecule reveals its secrets – The crystal structure of the unstable polymorph of benzamide solved after 173 years, Cryst. Growth & Des. 5, 2218–2224 (2005). 55. (a) Ö. Almarsson and M.J. Zaworotko, Crystal engineering of the composition of pharmaceutical phases. Do pharmaceutical co-crystals represent a new path to improved medicines? Chem. Commun.1889-1896 (2004); (b) C.B. Aakeröy, A.M. Beatty and B.A. Helfrich, “Total synthesis” supramolecular style: Design and hydrogen-bonddirected assembly of ternary supermolecules Angew. Chem., Int. Ed. 40, 3240–3241 (2001).

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56. C.P. Price, A.L. Grzesiak and A.J. Matzger, Crystalline polymorph selection and discovery with polymer heteronuclei J. Am. Chem. Soc. 127, 5512–5517 (2005). 57. D. Braga and F. Grepioni, Making crystals from crystals: a green route to crystal engineering and polymorphism Chem. Commun. 3635–3645 (2005). 58. A.V. Trask, N. Shan, W.D.S. Motherwell, W. Jones, S. Feng, R.B.H. Tan and K.J. Carpenter, Selective polymorph transformation via solvent-drop grinding Chem. Commun. 880–882 (2005). 59. E.Y. Cheung, S.J. Kitchin, K.D.M. Harris, Y. Imai, N. Tajima and R. Kuroda, J. Am. Chem. Soc., Direct structure determination of a multicomponent molecular crystal prepared by a solid-state grinding procedure 125, 14658–14659 (2003). 60. A. Burger and U.J. Griesser, Physical stability, hygroscopicity and solubility of succinylsulfathiazole crystal forms – the polymorphic drug substances of the European Pharmacopoeia. 7. Eur. J. Pharm. Biopharm. 37 118–125 (1991). 61. P. York, Supercritical fluids: realising potential, Chem. World 2, 50-53 (2005); B. Yu. Shekunov and P. York, Crystallization processes in pharmaceutical technology and drug delivery design J. Cryst. Growth 211, 122–136 (2001).

COMPLEMENTARITY: CORRELATING STRUCTURAL FEATURES WITH PHYSICAL PROPERTIES IN SUPRAMOLECULAR SYSTEMS

SUSAN A. BOURNE Department of Chemistry, University of Cape Town, Rondebosch 7701, South Africa

Abstract. In recent years a number of complementary techniques have been developed to study the correlation between crystalline structure and physical behaviour of inclusion compounds. In this article, case studies are presented to illustrate methods useful for the study of selectivity by host compounds towards particular guests and of the kinetics governing the formation and decomposition of inclusion compounds.

Keywords: Guest selectivity, kinetics, Arrhenius and Anti-Arrhenius behaviour, crystal structure

1. Introduction The process of inclusion, in which a host compound captures a guest molecule to form a crystalline host-guest compound, depends on the phenomenon of molecular recognition. The combination of relatively weak non-covalent interactions which include ion-dipole, dipole-dipole, π-interactions and hydrogen bonding may all have a structure-directing influence on the selfassembly process.1–3 Another class of non-directional forces which should not be overlooked are the interactions between aromatic molecules. These control many self-assembly and molecular recognition phenomena and therefore are important in the context of crystal engineering.4,5 Many types of organic host compounds are known, and there has been an exponential growth in the number of host compounds being designed and produced over the past thirty years. Some of these have been discovered serendipitously while others have been targeted at specific guests by optimizing the complementarity of the host-guest system, thus lowering the lattice energy of the resulting inclusion compound.6 While these approaches have 111 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 111–129. © 2008 Springer.

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been widely applied to the design and synthesis of novel organic host compounds, the past decade has also seen an explosive growth in the variety of metal-organic host compounds being produced with the aim of generating new functional materials.7 Thus a wide variety of coordination polymers8 and metal-organic frameworks (MOFs)9 have been reported, some of which are shown to possess enhanced optical, magnetic properties or to act as porous materials capable of absorbing a range of gaseous molecules. The use of hydrogen bonding interactions with metal salts to control the crystal structure produced has also recently received attention.10 Some of these approaches are yielding more predictable results, but competing interactions as well as changes in experimental conditions often have an impact on the materials produced. When the host is presented with two or more guests, its selectivity for a particular guest depends on the extent and the nature of the non-bonded interactions which occur between the various molecules in the crystal structure.11 This report surveys some of the useful techniques for studying the correlation of structural features and physical properties of crystalline inclusion compounds. Each is illustrated by means of examples drawn from the work done in the Centre for Supramolecular Chemistry Research at the University of Cape Town. 2. Selectivity by Organic Host Compounds 2.1. CLATHRATES WITH MIXED GUESTS

The separation of a particular component from a mixture may be carried out by exploiting differences in physical properties. In the case of liquids one relies on differences in vapour pressure, but when liquids have similar boiling points, distillation procedures may be inefficient or unusable. Thus the method of selective inclusion becomes an attractive possibility. There are two approaches: one may employ a porous material such as a zeolite, in which the framework remains essentially unchanged during the absorption and desorption of the guest molecules, and whose selectivity is governed by the size of the channels. Alternatively one may utilise organic or metal-organic compounds as hosts, in which case, for a two-component mixture, the separation process may be represented by the equation: H(s,α) + nA(l or v) + mB(l or v) → H⋅An(s,β) + mB(l or v) Here H represents the apohost in its non-porous α-phase, that when placed in contact with a mixture of guests A and B, which can be liquid or vapour, selects A and forms a solid inclusion compound H⋅An, the β-phase, while excluding B. If the host displays perfect selectivity, the process outlined in

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the equation above need only be carried out once, the solid compound filtered, guest A released by warming, and the host H recycled. This seldom occurs in practice, and one has to perform carefully designed competition experiments in order to establish the selectivity profile of a given host. These are carried out by dissolving the host in a series of guest mixtures of varying mole fraction, separating the ensuing crystals and analysing their guest contents by a suitable technique such as gas chromatography. The selectivity of a host for one of a pair of guests can be established by carrying out competition experiments in which the host is dissolved in a series of mixtures of guests of varying mole fraction (X). A huge excess of guest is maintained in the initial solutions to avoid artificial selectivity. The resulting crystalline inclusion compounds are analyzed by gas chromatography to establish the mole fraction (Z) of guest. The selectivity of the host for a pair of guests, A and B, can then be expressed as the selectivity coefficient12 such that KA:B = ZA/ZB * XA/XB where (XA + XB = 1) XA is the mole fraction of guest A in the liquid mixture, and ZA that of the guest included in the crystal. Three kinds of selectivity curves commonly result and are shown in Figure 1: the diagonal line, ‘a’, represents no selecivity with KA:B = 1, curve ‘b’ occurs when A is preferentially enclathrated over B over the whole concentration range with KA:B = 10, while curve ‘c’ arises when the selectivity is concentration dependent.

Figure 1. Typical selectivity curves obtained from competition experiments.

For example, the host 1,1,2,2-tetraphenyl-1,2-ethanediol (H1) forms inclusion compounds with toluene, chloro-, bromo- and iodo-benzene individually (scheme 1). The H:G ratio is 1:½ in each case, and the packing is isomorphous in the first three structures and closely related to that in the

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H1:½ IPh structure (Figure 2). Results of the 2-component competitions experiments found that KClPh:MePh = 1.7; KBrPh:MePh = 4.9 and KBrPh:ClPh = 2.0.

Figure 2. Packing diagrams of (a) H1.½ MePh (isomorphous with H1.½ ClPh and H1.½ BrPh) and (b) H1.½ IPh. Guest molecules are disordered about centres of inversion in each case.

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The experiment can be extended to consider 3-component mixtures of the guests which are liquid under ambient conditions. Figure 3 shows that there is a clear preference of the host for bromobenzene (consistent with the results of the two-component experiments).

Figure 3. Results of 2- and 3-component competitions experiments of H1 with toluene, chloro- and bromo-benzene. The 3-component experiment is plotted on an equilateral triangle with starting mixtures represented by the dots inside the inner grey triangle. The composition within the inclusion compounds are shown by the outer triangle of smaller dots.

When the competition was extended to 4-component mixtures (Figure 4), there is a sharp drift away from toluene and towards iodobenzene as the preferred guest. A lesser selectivity towards bromobenzene is also evident.

Figure 4. Results of the four-component competition experiment of H1 with toluene, chloro-, bromo- and iodo-benzene, presented in stereo. The inner tetrahedron represents the starting concentrations while the red tetrahedron in the foreground represents the concentrations of the components included by the host.

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The selectivity displayed by this host towards these guests is thus in the order iodobenzene > bromobenzene > chlorobenzene > toluene, which also correlates with the peak temperatures of the guest release endotherms in the DSC results for these inclusion compounds (Table 1).13 TABLE 1. Thermal analysis of H1.½XPh H1.½ MePh

H1.½ ClPh

H1.½ BrPh

H1.½ IPh

TG

Calc % mass loss Exp % mass loss

11.2 10.8

13.3 11.7

17.7 17.7

21.8 17.4

DSC

Tpeak (guest loss) (K)

355

365

375

385

2.2. MODIFYING SELECTIVITY BY CHANGING GUEST OR ENVIRONMENT

One approach to change the selectivity for a particular guest from a mixture, is to adjust the design of the host compound. Thus host compounds have been modified or designed anew to tune the channels formed by helical hosts,14 control ion selectivity by crown ethers,15 or by changing the chirality of substituents.16 Instead, we took the approach of subtly modifying the guests or their environment in order to vary selectivity. The host 1,4-bis(9-hydroxyfluoren-9-yl)benzene (H2) has been shown to enclathrate a variety of organic guest molecules17–19 including aniline and benzylamine.20 The crystal structures (H2.An and H2.3Bz) are unremarkable, except in the unusual cis-configuration of the host in H2.An (Figure 5). Both are stabilized by host-guest O-H...N hydrogen bonds with guests located in pockets within the host network structure (Figures 5 and 6).

Figure 5. The H2.An structure consists of ribbons of H-bonded host molecules with aniline molecules in pockets.

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Figure 6. H2.3Bz structure, showing the host in trans-configuration. Two benzylamine guests are H-bonded while one is not.

Competition experiments were carried out such that the molar ratio H2: (An + Bz)tot was 1: 200. The selectivity curve for the aniline-benzylamine system shows that the host does not discriminate between the two guests and the selectivity coefficient KAn:Bz ≈ 1 over the whole concentration range (Figure 7, curve a). Noting that, although both have boiling points of 184– 185°C, benzylamine, pKb = 4.6, is a stronger base than aniline with pKb = 9.4, we reasoned that by acidifying the aniline-benzylamine mixture the benzylamine would be preferentially protonated at the N atom, thus disrupting the host-guest hydrogen bonding and so favouring enclathration of aniline. The resulting selectivity profile, (Figure 7, curve b) yielded the expected result, showing that only aniline had been enclathrated over the whole concentration range. This result represents a method with potential to purify compounds with similar physical properties which do not lend themselves to traditional methods of separation.

Figure 7. Competition experiment between aniline and benzylamine with host H2. (a) selectivity of H2 for the neutral mixture (squares). (b) when mixture is acidified, H2 shows enhanced selectivity for aniline (triangles).

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2.3. CYCLODEXTRIN INCLUSION OF AJOENE: A CASE OF NON-SELECTIVITY

Chemical components contained in garlic (Allium Sativa, L.) have been determined to have beneficial effects on human health.21,22 Interest recently has focused on isolating and studying the specific effects of individual pharmacologically active components, which include allicin (allyl 2propenethiosulfinate) and its decomposition product ajoene (4,5,9trithiadodeca-1,6,11-triene-9-oxide). Ajoene is an oil which exists as either the E- or the Z- isomer (Scheme 2). Both (E)- and (Z)-ajoene have been shown to have antidiabetic and hypocholesterolemic activity and to lower the levels of uric acid in the blood,23 while (E)-ajoene can be used to against the fungus Candida Albicans24 and (Z)-ajoene is an experimental antileukemic agent.25 Our interest in ajoene lies in its complexation with cyclodextrins which, it was felt, could result in the formation of inclusion compounds with potential medicinal applications.26 Selecting well-defined, pharmacologically active garlic constituents for inclusion is more desirable than using mixtures or whole extracts. Advantages of this approach include the conversion of the liquid ajoenes into solids, rendering them more manageable for formulation while at the same time it is likely that the bioavailability of ajoene would be improved.

While complexes of both (E)- and (Z)-ajoene could be prepared with α-, β- and γ-cyclodextrins as well as the methylated derivatives, heptakis(2,6di-O-methyl)-β-cyclodextrin (DIMEB) and heptakis(2,3,6-tri-O-methyl)-βcyclodextrin (TRIMEB), only the latter CD yielded single crystals of suitable quality for structural elucidation.27 Thermogravimetric analysis showed a very small mass loss (0.6-0.8%) in the temperature range 30– 60°C for TRIMEB.(E)-ajoene which corresponds to ½ water molecule per complex unit. Following dehydration, this complex melted at 143.8°C. The complex TRIMEB.(Z)-ajoene is unsolvated and melts at 140.5°C.

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The host TRIMEB conformations in both structures are very similar. The conformations are stabilized by several analogous intramolecular C-H...O hydrogen bonds, similar to other reported structures.28 One significant difference is the tilt-angles of two methyl-glucose residues. In order to accommodate the hydrogen bonding interactions of the water molecule with the cyclodextrin unit in TRIMEB.(E)-ajoene, residues G4 and G5 are twisted towards (+11.5°) and away from (–4.1°) the host primary side relative to their orientations in TRIMEB.(Z)-ajoene. The primary methoxyl groups of residues G2, G4, G5 and G7 block the primary side of the host in both complexes, resulting in the host cavity taking on a cup-like shape which presents a large hydrophobic surface to the encapsulated ajoene guest.

Figure 8. Stereoview of the modes of inclusion of the stereoisomers of (E)-ajoene in TRIMEB (R-enantiomer, top; S-enantiomer, bottom).

The isomers of ajoene are elongated molecules with a high degree of conformational flexibility and this is manifested in their inclusion compounds by the presence of both stereoisomers of (E)- and (Z)-ajoene, in equal proportions. Figure 8 shows the modes of inclusion of the enantiomers of (E)-ajoene in TRIMEB while figure 9 depicts the disorder model invoked in the structure analysis, together with the individual enantiomers. A and B share common terminal atoms C1, C2, C3 and S10, C11, C12, C13. However, the twofold disorder of the sulfinyl group and S9 require that in model A, C7-C8 is formally the central double bond while in model B this role is assumed by C8-C8B. The torsion angles around the

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Figure 9. Disorder model in the crystal structure of TRIMEB.(E)-ajoene (A-B) and the individual enantiomers (A=R-, B=S-enantiomer) with atom assignments.

respective C-C=C-S bonds are 163(2) and 172(2)°, approximating the ideal value of 180° for the (E)-isomer. The stereogenic sulfoxide atoms S4A and S4B have R- and S- configurations respectively. The refined s.o.f.s indicate practically equal occupancy thus TRIMEB shows no stereorecognition. The modes of inclusion of both enantiomers are similar, with the disulfide moiety uppermost in the host cavity. The allylic and vinylic moieties are also included in the cavity, while the allyl group and its attached sulfinyl group protrude from the secondary face of the cyclodextrin. The S=O dipole orientations are reversed for the two stereoisomers and in one (the Renantiomer) there is a weak interaction S=O...H-C(host) to a secondary methyl group. An analogous situation arises in TRIMEB.(Z)-ajoene, with both R- and S-enantiomers of (Z)-ajoene included in a 1:1 H:G complex. Torsion angles around the respective C-C=C-S bonds are 16(3) and 24(3)°, approximating the ideal value of 0° for the (Z)-isomer. The modes of inclusion are different from those for the E-isomer. The disulfide group and allyl group are located outside the cavity while the sulfinyl group is within the host (Figure 10). In addition, the individual stereoisomers of (Z)-ajoene are in different environments; the R-enantiomer (A) has its S=O group at the ‘roof ’ of the cavity, in van der Waals contact with the capping primary methoxyl groups, whereas in the S-enantiomer (B) it is near the secondary face.

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Figure 10. Stereoview of the modes of inclusion of the stereoisomers of (Z)-ajoene in TRIMEB (R-enantiomer, top; S-enantiomer, bottom).

The complex units in TRIMEB.(E)-ajoene and TRIMEB.(Z)-ajoene are very similar, except at the secondary face where chemically different residues of the guest protrude. This difference induces very different packing arrangements and powder x-ray diffraction patterns (Figures 11 and 12).

Figure 11. (100) projection of the crystal packing in TRIMEB.(E)-ajoene. Only the Renantiomer is shown.

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Figure 12. (100) projection of the crystal packing in TRIMEB.(Z)-ajoene. Only the Renantiomer is shown.

3.

Kinetics of Guest Enclathration and Desorption

Relatively little attention has been paid to the thermal decomposition of inclusion compounds, possibly because decomposition often involves multiple steps, with formation of intermediate host-guest phases whose composition and structure are not readily established. Similarly, the kinetics and thermodynamic processes underlying guest inclusion are experimentally difficult to study, especially when the inclusion compounds formed are unstable under ambient conditions. We have developed methods for studying the kinetics of guest desorption and absorption from the vapour phase. An automated magnetic suspension balance constructed in-house29 allows us to monitor the mass change of an inclusion compound with time under controlled conditions of pressure and temperature (Figure 13).

Figure 13. Schematic diagram of automated magnetic suspension balance.

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Figure 14. (a) Packing diagram of inclusion compound H3.4(acetone) viewed along [001], (b) View down channels along [001] with guest molecules omitted.

The kinetics of enclathration and desorption were studied for a system comprising the host trans-9,10-dihydroxy-9,10-bis(p-tert-butylphenyl)9,10-dihydroanthracene (H3) with acetone as guest.30 The inclusion compound crystallises in the space group P21/c with host:guest ratio 1:4 (Figure 14). Two guests are hydrogen bonded to the hydroxyl groups of the host molecule. The packing of the host molecules results in criss-crossed channels running parallel to [100] (maximum cross section 4.1 × 4.1 Å) and [001] (maximum cross section 5.3 × 8.4 Å)in which the acetone molecules are located. The kinetic measurements were carried out by exposing finely powdered host compound to acetone vapour at fixed temperature but different pressures of acetone (Figure 15). The results fitted the contracting

Figure 15. Isothermal absorption curves at T=290 K, with vapour pressures of (A) 86 Torr, (B) 100 Torr), (C) 118 Torr, (D) 140 Torr, (E) 158 Torr.

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Figure 16. Plot of kobs vs. the pressure of acetone, P, at temperatures (A) 290 K, (B) 298 K), and (C) 306 K.

volume equation31 (f(α)=1-(1-α)1/3) which allowed the rate constants kobs to be determined. In this system, a threshold pressure P0 of guest is required before inclusion takes place. Figure 16 is a plot of kobs vs. the pressure of acetone, P, showing the following P0 values at given temperatures: 62 Torr (290 K), 115 Torr (298 K), 127 Torr (306 K). The increase in P0 with temperature is consistent with the inclusion compound having a greater propensity to decompose at higher temperatures, and gives rise to the antiArrhenius behaviour indicated by the decreasing rate of reaction with increasing temperature. This is illustrated in Figure 16 where, for example, at a pressure of 140 Torr, kobs is 0.061 min–1 at 290 K and 0.020 min–1 at 298 K. Similar behaviour has been observed in other vapour absorption systems with organic hosts.32,33 Using the same magnetic suspension apparatus, the kinetics of desolvation was studied by subjecting the system to vacuum at various temperatures. The desolvation curves were deceleratory and fit the first order equation (f(α)=-ln(1–α)). The semi-logarithmic plot of ln kobs vs. 1000K/T (Figure 17) yielded an activation energy of 48.4 kJ mol–1. This value is typical of activation energies obtained for guest desorption processes from organic inclusion compounds.34

Figure 17. Arrhenius plot for H2. 4acetone.

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A different method of studying guest desorption processes is to utilise isothermal thermogravimetry using a commercial thermogravimetric analyser (TGA). Whereas the magnetic suspension balance operates under vacuum for guest desorption, the TGA process allows one to operate under an atmosphere of purge gas (typically N2) at atmospheric pressure. Curvefitting techniques allow us to choose suitable models to describe the desolvation mechanism31 and to derive the Arrhenius parameters. We applied this technique to the desorption kinetics of a series of aromatic guests from the same metal-organic host framework. {[Ni (bipy)2(NO3)2] . arene} compounds (where bipy is 4,4’-bipyridine) were first reported by Zaworotko et al.35 They can be described as interpenetrating planar networks comprising (4,4) metal-organic networks and either (4,4) or (6,3) arene networks. An examination of the crystal structures (Figure 18) shows that there are no host-guest interactions of note. However, the guests form a close-packed network characterised by weak intermolecular interactions including edge-to-face π-stacking (benzene), C-H...Cl (chlorobenzene) and C-H...O (nitrobenzene), illustrated in Figure 19.

Figure 18. Crystal packing in [Ni(bipy)2(NO3)2].XPh (X= H, Cl or NO2) illustrated for X=H. The 2D coordination polymer includes a variety of aromatic guests with no host...guest interactions.

Figure 19. Guest...guest non-bonding interactions in [Ni(bipy)2(NO3)2] inclusion compounds: (a) benzene, (b) chlorobenzene, (c) nitrobenzene.

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A series of mass loss vs time curves were obtained for the isothermal desolvation of benzene, chlorobenzene and nitrobenzene from their [Ni (bipy)2(NO3)2] inclusion complexes, over a temperature range of 80 to 95°C. The data were reduced to fractional reaction (α) vs time curves (all of which were deceleratory). Various kinetic models were tested for linearity, giving a measure of the rate constant, kobs, at each temperature tested. A plot of ln kobs vs 1/T yielded the activation energy for each desorption reaction studied. Activation energies determined for these compounds are 82(3) and 84(3) kJ/mol (fitting a contracting volume mechanism with (f(α)=1–(1–α)1/3)) for [Ni (bipy)2(NO3)2].benzene and [Ni (bipy)2(NO3)2].nitrobenzene and 92(5) kJ/mol (fitting the D4 diffusion mechanism ((f(α)=(1–2α/3)–(1–α)2/3) for [Ni (bipy)2(NO3)2].chlorobenzene. Zaworotko had reported that the [Ni (bipy)2(NO3)2].XPh (X= H, Cl or NO2) crystal structures were all isostructural, and this was confirmed in this study by x-ray powder diffraction. XRPD further indicated that the crystalline material produced after desorption of the guests is the same phase in each case (Figure 20). This phase must represent a guest-free arrangement of the host [Ni (bipy)2(NO3)2] but it is dissimilar to both an “empty channel” 2D coordination polymer structure (calculated by deleting guests from the crystal structure and simulating the xrpd pattern) and from the crystalline phase that is produced when Ni(NO3)2 and 4,4-bipyridine are ground together in a solid-solid reaction.36 Further studies on the structure of this crystalline phase are ongoing.

Figure 20. PXRD traces of [Ni(bipy)2(NO3)2] complexes (a) before and (b) after desorption of guests.

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4. Conclusions The term complementarity has two relevant meanings in the context of this article. Firstly, the formation of supramolecular assemblies, specifically inclusion compounds, is dependent on the complementary interactions which form between host and guest. In the second place, this article aimed to illustrate the value of utilising a variety of analytical methods and techniques to fully explore the correlation between crystal structure and bulk physical properties of supramolecular complexes. 5. Acknowledgements The author is grateful to her colleagues in the Centre for Supramolecular Chemistry Research at the University of Cape Town, in particular Professors Mino Caira and Luigi Nassimbeni for their encouragement and collaboration.

References 1.

C. B. Aakeröy, A. M. Beatty and D. S. Leinen, A versatile route to porous solids: Organic-inorganic hybrid materials assembled through hydrogen bonds, Angew. Chem. Int. Ed., 38, 1815–1819 (1999) 2. C. B. Aakeröy, A. M. Beatty, D. S. Leinen and K. R. Lorimer, Deliberate combination of coordination polymers and hydrogen bonds in a supramolecular design strategy for inorganic/organic hybrid networks, Chem. Commun. 935–936 (2000). 3. C. Guilera and J. W. Steed, Topological control in coordination polymers by noncovalent forces, Chem. Commun., 1563–1564 (1999). 4. C. A. Hunter, Meldola lecture. The role of aromatic interactions in molecular recognition, Chem. Soc. Rev., 101–109 (1994). 5. L. R. MacGillivray, R. H. Groeneman and J. L. Atwood, Design and self-assembly of cavity-containing rectangular grids, J. Am. Chem. Soc., 120, 2676–2677 (1998). 6. Molecular Recognition: Receptors for Molecular Guests, edited by F. Vögtle. Vol. 2 in Comprehensive Supramolecular Chemistry, edited by J. M. Lehn, J. L. Atwood, J. E. D. Davies, D. D. MacNicol and F. Vögtle (Elsevier, Oxford, 1996). 7. D. Braga, G. R. Desiraju, J. S. Miller, A. G. Orpen and S. L. Price, Innovation in crystal engineering, Cryst Eng Comm, 4, 500–509 (2002). 8. A. J. Blake, N. R. Champness, P. Hubberstey, W. S. Li, M. A. Withersby and M. Schroder, Inorganic crystal engineering using self-assembly of tailored building blocks, Coord. Chem. Rev., 183, 117–138 (1999). 9. O. M. Yaghi, M. O’Keeffe, N. W. Ockwig, H. K. Chae, M. Eddaoudi and J. Kim, Reticular synthesis and the design of new materials, Nature, 423, 705–714 (2003). 10. D. B. Mitzi, Templating and structural engineering in organic-inorganic perovskites, J. Chem. Soc., Dalton Trans., 1–12 (2001).

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30. L. J. Barbour, M. R. Caira, T. le Roex and L. R. Nassimbeni, Inclusion compounds with mixed guests: Controlled stoichiometries and kinetics of enclathration, J. Chem. Soc., Perkin Trans., 2, 1973–1979 (2002). 31. M. E. Brown, D. Dollimore and A. K. Galwey in: Comprehensive Chemical Kinetics edited by C. H. Bamford and C. J. Tipper (Elsevier, Amsterdam, 1980), Vol. 22, p. 220. 32. M. R. Caira, A. Coetzee, L. R. Nassimbeni, E. Weber and A. Wierig, Complexation with diol host compounds. Part 24. Kinetics of desolvation of inclusion compounds of 2,7-substituted-2,2’-bis(9-hydroxy-9-fluorenyl)biphenyl hosts with acetone, J. Chem. Soc., Perkin Trans., 2, 237–242 (1997). 33. T. Dewa, K. Eudo and Y. Aoyama, Dynamic aspects of lattice inclusion complexation involving a phase change. equilibrium, kinetics and energetics of guest-binding to a hydrogen-bonded flexible organic network, J. Am. Chem. Soc., 120, 8933–8940 (1998). 34. A. Coetzee, Structure and reactivity of selected inclusion compounds, PhD Thesis, University of Cape Town, 215 (1996). 35. K. Biradha, A. Mondal, B. Moulton and M. J. Zaworotko, Coexisting covalent and noncovalent planar networks in the crystal structures of {[M(bipy)2(NO3)2].arene}n (M=Ni, 1, Co, 2; arene = chlorobenzene, o-dichlorobenzene, benzene, nitrobenzene, toluene or anisole), J. Chem. Soc., Dalton Trans., 3837–3844 (2000). 36. S. L. James, 2007, private communication.

MAKING CRYSTALS FROM CRYSTALS: A SOLID-STATE ROUTE TO THE ENGINEERING OF CRYSTALLINE MATERIALS, POLYMORPHS, SOLVATES AND CO-CRYSTALS; CONSIDERATIONS ON THE FUTURE OF CRYSTAL ENGINEERING DARIO BRAGA,a MARCO CURZI,b ELENA DICHIARANTE,b STEFANO LUCA GIAFFREDA,b FABRIZIA GREPIONI,a LUCIA MAINI,a GIUSEPPE PALLADINO,a ANNA PETTERSEN,a MARCO POLITOa a Dipartimento di Chimica G. Ciamician, Università degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy b PolyCrystalLine s.r.l. Via Stradelli Guelfi 40/c, 40138 Bologna, Italy

Abstract. Making crystals by design is the paradigm of crystal engineering. The main goal is that of obtaining and controlling the collective properties of a crystalline material from the convolution of the physical and chemical properties of the individual building blocks (whether molecules, ions, or metal atoms and ligands) with crystal periodicity and symmetry. Crystal engineering encompasses nowadays all traditional sectors of chemistry from organic to inorganic, organometallic, biological and pharmaceutical chemistry and nanotechnology. The investigation and characterization of the products of a crystal engineering experiment require the utilization of solid state techniques, including theoretical and advanced crystallography methods. Moreover, reactions between crystalline solids and/or between a crystalline solid and a vapour can be used to obtain crystalline materials, including new crystal forms, solvates and co-crystals. Indeed, crystal polymorphism, resulting from different packing arrangements of the same molecular or supramolecular entity in the crystal structure, represents a challenge to crystal makers.

Keywords: crystal engineering, polymorphism, solvato-morphism, co-crystal, solidsolid reactions, solid-gas reactions 131 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 131–156. © 2008 Springer.

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1. Introduction Crystal engineering (CE hereafter) is the bottom-up construction of functional materials from the assembly of molecular or ionic components.[1,2] Since molecules have nanometric dimensions the purposeful assembly of molecules in crystalline structures has relevant implications also in the burgeoning field of nanochemistry and nanotechnology.[3-5] In the supramolecular approach to the aufbau process of a crystalline solid from its component units, the crystals are seen as networks of interactions. These interactions can be covalent bonds between atoms (e.g. zeolites, intercalates, etc.) as well as coordination bonds between ligands and metal centres (metal organic framework structures, MOF), Coulombic attractions and repulsions between ions, and non-covalent bonds between neutral molecules (van der Waals, hydrogen bonds, etc.) or – of course – any combination of these linkages.

Figure 1. An approximate ranking in energy of covalent networks, coordination networks, hydrogen bonded networks and van der Waals solids.

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The difference in bonding types represents a practical way to subdivide CE target materials as a function of the energy involved in the bond breakingbond forming processes. These bonding interactions follow an approximate ranking in energy: from the high enthalpies involved in breaking and forming forming of covalent bonds between atoms to the tiny energies involved in the van der Waals interactions between neutral atoms in neutral molecules[6] (see Figure 1). 2. Crystal Engineering – Some Historical Notes The proceedings of the American Physical Society Meeting held in Mexico City in August 1956[7] report an abstract entitled “Crystal Engineering: a new concept in crystallography”, by R. Pepinsky of the Pennsylvania State University: “Crystallization of organic ions with metal-containing complex ions of suitable sizes, charges and solubilities results in structures with cells and symmetries determined chiefly by packing of complex ions. These cells and symmetries are to a good extent controllable: hence crystals with advantageous properties can be ‘engineered’… Pepinsky’s goal was that of exploiting complex ions in the application of direct methods for structure determination, in particular the absolute structure of optically active ions. The qualifier engineering associated to crystals was again employed by G. Schmidt and collaborators at the Weitzmann Institute in the early seventies to describe photodimerization reaction of cinnamic acid and its derivatives in the solid state.[8] Schmidt wrote: “The systematic development of our subject will be difficult if not impossible until we understand the intermolecular forces responsible for the stability of the crystalline lattice of organic compounds: a theory of the organic solid state is a requirement for the eventual control of molecular packing arrangement. Once such a theory exists we shall, in the present context of synthetic and mechanistic photochemistry, be able to ‘engineer’ crystal structures having intermolecular contact geometries appropriate for chemical reaction, much as, in other context, we shall construct organic conductors, catalysts, etc.” Schmidt’s idea was focused on the arrangement of molecules in crystals in order to achieve topochemical control on photochemical activated cyclization reactions, because the double bonds of the olefins were locked in place by the crystal packing at an appropriate distance for reaction (see Figure 2). In spite of many scientific efforts, however, the lack of true predictability of the arrangements that molecules with different shapes could adopt in the solid state, together with the difficulty of the solid state characterization of the resulting products, did not yield the desired results.

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α

β

Figure 2. A schematic representation of Schmidt’s photodimerization reaction of cinnamic acid in the solid state. The proximity and adequate orientation of the reacting groups is required for the cyclization to take place.

In 1988 Maddox wrote in a Nature editorial that “One of the continuing scandals in the physical sciences is that it remains in general impossible to predict the structure of even the simplest crystalline solid from a knowledge of their chemical compositions”.[9] This statement, taken from an article concerned with ab-initio calculations of silica, has been quoted many times to stress how far we all were from being able to understand and model the forces responsible for the cohesion of solids. At about the same time M. Etter was pointing out that “Organizing molecules into predictable arrays is the first step in a systematic approach to designing solid-state materials ”.[10] A couple of years later, G. R. Desiraju published the very first book devoted to organic crystal engineering; the term was given the following interpretation: “The understanding of intermolecular interactions in the context of crystal packing and in the utilization of such understanding in the design of new solids with desired physical and chemical properties”.[11] These hints, together with the results obtained, quite independently, by several research groups in the coordination, organic and organometallic solid state sciences,[12–22] indicated the direction of future development: the construction of “crystalline materials with a purpose”. Crystals were no longer perceived as “molecular containers”, useful for the detailed determination of molecular structures, but as supramolecular entities with collective chemical and physical properties. Therefore modern crystal engineering draws its strength from the synergistic interaction between design and synthesis of supermolecules on the one hand, and design and synthesis of crystalline materials with desired solid-state properties on the other hand. In a way, the definition of supramolecular chemistry put forward by J.-M. Lehn[22] in his Nobel lecture «chemistry beyond the molecule bearing on the organized entities of higher complexity that result from the association of two or more chemical species held together by intermolecular forces»

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seems to encompass crystal engineering. What is a (molecular) crystal if not an “organized entity of higher complexity held together by intermolecular forces”? In van der Waals solids the attractive forces acting between molecules, regarded as ensembles of atoms, fall off very rapidly with the distance. Repulsions are effective at very short distances and much dependent on the nature of the peripheral atoms, which determine the electrostatic potential hypersurface surrounding the molecule. In this way the bulk of the molecule provides attraction, while surface atoms determine recognition, optimum relative orientation and interlocking of molecules in the solid state. In general, a given supramolecular arrangement in the solid state can be seen as the result of the minimization of short-range repulsions, rather than the optimization of attractions. It is therefore important, when considering a molecular crystal, to focus on the relationship between molecular shape and nature of the peripheral atoms. In the absence of directing interactions, resulting, for example, from the presence of strong dipoles or hydrogen bonding donor-acceptor groups (see below), the recognition process will be controlled by the outer shape of the molecule and by the nature of the peripheral atoms. The formation of a stable dimolecular aggregate – as the initial step of a crystallization process - whether formed by the same molecule, i.e. AA, or by two different molecules/ions, i.e. AB, or A+/–B–/+, will depend primarily on the complementarity of shape. This concept was put forward by L. Pauling long ago[23] : “... in order to achieve the maximum stability, the two molecules must have complementary surfaces, like die and coin, and also a complementary distribution of active groups. The case might occur in which the two complementary structures happened to be identical; however, in this case also the stability of the complex of two molecules would be due to their complementariness rather than their identity”. The interaction between van der Waals molecules with different shapes is depicted schematically in Figure 3. As mentioned above, molecules and coordination networks are convenient nanometre-scale building blocks that can be used, in a bottom-up approach, to construct larger aggregates, whether supermolecules or crystalline materials. The controlled assembly and manipulation of three-dimensional nanostructures with well-defined shapes, profiles and functionalities present a significant challenge to nanotechnology. Since chemists know how to synthesize, characterize and exploit molecular aggregation, the molecular approach to functional nanostructures is a natural development of the progress in the field.

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Figure 3. Top: the interaction between van der Waals molecules with complementary shapes; molecules of type A can be joined by molecules of type B forming a van der Waals network structure; bottom: discoidal molecules (in projection) form a herringbone pattern.

3. Crystal Engineering and Polymorphism Crystal polymorphism,[24, 25] the existence of more than one crystal packing arrangement for the same molecular or ionic substance(s), has become one of the “hot issues” of CE. This is true even though the phenomenon is a drawback for the purposed bottom-up construction of functional solids because the actual packing arrangement or the existence of more than one packing for the same molecule, are unpredictable. The fact that crystallization cannot be considered, in many cases, a fully reproducible step, or that, on slightly changing preparation and crystallization conditions, one may obtain different crystal structures, hence attain different bulk properties, may be seen as the nemesis of crystal engineering ambitions to control the assembly of molecules into crystals and therefrom the crystal properties. To complicate the matter further, there is the possibility of formation of solvates. Solvatomorphism[26] refers to cases in which a given substance is known to crystallize with different amounts or types of solvent molecules.[27] Clearly the possibility of existence of polymorphic modifications of a given solvate ought also to be taken into account. Polymorphic and solvate modifications of the same substance can also be obtained by thermal and mechanical treatment and by solvation and desolvation (see below). A schematic representation of the relationship between polymorphic and solvatomorphic forms of a molecular crystal is shown in Figure 4.

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Polymorphic modifications can be seen as crystal isomers arising from different distributions of intermolecular interactions. Hence, the change in crystal structure associated with an interconversion of polymorphs, i.e. a solid-to-solid phase transition (between ordered phases), in which intermolecular interactions are rearranged, can be regarded as the crystalline equivalent of an isomerisation at the molecular level. Even though polymorphic modifications contain exactly the same substance, they usually differ in chemical and physical properties such as density, solubility, melting point, stability, reactivity, colour, bioavailability and mechanical properties etc. In spite of the efforts of a great number of research groups worldwide, and of a familiarity with the experimental factors that can lead to multiple crystal forms, our ability to predict or control the occurrence of polymorphism is still embryonic. The exploration of the “crystal form space” (polymorph screening) of a substance is the search of the polymorphs and solvates with a twofold purpose: 1) identification of the relative thermodynamic stability of the various forms including the existence of enantiotropic crystalline forms (that interconvert as a function of the temperature) or of monotropic forms (that do not interconvert) and of amorphous and solvate forms and 2) physical characterization

Figure 4. Schematic representation of the relationship between polymorphs, solvates and amorph of a molecular crystal. From top: two polymorphic modifications of the same molecular systems differing in the relative orientation of the components; a solvatomorphic modification of the two ideal crystals above, the circles representing cocrystallized solvent molecules or other guests. The possible presence of amorphous phases is also taken into account.

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of the crystal forms with as many analytical techniques as possible [microscopy and hot stage microscopy (HSM), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), infrared and Raman spectroscopy (IR and Raman), single crystal/powder X-ray diffraction (SCXRD, XRPD), solid state nuclear magnetic resonance spectroscopy (SSNMR)]. The relationships between the various phases and commonly used industrial and research laboratory processes are schematically illustrated in Figure 5. There has been a recent burst of activity in developing crystallization techniques and variables for obtaining new crystal forms,[28] some of which are described in the next section. The efficiency of screening protocols, whether high throughput automatic methods or manual procedures, can be considerably increased by carrying out preliminary HSM, DSC and variable temperature XRPD investigations for initial detection of multiple phases and the temperature ranges of their existence, as well as transformations among them. These observations can then be summarized with a semiempirical energy-temperature diagram;[29, 30] 1, 3, 11, 12

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Figure 5. Some general relationships between polymorphs, solvates and amorphous phases and the type of research lab or industrial process for preparation and interconversion: 1, Crystallization; 2, Desolvation; 3, Exposure to solvent/vapour uptake; 4, Freeze drying; 5, Heating; 6, Melting; 7, Precipitation; 8, Quench cooling; 9, Milling; 10, Spray drying; 11, Kneading; 12, Wet granulation. Analogous relationships apply to polymorphic modifications of solvate forms. Note that the figure represents general trends rather than every possible transformation; the presence or absence of an arrow or number does not represent the exclusive existence or absence of a transformation.

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in particular, it is possible to determine if various phases are related enantiotropically (reversibly) or monotropically (non-reversibly). Once the thermodynamic screening of the crystalline product has been completed, the quest for new forms can extend to the investigation of the effect of changing the solvent or the mixture of solvents and/or to the temperature gradient, the presence of templates or seeds. Examples of the utilization of variable temperature diffraction methods (VT-XRPD) to investigate phase transitions between enantiotropic systems and desolvation processes are shown in Figures 6 and 7, respectively.

Figure 6. DSC and VT-XRPD measurements applied to the investigation of phase transitions between Form I (bottom pattern, RT) and Form II (middle pattern, 89°C) of anthranilic acid. The top pattern is that of the molten acid.

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Form II calc. pattern

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Figure 7. Variable temperature XRPD measurements applied to the investigation of the dehydration of barbituric acid dihydrate with formation of Form I of barbituric acid.[35–39]

4. Crystal Engineering and Solid-State Reactivity Since crystal engineering deals with crystals, the investigation of solid-state reactions or of reactions involving crystalline materials benefits enormously from the understanding of the crystal packing. Moreover, most reactions occurring between solids or involving solids are solvent-free[40] which is an important development because of the strive for environmentally benign reaction conditions.[41] Another goal of great interest is the exploitation of solid-gas reactions as alternative routes for the construction of molecular traps, sieves and sensors. Diverse applications of host-guest chemistry in a variety of crystalline organic inclusion compounds have been described.[42–44] For instance inclusion compounds, in which chiral crystal structures are obtained from racemic or achiral molecules, have been investigated, with application of such compounds to the synthesis of species in which the crystal structure chirality is imprinted upon the achiral molecular components.[45] When achiral molecules cannot be arranged in a chiral form in the crystal, they can be arranged in a chiral form in inclusion complex crystals with a chiral host compound. Reactions

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of the inclusion complex in the solid state have been shown to give the optically active compound.[46, 47] 4.1. SOLID-GAS REACTIVITY

An important application of CE is the investigation of reactions between engineered molecular solids and molecules in the vapour phase (see Figure 8). Heterogeneous gas-solid reactions are well known in chemistry thanks to the pioneering work of Curtin and Paul.[48] It is important to appreciate that in the case of reactions between gases and solids the costs of removing and reprocessing solvents are eliminated. This goes along with the great pressure on developing solvent-free, i.e. environmentally more friendly reactions.

Figure 8. Schematic representation of the formation of a new molecular solid by solid-gas reaction and/or by gas uptake and solvate formation.

Uptake and release of solvent molecules (solvation, hydration) can often be paralleled to solid-gas reactions, whereby the reactants are respectively the molecules in the crystalline solid and the molecules in the gas phase, and the product is the solvated crystal.[49] Clearly, the same reasoning applies to the reverse process, i.e. generation of a new crystalline form by removal of volatile components from the crystal structure. In gas-solid reactions, gases are reacted directly with crystals or amorphous phases to give solid products, often in quantitative yields.[50, 51] Curtin and Paul have extensively investigated solid-gas reaction. In the benzoic acid-ammonia system, they were able to show that certain crystal faces are attacked preferentially by the ammonia vapour, and the resulting reaction front travels more rapidly through the crystals along directions corresponding to specific molecular arrangements.[52–55] Crystalline p-chlorobenzoic anhydride reacts with gaseous ammonia to give the corresponding amide and ammonium salt;[56] similar reactions have been investigated in the case of optically active cyclopropane carboxylic acid crystals.[52]

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Kaupp has explored a series of solid-state reactions in which gaseous amines are reacted with aldehydes to give imines. Analogous reactions with solid anhydrides, imides, lactones or carbonates, and isothiocyanates have been used to give, respectively, diamides or amidic carboxylic salts or imides, diamides, carbamic acids, and thioureas.[57] In a number of cases investigated the yields were found to be quantitative. Ammonia and other gaseous amines, in particular methylamine, have also been shown to aminolyse thermoplastic polycarbonates.[58–60] Gaseous acids have been shown to form salts with strong and weak solid nitrogen bases. Solid hydro halides are formed quantitatively by reaction with vapours of HCl, HBr and HI; the same applies to di-bases such as o-phenylendiamines. The products are much more easily handled than when they are formed in solution. The solid products can in turn be used to react with gaseous acetone to form the corresponding dihydrohalides of 1,5-benzodiazepines.[61, 62] The possibility of switching between neutral and charged hydrogen bonding interactions is at the basis of the gas-trap system obtained on reacting the organometallic complex [CoIII(η5-C5H4COOH)(η5-C5H4COO)] with both acid and base vapours (HCl, CF3COOH, HBF4, and NH3, NH2Me, NMe3) (see Table 1).[63, 64] TABLE 1. Products of the reaction of crystalline [CoIII(η5-C5H4COOH)(η5-C5H4COO)] with acid and base vapours

The salts resulting from the heterogeneous reaction contain the sandwich compound either in its fully protonated form [CoIII(η5–C5H4COOH)2]+ (in the reaction with acids) or in its fully deprotonated form [CoIII(η5– C5H4COO)2]– (in the reaction with bases), as shown in Figure 9. The two types of reactions imply the interconversion between neutral O-H···O hydrogen bonding interactions and (+)O–H···X(-) and (-)O···H—N(+) interactions, respectively.

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Figure 9. Reversible gas-solid reactions of the organometallic species [CoIII(η5–C5H4COOH) (η5– C5H4COO)] with vapours of HCl (a) and NH3 (b).

In the coordination chemistry field it has been reported that self-assembled organoplatinum(II) complexes, containing N,C,N terdentate coordinating anion “pincers”, reversibly and quantitatively bind gaseous SO2 in the solid state by Pt-S bond formation and cleavage, giving five-coordinate adducts.[65, 66] The five-coordinate adduct is also crystalline and the reverse reaction, viz. the release of SO2, preserve crystalline ordering. The Ptcomplex can thus be seen as a crystalline supermolecule able to switch “on” and “off” as a direct response to gas uptake and release. At the end of this section one may argue that the reaction of a molecular solid, whether formed of organic, organometallic molecules or coordination compounds, with a vapour is conceptually related to the supramolecular reaction of a crystalline material with a volatile solvent to form a new crystalline solid. Indeed, the two processes, solid-gas reaction and solid-gas solvation, differ only in the energetic ranking of the interactions that are broken or formed through the processes. In solvation-desolvation processes one is dealing mainly with non-covalent van der Waals or hydrogen bonding interactions, whilst in chemical reactions covalent bonds are broken or formed. This awareness is useful to devise crystal engineering strategies based on gas uptake, whereby the process can be exploited to generate new

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crystalline forms and to produce new materials. Clearly, the conceptual borderline between the two types of processes is very thin. One may purposefully plan to assemble molecules that are capable of absorbing molecules from the gas phase and, possibly, to react with them. Reaction implies sensing and could be exploited to detect molecules, if there is a measurable response from the solid state. If the reaction is quantitative and reversible, the same processes can be used to trap gases and deliver them where appropriate. The control on solid-state reactions, that can be used to trap environmentally dangerous or poisonous molecules, is an attractive goal for solid-state chemistry and crystal engineering. 4.2. LESS CONVENTIONAL METHODS TO OBTAIN CRYSTAL TRANSFORMATIONS

As mentioned in the previous section the size of the crystals will dictate the experimental method of choice. Unless one recurs to high intensity synchrotron radiations, microcrystals will allow only powder diffraction experiments, which only rarely can be used for ab-initio structure determination in order to get those precise structural information that are so essential to the crystal engineer. Clearly, the solvent-less reactions of a crystalline powder with a vapour or that between two crystalline powder are, generally speaking, not compatible with the formation of large single crystals since it will generally produce a material in the form of a powder. Non-solution methods to obtain new products require the chemist, or crystal engineer, to explore/exploit methods that are not routinely used in chemical labs. Reactions of the type described herein require broadening the view of typical chemical processes. Beside the conventional “academic” chemical reaction procedures (typically Schlenk techniques if air sensitive organometallic molecules are synthesised as building blocks) one has to resolve to methods, such as grinding and milling, that are less popular – when they are not dismissed as non-chemical – in research labs. These methods are related to the mechanical activation of reactions occurring between solids and to the control exerted on the crystallization process.[67–70] 4.2.1. Grinding and Milling Typically reactions, but also co-crystal formation, can be activated and carried out by grinding or milling of powder materials. Grinding is usually carried out either manually, in an agate mortar, or electro-mechanically, as in ball milling. In both cases the main difficulty is in controlling reaction conditions: grinding time, temperature, pressure exerted by the operator, etc. Furthermore, the heat generated in the course of the mechanical process can induce local melting of crystals or melting at the interface between the different crystals, so that the reaction takes place in the liquid phase even

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though solid products are ultimately recovered. One should also keep in mind that mechanical stress, by fracturing the crystals, increases surface area and facilitates interpenetration and reaction depending on the ability of molecules to diffuse through the crystal surfaces. Under this viewpoint, inter-solid reactions between molecular crystals can be conceptually related to the uptake of a vapour from a molecular solid to form a new crystalline solid. Mechanical processes, and more generally solid-state reactions, though little exploited at the level of academic research, are commonly used at industrial level mainly with inorganic solids and materials.[71–74] 4.2.2. Kneading (also called wet grinding, solvent drop grinding) Even though the discussion of the role of solvent in a chapter devoted to solvent-free reactions may seem contradictory, it is useful to remind the reader that, in some cases, the use of a small quantity of solvent can accelerate (when not make altogether possible) solid-state reactions carried out by grinding or milling.[75] The method of the grinding of powdered reactants in the presence of a small amount of solvent, also known as kneading, is commonly exploited, for instance, in the preparation of cyclodextrin inclusion compounds. Studies of kneading and development of lab/industry kneaders (mainly of pharmaceutical powders) have been carried out.[76, 77] As an example of preparatory lab scale, one could mention the preparation by kneading of binary β-cyclodextrin-bifonazole,[78] and of β-cyclodextrin inclusion compounds of ketoprofen,[79] ketoconazole[80] and carbaryl.[81] Clearly, the objection about whether a kneaded reaction between two solid phases can be regarded as a bona fide solid-state process is justified. However, in the context of this work, our interest lies more in the methods to make new crystalline materials rather than in the mechanisms. Kneading (also called wet grinding, solvent drop grinding) has been described as a sort of “solvent catalysis” of the solid-state process, whereby the small amount of solvent provides a lubricant for molecular diffusion. 4.2.3. Seeding An important consequence of the utilization of “non-crystallization” methods to prepare new crystalline materials is that the products of grinding, milling and kneading are generally in the form of a powdered material (whether polycrystalline or amorphous). Single crystals on the other hand are very useful, when not indispensable, for the full structural characterization of a reaction product. A way to control the growth of single-crystals of adequate size from a finely powdered material is by seeding the solution with a tiny amount of microcrystals of the desired materials. Seeding procedures are commonly employed in pharmaceutical and pigment industries to make sure that the desired crystal form is always obtained from a preparative process, a relevant problem when different polymorphic modifications can

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be obtained.[26, 82] It is also important to appreciate that seeding often allows to control whether a metastable or a stable crystal form is precipitated out from solution. Seeds of isostructural or quasi-isostructural species that crystallise well can also been employed to induce crystallisation of unyielding materials (heteromolecular seeding).[83–85] For instance, chiral co-crystals of tryptamine and hydrocinnamic acid have also been prepared by crystallization in the presence of seeds of different chiral crystals.[86] Of course, unintentional seeding may also alter the crystallization process in an undesired manner.[87] 4.2.4. Supercritical Fluids Recently, a new approach to crystallization and polymorph selection has been developed by using supercritical fluids as solvents.[88] A supercritical fluid is a dense non-condensable fluid that can behave as a solvent since the solvent power is proportional to the density. For organic materials, such as pharmaceuticals, the most widely used supercritical fluid is carbon dioxide because its supercritical state can be reached at a temperature where most organic species are perfectly stable (31.2°C, 7,4 MPa). Among the various new applications of supercritical carbon dioxide, the particle size engineering and polymorph screening are areas of intense investigation. 4.3. MECHANICAL PREPARATION OF HYDROGEN BONDED ADDUCTS AND CO-CRYSTALS

In this section we provide examples mainly coming from our own work of mechanical preparation of new materials. Manual grinding of the ferrocenyl dicarboxylic acid complex [Fe(η5-C5H4COOH)2] with solid nitrogen containing bases, namely 1,4-diazabicyclo[2.2.2]octane, 1,4-phenylenediamine, piperazine, trans-1,4-cyclohexanediamine and guanidinium carbonate, generates quantitatively the corresponding organic-organometallic adducts (see Figure 10a).[89, 90] The case of the adduct [HC6N2H12][Fe(η5-C5H4COOH) (η5-C5H4COO)] (see Figure 10b) is particularly noteworthy because the same product can be obtained in three different ways: (i) by reaction of solid [Fe(η5-C5H4COOH)2] with vapours of 1,4-diazabicyclo[2.2.2]octane (which possesses a small but significant vapour pressure), (ii) by reaction of solid [Fe(η5-C5H4COOH)2] with solid 1,4-diazabicyclo[2.2.2]octane, i.e. by co-grinding of the two crystalline powders, and by reaction in MeOH solution of the two reactants. Clearly, the fastest process is the solid-solid reaction. It is also interesting to note that the base can be removed by mild treatment regenerating the structure of the starting dicarboxylic acid. The processes imply breaking and reassembling of hydrogen-bonded networks, conformational change from cis to trans of the -COO/-COOH groups on the ferrocene diacid, and proton transfer from acid to base. As mentioned above

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in some cases it was necessary to resolve to seeding, i.e. to the use of a tiny amount of power of the desired compound, to grow crystals suitable for single-crystal X-ray experiments.

(a)

(b) Figure 10. (a) Grinding of solid [Fe(η5-C5H4COOH)2] (top centre) with the solid bases 1,4diazabicyclo[2.2.2]octane, C6H12N2 (top right), guanidinium carbonate, [(NH2)3C]2[CO3] (top left), 1,4-phenylenediamine, p-(NH2)2C6H4, (bottom right), piperazine, HN(C2H4)2NH, (bottom left) trans-1,4-cyclohexanediamine, p-(NH2)2C6H10, (bottom centre) generates quantitatively the corresponding adducts [HC6H12N2][Fe(η5-C5H4COOH)(η5-C5H4COO)], [C(NH2)3]2[Fe(η5-C5H4COO)2]·2H2O, [HC6H8N2][Fe(η5-C5H4COOH)(η5-C5H4COO)], [H2C4– H10N2] [Fe(η5-C5H4COO)2], [H2C6H14N2][Fe(η5-C5H4COO)2]·2H2O. (b) The solid-gas and solid-solid reactions involving 1,4-diazabicyclo[2.2.2]octane with formation of the linear chain.

The effect of mechanical mixing of solid dicarboxylic acids HOOC (CH2)nCOOH (n = 1–7) of variable chain length together with the solid base 1,4-diazabicyclo[2.2.2]octane, C6H12N2, to generate the corresponding salts or co-crystals of formula [N(CH2CH2)3N]-H-[OOC(CH2)nCOOH] (n = 1–7) has also been investigated.[90] The reactions implied transformation of interacid O-H—O bonds into hydrogen bonds of the O-H—N type between acid and base, an example is shown in Figure 11. The nature (whether neutral O-H—N or charged (–)O—H-N(+)) of the hydrogen bond was established by

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means of solid-state NMR measurement, the chemical shift tensors of the compounds obtained with chain length from 3 to 7.[91]

Figure 11. The product of the reaction of the solid base 1,4-diazabicyclo[2.2.2]octane, C6H12N2, with solid adipic acid generates a chain structure of formula [N(CH2CH2)3N]-H[OOC(CH2)4COOH]. Note how the O-H—O hydrogen bonds present in the solid acid are replaced by neutral O-H—N and charged (–)O—H-N(+) upon transfer of one proton from the acid to the base.

The mechanical formation of hydrogen-bonded co-crystals between sulphonamide (4-amino-N-(4,6-dimethylpyrimidin-2-yl) benzene sulphonamide) and aromatic carboxylic acids has been investigated by Caira et al.[92]

Figure 12. Hydrogen bonding patterns in Form I (top) and Form II (bottom) of [HN(CH2CH2)3NH][OOC(CH2)COOH]2. Form I is obtained by solid-state co-grinding or by rapid crystallization, while form II is obtained by slow crystallization.

In a related study[93] by us it has been shown that the reaction of [N(CH2CH2)3N] with malonic acid [HOOC(CH2)COOH] in the molar 1:2 ratio yields two different crystal forms of the salt [HN(CH2CH2)3NH]

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[OOC(CH2)COOH]2 depending on the preparation technique and crystallization speed: the less dense form I, containing mono-hydrogen malonate anions forming conventional intramolecular hydrogen bonds between hydrogen malonate anions, is obtained by solid-state co-grinding or by rapid crystallization while a denser form II containing intermolecular hydrogen bonds is obtained by slow crystallization (see Figure 12). Form I and II do not interconvert, while form I undergoes an order-disorder phase transition on cooling. These observations led the authors to wonder whether the two forms could be treated as bona fide polymorphs or should be regarded more appropriately as hydrogen bond isomers of the same solid supermolecule. 4.3.1.

Mechanical Preparation of Coordination Networks

Even though the mechanical preparation of the metallamacrocycles described in the previous section was not possible, coordination polymers with bidentate nitrogen bases can be prepared mechanically.[94] The coordination polymer Ag[N(CH2CH2)3N]2[CH3COO]·5H2O has been obtained by co-grinding in the solid state and in the air of silver acetate and of [N(CH2CH2)3N] in 1:2 ratio (see Figure 13). Single crystals suitable for X-ray diffraction have been obtained from a water-methanol solution and used to compare calculated and experimental X-ray powder diffractograms.

Figure 13. The coordination network in Ag[N(CH2CH2)3N]2[CH3COO]·5H2O. Note the chain of Ag—[N(CH2CH2)3N]—Ag—[N(CH2CH2)3N]—Ag with each silver atom carrying an extra pendant [N(CH2CH2)3N] ligand and a coordinated water molecule in tetrahedral coordination geometry.

When ZnCl2 is used instead of AgCH3COO in the equimolar reaction with [N(CH2CH2)3N], different products are obtained from solution and solid-state reactions, respectively. The preparation of single crystals of Ag[N(CH2CH2)3N]2[CH3COO]·5H2O was obviously indispensable for the determination of the exact nature of the co-grinding product. In order to do so the powder diffraction pattern computed on the basis of the single-crystal

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structure was compared with the one measured on the product of the solidstate preparation. Figure 14 shows that the structure of Zn[N(CH2CH2)3N]Cl2 is based on a one-dimensional coordination network constituted of alternating [N(CH2CH2)3N] and ZnCl2 units, joined by Zn-N bonds. As mentioned above, upon co-grinding of the solid reactants a new Zn compound of unknown stoichiometry is obtained as a powder material. Even though attempts to obtain single crystals of this latter compound have failed, there is a relationship between the compound obtained initially by co-grinding and the one obtained from solution. In fact, the co-grind phase can be partially transformed by prolonged grinding into the known anhydrous phase Zn[N(CH2CH2)3N]Cl2 shown in Figure 14.

Figure 14. The one-dimensional coordination network present in crystals of Zn[N(CH2CH2)3N]Cl2 a and a comparison of the powder diffraction pattern measured on the product of initial co-grinding and that obtained after prolonged grinding. Note how, this latter coincides with the diffractogram computed on the basis of the single crystal structure depicted on top.

Steed and Raston et al. have explored the use of mechanochemistry in the synthesis of extended supramolecular arrays.[95] Grinding of Ni(NO3)2 with 1,10-phenanthroline (phen) resulted in the facile preparation of [Ni(phen)3]2+ accompanied by a dramatic and rapid colour change. Addition of the solid sodium salt of tetrasulfonatocalix[4]arene (tsc) gives two porous π-stacked supramolecular arrays [Ni(phen)3]2[tsc4-]·nH2O and the related [Na(H2O)4

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(phen)][Ni(phen)3]4 [tsc4-][tsc5-]·nH2O depending on stoichiometry. It has also been reported that the co-grinding of copper(II) acetate hydrate with 1,3-di(4-pyridyl)propane (dpp) gives a gradual colour change from blue to blue-green over ca. 15 min. The resulting material was shown by solid state NMR spectroscopy to comprise a 1D coordination polymer with water-filled pores. The same host structure, [{Cu(OAc)2}2(μ-dpp)]n, could be obtained from solution containing methanol, acetic acid or ethylene glycol guest species.[96] 5. Crystal Engineering, Where to? Making crystals by design is the paradigm of crystal engineering.[10, 97] In 1999 we wrote in the preface of the proceedings of the Erice 1999 School on crystal engineering: “crystal engineering is an interdisciplinary area of research that cuts horizontally across traditional subdivisions of chemistry, e.g. organic, inorganic, organometallic, materials chemistry and biochemistry. The spectacular growth in the chemistry and properties of complex supramolecular systems has fuelled further interest in controlling and exploiting the aggregation of molecules in crystals.” [1] The field is still expanding and diversifying its goals. The advancement results as a sort of cultural hybridization between supramolecular chemistry, e.g. the chemistry of intermolecular bonding, and the chemistry of molecular materials, e.g. the utilitarian, application oriented side of molecular aggregation. Crystal engineering is a branch of the chemical science. The chemists know how to synthesize, isolate and characterize molecules and to assemble molecules in a bottom-up approach to larger and more complex aggregates. In a sense, crystal engineering is modern solid state chemistry, or, more appropriately perhaps, it is an evolutionary step of solid-state chemistry across disciplinary borders. Crystal engineering shares with supramolecular chemistry the idea that the collective properties of the solid aggregates depend upon the choice of intermolecular and inter-ion interactions between components, and are attained via processes of self-recognition and assembly (although crystallization is often under kinetic control). CE shares with materials chemistry the goal of preparing functionalized crystalline materials. Crystal-oriented synthetic strategies are finding applications in various directions, from nano-porous and meso-porous systems to ionic networks and molecular materials for applications in magnetism, but also in non-linear optics, conductivity, solid-state sensors etc. One can expect that these target properties will all be at the forefront of research in materials chemistry in the coming years. In this respect it is apparent that organometallic and coordination compounds represent an extraordinary source of new building

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blocks for crystal construction and, therefore, of new or improved solidstate properties. Where do we stand almost eight years later? Scientists know well the “parabolic” behaviour of scientific “hot topics”: a new topic starts slowly, then catches up and interest “explodes”, attracts funds and energetic scientists, the number of papers increases at an exponential pace, then a plateau is reached to then start a more or less rapid descent on the other side of the parable. The “life-time” of a new research subject depends on how deeply the results of the research efforts affect the development of knowledge as a whole and on the contamination of neighbouring areas of research. How does this apply to crystal engineering? Eight years the paradigm was clear: “make crystals with a purpose”. For this reason the 1999 Erice school was entitled “crystal engineering, from molecules and crystals to materials”. We all thought that by learning how to engineer crystals bottom-up by choosing molecular and ionic building blocks with a strategic view of the properties we wanted to obtain, we might be able to prepare useful crystals, i.e. materials. But perhaps no one could have guessed that crystal engineering was going to have such a large cross-disciplinary impact. Under the CE “umbrella topic” today we find papers on, for instance: (1) green chemistry. the preparation of new crystalline materials by means of solid state reactivity and by means of solid-solid and solid-gas reactions can be exploited to reduce pollution and solvent disposal;[98] (2) nanotechnology: molecules have nanometric dimensions, therefore the intelligent and purposeful assembly of molecules in crystalline structures, falls in the burgeoning field of nanochemistry;[2-4] (3) pharmaceuticals: crystal polymorphism, solvatomorphism, co-crystals are searched and investigated in view of the differences in physical and chemical properties with impact on the utilization, marketing and intellectual property protection of drugs. The pharmaceutical chemist is devoting more and more attention on the properties of solids and crystals;[99] (4) energy: metal-organic frameworks, MOF, nano- and meso-porous systems are investigated for potential application as gas storage devices, but also as electrolytes in fuel cell technology;[100] and this is only to mention few of the new crystal engineering fields of expansion. Large progresses have been made, both in those areas where the bottomup approach seemed more promising and in new ones, where old paradigms could be rediscovered and sometimes re-written. In 2007, we no longer question the assertion that crystal properties can be engineered bottom-up from molecules and ions and their intermolecular links. However, the “black magic” of crystallization remains an unmet challenge. No recipe

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exists to predict the shape or size, let alone space group, of the crystals that will eventually form from a solution of a new chemicals, nor whether the crystals will be thermodynamically stable or metastable, or whether they will undergo phase changes with temperature or pressure, or include solvent molecules upon crystallization, or whether this solvent could be removed or replaced without destroying the crystal edifice. Furthermore, we are brilliantly unable to predict whether crystallization will yield a powder, or a single crystal, or different single crystals, and which shape they will have, or amorphous materials, or all these together. Everything can be solid but not every solid obeys Bragg’s law. Indeed, many of the most interesting materials are disordered or amorphous and their characterization adds up to the challenge. The a-priori prediction of crystal polymorphism and solvatomorphism is still a chimera while not even the most thorough polymorph screening can guarantee above all doubts that the most thermodynamically stable crystals of a given species have been ultimately obtained. Fortunately, much remains on the road of “The Three Princes of Serendip”, who in their wandering “were always making discoveries, by accidents and sagacity, of things which they were not in quest of”.[101] Discoveries are still in front of us, which can be recognized and turned into new science because of training, readiness of mind and enthusiasm. 6. Acknowledgments Some of us acknowledge financial support from the University of Bologna and from MiUR. PolyCrystalLine s.r.l., the spinoff company of the University of Bologna, thanks the SPINNER project for financial support.

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90. D. Braga, L. Maini, M. Polito, L. Mirolo and F. Grepioni, Chem. Commun. 2960 (2002) 91. D. Braga, L. Maini, G. de Sanctus, K. Rubini, F. Grepioni, M. R. Chierotti and R. Gobetto, Chem. Eur. J. 9, 5538 (2003) 92. M. R. Caira, L. R. Nassimbeni and A. F. Wildervanck, J. Chem. Soc., Perkin Trans. 2 2213 (1995) 93. D. Braga and L. Maini, Chem. Commun. 976 (2004) 94. D. Braga, S. L. Giaffreda, F. Grepioni and M. Polito, CrystEngComm 6, 458 (2004) 95. P. J. Nichols, C. L. Raston and J. W. Steed, Chem. Commun. 1062 (2001) 96. W. J. Belcher, C. A. Longstaff, M. R. Neckenig and J. W. Steed, Chem. Commun. 1602 (2002) 97. D. Braga and F. Grepioni (Editors) Making Crystals by Design, Wiley-VCH (2006) 98. P. Anastas and J. Warner Green Chemistry: Theory and Practice (1998). K. Tanaka and F. Toda, Solvent-Free Organic Synthesis, Synthesis Wiley-VCH, London, 2003. D. Braga and F. Grepioni Angew Chem. Int Ed. 43, 2 (2004). D. Braga and F. Grepioni Chem. Commun. 3635 (2005). F. Toda ed. Topics in Current Chemistry, Springer, 254, 1-305 (2005) 99. R. Hilfiker, Polymorphism, Wiley VCH, Weinheim (2006). B. Rather, and M. J. Zaworotko Chem. Commun. 830 (2003). B. Moulton, H. Abourahma, M. W. Bradner, J. Lu, G. J. McManus and M. J. Zaworotko Chem. Commun. 1342 (2003). H. G. Brittain J. Pharm. Sc. 96, 705 (2006) 100. S. M. Haile, D. A. Boysen, C. R. I. Chisholm and R. B. Merle Nature 410, 910 (2001). X. Lin, J. Jia, X. Zhao, K. M. Thomas, A. J. Blake, G. S. Walker, N. R. Champness, P. Hubberstey and M. Schröder Angew. Chem., Int. Ed. 45, 7358 (2006). S. Takamizawa, E. Nakata and T. Akatsuka Angew. Chem. Int. Ed. 45, 2216 (2006). S. M. Neville, B. Moubaraki, K. S. Murray and C. J. Kepert, Angew. Chem., Int. Ed. 46, 2059 (2007). R. Matsuda, R. Kitaura, S. Kitagawa, Y. Kubota, R. V. Belosludov, T. C. Kobayashi, H. Sakamoto, T. Chiba, M. Takata, Y. Kawazoe and Y. Mita Nature 436, 238 (2005). 101. The Yale Edition of Horace Walpole’s Correspondence, ed. W. S. Lewis, New Haven, Yale University Press, 1937-83, vol. XVII, p. xxiii; R. K. Merton and E. Barber, The travels and adventures of serendipity, Princeton University Princeton University Press, Princeton (2004)

NANOSTRUCTURED FRAMEWORKS FOR MATERIALS APPLICATIONS

NEIL R. CHAMPNESS School of Chemistry, The University of Nottingham, University Park, Nottingham NG7 2RD, U.K. Tel: (+44)115-9513505; Fax: (+44)115-9513563; E-mail: [email protected]

Abstract. Strategies for the synthesis of frameworks materials based upon either coordination bonds or hydrogen-bonding interactions are described. The utilization of coordinate bonds for the construction of coordination frameworks is presented describing not only strategies for controlling framework structure but also illustrating how such networks can be used for applications in the storage of guest species, such as H2. The exploitation of hydrogen-bonding for generating self-assembled surface arrays is also described, again illustrating controlled molecular entrapment for nanostructure fabrication. Keywords: Coordination Frameworks; Metal-Organic Frameworks; Hydrogenbonding; Surface self-assembly; Nanostructures; Nanoscience

1. Introduction The study of framework materials has been an area of sustained interest in materials science for many years, predominantly due to the necessity to control solid-state structure on the micro-, meso- or nano-scale to infer given properties to a material. Porous materials have enjoyed a particularly high profile in this area of chemistry due to their ability to accommodate guest species within their overall arrangement thus acting as storage vessels for the guest. In addition porous arrays can act to position molecules, or small particles, acting as a synthetic mould to prepare new nano-structured arrays. This article serves to bring together two seemingly distinct areas of materials science, coordination frameworks and surface self-assembled structures, and draws comparisons between the respective strategies employed for ultimately similar aims. Both areas utilize supramolecular chemistry and intermolecular interactions, whether coordination bonds or 157 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 157–171. © 2008 Springer.

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hydrogen-bonds, to combine molecular building-blocks into extended arrays. The simple geometrical strategies employed are common to both areas as is the desire to create voids within the structures produced. The use of these nanostructured pores or channels as storage vessels for molecular species is also common to both areas. The major difference between the two areas lies only in the three-dimensional structure of the crystalline solid produced by coordination frameworks, whether comprised of one-, two-, three- or zero-dimensional subcomponents as with other molecular crystals, in comparison to the requirement to produce two-dimensional frameworks in the surface environment. 2. C oordination Frameworks for Materials Applications The study of coordination frameworks, or metal-organic frameworks (MOFs), is an area of research that has received a rapid rise to the forefront of modern materials science [1]. The area has grown from the initial reports of Robson [2] to highly advanced design strategies [3–5], structural appreciation [6,7] and fascinating materials properties [8–14]. This article will attempt to address some of the issues that need to be considered when preparing coordination frameworks including design strategies and will highlight selected examples of how the design of the framework can be utilized for a specific materials application.

2.1. SYNTHETIC STRATEGIES FOR COORDINATION FRAMEWORKS

2.1.1. The Building-Block Approach Although generic strategies for the synthesis of coordination frameworks have often been proposed, a recent article by Yaghi [6] indicates that designed synthesis of framework structures is still relatively undeveloped and requires significant further research. Despite the large number of published coordination frameworks a large proportion of these reported structures adopt the simplest and most symmetrical topologies. The prevalence of particular structures probably arises due to the simple brilliance of the building-block approach [2] that gives direction to how certain structures may be targeted. Thus if a tetrahedral node, or buildingblock, is employed, most commonly a tetrahedrally coordinating transition metal cation [Cu(I) [15], Ag(I) [16] etc.], then by far the most commonly observed structure is the diamond-net (Figure 1) [6]. Similarly, octahedrally-connected nets have a high tendency to form primitive cubic structures [6]. The large number of such structures that have been produced reflects the ease of employing particular metal cation building-blocks and

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the widespread use of linear bridging ligands, presumably due to their commercial availability. For other building-block geometries and hence connectivities, e.g. trigonal, square-planar and trigonal-bipyramidal arrangements there is less significant preference for a particular structure and a greater diversity is seen with these more flexible systems perhaps there is more scope for the directed synthesis of particular structural topologies [6]. Indeed, the absence of a significantly favored geometrical arrangement of the metal-based node, or indeed flexibility of ligand coordination modes, whether for the whole framework or for a specific component (metal, ligand), often leads to greater structural diversity in the final framework materials.

Figure 1. View of a diamond-like net formed by tetrahedral nodes and linear linking groups [16].

This point is clearly demonstrated by the lanthanide-based coordination frameworks [17] and in particular those formed with the ligand 4,4’bipyridyl-N,N’-dioxide. [18–23] For this series of coordination frameworks the geometrical flexibility of the lanthanide(III) cations accompanied by the coordinative flexibility of the N-oxide donor groups, giving a range of M-O-N angular arrangements, results in a highly diverse family of compounds (Figure 2) with unusual topological structures and connectivities including three-dimensional five- [19], six- [20, 21], seven-[21] and eight-connected [21, 22] frameworks in addition to highly-connected bilayer structures. [21, 23]

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(a)

(b)

(c)

Figure 2. Views of representative topological nets formed by lanthanide-based coordination frameworks with the ligand 4,4’-bipyridyl-N,N’-dioxide; (a) an eight connected threedimentional net [21]; 9b0 a five connected three-dimentional net [19] and (c) an eight connected bilayer net [21].

2.1.2. Secondary Building-Blocks; Anions and Solvent Framework structure is not only controlled by metal cation and bridging ligand geometry even though these represent the most significant buildingblocks in terms of their influence over coordination polymer structure. As with all aspects of crystal engineering, the crystal as a whole must be considered and weak forces and interactions may have a significant effect upon the stability of a particular structural arrangement over that of a different assembly. For coordination frameworks, other building-blocks or components can become highly significant in determining framework structure, in particular counter-anions and reaction solvent. Two distinct types of counter-anions can be employed in constructing coordination frameworks, coordinating and non-coordinating anions. Noncoordinating anions generally have less impact upon the frameworks structure, as they do not interfere directly with the geometry of the metal

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node but clearly have an impact in terms of occupying space or by additional weak interactions [24]. Coordinating anions can dramatically alter coordination framework structure and topology. It is possible to use anionic bridging ligands, such as dicarboxylates [8], to create neutrally-charged frameworks thus negating the need for ancillary, space-filling, counter-anions. However it is also possible to use simpler counter-anions that can act to coordinate metal centres and influence the overall framework structure. This is demonstrated by the role played by NO3– anions [25] for example in comparison to BF4– or PF6– [26]. The role played by the NO3– anions in comparison to weakly or non-coordinating BF4– or PF6– anions is demonstrated by the Ag(I) complexes of 4-pytz (4-pytz = 1,4-bis-(4-pyridyl)-2,3,4,5-tetrazine) [26]. The linear chain complexes formed by {[Ag(4-pytz)]PF6}1 and {[Ag(4pytz)]BF4}1, contrasts significantly with the “helical staircase” complex formed between AgNO3 and 4-pytz, {[Ag(4-pytz)]NO 3}1 (Figure 3). In the case of {[Ag(4-pytz)]NO3} 1 the structure of the complex comprises Ag(I) ions each coordinated to two 4-pytz ligands in a linear arrangement to give linear chains of alternate Ag(I) cations and bidentate N-donor ligands. Each Ag(I) ion also exhibits weak interactions with two NO3 – ions, Ag…O = 2.787(2)Å, which adopt positions perpendicular to the pyridyl–Ag–pyridyl axis. The NO3– ions bridge adjacent Ag–bipyridyl chains through two of their oxygen atoms so that each Ag(I) chain is related to the next by a 60° rotation and a step of 5.18 Å, generating a helical staircase. Thus, it can be

Figure 3. View of the helical staircase formed by {[Ag(4-pytz)]NO3 } 1 in which the NO3– anion plays a critical role in determining the three-dimensional structural arrangement.

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seen that the three-dimensional structure is controlled via the Ag–ONO2 interactions. It is clear that the coordinating ability of an anion can have a significant effect upon coordination polymer structure and in the case of the NO3– anion the role played by the anion has been recently reviewed [25]. It is also possible for non-coordinated anions to affect coordination polymer structure in more subtle, but potentially equally significant, ways. For example many anions have significant hydrogen-bonding ability such that the anion may interact with hydrogen bond donors, either as part of the ligands used or in the form of other species connected to the coordination framework structure such as coordinated water molecules [27]. Detailed and comprehensive studies of anion effects are scarce although examples are known for some Ag(I)-pyridyl based systems amongst others [28].

(a)

(b)

Figure 4. Views of (a) the ladder formed by [Zn 2(NO3 ) 4 (3-pytz) 3] 1 from the reaction of Zn(NO3 ) 2 with 3-pytz in either EtOH or iPrOH (b) the one-dimentional hydrogen-bonded chain formed from the reaction of Zn(NO3 ) 2 with 3-pytz in MeOH.

The reaction/crystallisation solvent may also have a significant impact on coordination polymer structure in a similar manner to that observed for anions. The coordinating ability of a solvent can have a particular influence on polymer structure, occupying coordination sites and influencing coordination sphere and geometry. This is demonstrated by the structures formed from the reaction of Zn(NO3)2 with 3-pytz (3-pytz = 1,4-bis-(3pyridyl)-2,3,4,5-tetrazine) [29]. When 3-pytz is reacted with Zn(NO3)2 in an EtOH (or iPrOH) – CH2 Cl2 mixture each Zn(II) centre adopts a T-shaped

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motif which is utilised in the formation of a ladder coordination polymer [Zn2(NO3)4(3-pytz)3]1, Figure 4a. However, the T-shaped geometry at the Zn(II) centre is disrupted when MeOH is used as the alcoholic solvent with the MeOH molecule coordinating the metal centre allowing only two residual sites for pyridyl coordination. This results in the formation of a hydrogen-bonded 1D polymer, Figure 4b. 2.1.3. Ligand Design – Multimodal Ligands Coordination framework structure can also be controlled by ligand design Clearly simple variation in numbers of donors and angular orientations can be used to control structure topology [30] but more intricate ligand design can also be employed such as demonstrated by multimodal ligands [31–35]. Multimodal ligands differ from simpler unimodal systems in that they offer both more than one binding site, usually both monodentate and chelating multidentate donor sites and in some cases more than one than one bridging mode. The influence that multimodal ligands can exert on the structure of a coordination framework is demonstrated by the products from the reaction of Ag(I) salts, AgBF4 or AgPF6 , with the multimodal ligand 2,2’-bipyrazine (bpyz) [33, 34]. When the reaction is performed using MeNO2 as a solvent, isotopological three-dimensional coordination polymers are formed, {[Ag(bpyz)](BF4)}1 [33, 34] or {[Ag(bpyz)](PF6 )}1 [33], both of which crystallize in the chiral space group P43212. The Ag(I) center adopts a uniform coordination sphere throughout the polymeric architecture being coordinated by three bpyz ligands in a pseudo-tetrahedral geometry, one chelating and two monodentate N-donors. Each Ag(I) center is linked to four nearest-neighbor Ag(I) centers, two via the chelating ligand and two more through two peripheral monodentate N-donors forming a distorted diamond-like array (Figure 5). Inspection of the framework structure reveals two distinct channels that represent different helices running through the network. The larger squareshaped channel constructs a 43 helix in which each Ag(I) center is linked to the next Ag(I) center along the helix via a short, single pyrazine bridging mode. In contrast, the smaller rhomboid-shaped channel forms a 21 helix in which adjacent Ag(I) centers are linked through a longer bridging mode via two peripheral N-donors of a bpyz ligand. In contrast to a conventional diamondoid lattice in which adjacent helices have opposing hands and are chemically identical, in {[Ag(bpyz)](BF4)}1 adjacent anti-parallel helices are chemically distinct, displaying different bridging modes and resulting in the chirality demonstrated by these architectures. The role of t he multimodal ligand is crucial in influencing the architecture of these compounds and in inducing the chirality of the framework that is observed.

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Figure 5. View of the chiral three –dimensional array formed by {[Ag(bpyz)](BF4 )}1 [33].

Other supramolecular interactions associated with the ligand design, such as 3-3 interactions, may influence the structure [36, 37], although this potential factor has not been studied in any detail for coordination polymer systems. Despite the structural flexibility for certain systems highly successful strategies for targeting families of coordination frameworks have been reported, the IRMOF series of compounds reported by Yaghi and coworkers for example [8], and design strategies for coordination polymers and frameworks have become increasingly well refined [38, 39]. As a result of the predictability of certain structures it has become possible to deliberately design porous coordination frameworks and as a result use the porosity of the structures to store guest molecules. 2.2. GUEST STORAGE IN COORDINATION FRAMEWORKS

The nanostructured pores of coordination frameworks allow such materials to be used to store guest molecules. Particularly elegant examples of using the porous nature of such materials [40] to store a variety of volatile organic compounds (VOCs) [41] and interestingly metal nanoparticles [42] have been reported illustrating the widespread potential of coordination frameworks in the role of storage agent.

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Perhaps the most widely studied type of storage is in the adsorption of gaseous molecules including N2, CO2, CH4 [40] and perhaps most interestingly H2 [43, 44]. Extensive studies by Yaghi [45], Ferey [46] and Long [47] amongst others have led to the formation of highly effective materials for the storage of H2 . We have recently demonstrated remarkable examples of coordination frameworks for the effective storage of H2 in copper-carboxylate based coordination frameworks [44]. The ligand 3,5,3’,5’-biphenyl tetracarboxylate acts as a 4-connected linker to join Cu2(O2CR)4 paddlewheel nodes into three-dimensional NbOtype coordination frameworks [44] (Figure 6). The length of the ligand linker between Cu(II) cation nodes in such structures can be varied by using biphenyl, terphenyl or quaterphenyl groups within the ligands backbone, leading to a family of isotopological framework structures without interpenetration. The desolvated samples have the chemical composition [Cu2(L)]1 where L = L1, L2, L3 (L1 = 3,5,3’,5’-tetracarboxylate biphenyl; L2= 3,5,3’,5’-tetracarboxylate terphenyl, L3= 3,5,3’,5’-tetracarboxylate quaterphenyl). Increasing ligand length results in increasing BET surface areas and MOF pore volumes with values of 1670 m2/g (pore volume = 0.680 cm3/g), 2247 m2/g (pore volume = 0.886 cm3/g), and 2932 m2/g (pore volume = 1.138 cm3/g), for [Cu2(L1)]1, [Cu2(L2)]1, and [Cu2(L3)]1, respectively. Thus, longer linking ligands generate higher porosity as long as the framework topology remains unchanged and no interpenetration occurs. The H2 adsorption data for [Cu2(L1)]1, [Cu2(L2)]1, and [Cu2(L3)]1 were recorded over two pressure regions revealing H2 adsorption of 2.57 wt% for [Cu2(L1)]1, 2.52wt% for [Cu2(L2)]1, whilst the most porous [Cu2(L3)]1 can only adsorb 2.24wt% at 1 bar H2 pressure. These adsorption values appear to be in contradiction to the surface area/pore volume measurements for each framework material. However, H2 uptakes at 20 bar increase in a consistent manner with the increasing pore volume with values of 4.02wt% [Cu2(L1)]1, 6.06wt% [Cu2(L2)]1 and 6.07wt% [Cu2(L3)]1 at 77K. These values are close to adsorption saturation, however, H2 adsorption of [Cu2(L2)]1 and [Cu2(L3)]1 has not reached saturation at 20 bar. The estimated saturation uptake for [Cu2(L3)]1 is at least 7.01wt%, depending on the theoretical model applied comparable to values observed for MOF-177 [45] the other coordination framework that exhibits the highest values for H2 adsorption.

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Figure 6. View of the structure of [Cu2 (L )] 1. This coordination framework absorbs up to 7.01wt% of H2 at 20bar and 77K.

3.

Using Crystal Engineering Strategies for Surface Based Self-Assembly

The use of hydrogen-bonds to create multi-dimensional arrays in the solid-state has a relatively long tradition and has provided the backbone for the development of crystal engineering as a discipline [48]. The hydrogen-bonding supramolecular synthons open to the crystal engineer are many, some exhibiting greater reliability than others. One such interaction is that formed between diaminopyridine and imide moieties [49] which comprise a robust and highly predictable triple intermolecular hydrogenbond. By utilizing this interaction solid state arrays have been successfully prepared with the archetypal example illustrated by the adduct formed between cyanuric acid (CA) and melamine (M) [50]. 3.1. SURFACE SELF-ASSEMBLY USING HYDROGEN BONDS ENABLING NANOSTRUCTURE FABRICATION

We have employed a strategy of using the robust triple hydrogen-bond between diaminopyridine and imide moieties to generate two-dimensional arrays on surfaces. Such arrays are typically constructed by the selfassembly of the two components when adsorbed on a suitable surface in ultra-high vacuum (UHV) conditions [51–54]. It is also possible to use

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intermolecular interactions to assemble molecules on surfaces in a solutionbased environment [55–57]. In our studies we have predominantly focused on the self-assembly of hydrogen-bonded arrays in UHV. Thus we have successfully prepared a series of one- and two-dimensional arrays on either the Ag–Si(111)(23x 23)R30o or Au(111) surface. In particular we have demonstrated the assembly of the archetypal CA-M network that can be formed either by sequential deposition of CA followed by M or, significantly, by simultaneous deposition of CA and M (Figure 7). The framework formed is studied by scanning tunneling microscopy (STM) allowing molecular imaging of the self-assembled array. CA forms large hexagonally ordered islands with a lattice constant equal to that of the Ag–Si(111)(23x 23)R30o surface, 6.65 Å. After sublimation of melamine a honeycomb structure is formed at the edges of the CA domain which is identified as the CA-M framework. In contrast to some other systems CA desorbs overnight under the conditions of the experiment leaving only the less volatile heteromolecular CA-M complex on the surface. In addition the CA-M complex can be formed directly, without traces of the single component CA islands, by simultaneous deposition of CA and M, indicating a significant preference for incorporation of CA molecules into the CA-M network under these conditions. This is a direct consequence of the greater stability of the CA-M phase as compared with CA or M islands. These studies demonstrate a direction relationship between the solid-state chemistry of the CA-M framework and the structure formed in the surface environment. We have also demonstrated the formation of other self-assembled arrays with a notable example being that formed by the triple hydrogen-bond formed between melamine and perylene tetra-carboxylic di-imide (PTCDI) on either a Ag–Si(111)(23x 23)R30o [52] or Au(111) surface [54]. Self-assembly of melamine and PTCDI forms an open honeycomb network formed in which melamine molecules, which have three-fold symmetry, form the vertices of the network while the straight edges correspond to PTCDI (Figure 8). The network is stabilized by melamine–PTCDI hydrogen-bonding. Melamine and PTCDI are particularly applicable to form such a network due to their expected stronger hetero- as opposed to homo-molecular hydrogen bonding. The resultant structure was studied by STM housed within the UHV system, at room temperature, and it is possible to clearly discern the positions of the two molecules. The incorporation of linear PTCDI edge molecules into the bimolecular melamine-PTCDI assembly yields pores that are much larger, 2.5 nm in diameter, than the constituent building blocks of the network and thus capable of serving as traps, or vessels, for the co-location of several large molecules.

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Figure 7. STM image of the CA-melamine network formed on a Ag– Si(111)(23x 23)R30o surface.

Figure 8. (a) STM image of the PTCDI-melamine framework formed on a Ag–Si(111) o (23x 23)R30 surface; (b) schematic representation of the triple hydrogen-bonding interactions observed between melamine and three PTCDI molecules forming the node of the PTDCI-array.

The potential of the framework to act as a trap for other molecules has been demonstrated by subliming either C60 [52, 54] or C84 [58] onto the hexagonal network. As can be seen in the STM image (Figure 9) heptameric C60 clusters with a compact hexagonal arrangement of the individual molecules form within the pores following deposition of 0.03ML of C60 [52]. The heptameric clusters are stabilised by the PTCDI–melamine network and the fraction of pores containing adsorbed molecules and stabilized heptameric clusters increases with increasing C60 coverage. Addition of further adsorbed C60 molecules results in the formation of a second layer of C60 which reproduces the pattern of the underlying hydrogen-bonded melamine-PTCDI hexagonal network. The formation of clusters of C60 molecules controlled by the hydrogen-bonded framework illustrates the potential to use such self-assembled structures for the controlled fabrication of nanostructures on the 2–5 nm scale.

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Figure 9. (a) STM image and (b) schematic representation of encapsulated heptamers of C6 0 trapped framework formed on a Ag–Si(111) (23x 23)R30o surface.

4.

Conclusions

This article has attempted to illustrate that by exploiting the predictable intermolecular interactions provided by supramolecular chemistry both twodimensional and three-dimensional structures can be generated either on surfaces or in the solid-state respectively. In both instances it is possible to create pores within the self-assembled structure which can be used to trap molecular species, notably gaseous molecules for crystalline coordination frameworks or fullerenes for surface based arrays. In the latter case it has been demonstrated that by creating large surface-based pores multimolecular nanostructures can be fabricated. The parallels between the two approaches are apparent and illustrate how cross-fertilization of ideas between what may be viewed as distinct areas serves to allow the development of entirely new materials chemistry.

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8. N.L. Rosi, J. Eckert, M. Eddaoudi, D.T. Vodak, J. Kim, M. O’Keeffe and O.M. Yaghi, (2003) Science, 300, 1127–1129. 9. X.B. Zhao, B. Xiao, A.J. Fletcher, K.M. Thomas, D. Bradshaw and M.J. Rosseinsky, (2004) Science, 306, 1012–1015. 10. R. Kitaura, S. Kitagawa, Y. Kubota, T.C. Kobayashi, K. Kindo, Y. Mita, A. Matsuo, M. Kobayashi, H.C. Chang, T.C. Ozawa, M. Suzuki, M. Sakata and M. Takata, (2002) Science, 298, 2358–2361. 11. D. Maspoch, D. Ruiz-Molina, K. Wurst, N. Domingo, M. Cavallini, F. Biscarini, J. Tejada, C. Rovira and J. Veciana, (2003) Nature Mater., 2, 190–195. 12. E. Coronado, J.R. Galan-Mascaros, C.J. Gomez-Garcia and V. Laukhin, (2000) Nature, 408, 447–449. 13. A.R. Millward and O.M. Yaghi, (2005) J. Am. Chem. Soc., 127, 17998–17999. 14. O. Kahn, (2000) Acc. Chem. Res., 33, 647–657. 15. L.R. MacGillivary, S. Subramanian and M.J. Zaworotko, (1994) J. Chem. Soc. Chem. Commun., 1325–1326; A.J. Blake, N.R. Champness, S.S.M. Chung, W.-S. Li and M. Schröder, (1997) Chem. Commun., 1005–1006. 16. L. Carlucci, G. Ciani, D.M. Proserpio and A. Sironi, (1994) J. Chem. Soc., Chem. Comm., 2755–2756. 17. R.J. Hill, D.-L. Long, N.R. Champness, P. Hubberstey and M. Schröder, (2005) Acc. Chem. Res., 38, 337–350. 18. P. Hubberstey, M. Schröder and N.R. Champness, (2005) J. Solid State Chem., 178, 2414–2419. 19. D.-L. Long, A.J. Blake, N.R. Champness, C. Wilson and M. Schröder, (2001) J. Am. Chem. Soc., 123, 3401–3402. 20. D.-L. Long, R.J. Hill, A.J. Blake, N.R. Champness, P. Hubberstey, C. Wilson and M. Schröder, (2005) Chem. Eur. J., 11, 1384–1391. 21. D-L. Long, A.J. Blake, N.R. Champness, C. Wilson and M. Schröder, (2001) Angew. Chem., Int. Ed., 40, 2444–2447. 22. D-L. Long, R.J. Hill, A.J. Blake, N.R. Champness, P. Hubberstey, D.M. Proserpio, C. Wilson and M. Schröder, (2004) Angew. Chem., Int. Ed., 43, 1851–1854. 23. R.J. Hill, D-L. Long, M.S. Turvey, A.J. Blake, N.R. Champness, P. Hubberstey, C. Wilson and M. Schröder, (2004) Chem. Commun., 1792–1793. 24. C.A. Black, L.R. Hanton and M.D. Spicer, (2007) Inorg. Chem., 46, 3669–3679 25. S.A. Barnett and N.R. Champness, (2003) Coord. Chem. Rev., 246, 145–168. 26. M.A. Withersby, A.J. Blake, N.R. Champness, P. Hubberstey, W.-S. Li and M. Schröder, (1997) Angew. Chem., Int. Ed. Engl., 36, 2327-2329. 27. R.W. Gable, B.F. Hoskins and R. Robson, (1990), J. Chem. Soc. Chem. Commun., 1677– 1678. 28. A.J. Blake, G. Baum, N.R. Champness, S.S.M. Chung, P.A. Cooke, D. Fenske, A.N. Khlobystov, D.A. Lemenovskii, W.-S. Li and M. Schröder, (2000) J. Chem. Soc., Dalton Trans., 4285–4291. 29. M.A. Withersby, A.J. Blake, N.R. Champness, P.A. Cooke, P. Hubberstey, W.-S. Li and M. Schröder, (1999) Inorg. Chem., 38, 2259–2266. 30. O.V. Dolomanov, D.B. Cordes, N.R. Champness, A.J. Blake, L.R. Hanton, G.B. Jameson, M. Schröder and C. Wilson, (2004) Chem. Commun., 642–643. 31. N.S. Oxtoby, A.J. Blake, N.R. Champness and C. Wilson, (2002) Proc. Natl. Acad. Sci. (USA), 99, 4905–4910. 32. F. Thebault, A.J. Blake, C. Wilson, N.R. Champness and M. Schröder, (2006) New. J. Chem., 30, 1498–1508.

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Commun. 665–666. 35. A. Jouaiti, V. Jullien, M.W. Hosseini, J.-M. Planeix and A. De Cian, (2001) Chem.

Commun., 1114–1115. 36. A.J. Blake, N.R. Champness, A.N. Khlobystov, D.A. Lemenovskii, W.-S. Li and M. Schroder, (1997) Chem. Commun., 1339–1340. 37. I. Dance, (2005) Mol. Cryst. Liq. Cryst., 440, 265–293. 38. A.J. Blake, N.R. Champness, P. Hubberstey, W.-S. Li, M.A. Withersby and M. Schröder, (1999) Coord. Chem. Rev., 183, 117–138. 39. A.N. Khlobystov, A.J. Blake, N.R. Champness, D.A. Lemenovskii, A.G. Majouga, N.V. Zyk and M. Schröder, (2001) Coord. Chem. Rev., 222, 137–158. 40. S. Kitagawa, R. Kitaura and S. Noro, (2004) Angew. Chem. Int. Ed., 43, 2334–2375. 41. X. Lin, A.J. Blake, C. Wilson, X.Z. Sun, N.R. Champness, M.W. George, P. Hubberstey, R. Mokaya and M. Schröder, (2006) J. Am. Chem. Soc.,128, 10745–10753. 42. S. Hermes, M.K. Schroter, R. Schmid, L. Khodeir, M. Muhler, A. Tissler, R.W. Fischer, R.A. Fischer, (2005) Angew. Chem. Int. Ed., 44, 6237–6241. 43. J. Jia, X. Lin, C. Wilson, A.J. Blake, N.R. Champness, P. Hubberstey, G. Walker, E.J. Cussen and M. Schröder, (2007) Chem. Commun., 840–842. 44. X. Lin, J. Jia, X. Zhao, K.M. Thomas, A.J. Blake, G.S. Walker, N.R. Champness, P. Hubberstey and M. Schröder, M. (2006) Angew. Chem. Int. Ed., 45, 7358–7364. 45. A.G. Wong-Foy, A.J. Matzger and O.M. Yaghi, (2006) J. Am. Chem. Soc., 128, 3494– 3495. 46. M. Latroche, S. Suble, C. Serre, C. Mellot-Draznieks, P.L. Llewellyn, J.-H. Lee, J.-S. Chang, S.H. Jhung and G. Ferey, (2006), Angew. Chem. Int. Ed., 45, 8227–8231. 47. M. Dinca, A. Dailly, Y. Liu, C.M. Brown, D.A. Neumann and J.R. Long, (2006) J. Am. Chem. Soc., 128, 16876–16883. 48. “Perspectives in Supramolecular Chemistry: The Crystal as a Supramolecular Entity”, ed. G. R. Desiraju, Wiley, Chichester, 1996, vol. 2. 49. G.M. Whitesides, E.E. Simanek, J.P. Mathias, C.T. Seto, D.N. Chin, M. Mammen and D.M. Gordon, (1995) Acc. Chem. Res., 28, 37–44. 50. A. Ranganathan, V.R. Pedireddi and C.N.R. Rao, (1999) J. Am. Chem. Soc., 121, 1752– 1753. 51. L.M.A. Perdigão, N.R. Champness and P.H. Beton, (2006) Chem. Commun., 538–540. 52. J.A. Theobald, N.S. Oxtoby, M.A. Phillips, N.R. Champness and P.H. Beton, (2003) Nature, 424, 1029–1031. 53. D.L. Keeling, N.S. Oxtoby, C. Wilson, M.J. Humphry, N.R. Champness and P.H. Beton, (2003) Nano Lett., 3, 9–12. 54. L.M.A. Perdigão, E.W. Perkins, J. Ma, P.A. Staniec, B.L. Rogers, N.R. Champness and P.H. Beton, (2006) J. Phys. Chem. B, 110, 12539–12542. 55. K.E. Plass, A.L. Grezesiak and A.J. Matzger, (2007) Acc. Chem. Res., 40, 287–293. 56. S. de Feyter, A. Miura, S. Yao, Z. Chen, F. Würthner, P. Jonkheijm, A.P.H.J. Schenning, E.W. Meijer and F.C. de Schryver, (2005) Nano Lett. 5, 77–81. 57. S. Griessl, M. Lackinger, M. Edelwirth, M. Hietschold and W.M. Heckl, (2002) Single Mol., 3, 25–31. 58. J.A. Theobald, N.S. Oxtoby, N.R. Champness, P.H. Beton and T.J.S. Dennis, (2005) Langmuir, 21, 2038–2041.

CRYSTAL ENGINEERING OF MULTIFUNCTIONAL MOLECULAR MATERIALS

EUGENIO CORONADO, CARLOS GIMÉNEZ-SAIZ, CARLOS MARTÍ-GASTALDO Instituto de Ciencia Molecular, Universitat de Valencia Polígono de la Coma, s/n, 46980 Paterna, SPAIN

Abstract. In this paper we will focus on the crystal engineering of molecular materials exhibiting magnetic and/or electrical properties. The complexity of these materials needs of a precise design of the molecular building blocks, a control of the intermolecular interactions (hydrogen bonds, host/guest interactions, etc.) and a mastery in crystallization techniques in order to design crystal structures exhibiting useful physical properties. We will illustrate this concept through some relevant examples based on two-component hybrid materials.

1.

Introduction

Multifunctionality is a general trend in the materials community, and molecule-based materials are attracting much attention in this regard as they are already known to exhibit most technologically important properties traditionally considered to be solely available for atom-based inorganic solids (e.g., magnetic ordering, electrical conductivity, superconductivity, ferroelectricity, non-linear optics, etc.). In this aspect the possibilities offered by the molecular bottom-up approach are unparalleled in the world of continuous lattice solids. Thus, the control attained in both molecular design and supramolecular assembling of the building blocks can be useful to design the crystal structure of the material allowing for a fine-tuning of its cooperative properties. In this lecture we will try to illustrate this concept in the case of molecular materials formed by two-component structures obtained through a self assembling of two different molecular building blocks. In particular, we will focus on the crystal engineering of molecular materials exhibiting magnetic and/or electrical properties.

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Magnetic Molecular Materials

The magnetic properties of a molecular material are strongly dependent on the way the molecular building blocks are interconnected and interacting. Thus, many synthetic efforts have been devoted in this area to control these interactions. Apart from the covalent bonding, other supramolecular interactions as hydrogen bonding or even electrostatic interactions can play an important role in this direction. In this part we will illustrate with several examples taken from coordination chemistry how the topology and dimensionality of a magnetic lattice can be controlled by taking advantage of these supramolecular interactions. The oxalate dianion (ox = C2O42–) has demonstrated to be one of the most versatile ligands used in the search for molecule-based magnets. In its bis-bidentate chelate form, it affords a wide number of possibilities for the tuning of magnetic properties. Thus, in these systems, the topology, dimensionality and the sign of the magnetic exchange can be controlled at will allowing for the preparation of a large variety of novel multifunctional magnetic materials (hybrid magnets1, 2, chiral magnets3, 4, conducting magnets5 or photoactive magnets6, 7). A high number of oxalate-based molecular magnets has been obtained following the well-known “bimetallic approach”. In this synthetic strategy a molecular building block, [Cr(ox)3]3– (see Figure 1) is used as a ligand towards divalent metallic cations resulting in the formation of lowdimensional anionic complexes which remain in solution. The addition of a bulky inorganic cation, [XR4]+, pushes these anionic moieties to self-assemble in solution resulting in the precipitation of non-soluble coordination polymers. The first example in this direction was reported by Okawa in the beginning of the 90’s with the synthesis of a family of 2D layered magnets (see Figure 1) with general formula: [XR4][MIIMIII(ox)3] (XR4+ = NBu4+; MIII = Cr; MII = Mn, Fe, Co, Ni, Cu, Zn) which presented ferromagnetic ordering from 6 to 12 K.8 Following this same synthetic strategy, the magnetic behaviour of the final material can be controlled by tuning the chemical identity of its components. The synthesis of the Fe (III), Ru (IIII), V(III) and Mn(III) derivatives has yielded analogous layered molecular magnets showing ferro-, ferri- and weak ferromagnetic ordering with critical temperatures up to 45 K.9–15 Although the stabilization and isolation of anionic polymeric oxalatebased networks in solution is accomplished by the addition of bulky alkylic cationic counterions these cations also act as templating agents. Therefore, the dimensionality of the final system can be controlled by the suitable choice of the cationic molecule. This point is exemplified by the use of [ZII(bpy)3]2+ chiral cations which stabilize a chiral 3D lattice affording hybrid materials of formula [ZII(bpy)3][ClO4][MIIMIII(ox)3] (Z = Fe, Co, Ni

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and Ru).3,4 To explain this higher dimensionality we must focus on the chirality of the bimetallic network. While metallic centers exhibit alternated chirality in the honeycomb 2D systems, the 3D polymers are composed of homochiral units. From a geometrical point of view, the existence of only one diasteroisomer building-block avoids the possibility of growing along the plane, forcing the system to grow in a 3D manner. These compounds behave as ferro- and ferrimagnets with lower temperatures than their 2D analogues. This point can be explained attending to weaker magnetic exchange resulting from the longer metal to metal distances and the different relative orientation of the magnetic orbitals.

Figure 1. Schematic representation of the “bimetallic-approach”, illustrating the importance of templating cations in the formation of oxalate-based polymeric networks.

In the two previous examples, the shape, size, geometry and bulkiness of the cations are key elements for the preparation of the different oxalatebased architectures. This consideration pushed us to use as templating cations complexes based on crown ethers, as for example [K-(18-crown6)]+ (see Figure 2) because two main reasons Its planar shape could result in the formation of novel magnetic topologies, while the presence of hydrogen-bonding oxygen donors in its structure could introduce supramolecular interactions that would play an important role in determining the final assembling of the molecular entities. Besides, this cation can make the final material more soluble in water and polar solvents. The combination of long range magnetic ordering and solubility turns these compounds into a novel family of “dual-function materials”. In fact, this unprecedented feature makes these compounds excellent candidates for materials processing and hybrid materials preparation by intercalation chemistry. The first successful example in this direction has been the isolation of the ferromagnetic oxalate-based polymeric chain: {[K-(18-crown-6)][Mn (H2O)2Cr(ox)3]}∞ (1).16 This compound is built up by three alternated layers,

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Figure 2. Structure of the 1,4,7,10,13,16-hexaoxacyclooctadecane (18-crown-6) (left) and and 1,4,7,10,13-Pentaoxa-cyclopentadecane (15-crown-5) (right) organic molecules.

formed respectively by [K(18-crown-6)]+ cationic molecules (A), [Mn(H2O) Cr(ox)3]– anionic chains (B) and neutral 18-crown-6 molecules (C) with a repeating pattern. The polymeric chains are conformed by [Cr(ox)3]3– molecules covalently bonded to Mn (II) ions through the organic ligand acting as a bis-bidentate linker. While the divalent ions are octahedrally surrounded by two chelating oxalate ligands and two coordinating water molecules the Cr(III) atoms are coordinated in an octahedral fashion to two bridging and one terminal oxalate ligand. One water molecule bounded to the Mn (II) center is pointing towards the neutral crown ether molecule while the other is interacting with the neighbouring chain through a quite strong hydrogen bond (O•••O 2.176 Å) with an oxygen atom from an

Figure 3. Perspective showing the alternated packing of the alternated layers. Hydrogen bonding interactions directing the oxalate-based anionic chains assembling. Dc and heat capacity measurement for compound 1.

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oxalate terminal ligand. The rest of the oxalate terminal ligands are oriented towards the cationic [K(18-crown-6)]+ complexes as a consequence of the electrostatic interaction between the potassium atom located within the crown cavity and one of the oxygen atoms belonging to the organic ligands (O•••K 2.654 Å). This interaction also determines the pseudo-hexagonal packing of the cationic crown ether complexes on the ab plane. Each neutral layer is sandwiched by two anionic layers in such a way that oxygen atoms from the 18-crown-6 ether molecules show some hydrogen bonding contacts with two water molecules from the adjacent anionic layers, one above and one below (O•••O 2.778 and 2.879 Å). These weak supramolecular interactions in the solid state force these crown ether molecules appear perfectly ordered if compared to those belonging to the cationic layer. This compound exhibits ferromagnetic ordering below 3.5 K resulting from the ferromagnetic intrachain and weak ferromagnetic interchain interactions provided by the existence of hydrogen bonding interactions connecting the chains. Small modifications in the synthetic procedure has allowed for an increase of the dimensionality of this sort of compounds leading to the synthesis of a quasi- 2D honeycomb lattice with formula [K-(18-crown6)][Mn3(H2O)4{Cr(ox)3}3]17 (2). This compound is composed by cationic [K-(18-crown-6)]+ and anionic [Mn3(H2O)4{Cr(ox)3}3]– layers. The anionic polymeric network reminds the well-known honeycomb structural motif but, in this case, the connectivity is broken by the presence of water molecules in the divalent ions coordination sphere, pushing part of the oxalate groups to act as terminal ligands. The hydrogen bonding interactions between these later water molecules and the oxygen atoms belonging to the terminal oxalate ligands (O•••O 2.588 and 2.634 Å) retains the pseudo-hexagonal structural motif. In fact, if the coordinated water molecules were eliminated, with the corresponding H-bonded oxalate ligands taking its place as chelating moieties, the result would be the formation of the typical 2D structure. The cationic crown ether complexes packing must be also attributed to noncovalent interactions. In fact, electrostatic interactions between the K+ atom (O•••K 3.104 and 3.180 Å) and the terminal organic ligand take place, along with hydrogen bonding between the oxygen atoms belonging to the crown ether molecules and the water molecules bonded to the Mn (II) centers belonging to the anionic layers (O•••O 2.712 and 2.738 Å). As a consequence, the [K(18-crown-6)]+ units adopt a pseudo-hexagonal packing, with the mean plane for the crown ether molecules essentially perpendicular to the c axis, and therefore forming an angle of approximately 26º with the ab plane. This particular orientation creates an interlayer separation of 8.18 Å, as the distance between the mean plane of adjacent anionic layers. The lower connectivity of the metals within the layer forces the magnetic ordering to occur at a lower temperatures than for the classical

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Figure 4. Perspective showing the 2D fragmented honeycomb structure of the oxalate-based anionic network on the ab plane. Alternated packing of the anionic and cationic layers along the space (up). Dc and Ac measurements performed onto compound 2 (down).

2D network (Tc = 3.3 K for the MnIICrIII derivative, compared to 5.5 K in the classical 2D lattice). An interesting structural feature in 2 is that the cationic crown ether complexes are slightly displaced from the central position of the hexagonal channels defined by the bimetallic anionic oxalate-based network. This result contrasts with that found in other 2D polymeric networks where the cations locate at the centre of the channels (see for example the series [MIICp*2][MIIMIII(ox)3],2,18. Therefore, this displacement is somehow avoiding the formation of the regular 2D hexagonal structure. A possible reason for this difference is the larger diameter of the 18-crown-6 ether molecule compared to that of the [MIICp*2]+ (see Figure 5). In order to prove our considerations, we introduced in the bimetallic lattice the smaller 15-crown-5 ether molecule. This way, we succeeded in the isolation of the [K-(15-crown-5)2][MnCr(ox)3] (3) 2D magnet, which is composed by the classical 2D bimetallic oxalate-based layers, [MnCr(ox)3]–,

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Figure 5. Bulky space representation of the cationic complexes: [K-(18-crown-6)]+ (left),[FeCp*2]+ (middle) and [K-(15-crown-5)2]+ (right).

Figure 6. Perspective of compound 3 structure along the ab plane showing the [K(15-crown5]+ sandwich complexes alignment along the hexagonal channels defined by the classical 2D honeycomb structure (down-left). View of the multirayed structure of 3 (down-right).

and by cationic layers of [K-(15-crown-5)2]+ complexes. The cationic [K(15-crown-5)2]+ complexes show a typical sandwich structure, similar to that of the [MIICp*2]+, with the potassium atom located in the central position as a consequence of the electrostatic interactions with its neighbouring oxygen atoms (O•••O from 2.888 to 3.235 Å). In this case the

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cationic units are, as expected, perfectly located in the central position defined along the hexagonal channels. They adopt a pseudo-hexagonal packing along the ab plane, defining an anionic interlayer separation of around 13 Å.

Figure 7. Perspective showing the structure of the 2D oxalate-based framework on the ac plane (left). Picture showing the hydrogen bonding interactions (dashed line) between the oxalate network and the neutral guest crown ether molecule (right).

Another valuable example has been obtained following a similar synthetic strategy, but employing 18-crown-6 neutral molecules instead of the potassium cationic complex. This change has afforded the isolation of the first neutral layered compound of the bimetallic oxalato series: {[Co(H2O)2]3[Cr(Ox)3]2}(18-crown-6)2 (4). This compound is build up by neutral layers of formula [Co(H2O)2]3[Cr(Ox)3]2, leaving holes in the 2D structure occupied by the 18-crown-6 guest molecules (see Figure 7). Each layer is formed by twelve membered rings, constituted by six [Cr(ox)3]3– units and six Co (II) atoms. While each chromium atom is shared between three rings the cobalt centers are shared between two adjacent rings. Within these rings each Co(II) ion is coordinated by two bridging oxalate ligands from [Cr(ox)3]3– units and two water molecules. The importance that hydrogen bonding interactions play in the formation of this compound is also remarkable. The two crown ether molecules located in the middle of each 12-membered structural unit are interacting through their oxygen atoms with the bonded water molecules (O•••O 2.692 and 3.043 Å). In this case, the existent supramolecular interactions not only determine the packing of the crown ether molecules in the solid state but act as the driving force in the isolation of the polymeric network without the requirement of an external templating cation. This neutral complex behaves as a soft ferromagnet below 7.5 K and is also soluble in water and polar solvents.

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A rational approach to decrease the dimensionality of these types of complexes consists of using capping organic ligands. This way bimetallic chains as well as discrete polynuclear compounds, such as oxalate-bridged dimers,19,20 trimers21,22 or tetramers23,24 have been obtained. An illustrative result of this approach has been provided by substituting in compound 2 the coordinating water molecules bounded to the Mn (II) centers with capping organic ligands. Thus, the use of Mn(bpy)Cl2 (bpy = C10H8N2) instead of MnCl2 in the synthesis 2 results in the isolation of the chain compound [K(18-crown-6)][Mn(bpy)Cr(ox)3] (5).25

Figure 7. Pespective showing the alternated packing of cationic and anionic complexes along the ac plane and the zig-zag conformation of the 1D oxalate-based polymeric chains. Dc measurements for compound 5 (solid line represents the best fitting to a 1D Heisenberg chain model).

This compound is made up by alternated anionic [Mn(bpy)Cr(ox)3]– oxalate-bridged bimetallic chains and cationic [K(18-crown-6)]+ complexes. The bimetallic chain is composed by [Cr(ox)3]3– complexes and MnII ions bridged through bidentate oxalate ligands. Each Cr center is surrounded by two oxalate bis-bidentate and a terminal oxalate ligands in a regular octahedral coordination geometry. The MnII metallic centres are also octahedrally coordinated by two chelating oxalate bridging molecules and an organic 2,2´-dipyridyl molecule. It is important to note how the substitution of the coordinating water molecules bonded to the M (II) ions with the bpy capping ligand gives raise to a better isolation between the chains. While for compound 5 the shortest M-M interchain distance is 7.847 Å, the same value is rather smaller for compound 1 (6.897 Å). As we have observed in the previous examples, non-covalent interactions play again a determinant role in directing the cationic [K(18-crown-6)]+ complexes packing. The electrostatic interaction between the metallic ion and the terminal oxalate ligand bonded to the Cr (III) center ( O•••K = 2.687 Å) might direct the eclipsed packing of the cationic units along the a axis. Compound 5 does

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not exhibit magnetic ordering down to 2 K. This fact must be attributed to the increase in the interchain metal distances which result in a lower intensity of magnetic dipolar interactions (∝ 1/r3) acting between the chains. The above results open the way for a better control and tailor of the structure and magnetic properties in this class of hybrid molecule-based magnets, playing not only with covalent bonds, but also with weaker supramolecular interactions, such as H bonding and electrostatic interactions. This approach could be extended to other families of molecular magnets. Finally, the solubility of these compounds in water and polar solvents is also remarkable and turns them into suitable candidates for materials processing and hybrid materials preparation by intercalation chemistry. 3.

Hybrid Molecular Conductors Based on Polyoxometalates

Another important class of two-network hybrid materials is that provided by the molecular conductors based on -electron donor molecules of the tetrathiafulvalene (TTF) family (see Figure 8, left). Typically, the structure of these materials is formed by segregated stacks of self-assembled organic donors, and charge compensating inorganic counter-anions. In this part we will show that by playing with the size, shape, symmetry and charge of these inorganic anions it is possible to control the packing of the organic sublattice and therefore the conducting properties. On the other hand, the possibility to accommodate in these anions magnetic centers allows to add a second property to the conducting material. To illustrate this point, we will use as anions metal-oxide clusters of W and Mo (see Figure 8, right). This topic has been already reviewed is several papers26,27 from the point of view of the properties. In this work we will focus on the aspects connected to the crystal engineering of these hybrid materials.

Figure 8. Some common -electron donor molecules of the TTF family (left) and some structures of polyoxometalates (right) used in this work.

The method of synthesis of these materials involves a slow oxidation of these electron donor molecules to form radical cations that can crystallize with the anions present in the solution. The solids so formed can exhibit conducting properties if a number of requirements is satisfied. For example,

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an extensive array of S...S (or S...Se, Se...Se) short intermolecular contacts (shorter than the sum of the van der Waals radii) must be formed in the organic sublattice to allow a path for the electrons to follow. Due to their planar geometry the TTF-type donors easily form stacks and even layers in which these kind of contacts are established. If isolated organic stacks are formed the compound will be a one-dimensional conductor or, if layers are formed, a two-dimensional system can be obtained. Figure 9 shows some different types of layers that are commonly observed in TTF-based radical salts.

Figure 9. Some common types of organic packings observed in radical salts of the TTF family. Each line represents the donor molecule viewed along the long molecular axis.

Some types of layers favor better conducting properties than others. For example β and κ phases often exhibit metallic behaviour or even superconductivity, while α phases are usually semiconducting. Due to the arrangement of the organic donors in the layers, the interactions with the anions will take place through the ethylene groups of the organic molecules. If the anions contain oxygen or halogen atoms weak hydrogen bonds can be formed which can have some influence on the type of organic phase that is formed and therefore (indirectly) in the conductivity of the solid. Another requirement for the formation of conducting salts is that the organic donors must have partial oxidation states in order to have partially filled electronic bands. The formation of regular stacks of the donors favors a homogeneous electronic distribution in the organic sublattice and therefore the occurrence of partial oxidation states in the donors is more likely. From the structural point of view, the use of polyoxometalates as inorganic component in these molecular conductors has very important consequences in the organic packing.28 Thus, these bulky anions have a strong tendency to form closed cubic or hexagonal packings in the solid state when they crystallize with alkali metals. Therefore in the materials obtained by the combination of the planar TTF-type donors with polyoxometalates a compromise will have to be reached between the tendency of the donors to

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form layers and the tendency of the polyoxometalates to form closed packings. 3.1. THE RADICAL SALT BEST3H[PMo12O40]

As a first example let us consider the radical salt formed by the Keggin polyoxometalate [PMo12O40]4– and the seleniated donor BEST: BEST3H [PMo12O40].29 In Figure 10 the structure of the inorganic sublattice is shown. The Keggin polyoxometalates form layers which are shown in Figure 10a with different colors. If one observes two of these layers from the perpendicular direction (see Figure 10b) one can see that in the second layer (the yellow one) the polyoxoanions are placed in the holes left by the first layer (in purple). This polyoxometalate packing resembles that shown by the alkali salts of polyoxometalates. The main difference is that polyoxometalates are more separated here. In this example the tendency of these anions to form closed packings overcomes the tendency of the donors to form layers. Actually, the organic donors in this salt do not have enough room to be organized in layers, so, they are located in between the anions forming dimers or almost isolated molecules (see Figure 11). Therefore this compound behaves as an insulator.

Figure 10. (a) A view of the inorganic sublattice of the radical salt BEST3H[PMo12O40] parallel to the layers (the layers of polyoxometalates are shown in different colors). (b) A perpendicular view of two consecutive layers.

Figure 11. The structure of the salt BEST3H[PMo12O40] showing the absence of organic layers.

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Figure 12. The layered structure of the compounds ET8[Keggin] (left).Views of the two different organic stacks in the compounds ET8[Keggin] (right).

3.2. THE RADICAL SALTS ET8[Keggin]30

In the previous structure there are no organic layers although there are some short Se…Se contacts between the “almost” isolated molecules. Substitution of these seleniated donors by the analog donor containing only S atoms should result in the weakening of the intermolecular S…S interactions since the van der Waals radius of the S atom is much smaller than the one of Se. When the ET donor (containing only S atoms) is combined with Keggin polyoxometalates one obtains a radical salt which contains layers of organic donors and layers of polyoxoanions (see Figure 12, left). In these radical salts, two types of stacks of organic donors are formed. One stack contains fully eclipsed organic donors, while the other stack has to be accommodated in the holes left by the bulky polyoxometalates in the inorganic layer. Therefore, they form zigzag chains (see Figure 12, right). This irregular arrangement of the organic molecules produces a nonhomogeneous electronic distribution that gives rise to poor electrical properties (semiconducting behaviour and strong electron localization). 3.3. THE RADICAL SALT BEDO6K2[BW12O40]31

A strategy that can be followed to get more homogeneous organic stacks consists on filling the holes left by the polyoxometalates in the inorganic sublattice with alkali cations. The alkali cations will locate between the

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bulky anions and will prevent the organic molecules to “dock” in the holes left by the polyoxometalates. This strategy has been succesful in the radical salt formed by the BEDO donor and the polyoxometalate [BW12O40]5– formulated as BEDO6K2 [BW12O40] (see Figure 13).

Figure 13. Crystal structure of the salt BEDO6K2[BW12O40].

In this salt the separation between the Keggin polyoxoanions inside the inorganic layers is reduced. Here the anions are separated by approximately the same distance found in the potassium salt of the polyoxometalate. So, the organic donors do not find significant holes in the inorganic layers to penetrate and to form zigzag chains. Then, the organic chains are homogeneous and form a β packing which favor the electron delocalization (see Figure 14). As a consequence, the compound shows a large room temperature conductivity and is metallic down to very low temperatures (see Figure 15).

Figure 14. Views of the layers and the organic stacks in the salt BEDO6 K2 [BW12O40].

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Figure 15. Conductivity of a single crystal of BEDO6K2[BW12O40].

3.4. A RADICAL SALT CONTAINING CHIRAL POLYOXOMETALATES: ET9[H4Co2Mo10O38]32

The use of chiral anions in radical salts of TTF-type donors is of interest as they allow the design of dual-function materials wherein chirality (optical activity) is combined or even coupled with conductivity. The effect of the chiral polyoxometalate in the packing of the organic donors has been observed in the radical salt formulated as ET9[H4Co2Mo10O38] which contains both enantiomers of the chiral polyoxometalate [H4Co2Mo10O38]6– (see Figure 16).

Figure 16. Polyhedral representation of the two enantiomers of the chiral polyoxometalate [H4Co2Mo10O38]6–.

Figure 17. Crystal structure of the radical salt ET9[H4Co2Mo10O38].

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The crystal structure shows the typical layered structure in which the inorganic layers are formed by chains of polyoxometalates which stack in the direction perpendicular to the sheet in Figure 17. Figure 18 shows one of these stacks of polyoxometalates which is formed by only one of the two enantiomers. In fact, every polyoxometalate stack is made of only one enantiomer and alternate with stacks made with the other enantiomer.

Figure 18. A polyoxometalate stack formed by only one enantiomer of the anion [H4Co2Mo10O38]6–.

The organic layers adopt an unusual packing in which the donors of three adjacent stacks are parallel and form an angle of 54º with the donors of the next three stacks (see Figure 19). Therefore the organic sublattice presents characteristics of the well-known α and β packings. Bearing this in mind, the most striking feature of this structure is that each of the inorganic stacks lies near three consecutive organic stacks having the ET molecular planes parallel, while the next three neighboring organic stacks are nearer the inorganic stack made of polyoxometalates having the opposite chirality. Therefore, the unusual packing observed in the organic sublattice has likely been induced by the chirality of the polyoxometalates which could have been mediated through short contacts of the type C-H•••O between the organic and inorganic sublattice. These packings lead to semiconducting properties and a high room temperature conductivity of 20 S cm–1.

Figure 19. Projection of the structure of ET9[H4Co2Mo10O38] along the long molecular axis of the ET molecules.

A radical salt containing only one pure enantiomer would probably produce a compound in which all the ET donors would be parallel giving rise to a β phase. Still, all attempts to obtain such a compound have failed.

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Conclusions

In this paper we have learnt that crystals formed by molecules can be of interest not only from an aesthetic point of view, but also from the point of view of their properties. This functionality is intimately connected to the supramolecular interactions in the solid, so, a control of the packing of the molecular building blocks is essential to tune and improve their physical properties. We have illustrated this concept in hybrid materials formed by the self-assembling of two molecular networks. As a result, novel magnetic materials are designed in which the topology and dimensionality of the magnetic lattice can easily be tuned by the presence of a second molecular lattice. On the other hand, novel molecular conductors have been designed in which the packing of the organic donors and, therefore, the electrical properties can be tuned. In this last class of hybrids the organic packing is controlled by the presence of bulky inorganic anions (polyoxometalates) which establish intermolecular and electrostatic interactions with the organic component. Crystal engineering of these hybrid materials is only now beginning to move forward and many interesting and challenging combinations molecular components can be still imagined.

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A. Alberola, E. Coronado, C. Gimenez-Saiz, C. J. Gomez-Garcia, F. M. Romero and A. Tarazon, Hybrid magnetic materials based on nitroxide free radicals and extended oxalato-bridged bimetallic networks Eur. J. Inorg. Chem. 389–400 (2005). E. Coronado, J. R. Galan-Mascaros, C. J. Gomez-Garcia, J. Ensling and P. Gutlich, Hybrid molecular magnets obtained by insertion of decamethyl-metallocenium cations into layered, bimetallic oxalate complexes: [Z(III)CP(2)*][(MMIII)-M-II(ox)(3)] (Z(III) = Co, Fe; M-III = Cr, Fe; M-II = Mn, Fe, Co, Cu, Zn; ox = oxalate; Cp* = pentamethylcyclopentadienyl) Chem. Eur. J. 6, 552–563 (2000). E. Coronado, J. R. Galan-Mascaros, C. J. Gomez-Garcia and J. M. Martinez-Agudo, Molecule-based magnets formed by bimetallic three-dimensional oxalate networks and chiral tris(bipyridyl) complex cations. The series [Z(II)(bpy)(3)][ClO4][(MCrIII)-CrII(ox)(3)] (Z(II) = Ru, Fe, Co, and Ni; M-II = Mn, Fe, Co, Ni, Cu, and Zn; ox = oxalate dianion) Inorg. Chem. 40, 113–120 (2001). M. Clemente-Leon, E. Coronado, C. J. Gomez-Garcia and A. Soriano-Portillo, Increasing the ordering temperatures in oxalate-based 3D chiral magnets: the series [Ir(ppy)(2)(bpy)][(MMIII)-M-II(ox)(3)]center dot 0.5H(2)O ((MMIII)-M-II = MnCr, FeCr, CoCr, NiCr, ZnCr, MnFe, FeFe); bpy=2,2 '-bipyridine; ppy=2-phenylpyridine; ox = oxalate dianion) Inorg. Chem. 45, 5653–5660 (2006). E. Coronado, J. R. Galan-Mascaros, C. J. Gomez-Garcia and V. Laukhin, Coexistence of ferromagnetism and metallic conductivity in a molecule-based layered compound Nature 408, 447–449 (2000). S. Benard, E. Riviere, P. Yu, K. Nakatani and J. F. Delouis, A photochromic moleculebased magnet Chem. Mater. 13, 159–162 (2001).

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E. CORONADO, C. GIMÉNEZ-SAIZ AND C. MARTÍ-GASTALDO S. Benard, P. Yu, J. P. Audiere, E. Riviere, R. Clement, J. Guilhem, L. Tchertanov and K. Nakatani, Structure and NLO properties of layered bimetallic oxalato-bridged ferromagnetic networks containing stilbazolium-shaped chromophores J. Am. Chem. Soc. 122, 9444–9454 (2000). H. Tamaki, Z. J. Zhong, N. Matsumoto, S. Kida, M. Koikawa, N. Achiwa, Y. Hashimoto and H. Okawa, Design of Metal-Complex Magnets – Syntheses and Magnetic-Properties of Mixed-Metal Assemblies (Nbu4[Mcr(Ox)3])X (Nbu4+=Tetra (Normal-Butyl)Ammonium Ion Ox(2-)= Oxalate Ion M=Mn2+,Fe2+,Co2+,Ni2+,Cu2+, Zn2+) J. Am. Chem. Soc. 114, 6974–6979 (1992). K. S. Min and J. S. Miller, Synthesis of layered (2-D) V-based bimetallic oxalates from non-aqueous media that cannot be synthesized from aqueous media Dalton Trans. 2463–2467 (2006). E. Coronado, J. R. Galan-Mascaros and C. Marti-Gastaldo, Oxalate-based 2D magnets: the series [NBu4][(MMnIII)-Mn-II(ox)(3)] (M-II = Fe, Co, Ni, Zn; ox = oxalate dianion) J. Mater. Chem. 16, 2685–2689 (2006). R. Pellaux, H. W. Schmalle, R. Huber, P. Fischer, T. Hauss, B. Ouladdiaf and S. Decurtins, Molecular-based magnetism in bimetallic two-dimensional oxalate-bridged networks. An X-ray and neutron diffraction study Inorg. Chem. 36, 2301–2308 (1997). C. Mathoniere, C. J. Nuttall, S. G. Carling and P. Day, Ferrimagnetic mixed-valency and mixed-metal tris(oxalato)iron(III) compounds: Synthesis, structure, and magnetism Inorg. Chem. 35, 1201-1206 (1996). S. G. Carling, C. Mathoniere, P. Day, K. M. A. Malik, S. J. Coles and M. B. Hursthouse, Crystal structure and magnetic properties of the layer ferrimagnet N(n-C5H11)(4)MnIIFeIII(C2O4)(3) J. Chem. Soc., Dalton Trans.1839–1843 (1996). C. Mathoniere, S. G. Carling, Y. S. Dou and P. Day, Molecular-Based Mixed-Valency Ferrimagnets (Xr(4))(Feiifeiii)(C2o4)(3) (X=N, P, R=N-Propyl, N-Butyl, Phenyl) – Anomalous Negative Magnetization in the Tetra-N-Butylammonium Derivative J. Chem. Soc., Chem. Commun. 1551–1552 (1994). H. Okawa, N. Matsumoto, H. Tamaki and M. Ohba, Ferrimagnetic Mixed-Metal Assemblies (Nbu4[Mfe(Ox)3])X Mol. Cryst. Liq. Cryst. 232, 617–622 (1993). E. Coronado, J. R. Galan-Mascaros, C. J. Gomez-Garcia and C. Marti-Gastaldo, Synthesis, structure, and magnetic properties of the oxalate-based bimetallic ferromagnetic chain {[K(18-crown-6)][Mn(H2O)(2)Cr(ox)(3)]}(infinity) (18-crown-6=C12H24O6, ox = C2O42-) Inorg. Chem. 44, 6197–6202 (2005). E. Coronado, J. R. Galan-Mascaros and C. Marti-Gastaldo, Synthesis and characterization of a soluble bimetallic oxalate-based bidimensional magnet: [K(18-crown6)](3)[Mn-3(H2O)(4){Cr(ox)(3)}(3)] Inorg. Chem. 45, 1882–1884 (2006). E. Coronado, J. R. Galan-Mascaros, C. J. Gomez-Garcia, J. M. Martinez-Agudo, E. Martinez-Ferrero, J. C. Waerenborgh and M. Almeida, Layered molecule-based magnets formed by decamethylmetallocenium cations and two-dimensional bimetallic complexes [M(II)Ru(III)(ox)(3)](-)(M(II) = Mn, Fe, Co, Cu and Zn; ox = oxalate) J. Solid State Chem. 159, 391–402 (2001). S. Triki, F. Berezovsky, J. S. Pala, E. Coronado, C. J. Gomez-Garcia, J. M. Clemente, A. Riou and P. Molinie, Oxalato-bridged dinuclear complexes of Cr(III) and Fe(III): Synthesis, structure, and magnetism of [(C2H5)(4)N](4)[MM '(ox)(NCS)(8)] with MM ' = CrCr, FeFe, and CrFe Inorg. Chem. 39, 3771–3776 (2000). O. Kahn, Dinuclear Complexes with Predictable Magnetic-Properties Angew. Chem., Int. Ed. Engl. 24, 834–850 (1985). F. D. Rochon, R. Melanson and M. Andruh, [Cr(bipy)(C2O4)(2)](–): A versatile building block for the design of heteropolymetallic systems. Crystal structures of [BaCr2(bipy)(2)(C2O4)(4)(H2O)](n)center dot nH(2)O, [MnCr2(bipy)(2)(mu-C2O4) (4)](n), and [CoCr2(bipy)(2)(mu-C2O4)(2)(C2O4)(2)(H2O)(2)]center dot H2O Inorg. Chem. 35, 6086–6092 (1996).

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22. N. Stanica, C. V. Stager, M. Cimpoesu and M. Andruh, Synthesis and magnetic properties of a new oxalato-bridged heterotrinuclear complex, [NiCr2(bipy)(2)(C2O4)(4) (H2O)(2)]center dot H2O. A rare case of antiferromagnetic coupling between Cr(III) and Ni(II) ions Polyhedron 17, 1787–1789 (1998). 23. G. Marinescu, M. Andruh, R. Lescouezec, M. C. Munoz, J. Cano, F. Lloret and M. Julve, [Cr(phen)(ox)(2)](-): a versatile bis-oxalato building block for the design of heteropolymetallic systems. Crystal structures and magnetic properties of AsPh4[Cr(phen) (ox)(2)]center dot H2O, [NaCr(phen)(ox)(2)(H2O)]center dot 2H(2)O and {[Cr(phen) (ox)(2)](2)[Mn-2(bpy)(2)(H2O)(2)(ox)]}center dot 6H(2)O New J. Chem. 24, 527–536 (2000). 24. E. Coronado, M. C. Gimenez, C. J. Gomez-Garcia and F. M. Romero, Synthesis, crystal structure and magnetic properties of [Cr2CU2(bpy)(4)(ox)5]center dot 2H(2)O. An oxalato-bridged heterometallic tetramer Polyhedron 22, 3115–3122 (2003). 25. E. Coronado, J. R. Galán-Mascarós and C. Marti-Gastaldo, Controlling the dimensionality of oxalate-based bimetallic complexes: The ferromagnetic chain [K(18-crown6)][Mn(bpy)Cr(ox)3] (18-crown-6 = C12H24O6; ox = C2O42-; bpy = C10H8N2) Polyhedron doi: 10.1016/j.poly.2006.10.024, (2006). 26. E. Coronado, C. Gimenez-Saiz and C. J. Gomez-Garcia, Recent advances in polyoxometalate-containing molecular conductors Coord. Chem. Rev. 249, 1776–1796 (2005). 27. E. Coronado and C. J. Gomez-Garcia, Polyoxometalate-based molecular materials Chem. Rev. 98, 273–296 (1998). 28. E. Coronado and J. R. Galan-Mascaros, Hybrid molecular conductors J. Mater. Chem. 15, 66–74 (2005). 29. E. Coronado, J. R. Galan-Mascaros, C. Gimenez-Saiz, C. J. Gomez-Garcia, L. R. Falvello and P. Delhaes, Charge transfer salts based on polyoxometalates and seleno-substituted organic donors. Synthesis, structure, and magnetic properties of (BEST)(3)H[PMo12O40] center dot CH3CN center dot CH2Cl2 (BEST = bis(ethylenediseleno)tetrathiafulvalene) Inorg. Chem. 37, 2183–2188 (1998). 30. E. Coronado, J. R. Galan-Mascaros, C. Gimenez-Saiz, C. J. Gomez-Garcia and S. Triki, Hybrid molecular materials based upon magnetic polyoxometalates and organic pi-electron donors: Syntheses, structures, and properties of bis(ethylenedithio) tetrathiafulvalene radical salts with monosubstituted Keggin polyoxoanions J. Am. Chem. Soc. 120, 4671–4681 (1998). 31. E. Coronado, C. Gimenez-Saiz, C. J. Gomez-Garcia and S. C. Capelli, Metallic conductivity down to 2K in a polyoxometalate-containing radical salt of BEDO-TTF Angewandte Chemie-International Edition 43, 3022–3025 (2004). 32. E. Coronado, S. Curreli, C. Gimenez-Saiz, C. J. Gomez-Garcia and J. Roth, A new BEDT-TTF salt and polypyrrole films containing the chiral polyoxometalate [H4Co2Mo10O38](6-) Synth. Met. 154, 241–244 (2005).

TOPOLOGICAL APPROACHES TO THE STRUCTURE OF CRYSTALLINE AND AMORPHOUS ATOM ASSEMBLIES

LINN W. HOBBS Department of Materials Science & Engineering Department of Nuclear Science & Engineering Massachusetts Institute of Technology Room 13-4054, 77 Massachusetts Avenue Cambridge, MA 02139-4307, USA

Abstract. Crystalline assemblies of atoms possess not only symmetry and periodicity but also a topology that provides additional information not explicit in a conventional description. A topological description of structure is likewise shown to be the only sensible approach to the assessment of non-crystalline atom assemblies and to reveal useful similarities between crystalline and non-crystalline structures at intermediate range. Amorphizability of crystalline solids is shown to derive from topological properties of connectivity, and the defect structures of highly defective or amorphizing solids can be individually identified and categorized in model simulations using topological tools. Polyamorphic phase transformations between alternative amorphous arrangements can be similarly characterized. Examples of topological assessment tools are given for SiO2, Si3N4, SiC, ZrSiO4 and GeO2 systems.

1. Introduction The long-range ordered crystalline state is invariably the state of lowest free energy for elemental and compound solids. Higher energy aperiodic states, such as melt-quenched glasses, represent a failure to crystallize, and few such metastable atomic arrangements survive over geological time scales. Crystallography began with the observation that many minerals found in nature exhibited facets, later understood to be growth facets corresponding to rapid lateral growth on certain crystalline planes, the angles between which were found to be characteristic of the mineral type. The symmetries defined by these facets were also noted and later, with 20th-century revelation of the atomistic structure of crystalline materials by X-ray diffraction, 193 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 193–230. © 2008 Springer.

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led to compilation of the 32 three-dimensional point groups as a way to describe atom environments. The notion of periodic translation introduced the construct of the crystal lattice and the replication of a structure by periodic translation of a fundamental structural unit, the unit cell. Their combination1 led to a formally complete (though arcane) description2 of the 230 possible ways of combining point-group symmetries with periodic translation that circumscribe all crystalline assemblies. The special and general positions generating the equipoints of a unit cell represent a set of rules for assembly of the constituent atoms according to the symmetries present. Though both powerful and inclusive, the methods of crystallography do not constitute the only way of specifying atom assemblage and describing atomic arrangement, nor can they be applied to randomly distorted or highly defective crystalline solids or to non-crystalline assemblies. The present contribution presents an alternative way3 to look at atomic structure, based on connectivity and topology instead of symmetry, which is applicable to crystalline and non-crystalline arrangements alike. An alternative set of prescriptive assembly rules is described, whose frustration leads operationally to non-crystalline arrangement, and a set of constraints is derived which dictate the relative amorphizability of an initially crystalline arrangement. Finally, a topological approach to structural analysis is developed that defines a characteristic structural unit, analogous to a unit cell, that is based on connectivity and not symmetry and can be applied alternatively to crystalline structures and advantageously to non-crystalline ones. The approach can distinguish between crystalline and non-crystalline regions in an amorphizing crystal and between different non-crystalline arrangements of the same chemistry. It can also be used to uniquely identify defects in highly defective structures to which a reference lattice overlay cannot be sensibly applied. The limitations of crystallography are readily apparent from Figure 1, in which two connected arrangements of [MX3] triangular units (inset) in two dimensions is explored. The first arrangement in Fig. 1a represents perfect crystallinity—an elegantly aesthetic, if ultimately limited and boring, way to populate the two-dimensional space. The second arrangement in Fig. 1b is clearly non-crystalline and cannot be rendered crystalline by any manipulation short of breaking all bonds, though the basic connection motif remains the same. Like all crystals, the first arrangement exhibits both translational and orientation order and can be compactly described by the repeatable unit cell outlined. The second arrangement formally lacks both translational and orientation order but is fully connected and occupies space just as efficiently. In most communities, the latter would be acknowledged as an amorphous arrangement. Since amorphous means “without form”— and it will be shown later that Fig. 1b in fact contains considerable structural regularity—a preferable description is topologically disordered.

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The epithet “amorphous” is, however, so ingrained in the scientific literature that its use will be retained in this exposition, with the understanding that it implies formal topological disorder and not just any distorted or highlydefective solid arrangement. It should also be noted, for completeness, that quasi-crystalline arrangements preserve orientational order but lack transla-

Figure 1. Planar arrangements of corner-sharing [MX3] triangular polytopes (inset) in a) a long-range ordered crystalline arrangement (unit cell outlined), and b) a non-crystalline topologically disordered arrangement, first explored by Zachariasen.4 Bold lines indicate ring-ring correlations (that are also unit cell translations for the topologically-ordered crystal).

2. Topological Character of Atom Assemblies Topology is formally the study of the properties of geometric objects that are invariant under continuous transformations and with continuous inverses. What is most often meant by the topology of atomic arrangements is the way atoms or groups of atoms are connected together.3 Mathematically, the connection points describe a graph comprising sets of nodes (or vertices) V and a set of edges E defined by pairs of adjacent nodes. A regular graph is one in which the nodes all have the same number of edges. A network is an arrangement of connected nodes and can thus be described mathematically as a graph. A network structure comprises an arrangement of connected structural units, such as predictably coordinated atoms or (in compounds) cation-coordination polyhedra, that is extendable in space. Such structural units reflect short-range chemical and structural order and may be generalized to any dimension as coordination polytopes (one-dimensional rods, twodimensional triangles or hexagons, three-dimensional tetrahedra or octahedra, etc.). These polytopes may share corners (polytope vertices), edges or faces. Figures 2 and 3 shows three different representations each of the connectivity of two elemental solids: the two-dimensional layer structure of graphite (C) and the three-dimensional network structure of diamond (C) or

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silicon (Si). Either structure may be represented by [CC] rods which are, respectively, connected three or four to a vertex. Alternatively, graphite may be represented by [CC3] triangles, connected three to a vertex, and diamond by [CC4] tetrahedra connected two to a vertex. A third representation is possible in which the geometry of the bonding is reflected in, respectively, a [C–3] triangle or a [C–4] tetrahedron centered on an atom but with its vertices at the bond midpoints ( where “–” represents a vertex with no atom located on it). For graphite or diamond, the third representation implies 180° (C- – -C) bond angles for both structures. The utility of this third representation is that, if the vacant vertex is populated by an atom, another structure type is generated. For example, if the atoms in Fig. 2 are boron and the vacant vertices are decorated with O atoms, the structure generated is that of crystalline B2O3; similarly, if the atoms in Fig. 3 are Si and the vacant vertices again decorated with O, the structure generated is cristobalite SiO2. That these structures are so related topologically would not be readily apparent from crystallographic, rather than connectivity, representations.

Figure 2 (left). Hexagonal two-dimensional network of graphite (0001) sheet, with three connectivity representations using [CC] rods, [CC3] coordination triangles, and [C–3] triangles with vertices at the C-C bond midpoints and 180°C – C bond angles, where “–” represents a vertex without an atom located on it.18 Figure 3 (right). Diamond structure of silicon (or diamond-C), with three connectivity representations, using [SiSi] rods, [SiSi4] coordination tetrahedra, and [Si–4] tetrahedra with vertices at the Si-Si bond midpoints and 180° Si – Si bond angles.18

Zachariasen4 was the first to recognize, three-quarters of a century ago, the topological implications for construction of infinitely extendable aperiodic networks, which mathematically can be described also as regular graphs. In order to ensure comparable energies for inorganic non-metallic compound glasses and their crystalline analogues, he focused on the same coordination polyhedra governing Pauling’s rules for crystal stability5 and explored ways

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of connecting them that would ensure extendability without translational periodicity or orientational order. Zachariasen’s classical depiction of [MX3] triangular units sharing corner X atoms (Fig. 1) is characterized in the crystalline state (Fig. 1a) by orientational invariance and translational periodicity (as evidenced by existence of a unit cell). The non-crystalline state (Fig. 1b) is characterized by no fixed bonding angles except those within the short-range ordered units and consequently lacks both orientational order and translational invariance; the consequence is that connectivity paths are no longer invariantly predictable, and the arrangement may therefore be said to be topologically disordered.6 Despite their apparent large structural difference and the seeming randomness of the non-crystalline arrangement, a surprisingly close topological relationship between the two arrangements exists and is explored in §5. 3. Self-Assembly by Local Rules Crystal structures are heuristically thought of as arising from repeated application of a unit cell translation, the contents of the unit cell itself having been generated by application of the set of symmetry-based crystallographic rules for the equipoint, appropriate to the space group. During crystal growth from melts, liquid solutions or a gas phase, the assembling atoms do not however comport themselves in accordance with the symmetry-based relationships of crystallography, which are necessarily long-range. Although Coulomb forces in ionic solids are likewise long-range, atoms in solids do not generally assemble with knowledge of such global information and certainly are little influenced by distant arrangements. Atoms sense only their relatively immediate environment at short range and consequently obey only local assembly rules,7 whose invariant application locally results in the long-range translational order and global symmetries prescribed by crystallography and the propagation of topological order. Accumulating departures from these rules leads inevitably to less well ordered, topologically-disordered assemblies. It is instructive therefore to first explore, in this section, these assembly rules and the consequences of deviations from regularity in their application. Topologically disordered arrangements, like glasses (whose formation involves a second-order structural phase transition from a molten state) or amorphous solids generally, represent fundamentally failure to crystallize. So what stands in the way of any initially less ordered arrangement of atoms subsequently adopting a crystalline arrangement? The answer lies in the fact that arrangements in amorphous solids are not random but are constrained by topological construction considerations, just as are crystals, and appreciable changes from one topology to another may introduce unacceptable energetic barriers to rearrangement. The latter situation is discussed in §4.

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Consider the rules file depicted in Fig. 4 prescribing a sequence for selfassembly of the high-temperature cubic β-cristobalite polymorph of SiO2 (cubic, space group Fd3m) from [SiO4] tetrahedral polytopes. The first line indicates that there is only one (“1”) type of assembly unit or node of the structure, the “4 1” unit given in second line, comprising in this case a regular [SiO4] tetrahedral polytope (the fundamental short-range ordered structural unit of almost all forms of silica and silicates) comprising four vertices, each of which is connected to a vertex of one other polytope. The initial tetrahedron is inscribed in a unit cube and positioned in the canonical orientation shown, with vertices labeled 0,1,2,3 corresponding to coordinate vectors [–0.5,–0.5, 0.5], [–0.5,0.5,–0.5], [0.5,0.5,0.5] and [0.5,–0.5,–0.5] in the unit cube. For “idealized” cristobalite (represented by Fig. 3 for silicon if each [Si—4] tetrahedron vertex is decorated with an oxygen atom) the canonical representation is retained, yielding an Si-O-Si bond angle of 180°. To instead generate the β-cristobalite polymorph, the initial tetrahedron is rotated by 23° about the y-axis, yielding a Si-O-Si bond angle of 148°. The less-symmetric low-temperature α-cristobalite polymorph (tetragonal, space group P41212) is generated with an analogous rotation of 24.7° about the yaxis, leading to an Si-O-Si bond angle of 145.3°. The next lines indicate, for each polytope type, the rules for connecting to each of its (four) vertices in turn. The initial tetrahedron (type 0) is replicated, rotated by ±90° as specified, and the numbered vertex indicated connected to the vertex of the initial tetrahedral polytope represented by the line (first line is vertex 0). The procedure is then repeated for each of the three remaining polytope additions. A crystal of β-cristobalite thus assembled is illustrated in Fig. 5a. Figure 4b compares the analogous rules for the low-temperature αquartz polymorph (trigonal, space group P3121, assembled in Fig. 6a), which Beta-Cristobalite 1 4 1 REGULAR y 23 ; 0 1 z 90 ; 0 0 z -90 ; 0 3 z 90 ; 0 2 z -90 ;

θ = 148˚

Alpha-Quartz 1 4 1 REGULAR y = 24 ; 0 1 z 60 ; 0 0 z -60 ; 0 3 z 60 ; 0 2 z -60 ;

θ = 143.6˚

Figure 4. a) Local rules for self-assembly of β-cristobalite by successive addition of [SiO4] tetrahedral polytopes. The x-axis is horizontal, y-axis vertical and z-axis normal to the plane of the diagram. To form β-cristobalite, the initial tetrahedron is rotated by 23° about the yaxis, yielding an Si-O-Si angle θ = 148°; to form α-cristobalite, the initial tetrahedron is rotated instead by 24.7° about the y-axis. b) Local rules for self-assembly of α-quartz.7

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(b)

Figure 5. [SiO4] tetrahedra assembled a) following local rules for β-cristobalite in Fig. 4a, b) following cristobalite rules altered to specify 85° tetrahedron rotations (instead of the 90° specified in Fig. 4a) to form a cristobalite-like non-crystalline structure.

are identical to cristobalite rules except for rotations of ±60° instead of ±90°. Thus, in terms of self-assembly, these two crystallographically widely disparate forms of SiO2 are surprisingly closely related and are distinguished merely by a simple 30° change in assembly rotation angle! Cristobalite (ρ = 2.21×103 kg/m3) and quartz (ρ = 2.65×103 kg/m3) are comparatively “open” network structures, but the approach is generalizable to higher density structures. Figure 7 presents local assembly rules for the densest tetrahedral polymorph of silica, the high-pressure phase coesite (monoclinic, space group C2/c, ρ = 3.01×103 kg/m3, assembled in Fig. 6b), which has two nonequivalent [SiO4] tetrahedral polytope sites (represented by shaded and unshaded tetrahedra) and therefore two different sets of assembly rules (doubled in the assembly table of Fig. 7, for convenience in implementing a computer-based assembly algorithm). The lesson is that self-assembly using certain local rules choices can propagate one (or several) topologicallyordered crystalline configurations which have particularly low minima in the overall free energy landscape; but there are (many) other choices that can propagate not terribly different topologically-disordered assemblies. In silica, because all of the tetrahedral structures illustrated (and the half-dozen more compact crystalline forms that exist) are still topologically identical after the first set of five assembled tetrahedra (and differ topologically only at second-neighbor tetrahedra, or in most cases only at third-neighbor tetrahedra), these assemblies will have assembly enthalpies (per tetrahedron) that differ very little and therefore contribute to populating an especially crowded energy landscape.

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Figure 6. [SiO4] tetrahedra assembled a) following α-quartz rules in Fig. 4b, and b) following coesite rules in Fig. 7.7

Figure 7. Local rules for assembly of coesite, the densest tetrahedral silica crystalline polymorph. Four rules sets are displayed for convenience in assembling the two inequivalent tetrahedron environments (shaded and unshaded).7

Non-crystalline arrangements represent, again, the failure of a structure to crystallize—for example, from a liquid melt when cooled or a radiationdisordered atomic arrangement. Non-crystalline arrangements have higher free energies than crystalline arrangements—though only slightly higher, because the local structures are usually nearly identical or very similar (as pointed out for the crystalline polymorphs) and govern most of the assembly free energy—but it is not sometimes possible to access the crystalline arrangement from a non-crystalline one because the transformation is too reconstructive; even in non-crystalline structures derived from crystalline ones by disordering, the stochastic route cannot be easily reversed to

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reclaim the original crystalline arrangement. There is no intrinsic limitation that precludes the local rules approach used for crystalline assembly from being applied to propagate topological disorder, and indeed, local rulesbased self-assembly can mimic the stochastic routes responsible for stabilizing non-crystalline arrangements and preserving topological differences in alternative amorphous forms. Figure 5b illustrates one approach in which the rotation angle for selfassembly of silica tetrahedra is altered from the 90° for cristobalite to 85°. The first few assembled tetrahedra will bond as in cristobalite, accompanied by some tetrahedral angle or bond-length distortion, but eventually the rotation error accumulates and a tetrahedron will be forced to bond in some alternative way, locally altering the topology. If the error propagates with any randomness, the result is a non-crystalline assembly, such as that resulting in Fig. 5b. A physicist might call such a structure a frustration glass (though it may not formally exhibit a second-order glass transition) and a glass scientist a strong9 one. This structure is very close to cristobalite, both locally and globally (as will be shown in §5) but no longer supports long-range correlations. It is also fully connected, though such assemblies may not be initially. To ensure full connectivity, some form of optimization may need to be imposed: for example, a crude but effective approach is to connect Hookeian “springs” between tetrahedron vertices and then globally minimize the total elastic energy in the springs after each tetrahedron addition. One result of the accumulating disorder is a broadening of the Si-O-Si intertetrahedron angle; another is distortion of the tetrahedra through O-Si-O bond angle and bond length changes (remanent “springs” essentially represent these tetrahedron distortions). Both manifestations are found experimentally in silica glasses. These results are, of course, generalizable to other polytopes and other assemblies, both crystalline and amorphous, but it is heuristically instructive to explore connectivity options for tetrahedral polytopes a little further. Still more compact assemblies of tetrahedral polytopes are possible in which more than two tetrahedra share a vertex: three [SiN4] tetrahedra share vertices in silicon nitride polymorphs, Si3N4, for example, and four [SiC4] tetrahedral share vertices in SiC polytypes. Figure 8 depicts self-assembly local rules for β-Si3N4 (rhombohedral, space group P63) and β-SiC (cubic, space group Fd3m) that are easily implemented to generate these crystalline structures; minor variants yield α-Si3N4 and α-SiC. Polytopic representations of the assembled structures of β-Si3N4 and α-SiC are shown in Fig. 9. A significantly different result for these two more compact tetrahedral compounds (Si3N4 ρ = 3.44, SiC ρ = 3.22) is that, unlike silica, modified rules will not generate well-connected topologically-disordered versions. In Fig. 10, unsuccessful attempts are shown to assemble [SiN4] and [SiC4] tetrahedra

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more arbitrarily, with respectively 3 and 4 tetrahedra sharing vertices, leaving the assemblies with serious underconnection and substantial tetrahedron distortions.10 The empirical surmise is that these solids cannot be fully connected in any but topologically ordered ways. It is a significant conclusion that full connectivity may not be compatible with more arbitrary connection schemes, raising intriguing questions about the uniqueness of crystalline structure and the origins of amorphizability.

Figure 8. Local rules for a) β-Si3N4 and b) β-SiC, which join respectively three [SiN4] and four [SiC4] tetrahedra at tetrahedral vertices.28

Figure 9. Polytopic representations of the {4,3} and {4,4} respective corner-sharing structures of a) β-Si3N4 (three [SiN4] tetrahedra sharing vertices) and b) α-SiC (four [SiC4] or [CSi4] tetrahedra sharing vertices).28

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Figure 10. Unsuccessful attempts to assemble fully-connected a) a-Si3N4 and b) a-SiC.10

4. Rigidity, Structural Freedom and Amorphization Not all solids are so easily representable in non-crystalline assemblies as is that depicted in Fig. 5b—which has rather low connectivity—as was just discovered in Fig. 10 for two tetrahedral solids with higher connectivity. In fact, many solids are found not to exist in amorphous states at all. Two prominent examples are MgO (or any diatomic solid with the NaCl structure) and most elemental metals. There is a connection, as it turns out, between connectivity, structural rigidity and amorphizability,11 as the following treatment will demonstrate. The pioneering work on the relationship between connectivity and rigidity was carried out by James Clerk Maxwell12 in the 1850’s, with obvious immediate relevance to an important engineering problem at the time: the construction of railway bridges. Consider the twodimensional (d = 2) assemblies of polytopes in Fig. 11, distinguished as {V,C} networks by the number of vertices to be shared per polytope (V) and the number of polytopes connected to each vertex (C). In the first, onedimensional (δ = 1) rods with two vertices (V = 2) are connected three to a vertex (C = 3) in a {2,3} network; in the second, two-dimensional (δ = 2) triangles (V = 3) are connected two to a vertex (C = 2) in a {3,2} network. Thorpe and co-workers13 have shown that the rigidity of these assemblies can be assessed by Maxwell constraint counting to identify the zero-frequency (floppy) modes of the networks. Each vertex in the network has d degrees of freedom, constrained by its connections to the rest of the network through rigid bonds and bond angles, and the task is to identify the constraints and assess if the constraints are greater than, equal to, or less than its degrees of freedom for each vertex. A somewhat more relevant way to ask the question is how many bonds have to be removed (broken) and from where before the

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network is rendered floppy, i.e. which bonds are redundant. A starting point is a theorem by Laman14 that relates vertices and edges (bonds) in a generic graph and its subgraphs, from which it can be shown that network rigidity is notably not a local property.

Figure 11. Two-dimensional networks constructed using one-dimensional (rods, V = 2) and two-dimensional (triangles, V = 3) structuring polytopes, with respective connectivities and structural freedoms f indicated. The top two are floppy (with the boundaries unconstrained), the bottom two rigid.18

Rigid polytopes of dimension δ = 2 or 3 offer a modest simplification by subsuming some of the angular constraints and were first used by Cooper15 to explore the correlation that exists between the freedom for structuring polytopes to rearrange (structural freedom f) and the extendability of topologically-disordered arrangements like glasses. Structural freedom is defined as the number of degrees of freedom at a polytope vertex (equal to network dimension d) less the number of constraints h acting on that vertex, f = d–h.

(1)

The planar {2,3} network in Fig. 11 is underconstrained (f = +0.5) and floppy; the planar {3,2} network is marginally constrained (f = 0) and rigid only if the boundary is pinned. The planar {2,3} network is a graph representation of the planar {3,2} network of triangles; the reason for its greater freedom is the use of regular triangular polytopes in the {3,2} network that constrains the equivalent graph angles to 120° and therefore introduces additional constraints. There are thus differences in graph and geometrical rigidity. Increasing the connectivity, as in {2,6} or {3,3} networks, leads to network rigidity (f = –1). The {2,6} network will be recognized as a familiar bridge truss, studied by Maxwell. Gupta16 has generalized the formulation of this definition of structural freedom to three dimensions, for structures containing rigid congruent regular

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polytopes sharing a fraction Y of edge-sharing vertices and a fraction Z of psided faces (if these additional connection modes are applicable), as f = d–h = d–C{δ–[δ(δ+1)/2V]} – (d–1)(Y/2) – [(p–1)d – (2p–3)](Z/p). (2)

The most convincing circumstantial support for the extension to the third dimension comes from assessment of the relative ease of radiation-induced amorphization for differently connected structural types (Table 1).17,18 A plot of collisional energy D deposited per atom (in eV/atom) against structural freedom f (Fig. 12)18 shows a surprising correlation over four orders of magnitude in energy deposition and across a large range of structural types. Displacive radiation (for example, fast electron or ion irradiation dose) severs bonds between atoms as atoms are displaced and therefore removes constraints. The dependence of amorphizability on structural freedom, displayed in Fig. 12, can be rendered into a functional relationship of approximate form f = 3 – 2.5 D3/16 ,

(3)

whose resemblance to (1) suggests that the role of the irradiation is—in some integrative way—to eradicate constraints, so that a critical amorphization dose renders the assembly floppy. In dense collision cascades, the cores of

Figure 12. Correlation of topological freedom f with amorphization displacive irradiation dose D in log-log plot of |f – 3| against D. The line is a non-linear least-squares fit to the experimental data (for D in eV/atom).18

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which may be briefly liquid-like and certainly for a time at least topologicallydisordered, displaced atoms will recrystallize epitaxially inwards from a still-crystalline periphery within a few picoseconds following the collision, and the fewer constraints that are imposed on these atoms from the crystal template, the more likely they are to explore or remain in alternative arrangements that are topologically- disordered. [SiO4] regular polytopes (V = 4, δ = 3) share corners with one other tetrahedron (C = 2) in all polymorphic forms of silica, e.g. cristobalite (Fig. 5a), except in the high-pressure rutile-structure (Fig. 18) polymorph stishovite (found in meteoritic impacts), where [SiO6] octahedra (V = 6, δ = 3) share edges (Y = 0.5) as well as corners (C = 3). Values of f for these two polytopic classes of silica are listed in Table 1, together with those for a range of other structure types and experimentally-determined critical collisional-energy depositions for amorphization. Like the two-dimensional {3,2} triangular network in Fig. 11, the three-dimensional {4,2} tetrahedral silica network is marginally constrained (f = 0), and this renders tetrahedral silica a ready glass former and the {4,2} crystalline polymorphs among the solids most easily amorphizable by displacive radiation (7 eV/atom collisional energy deposited). By contrast, TiO2 rutile, which is isostructural with stishovite, is far more constrained (f = –3.7) and amorphizes only at ten times higher energy deposition (65 eV/atom). The larger connectivity of tetrahedral Si3N4 networks, in which [SiN4] tetrahedra are shared three-to-a-corner (C = 3), provides more constraint (f = –1.5) than tetrahedral silicas, and Si3N4, too, amorphizes with much more difficulty. Silicon carbide, sharing four [SiC4] tetrahedra to a corner (C = 4) should be still more constrained (f = –3), but surprisingly it amorphizes almost as readily as tetrahedral silicas. The reason has to do with a key role of chemical disorder in this compound, discussed in §6. Phosphate networks, in which [PO4] tetrahedra (V = 4, δ = 3) share only three of their four corners with a second tetrahedron (Cavg = 1.5), have by contrast excess structural freedom (f = +0.75) and are much more readily amorphized (often at < 1 eV/atom) than tetrahedral silicas. Threedimensional (d = 3) B2O3 networks (represented two-dimensionally in Fig. 1b), in which [BO3] triangles (V = 3, δ = 2) share corners (C = 2) is still less constrained (f = +1) and is an exceptionally facile low-temperature glass former. Elemental silicon is an interesting case, because it can be amorphized and utilized as such in semiconductor devices. Representing silicon as {2,4} polytopes (Fig. 3) underestimates (f = +1) the constraints, because the rigid 109.5° tetrahedral sp3 hybrid bond angle constraints are not accounted in the Cooper-Gupta approach (2). Representation by {4,4} [SiSi4] tetrahedra overestimates (f = –3) the constraints, for the same reason that {3,3} [CC3] triangles overestimate constraints in graphite layers (Fig. 2), namely the indistinguishability of Si atoms in the center and corner positions of the

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TABLE 1. Coordination, connectivity, structural freedom and amorphizability for some common inorganic structures Structure

polytope:sharing

{V,C}

f

MgO UO2 α-Al2O3

octahedra:edges cubes:edges octahedra:faces,edges octahedra:edges tetrahedra:corners octahedra:edges,corners rods:ends dodecahedra:edges tetrahedra:edges triangles:corners tetrahedra:corners rods:ends tetrahedra:corners tetrahedral:corners tetrahedral:corners tetrahedra:corners triangles:corners

{6,6} (8,4} {6,4} {4,4} {6,4} {6,3} {2,12} b {4,2.5} {3,2} {4,4}b {2,8} {4,2} {4,2} {4,2} {4,1.75} {3,2}

–10 –7 –6.25

Amorphization dose (eV/atom) 5 000 > 3 000 3 400

–4.7

400

–4 –3a

75 63

–0.75b

36

<0 –3c –1a <0 0 0 +0.6 +1

15 13 11 11 10 7 0.5d e

MgAl2O4 TiO2 (stishovite) Zr3Al ZrSiO4 C (graphite) SiC NiTi Si Al0.5P0.5O2 SiO2 2PbO•P2O5 B2O3 a

b

amorphization likely driven by chemical disorder. amorphization driven by [SiO4] c polymerization. anomalous because chemical disorder renders SiC topology closer to {4,2}, d e f ~ 0. value for 2PbO•P2O5. not measured.

[SiSi4] tetrahedron. If these are distinguishable, as they are in SiC ([SiC4] tetrahedra), then indeed f = –3; but if not, the appropriate representation is as {4,2} [Si–4] corner-sharing tetrahedra (cristobalite without the oxygen atoms, hence f ~ 0). Indeed, silicon (11 eV/atom) and graphite (15 eV/atom) are only marginally more difficult to amorphize than silicas (7 eV/atom). The difference doubtless derives from the small additional constraint that arises because, for silicon in the [Si–4] representation (f ~ 0), the Si- – -Si bond is constrained to be 180º (as is the Si-O-Si angle in “ideal” cristobalite, but not as in β-cristobalite where it is 148°), and similarly for the C- – -C bond in graphite in the [C–3] representation (f ~ 0). More highly connected structures are far less easily amorphized (if at all) because of their much more negative structural freedom values. Rutile structure, comprising [MX6] octahedra, half corner-, half edge-shared (f = –3.7) has been discussed. α-Alumina (Al2O3), which is very difficult to amorphize, consists of pairs of [AlO6] octahedra sharing faces to form [Al2O9] super-polytopes,19 which then share edges (Y = 1, f = –5). Fluorite structure compounds (CaF2, UO2, Fig. 13b) consist of [MX8] cubes sharing all edges (Y = 1, f = –7) and are practically unamorphizable. Rocksalt-structure compounds (Fig. 13a), like NaCl or MgO, comprise [MX6] octahedra sharing all edges (Y = 1, f = –10) and are truly unamorphizable. Close-packed metals can be represented as 12-coordinated {2,12} structures, for which f = –3,

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and are difficult to amorphize unless high concentrations of metalloids or metal atoms with widely divergent radii are incorporated, and then form metallic glasses20 only in fast quenches or (sometimes) during irradiation. The intermetallic alloy Zr3Al, for example, has the L12 structure (ordered occupation of face-centered cubic lattice sites) and amorphizes at about 63 eV/atom (~1 displacement/atom, or 1 dpa),21 more or less in keeping with the f ~ –3 estimate for a close-packed arrangement.

(a)

(b)

Figure 13. Polytopic representations of a) rocksalt (NaCl) structure of MgO with edgesharing [MgO6] octahedra, b) fluorite (CaF2) structure of UO2 with edge-sharing [UO8] cubes.

In response, then, to the earlier question raised at the end of §3 about the robustness of the crystalline paradigm, it appears that the possibility of topologically-disordered states is topologically mediated. A salient case-inpoint is the well-documented substance known as biogenic “amorphous calcium carbonate” (ACC)22 that plays an important transient precursor role in biomineralization processes ending with formation of the stable crystalline polymorphs of calcium carbonate: calcite, aragonite (and sometimes vaterite), found e.g. in sea urchin spicules and mollusk shells. Calcite has a crystal structure that is a distorted form of the rocksalt structure, with Ca2+ cations and CO3– molecular anions, and the same topology; indeed, when calcitic limestone is calcined at high temperature, with the evolution of CO2, the product is lime, CaO, with the rocksalt structure (aragonite is analogous). It is topologically unlikely, then, that calcium carbonate would exist in an “amorphous” topologically-disordered form in its pure state, since the rocksalt structure (or modifications thereof) is so highly overconstrained. What is more likely is that ACC contains substantial amounts of incorporated hydrogen

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(e.g. as OH-) that relax some structural constraints and render “amorphous” assemblies of Ca2+ and CO3– ions topologically possible. 5. Topological Analysis by Local Cluster It was shown in §3 that local self-assembly rules contain all the information for generating an entire structure, and in a particularly compact form that is generative in the way space-group rules derived from symmetry are generative. Conventional structural analysis of the resulting crystal consists of identifying the unit cell, which is of course based on symmetry and the presence of long-range order; such analysis cannot be used for topologically disordered structures. An analogous approach can be employed, however, utilizing topology instead of symmetry and periodicity, that is applicable to crystalline and non-crystalline assemblies alike. The power of the method is that it provides complete information about intermediate-range structure that is not explicit in the unit cell of a crystal, is of critical interest for describing the structure of non-crystalline solids, and can be used to compare the structures of crystalline solids to those of their non-crystalline analogues. 5.1. RINGS AND TESSELATIONS

Closed circuits along a graph or network are known as cycles or rings. Rings are of interest because, in two dimensions (Fig. 1), a set of contiguous rings can be found which circumscribe polygons that tile the two-dimensional surface (like tiles on a bathroom floor). An analogous tiling in any dimension is known as a tessellation. A particular type of graph usefully studied is a graph without cycles, a tree graph. Tree graphs are ever-branching networks (like the trunk, limbs, branches and twigs of a tree, whose self-similar elements increase in number exponentially, as 2N for binary trees, where N is the order of the non-Euclidean network distance from the origin). Unlike trees in nature, whose elements get progressively smaller and thus exhibit fractal dimension, non-fractal tree graphs eventually exhibit a density catastrophe (Fig. 14) because each successive element remains of the same size. The catastrophe can be avoided if the network doubles back on itself in a closed circuit; rings are therefore a steric necessity and can always be found in real structures. In studying any piece of the network, the issue is then to decide which rings are the most important for describing the local properties of the network. An appropriate choice is the rings of smallest size and number that pass through an element of the network. These have been dubbed primitive rings by Marians and Hobbs23–25 and deemed to include all rings passing though a given polytope in the network that cannot be decomposed into two or more sets of rings, all of which are smaller than the original ring. The set

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Figure 14. A tree network, which should be compared to the networks in Fig. 1, illustrating the density catastrophe arising in a network without rings.27

of all structuring polytopes that belong to a set of primitive rings is known as the local cluster of that polytope location. Figure 15 shows this approach applied to the two two-dimensional networks of Fig. 1. What is striking is that both topologically-ordered and corresponding topologically-disordered structures shown share the same hierarchy of topologies (structuring polytope, primitive rings, local cluster) and—at least on average—close to identical topological entities. The local cluster is the topological equivalent to the unit cell of a crystal, not appreciably larger, and embodies the inherent topologies, instead of the inherent symmetries. In three dimensions, the two-dimensional polygons defined by onedimensional rings no longer tile the three-dimensional structure, as they do in two dimensions; instead, the space is filled by the interstitial voids.26 Nonetheless, one-dimensional primitive rings are still, remarkably, sufficient to distinguish even closely related polymorphic forms of crystalline assembly—and and therefore are of great utility in characterizing topologically-disordered

Figure 15. Topological entities of structuring polytope, primitive ring and local cluster identified for the a) crystalline and b) amorphous two-dimensional graphs of Fig. 1.

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atomic arrangements. The process of finding primitive rings in three-dimensional model assemblies relies on implementing efficient breadth-firstsearch shortest-path algorithms,27 which have been applied to crystalline and amorphous silicas7,8, Si3N410,28 and SiC,10,28 and with modification29 to the sometimes very large rings found in alkali silicate glasses, where the alkali ions break up the silica network connectivity. 5.2. LOCAL CLUSTERS

Figures 16 and 17 show the local clusters of quartz and cristobalite in both polytopic and atomic representations. In the tetrahedral polytopic representation of Fig. 16, cristobalite contains only 6-rings (of tetrahedra), and the local cluster contains 29 [SiO4] tetrahedra through which pass 12 6-rings (of tetrahedra). In fact, 12 6-rings represents a density minimum; fewer would lead to underconnection and a density increase (like the tree network); more than 12 6-rings leads to steric crowding. In the atomistic representation in Fig. 17, the silicon-centered local cluster of cristobalite comprises 29 silicon atoms and 40 oxygen atoms (for a total of 69 atoms). Twelve 12-rings pass through these Si atoms (the ring size is doubled because the network distance between two Si atoms now contains an Si-O and an O-Si step in atomic rings). A local cluster centered on an oxygen atom contains a total of 45 atoms, with 6 12-rings passing through each O atom. Tetrahedra in quartz assemble in a more compact way (20% more dense than cristobalite) by incorporating larger rings (in this case 8-rings in the polytopic representation, 16-rings in the atomic representation) that, unlike relatively planar 6- (and smaller polytopic) rings, can pack more efficiently by bending up on themselves. Quartz, with 40 8-rings in the local cluster, is in fact dominated by 8-rings. Coesite (14% more dense still than quartz) contains two non-equivalent tetrahedron-based local clusters (75 tetrahedra,

Figure 16. Polytopic representation of local clusters of a) cristobalite and b) quartz. One of the 12 6-rings in cristobalite and one of the 40 8-rings in quartz are highlighted.7

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(a) β-Cristobalite Silicon Oxygen 45 atoms 69 atoms 12 12-rings 6 12-rings

(b) α-Quartz Silicon Oxygen 111 atoms 155 atoms 6 12-rings 3 12-rings 20 16-rings 40 16-rings

Figure 17. Atomic representation of Si-centered local clusters of a) cristobalite and b) quartz. The rings counts through the Si atoms are the same as for the [SiO4] tetrahedra depicted in Fig. 16, but the ring size is doubled. Topologies for oxygen-centered clusters (not illustrated) are different and listed for comparison.

81 tetrahedra) corresponding to the two non-equivalent tetrahedron sites, with an array of 4-, 6, 8-, 9-, 10-, 11- and 12-rings (mostly 9- and 11-rings) in each cluster involved in achieving the denser packing. The presence of odd 9- and 11-membered rings in this crystalline structure (as well as in keatite, which has odd 5- and 7- rings) contradicts the common assumption that odd rings are involved only in amorphous arrangements (of course, the atomic rings are even: e.g. dominant 18- and 22-rings in coesite). There is in fact a convincing monotonic relationship between average ring size (and average local cluster size) and density in the six tetrahedral compact forms of silica (as opposed to cage structures like silicalite30), evident in Table 2. Table 2 reveals, however, no particular relationship between bond angle and density (or topology), which questions the utility of attempts to generate “realistic” models of amorphous vitreous silica by trying to get the bondangle distribution right as the first consideration. Denser forms of silica networks than {4,2} require a change of topology, either more tetrahedra shared per vertex, or a higher-coordinated polytope. Figure 18b shows a Si-centered atomic local cluster of the high-pressure very dense (ρ = 4.3×103 kg/m3) silica form stishovite, found in meteoritic impacts. Its tetragonal (space group P42/mnm) structure is the same as that of rutile (the commonest polymorph of TiO2) and features chains of edge-sharing [SiO6] octahedra that share corners with adjacent chains (Fig. 18a). Both octahedral coordination and edge-sharing increase the connectivity (to {6,3}) from the {4,2} connectivity of tetrahedral silicas. The local cluster is rather

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compact (53 atoms in the Si-centered atomic representation), and the ring complement is made up of small rings: 4-rings (from the edge-sharing), 6rings and (dominated by) 8-rings (atomic), as compared to 12- and 16-rings (atomic) in cristobalite and quartz; the small rings are made sterically possible by the edge sharing. TABLE 2. Relationship between topology and density in compact tetrahedral silicas Polymorph

Avg. Si-O-Si Avg. tetrahedral Avg. tetrahedral Density bond angle (°) ring size local cluster size (×103 kg/m3) HP-Tridymite 149.5 6 27 2.18 148 6 29 2.21 β-Cristobalite Keatite 154.1 6.9 39 2.50 138.5 7.4 41 2.62 α-Moganite 143.6 7.7 63 2.65 α-Quartz Coesite 150.8 10.0 78 3.01 Vitreous silica 145 ~6? <30? 2.21 Metamict quartz 134 ~6? <30? 2.26 “a-Cristobalite”* 145.9 6.6 24 2.29 “a-Quartz”† 153.7 7.6 40 2.77 *Assembled with deviant cristobalite assembly rules. †Assembled with deviant quartz assembly rules. Amorphous forms of silica shaded.

Stishovite

• Si ° O

Silicon 53 atoms 2 4-rings 12 6-rings 24 8-rings

Oxygen 33 atoms 1 4-ring 6 6-rings 12 8-rings

(a) (b) Figure 18. a) Polytopic representation of the local cluster of rutile-structure silica polymorph stishovite, which features corner- and edge-sharing [SiO6] octahedra; b) atomic representation of the Si-centered local cluster of stishovite, containing 53 atoms. (Corresponding O-centered local cluster, containing 33 atoms, not illustrated).

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Increasing tetrahedral connectivity at corners (e.g. {4,3} or {4,4}) leads to SiX3 and SiX4 stoichiometries that are incompatible with SiO2, but do occur for Si3N4 (30% denser than quartz) and SiC (21% denser than quartz). Polytopic representations of two of the structural variants of these compounds (β-Si3N4 and α-SiC) were depicted in Figure 9. Because SiC will be used as an interesting case study in §6, the topology of SiC will be explored here; Si3N4 topologies are discussed elsewhere. 10,28 Figure 19b depicts the atomic representation of the Si-centered local cluster of β-SiC (cubic zincblende structure, space group F43m) comprising 16 Si atoms and 13 C atoms (for a total of 29 atoms) and a ring complement of 12 6-rings. The polytopic representation is more intuitive (19 tetrahedra, 12 3-rings of tetrahedra, 124-rings of tetrahedra), but the atomic representation is topologically simpler (only 12 6-rings), because the (now doubled) 8-rings are no longer primitive. The local cluster of α-SiC (hexagonal wurtzite structure, space group P63mc) has an identical ring content but only 27 atoms (Fig. 19a). Si and C atoms occupy equivalent positions in either structure.

α-SiC Silicon 27 atoms 12 6-rings

β-SiC Carbon 27 atoms 12 6-rings

Silicon 29 atoms 12 6-rings

Carbon 29 atoms 12 6-rings

Figure 19. Atomic representations of local clusters of a) α-SiC and b) β-SiC, containing respectively 27 and 29 atoms. (Si- and C-centered local clusters are identical.)

5.3. AMORPHOUS STRUCTURES

For topologically-disordered assemblies, the local cluster must be determined uniquely at every node. Ensemble averages are given (for example, average ring counts or ring size or average number of tetrahedra or octahedra in a local cluster) are useful for comparing models, but only sets of connected representative local clusters provide an accurate topological sense of the

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structure. Table 1 lists local structural properties for the “amorphouscristobalite” model of silica shown in Fig. 5b, assembled from deviant cristobalite rules, and a similar “a-quartz” assembly. Even though both structures are formally amorphous and close to fully connected, their topologies are surprisingly similar to those of their parent crystals and are distinguishably different topologically from each other. Both structures start out with local clusters identical to those of the crystals around the first tetrahedron, but the topology shifts as the assembly must accommodate the accumulating assembly error; nevertheless, Fig. 20 shows that, even 158 tetrahedra out into the “a-cristobalite” assembly, topologically cristobalite (though geometrically distorted) clusters are still being generated, while 99 tetrahedra out in the “a-quartz” assembly the (slightly altered) topologies remain still very quartz-like. The distributions of even just the primitive rings can be quite characteristic of amorphous structure. Figure 21 depicts three different amorphous SiO2 assemblies, engineered with large initial differences in topology (cristobalite-like and quartz-like from assembling using deviant local rules, and a “random” liquid-like assembly) and maximally matched31 to remove underconnection and equilibrated to an empirical potential using MD.32

Figure 20. Local clusters of a) “a-cristobalite” and b) “a-quartz” well out into their assembly sequence using altered local assembly rules, showing persistence of local cluster topologies (polytopic representation) similar to those of the analogous crystals.

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Figure 21. Local-cluster primitive ring distributions for three amorphous SiO 2 assemblies engineered with different starting [SiO4]-tetrahedron connection topologies (cristobalite-like, quartz-like, and random), and subsequently equilibrated at 2500 K to an empirical potential using MD methods.32

The strong correlation of crystalline silica polymorph topologies with density, together with the persistence of topological motifs similar to those of crystals, suggests that the topologies of real amorphous silicas may be inferable from their densities. Thus, vitreous silica is likely to have a structure dominated by 6-rings of tetrahedra, as in cristobalite or tridymite (Table 1). When crystalline quartz is irradiated, it progressively amorphizes to metamict (to use the geological term) silica with a 14% decrease in density;33 hence, it is likely that the irradiation-induced displacements break up the 8-rings in the more densely assembled quartz, and the reassembly is largely in 6-ring format with a corresponding density close to the 6-ring crystalline polymorphs. In the case of irradiation-induced topological changes, for example amorphization in displacement collision cascades,34 it is straightforward to distinguish the amorphous fraction from the remanent crystalline fraction by applying a sorting algorithm, based on the crystalline local clusters, for each atom in the assembly to determine whether its local environment is crystalline or non-crystalline. Figure 22 illustrates the approach for successively overlapped collision cascades in ZrSiO4 (zircon), where the amorphous and crystalline fractions have been separated.35 In fact, it is possible to show in this way that even a single low-energy (e.g. 1 keV collisional energy deposited) cascade in zircon leaves the central portion amorphous (direct impact amorphization), as opposed to the necessity to accumulate some critical density of displacement-induced point defects before amorphization sets in. The topological structures of such modelled amorphous regions can of course be deduced, as they evolve, and compared to that of the original (and surrounding) crystal.

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Cascade Structure

Non-Crystalline Atoms

217

Crystalline Atoms

Figure 22. Production of amorphous ZrSiO4 from overlap of 24 5-keV (displacive) Zr PKA collision cascades. The simulation volume may be decomposed into amorphous and crystalline regions using a crystalline local-cluster algorithm.35

6. A Topological Approach to Structural Analysis The strength of the topological approach is that structural similarities between crystalline and amorphous forms and between different topologicallydisordered arrangements can be explored, even though the familiar metrics of crystallography have been lost. The focus on connectivity frees one from the shackles of formal crystallography, with its unrelenting emphasis on symmetry and unforgiving stance on random structural distortion. The approach also serves to show how locally similar to crystalline structures amorphous arrangements can be—which on reflection is not so surprising for a notoriously conservative Mother Nature! It also underscores the conclusion that the thermodynamics of structure is largely a local affair that cares little about symmetries and long-range translational order. This exposition on the utility of topology concludes with three model examples illustrating the power of topological methods to follow the progressive loss of crystalline order and even track the transitions between different topologically-disordered structures. Regrettably, experimental tools to deduce topology lag far behind our ability to model structural assemblies with molecular dynamics or first-principles approaches. Structure-deducing methods involving diffraction phenomena (X-ray, electron or neutron diffraction; EXAFS, XANES, EXELFS, ELNES) are exquisitely sensitive to shortrange order (on the scale of coordination polyhedra) and to longer-range structure only in crystals because the unit cell is periodically repeated. The same is true of resonance methods, such as NMR, Raman and Mößbauer spectroscopies. In fact, most structural information about non-crystalline arrangements peters out beyond the second- or third-nearest neighbor atom— and, of course, the information is diluted because every site environment is

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then a little different and does not reinforce information from its equivalent neighbor sites as it does in crystals.36 It is salient to reiterate that all compact forms of tetrahedral silica are identical up to first-neighbor tetrahedra (which means fourth-neighbor atoms) and most are topologically identical through to second-neighbor tetrahedra. Thus, what is significant topologically is intermediate-range structure, on the scale of local clusters, and diffraction and resonance techniques are notoriously insensitive to this range of atom correlation. Figure 23 illustrates how insensitive diffracted intensity distributions, and the real-space correlation functions derived from them, are for very large differences in topology of alternative isocompositional amorphous assemblies. One piece of diffraction information that does probe this length range is the first sharp diffraction peak—the first maximum in reciprocal space, hence the largest real-space structural feature whose persistence is probed; while there is debate about exactly what this first peak represents,38 it’s position indicates something like ring-ring correlation (Fig. 1), which is at the scale of local-cluster topology. The peak is sufficiently well defined in its position to be able to distinguish between model assemblies of different amorphous silicas (Fig. 24), and experimentally even differences between electron- and neutron-irradiation induced metamict forms.39

Figure 23. Total radial correlation function in real space derived from the three amorphous silica configurations whose local-cluster ring distributions appear in Fig. 21 and whose topologies are vastly different, compared to that derived from neutron diffraction of vitreous silica.32,37

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Figure 24. First-sharp diffraction peaks (FSDP) in diffracted intensity i(Q), normalized by diffraction vector Q = 4π sin(Θ/2λ), from three model assemblies of amorphous silicas derived from modified cristobalite, modified quartz, and random assembly rules, equilibrated by molecular dynamics (MD). The FSDP positions differentiate the three amorphous forms.37

6.1. AMORPHIZATION OF SiC

Table 1 indicates an anomaly (shaded) in the structural freedom criterion for amorphizability of SiC, a structure well-constrained by {4,3} connectivity with f = –3, but which amorphizes comparatively easily. In fact, SiC can be topologically disordered even by single atom displacements from electron irradiation, and both α and β polymorphs are found to amorphize at ~0.4 dpa, below a threshold temperature ~400 K.40 In amorphization models, it is useful to identify damaged regions by effectively applying an overlay grid based on the original crystal structure and noting atoms not residing at the grid nodes; this approach works for identifying vacant sites and displaced atoms residing in interstitial sites not on the grid for small numbers of displacements, but it notoriously fails at high defect density when the crystal (though still largely topologically ordered) becomes highly distorted relative to the overlay metric. It is, however, relatively easy to distinguish atoms residing in topologicallydisordered regions from atoms residing in topologically-ordered (remanent crystalline) regions by applying at each atom site an alternative topological metric: the full—or some subset of—the crystal local cluster. (A subset of the 12 6-ring [atomic] local cluster complement suffices for SiC.) Figure 25 illustrates this differentiation in a SiC crystalline assembly partially amorphized by introducing an atom with large kinetic energy (a “primary knockon atom,” or PKA, given say 10–50 keV kinetic energy) that displaces many atoms in a collision cascade. The advantage of this topological filter is that

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Figure 25. Non-crystalline atoms in a molecular dynamics simulation of a collision cascade irradiation event in SiC (50 keV [collisional] Si PKA), identified by removing atoms that are still associated with the local cluster for the crystal. Various point defects are also distinguished by their topological signatures.

it identifies, as still crystalline, highly-distorted but still topologically-ordered atom arrangements. Additionally in Fig. 25, individual point defects (vacant atoms sites, interstitial atoms in various configurations) arising from the displacement can also be identified, even in amorphizing (and indeed amorphous) material, because each defect introduces a characteristic change in the local topology (Fig. 26): a vacant Si site in SiC, for example, eliminates 12 6-rings and substitutes 12 12-rings; a split C interstitial along <110> adds 2 3-rings and 2 7-rings; and a C interstitial in a tetrahedral interstice adds 6 4-rings.

QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

CC110 +2 3-rings +2 7-rings

CtSi +6 4-rings

VSi –12 6-rings +12 12-rings

Figure 26. Changes in local-cluster ring topology introduced by three defects in SiC. The changes may be used to identify the defects in model simulations of radiation disorder.

The amorphizability anomaly in SiC is not a failure of constraint theory but instead derives an important structural possibility that appears to play a role in the amorphizability across a range of materials, including metals: the

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possibility of chemical disorder.3,17 In SiC, Si and C atom both function similarly in a chemical sense, using covalent hybridized sp3 tetrahedral orbitals, and are not hugely different in atom size; they can therefore substitute for each other, with a small energy cost, particularly when displaced. Characterizing SiC by [SiC4] tetrahedral polytopes therefore makes no sense in SiC that is being disordered chemically, because they represent no unique additional structural constraint if they can just as easily morph into [CSi4] tetrahedra. Indeed, β-SiC with random population of Si and C on atoms sites is structurally just Si, with an average atom type, and Si is easily amorphized (f ~ 0). The extent to which SiC becomes silicon-like can be characterized by the degree of chemical disorder: how many of one kind of atom are on the other atom’s sites. At low levels of disorder, the chemical disorder is represented by classical anti-site point-defect pairs (C exchanged for Si, leading to an SiSi4 local configuration; Si exchanged for C, leading to a CC4 local configuration). At higher levels of disorder, these local chemically aberrant configurations begin to overlap, and it no longer makes sense to identify individual anti-site defect pairs. Instead, it is useful to monitor the resulting homopolar (Si-Si or C-C) bonds, which are found to be prominent components in amorphized SiC assemblies.41 A appropriate measure of chemical disorder in SiC is thus the fraction χ of homopolar bonds. If chemical disorder is crucial to amorphizability of well-connected compounds like SiC, then there must be some threshold value χ* that induces amorphization. Figure 27 illustrates the result of a modeling exercise in which random chemical disorder at various levels is introduced into an

χ0 = 0.23 χ = 0.23

χ0 = 1.0 χ = 0.85

Figure 27. Initially crystalline SiC assemblies (bond representation) into which chemical disorder has been randomly introduced (χ is the fraction of homopolar bonds) and equilibrated by molecular dynamics methods at 2000 K. Assemblies illustrated are below (χ = 0.23) and above (χ = 0.85) a threshold chemical disorder χ* ~ 0.3.41

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initially crystalline SiC assembly, and the chemically disordered assembly then equilibrated by molecular dynamics methods at 2000 K. Assemblies with χ < 0.3-0.4 remain crystalline, while those with χ > 0.4 spontaneously amorphize, given thermal assistance. In fact, the process represents a formal second-order glass transition, as distinguished from crystalline melting at a unique melting point temperature. Below a critical chemical disorder threshold χ* ~ 0.3, the assembly melts as a crystal; above χ* the assembly undergoes a glass transition (Fig. 28). 6.2. AMORPHIZATION OF ZIRCON

Zircon, ZrSiO4, is a well-studied mineral, some samples of which have long been known to exist in amorphous (metamict) states on account of α-decay radiation damage from naturally incorporated U and Th impurities.42 It has also been considered as a potential host for actinide sequestration in a crystalline ceramic high-level nuclear wasteform.43 Table 1 indicates that zircon is moderately amorphizable, like most tetrahedral silicates, but it is unusual in that the constituent [SiO4] tetrahedra are initially isolated from each other (an orthosilicate). The Zr, Si and O local clusters for zircon are shown in Fig. 29. When zircon is irradiated (for example in the simulated collision cascades of Fig. 22), significant changes in topology result (Fig. 30)35. In particular, the local clusters are larger than those of the crystal, and widespread polymerization of the initially isolated [SiO4] tetrahedra is observed.

Figure 28. Solid-liquid transition in a suite of chemically disordered SiC assemblies. Those with chemical disorder χ < χ*~ 0.3 exhibit a well-defined crystalline melting temperature; those with χ > χ* increasingly exhibit a glass transition.41

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Zr Local Cluster 63 atoms 6 4-rings 64 8-rings

Si Local Cluster 39 atoms 2 4-rings 32 8-rings

223

O Local Cluster 37 atoms 2 4-rings 24 8-rings

Figure 29. Atomic local clusters about Zr, Si and O atoms in ZrSiO4. [SiO4] tetrahedra are not connected to each other in this structure, so all rings through Si must go through a Zr ion.

Zr Local Cluster

80 atoms 5 4-rings 3 6-rings 15 8-rings 10 10-rings 8 14-rings 2 18-rings

Si Local Cluster

70 atoms 4 8-rings 12 10-rings 2 12-rings 5 14-rings 1 18-ring

Figure 30. Representative Zr- and O-local clusters for the amorphous region of cascadeamorphized zircon in Fig. 22. The local clusters are significantly larger than for crystalline zircon, and widespread polymerization of initially isolated [SiO4] tetrahedra is observed.35

The significance of [SiO4] polymerization, a feature of the tetrahedral silicas discussed in §5.2, is that it represents a topological phase separation of the SiO2 and ZrO2 constituents that can be thought of as reacting initially to form the ZrSiO4 compound (sometimes alternatively represented as ZrO2•SiO2 to emphasize the stoichiometry). Figure 31 indicates the extent of this phase separation, which remains quite local (at most to about thirdneighbor tetrahedra); but it is quite effective in preventing substantially disordered zircon from returning to its original crystalline structure, without the wholesale reconstruction that would amount to melting and then recrystallizing the assembly. The amorphization thus appears driven by essentially

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one structural component, the [SiO4] polymerization, illustrating a general principle that—along with chemical disorder—serves to explain details of the amorphizability of many multi-polytopic assemblies beyond the generic connectivity constraints enumerated in Table 1. 6.3. POLYAMORPHISM IN a-GeO2 UNDER PRESSURE

Crystallography is exquisitely sensitive in distinguishing between different polymorphic crystalline forms of the same chemistry (e.g. the several crystalline silica polymorphs listed in Table 2), both conceptually and experimentally. Topology is useful in the same way for distinguishing different amorphous assembly alternatives of the same chemistry (e.g. the different amorphous tetrahedral silicas shaded in Table 2), as well as for also distinguishing between alternative crystalline forms. The utility of the topological

(a)

Percentage of Si polymerized

70 60 50 40 30 20 10 0 0

5

10

15

20

25

20

25

Number of PKA

(b)

Average number of bridging O atoms

1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

5

10

15

Number of PKA

Figure 31. Evolution of a) fraction and b) spatial extent of polymerization of [SiO4] units in cascade-amorphized ZrSiO4 with increasing displacive irradiation fluence.35

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approach in amorphous assemblies is well illustrated in the example of polyamorphism in a silica analogue, vitreous germania (v-GeO2), induced by application of high pressure.44 Crystalline GeO2 exhibits the quartz and stishovite (rutile structure) polymorphs of SiO2. Like silica, germania undergoes pressure-induced polymorphic phase changes at room temperature from a tetrahedral quartz structure to denser edge-sharing structures: disordered-NiAs (edge-sharing [GeO6] trigonal prisms) or rutile, but at somewhat lower pressure (7 GPa in GeO2 vs. 20 GPa in SiO2) via a poorlycrystallized intermediate tetrahedral phase of lowered monoclinic symmetry P21/c.45 (At still higher pressures, >26 GPa and >55 GPa respectively, at elevated temperature, additional transformations to octahedral, wholly edge-sharing, CaCl2 and α-PbO2 structure types are observed.) Silica and germania glasses have been shown to undergo analogous polyamorphic structural changes under pressure,45–47 first to an amorphous phase with 6-coordinated Si or Ge (at 10 GPa for SiO2, 6 GPa for GeO2) and then, with additional thermal activation at higher temperature, to disordered-NiAs or rutile crystalline phases at pressures below 25-30 GPa. (Still higher pressures at elevated temperature analogously yield CaCl2 and α-PbO2 structure types, as for crystalline precursors.) Figure 32 illustrates three v-GeO2 assemblies MD-modelled at densities of 3660, 4800 and 6000 kg/m3, corresponding to approximate hydrostatic pressures of 0.21, 2.7 and 22.8 GPa (~2, 27 and 230 kbar).

3600 kg/m3

4800 kg/m3

6000 kg/m3

Figure 32. Assemblies of v-GeO2, modelled by molecular dynamics at densities of 3600, 4800 and 6000 kg/m3, corresponding to pressures of 0.21 GPa (2.1 kbar), 2.7 GPa (27 kbar) and 22.8 GPa (228 kbar).44

The local cluster ring statistics and size distribution alter in revealing ways (Fig. 33). Starting with a ring-size distribution initially peaking near 7-rings (Ge-centered polytope representation), initial densification (to 4000 kg/m3) shifts the structure to a broad, stable distribution peaking at 6-rings. As the structure densifies further, 7- and 8- rings increase quickly in number, and the peak of the ring distribution shifts beyond 7-rings, reminiscent of

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the sort of topological shift in going from cristobalite (low density, 6-rings) to quartz (higher density, mostly 8-rings) in crystalline SiO2. At a critical density around 5500 kg/m3, a precipitous loss of 8-, 9- and larger rings occurs, and the ring distribution shifts back to a peak near 6-rings. The densification is accompanied all the while by a continual growth in 2-, 3- and 4-rings (polytope representation), all components of the rutile ring complement, Fig. 18b. At the same time, the Ge coordination increases monotonically from 4 to 5.7 and the O coordination from 2 to 2.85 (Fig. 34a) [cf. (4,2)-coordinated quartz, (6,3)-coordinated rutile], while the Ge and O local cluster sizes drop from about 85 and 55 atoms respectively (Fig. 34b) [quartz is 155 and 111, Fig. 17b; cristobalite is 69 and 45, Fig. 17a] to about 64 and 46 atoms [rutile is 53 and 33, fig. 18b]. At the highest density (6000 kg/m3), the number of 5- and 6-rings (polytopic) per local cluster has saturated or has begun to fall, while the 2-, 3- and 4-rings (polytopic) continue their rise.

Figure 33. Ge local-cluster ring size distribution for the v-GeO2 assemblies in Fig. 32, showing initial shift from near 6-ring (polytope representation) to near 8-ring dominance, followed by drop to 6-ring dominance as the Ge coordination increases from 4 O (GeO4 tetrahedra) to 6 O (GeO6 octahedra) at imposed densities between 5000 and 5500 kg/m3 for pressures of ~5–6 GPa (50–60 kbar). 2-rings represent the edge-sharing of [SiO6] octahedra found in the rutile structure.44

A proposed interpretation runs as follows: The starting structure of the simulated a-GeO2 is tetrahedral and lies somewhere between cristobaliteand quartz-like, but applied pressure quickly settles the structure into a stable

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distribution more like cristobalite (which is not a normal crystalline phase of GeO2), probably by closing up any initial underconnection or evening out heterogeneity in the starting configuration. As the glass is further pressured, the structure first attempts to deal with the imposed density increase with an increase in 7- and 8- rings (polytopic) that pack more densely than 6-rings, as in quartz or quartz-like silicas. Eventually, no more density increase can be wrought in this way with a 4-coordinated Ge network, and the Ge coordination changes to 6 by forming [GeO6] octahedra that can begin to edgeshare, further accommodating the imposed density increase. The conversion is not complete, however, with about 5% of the Ge atoms still 4-coordinated and probably interrupting the chain-like edge-sharing motif found in crystalline rutile, or perhaps favoring a slightly different {6,3}-connected motif as an alternative option—such as one based on anatase (ρ = 3.9×103 kg/m3, vs. 4.1×103 for rutile), which (unlike rutile) notably exhibits the 5-rings prominently observed in Fig. 33. R P L

Average coordination number 6.0

n o i t 5.5 a n i 5.0 d r o 4.5 o C

Average local cluster size 100

n i

O Ge

s 90 m o t a 80 f o

O Ge

r 70 e b m u N 60

e 4.0 g a r 3.5 e v A 3.0

50

2.5

2.0 3500

4000

4500

5000

Density

5500

6000

40 3500

4000

4500

5000

5500

6000

Density

Figure 34. Topological changes in v-GeO2 MD model under pressure, shown in evolution of a) average Ge coordination by O, and O by Ge, b) local cluster size (number of atoms) with increasing ensemble density.44

7. Conclusions A focus on connectivity, rather than symmetry and periodicity, provides a useful alternative way to characterize and relate crystalline structures and the easiest way to systematize topologically-disordered atomic arrangements

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and relate them to crystalline arrangements, to which they are very similar locally. The concept of the local cluster, embodying local connectivity rather than global symmetry, provides a characteristic unit entity of similar size to a crystalline unit cell for manageably describing extensive atomic arrangements, both crystalline and non-crystalline, and for identifying defects in both sorts of arrangement. The amorphizability of crystalline arrangements is seen to be, in broad outline, governed by topological properties of connectivity. In constructing models, self-assembly rules not only mimic nature but provide both a vehicle to, and an understanding of, the formation of non-crystalline atomic arrangements. 8. Acknowledgments The author is indebted to his former students and colleagues at MIT over the last quarter-century, for their willingness to share their own creative ideas and for the inspiration they provided where the ideas were his: Drs. Carol Marians, Esther Jesurum and Xianglong Yuan especially; Drs. A. N. Sreeram, Lu-chang Qin, Yi Zhang, and Profs. Bonnie Berger and Martin Bazant. Drs. Russell Schwartz and Alex Coventry and Mr. Vinay Pulim contributed creative assembly and maximal-matching codes, graphic user interfaces and artful realizations. Several more distant colleagues provided encouragement and useful sounding boards for the approaches described: Profs. Adrian Wright, Prabhat Gupta, Stephen Elliott, Austen Angell, Martin Dove, John Kieffer, Alastair Cormack, Michael Thorpe, Matthieu Micoulaut, Lia Addadi, Drs. David Griscom and Maria Orlova, and the late Dr. Frank Galeener. Finally, particularly fond tributes are owed to the late Prof. Alfred R. Cooper, friend and former colleague, for his pioneering insights into the amorphous state, and the late Prof. Cyril Stanley Smith, likewise friend and former colleague, for his almost religious fascination with the aesthetic of structure toward the end of his life; they taught me how to wrestle doggedly with an incomplete idea until it yielded up its connection to even greater mysteries. The support over the last three decades from the US Department of Energy, the Cambridge-MIT Institute, and the John F. Elliott chair is gratefully acknowledged.

References 1. M. J. Buerger, Elementary Crystallography (MIT Press, Cambridge, MA 1978), pp. 199–459. 2. The International Tables of Crystallography, Volume A: Space-Group Symmetry, 4th ed. (Kluwer Academic Publishers, Dordrecht, Netherlands, 1996).

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3. L. W. Hobbs, Network topology in aperiodic networks, J. Non-Cryst. Solids 192/193, 79–91 (1995). 4. W. H. Zachariasen, The atomic arrangements in glass, J. Amer. Chem. Soc. 54 (1932) 3841–3851. 5. L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell Univ. Press, Ithaca, NY, 1960). 6. P. Gupta and A. R. Cooper, Topologically disordered networks of rigid polytopes, J. Non-Cryst. Solids 123, 14–25 (1990). 7. L. W. Hobbs, C. E. Jesurum, V. Pulim and B. Berger, Local topology of silica networks, Philos. Mag. A78, 679–711 (1998). 8. L. W. Hobbs, C. E. Jesurum and B. Berger, The topology of silica networks, in: Structure and Imperfections in Amorphous and Crystalline Silicon Dioxide, ed. R. A. B. Devine, J.-P. Duraud and E. Dooryhée (John Wiley & Sons Ltd., Chichester, UK, 2000), pp. 3–48. 9. A. Angel, Strong and fragile liquids, glass transitions and polyamorphic transitions in covalently-bonded glassformers, in: Amorphous Insulators and Semiconductors, ed. M. F. Thorpe and M. I. Mitkova (NATO-ASI series, Plenum Press, 1997) p. 1–20. 10. L. W. Hobbs, C. E. Jesurum, V. Pulim and B. Berger, Topological modeling of cascade amorphization in network structures using local rules, Mater. Sci. Eng. A253, 16–29 (1998). 11. L. W. Hobbs, The role of topology and geometry in the irradiation-induced amorphization of network structures, J. Non-Cryst. Solids 182, 27–39 (1995). 12. J. Clerk Maxwell, On reciprocal figures and diagrams of force, Philos. Mag. 27, 250– 261; 294–299 (1864). 13. M. F. Thorpe, D. J. Jacobs, N. V. Chubynsky and A. J. Radar, Generic rigidity of network glasses, in: Rigidity Theory and Applications, ed. M. F. Thorpe and P. M. Duxbury, (Kluwer Academic/Plenum Publishers, New York, 1999) pp. 239–277. 14. G. Laman, On graphs and rigidity of plane skeletal structures, J. Engng. Math. 4, 331–40 (1970). 15. P. K. Gupta and A. R. Cooper, Topologically disordered networks of rigid polytopes, J. Non-Cryst. Solids 123, 14–25 (1990). 16. P. K. Gupta, Rigidity, connectivity, and glass-forming ability, J. Amer. Ceram. Soc. 76, 1088–1095 (1993). 17. L. W. Hobbs, A. N. Sreeram, C. E. Jesurum and B. A. Berger, Structural freedom, topological order, and the irradiation-induced amorphization of ceramic structures, Nucl. Instrum. Meth. Phys. Res B 116, 18–25 (1996). 18. L. W. Hobbs, C. E. Jesurum and B. Berger, Rigidity constraints in amorphization of singlyand multiply-polytopic structures, in: Rigidity Theory and Applications, ed. M. F. Thorpe and P. M. Duxbury, (Kluwer Academic/Plenum Publishers, New York, 1999) pp. 191–216. 19. L. W. Hobbs, C. E. Jesurum and B. Berger, Rigidity constraints in amorphization of multiply-polytopic multiply-connected ceramics structures, Mat. Res. Soc. Symp. Proc. 540, 717–728 (1999). 20. see, e.g., the short informative review by M. Telford, The case for bulk metallic glass, Materials Today (March 2004) 36–43. 21. L. M. Howe and M. Rainville, A study of the irradiation behaviour of Zr3Al, J. Nucl. Mater. 68, 215–234 (1977). 22. L. Addadi, S. Raz and S. Weiner, Taking advantage of disorder: Amorphous calcium carbonate and its roles in biomineralization, Adv. Mater. 15, 959–970 (2003). 23. C. S. Marians and L. W. Hobbs, The phase structure of aperiodic SiO2 as a function of network topology, J. Non-Cryst. Solids 106, 309–312 (1988). 24. C. S. Marians and L. W. Hobbs, Local structure of silica glass, J. Non-Cryst. Solids 119, 269–282 (1990). 25. C. S. Marians and L. W. Hobbs, Network properties of crystalline polymorphs of silica, J. Non-Cryst. Solids 124, 242–253 (1990).

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26. J. F. Shackleford, The interstitial structure of non-crystalline solids, J. Non-Cryst. Solids 204, 205–216 (1996). 27. C. Esther Jesurum, Local rules-based topological modelling of ceramic structure, Ph.D. thesis (Massachusetts Institute of Technology, Cambridge, MA, 1998). 28. C. E. Jesurum, V. Pulim and L. W. Hobbs, Topological modelling of amorphized tetrahedral ceramic network structures, J. Nucl. Mater. 253, 87–103 (1998). 29. X. Yuan and A. N. Cormack, Efficient algorithm for primitive ring statistics in topological networks, Computational Mater. Sci. 2, 343–360 (2002). 30. D. M. Bibby, N. B. Milestone and L. P. Aldridge, Silicalite-2: a silica analogue of the aluminosilicate zeolite ZSM-11, Nature 280, 664–665 (1979). 31. L. W. Hobbs, C. E. Jesurum, A. Coventry, V. Pulim, R. Schwartz and B. Berger, Towards a topological description of poorly-crystalline networks, in: Advanced Materials for the 21st Century: The Julia R. Weertman Symposium, ed. Y-W. Chung, D. Dunand, P. Liaw and G. Olson (TMS Publications, Warrendale, PA, 1999) pp. 475–486. 32. Xianglong Yuan, Vinay Pulim and Linn W. Hobbs, Molecular dynamics refinement of topologically generated reconstruction of simulated irradiation cascades in silica networks, J. Nucl. Mater. 289, 71–79 (2001); erratum, 295, 132 (2001). 33. W. Primak, Fast neutron-induced changes in quartz and vitreous silica, Phys. Rev. 110, 1240–1254 (1958). 34. F. W. Clinard, Jr. and L. W. Hobbs, Radiation effects in non-metals, Ch. 7 in: Physics of Radiation Effects, ed. R. A. Johnson and A. N. Orlov (Elsevier, Amsterdam, 1986) pp. 387–471. 35. Yi Zhang, Computer Simulation and Topological Modeling of Radiation Effects in Zircon, Ph.D. Thesis (Massachusetts Institute of Technology, Cambridge, MA, 2006). 36. A. C. Wright, The structure of vitreous silica: What have we learned in 60 years of diffraction studies, J. Non-Cryst. Solids 179, 84–115 (1994). 37. L. W. Hobbs and X. Yuan, Topology and topological disorder in silica, in: Defects in SiO2 and Related dielectrics: Science and Technology, ed. G. Pacchioni, L. Skuja and D. Griscom (Kluwer, Dordrecht, Netherlands, 2000), pp. 37–71. 38. S. R. Elliott, “Extended-range order, interstitial voids, and the first sharp diffraction peak of network glasses,” J. Non-Cryst. Solids 182, 40–48 (1995). 39. L. C. Qin and L. W. Hobbs, “Energy-filtered electron diffraction study of vitreous and amorphized silicas,” J. Non-Cryst. Solids 192/193, 456–462 (1995). 40. W. J. Weber, L. M. Wang and N. Yu, The irradiation-induced crystalline-to-amorphous phase transition in α-SiC, Nucl. Instrum. Meth. Phys. Res. B 116, 322–326 (1996). 41. X. Yuan and L. W. Hobbs, Modeling chemical and topological disorder in irradiationamorphized silicon carbide, Nucl. Instrum. Meth. Phys. Res. B 191, 74–82 (2002). 42. R. C. Ewing, B. C. Chakoumakos, G. R. Lumpkin and T. Murakami, The metamict state, Materials Research Bulletin 12, 58–66 (1987). 43. W. J. Weber, R. C. Ewing, C. R. A. Catlow, T. Diaz de la Rubia, L. W. Hobbs, C. Kinoshita, Hj. Matzke, A. T. Motta, N. Nastasi, E. K. H. Salje, E. R. Vance and S. J. Zinkle, Radiation effects in crystalline ceramics for immobilization of high-level nuclear waste and plutonium, J. Mater. Res. 13, 1434–1484 (1998). 44. M. Micoulaut, X. Yuan and L. W. Hobbs, “Coordination and intermediate-range order alterations in densified germania,” J. Non-Crystalline Solids 353, 1961–1965 (2007). 45. V. P. Prakapenka, Guoyin Chen, L. S. Dubrovinski, M. L. Rivers and S. R. Sutton, Highpressure induced phase transformation of SiO2 and GeO2: difference and similarity, J. Phys. Chem. Solids 65, 1537–1545 (2004). 46. A. Polian and M. Grimsditch, Room-temperature densification of a-SiO2 versus pressure, Phys. Rev. B 41, 6086–6087 (1990). 47. C. H. Polsky, K. H. Smith and G. H. Wolf, Effects of pressure on the absolute Raman scattering cross section of SiO2 and GeO2 glasses, J. Non-Cryst. Solids 248, 159–168 (1999).

HYDROGEN-BONDED CRYSTALS OF EXCEPTIONAL DIELECTRIC PROPERTIES

ANDRZEJ KATRUSIAK Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Pozna (Poland)

Abstract. Hydrogen bonds are well known for governing the molecular association and crystal packing, as well as for their contribution to the chemical and physical properties of substances. They affect the properties of materials as versatile as amphibole minerals, KDP-type (–OH···O= bonded) ferroelectrics or biopolymers (e.g. cellulose). While the classical examples of such materials usually concentrate on the –OH···O= bonds, recently analogical and completely new features were observed in –NH···N= bonded substances. The key factor for understanding these new properties is the structural coupling between molecular arrangements and H-atom position in the NH···N hydrogen bonds. In this paper the very weak NH···N involving Nsp3 nitrogen atoms in secondary and tertiary amines has been compared. Clear preferences for the molecular orientation depending on the H-atom position have been revealed for the small, weakly interacting molecules for the molecular crystals of aziridine, C2H5N, and difluoroamine, HNF2. This coupling explains the microscopic mechanisms accompanying reorientations or inversions of the ammonium groups and molecular rearrangements, which are essential for understanding dynamics of protons in H-bonds, or spontaneous polarization and phase transitions in NH···N hydrogen-bonded materials. The directional preferences of NH···N hydrogen bonds can be employed for engineering transformable crystal structures, for predicting physical properties of crystals built of small molecules, for analyzing the molecular associations and conformations of larger molecules and biopolymers, or validating structural determinations. On the other hand, specific features of molecular structure, conformation or molecular arrangement in aggregates and crystal structure can compete with the subtle orientational preferences induced by NH···N bonds. Such systematic conformational preferences in molecular aggregates exist in the structures of piperazine, piperidine and morpholine. Very weak coupling between the H+-site and ionic displacements in dabco NH+···N bonded complexes is connected with

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the ferroelectric and relaxor-like behaviour of these compounds. The structural preferences of even very weak NH···N bonds are very highly unlikely to be exactly matched by the requirements of crystal packing, which results in strains and competitions between the H-bonds and other cohesion forces. This feature can be employed for designing crystal structures where polarizability of the hydrogen bonds contributes to the properties of the materials.

1. Introduction The importance of hydrogen bonds for properties of various materials, minerals or biological substances, has been recognized and investigated for decades (e.g. see Refs. [1–5]). Due to relatively weak energy associated with hydrogen bonds – intermediate between covalent bonds or electrostatic forces and van der Waals interactions – the hydrogen bond can transform at room temperature. However the mechanisms and origins of these transformations, such as H-transfers, H-disordering, or reorientations of the H-donor groups, are still not fully understood. One of main experimental difficulties in precisely investigating the properties and transformations of hydrogen bonds in general is that their energy is comparable, and indeed often much lower, than the energy of other cohesion forces in crystals. Hence it is apparent that the studied effects are not undisturbed, but often blurred by other interactions. For this reason the best investigated are strong homoconjugated OH···O hydrogen bonds. In some materials the hydrogen bonds are associated with a spontaneous polarization and ferroelectric properties, like in the prototypic OH···O= bonded KH2PO4 ferroelectric (usually abbreviated KDP); also ordered phases of the H2O ice exhibit ferroelectricity in the KOH-doped samples [6]. These transformations and properties of the crystals cannot be restricted to the hydrogen bonds themselves. It was already shown for strong OH—O and NH—N homoconjugated bonds, that the Hsite in the hydrogen bond is coupled to the molecular or ionic arrangement. Initially, strong OH···O= hydrogen bonds in the KDP-type ferroelectrics [7,8], and then weaker OH···OH hydrogen bonds involving Osp3 oxygens [9] were investigated. Meanwhile, the NH···N hydrogen bonds are known for their high polarizability [10,11]. The polarizability of the H-bonds can be attributed to the intrinsic and external factors [11]. The external factors, which are due to the interactions of the molecules or ions with the environment, are responsible for the coupling between the H-site and the structure of the hydrogen-bonded molecules or ions. The interdependence between the H-site and molecular environments in crystal structures was described

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for the NH···N hydrogen bonds involving Nsp2 nitrogens [12]. A very weak coupling between proton-site and structure result in ferroelectric properties of the NH+···N bonded dabcoHA monosalts (dabco stands for 1,4-diazabicyclo [2.2.2]octane, and HA for mineral acids) [13, 14], where both the nitrogens are in the sp3 hybridisation. In NH+···N bonded pyrazine monosalts [15] this coupling is much stronger. It was confirmed that in the ionic crystals the proton site in hydrogen bonds depends on its immediate surroundings and on the anionic arrangement. Weak relaxor-like properties were detected in the H-bonded complexes of dabco, and this behaviour was associated with transformations of the Nsp3H+···Nsp3 bonds [16]. Most recently analogous behaviour was detected in pyrazinium H-bonded complexes, with the NH+···N hydrogen bonds involving Nsp2 atoms. Presently we describe the structural correlations in the crystals built of hydrogen-bonded secondary amines with the weakest of NH···N bonds involving the Nsp3 nitrogen atoms. To observe the structural correlations with molecular arrangements, the other cohesion forces and the molecular shape should be minimized. The subtle effects of the strains induced by NH···N bonds are also essential for understanding the coupling of the H transfers with lattice-mode vibrations in all hydrogen-bonded crystals, or with conformational transformations in supramolecular aggregates and macromolecules. Substances of very weakly interacting molecules of low molecular weight are usually liquids or gases at normal conditions. Therefore their association should be studied either at low temperatures or elevated pressures [17,18], which considerably complicates the measurements of the X-ray intensity data. Thus, despite the abundance of crystal structures with NH···N bonds in crystallographic literature and databases, the study of the subtle effects of the stereochemical preferences of the Nsp3H+···Nsp3 bonds can be limited to very few specific structures only, for which the effects of other intermolecular interactions for molecular arrangement can be considered small and the role of NH···N hydrogen bonds is dominant. The search for the suitable structures for such an analysis has been based on the following criteria: (i) the structure should have a weak Nsp3H···Nsp3 hydrogen bond involving (ii) only one H-donor, and one H-acceptor group per molecule, to minimize the effects of strains due to the formation of a network of hydrogen bonds; (iii) the molecule should be symmetric with respect to the possible H-atom transfers between the H-donor and acceptor sites; (iv) it should be a molecular crystal, with all intermolecular forces other than Nsp3H···Nsp3 bond possibly weak; (v) the molecular weight of the substance should be possibly low, to minimize the effect of crystal packing on the Nsp3H···Nsp3 bond dimensions.

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The search for suitable candidates fulfilling these criteria resulted in two structures, of aziridine and difluoroamine. For these two structures the interplay of directional preferences of NH···N bonds and molecular arrangements has been analyzed below. Aziridine is the simplest nitrogen heterocycle with strongly strained ring, and difluoroamine is a simple acyclic compound. In both these structures small molecules are linked by weak NH···N bonds, with the N···N distances longer than 3 Å, into one-dimensional aggregates. Owing to the small molecular size and absence of strong ionic or other intermolecular interactions, these crystals are uniquely suited for investigating most subtle structural effects of molecular arrangement induced by very weak bonds. Structural preferences related to the NH···N bonding exist also in the structures, where the H-transfers are very unlikely due to conformational preferences of the H-bonded molecules. Such structures can be exemplified by a series of three analogous secondary amines built of small molecules: piperazine, piperidine and morpholine. For these compounds the condition (ii) of the molecules being symmetric with respect to the H site is not fulfilled, and it is shown below that this considerably changes the molecular arrangement with respect to the NH···N bonds binding the aggregates. The structural correlations in Nsp3H+···Nsp3 bonded complexes of dabco with mineral acids involve the conformational transformations of the cations and electrostatic interactions, shifts and rotations of the anions. 2. Aziridine and Difluoroamine Crystals The crystal structure of aziridine was determined at 145 K [19] and that of difluoroamine at 123 K [20], by X-ray diffraction with an exceptional precision for such elaborate experiments. All H-atoms have been located and refined. In aziridine the determined positions of the H-atoms are very consistent between three symmetry independent molecules. The molecules are hydrogen bonded into chains along the crystal [010] direction, as shown in Figure 1. The neighbouring chains are related by a centre of symmetry, however each chain is asymmetric (except for the crystal translationalsymmetry vector b). Thus a polarization can be assigned to each of the chains. The sense of this polarization will be further assumed as indicated by the sense of the N-H bonds of the molecules within the chain. One-dimensional polarized aggregates are formed also in the crystals of difluoroamine, as shown in Figure 2, however in this structure one molecule constitutes the asymmetric part of the unit cell. Owing to the parallel arrangements of the chains this structure may be ferroelectric. It can be observed from Figure 3, that the molecules are tilted with respect to the direction of the chain, so the reversal of the chain polarization requires not only that the H-atoms change

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their sites in the hydrogen bonds (from NH···N to N···HN), but also that the molecules reorient by 9.0° to change their tilt with respect to the chain direction (in HNF2 the ring plane is inclined by 4.50°, and in in DNF2 by 4.63°, to the [001] axis).

Figure 1. Two symmetry-independent intervals of the NH···N bonded chain of aziridine crystal. The H-bonds in the other network are represented as dashed lines. The crystal [010] direction is horizontal in this drawing.

Figure 2. The NH···N bonded chain of difluoroamine molecules.

The aziridine structure is centrosymmetric, space group P 1 , and the chains are antiparallel. The crystal environment (paracrystal) of each symmetryindependent aziridine is considerably different for the symmetry-independent molecules [19], as can be seen in Figures 1 and 4. Thus the orientation of the molecules with respect to the H-bonded aggregate is more complicated than in difluoroamine, where only one molecule is symmetry-independent. However in both these structures the NH···N hydrogen bonds can be regarded as the main motive governing the molecular arrangement, and therefore the molecular orientation will be referred to the directions of the NH···N bond, to the H-atom position and to the H-accepting nitrogen atom.

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Figure 3. The molecular packing of the NH···N bonded chains in the difluoroamine crystal structure. Two NH···N bonded chains are shown in the autostereographic projection approximately down the [010] crystal axis, the [001] axis is horizontal in this drawing.

Figure 4. The molecular packing of the NH···N bonded chains in the aziridine crystal structure. Four NH···N bonded chains are shown in an autostereographic projection approximately down the [100] crystal axis.

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3. Polarization-Structure In this study, the structural coupling related to the chain polarization (Hatoms sites) has been investigated by two different methods: (i) by comparing the Donohue angles [21], the magnitudes of which can be calculated without the knowledge of the H-atom position; and (ii) by comparing the molecular arrangements and NH···N bonds dimensions experimentally determined by x-rays [19, 20], with a hypothetical structure where the chain polarization has been reversed by moving the aminohydrogens to the opposite side of the NH···N bond (i.e. to the other side of the molecular plane). The Donohue angles C–N····N and N····N–C, plotted in Figure 5, demonstrate clearly that the location of the H-atom influences the arrangement of the hydrogen-bonded aziridine molecules. It is evident that the Donohue angles are smaller on the donor side of the N-H···N bond than on the acceptor side. The magnitudes of the H-donor Donohue angles are within 93.3° and 110.9°, and the H-acceptor Donohue angles within 105.9o and 132.5o. The average values of the donor and acceptor angles are 99.95° and 120.52°, respectively, so the average difference of 20.57° is substantial. Also the inspection of the dimensions of the hypothetical H-locations confirmed the existence of the coupling of the H-site and molecular arrangement in the crystal. The physical process, which would lead to the H-site change, could be realized by the N-inversions, rotations of the molecules by 180° about the axis passing through the N-atom and lying in the molecular plane, or by the H-transfer to the other side of the NH···N hydrogen bond. The N-inversion (which would require the energy of 76(1) kJ/mol [22]), molecular rotations and H-transfers all appear unlikely for aziridine in the crystalline state at low-temperature conditions. For our theoretical considerations we have chosen to obtain the locations of the hypothetical acidic H-atoms by rotating the experimentally determined H-atoms by 180° about the line bisecting the C-N-C angles. The dimensions of the real and hypothetical hydrogen bonds have been compared in Table 1. Only for one of three hypothetical hydrogen bonds, the H*···N distance is marginally shorter, by 0.008 Å, than the experimentally determined counterpart. This difference is even smaller than the standard deviation of the measurements, hence hardly significant. Meanwhile the calculated H*···N distances in two other hydrogen bonds are significantly longer than the observed ones (Table 1). The average H*···N distance of three hypothetical bonds is 2.280 Å, compared to the average H···N distance of those determined experimentally of 2.216 Å, and the average of three hypothetical N-H*···N angles is 150.2° compared to the experimental

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average of angles of 164.8°. Thus the average H···N distance realized in the crystal structure of aziridine is by 0.064 Å shorter than the average of the hypothetical hydrogen bonds – a similar result as was obtained for NH···N bonds involving sp2 nitrogens [12]. TABLE 1. Dimensions of NH···N bonds in aziridine. The values denoted with asterisks are the dimensions of the hypothetical hydrogen bonds, which would be formed by the H-atom moved to the other side of the aziridine plane, but without any changes in molecular dimensions or arrangement (see the text) Hydrogen Bond N(1)H(1)···N(3) H(1*)···N(2) N(2)H(2)···N(1) H(2*)···N(3) N(3)H(3)···N(2) H(3*)···N(1)

N· · ·N (Å) 3.082(1) 3.085* 3.085(1) 3.069* 3.069(1) 3.082*

H···N (Å) 2.240 2.232* 2.200 2.328* 2.209 2.280*

N-H···N (°) 157.1 159.8* 175.8 141.1* 161.4 149.3*

The difference between the observed and hypothetical hydrogen-bonded structures in principle can be applied for calculating lattice energy difference associated with the transformations from one structure to the other. However such calculations cannot be generalized from statistical distributions, but should be done for specific structures [23]. Although the arrangements of molecules or ions may be successfully correlated to thermodynamic characteristics of hydrogen-bonded crystals [8], such considerations should be related to individual structures. Meanwhile the surroundings of the aziridine or difluoroamine molecules are unique and very different (Figs. 1 and 2), which is due to their different positions in the supramolecular chains. These differences can be illustrated for the aziridine crystal by torsion angles along the N···N hydrogen bonds and to the bisecting lines of the C-N-C angles: 68.8, 167.9 and 106.9° for the hydrogen bonds with N(1), N(2) and N(3) as H-donors, respectively. It can be noted from the plot comparing the Donohue angles in Figure 5, that the difference between these angles on the H-donor and H-acceptor sites are considerably larger for the strained aziridine rings than for the difluoroamine molecules. It is plausible, that these differences introduce distortions in the arrangement of molecules from their positions favoured by the van der Waals interactions alone. The larger differences between the donor and acceptor Donohue angles, and hence larger strains of the hydrogen bonds and in close packing of molecules, are likely to contribute to the crystal symmetry with three symmetry-independent molecules in the aziridine crystal: fewer symmetry constrains give more options to release these strains.

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Figure 5. The H-donor Donohue angles plotted against the H-acceptor Donohue angles (C–N····N’ and F–N····N’) for the three symmetry-independent aziridine molecules in the crystal (full triangles pointing up) and for difluoroamine (full triangles pointing down). The open symbols show the C-N-H or F-N-H angles averaged for each molecule, plotted against the averaged H···N-C and H···N-F angles (see the text), respectively.

The coupling between the H-site and crystal structure is of particular importance for these structures, where the H-atoms can change their sites. Such H-site changes can reverse the polarization of the hydrogen-bonded aggregates, and of the spontaneous polarization of the crystal. The ability of the H-atom to change its site in the NH···N bond is regulated, apart from the length of the NH···N distance or the mobility of the NH group, by the ability of the molecular arrangement to adjust in the way relaxing the strains of the hydrogen bonds after the H-transfer. The interdependence between the Hsite and molecular arrangement is essential for understanding the role of molecular and lattice-mode vibrations for the H-transfers. Rotations of the H-bonded groups can reverse the favoured site of the H-atom. In this way the H-atom site can be coupled to the lattice-mode vibrations. The Htransfer can proceed either in the adiabatic or non adiabatic mode [25], as shown in Figure 6, however even the adiabatic mode of transformations (such as in paraelectric phases of dabcoHBF4 or KH2PO4) the proton transfers are coupled to vibrations of the H-bonded groups and of ions.

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EP

>N H

N<

Figure 6. Adiabatic (red line) and non-adiabatic (i.e. diabatic – blue line) potential energy functions describing the NH···N bond transformations.

4. Non-Equivalent H-Sites in Piperazine, Piperidine and Morpholine The crystals of piperazine (m.p. 379K), piperidine (m.p. 264K) and morpholine (m.p. 268K) are convenient structures for illustrating a reverse situation, when the H-site in the hydrogen bond is fixed by the favoured conformation of the hydrogen-bonded molecules. The molecular packing depends on the molecular conformation, and thus the H-site can be considered to be determined by the given molecular conformation and arrangement. We shell investigate below, if for such arrangements the structural preferences of the NH···N hydrogen bonds, as observed for aziridine and difluoroamine, are still realized in the crystal structures. In piperazine, piperidine and morpholine the molecular conformation is coupled to the site of the H-atom involved in the hydrogen bonding. The H sites in the NH···N bonds are not equivalent, and the occupied sites are in the equatorial position in all these molecules. Such a conformational preference, of the equatorial versus axial H-atom position, considerably affects the subtle nature of relations between the NH···N bonds structure and molecular arrangement. The crystal structures of piperazine, piperidine and morpholine all were determined at 150K [24]. In piperazine the NH···N bonds link the molecules into sheets (Figure 7a), while in piperidine (Figures 7b and 8) and morpholine these are C(2) chains (Figures 9 and 10).

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Figure 7a. The molecular packing of the NH···N bonded sheet in the piperazine crystal structure. The NH···N bonded chains are shown in the autostereographic projection approximately down the [100] crystal axis, the C(2) NH···N bonded chains run along the [010] axis.

Figure 7b. The NH···N bonded chains in the piperidine crystal structure shown in the autostereographic projection approximately down the [–102] crystal axis, the C(2) NH···N bonded chains run along the [010] axis.

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Figure 8. The arrangement of NH···N bonded chains in the piperidine crystal structure shown in the autostereographic projection approximately down the [–102] crystal axis, the C(2) NH···N bonded chains run along the [010] axis.

Figure 9. The NH···N bonded chains in the piperidine crystal structure shown in the autostereographic projection approximately down the [–102] crystal axis, the C(2) NH···N bonded chains run along the [010] axis.

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Figure 10. The arrangement of NH···N bonded chains in the morpholine crystal structure shown in the autostereographic projection down the [001] crystal axis, the C(2) NH···N bonded chains run along the [100] axis.

The distribution of the Donohue angles in piperazine, piperidine and morpholine, shown in Figure 11, is clearly less well defined than in aziridine and difluoroamine (cf. Figure 5) in this respect, that the donor angles are not always smaller than the acceptor angles. The same applied to the C-N-H and H···N-C angles in piperazine, piperidine and morpholine (compare Figures 5 and 11). The common features of the distributions of the Donohue and C-N-H vs. H···N-C angles are the ranges of the distributions of these angles, considerably (i.e. almost twice) larger on the acceptor side than on the donor side. The comparison of crystal structures of piperazine, piperidine and morpholine illustrates the competition between the molecular arrangement favoured by hydrogen bonds and the molecular orientation compatible with van der Waals close packing. Table 2 lists the H···N distances of the ideally located H atoms in their (observed) equatorial and (unoccupied) axial locations. It can be seen, that despite the conformational preference of the H-atom to assume the equatorial location, the crystal structures have been

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arranged in the way favouring the closer H···N contacts, albeit only marginally for the piperazine and piperidine crystals. 5. Dabco NH+···N Bonded Complexes Dabco (1,4-diazabicyclo[2.2.2]octane, C6H12N2) NH+···N bonded complexes with mineral acids constitute an important group of hydrogen-bonded compounds, for which ferroelectric properties and relaxor-like behaviour were observed [26]. In the dabcoHA complexes of this type, for example dabcoHBF4, dabcoHClO4, dabcoHReO4, dabcoHBr, the proton is located in the cation exceptionally in this respect, that it lies along the molecular C3 morpholine Donohue angles morpholine C−N−H and H---N−C angles piperazine H-bond Donohue angles piperazine C−N−H and H---N−C angles piperidine H-bond Donohue angles piperidine C−N−H and H---N−C angles line of equal donor and acceptor angles 126 124 122 120 118

H-bond acceptor angles (deg.)

116 114 112 110 108 106 104 102 100 98 96 94 92 90 88 102

104

106

108

110

112

114

116

118

120

122

H-bond donor angles (deg.)

Figure 11. The H-donor Donohue angles plotted against the acceptor Donohue angles (C–N····N’) for the piperazine, piperidine and morpholine crystals at 150 K (full symbols). The open symbols show the C-N-H angles plotted against the H···N-C angles.

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symmetry axis, and also the preferred direction for accepting the proton by the other nitrogen atom lies along the same direction. Consequently, the coupling of the proton site in the hydrogen bond with the arrangement of the hydrogen-bonded ions is very weak. When combined with the low disproportionation energy between the dabco molecule, dabco onocations and dabco dication, this property leads to the disproportionation defects in the chains, as illustrated in Figure 12, and polar nano-regions even in centrosymmetric crystals. These regions are considered responsible for the exceptional dielectric properties of these compounds. TABLE 2. The H···N distances in the NH···N hydrogen bonds in piperazine, piperidine and morpholine for the ideally positioned H-atoms in their equatorial (observed in the crystal structures) and axial (not observed) conformations. The N-H distance of 0.97 Å was assumed in for all these calculations Piperazine Piperidine Morpholine

N···H(equatorial – observed) 2.299 Å 2.294 Å 2.345 Å

N···H(axial – hypothetical) 2.300 Å 2.295 Å 2.404 Å

Figure 12. The molecular packing of the NH+···N bonded sheet in the piperazine crystal structure. Two NH···N bonded chains are shown in the autostereographic projection approximately down the [100] crystal axis, the C(2) NH···N bonded chains run along the [010] axis.

Figure 13. The molecular packing of the NH+···N bonded chain in the dabcoHBF4 crystal structure. Two NH···N bonded chains are shown in the autostereographic projection approximately down the [100] crystal axis, the C(2) NH···N bonded chains run along the [010] axis.

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In principle, owing to their C3-symmetric structure of the dabco cation, the proton sites in the hydrogen bonds in the dabcoHA complexes with the cations NH+···N bonded into perfectly linear chains should be decoupled from the molecular arrangement, if the Donohue angles were to be considered only. Such a structure with perfectly linear NH+···N bonded cationic chains was observed in the dabcoHBr complex, forming P 6 2m symmetric crystals [27]. In this crystal the protons are disordered in two half-occupied sites in the NH+···N bonds at room temperature. A stronger coupling between the proton site and crystal structure exists in the NH+···N bonded dabco complexes with HBF4, HClO4 and HReO4 acids. In these complexes the protons are ordered in the NH+···N bonds at room temperature, and the crystals are ferroelectric till about 370 K when the protons become disordered and the crystals transform into paraelectric phases. In these ionic structures, apart from the geometric preferences depending on the H-bond dimensions and arrangement of the H-bonded groups, the proton site is coupled to the location of the counter ions. The closest distances of the nitrogen atoms in the dabco complexes are listed in Table 3. It can be observed, that in dabcoHBF4 and dabcoHClO4 structures the central atoms of the tetrahedral counter-ions are located almost 0.3 closer to the protonated nitrogens than to those not protonated. The closest distance of the F atoms of the anion to the protonated nitrogen is marginally closer in dabcoHBF4, than to the unprotonated nitrogen. In dabcoHClO4 the distances of the oxygen atoms to the protonated nitrogen is marginally longer, by 0.01 , than to the unprotonated one. In dabcoHReO4 the central Re atom of the tetrahedral anion is 0.136 closer to the unprotonated nitrogen, but these are the oxygen atoms in this compound which are significantly closer to the protonated nitrogens, by 0.155 (Table 3). The different correlation between the protonation site and closest distances in these complexes TABLE 3. Distances of the nitrogen atoms involved in the NH+···N hydrogen bonds in dabcoHBF4, dabcoHClO4 and dabcoHReO4, to three closest atoms of the counterions (Å) dabcoHBF4 N+···B 4.293 Å 5.509 6.041 N ···B 4.570 Å 5.421 5.747 N+···F 3.950 Å 3.950 4.144 N ···F 3.974 Å 3.974 4.415

DabcoHClO4 N+···Cl 4.389 Å 5.565 6.117 N ···Cl 4.650 Å 5.516 5.796 N+···O 4.031 Å 4.031 4.286 N ···O 4.021 Å 4.021 4.377

dabcoHReO4 N+···Re 4.722 Å 4.912 4.912 N ···Re 4.586 Å 4.746 4.746 N+···O 3.672 Å 3.672 4.043 N ···O 3.827 Å 3.827 4.227

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coincide with their different symmetries: dabcoHBF4 and dabcoHClO4 are isostructural in their orthorhombic ferroelectric phase at 293K, and their NH+···N bonded chains are antiparallel, whereas dabcoHReO4 is monoclinic and the chains are parallel. It was shown also for other compounds that the ionic character of the crystal introduces a strong electrostatic preferences for the proton site [12]. 6. Validation of Molecular Structures The valency angles C-N-H determined experimentally [19] (calculated from the crystal data deposited in Cambridge Crystallographic Database Centre) gave the average value of 107.6(10)° (the standard deviation from the distribution of values). We have found that the H···N distances and NH···N angles are very sensitive to these molecular dimensions. As a test for the significance of the H···N distances and N-H···N angles for the structural correlations described above we have calculated the acidic H-atoms coordinates by using a standard procedure for generating H-atom positions from the molecular skeleton. So located N-H bonds were at 117.8° to the N-C bonds in all three symmetry-independent molecules. So located H-atoms in two of three independent hydrogen bonds favoured the opposite than observed polarizations, while in the third case the difference indicating the observed polarization would be considerably smaller. Thus, the coupling rules can be employed as a sensitive method for validating information on molecular geometry. The molecular aggregation also provides unique information about the H-accepting properties of molecules. Thus it is plausible, that the arrangement of molecules can be applied for verifying the directions of lone-electron pairs at N-atoms, basing on the assumption that the C-N···H angles depend on the position of the lone electron pair. The average position of six C-N···H angles in aziridine is 120.8°. We have found that similar angles are formed to the direction equally inclined to the C-N and H-N bonds in aziridine: 122.0°, 121.6° and 122.3° in molecules (a), (b) and (c), respectively. Also in the structure of difluoroamine [10] the angle equally inclined to two F-N and one N-H bonds is 115.6°, very close to the observed F-N···H angles of 114.8 and 114.9°. 7. Conclusions It has been shown that the structural coupling of the H-atom site in NH···N hydrogen bonds persists even for very weak hydrogen bonds involving Nsp3 nitrogen atoms. Although these geometrical effects are often overwhelmed by other stronger interactions in crystal lattices – like electrostatic forces in

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ionic crystals, van der Waals forces between large molecules arranging according to the close-packing rule, or other hydrogen bonds – they nevertheless contribute to the molecular arrangement in the crystal. The existence of such subtle effects has far reaching consequences: they constitute a factor introducing into a crystal structure a small ‘frustration’ – molecular displacements, which along with the H-atom position contribute to breaking the crystal symmetry. Thus such structural transformations can lead to phase transitions, drastically changing properties of the crystal, or to formation of molecular switches, i.e. the molecules changing their polarization in the crystal or liquid state. On the other hand, the frustrations can provide information on the electronic structure of molecules, including the direction of the lone-electron pair at the N-atom and its best H-accepting properties. The crystal arrangement in aziridine crystals indicates that in these strained molecules the lone pair is equi-inclined to the C-N and N-H bonds. A similar observation has been made for the unstrained molecule of difluoroamine. The directions of the N-H bond and of the lone-electron pair combined with the directionality of hydrogen bonds explain the origin of the coupling of molecular arrangement to the H-site in the hydrogen bond. This coupling equally applies to H-atom dynamics in hydrogen bonds, coupled to the lattice mode vibrations in crystals, and involving momentary rearrangements of molecules. For the linear NH+···N bonded dabco aggregates the coupling between the proton site and molecular orientation is very week, and therefore a new kind of phenomena connected with the polarisation of this system can be expected [13-16]. The NH+···N bonds in dabco monosalts can undergo also other types of transformations [28]. Studies on these and also on other model NH···N bonded compounds are continued [29]. Naturally, this chapter outlines only the topic of the coupling of H-transfer and H-disordering in hydrogen bonds with atomic/ionic displacements, and its consequences for macroscopic properties of crystals, mainly ferroelectrics. The general structure-property relations for H-bonded substances are far more reaching, and one can easly find numerous publicadions devoted to this subject. 8. Acknowledgments This study was supported by the Polish Committee for Scientific Research, Grant N202 14631/2707.

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References 1. L. Sobczyk (Ed.), Hydrogen Bonds, (PWN, Warsaw, 1969). 2. A. J. Barnes and H. Ratajczak (Eds.), Hydrogen Bonds and Proton Transfer Phenomena, J. Mol. Struct. 270 (1992). 3. P. Schuster, G. Zundel and C. Sandorfy (Eds.), The Hydrogen Bond, Vols. 1-3 (North Holland, Amsterdam, 1976). 4. G. A. Jeffrey and W. Saenger, Hydrogen Bonding in Biological Structures (SpringerVerlag, Berlin, 1991). 5. J. F. Nagle, M. Mille and H. J. Morowitz, Theory of hydrogen bonded chains in bioenergetics, J. Chem. Phys. 72, 3959–3971 (1980). 6. A. Minagawa, Ferroelectric phase-transition and anisotropy of dielectric-constant in ice IH, J. Phys. Soc. Japan 50, 3669–3676 (1981). 7. A. Katrusiak, Geometric effects of H-atom disordering in hydrogen-bonded ferroelectrics , Phys. Rev. B 48, 2992–3002 (1993). 8. A. Katrusiak, Coupling of displacive and order-disorder transformations in hydrogenbonded ferroelectrics, Phys. Rev. 51, 589–592 (1995). 9. A. Katrusiak, Modelling Hydrogen-bonded Crystal Structures beyond Resolution of Diffraction Methods, Pol. J. Chem. 72, 449–459 (1998). 10. A. Rabold, R. Bauer and G. Zundel, Structurally Symmetrical N+H· · ·N - N · · ·H+N Bonds. The Proton Potential as a Function of the pKa of the N-Base. FTIR Results and Quantum Chemical Calculations, J. Phys. Chem. 99, 1889–1895 (1995). 11. G. Zundel and J. Fritsch, Environmental interaction of hydrogen bonds showing a large proton polarizability. Molecular processes and the thermodynamics of acid dissociation, J. Phys. Chem. 88, 6295–6302 (1984). 12. A. Katrusiak, Stereochemistry and transformations of NH···N hydrogen bonds. Part I. Structural preferences for the H-site, J. Mol. Struct. 474, 125–133 (1999). 13. A. Katrusiak and M. Szafra ski Ferroelectricity in NH···N Hydrogen-Bonded Crystals, Phys. Rev. Lett. 82, 576-579 (1999). 14. M. Szafra ski, A. Katrusiak and G. J. McIntyre, Ferroelectric order of parallel bistable hydrogen bonds, Phys. Rev. Lett. 89, 215507-1–4 (2002). 15. A. Katrusiak and M. Szafra ski, Disproportionation of pyrazine in NH+ ...N hydrogenbonded complexes: new materials of exceptional dielectric response, J. Am. Chem. Soc. 128, 15775–15785 (2006). 16. M. Szafra ski and A. Katrusiak, Short-Range Ferroelectric Order Induced by Proton Transfer-Mediated Ionicity, J. Phys. Chem. B 108, 15709–15713 (2004). 17. M. Bujak and A. Katrusiak, In-situ pressure crystallization and X-ray diffraction study of 1,1,2,2-tetrachloroethane at 0.5 GPa, Z. Kristallographie 219, 669–674 (2004). 18. K. Dziubek and A. Katrusiak, Compression of Intermolecular Interactions in CS2 Crystal, J. Phys. Chem. B 108, 19089–19092 (2004). 19. N. W. Mitzel, J. Riede and Ch. Kiener, The Crystal Structure of Aziridine, Ang. Chem. Int. Ed. 36, 2215–2216 (1997). 20. M. F. Klapdor, H. Willner, W. Poll and D. Mootz, The Crystal Structure of Difluoroamine, Angew. Chem. Int. Ed. 35, 320–321 (1996). 21. J. Donohue, In Structural Chemistry and Molecular Biology (Eds. A. Rich and N. Davison), pp. 443–465 (Freeman, San Francisco, 1968). 22. P. T. Trapentsier, I. Ya. Kalvin’sh, E. E. Liepin’sh and E. Lukevits, Sintez i vosstanovlenie proizvodnih aziridinmono- i dikarbonovih kislot. Khimia Geterotcilk. Soed. 9, 1227– 1235 (1983). 23. H.-B. Bürgi and J. D. Dunitz, Can statistical analysis of structural parameters from different crystal environments lead to quantitative energy relationships? Acta Cryst. B 44, 445–448 (1988).

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24. A. Parkin, I.D.H. Oswald and S. Parsons, Structures of piperazine, piperidine and morpholine, Acta Cryst. B 60, 219–227 (2004). 25. A. Katrusiak, Crystal Engineering: From Molecules and Crystals to Materials, Eds.: D. Braga, F. Grepioni, A. G. Orpen, pp. 389–406 (Kluwer Academic Publishers, Netherlands, 1999). 26. M. Szafranski and A. Katrusiak, Short-Range Ferroelectric Order Induced by Proton Transfer-Mediated Ionicity, J. Phys. Chem. B 108, 15709–15713 (2004). 27. A. Katrusiak, M. Ratajczak-Sitarz, and E. Grech, Stereochemistry and transformations of NH···N hydrogen bonds. Part II. Proton stability in the monosalts of 1,4-diazabicyclo [2.2.2]octane, J. Mol. Struct. 474, 135–141 (1999). 28. A. Budzianowski, and A. Katrusiak, Pressure Tuning between NH···N Hydrogen-Bonded Ice Analogue and NH···Br Polar dabcoHBr Complexes. J. Phys. Chem. B. 110, 9755– 9758 (2006). 29. A. Budzianowski, A. Olejniczak and A. Katrusiak, Competing hydrogen-bonding patterns and phase transitions of 1,2-diaminoethane at varied temperature and pressure. Acta Cryst. B 62, 1078–1089 (2006).

CHIRALITY IN CRYSTALS

REIKO KURODA Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo, 153-8902 Japan & JST ERATO-SORST Kuroda Chiromorphology Team, 4-7-6, Komaba, Meguro-ku, Tokyo, 153-0041 Japan

Abstract. Chirality is recognized strongly in the crystalline state and often only in the phase. Chiral supramolecular structures can be engineered by using conformationally flexible achiral or chiral compounds of axial asymmetry and by transferring and fixing the chirality in the solid state. Solid-state reactions in the chiral environment thus created can proceed enantioselectively. To understand chiral nature of solid samples, we have developed Universal Chiroptical Spectrophotometers (UCS-1, 2), as commercially available instruments in general cannot cope with macroscopic anisotropies.

1. Introduction The majority of the synthetic chiral compounds employed in biological applications are racemates, although it has been known from the time of Pasteur1 that the individual optical isomers in a racemic mixture generally have a differential bioactivity. This is because biological world is totally homochiral at the molecular level; that is, all living organisms on Earth use molecules of a unique invariant handedness: only D- (deoxy) ribose in nucleic acids and only L-amino acids in proteins. In contrast, in the non-biological world, left- and right-handed molecules can be found in roughly equal number. Macroscopic objects such as crystals also express chiromorphology as hemihedral and holohedral facets, and this feature must arise from chirality at the molecular level. How do molecules recognize and discriminate handedness of their neighbouring molecules to form macroscopic phases?

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Significantly, the chiral discrimination energy is orders of magnitude larger in the solid state, where molecules are densely packed and their relative orientations are fixed, compared to that in the gaseous and solution states. Chiral discrimination often occurs only in the solid phase. Thus, chirality in the solid phase may be relevant to the homochiral biological world, as it seems plausible that the selection of handedness in the molecules of life on the primordial Earth happened in the solid-state or on the surface of a solid. Given their fundamental importance, we have been working on chiral discrimination, recognition, generation and transfer in the solid state. In parallel to this, we have designed and developed new instruments to measure solid-state chirality, as this cannot be usually carried out on commercially available instruments. Although the history of solid-state stereochemistry began when Louis Pasteur carried out his famous work on the crystallization of the sodium ammonium salt of tartaric acid1, chirality in the solid state has been a relatively minor research area until very recently. 2. Formation of Chiral as Well as Racemic Crystals Crystallization is intrinsically an autocatalytic process, and hence, a small difference in free energy can be amplified during crystallization. There are two classical methods for the optical resolution of racemates. The first involves the direct crystallization of enantiomeric mixtures and the second concerns the fractional crystallization of the diastereomers formed with a second chiral reagent. The former, so called spontaneous optical resolution by crystallization, is quite rare and in even rarer cases, racemic crystals are also formed under slightly different conditions as polymorphs. The factors which govern the formation of either the chiral or racemic crystal are of interest. 2.1. FIRST EXAMPLE OF SPONTANEOUS OPTICAL RESOLUTION-SODIUM AMMONIUM TARTRATES

2.1.1. Crystal Morphology and the Optical Rotatory Power About 160 years ago, Pasteur noticed1 that the sodium ammonium salt of racemic acid (later proved to be the same as racemic tartaric acid) formed two different sets of crystals (Figure 1a,b). They have the arrangements of the facets of the crystals in mirror image relationships to one another, and their aqueous solutions rotated the plane of polarized light in opposite directions. Scacchi, on the other hand, crystallizing the racemic salt at higher temperature, obtained2 a single optically inactive crystal type, morphologically holohedral, i.e., achiral in shape (Figure 1c). Later, it was found that below 27oC,

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Figure 1. A pair of dextrorotatory (a) and levorotatory (b) crystals of Na(NH4)C4H4O6.4H2O discovered by Pasteur and optically inacitive crystal (c) of Na(NH4)C4H4O6.H2O discovered by Scacchi.

Spontaneous optical resolution is achieved, whereas above this temperature, racemic crystals containing equivalent amounts of the (+)- and (–)-tartrate ions, are produced. 2.1.2. Crystal and Molecular Structures of Chiral and Racemic Crystals of Sodium Ammonium Tartrates The structures of the crystal of Pasteur (Mitscherlich)3 and of Scacchi were determined by myself 4 long after the Pasteur’s discovery of spontaneous optical resolution. The Pasteur crystal is the tetrahydrate, whereas that of Scacchi is the monohydrate. In both cases, there is a dense network of hydrogen bonding among hydroxyl and carboxylate groups of tartrate ions, ammonium ions and water of hydration (Figure 2). Only the chiral source involved in the chiral discrimination is the tartrate ions.4

Figure 2. Crystal structures of chiral Na(NH4)C4H4O6.4H2O (left) and achiral Na(NH4)C4H4O6.H2O (right), showing extensive hydrogen bonding networks.

The molecular structure of the tartrate ion in the two crystals differs in the orientation of a hydroxyl group (Figure 3). In the active crystal, the two carboxylate groups are placed to form an intramolecular hydrogen bond with each hydroxyl group. In the racemic structure, only one of the hydroxyl groups of a tartrate ion forms a similar intramolecular hydrogen bond, while the other hydroxyl group is directed towards another tartrate ion, related by a translation along the b crystal axis, and forms an intermolecular hydrogen bond.4

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Figure 3. Tartaric acid forms two intramolecular hydrogen bonds in the chiral crystal (left), whereas only one in the racemic crystal (right). All the hydrogen atoms are involved in the intra and intermolecular hydrogen bonding.

2.1.3. 1,1’-binaphthyl The flexibility of molecular conformation found in the case of tartrate ions is important for the formation of both the racemic and the chiral crystals of the same compound. Similar feature was observed in the case of 1,1’binaphthyl as well. Thermodynamically the racemic crystal is the more stable up to a transition temperature at 76oC. Above the transition temperature the racemic crystals undergo a solid-state transformation to a conglomerate of active crystals, and crystallization from the melt at 150oC similarly affords a mixture of crystals which individually contain solely the R(–)- or the S(+)isomer.5 Chiral and racemic crystals adopt different molecular conformations in the two crystal forms, i.e., the transoid6 with the dihedral angle between the mean planes of the two naphthalene nuclei of 103o and the cisoid7 with the corresponding angle of 68o, respectively (Figure 4). In the R(-)-1,1’-binaphthyl crystal the molecules are packed around a 41 screwaxis along the c direction of the crystal in the space group of P41212. The conformational flexibility of 1, 1’-binaphthyl afforded the presence of both the chiral and racemic crystal forms, although the racemic crystal in the space group of C2/c is closely packed with a density 9.4% larger that that of the active crystal.

Figure 4. 1,1’-binaphyl molecule adopts the transoid conformation in chiral crystal (left), whereas it adopt the cisoid conformation in the racemic crystal (right).

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3. Measurement of Chirality in the Crystalline State 3.1. MACROSCOPIC ANISOTROPIES OF CRYSTALS

Some compounds exhibit chirality only in the crystalline phase, or form a chiral supramolecular structure only in the solid state. In these instances, chirality must be analyzed in the solid state. Crystalline circular dichroism (CD) has an advantage that it provides information which is directly correlated with known X-ray crystal structures and does not suffer from solvent interactions as often encountered in solution CD measurements. Also in circumstances in which single-crystal X-ray structure determination is not affordable due to small crystal size or poor quality of crystals, solid-state CD should provide chiral structural information. For all these reasons, solid-sate CD spectroscopy is one of the most important tools in chiral chemistry. Nevertheless, solid-state CD has been rarely recorded, as it suffers from a severe artifact due to macroscopic anisotropies which are unique to the solid-state samples, and an artifact due to the coupling effect between the macroscopic anisotropies of a sample and the non-ideal characteristics of the polarization-modulation instrument.8–10 Based on the Muller matrix analysis, the 50 kHz signal detected by the lock-in amplifier can be expressed10 as Signal50kHz = G1(Px2 + Py2) [CD + ½ (LD' · LB – LB' · LD) + (LD' sin 2θ – LD cos 2θ) sin α] + G1(Px2 – Py2) sin 2a {LB' sin 2θ – LB cos 2θ + [– CB + ½ (LD2 + LB2 – LD'2 – LB'2) sin 4θ + (LD' · LD + LB' · LB) cos 4θ] sin α} + G1(Px2 – Py2) cos 2a {LB' cos 2θ – LB sin 2θ + [1 + ½ (LD'2 – LB2) sin22θ + ½ (LD2 – LB'2) cos22θ – 2(LD' · LD + LB' · LB) sin 4θ] sin α}. (1) Here, G1 is the apparatus constant related to the sensitivity of the spectrometer at 50 kHz, Px2 and Py2 are principal transmittance of the detector in the x and y directions, respectively, “a” is the azimuth angle of the partial polarizer with respect to the x axis, α is the residual static birefringence of the photoelastic modulator (PEM), and θ is the rotation angle of the sample with respect to x axis. Without macroscopic anisotropies such as LD and LB, the signal detected at 50 kHz without an analyzer indeed gives CD (equation (1)). In solid samples, however, we have to deal with these extra terms which are sometime hundreds times more intense than true CD signals. One exception to this is the measurement of a crystal along its unique optic axis, wherein the

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CD is free from anisotropic effects. Some metal complexes are often crystallized in uniaxial space groups and hence studied by this method.11–14 We have also established methods for measuring CD spectra of solid samples, which alleviate the macroscopic anisotropies by forming a transparent KBr disk or a nujol mull of randomly oriented finely pulverized microcrystallines.13,14 These methods are now being widely used. However, there may still exist anisotropy in these specimens and samples may react with the matrix material or dissolve in nujol. Therefore, developing an instrument which is capable of measuring artifact-free CD spectra of nonhomogeneous materials such as crystals, gels and films, was an urgent necessity. Commercially-available instruments do not cope with the artifacts, and hence, we have developed novel instruments which can overcome the effect of macroscopic anisotropies, UCS-1 and UCS-2, where UCS stands Universal Chiroptical Spectrophotometer.10 3.2. DEVELOPMENT OF UCS-1

The first spectrophotometer we have developed is UCS-1 (will be commercialized by Jasco as J-800KCM), which is capable of measuring artifact-free CD and circular birefringence (CB) spectra as well as linear dichroism (LD) and linear birefringence (LB) simultaneously.10 A Block diagram of UCS-1 is shown in Figure 5. The spectrometer was based on the commercial CD instrument, J-800, produced by Jasco, but it houses both 50 and 100 kHz lock-in amplifiers. An analyzer can be taken in or out of the light path between sample and detector and can be rotated by computer control. A special sample holder was made which enables the face- and back-side measurement of a sample. A PEM having a smaller residual static birefringence (α = 0.2) was chosen in our CD spectrophotometer, hence the terms in equation (1) which are multiplied by sin α are negligibly small. As we set the photomultiplier (PM)’s azimuth angle so as to make cos2a 0 in the baseline calibration, we can also neglect the contribution of the term containing cos2a in the equation. Thus, the 50 kHz signal in equation (1) can be simplified as (CD): 50 kHz signal without an analyzer = G1 (Px2 + Py2) [CD + ½ (LD ' · LB – LD · LB') + G1 (Px2 – Py2) sin 2a (– LB cos 2θ + LB' sin 2θ)]

(2)

Measurement can be made in four modes corresponding to CD, LD, LB and CB, with or without an analyzer and with either the 50 or the 100 kHzmonitored Lock-in amplifier. The Muller matrix analyses give the following equations for the rest three measuring modes. Here, G2, G3, G4 are apparatus constants related to the sensitivity at each measuring mode, respectively.

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Figure 5. Block diagram of UCS-1.

(LD): 100 kHz signal without an analyzer = G2 (Px2 + Py2) (LD' sin 2θ – LD cos 2θ) + G2 (Px2 – Py2) sin 2a [– CB + ½ (LD2 + LB2 – LD'2 – LB'2) sin 4θ + (LD' · LD + LB' · LB) cos 4θ] (3) (LB): 50 kHz signal with an analyzer = G3 [CD + ½ (LD' · LB – LD · LB') – LB cos 2θ + LB' sin 2θ]

(4)

(CB): 100 kHz signal with an analyzer = G4 [– LD' sin 2θ + LD cos 2θ + CB – ½ (LD2 + LB2 – LD'2 – LB'2) sin 4θ – (LD · LD' + LB · LB') cos 4θ] (5) As shown in equations (2) – (5), even with our UCS-1, the four optical properties (LD, LB, CD, and CB) are coupled with each other to give complex signals for each measuring mode in the case of solid samples. However, we have devised a set of procedures for obtaining true CD, CB, LB and LD based on the Muller matrix method.10,20 3.2.1. Analytical Methods for the True CD Measurements CD measurement (50 kHz without an analyzer) is carried out by rotating the sample 360 degrees in the (X-Y) plane at the absorption maximum. If the CD value changes on rotating the sample, it is clear that the macroscopic anisotropies contribute to the CD spectrum. With an analyzer, LB measurement is carried out by rotating the sample similarly. This gives the LBmax and LBmin positions. The sample is rotated 45 degrees from the LBmax position, wherein the LB value becomes zero and the LB' value maximum.

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The wavelength scan is then carried out at the 50 kHz without an analyzer. From equation (2), the apparent CD signal of the face side is given as [appCD]face = G1{(Px2 + Py2)[CD – ½LDLB'] + (Px2 – Py2) sin 2a LB'}.

(6)

The sample is then rotated by 180 degrees about the Y axis and the wavelength scan is carried out. This corresponds to the backside measurement. By this rotation, the CD and LD do not change their signs, but LB' becomes –LB'. Hence, the apparent CD signal of the backside becomes [appCD]back = G1{(Px2 + Py2)[CD + ½LDLB'] – (Px2 – Py2) sin2a LB'}.

(7)

It is obvious that the average of equations (6) and (7) gives G1(Px2 + Py2) CD, i.e., true CD. Thus, measurement of [appCD] face and [appCD]back spectra at 45 degrees from the LBmax position using our special sample holder, and averaging the two spectra give true CD spectrum. 3.2.2. Achiral Polyvinyl Alcohol (PVA) Film PVA film dyed with Congo red was used as an achiral sample. Although it is achiral, it exhibits strong CD (Figure 6) which is the artifact resulting from the LB and partly from the coupling of the LB with the non-ideal characteristics of the instrument. As discussed above, averaging the face and the back wavelength scan spectra at the LB = 0 position should give true CD by canceling out the artifact CD spectra. This is what we have actually observed.10 The substantially strong CD spectra observed for the face and back of the achiral PVA film are almost mirror images to each other, and they cancel out when added to give almost zero spectrum throughout the wavelength. The results prove that our instrumentation and the set of measuring procedure are correct.

Figure 6. CD spectra of a stretched achiral PVA film dyed with Congo Red. The top and bottom spectra are the apparent CD of face and back side, respectively. The middle trace is the true CD spectrum.

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3.2.3. Biological Samples Biological samples such as proteins and nucleic acids are chiral and hence good target of chirality study. Some peptides including β-amyloids are known to cause mental disorders in their aggregate forms. We measured the CD spectra of bovine serum albumin (BSA) both in solution and in cast films on a quartz plate. Although a research group reported that BSA, like β-amyloids, changed its secondary structure from α-helix to β-sheet upon casting,15 we could prove16 that this is an incorrect statement based on poor experiments. Their CD spectra most likely contain signals from large macroscopic anisotropies.

Figure 7. LB, CD and LD signals at 230 nm by rotating the sample in the (X-Y) plane (top) and wavelength scan CD spectra (bottom). The BSA cast film was made properly in (a), whereas poorly trying to introduce macroscopic anisotropies in (b). High Tension Voltage is 456–468 V and 337 V for (a) and (b), respectively. The solution CD spectrum is shown for comparison.

Our careful experiments using UCS-1 and our analysis methods have shown that BSA in the cast film prepared properly exhibits a CD spectrum typical of α-helix-rich peptides (Figure 7(a) bottom). The LD signal at 230 nm is small, and LD and CD at 230 nm did not change on rotating the sample (Figure 7(a) top). In contrast, a BSA cast film that was made by rapid evaporation deliberately to induce macroscopic anisotropies shows strong LB and LD signals at 230 nm and they changed substantially on rotating the sample in the (X-Y) plane (Figure 7(b) top). The wavelength scan CD spectra are different depending on the rotation position and one of

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them (labeled CDmax) is very similar to a representative CD of proteins in βsheet form (Figure 7(b) bottom). Using this spectrophotometer, we could measure LD, LB, CD, and CB spectra of single crystals, KBr disks containing chiral compounds, chiral supramolecular compounds formed with non-chiral components, and Langmuir-Blodgett- and cast films of proteins. 3.3. DEVELOPMENT OF UCS-2: DIFFUSE REFLECTANCE CD AND HORIZONTAL SAMPLE STAGE FOR REATL–TIME MEASUREMENTS

We have developed17 another entirely new CD spectrophotometer, UCS-2 (J-800KCMF), which is capable of measuring diffuse reflectance CD (DRCD) as well as transmittance CD. The new instrument is equipped with an integrating sphere which collects the light diffused or reflected by the samples. This is an ideal method for in situ measurements of microcrystallines. It also houses a right-angle prism so that a sample can be placed on a horizontal plane. This was designed to measure CD spectra of soft materials which are affected by gravity, e.g., gels. The instrument therefore has two PMs, one for DRCD and the other for transmittance CD. As the first application of this new spectrophotometer, we observed the aggregation process of a segment of a protein responsible for Alzheimer’s disease, β-amyloid. We followed the change from the solution phase to a cast film while evaporating the solvent. Our real-time measurement on UCS-2 indeed showed that, during the phase transition from solution to a cast film, the secondary structure of the fragment peptide of β-amyloid protein changed from α-helix to β-sheet. The time-course experiments showed the transition occurs in a rather short period of time.18 We are currently improving the instrument to achieve higher sensitivity for the DRCD. 4. Chirality Achieved Only in the Crystalline State - Inorganic Compounds Some compounds exhibit chirality only in the crystalline state. One of the most famous examples is quartz. In nature, there is the right-handed and left-handed quartz crystals in almost equal amount. Quartz is made up of Si and O atoms and the crystal chirality arises only from the chiral arrangement of the non-chiral components. Nickel sulfate, sodium chlorate and sodium bromate are other examples of chiral crystals made up of non-chiral components.

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4.1. SINGLE CRYSTALS OF α-Ni(H2O)6‚SO4: KRONIG - KRAMERS RELATION

α-Ni(H2O)6‚SO4 exhibits a chiral nature only in the crystalline state as a result of its chiral crystal packing. Its single crystal belongs to a uniaxial system with the enantiomorphic tetragonal space group of P41212 or P43212.19,20 The CD and CB were reported by several researchers21a–g including ones as early as 1940’s, but we measured on UCS-1 true CD and CB spectra which are devoid of artifacts.22 A single crystal polished perpendicular to the four-fold screw axis was mounted on our special sample holder for the analysis on UCS-1 spectrophotometer. In one case, a crystal was mounted with its plane as perpendicular as possible to the light, whose LB390max was found to be 0.6o (Case I). In another case, substantial anisotropy was deliberately introduced by tilting the polished crystal when mounted on the sample holder (Case II). Its LB390max was determined to be 14.2o. This is to examine whether UCS-1 instrument and the set of our procedures correctly eliminate macroscopic anisotropy to give true CB and CD, so that they can be applied for general non-uniaxial crystals. True CD and CB were measured according to the methods we have devised.10,22 (The methods for CD is described in 3.2.1. Those for CB is reported in Ref. 20). The CB corresponding to the 3A2 → 3T1g(P) Ni d-d transition (at 390 nm) was calculated by eliminating the Drude's dispersion expression from the observed CB spectrum. Figure 8(A) shows that the artifacts-free CB spectra in the d-d region thus obtained (curve c) agree well with those calculated (curve b) from the artifacts-free CD (curve a) by assuming the Kramers - Kronig relationship. The CB spectra exhibit an anomalous dispersion with a substantial change in their sign and intensity at the position of the CD maximum. The negative CB and positive CD around 3 3 550–600 nm are the tail of the neighbouring transition A2g → T1g(F) at 647 nm. Similarly, the negative CB below 280 nm is the tail of the transition at 188 nm. We could show that the Kramers - Kronig relation actually holds in the solid state, even in Case II where LB was deliberately introduced (Figure 8(B)), as it should if CD and CB are measured correctly. This is the first case for which the Kramers - Kronig relation has been demonstrated experimentally in the solid state. If CB spectrum is recorded by conventional way and not by our methods and contains artifacts arising from LB and LB' of case II (Figure 8(C), curve d), the Kramers - Kronig relation does not hold. These prove the integrity of our instrumentation and procedures for the study of solid-state chiroptical properties.

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262 (A)

0 .0 2

(B)0.02

0 .0 1 5

0.015

0 .0 1

0.01

a

0 .0 0 5 O D

OD

0

a

0.005 0 -0.005

- 0 .0 0 5

b c

- 0 .0 1 - 0 .0 1 5

-0.01 -0.02

- 0 .0 2 250

350 450 w a v e le n g th / n m

550

b

-0.015

c 250

350

450 wavelength/nm

550

0.02

(C)

0.01

OD

a 0

b

-0.01

d

-0.02 250

350

450

550

w avelength/nm

Figure 8. CD and CB spectra of α-Ni(H2O)6‚SO4 associated with the 3A2 → 3T1g(P) Ni d-d transition. (A) Case I without LB, and (B) Case II with LB contribution. Pure CD (a) and pure CB (c) spectra satisfy the Kramers - Kronig relationship. The CB calculated from the CD assuming the Kronig - Kramers relationship (b) is also shown for comparison. (C) d is the observed CB spectrum of Case II, including the artifact contribution from LB terms. The spectrum is quite different from spectrum b.

5. Chirality Achieved Only in the Crystalline State – Organic Compounds Molecules with more than one asymmetric carbon atoms are not necessarily chiral. The meso tartrate ion is an interesting example. The ion is achiral when it adopts the most unstable eclipsed (θ = 0o) as well as the most stable anti (θ = 180o) conformations, possessing mirror and inversion symmetry, respectively. θ is the torsion angle COOH - C - C - COOH. Except for the two cases, the ion is chiral. Simply because the probabilities of the ion to adopt θ = x and θ = –x are exactly the same, overall it is achiral.23,24 Equally, molecules devoid of asymmetric carbon atoms can become chiral, if they are conformationaly flexible. The same reasoning for the mesotartrate applies to this case. They can be either chiral or achiral depending on the conformation. The molecules become chiral, if they lose the conformational flexibility and adopt a particular chiral conformation, which must be achieved in the solid state. The examples we have studied are cis-1,2dichloroethane23 and 1-chloropropane.23 We aimed to trap one of the chiral enantiomers with high potential energy which cannot be realized in solution

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or gaseous phase. When a chiral compound, (+)-7-bromo-1,4,8-triphenyl2,3-benzo[3,3,0]octa-2,4,7-trien-6-one (H1) is crystallized from cis 1,2dichloroethane solution, a 1:1 adduct is formed with the solvent trapped as a guest.25 The torsion angle Cl - C - C - Cl of the hydrocarbon is –36 (2)o.25 This is rather surprising as it is between the gauche and the unfavourable eclipsed conformation. If the opposite enantiomer of H1, (R)-(+)-H1, is used, the guest molecule adopts the opposite chirality with the torsion angle of 36 (2)°. Ph With 1-chlorpropane as a solvent, even more Br Ph surprisingly, the hydrocarbon adopts the eclipsed conformation with the central torsion angle of 5(4)o in a O 1:1 adduct crystal with H1.23 The two inclusion crystals Ph are isomorphous to each other and H1 takes very similar molecular structure and locations in the unitcell (S)-(-)-H1 (Figure 9). The guest molecules are placed in the tight cavity formed by the host molecules, wherein positioning of the large chloride atoms and the methyl group are limited. This determines the conformation of the guest molecules.

Figure 9. The crystal c axis projection of the crystal structures of 1:1 adduct of H1 with cis1,2-dichloroethane (left) and 1-chloropropane (right). Newman projections of the guest halocarbons are shown at the bottom.

6. Enantioselective Reactions in the Crystalline State Chirality induced in prochiral compounds in the solid state, as we discussed in paragraph 5, can be utilized for synthesizing enantio pure compounds by solid-state reactions. There are many interesting works in this area, but we shall briefly describe our own work, as the review of the area is beyond the scope of this article.

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Enantioselective photocyclization of 2-arylthio-3-methylcyclohexen-1ones (1) to the corresponding dihydrobenzothiophenes (2) was achieved by complexing the compound with a chiral host, (-)-(R,R)-(-)-trans-2,3bis(hydroxydiphenylmethyl)-1,4-dioxaspiro-[4,4] nonane (H2) and carrying out the photoirradiation in the solid-state.26 Compounds 1 are not chiral in solution due to their conformational flexibility. When trapped in the 1:1 adduct with H2, they adopt only one of the enantiomeric forms as a result of chirality transfer from the host compound. The enantiomeric excess (ee) is 32–83% depending on the kind and position of the substituent, X, on the phenyl group of the reactants (1). The corresponding reaction in solution results in a racemic mixture. Not only chirality but also regioselectivity is different between solution and solid-state reactions. O H

O S Me

X

Ph2COH

O H

S

Me

S

(2S,3R)-2

H

H

O

X

Me

1 a: X = o-Br

O

(2S,3S)-2

Ph2COH

X

(R,R)-H2

We have found that photoreaction of the 1: 1 adduct of H2 and 1a which possesses Br atom at the orto position occurs single-crystal to single-crystal manner and the reaction process is followed by solid-state CD spectroscopy.27 To obtain the reaction product after the irradiation of the 1:1 adduct, it is necessary to remove the host compound. We have found that the compound 1a displays polymorphism. Interestingly, both chiral and achiral crystals are formed depending on the crystallization conditions, although achiral solvents are employed in all cases.28 In the case of photoreaction using the chiral crystals, enantioselective reaction was achieved.28 Synthesis like this which does not use any outside chiral source is called “absolute asymmetric synthesis”. 7. Chiral Discriminations During Crystallization from Solution 7.1. EFFICIENT OPTICAL RESOLUTION OF SECONDARY ALKYL ALCOHOLS BY CHIRAL SUPRAMOLECULAR HOSTS

We could develop a novel tunable multi-chiral supramolecular host system from non-chiral dicarboxylic acid and chiral diamine via chirality transfer, and the system enabled highly efficient optical resolution of secondary alkyl alcohols by simple crystallization of host compounds from alcohol solution.29 The carboxylic acid is either biphenic acid (3) or 2,2’-binaphthyl-3,3’dicarboxylic acid (4), and the amine is (1R, 2R)- diphenylethylenediamine

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((1R, 2R)-5). These dicarboxylic acids are not chiral in solution due to rotation around the central carbon-carbon bonds, however, they can exhibit axial chirality when rotation is restricted in crystalline phase.

COOH HOOC

COOH

COOH

COOH

HOOC

H2N

3

4

NH2

(R,R)- 5

(aS)-6

When a solution of 3 and (1R, 2R)-5 in racemic alcohol was kept at room temperature for several days, an inclusion complex was obtained as colourless crystals. Crystal I, obtained from a racemic 2-butanol solution of 3 and (1R, 2R)-5 exhibits a columnar supramolecular hydrogen-bonded network around the 21-axis, which is formed using ammonium hydrogens and carboxylate oxygens (Figure 10). A water molecule is included within the hydrogen-bonded column structure, and contributes to the maintenance of the column framework. The torsion angle of 3 in crystal I is 78.2°, and the axial chirality was fixed to the (aR)-conformation by chirality transfer from the amine. Consequently, although only one chiral molecule (1R, 2R)5 is used, this supramolecular host has two kinds of chiral moieties in the crystal. In the cavity formed between columns, (S)-2-BuOH is trapped by a hydrogen bond between the alcohol hydroxyl group and the carboxylate oxygen of a biphenic acid anion. The enantioselectivity was as high as 91% for (S)-2-butanol (BuOH), but decreased as the size of the guest alcohol molecule increased: for 2-pentanol and 2-hexanol, ee was 61% for the (S)and 22% for the (R)- enantiomer, respectively. Generally, it is difficult to carry out optical resolution of secondary alkyl alcohols, RCH(CH3)OH.30 The excellent high ee is in sharp contrast to those based on the standard method using tartaric acid derivatives, which are 0%, 0.2% and 0.05% ee for 2-butanol, 2-pentanol, and 2-hexanol, respectively.30 Common 21-column structure was observed in all the crystals, but without strong interaction among them. Thus, a variety of guest molecules may be included by changing the packing of the 21-columns. The other novel feature of the host system is that it is possible to tailor the host system to a particular guest by changing the combination of host component molecules. To achieve higher enantioselectivity for larger alcohols, binaphthyldicarboxylic acid 4, instead of 3, was employed to construct a supramolecular host. Similar to 3, compound 4 can exhibit axial chirality when a rotation around the central carbon-carbon bond is restricted.

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Because of the larger aromatic moiety than 3, enantioselectivity of 4 • (1R, 2R)-5 host was higher for bigger guest alcohols, a reversed trend that was observed in the case of 3 • (1R, 2R)-5 host. Highest ee was ca. 70% for (S)2-hexanol and (S)-2-heptanol.

Figure 10. Structure of Crystal I. (S)-2-butanol in 91% ee (shown in space filling mode) is trapped in a cavity created between the hydrogen-bonded columns made up of 3, (R,R)-5 acid and water.

7.2. SUCCESSIVE OPTICAL RESOLUTION OF TWO COMPOUNDS BY ONE ENANTIOPURE COMPOUND

Successive optical resolution of rac-1,1’-binaphthyl-2,2’-dicarboxylic acid (6) and secondary alkylalcohols was achieved in one experiment by using one enantiopure compound.31 Unlike 3 and 4, dicarboxylic acid 6 is chiral, and aS and aR forms exist. (1R, 2R)-5 and rac-6 were dissolved in racemic alcohol solution with heating and left to stand at room temperature. After a day, many colourless crystals (II) were produced which contain (1R, 2R)-5 and (aS)-6, with as high as 98–99% ee for 6. The crystal has the characteristic columnar supramolecular hydrogen-bonded network between the ammonium hydrogen of amine/H+ and the carboxylate oxygen of a dicarboxylic acid anion around the 21-axis, with the contribution of water molecule to the maintenance of the column frame. The first step provides a simple and excellent method for the optical resolution of rac-6. 1,1’-Binaphthyl-2,2’-dicarboxylic acid, 6, is one of the most important chiral sources for deriving various chiral organic compounds.32 However, up to now, an effective optical resolving reagent for 6 has not yet been reported except for caustic quinine and brucine, or toxic 1-cyclohexylamine.32,33 The solution was filtered to remove crystals II, and the resulting filtrate was left to stand at room temperature. After two days, plenty of colourless crystals, III, were formed, which contain (1R, 2R)-5, (aR)-6 and the solvent alcohol. The optical purity of 6 is 94–96%. The effective optical resolution of rac-alkylalcohols was also achieved in the chiral cavity formed by (1R, 2R)-5 and (aR)-6. Although the ee is not very high (21% and 41% ee for the

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(S)-2-butanol and (S)-2-pentanol, respectively, and 62% for (R) in 2hexanol), the optical resolution of secondary alkylalcohols is also known to be difficult compared with its aromatic counterparts.30

Figure 11. Successive optical resolutions of compound 5 and rac-2-hexanol by crystallization with (R,R)-5.

8. Conclusion We have been able to develop novel solid-state chiral chemistry including chirality generation, transfer and separation through crystallization. For example, we created a chiral environment by forming supramolecular helical structures in the solid state. When a prochiral compound (an achiral compound which can adopt enantiomeric conformations in equal probability) is involved, chirality can be transferred and fixed during the co-crystallization process with a chiral compound, or by spontaneous resolution upon crystallization. Chirality thus induced in prochiral compounds in the solid state is utilized in synthesizing enantiomerically pure chiral compounds by photochemical reactions in the crystal. This contrasts to the corresponding reaction in solution which results in a racemic mixture. Conformational flexibility is the key to engineer chiral and not chiral supramolecular systems. The discrimination and transfer of chirality are observed not only upon crystallization from solution but also in solvent-free, solid-state crystallizations. We have been working on the area34–38 but the work was not covered in this article. Circular dichroism (CD) spectroscopy provides valuable information on the absolute configuration and their conformation and electronic states of molecules as well as supramolecular nature of the crystals. We have developed one-in-the-world instruments which can measure true CD, CB, LD

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and LB spectroscopy of solid-state samples with macroscopic anisotropies. The process of molecular aggregation to form supramolecular structures is followed on our UCS instruments, by detecting induced chirality of aggregates made of non-chiral molecules. Application of artifact-free CD spectroscopy of solid materials is not restricted to research on crystals and is already expanding to pathologically important proteins whose supramolecular aggregation seems to be the cause of diseases such as Alzheimers.

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17. T. Harada and R. Kuroda, Development of a new CD spectrophotometer for in situ and real-time measurements, to be published. 18. T. Harada and R. Kuroda, Real-time CD measurement of aggregation of β-amyloids, to be published. 19. C. A. Beevers, H. Lipson, The crystal structure of nickel sulfate hexahydrate, NiSO4.6H2O, Z. Krist. 83, 123–135 (1932); B. H. O’Connor, D. H. Dale, A Neutron diffraction analysis of the crystal structure of tetragonal nickel sulphate hexadeuterate, Acta Cryst., 21, 705–709 (1966). 20. K. Stadnica, A. M. Glazer, M. Koralewski, Structure, absolute configuration and optical activity of α-nickel sulfate hexahydrate, Acta Cryst. B43, 319–325 (1987). 21. a) F. G. Slack, P. Rudnick, Optical activity and magneto-optical activity of crystalline nickel sulfate in the near ultraviolet, Phil. Mag., 28, 241–247 (1939); b) N. Underwood, F. G. Slack, E. B. Nelson, Optical activity of crystalline nickel sulfate α-hexahydrate, Phys. Rev., 54, 355–357 (1938); c) L. R. Ingersoll, P. Rudnick, F. G. Slack, N. Underwood, Optical activity, circular dichroism, and absorption of crystalline nickel sulfate, Phys. Rev. 57, 1145–1153 (1940). d) W. C. Knopf, W. C. Gilmor, Ultraviolet Rotatory power of crystalline nickel sulfate at the temperature of liquid oxygen, J. Opt. Soc. Amer. 32, 619–621 (1942). e) P. Rudnick, L. R. Ingersoll, Natural rotatory power of nickel Sulphate at low temperature, J. Opt. Soc. Amer. 32, 622–626 (1942). f) J. P. Mathieu, G. Vuldy, Optical properties of crystalline nickel sulfate hexahydrate in the near ultraviolet, Compt. rend. 222, 223–224 (1946). g) G. Vuldy, Near ultraviolet absorption of NiSO4‚6H2O and NiSeO4‚6H2O, Compt. rend. 228, 1414–1416 (1949). h) F. Castaño, Complete circular dichroism tensor parameter in uniaxial crystals-I Theory. Application to benzil and -NiSO4‚(H2O)6, Spectrochim. Acta. 25A, 401–405 (1969). i) R. Grinter, M. J. Harding, S. F. Mason, Optical rotatory power of Co-ordination Compounds. Part XIV, Crystal Spectrum and Circular Dichroism of -Ni(H2O)6‚SO4, J. Chem. Soc. A, 667–671 (1970). j) V. I. Burkov, V. A. Kizel, I. N. Ivanova, G. M. Safronov, G. S. Semin, P. A. Chel’tsov, Comparison of the optical activity of α-nickel sulfate hexahydrate and α-nickel selenate hexahydrate, Opt. Spektrosk. 35, 884–887 (1973). 22. T. Harada, Y. Shindo and R. Kuroda, Crystal chirality of the non-chiral inorganic salt, αNi(H2O)6‚SO4. Chem. Phys. Lett., 360, 217–222 (2002). 23. R. Kuroda, Chiromorphology at the Molecular Level, Enantiomer, 5, 439-450 (2000). 24. R. Kuroda, P. Biscarini and F. Toda, Molecular chirality recognized by achiral compounds. Supramolecular Chemistry, 12, 181–191 (2000). 25. F. Toda, K. Tanaka and R. Kuroda, Isolation of nearly eclipsed chiral rotamer of 1,2dichloroethane as an inclusion crystal with a chiral host compound, J. Chem. Soc., Chem. Comm., 1227–1228 (1997). 26. F. Toda, H. Miyamoto, S. Kikuchi, R. Kuroda and F. Nagami, Enantioselective photocyclization of 2-arylthio-3-methylcyclohexen-1-ones to dihydrobenzothiophen derivatives in an inclusion crystal with optically active host, J. Am. Chem. Soc., 118, 11315–11316 (1996). 27. R. Kuroda and T. Honma, CD spectra of solid state samples, Chirality, 12, 269–277 (2000). 28. R. Kuroda, Single-crystal to single-crystal photoreaction to achieve enantio- and regionselectivity. To be published. 29. Y. Imai, M. Takeshita, T. Sato and R. Kuroda, Efficient optical resolution of secondary alkyl alcohols by chiral supramolecular hosts. Chem. Comm., 3289–3291 (2005). 30. C. Kassai, Z. Juvancz, J. Balint, E. Fogassy and D. Kozma, Optical resolution of racemic Alcohols via diastereoisomeric supramolecular compound formation with O,O’-dibenzoyl(2R,3R)-tartaric acid, Tetrahedron, 56, 8355–8359 (2000). 31. Y. Imai, M. Takeshita, T. Sato and R. Kuroda. Successive optical resolution of two compounds by one enantiopure compound. Chem. Comm., 1070–1072 (2006).

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32. (a) D.-H. Tang, X.-M. Chen, and Q.-H. Fan, A convenient route to dendritic binaphthylcontaining chiral crown ethers, J. Chem. Res., 2004, 702–703 (2004). (b) M. T. Reetz, L. J. Goossen, A. Meiswinkel, J. Paetzold and J. F. Jansen, Enantioselective Rh-catalyzed hydrogenation of vinyl carboxylates with monodentate phosphite ligands, Org. Lett., 5, 3099–3101 (2003). (c) T. Furutani, M. Hatsuda, T. Shimizu and M. Seki, An efficient synthesis of C2-symmetric chiral binaphthyl ketone catalysts, Bioscience, Biotechnology, and Biochemistry, 65, 180–184 (2001). (d) M. Seki, S. Yamada. T. Kuroda. R. Imashiro and T. Shimizu, A practical synthesis of C2-symmetric chiral binaphthyl ketone catalyst. Synthesis, 2000, 1677–1680 (2000). (e) T. Kuroda, R. Imashiro and M. Seki, Facile synthesis of 11-membered C2 symmetric chiral binaphthyl ketone via Co(salen)catalyzed macrolactonization, J. Org. Chem., 65, 4213–4216 (2000). 33. (a) D. M. Hall, E. E. Tumer, 9 : 10-Dihydrophenanthrenes. Part III. Optically active 9 : 10-dihydro-3 : 4-5 : 6-dibenzophenanthrene, J. Chem. Soc., 1242–1251 (1955). (b) S. Kanoh, Y. Hongoh, M. Motoi, H. Suda, Convenient optical resolution of axially chiral 1,1'-binaphthyl-2,2'-dicarboxylic acid, Bull. Chem, Soc. Jpn., 61, 1032–1034 (1988). 34. Y. Imai, N. Tajima, T. Sato and R. Kuroda, Molecular recognition in solid-state crystallization: Colored chiral adduct formations of 1,1’-bi-2-naphthol derivatives and benzoquinone with a third component. Chirality, 14, 604–609 (2002). 35. V. V. Borovkov, J. M. Lintuluoto, M. Sugiura, Y. Inoue and R. Kuroda, Remarkable stability and enhanced optical activity of a chiral supramolecular bis-porphyrin tweezer in both solution and solid state. J. Am. Chem. Soc., 124, 11282–11283 (2002). 36. R. Kuroda, Y. Imai, and N. Tajima, Generation of a co-crystal phase with novel coloristic properties via solid state grinding procedures. Chem. Comm., 2848–2849 (2002). 37. V. V. Borovkov, T. Harada, G. A. Hembury, Y. Inoue, and R. Kuroda. Solid-state supramolecular chirogenesis: High optical activity and gradual development of zinc octaethylporphyrin aggregates. Angew. Chem. Int. Ed., 42, 1746–1749 (2003). 38. R. Kuroda and Y. Imai, Spontaneous rearrangement of hydrogen bonding in a crystalline state. Mendleev Comm. (dedicated to Homochirality discovered by Louis Pasteur in 1848), 148–149 (2003).

DESIGN, CHARACTERIZATION AND USE OF CRYSTALLINE THIN FILM ARCHITECTURES AT THE AIR-LIQUID INTERFACE

LESLIE LEISEROWITZ, ISABELLE WEISSBUCH, MEIR LAHAV Dept. Materials & Interfaces, The Weizmann Institute of Science, Rehovot, Israel

Abstract. The lecture notes describe the design, characterization and use of crystalline thin film architectures at the air-water interface. Grazing incidence X-ray diffraction (GIXD) using synchrotron radiation has been applied as the key method for structural elucidation of the crystalline films, which are generally composed of amphiphilic molecules. The following topics are covered in these notes. (a) A brief description of GIXD, given in the Appendix; (b) the design of α-amino acid amphiphiles, a racemic mixture of which on water spontaneously separates into two-dimensional (2D) crystalline islands of opposite handedness according to GIXD measurements; (c) the use of amphiphilic monolayers for induced nucleation of molecular 3D crystals at the air-solution interface, with a focus on the induced nucleation of ice; (d) casting light on pathological crystallization of cholesterol, which precipitates in gallstones and atherosclerotic plaques, via the use of GIXD for trapping the cholesterol nucleation process. 1. Introduction Ordered molecular clusters at interfaces with length scales down to few nanometers are currently attracting wide attention in the physical and biological sciences. The design and preparation of functional materials such as thin-layered microstructures, reagent films for biosensors, devices for optoelectronics requires knowledge and control of nanoarchitectures from the very early stages of self-organization. There is also a link to the control of nucleation and habit of crystals and to a better characterization of the self-organization of biological membranes.

271 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 271–290. © 2008 Springer.

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The enormous strides made over the past two decades for the elucidation of molecular ordering at interfaces has been made possible by the development of a variety of experimental tools. These include surface-specific X-ray diffraction, X-ray and neutron reflectivity, scanning-tunneling and scanning-force microscopy, cryo-electron microscopy, non-linear optics and surface reflectance IR spectroscopy. Regarding surface X-ray diffraction, it was with the advent of intense and highly collimated synchrotron X-ray beams of variable wavelength that grazing incidence X-ray diffraction (GIXD) has become a valuable tool to obtain structural information at the subnanometer scale of crystalline films at interfaces. Much use has been made of GIXD for such liquid surface studies. It led to a boost in design and characterization of thin film architectures at the air-liquid interface. Indeed this cooperative effort resulted in a continual tandem interplay between film design and structural elucidation, leading from simplicity to complexity. This field, recently reviewed,1 encompassed the following topics: An outline of phase behavior from the ‘gaseous’ to the ‘solid’ state upon compression of the film on the liquid surface, crystalline selfassembly of achiral and chiral amphiphiles and their monolayer packing arrangements, control of crystalline domain size, topochemical behavior of photoreactive amphiphiles and the impact of crystallinity in monolayer films on catalysis. It also covered interactions between the amphiphilic head groups and the solution subphase, sometimes leading to intercalation of the water-soluble species resulting in a two-component system on the water surface, as well as induced nucleation of three-dimensional (3D) crystals at the monolayer-solution interface. Spontaneous generation of multilayer crystals at the surface of a pure liquid was also discussed in terms of the nature of the subphase and the various types of water-insoluble molecules such as amphiphiles, bolaform amphiphiles, and pure hydrocarbons. Also covered was generation by reaction of water-insoluble species with solutes from the subphase to form complex architectures such as interdigitated bilayers, metal salts of dicarboxylic acids, supramolecular grids and complexed ionophores. Formation of multilayer crystallites obtained by compression of the monolayer film beyond the collapse point, leading to multilayers composed of interdigitated bilayers or bilayers separated by organized water layers, was also discussed. Reviews embodying other viewpoints and aspects of Langmuir monolayers of long-chain amphiphiles, in particular their physical properties, such as phase transitions and morphological patterns, have been recently published.2–5 The review presented here shall not be as broad as that alluded to above1. It will be given in terms of three different types of ordered films at the air-solution interface (Scheme 1): firstly, two-dimensional (2D)

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crystalline arrangements of amphiphilic molecules at the air-liquid interface of the molecules (Scheme 1a). Next, we describe the use of amphiphilic crystalline monolayers to induce nucleation of 3D crystals by virtue of a complementarity between the amphiphilic head-group monolayer and the top surface of the to-be-nucleated 3D crystal (Scheme 1b). Finally, we discuss formation and characterization of multilayers composed of waterinsoluble molecules (Scheme 1c) in order to monitor crystal nucleation at the near atomic level by an X-ray diffraction “snapshot” technique. The principles of GIXD for the characterization of 2D crystalline films of amphiphilic molecules at the air-liquid interface have been detailed in various reviews.1,6 A description thereof is given in an Appendix, to facilitate understanding of the results presented here.

Scheme 1.

We shall first examine crystalline self-assembly of chiral long-chain αamino acid amphiphiles and show how by molecular design a spontaneous separation of a racemic mixture of long-chain α-amino acids into 2D crystalline islands of opposite handedness may be achieved. Next, we discuss induced nucleation of 3D crystals at the monolayer-solution interface, focusing primarily on the nucleation of ice using long-chain alcohols. Finally, we describe the formation of multilayer crystallites of cholesterol obtained by compression of the monolayer film beyond its collapse point. 2. Separation of Racemic Mixtures into 2D Crystals of Opposite Handedness 2.1. INTRODUCTION

The spontaneous separation of left- and right-handed molecules (i.e. enantiomers) from a racemic mixture has intrigued scientists since it was discovered by Pasteur a century and half ago. This phenomenon might have

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played a significant role in an abiotic process proposed to explain the transformation from a racemic chemistry to a chiral biology. In this regard the separation of enantiomers in two dimensions may have relevance to the transfer of chiral information within or across an interface. This possibility prompted an investigation of the structural requirements for separation of left- and right-handed hydrophobic α-amino acids into chiral 2D crystalline arrays, from a racemic mixture at the air-water interface.7 Unlike in 3D crystals, the detection of spontaneous separation in twodimensions is not straightforward. The macroscopic methods of surface pressure-area isotherms, Brewster angle and epifluorescence optical microscopy may not be sufficiently reliable for the purpose. Chiral segregation in 2D crystals has been detected by methods that probe the structure at the nanometer scale such as scanning force8 and scanning tunneling9 microscopy, and GIXD.7,10 Racemic mixtures of molecules tend to form 3D crystals which embody centers of inversion or glide symmetry that relate chiral molecules of opposite handedness. Only translation or a glide but whose plane is perpendicular to the water surface, are the symmetry elements common for 2D crystals composed of amphiphilic chain-like molecules on water Under such conditions, a racemic mixture depicted in Scheme 2a for a set of hands, can either resolve spontaneously into crystalline 2D islands of opposite handedness (Scheme 2c) in which the hands are related by translation symmetry only, or form a racemate (Scheme 2b) in which the left and right hands are related by glide symmetry. If the glide can be prevented, spontaneous segregation of enantiomeric territories at the solution surface may be induced. However, since amphiphiles generally incorporate an aliphatic chain CnH2n, which tends to pack in the herringbone motif generated by glide symmetry (see Fig. 1a), the molecule may require a functional group within the chain that will override a tendency for the herring-bone motif and thus promote translation packing only (Fig. 1b).

Scheme 2.

Figure 1. The two common ways of packing layer structures of chain CnH2n molecules (a) By glide, (b) by translation.

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2.1.1. α-Amino Acids Reasoning along the above lines was applied for obtaining enantiomeric segregation into 2D islands of racemic mixtures of long chain α-amino acids7 +H3NCHXCOO–, where X is a long-chain, by making use of the two common types of H-bonding layer motifs of the +H3NCHXCOO– moieties (Fig. 2a,b). The motif in which the moieties are interlinked by translation only, (Fig. 2b, top), embodies axes of length appropriate for intermolecular N-H...O=C hydrogen bonding between secondary amide groups CONH introduced within the aliphatic X chains. Such chains cannot form favorable intermolecular N-H...O=C bonds adopting the herring-bone chain motif (Fig. 1a), which would be incorporated within the arrangement shown in Fig. 2a, top. Thus an amide group within the hydrocarbon chain should induce the translation motif.

Figure 2. (Top) Schematic views of the monolayer arrangements of α-amino acid amphiphiles XCHNH3+CO2– (X=chain). (a) Molecules of opposite handedness, R and S, related by glide symmetry. (b) Molecules of a single handedness, R or S, related by translation. (Bottom) The GIXD patterns, presented as 2D intensity contour plots I(qxy, qz) of monolayers of racemic, R,S, and enantiomeric, R or S, amino acid C16H33CH(NH3+)CO2– on water.

Figure 3. (a,b) The GIXD patterns in the form of 2D intensity contour plots I(qxy, qz) of monolayers on water of R,S and S amino acid amphiphile C17H35CONHC4H8CHN H3+CO–. (c) Packing arrangement of the R,S mixture viewed parallel to the water surface. Upper chain section not shown.

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This reasoning was substantiated as follows. When X was chosen to be CnH2n+1, n = 12,16, the racemic mixture crystallized into heterochiral domains according to the GIXD pattern (Fig. 2a, bottom), in a cell containing molecules related by glide (Fig. 2a, top) in a herring-bone chain motif. The enantiomeric form yielded a GIXD pattern (Fig. 2b, bottom) corresponding to molecules related by translation in an oblique cell (Fig. 2b, top). Chiral separation was achieved by introducing into the chain X an amide group, four CH2 groups from the amino acid chiral C atom, to yield X = CnH2n+1CONH(CH2)4, n = 15, 17, 21. The enantiomer for n = 17, yielded a GIXD pattern (Fig. 3b) indicative of an oblique unit cell, with translation symmetry only. The GIXD patterns of the racemic mixture for the three monolayers n = 15, 17, 21 (see Fig. 3a for n = 17), are very similar to those of their corresponding enantiomeric forms. Thus this mixture spontaneously separated into domains of opposite handedness induced by amide N-H..O bonds along a 5 Å translation axis, complemented by the N-H..O network of the +H3NCHCOO– moieties (Fig. 3c). 3. Surfaces of Amphiphilic Monolayers Tailored for Inducing Crystal Nucleation 3.1. INTRODUCTION

Here we focus on the design and use of synthetic monolayer templates to promote crystal nucleation. The monolayers are composed of amphiphilic molecules whose polar head groups in contact with the aqueous solution subphase are expedient crystal nucleating agents through a structural complementarity between the polar head groups and a layer of the to-benucleated crystal, depicted in Scheme 3. With this method it is possible to obtain insight into the nucleation process as well as a measure of control on the size and orientation of the precipitated crystals. This method was initiated several years ago via the use of natural hydrophobic α-amino acids for induced oriented crystallization of the α-glycine at the air-aqueous solution interface.11 Similar results were obtained on replacing the natural amino acids by Langmuir monolayers composed of long-chain α-amino acid amphiphiles,12 which were also used to induce nucleation of NaCl crystals via its {110} face by virtue of a partial structural complementarity.13 This approach has since been extended along various lines by various groups, involving nucleation of organic and inorganic compounds. The results yield information on the extent of structural match required for epitaxial growth,13–17 on molecular and atomic rearrangement within the monolayer and the nucleated crystal,18,19 on the interplay between the orientation of the nucleating polar head groups and the nucleation process,16

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on the critical size of nuclei,20,21 on biological mineralization14,22 and oriented formation of semiconductor nanocrystals.15,23

Scheme 3.

Here we shall describe the ice-nucleating ability of long hydrocarbon chain alcohol monolayers, the structural characterization of the monolayers by GIXD complemented by sum frequency generation (SFG) and how an in-situ GIXD study of an alcohol monolayer inducing nucleation of supercooled drops of water led to an estimate of the critical size of the ice nucleus.

Figure 4. (a) Schematic view of herring-bone packing of CnH2n+2 chains in a rectangular cell (a,b), viewed along the chain axis, depicting also the distorted hexagonal representation of the cell (ah,bh). (b) Schematic representation of the a,b layer of hexagonal ice in terms of the hexagonal cell (a,b) and of a c-centered rectangular cell (ar,br). (c) 3D structure of hexagonal ice showing O atoms interlinked by H-bonds.

3.2. INDUCED NUCLEATION OF ICE UNDER MONOLAYERS OF LONG-CHAIN ALCOHOLS

3.2.1. Introduction Pure water can be supercooled to below –20°C. Therefore inhibition or induction of freezing of water into ice, through the role of auxiliaries,

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has far-reaching ramifications for the living and non-living world. Promotion of ice nucleation has been exploited for induced precipitation of rain by silver iodide seeded in clouds. Induced ice nucleation, on the other hand, can result in wide-scale damage to non-coniferous plants in temperate climates by frost bacteria, which promotes ice nucleation, preventing supercooling of water below –2°C. 3.2.2. Alcohol Monolayers as Ice Nucleators Structural considerations suggested that monolayers of water-insoluble long-chain alcohols CnH2n+1OH would promote ice nucleation. There is a close lattice match between the arrangement of O atoms in the ab layer of hexagonal ice Ih (Fig. 4b) and of the O atoms in the alcohol molecules when packed in the herring-bone arrangement of hydrocarbon chains aligned upright, of unit cell dimensions 5×7.5 Å2 (Fig. 1a and Fig. 4a). Indeed, alcohols of the series CnH2n+1OH, n =13–31, deposited in monolayer form on drops of water catalyzed the freezing thereof (Fig. 5).24,25 The induced freezing into ice for n odd reaches an asymptotic temperature just below 0°C for an upper value of n = 31; the freezing temperature for n even reaches a plateau of –8°C for n in the range 22–30. The catalytic action of the alcohol monolayers was also demonstrated by the time taken to freeze

Figure 5. Freezing temperatures of supercooled water drops covered by alcohol CnH2n+1OH and carboxylic acid CnH2n+1COOH monolayers. Curves are drawn separately for alcohols with n odd and n even.

Figure 6. (a) ED pattern from a crystal of a C31H63OH monolayer on a crystal of ice. (b) Relation between the reciprocal lattice of ice and of the monolayer, showing the 6 {1,0,0} reflections of ice (o) and the 4 {1,1} and 2 {0,2} monolayer reflections (3).

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supercooled water drops covered by a C30H61OH monolayer,26 and by experiments performed by Seeley and Seidler27,28 involving repeated freezing of water drops under alcohol monolayers. 3.2.3. The Alcohol Monolayer Structures The epitaxial nature of the induced ice nucleation from an essentially single crystal of the C31H63OH monolayer was demonstrated by electron diffraction (Fig. 6).29 GIXD studies of monolayers of the alcohol series, n = 13–31, on water at 5°C revealed information that could be correlated with the ice freezing behavior.16,30 For example, the epitaxial relation between ice and the alcohol monolayers is obvious from the similarity between the arrangement of oxygen atoms in the (001) layer of ice and in the alcohol monolayers CnH2n+1OH, n = 31, 30 (vide infra, Fig. 9e). The alcohols crystallize in a rectangular cell, with the chains adopting the herring-bone motif. There is a gradual change in crystal structure with chain shortening that may be correlated with poorer ice nucleation behavior; the molecules become more tilted (Fig. 7), there is an increase in lattice area mismatch between ice and the alcohol monolayer, a significant increase in chain librational motion and a reduction in the relative amount of alcohol monolayer crystallites formed and their extent of lateral coherence.

Figure 7. 2D crystalline arrangements of alcohols CnH2n+1OH, n = 31, 20 viewed perpendicular to the glide plane.

Figure 8. Monolayer crystalline arrangements of the hydroxyl alkyl esters C19H39CO2(CH2)nOH n = 9, 10 showing their different COH groups orientations.

The odd-even effect in the ice-nucleating behavior of CnH2n+1OH, and the GIXD data implies that the absolute azimuthal orientation of the hydrocarbon chains differing in length by one CH2 group are the same, leading to a difference in orientation of their CH2OH groups. The absolute

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orientation of the molecular chains, and thus of the CH2O(H) groups, was established for the alcohols CmH2m+1CO2CnH2nOH, m = 19, n = 9, 10, (Fig. 8), by GIXD complemented by lattice energy calculations16 and independently by sum frequency generation measurements via a determination of the orientation of the alcohol CH3 groups vis-à-vis the water surface.31 For n = 9, which is the poorer ice nucleator, the O-H bond and the O lone-pair electrons are equally exposed to water (Fig. 8a), whereas for n = 10, the better ice nucleator, the O-H bond may point vertically into the water subphase (Fig. 8b). This model was confirmed from an assignment of the absolute azimuthal orientation of the alcohols BrCnH2nOH, n = 21, 22 on water, determined directly from an analysis of the GIXD data, noting that these molecules pack in an 2D structure similar to that of the ester alcohols.31 3.2.4. Molecular Dynamics (MD) Simulation of Alcohol Monolayers on Water and Ice Formation An MD computation of the C22H43OH monolayer on ice by Bell and Rice32 yielded monolayer unit cell dimensions in agreement with the GIXD findings. A recent MD computation by Dai and Evans33 simulating the freezing of water via the alcohol monolayers, CnH2n+1OH, n = 29, 30, 31 proved to be in reasonable agreement with the experiments described above, both in respect to the monolayer physical parameters and, more importantly, the ice nucleating behavior. They found that as the simulation temperatures approached the water freezing points, the water layer immediately below the monolayer surfaces adopted ‘ice-like’ Ih lattice parameters and geometries characteristic of the ice structure in the {001} plane. Furthermore, the odd-carbon monolayers provide a closer ab-plane lattice match to the {001} ice interface and a larger percentage of water molecules hydrogen-bonded to the alcohol headgroups. 3.2.5. Towards a Value of the Critical Size of the Ice Nucleus An estimate of the critical size of ice nuclei as induced by an alcohol monolayer, just below 0°C, was gleaned from a GIXD study monitoring growth of {001} plates of ice by a C31H63OH monolayer (Fig. 9a–d).21 These ice crystals had an average lateral coherence length of 25 Å, as determined from the width of the (100) reflection of ice (Fig. 9d) This value compares well with the domain diameter of about 30–35 Å, over which there is a match to within 0.5 Å between the O positions of the a,b lattice of ice and that of the C31H63OH monolayer on water (Fig. 9e). A value of about 30 Å was also obtained as the calculated size of ‘defect-free’ domains in a monolayer of C29H61OH in a study simulating the observed ice nucleating efficiency of C29H61OH when contaminated with tailored additives such as longer chain alcohols or the C30H62 alkane.34

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Thus, for this heterogeneous ice nucleation, an assumed maximum diameter of the ice critical nucleus of 30 Å is not unreasonable. For this system a hemispherical ice nucleus would probably be correct. All that may be required is an interleaving ice-like “phase” containing a few water layers because pure ice is proton-disordered, whereas the alcohol monolayer induces ordering in the direction perpendicular to its plane.25 An interleaving ice-like “phase” is in keeping with a similarity in the infraredvisible sum-frequency generation spectrum of water covered by an alcohol monolayer and the infrared spectrum of bulk ice, suggesting that the top layer of water molecules adopts an ice-like structure.35 This result is also in agreement with the MD computations by Dai and Evans, discussed above. Furthermore, a critical ice nucleus composed of a monolayer was recently suggested by Seeley and Seidler, following their analysis of repeated freezing of water drops under alcohol monolayers.28

Figure 9. GIXD measurements made on a monolayer of C31H63OH over water cooled to freezing. (a) Bragg peaks {1,1} and {0,2} of the monolayer on water at 4°C. (b) First stage of ice nucleation just below 0°C under the monolayer. Both {1,1} Bragg peak of the monolayer and the (100) Bragg peak of ice visible. (c) Same as (b) but after a time interval of 15 min. (d) After a further 15 min only the (100) Bragg peak of ice is visible. The disappearance of the crystalline monolayer Bragg peaks were not due to its destruction, but because the ice crystals bound to the monolayer no longer parallel. (e) A diagram of the oxygen positions within the ab layer of hexagonal ice (triangles in unit cell of dimensions 4.5×7.8 Å2) superimposed on the O positions in the monolayer of C31H63OH (squares in cell of 5.0×7.5 Å2). Within each ellipse the O atoms of ice and the monolayer match to within 0.5 Å.

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On the basis of the GIXD findings (Fig. 9a–d), an assumption of a spherical ice nucleus of minimum diameter 30 Å for homogeneous ice nucleation just below 0°C, would suggest that the critical ice nucleus contains no less than 500 water molecules. Such a threshold value appears compatible with electron diffraction studies of clusters of water molecules formed on expansion through a nozzle, the crystalline ice core formed in a water cluster had a diameter of about 45 Å containing about 1200 water molecules.36 A threshold diameter of 30 Å is also consistent with recent MD simulation of the ice nucleation process carried out by Ohmine and coworkers,37 which took into account the disordered H-bonding networks. They ‘quenched’ the water molecules to a temperature of 230 K. They found that nucleation occurs once a sufficient number of relatively longlived hydrogen bonds develop spontaneously in the same region to form a compact initial nucleus. They report that at first long-lasting clusters of about 50–100 water molecules appear intermittently, eventually a critical cluster of about 150 molecules is formed leading to stable cluster of about 500 molecules. This number is in the same ballpark region as our estimate from a sphere of 30 Å. 4. Monitoring Crystal Nucleation by GIXD 4.1. INTRODUCTION

Experimental monitoring of the early stages of molecular assembly into ordered arrays is a daunting task. X-ray diffraction would seem to be an obvious general method of choice to monitor a process of crystal nucleation in solution. However, no concrete results thereby have yet been published, presumably because of the drawback of high background scattering from the solution, the inherently broad and weak nature of X-ray reflections from crystal nuclei coupled with their random orientations, which do not all necessarily develop at the same rate. These problems may, to some measure, be circumvented by monitoring the crystallization of amphiphilic molecules at the air-water interface via GIXD using synchrotron radiation. We shall touch upon, in broad outline, how GIXD has revealed the nucleation process of a metastable polymorph of crystalline cholesterol monohydrate evolving into a film three bilayers thick at the air-water interface containing ordered water interleaved between the cholesterol bilayers. The molecular layer assembly was monitored through a ‘snapshot’ technique involving a change in molecular packing of the cholesterol film as it grew in thickness and eventually transformed into the stable monohydrate phase.

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4.2. NUCLEATION OF CHOLESTEROL.H2O AT THE AIR-WATER INTERFACE

Abnormally high physiological levels of cholesterol may develop into detrimental precipitants containing cholesterol crystallites that are associated with arterosclerotic plaques and with gallstones in human bile. Studies on cholesterol crystallization in model or native bile solutions by light, electron microscopy and X-ray diffraction38 have provided evidence that crystallites form through aggregation of cholesterol-rich vesicles. Furthermore, an X-ray powder diffraction pattern obtained from earlyformed filamentous crystallites of cholesterol in bile solution, which eventually transforms into the monohydrate phase, has been interpreted as depicting an unknown crystalline polymorph of cholesterol.39 It has been reported that the site of nucleation in atherosclerotic plaques may occur within the biomembrane,40 which is compatible with the finding by GIXD that cholesterol forms a crystalline bilayer on the water surface.41 This bilayer structure is different than that of the thermodynamically stable triclinic form of cholesterol.H2O,42 which leads to the question of the nucleation process of cholesterol H2O under pathological conditions. Shown in Fig. 13a,b is the Bragg peak I(qxy) and corresponding Bragg rod (dotted line) of an uncompressed pure cholesterol monolayer on water.41 The GIXD data was interpreted in terms of a 2D crystal structure in which the molecules appear in the trigonal plane group p3 in an arrangement shown in Fig. 13d. The Bragg rod computed from this arrangement (Fig. 13b, full line) fits well to the observed Rod (Fig. 13b, dotted line).

Figure 13. (a) GIXD pattern I(qxy) of an uncompressed cholesterol monolayer on the water surface. (b) Corresponding Bragg rod I(qz) at I(qxy) = 1.1 Å–1, showing the obs. (dots) and calc. (line) values. (c) Cholesterol molecule. (d) The proposed cholesterol monolayer structure that yields the calculated Bragg rod (line) shown in scan (b).

Compressing a cholesterol film beyond monolayer collapse in the presence of ~15–20% phospholipid, yields crystallites containing about 1, 2 and 3 bilayers, depending upon surface pressure applied. Fig. 14 depicts representative Bragg rods of the 1–3 cholesterol bilayer films. The thickness

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of each film was estimated from the widths the individual maxima along the Bragg rods of that film. These maxima become sharper with increasing film thickness and may be treated as distinct (h,k,l) reflections for the three bilayer film (Fig. 14c), from which it has proven possible to extract the unit cell dimensions and monoclinic space group (A2) and also determine the crystal structure (Fig. 15a,b) by constrained X-ray structure-factor leastsquares refinement; the fit between obs, and calc. F2(hkl) being shown in Fig. 16.43

Figure 14. (left): (a–c) Bragg rods of three different crystalline films on water corresponding to one, two and three cholesterol bilayers respectively. Figure 15. (right): (a) Packing arrangement of the multilayer structure of the monoclinic A2 phase of cholesterol.H2O, depicted as a ‘unit cell’, viewed along the b axis. (b) H-bonding layer viewed along a direction perpendicular to the a,b plane. The sterol and water O atoms are colored grey and black respectively. (c) H-bonding layer arrangement of the thermodynamically stable form of cholesterol.H2O.

The cholesterol bilayers are interlinked via H-bonded water layers in the monohydrate structure. This H-bond arrangement (Fig. 15b) is less favorable than that in the stable monohydrate dimorph42 (Fig. 15c) the former containing fewer H-bonds per O atom than the latter. According to GIXD experiments43 the monoclinic multilayer phase converts to a multilayer of the stable monohydrate structure. This is compatible with the deduction based on diffraction data that the monoclinic A2 structure is very similar to that of the early-formed filamentous crystallites of cholesterol in bile solution, discussed above,39 and confirmed by an electron diffraction (ED) study of single crystals of cholesterol from bile.44 The initial formation of the metastable phase is due to the observation that the cholesterol bilayer of this monoclinic phase is energetically more favorable than that of the triclinic structure so that the phase transformation is water-mediated.43

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Figure 16. The obs. (filled bars) and calc. (empty bars) values of the X-ray structure-factors |F(h,k,l)|2, the latter based on the structural model of the monoclinic phase of cholesterol.H2O The |F(h,k,l)|2 values are displayed as a function of increasing q(hkl), equally separated for clarity .

As mentioned above, cholesterol assumes a crystalline filamentous phase before evolving into plate like monohydrate crystals.39,44 The rectangular bilayer phase has similar d-spacings as those of the filamentous cholesterol. It has thus been proposed43 that the 2D phases and phase transition pathways of cholesterol in ultrathin films may have bearing on the nucleation processes occurring at the onset of cholesterol crystallization in the human body. The above study brings to the fore the difficulty gleaning concrete information on crystal nucleation at the molecular level from in situ monitoring of supersaturated solutions by X-ray diffraction. This is evident comparing the rich information derived from GIXD patterns of the multilayer crystalline films of cholesterol43 with the paucity of data from X-ray diffraction powder data of the metastable filamentous phase of cholesterol even after removal from solution,39 although the ED studies of single crystals44 revealed much more information. 5. Appendix 5.1. SURFACE SENSITIVE X-RAY METHODS

The intensity measured in a conventional X-ray scattering experiment is proportional to the number of scatterers, i.e., the irradiated sample volume. This, in turn, is proportional to the penetration depth of the radiation in a sample. For X-rays of about 1 Å wavelength, this penetration ranges from a few micrometres for highly absorbing materials to a few millimetres for low absorbing materials. Consequently scattering from the top region about 100 Å deep shall be so weak compared to that from the bulk that it will be completely swamped. A method restricting the penetration depth to the surface region is therefore a prerequisite for all surface diffraction/ scattering experiments. This can be achieved by using grazing angles of incidence and employing the phenomenon of total external reflection from the surface.

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5.1.1. Principles of Grazing Incidence X-ray Diffraction In 3D crystals, diffraction from a set of crystal planes with an interplanar spacing d occurs only when the Bragg law is satisfied. Namely when, firstly, the scattering vector length q (given by |kout-kin| = 4πsinθ/λ, where the wave vector k is of length 2π/λ and the angle between kout and kin is 2θ) is equal to 2πd*, where d* is the reciprocal of the interplanar spacing d, and, secondly, the normal to the planes bisect between the incident and outgoing beams (Fig. A1, left). This condition may be mathematically expressed in terms of the reciprocal lattice vectors d* = ha* + kb* +lc*, where a*,b*,c* are the reciprocal vectors of the unit-cell axes a,b,c and h,k,l are integers that represent the Miller indices of planes with a spacing dhkl = 1/d*hkl. Diffraction therefore takes place in 3D crystals from a set of planes with indices (h,k,l) only when the scattering vector q coincides with the vector 2πd* (Fig. A1, left).

Figure A1. Conditions for diffraction from 3D and 2D crystals. Diffraction from h,k,l planes of a 3D crystal (left) will be achieved if the scattering vector q (= 4πsinθ/λ) is coincident with the reciprocal lattice vector 2π(ha*+kb*+lc*). For a 2D crystal (right) the diffraction for a particular value of qz (i.e. the vertical component of q) of an (h,k) Bragg rod requires that the horizontal component qxy of the vector q, is coincident with the vector 2π(ha*+kb*).

For a 2D crystal there are no selection rules or restriction on the scattering vector component qz along the film normal. Thus the Bragg scattering extends as continuous Bragg rods (BR) through the 2D reciprocal lattice points (Fig. A1, right).45,46 Diffraction therefore takes place only when the horizontal component of q, given by qxy, coincides with a vector 2π(ha* + kb*). The finite thickness of the 2D crystal causes the BR to extend over finite qz intervals. The intensity distribution along these intervals is determined by the vertical electron density distribution in the molecules and is expressed as the Fourier transform of the resulting electron density along the film normal. In the GIXD geometry (Fig. A2), the angle of incidence of the X-ray beam αi is kept just below the critical angle limiting the beam penetration to that of an evanescent wave with a depth in the range 50–100 Å. X-ray scattering due to the subphase is thus efficiently eliminated, so allowing an

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accurate measurement of weak signals from the crystalline film. The evanescent wave is diffracted by the 2D order in the film, resulting in a beam making an angle αf with the water surface (Fig. A2). If the order is crystalline, the evanescent wave may be Bragg scattered from a grain oriented so its h,k lattice “planes”, with a dh,k-spacing, make an angle θh,k with the evanescent beam fulfilling the Bragg condition λ=2dhksinθhk. The incident beam illuminates a certain footprint of the surface. In general, the layerlike crystallites on the water surface are azimuthally randomly oriented, and so described as a “2D powder”. Figure A2. (Top) Liquid surface diffractometer at Hasylab. The Xray beam is monochromated and deflected down toward the sample by tilting the monochromator crystal so that the incident beam strikes the water surface at grazing incidence. The diffracted beam is detected with a PSD. (Bottom) Side and top views of the GIXD geometry. Only the cross-beam area contributes to the measured scattering.

As shown in Fig. A2, the collection of the diffracted radiation by means of a position-sensitive detector (PSD) is made by scanning the detector over a range along the horizontal scattering vector qxy (≈4 sinθxy/λ), where 2 θxy is the angle between the incident and diffracted beams projected onto the horizontal plane, and integrating over the whole qz window of the PSD, to yield the Bragg peaks. Simultaneously, the scattered intensity recorded in channels along the PSD, but integrated over the scattering vector qxy in the horizontal plane across a Bragg peak, produce qz-resolved scans called Bragg rods. The scattered intensity may also be presented in 2D contour plots as a function of qxy and qz. Several different types of information may be extracted from the measured profiles. The angular 2θ positions of the Bragg peaks yield the repeat distances d = 2 /qxy, for the 2D lattice structure. The Bragg peaks may be indexed by the two Miller indices h,k to yield the a,b unit cell. The full width at half maximum (FWHM) of the Bragg peaks in qxy units yields the crystalline coherence length L in the a,b plane associated

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Figure A3. Three monolayer crystal packing arrangements of alkyl chains (left column) and their diffraction patterns (central and right columns) assuming the monolayer is in a 2D “powder” form. We assume the chains are cylindrical rods. The middle column shows the Bragg peaks I(qxy) each integrated over qz, and the right column shows the Bragg rod pattern I(qxy,qz) in the form of a contour plot. When the molecular axis is perpendicular to the water surface the lattice is hexagonal (top row), and the{1,0}, {0,1} and {1,–1} reflections coincide. The Bragg rod obtained from the single in-plane diffraction peak has its maximum at qz = 0 Å–1. When the molecular axis is tilted along the b axis (middle row), the unit cell is centered rectangular, yielding two Bragg peaks. One comprises two coincident reflections and the other is a singlet. The Bragg rod of the two degenerate reflections (1,1) and (1,–1) is centered at qz ≥ 0 Å–1, the position of the center depending upon the extent of the molecular tilt. The singlet corresponds to the (0,2) reflection whose Bragg rod will generally be centered at a qz value larger than for the {1,1} doublet. Finally, the molecular axis tilted in a non-symmetry direction, yields an oblique 2D lattice (bottom row). The peak positions of the three Bragg rods determine the chain tilt angle as well as the azimuthal position of the chain vis-a-vis the unit cell axes.

with the h,k reflection. The intensity at a particular value of qz in a Bragg 2

rod is determined by the square of the molecular structure factor |Fh,k(qz)| . The structure factor Fh,k(qz) is given by Equation (1), where fj is the scattering factor of the atom j, xja + yjb is the vector specifying the position of the atom j in the unit cell and zj is the atomic coordinate along the vertical direction. Fh,k(qz) = Σfj exp i[2π(hxj+ kyj) + qzzj]

(1)

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The measured intensity is given by equation (2) Ih,k(qz) = IV(qz)|Fh,k(qz)|2

(2)

In general the observed Bragg rod intensity is a sum over the (h,k) and (-h,-k) reflections because the crystalline film on the liquid surface is generally a “2D-powder”. The factor V(qz) describes the interference of Xrays diffracted upwards with X-rays diffracted down and subsequently reflected up by the interface.45 The factor V(qz) differs from 1 only in the vicinity of qz = 1/2qc, where it contributes a sharp peak to the intensity. Thus in equation (1) the most important variation is due to the structure factor |Fh,k(qz)|2. For molecules of arbitrary shape the overall crystalline structure can be established from a known analogous 3D crystal structure, or by trial and error, and eventually by constrained least-squares refinement to near atomic resolution in favorable systems. For simple surfactants made of aliphatic chains, |Fh,k(qz)|2 is a bell-shaped function which reaches its maximum when the scattering vector q = (qhk, qz) is orthogonal to the molecular axis. Thus for chainlike molecules, precise information on chain orientation in a 2D crystal may be obtained from the positions of the maxima of the Bragg rods6 as depicted in Fig. A3 for three different packing arrangements.

References 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Kuzmenko, I.; Rapaport, H.; Kjaer, K.; Als-Nielsen J.; Weissbuch, I.; Lahav, M.; Leiserowitz, L.; Design and Characterization of Thin Film Architectures At the AirLiquid Interface: Simplicity To Complexity, in Chem. Rev. 2001, 101, 1659. McConnell, M. Annu. Rev. Phys. Chem. 1991, 42, 171. Knobler, C. M.; Desai, R. Annu. Rev. Phys. Chem. 1992, 43, 207. Seul, M., Andelman, D. Science 1995, 267, 476. Kaganer, V. M.; Mohwald, H., Dutta, P. Rev. Mod. Phys. 1999, 71, 779. Als-Nielsen, J.; Kjaer, K., in Phase Transitions in Soft Condensed Matter; Plenum Press, New York: Geilo, Norway, 1989, 211, Series B, p. 113. Weissbuch, I.; Berfeld, M.; Bouwman, W.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Am. Chem. Soc. 1997, 119, 933. Eckardt, C. J.; Peachey, N. M.; Swanson, D. R.; Takacs, J. M.; Khan, M. A.; Gong, X.; Kim, J.-H.; Wang, J., Uphaus, R. A. Nature 1993, 362, 614. Stevens, F.; Dyer, DJ.; Walba, DM. Angew. Chem. Int. Ed. Engl. 1996, 35, 900. Nassoy, P.; Goldmann, M.; Bouloussa, O.; Rondelez, F. Phys. Rev. Lett. 1995, 75, 457. Weissbuch, I.; Addadi, L.; Berkovitch-Yellin, Z.; Gati, E.; Lahav, M., Leiserowitz, L. Nature 1984, 310, 161. Landau, E. M.; Levanon, M.; Leiserowitz, L.; Lahav, M., Sagiv, J. Nature 1985, 318, 353. Landau, E. M.; Popovitz-Biro, R.; Levanon, M.; Leiserowitz, L.; Lahav, M. Mol. Cryst. Liq. Cryst. 1986, 134, 323.

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14. Mann, S.; Heywood, B. R.; Rajam S.; Birchall J. D. Nature 1988, 334, 692. 15. Zhao, X.K, Yang, J; McCormic, L.D, Fendler, J.H. J. Phys. Chem. 1992 96 9933. 16. Wang, J. L.; Leveiller, F.; Jacquemain, D.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L.; J. Am. Chem. Soc. 1994, 116, 1192. 17. Frostman, L. M., Ward, M. D. Langmuir 1997, 13, 330. 18. Weissbuch, I.; Berkovic, G.; Leiserowitz, L.; Lahav, M. J. Am. Chem. Soc. 1990, 112, 5874. 19. Kmetko, J.; Yu, C.; Evmenenko, G.; Kewalramani, S.; Dutta, P. Phys. Rev. Lett. 2002, 89, 186182. 20. Weissbuch, I.; Majewski, J.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Phys.Chem. 1993, 97, 12848. 21. Majewski, J.; Popovitz-Biro, R.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Phys. Chem. 1994, 98, 4087. 22. Mann, S. Nature 1988, 332, 119. 23. Zhao, X. K., Fendler, J. H. J. Phys. Chem. 1990, 94, 3384. 24. Gavish, M.; Popovitz-Biro, R.; Lahav, M., Leiserowitz, L. Science 1990, 250, 973. 25. Popovitz-Biro, R.; Wang, J. L.; Majewski, J.; Shavit, E.; Leiserowitz, L., Lahav, M. J. Am. Chem. Soc. 1994, 116, 1179. 26. Davey, R. J.; Maginn, S. J.; Steventon, R. B.; Ellery, J. M.; Murrell, A. V.; Booth, J.; Godwin, A. D.; Rout, J. E. Langmuir 1994, 10, 1673. 27. Seeley, L. H.; Seidler, G. T. J. Chem. Phys. 2001, 114, 10464. 28. Seeley, L. H.; Seidler, G. T. Phys. Rev. Lett. 2001, 87, 055702. 29. Majewski, J.; Margulis, L.; Jacquemain, D.; Leveiller, F.; Bohm, C.; Arad, T.; Talmon, Y.; Lahav, M.; Leiserowitz, L. Science 1993, 261, 891. 30. Majewski, J.; Popovitz-Biro, R.; Bouwman, W. G.; Kjaer, K.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. Chem. Eur. J. 1995, 1, 304 31. Edgar, R.; Huang, J. Y.; Popovitz-Biro, R.; Kjaer, K.; Buwman, W. G.; Howes, P. B.; Als-Nielsen, J.; Shen, Y. R.; Lahav, M.; Leiserowitz, L. J. Phys. Chem. B 2000, 104, 6843. 32. Bell, K. P.; Rice, S. A. J. Chem. Phys. 1993, 99, 3. 33. Dai, Y.; Evans, J. S. J. Phys. Chem. B. 2001, 105, 10831. 34. Majewski, J.; Popovitz-Biro, R.; Edgar, R.; Arbel-Haddad, M.; Kjaer, K.; Bouwman, W.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. J. Phys. Chem. B 1997, 101, 8874. 35. Du, Q.; Superfine, R.; Freysz E.; Shen, Y.R. Phys. Rev. Lett. 1993 70, 2313. 36. Torchet, G.; Schwartz, P.; Farges, J.; Feraudy, M. F. d.; Raoult, B. J. Chem. Phys. 1983, 79, 6196. 37. Matsumoto, M.; Salto, S.; Ohmine, I. Nature 2002, 416, 409. 38. (a) Kaplun, A.; Talmon, Y.; Konikoff, F.M.; Rubin, M.; Eitan, A.; Tadmor, M.; Lichtenberg, D.; FEBS Lett, 1994 340, 78; (b) Somjen, G.J.; Lipka, G.; Schulthess, G; Koch, M.H.J.; Wachtel, E; Gilat, T; Houser, H.; Biophys. J. 1995 68, 2342; (c) Wang, D.; Carey. MC.; J. Lipid Res. 1996, 37, 2539. 39. Konikoff, F.; Chung, D.; Donovan, J.; Small, D.; Carey, M.C. J. Clin. Invest. 1992, 90, 1155. 40. Kellner-Welbel, G. et al Arterioscler. Thromb. Vasc. Biol. 1999 19, 1891. 41. Rapaport, H.; Kuzmenko, I.; Lafont, S.; Kjaer, K.; Howes, P. B.; Als-Nielsen, J.; Lahav, M.; Leiserowitz, L. Biophys. J. 2001, 81, 2729. 42. Craven, B. M. (1976) Nature 260, 727. 43. Solomonov, I.; Weygand, M.J.; Kjaer, K.; Rapaport, H.; Leiserowitz, L. Biophys. J 2005, 88, 1809. 44. Weihs, D.; Schmidt, J.; Goldiner, I.; Danino, D.; Rubin, M.; Talmon, Y.; Konikoff, F. M.; J. Lipid Research, 2005, 46, 942. 45. Vineyard, G. Phys. Rev. B 1982, 26, 4146. 46. Feidenhans’l, R. Surf. Sci. Rep. 1989, 10(3), 105.

DESIGN, SYNTHESIS, AND CHARACTERIZATION OF MOLECULE-BASED MAGNETS

JOEL S. MILLER Department of Chemistry, University of Utah, 315 S. 1400 E. Room 2120, Salt Lake City, UT 84112-0850

Abstract. The discovery of organic- and molecule-based magnets has led to several design criteria for their design and synthesis, and several families with magnetic ordering temperatures as high as ~125°C have been reported. Examples of soft and hard magnets with coercivities as high at 27 kOe have also been reported. Examples from our laboratory of organic-based magnets using the tetracyanoethylene radical anion, [TCNE]• –, are discussed. In addition, several molecule-based magnets based on Prussian blue structured materials as well as ruthenium acetate are discussed.

1. Introduction

Magnetism is a technologically important phenomenon that permeates our daily life and is crucial to our quality of life. Improvement of the magnetic properties of materials is important research area pursued worldwide.1 All commercially available magnets possess unpaired electron spins that reside in either d- or f- orbitals and have structures that possess extended three dimensional (3-D) network bonding. These materials are insoluble. The relatively recent discovery of organic- and molecule-based magnets 2 suggests that enhanced solubility and processing comparable to that enjoyed by organic polymers may be feasible. Also, the presence of organic and/or molecular components suggest materials with properties in addition to magnetic ordering may be possible, e.g. photo-controllable magnetic ordering.3 In general, organic/molecule-based magnets have different types of structural frameworks with respect to metal and metal oxide magnets, and thus may lead for new phenomena in addition to combinations of properties not observed for commercially available magnets. The first organic-based ferromagnet, [Fe(C5Me5)2][TCNE] (TCNE = tetracyanoethylene), is best described a zero-dimensional (0-D), ionic salt, and is organic-solvent soluble. It magnetically orders as a ferromagnet at 4.8 K. 4,5 291 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 291–306. © 2008 Springer.

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The worldwide discoveries of numerous organic-/molecule-based magnets6 have led to the development of a broad array of new materials and new phenomena.4,5 Table 1 lists some representative contributions. Additionally, Giant7 as well as Colossal8 magnetoresistance have been observed for 3-D network solids might suggesting that they also be achievable for organic/ molecule-based magnets. TABLE 1. Representative new magnetic materials and phenomena Ferri- and ferrimagnets based on organic/molecular components4,9,10 with Tc > 300 K 4,5,11 Prussian blue structured magnets with Tc > 300 K12–15 Single molecule magnet16 Spin-crossover materials with hysteretic effects above room temperature17 Materials exhibiting large, negative magnetizations18 Electrochemical18d,22 control of the magnetic behavior Valence tautomers exhibiting spin crossover-like behavior19 Single chain magnets20 Photoinduced magnetism3,21,22b Spin ladders23

(a) Paramagnet Disordered Spins (2-D)

(b) Ferromagnet Ordered (Aligned) Spins (2-D)

(c) Antiferromagnet (d) Ferrimagnet Ordered (Opposed) Spins (2-D)

(e) Canted Ferromagnets (2-D) Figure 1. Illustration of common spin coupling interactions.

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The electron spin is the essence of any magnet. The stronger the electron spins interact (J) the higher temperature magnetic ordering can occur. The coupling must be noncompensated or an antiferromagnet or a weak ferromagnet/canted antiferromagnet may result, Figure 1. Albeit of academic concern, the major focus worldwide lies toward ferro-/ferriimagnetic coupling/ordering. However, achievement of ferri- or in particular ferromagnetic coupling let alone ordering remains challenging. In collaboration with Arthur J. Epstein’s group at The Ohio State University, numerous organic/molecule-based magnets have been synthesized and characterized, and are herein discussed.24 2. Models for Molecule-Based Magnetic Materials A few mechanisms for achieving pairwise spin interactions necessary for ferromagnetic ordering in an organic/molecule-based material have been identified. They include: 1. Configuration mixing of a virtual triplet excited state with the ground state. 2. Heitler-London spin-exchange between positive and negative spin densities on adjacent radicals. 3. High spin-multiplicity radicals resulting from strong interactions between unpaired electron spins in orthogonal orbitals. 4. Antiferromagnetic coupling of alternating spin sites with a differing number of spins per site leading to ferrimagnetic behavior. These models are described in more detail in a review.4c While not leading to ferromagnetic ordering, the last model is fairly reliable for achieving a ferrimagnet. This has been exploited by Gatteschi and Rey groups5e with antiferromagnetic coupling between Mn(II) ions and nitroxide radicals with extended 1-D network structures. Hence, with alternating sites with a greater number of spins (i.e. 5 for S = 5/2 Mn(II)) with sites with less spins (i.e. 1 for S = 1/2 nitroxides), the Ss do not cancel and thus lead to a ferrimagnetic system (see Figure 1d). Ferrimagnets were reported based on this mechanism; e.g. Mn(hfac)2NIT (hfac = hexafluoroacetylacetonate; NIT = ethyl nitronyl nitroxide) has Tc = 8.1 K.25 Extension to higher dimensions with enhanced ordering temperatures, Tc, were achieved by Iwamura’s group for related polyfunctional nitroxides. Gatteschi’s group later showed that using Co(II) ions with nitroxides, single chain magnets an be prepared.20 Kahn’s group also reported several examples based on this strategy using Mn(II)/Cu(II): e.g. CuMn(obbz) [obbz = oxamidobis(benzoato)] has Tc = 14 K.26 Related to this is our 1-D chains of [Mn(III)TPP][TCNE] [H2TPP = meso-tetraphenylporphyrin]4a,27 that order below 28 K.

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Molecule-based magnets have numerous bonding and structural not to mention spin interaction pathways. The structural arrangements include (a) isolated molecules (zero-dimensional, 0-D), (b) chains (1-D), (c) layers (2-D), and (d) 3-D network structures. To further emphasize the structural diversity they can be grouped by the orbitals, i.e. p, p/d, or d) in which the electron spins reside and by whether or not they are connected by covalent bonds. 3. Magnets with Electron Spins in p Orbitals The best characterized organic-based magnet is 4-nitrophenyl nitronyl nitroxide (NPNN). Of the four known polymorphs, only the β-polymorph orders a ferromagnet below (Tc of 0.6 K).5b The ferromagnetic nature is verified by the saturation magnetization that corresponds to the expected one spin per nitroxide. The reaction of tetrakis(dimethyl-amino)ethylene, TDAE, with C60 forms a semiconducting material of [TDAE][C60] composition with a relatively high magnetic ordering at 16.1 K.28 The fascinating material is an enigma as the saturation magnetization is substantially attenuated with respect to the expectation from simple models, and the type of magnetic ordering is still subject to discussion. Additionally, there are several interesting reports of canted antiferromagnet/weak ferromagnets arising from incomplete antiferromagnetic coupling.29 Foremost, is the canted antiferromagnet β-4’-cyanotetrafluorophenyldithia-diazolyl. This compound orders with a Tc of 35.5 K, which is dramatically enhanced to 65.4 K under 16 kbar pressure.30 This in contrast to NPNN whose Tc drops to 0.35 K under an applied pressure of 7.2 kbar.31 In addition, [benzobis(1,3,2dithiazolyl][GaCl4] has a 6.7 K Tc.32 F

•O O N O

N +N NPNN O

4-nitrophenyl nitronyl nitroxide (NPNN)

F N

NC

• N F

S S

F

4'-cyanotetrafluorophenyldithiadiazolyl

These and other studies demonstrate that magnetic ordering can occur for demonstrate that magnets can be made from organic radicals where the electron spins solely reside in the p orbitals. 4. Magnets with Electron Spins in p and d Orbitals The first organic-based magnet [Fe(C5Me5)2].+[TCNE].– has unpaired electron spins in both p and d orbitals. The related salt [Fe(C5Me5)2].+–[TCNQ].–

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(TCNQ = 7,7,8,8-tetracyano-p-quinodimethane) forms two polymorphs that order as magnets; namely, a metamagnet with a Tc of 2.5 K and a critical field, Hc, of 1.3 kOe, and a ferromagnet with a Tc of 3.1 K and a coercive field, Hcr, of 50 Oe, Figure 2.33 Studies whereby TCNE was replaced with (a) alternative electron acceptors than even TCNQ, as well as (b) the C5 ring was substituted with nonmethyl groups, and (c) other first row transition metal ions were employed to identify the key structural features that influenced the magnetic behavior.

Figure 2. M(H) data for the metamagnetic and ferromagnetic polymorphs of [Fe(C5Me5)2] [TCNQ].33a

With the goal of stabilizing the ferromagnet behavior with respect to metamagnet behavior, the smaller TCNE electron acceptor, by a factor of two, was substituted for TCNQ to increase the spin density and enhance the spin coupling. [Fe(C5Me5)2].+[TCNE].– (DA) and [Fe(C5Me5)2].+[TCNQ].– are structurally similar as both possess the same ...D.+A.–D.+A.–...-chain solid state motif (Figure 3) and lack extended covalent bonding in any direction. This hypothesis driven research was successful and [Fe(C5Me5)2].+[TCNE].– was established to be a bulk ferromagnet with a Tc of 4.8 K and exhibit history-dependent behavior expected for a magnet. Its saturation magnetization is in accord with collinear, ferromagnetic spin alignment and exceeds that observed for iron (on an iron basis) by 36%. The importance of the presence of electron spins on both the [Fe(C5Me5)2].+ and [TCNE].– was

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noted, as the removal of a few unpaired electrons by the random substitution by small amounts of diamagnetic [Co(C5Me5)2]+ for the spin-containing [Fe(C5Me5)2].+ leads to the rapid reduction of Tc. Furthermore, loss of the porbital spins by replacement of S = 1/2 [TCNE]–. with S = 0 [C3(CN)5]– destabilizes the ferromagnetic state. This reveals that both the D and A components need to have unpaired electrons spins to stabilize ferromagnetic coupling for these ...D.+A.–D.+A.–... structured materials.

Figure 3. ...D.+A.-D.+A.-... chain structure illustrated by [Fe(C5Me5)2].+[TCNE].-. The dots schematically refer to the orbitals in which the unpaired electrons reside.

N

N

N

N

N N

N

N TCNQ

N

N TCNE

_

N

N

N

[C3(CN)5]–

Increasing Tc to 8.8 K occurred by increasing the number of unpaired electrons spins on the cation from one to two with [Mn(C5Me5)2]+[TCNE].–. However, further increasing the number of unpaired electrons to three in [Cr(C5Me5)2]+[TCNE].–, however, produces a magnet with a 3.65 K Tc that is lower than that for the one-spin per cation [Fe(C5Me5)2].+[TCNE].. Furthermore, ferromagnetic ordering has been also found for [M(C5Me5)2][TCNQ]

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(M = Fe, Mn, Cr)34 and the trend in the magnetic properties parallels those for the similarly structured [TCNE].– salts, albeit the Tc’s are reduced. 5. Magnets with Spins Residing in p and d Orbitals Connected via Covalent Bonds Some molecule-based magnets have unpaired electrons in p- and d-orbitals that are covalently linked together via covalent bonds to form 1-, 2-, and 3-D structured materials. These magnetic materials are ferrimagnets as the adjacent spins are of different magnitudes and they couple antiferromagnetically leading to a reduced moment. Representative materials include metal/nitroxide and metal-ion/TCNE complexes. Due to the inherent partial cancellation of spins, ferrimagnets have lower saturation magnetizations than ferromagnets, but they may have significantly higher Tcs. Using a three-spin 1,3,5-tris(4-butylnitroxyphenyl)benzene its 2:3 adduct with Mn(hfac)2 Hhfac = hexafluoroacetlyacetonate) forms a layered structure (Figure 4) possessing hexameric rings that orders as a ferrimagnet with a 3.4 K a Tc.35 The behavior corresponds to nine net unpaired electrons spins per repeat unit arising from the three five-spin Mn(II)’s antiferromagnetically coupling to two three-spin trinitroxides. But

O

•N But

N•

O

N

But

•

O

1,3,5-tris(4-butylnitroxyphenyl)benzene

Spins in d-orbital sites also have been observed to antiferromagnetically coupled with [TCNE].–-p-orbital spins. [Mn(III)TPP]-[TCNE] [H2TPP = meso-tetraphenylporphryin) is comprised of chains of alternating four-spin [MnTPP]+ and one-spin [TCNE].– trans-µ-bridging the Mn(III) sites (Figure 5). It is a ferrimagnet with a Tc of 16 K with hysteretic M(H) data. This magnetic material is prototypical of several metallomacrocyclic coordination polymers exhibiting intriguing magnetic behaviors. They are ferrimagnets, as confirmed with the report of a compensation temperature of 8 K (Figure 6).4a

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Figure 4. Hexameric units of the layered structure of [1,3,5-tri(4-butylnitroxy-phenyl)benzene]2 [Mn(hfac)2]3.

Figure 5. Segment of a uniform 1-D ...D+A.– D+A.–... chain of [Mn(III)TPP]+[TCNE] –. This material is a ferrimagnet below 16 K.

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Figure 6. Ferrimagnetic compensation behavior observed for [Mn(III)TTP][TCNE].

Figure 7. 5 Oe M(T) of V(TCNE)x.zCH2Cl2 revealing a ~400 K Tc.36

An extended 3-D network structure is proposed for the magnet formed from the reaction of TCNE and V(C6H6)2 [or V(CO)6] carried out in our laboratories.4a This material has the composition of V(TCNE)x•zCH2Cl2 (x ~ 2; z ~1/2). However, due to its extreme insolubility and reactivity with both air and water, variations in composition with preparation condition occur and its structure has yet to be pinned down. Nonetheless, EXAFS studies reveal that each V is divalent and surrounded by six nitrogens at

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2.084 Å at room temperature.37 This material is a room-temperature magnet (Tc ~ 400 K) (Figures 7 and 8) with and exhibits hysteresis characteristic of being a soft magnet.

Co 5 Sm Magnet

V(TCNE) x • y(CH 2 Cl2 ) Magnet

Ampule

Figure 8. Photograph of a powder sample of the V(TCNE)x•zCH2Cl2 magnet being attracted to a Co5Sm magnet.

Extensive studies of the V(TCNE)x•zCH2Cl2 magnet suggest that the magnetic properties are dominated by the effects of variation of magnetic interactions from site to site due to the solvent and disorder in the system. This effect leads to complex magnetic behavior termed a correlated spinglass that is magnetically less-rigid, but similar to a ferrimagnet. 6. Magnets with Spins Residing only in d Orbitals Connected via Covalent Bonds A few magnets have been made with spins residing only in metal d orbitals not covalently bonded to each other. While magnetic ordering has been noted, hysteretic behavior has not been observed. These embryonic studies, however, led to the development of materials with d-orbital spins sites connected to each other by covalent bonds and have been prepared using organic synthesis. These magnets can be classified as belonging to two groups, i.e. those with unpaired electron spins in adjacent sites in orthogonal orbitals that couple ferromagnetically, and those that do not. The unpaired electron spins in the latter group couple antiferromagnetically leading to ferrimagnetic behavior. These behaviors can be modulated by selecting metal-ions with spins residing in differing orbitals.

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Figure 9. Segment of the extended layered [CrCl4]2– structure.

Figure 10. Idealized structure of Prussian blue possessing M-CN-M’ linkages in 3-D. When M = Cr and M’= Ni the material is a ferromagnet with a 90 K Tc, however, for M = V and M’ = Mn the material is a ferrimagnet with a 125 K Tc.

There are several examples with two and three-dimensional extended structures of that magnetically order as ferromagnets. A2[CrCl4] {A = Rb+, [RNH3]+ (e.g. R = Me, PhCH2)} forms a layered structure (Figure 9) for which each Jahn-Teller distorted Cr(II) site in such a way that the four spins on adjacent spin sites are in orthogonal orbitals. This leads to ferromagnetic behavior below about 55 K.38 Their critical temperatures are independent of interlayer separation and they are relatively transparent.

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In addition, Prussian blue are examples of three-dimensional extended structured materials for which either ferromagnetic or ferrimagnetic behavior has been stabilized via substituting the metal ions. Prussian blue, Fe(III)4[Fe(II)(CN)6]3•zH2O, has M←C≡N→M’ linkages in all three Cartesian directions (Figure 10).12 The metal ions used, their oxidation states, and defects in the lattice all affect the magnetic properties. When the unpaired electron spins reside in orthogonal orbitals on adjacent spin sites (as occurs when the metal ions are Ni(II) and Cr(III), the saturation magnetization for CsNi[Cr(CN)6]•2H2O (Tc = 90 K)) is consistent with five spins per formula unit, as expected for ferromagnetic behavior. However, when the unpaired electron spins resides in orbitals that are not orthogonal, ferrimagnet behavior is observed. This is the situation for Cs2Mn(II)-[V(II)CN)6] that has a magnetization consistent with two spins per formula unit and is a ferrimagnetic with a Tc of 125 K. More complex compositions possessing vacancies in the Prussian blue structure type can lead to ordering temperatures that exceed room temperature, as occurs for V[Cr(CN)6]0.86•2.8H2O.13 Note, however, that it is a ferrimagnet with a net moment of 1/6 of a single spin per formula unit. Me

Me O Ru O

O O

O O Ru

O

O

Me Me Ru2(O2CMe)4

Ruthenium acetate, Ru2(O2CMe)4, was reported to be a key building block to develop a new family of molecule-based magnets of [Ru2(O2CMe)4]3 [Cr(CN)6] composition. This is due to its cation having three unpaired electron spins that are needed for magnetic ordering, and each Ru possesses a vacant coordination site needed for construction of a 3-D extended structure.39 [Ru2(O2CMe)4]3[Cr(CN)6] has a cubic structure (Figure 11), as well as magnetically orders as a ferrimagnet at 33 K.

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Figure 11. Structure of [Ru2(O2CMe)4]3[Cr(CN)6] showing its two Interpenetrating cubic lattices.

References 1. (a) R. M. White, Science, 229, 11 (1985). R. M. White, J. Appl. Phys. 57, 2996 (1985). (b) W. E. Wallace, J. Less-Common Met, 100, 85 (1984) (c) J. S. Miller. A. J. Epstein, MRS Bull, 25, 11 (2000) (d) J. S. Miller, M. Drillon, Eds., Magnetism – Molecules to Materials, (Wiley-VCH, Vols 1–5, 2001–2005). 2. (a) J. S. Miller, A. J. Epstein, W. M. Reiff, Mol. Cryst., Liq. Cryst. 120, 27 (1985). J. S. Miller, J. C. Calabrese, A. J. Epstein, R. W. Bigelow, J. H. Zhang, W. M. Reiff, J. Chem. Soc. Chem. Commun. 1026 (1986). (b) J. S. Miller, J. C. Calabrese, H. Rommelmann, S. Chittipeddi, A. J. Epstein, J. H. Zhang, W. M. Reiff, J. Am. Chem. Soc. 109, 769 (1987). (c) S. Chittipeddi, K. R. Cromack, J. S. Miller, A. J. Epstein, Phys. Rev. Lett. 58, 2695 (1987). 3. (a) C. J. O’Connor, NATO ASI, E321, 521 (1996). (b) J. S. Jung, L. Ren, C. J. O’Connor, J. Mater. Chem. 2, 829 (1992). (c) F. Varret, M. Nogues, A. Goujon, Magnetism: Molecules to Materials 1, 257 J. S. Miller, M. Drillon, Eds., (Wiley-VCH, 2000). 4. (a) J. S. Miller, A. J. Epstein, J. Chem. Soc., Chem. Commun. 1319 (1998). (b) A. J. Epstein, J. S. Miller, Adv. Chem. Ser. 245, 161 (1995). (c) J. S. Miller, A. J. Epstein, Angew. Chem. 106, 399 (1994); Angew. Chem. internat. Edit. 33, 385 (1994). (d) J. S. Miller A. J. Epstein, Chem. Brit. 30, 477 (1994). (e) J. S. Miller, A. J. Epstein, Chem & Ind. 49 (1996) (f) J. S. Miller, A. J. Epstein, Chem. & Eng. News, 73, 40, 30 (1995). 5. (a) V. I. Ovcharenko, R. Z. Sagdeev, Russ. Chem. Rev., 68, 345 (1999). (b) M. Kinoshita, Phil. Trans. R. Soc. Lond (A) 357, 2855 (1999). (c) P. Day, J. Chem. Soc., Dalton Trans. 701 (1997). (d) O. Kahn, Adv. Inorg. Chem. 43, 179 (1995). (e) A. Caneschi, D. Gatteschi, P. Rey, Adv. Mat. 6, 635 (1994). (e) O. Kahn, (VCH Publishers, New York, NY, 1993).

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FROM BONDS TO PACKING: AN ENERGY-BASED CRYSTAL PACKING ANALYSIS FOR MOLECULAR CRYSTALS

JUAN J. NOVOA*, EMILIANA D’ORIA Departament de Química Física, Fac. Química & CERQT, Parc Cientìfic de Barcelona, Universitat de Barcelona, Av. Diagonal, 647, 08028-Barcelona (Spain)

Abstract. The analysis of the crystal structure based only on distance considerations (short-contact analysis) presents some problems, as not always the shortest contacts are the most attractive. Here, it is shown how a full understanding of the crystal packing of molecular crystals can only be obtained using energetic considerations (intermolecular bonds and intermolecular repulsions). The properties of these interactions are analyzed in theoretical qualitative expressions, obtained from accurate theoretical studies. The forms in which this information can used for the study of molecular crystals are described in detail, justifying the convenience of using intermolecular bonds. The properties of all relevant intermolecular bonds are presented in simple terms. 1. Introduction Molecular Materials, that it, materials that results when molecules aggregate in solids (not necessarily ordered). Therefore, their design can be considered as a branch of Crystal Engineering,1 here understood as the art of doing a rational design of crystals presenting specific properties. A first step in such design process is being able to rationalize of the packing of the known crystals that present the property of interest. Without this rationalization it is impossible to design molecules oriented in the specific directions (those where the property of interest is generated by the molecule-molecule interactions), as needed in a rational design of Molecular Materials. The most popular procedure nowadays employed to rationalize the structure of molecular is based on the analysis of the shortest contacts (shortest-contact analysis). It works under the assumption that the shortest contacts are also the energy-determinant interactions, which also receives the name of strength-length correlation. Shortest-contacts analysis works in

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many cases, because it uses in an implicit way energetic considerations. However, there are cases where it has been found to fail,2 as the strengthlength correlation (implied when doing such analysis) is not always a valid one.3 This failure was found when doing a proper evaluation of the molecule-molecule interactions within the crystal (prompted by contradictory conclusions obtained when doing the usual short-contacts analysis). This energy evaluation can be performed by doing ab-initio calculations4 on all unique molecule-molecule interactions (that is, the intermolecular interactions) within the crystal. Alternatively, the energy can be estimated by using qualitative theoretical considerations based on the accumulated the knowledge about these interactions previously, obtained from ab-initio calculations on model systems. Here we describe how by using the second approach the crystal packing of molecular crystal can be properly rationalized. In another words, we will to show that it is possible to qualitatively rationalize the packing of molecular crystals (“read” the crystal) by a using in a qualitative way the information on the energy of the molecule-molecule interactions (the intermolecular interactions). 2. Energy is the Key for a Proper Crystal Packing Analysis 2.1. ENERGY AND CRYSTAL PACKING

Molecular crystals are molecular aggregates in their solid state that also posses long-range order. They are formed whenever the sum of all intermolecular interactions becomes enough more stable than the thermal energy at the working temperature T, whose average value is (3/2)RT. When this sum is only slightly more stable than the thermal energy the molecule-molecule vibrational motions are in a high vibrational level, where wide amplitude molecule-molecule motions are possible. As a result of these motions, the structure of the aggregate is constantly changing, that is the aggregate is in its liquid state. This is not the case in the solid state, where the amplitude of the molecule-molecule vibrations is small compared to the distance and thus the aggregate can be considered as nearly frozen in a given position. The observable structure of a solid molecular aggregate results from a complex compromise among all non-negligible intermolecular interactions. Their number in non-ordered solids can be very large, but in crystals, symmetry simplifies their analysis, as the number of unique non-negligible interactions is small enough. Even so, it is known that in many cases the experimental free energy surface of a molecular solid presents multiple minima. Each of them is a stable experimental structure of the crystal, that is, one of its polymorphs. Experimentally, there are many crystals for which more than one polymorph is known,5 although most crystals reported in the

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CSD have only one known polymorph. Theoretical calculations reproduce the existence of polymorphs for any crystal, although they systematically predict the existence of many polymorphs in a small energy range,6 a puzzling results that can be attributed to various factors (lack of accuracy of the intermolecular potentials, most of the atom-atom type, lack of entropy term in most calculations, …). Figure 1 shows a possible free energy surface for a crystals presenting multiple polymorphs, and that computed using ab-initio intermolecular potentials for a crystal.

Figure 1. Free energy surface as a function of an arbitrary coordinate r (which can symbolize a combination of coordinates). Four polymorphs are present, being the most stable energetically P2.

If energy is the property behind the stability and packing of crystals, it seems natural that one has to follow energetic considerations when trying to rationalize these two properties (at least in all their complexities). This statement that could seem revolutionary at the beginning, is not so. As justified in detail in the next section, energy is implicitly included in most of the methods currently used to rationalize the packing of crystal. 2.2. THE KEY ROLE OF ENERGY IN PREVIOUS CRYSTAL PACKING ANALYSIS METHODS

Crystal packing analysis is nowadays still an art where user judgement is still an important factor, although based on solid principles. In the exercise of this art, over the years, there have been some important milestone principles that have provided to such an art a solid background. Here, we describe these milestones, and analyze the energetic information that they contain. Without aim of being exhaustive, we have considered as the most relevant approaches to crystal packing analysis the following ones: (1) Kitaigorodsky’s Close Packing Principle,7 (2) short-contact analysis of crystals,8 (3) analysis based on statistical analysis of intermolecular contacts,9 (4) Etter’s Principles for hydrogen bonded crystals,10 and (5) the supramolecular synthon approach.11

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The historical first relevant milestone in crystal packing analysis was the Close Packing Principle, put forward by Kitaigorodsky7 around the early 60’s. Phrased in simple words, his principle stated that “the most efficient packing is the most dense”, that is, a supramolecular structure where the molecules were oriented minimizing the voids (or if one prefers a complementary perspective, by maximizing their contacts). Thus, he proposed that it was possible to find optimum crystal structures by looking at aggregates where the solid was packed in the densest forms. Nowadays, we know that although it is not always obeyed, but that it works in most cases. Why this is so? Because by maximizing the number of contacts that a molecule makes with all others one is maximizing the sum of the attractive intermolecular interactions. This has to be done whilst minimizing the total energy of the repulsive ones (see below). The fact that the maximum density packing is not always the energetically most stable one indicates that other subtle effects, not considered by this principle, are also playing a key role in crystal packing. Distance-based short-contact analysis8 is based on the principle that “the shortest contacts are the strongest ones”, and that these energetically dominating contacts are also those determining the structure. Its energetic basis is thus evident. However, as already mentioned, ab-initio studies have shown that the shortest=strongest assumption not always holds,3 a fact that we have solved by estimating the energy of these short interactions (by exact calculations on model systems, or using qualitative approximations). One can obtain information about the nature of these short-contacts in short-contacts analysis from statistical analysis of a large number of crystals where the interaction of interest is available.9 Its basic assumption is that “the most probably orientation of crystals is the most stable one”. Therefore, the method is implicitly energy based. The information provided by statistical studies is in good agreement with that obtained from accurate theoretical calculations (this can be demonstrated, for instance, on the C-H…O interactions, where statistical crystal packing analysis12 and theoretical calculations13 agreed in their hydrogen bonded nature). However, one has to be careful as contacts with a similar topology can appear is completely various crystals for different energetic reasons. Besides, as crystals pack trying to first satisfy the requirements imposed by their strongest interactions, one can sometimes find short contacts (expectedly attractive) that are energetically repulsive when its energy is explicitly computed. Etter’s main conclusion from her analysis of hydrogen bonded crystals10 was that these molecules try maximize the possible hydrogen bonds, a fact that induced the formation of patterns (which could be of various classes: self, chains, rings, …). These patterns were different from polymorph to polymorph, a fact that made them useful to distinguish polymorphs. These

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principles could be understood in energetic considerations as follows: the sum of the interaction energy is maximized when the energy of the strongest intermolecular bonds (hydrogen bonds in the crystals analyzed by Etter) is also maximized. Different polymorphs only represent different local energy minima for the sum of interaction energies. Finally, Desiraju11 extended Etter’s analysis when he proposed that the most energetically robust patterns could be considered as the synthetic originators of the crystal, suggesting that they should be called supramolecular synthons. In his proposal, these robust synthons were identified by doing statistical analysis, and no energetic estimation of their stability was done. However, it is obvious that the strongest synthons are those where the number and strength of they intermolecular bonds is maximized. These will be the most robust ones according to the laws of Thermodynamics and Kinetics. Therefore, all methods described in this section make implicit use of the energy in their analysis. However, they do it in an approximate way, and/or make assumptions that not always are correct. The consequence is that these methods in some cases fail to rationalize the packing of some crystals, or even worst, rationalize in the wrong way the packing (that is, give good results for the wrong reasons). The problem is solved when the nature of the intermolecular interactions is explicitly computed using accurate theoretical expressions (or doing accurate ab-initio calculations). 3. The Nature of the Intermolecular Interactions Intermolecular interactions are the interactions that a stable molecule experiences in presence of other molecules, not necessarily of the same kind.14 We consider as stable molecules any aggregate of atoms having a long enough stability and lifetime, on a chemical scale. This definition considers also as stable molecules open-shell radicals whose chemical structure makes them long-living, like those found in molecule-based magnets. The first consistent identification of the attractive nature of intermolecular interactions was done by van der Waals in his study of gases. However, its origin and properties were only understood after the development of Quantum Mechanics. Within Quantum Mechanics the interaction energy between a pair of molecules of a supramolecular aggregate (as are molecular crystals) can be obtained by subtracting the total energy for the complex and each isolated molecule computed in the stationary Schrödinger equation ( HΨ = EΨ , where E is the total energy, H the Hamiltonian operator, and Ψ the wavefunction that describes the ondulatory behavior of the system).4,15 However, even when this equation can be accurately solved, the value of E obtained refers to all interactions

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presents in the molecule-molecule interaction, and does not provide any understanding about why its size. However, one has to rationalize that value using models and concepts developed in for such a task. The Quantum Mechanics study of the interaction between two molecules, indicates that there are orientations for which the interaction energy (that is, the difference between the energy of the complex and the sum of the energies of each isolated molecule) is attractive (negative sign), while it can be repulsive (positive sign) for other relative orientations. This behaviour is illustrated in Figure 2 for the interaction energy of two coplanar water molecules (computed as a function of O…O distance, for various water-water orientations). In the case of the water dimer interactions of Figure 2, the interaction curves are repulsive for the orientations from 120º to 180º, and attractive for all other orientations, being the most stable orientation that at 60º (where a O-H…O bond is formed; the interaction energy in such minimum is 4.5 kcal/mol, typical of moderate hydrogen bonds). The attractive curves for intermolecular interactions follow a Morse-like shape, similar to that found in chemical bonds but with the following major differences: (a) attractive intermolecular interactions are much weaker than chemical bonds (usually the first are smaller than 30 kcal/mol, while the second are above 100 kcal/mol), (b) the minima in intermolecular curves is usually placed at much longer distances (generally above 2 Å), while typical chemical bond have minima around 1.3 Å.

Figure 2. Interaction energy (in kcal/mol) for the interaction of two coplanar water molecules (computed at the MP2/aug-cc-pVTZ level) for various relative orientations of the two molecules. At 180° the two molecules have their dipoles collinearly pointing against each other, while at 0° these dipoles are collinear but both pointing in the same direction. The minimum is found at 60°, where a O-H…O hydrogen bond is made. An symmetrical set of curves (not plotted here) exists between 180° and 360°.

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Figure 2 also shows that at short distance all intermolecular interactions become energetically repulsive, with values much larger than the minimum at any orientation. This region, sometimes called the repulsive wall, has its origin in the Pauli repulsion (the impossibility of two electron to occupy the same position in the space, as would happen at very short intermolecular distances). The repulsion wall makes impossible (in the range of chemical energies) to compress matter beyond some small percentage. Due to this, the most stable relative orientation of molecules is always that minimizing the repulsive wall interactions (also in good agreement with the Close Packing Principle), as already recognized in the crystal packing literature by some authors.16 Not all intermolecular interactions are due to the same forces, a fact that allows to classify them into physically meaningful classes. The most rigorous form of doing such classification is by looking at the dominant energetic components of their interaction energy, a sort of fingerprint procedure. Using perturbation theory15 it is possible to derive expressions for the interaction energy of two molecules as a sum of physical meaningful terms. One of these perturbational procedures is the IMPT method17 (an acronym for Inter Molecular Perturbation Theory). Equivalent expressions can be obtained using other similar perturbation formalisms.18 Within the IMPT theory, the interaction energy between two closed-shell molecules is equal to the sum of five components: Eint = Eer + Eel + Ep + Ect + Edisp

(1)

whose physical meaning is as follows: 1) Eer is the exchange-repulsion component, a combination of the Pauli repulsion that two electrons experience when forced in the same region of the space, and the attractive exchange component. The sum of these two part is always repulsive. It is the component responsible for the existence of the repulsive wall; 2) Eel is the electrostatic component, associated to the electrostatic interaction of two unpolarized molecules (having the same electronic distribution than in their isolated molecules); 3) Ep is the polarization component, which describes the change in the electrostatic interaction component due to the fragments polarization when they are close enough. In classical terms, each fragment polarization is proportional to its polarizability; 4) Ect is the charge-transfer component, associated to transfer of electronic charge from one interacting molecule to the other; 5) Edisp, is the dispersion component, a non-classical term whose existence is due to the correlated motions of the electrons. This component originates from quantum effects that have no exact classical translation.

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Its closest classical analogy14 is the interaction between the instantaneous dipole moments of the two molecules (each one induced by the electron motions of the other molecule). It is worth pointing here that the addition of the electrostatic and polarization components is equal to the real electrostatic contribution to the interaction energy. One can understand the relative importance of these IMPT components by looking at Figure 3, where their values are shown for various points on the intermolecular potential energy curve of the water dimer (as a function of the H…O distance). The curves in Figure 3 shows that: (1) the exchangerepulsion component is repulsive at all values of the H…O distance, (2) all remaining energy components are attractive at the plotted distances, (3) the dominant attractive component in this interaction is the electrostatic component, although a non-negligible attractive dispersion component also exists, (4) the total IMPT energy curve (obtained by adding all components) is similar to the MP2 interaction energy curve, a fact that guarantees the validity of the IMPT perturbative calculation. 10

5

E

0

-5

-10 2

3

4

r

Figure 3. Variation of the IMPT components (in kcal/mol) with the shortest H…O distance (r, in Å) for the interaction of a water dimer in its optimum geometry. The value of r was increased while preserving the relative orientation of the two fragments. The components are identified as follows: electrostatic ( ), exchange-repulsion ( ), polarization ( ), charge transfer ( ), and dispersion ( ). We have also plotted the sum of the previous components ( ), and the MP2 interaction energy ( ).The calculations were done using the aug-ccpVDZ basis set.

On top of these components, when the interacting molecules have unpaired electrons, there is an extra one: the bond component (Ebond), which arises from well known tendency of unpaired electrons to pair when their orbitals overlap. It is found whenever two stable (that is, long-lived)

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radicals are placed at a distance where their SOMO orbitals overlap, for instance, when two TCNE.– anion-radicals are placed parallel at C…C distance of 2.9 Å. In this case, long C-C bonds are formed between the two TCNE.– anion-radicals.19 These long C-C bonds show all the properties of the usual covalent C-C bonds, but at much larger separations (around 2.9 Å).19 They can only exist in ionic crystals where the cation…anion interactions overweight the sum of the anion…anion and cation…cation repulsions (for this reason, they have also received the name of chargemediated bonds,19 as the cations “mediate” the existence of these bonds). The previous IMPT analysis of the interaction energy can be applied to any dimeric complex found in molecular crystals. One can then use these results to classify any intermolecular interactions according to their dominant component. This classification is a more clear and quantitatively rigorous criteria than others available in the literature.8,14,20,21,22,23 Besides, most the classes found in these other criteria are also present in the dominant component classification. Obviously, four different types of interactions can be defined for closed-shell molecules (we have consider only an electrostatic subset, resulting from the addition of the electrostatic and polarization components, as this is the real electrostatic component): (1) exchange-repulsion interactions (sometimes known as steric interactions, one case of them being the agostic interactions); (2) electrostatic interactions (also called Coulombic or ionic interactions); (3) charge-transfer interactions (usually, not dominanting in IMPT evaluations), and (4) dispersion interactions, also called van der Waals interactions. Besides these types, when the interacting molecules are radicals, one can also have the bonding interactions, better known as covalent interactions. The classes are non-excludent. Sometimes more than one component is relevant and with a similar weight. Then, the interaction has to be classified in a mixed class, for instance, electrostatic-dispersion. A prototypical example in found in the C-H…O interactions, which present a nearly 50% weight of the electrostatic and dispersion dominant attractive components, and thus should be classified as an electrostatic-dispersion interaction. When the size of the molecule makes the IMPT or similar analysis very expensive, it is possible to qualitatively estimate the weight of these components using analytical expressions obtained from rigorous theoretical studies.14 The two forms of searching for the dominant components provide similar conclusions.14 Hereafter we present the analytical expressions that are thought to be the most reliable ones at the present moment: (1) The exchange-repulsion component (Eer) can be taken as proportional to the overlap between the densities of the interacting molecules:24

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Eer ≈ K <ρA|ρB>

(2)

where K is a proportionality constant that depends on the specific interacting molecules, and <ρAρB> is the overlap of the electron densities of molecules A and B. It can be shown that Eer follows an exponential behaviour respect to the shortest intermolecular atom-atom distance: Eer ≈ exp(-rij)

(3)

This exponential behaviour justifies its dominant nature at short atomatom distances between the molecules. (2) The electrostatic component (Eel) describes the electrostatic energy between molecules A and B when they have their isolated electronic structure. Using classical electrostatics, the electron density of a molecule can be represented by a multipole expansion centered on only one point,14 usually the centre of mass of the molecule (for accurate studies, the multipole expansion is done on all atoms of both interacting molecules, doing the so-called distributed multipole expansion,25 but this is not needed for qualitative analysis, as those required here). Tabulated values for the multipoles of a molecule are available in the literature for many isolated molecules,14 or can be easily computed with ab-initio methods. When the central multipole expansion is truncated the after the dipole moment (this allows to analyze electrostatic interactions in molecules that have non-zero charge and dipole; higher quadrupoles have to be considered, for instance, for the interaction between CO2 dimers), the electrostatic component between two frozen molecules can be written as: E

el

=

q q A B r 4 πε o

−

−

1

q μ q μ A B cosθ − 1 B A cosθ 1 2 2 r r2 4πε 4πε o o

(4)

1

1 4πε o

μ μ

(

)

A B 2cosθ cosθ − sinθ sinθ cos φ − ... 1 2 1 2 r3

where r is the distance between the two centers of mass, 1 and 2 the angles between the dipole of each molecule and the axis that links these centers of mass, and φ the dihedral angle of the dipoles around that center-center axis. Furthermore, qI and μi are the charge and dipole on molecule I.

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The term in the first row of (4) is the charge-charge (E(q,q)) term, those in the second row one are the two components of the chargedipole (E(q,μ)) term, and these on the third row is the dipole-dipole (E(μ,μ) term. Equation (4) can then be written in a more compact and physically meaningful form: Eel = E(q,q) + E(q,μ) + E(μ,μ) +…

(5)

At the typical range of intermolecular interactions found in molecular crystals (1.8 – 3 Å), the first term (1/r dependence) dominates over the remaining two (1/r2 and 1/r3 dependence) if the three are present (as when both interacting fragments are charged and have a non-negligible dipole). However, when only one fragment is charged and both have a non-negligible dipole, the first term in zero and the second term dominates. Only when the two fragments are non-charged and have a non-negligible dipole moment interact the third term dominates. Examples of each type of situation are found in ionic salts, the ionwater interactions, and water-water interactions. (3) The polarization component (Ep) takes into account the part of the electrostatic interaction that comes from the mutual polarization of the electronic density (remember that Eel + Ep is the real electrostatic energy). Usually Ep is smaller than Eel. An analytical expression (up to the dipole moment) is available within the central multipole expansion model:14 ⎛ ⎞ ⎜q 2 α + q 2 α ⎟ B A⎠ ⎝ A B E =− 2 p r4 2 4 πε o ⎞ ⎛ 2 ⎜μ α (1+ 3cos 2 θ1 ) + μ 2 α (1+ 3cos2 θ 2 )⎟ B A 1 ⎠ ⎝ A B − − ... 2 6 r 2 4 πε o

1

( )

( )

(6)

where αI is the polarizability of molecule I, and all other symbols have the same meaning as in (4). Physically, the first term corresponds to the polarization induced by a charge, while the second term is the polarization induced by a dipole. Obviously, the first term disappears when the molecules have no charge and the second when they have no dipole. (4) The dispersion component (Edisp) between molecules A an B can be approximated by the following expression, due to Drude:26 Edisp =−

3 2(4πεo)

2

[I(A)I(B)/(I(A)+ I(B))]αAαB r6

(7)

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where αJ is the polarizability of molecule J, I(J) is the ionization energy of molecule J from its ground state, and all other symbols have the same meaning than in (4). (5) No general analytic expressions are available for the bond (Ebond) or charge transfer (Ect) components. When a bond component exists, one has to estimate it by doing quantum chemical calculations that use the appropriate models and computational methods (CCSD(T), MPn, …). As already mentioned, the charge transfer component is usually not dominating, and thus there are no qualitatively estimates for it. One should note that equations (4)–(7) are valid for molecules in vacuum. However, the extrapolation to condensed phases is straightforward: one only has to substitute εo by εoεr in these equations (εr is the relative dielectric constant of the condensed medium). We also remind the reader that these expressions describe the interaction of molecules fixed in the space (as is the case within crystals). When the molecules are freely moving, as in liquids, one can obtain more simplified expressions presenting no angular dependencies.14 Lets finish this section by indicating that the recently proposed Pixel molecule-molecule potential27 is based on the principles described above. The main change is in the form in which the electrostatic component is computed (as a sum of pixel-pixel Coulombic interactions, the sum running over a set of pixels distributed around each molecule and large enough as to mimic its electronic density). The results obtained using these pixel molecule-molecule potentials are comparable to these obtained from IMPT calculations.28 They are also similar to those obtained with equations (4)– (7), although pixel molecule-molecule potentials are expected to represent better that a single-point multipole expansion the anisotropy of the electron density (pixel potentials should describe the electronic density with a quality similar to that obtained from a distributed multipole expansion, but are expected to be computationally more efficient for complex molecules). 4. Crystal Packing Analysis on the Basis of Molecule-Molecule Interactions Using the equations (4)–(7) or doing IMPT or other ab-initio calculations, one can perform a first-level analysis of the crystal packing. This is done by looking at the energy of all molecule-molecule interactions for all unique molecules in the crystal. According to equations (4)–(7), the first-nearest neighbours make the strongest intermolecular interactions with a given molecule (because they present the shortest distances between the centers of mass), but one can also include second-nearest neighbours, or even higher ones, when more accuracy is desired.

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Such analysis is very informative to understand the crystal packing, as: (a) identifies the attractive and repulsive interactions, an important fact, (b) defines the energetic relevance of the attractive and repulsive interactions. Molecular crystals are energetically stable supramolecular aggregates, that are only possible when the sum of all intermolecular interactions is attractive. This stability can be improved by decreasing the repulsive interactions or by increasing the attractive ones. In such a task, the analysis is greatly simplified when one knows the most energetically relevant interactions. It is also worth pointing here that molecule-molecule calculations can also be directly applied to define the most robust (that is, energetically stable) supramolecular synthons11 or patterns.10 For such a task, one only has to find a set of possible candidates (from statistical analysis, for instance) and the compute their intermolecular energy using any of the above procedures. 5. Going Deeper Using Intermolecular Bonds 5.1. THE NEED FOR INTERMOLECULAR BONDS WHEN UNDERSTANDING INTERMOLECULAR INTERACTIONS

Molecule-molecule calculations give very important information on the crystal packing of solids. However, one only obtains a number, the value of the interaction energy. If one wants to understand why this number is larger or smaller than that for other interactions one need to analyze where this number comes from.

Figure 4. Dimer and chain patterns found in carboxylic acid crystals. The similar antiparallel orientation of the dipole moment of the two interacting fragments are also shown (arrows with origin in the C atom).

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A first level understanding, which for some purposed is appropriate, can be obtained on the basis of the molecular properties (charge, dipole, polarizability, …) by using equations (4)–(7). But molecular magnitudes are average values, that is, result from combined effect of all the atoms and functional groups of the molecule. A much better understanding is obtained when intermolecular bonds are introduced. This second level allows, for instance, a proper rationalization of why dicarboxylic molecules prefer to form cyclic-dimers rather than chain-dimers (see Figure 4), a fact that is difficult to justify using equation (4), as the orientations of the dipoles in both conformations are anti-parallel and geometrically not very different. It also provides an direct justification to Etter rules, which are far from trivial to justify when looking at equation (4), or another similar one. Intermolecular bond are as useful tools to unerstand the structure and stability of supramolecular aggregates, as chemical bonds were to rationalize the structure and stability of molecules. In both cases, the use of bonds introduces simplicity amid the complex networks of interactions present in the system, making easy their analysis. However, for its proper use, one has to fully understand the properties of these bonds, and the limitations that the bond concept presents. 5.2. WHAT IS A BOND?

The most fundamental definition of a bond is that due to Pauling,21 first introduced in 1939: “There is a chemical bond between two atoms or group of atoms in case that the forces acting between them are such as to lead to the formation of an aggregate with sufficient stability to make it convenient for the chemist to consider it as an independent molecular species”. He also listed a few examples of intramolecular bonds: the covalent bond, the ionic bond, and the coordination bond. Besides, he also stated the following: “In general we do not consider the weak van der Waals forces between molecules as leading to chemical-bond formation; but in exceptional cases, such as the weak bond that holds together the two O2 molecules in O4, it may happen that these forces are strong enough to make it convenient to describe the corresponding intermolecular interaction as a bond formation”. That is, he identified the existence of intermolecular bonds om energetic terms, and distinguished them from the intramolecular bonds (by their weaker strength and the entities being bonded, molecules in intermolecular bonds, atoms in intramolecular bonds). The previous definition is fully functional only on diatomic systems, as H2 or He2. However, when applied to complex systems, although it recognizes the existence of a bond, does not indicate the atoms involved in such a bond, or if more than one bond is present. For instance, it identifies that benzene is a chemically stable aggregate (that is, where bonds are

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formed), but does not indicate which bonds are formed or their number. The same applies to intermolecular bonds: it does not say how many intermolecular bonds can be found in the most stable geometry of the water dimmer, although it recognizes that the two fragments are bonded.

Figure 5. Two view of the electronic density of benzene. Left: plane of 0.002 atomic units of isodensity in a transparent representation, done to allow a view of the atom position and the molecular graph. Right: Cut of the same electron density along the plane of the molecule (the bond critical points are the regions of minimum density found in the center of the C-C bonds along the sides of the hexagon, and between the C and H bonds). Notice that no C-C bond is found along the diagonals.

Figure 6. Electronic density of the water dimer. Left: Isodensity plane of 0.002 atomic units, in a transparent representation that allows a view of the atoms and the molecular graph; Right: Cut of the same electron density along the plane of the left water molecule (the intermolecular bond critical points are the regions of minimum density located between the H…O bond).

The previous problem founds a rigorous answer within the Quantum Theory of Atoms in Molecules29 (also known as QTAIM or AIM), which has solid Quantum Mechanical fundations. Using the AIM method, bonds are located by looking at the electron density of the molecule for the molecule or supramolecular aggregate. The existence of a bond between two atoms requires: (1) The presence of a (3,–1) bond critical point (in short, BCP) in the electronic density. This is a point in the density where the gradient of

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the density is zero, and its second derivative has two positive and one negative eigenvalues (in another words, curvatures). (2) A line of maximum curvature connecting the two bonded atoms and passing through the BCP. The lines of maximum curvature that connects all bonded atoms allows to make a graphical representation of the molecule based on quantum mechanical considerations, the molecular graph. They are in good agreement with the usual representations of molecules. This is illustrated in Figure 5 for a complex isolated molecule (benzene), and in Figure 6 for a supramolecular aggregate (the water dimer). The AIM analysis of the electronic density of benzene (Figure 5) concludes that there are 12 bonds: six C-C along the sides of the hexagon, and six C-H bonds collateral to that hexagon. This result agrees with the well know Kekule graphical representation of this molecule. The position of these BCP is not seen by looking at representations of isodensity planes (Figure 5-left), but is clearly seen when looking at the density in a plane that contains the bonds (as the plane of the benzene molecule, Figure 5right). Each of the 12 minima (located along the C-C and C-H lines) marks the position of a BCP. The AIM analysis of the density of the (H2O)2 complex in its optimum geometry is a bit more complex, as now we find intramolecular and intermolecular bonds, which can be distinguished by the properties if their BCP. The analysis finds two intramolecular O-H bonds and only one intermolecular H…O bonds. The graphical representation of this complex is that found in Figure 6-left, where only the intramolecular bonds have been marked. The intermolecular bond is clearly seen in the plane-cut representation (Figure 6-right) and also in the isodensity plot (Figure 6-left). Intramolecular and intermolecular bonds can be differentiated by the properties of their BCP. Intermolecular BCP have: (1) a much smaller density than intramolecular BCP (consistent with their larger bond distance), and (2) a positive Laplacian (sum of the diagonal elements of the second derivative of the density), while intramolecular BCP present a negative Laplacian. These two differences are clearly observed when looking at the values in Table 1, where the properties of the H…O and O-H bonds present in the water dimer are collected. The values of the density at the BCP can also be correlated with various bond parameters, among them the strength of the bond.30 Bond critical points are also very helpful in complex geometrical arrangements to define in a rigorous way when a short A-H…B contact is a hydrogen bond or a van der Waals bond,31 an otherwise controversial and subjective issue. The AIM

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analysis solves in a natural form this problem: it is a hydrogen bond when a H…B BCP is found, but a van der Waals bond when an A…B BCP is instead present. TABLE 1. Value of the density (ρ) and Laplacian (∇2) at the BCP, for the intermolecular (O…H) and intramolecular (O-H) bonds found in the water dimer (Figure 7). All values are given in atomic units Bond type O…H O-H

ρ 0.020 0.364

∇2 0.075 –0.262

Although the AIM theory is the most advanced and rigorous form of locating bonds within Quantum Mechanics, some of its issues are still being developed. The most relevant one is related with whether the presence of a BCP indicated automatically the existence of a bond (that is, is a necessary and sufficient condition for it), are originally pointed by Bader,29 or instead is a necessary but not sufficient condition. The second option is based on the presence of BCP in situations where no bond would be expected according to Quantum Mechanics calculations.32 Although the matter is still subject of debate, the current opinion of the authors is that only when the BCP are associated to energetically stabilizing interactions, it has to be considered a bond (in good agreement with what was proposed by Pauling21). Methods are being currently developed in some groups to allow a precise but fast estimate of the energy of a single bond within a complex network of bonds. The use of AIM theory provides a systematic, rigorous, and nonintuitive form of locating intra and intermolecular bonds in aggregates, which has already been applied to search bonds in molecular crystals, using theoretical33 or experimental34 densities. The bond critical points obtained with these two types of densities are similar in all the cases studied.34 The validity of using the AIM method in molecular crystals was questioned35 on the basis that it provides the same results than the promolecule model (an independent atom model in which the density is obtained by adding the spherical densities of all atoms that constitute the molecule). Besides the fact that this could be a proper behaviour in some weakly interacting complexes (where the polarization of the density is generally small), recent theoretical studies33 done on the (3,4-bis(dimethylamino)-3-cyclobutene1,2-dione crystal (refcode NANQUO02) have shown that the critical points obtained using the promolecule model and the real electron densities are different, and that there are fundamental reasons for the two densities to be different.

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5.3. THE PROPER PHYSICAL MEANING OF BONDS

Bonds are not the only attractive interactions in molecules and supramolecular aggregates. This is clearly demonstrated by noticing that in the AIM study of the benzene molecule one does not find bonds across the diagonals of the six-membered ring (as would be predicted by if the nonKekule structures will be evaluated, and these structures are stable resonant forms for this molecule). It is also concluded when looking water dimer bonds, where one does not draw intermolecular bonds between the O-H…O interactions not presenting BCP, despite that they are also stable when computed using model calculations. However, we do not miss these stable interactions, because the computed chemical graph without these extra bonds is the one that agrees with the accumulated empirical experience and Quantum Mechanical studies. If this is so, what is the proper physical menaing of bonds? The answer to this question can be found the AIM analysis of benzene and (H2O)2: the bonds found in the molecular and supramolecular chemical graphs are the set of dominant attractive interactions within the system. Why bonds are thus such a powerful concept? Because bonds talk about the dominant energetic interactions, and energy is the driving force behind the existence of chemical systems, according to the Laws of Thermodynamics. Thus, they make easy to understand the stability of chemical structures and also their chemical reactions, by looking at the energy of the bonds broken and created. And also, in a direct form or using valence theories, the structure of chemical systems.20,21 5.4. CONTACTS, INTERACTION, AND BONDS

Although sometimes taken as equivalent concepts, they are clearly different things. As used here, the concept contact is a purely geometrical concept based on distances and angles. However, interaction indicates that due to their geometry there is an interaction energy. Finally, we now know that the concept bond refers to the dominant attractive energetic interactions in a molecule or supramolecular aggregate. The previous differentiation is relevant, as the use of intermolecular bonds in crystal packing analysis has been a matter of debate. Some authors36 suggested the use of hydrogen bridges instead of hydrogen bonds, on the basis that “The terminology of a hydrogen bridge does not carry with it the unnecessary and incorrect implication that a hydrogen bond is like a covalent bond but only much weaker”. However, in our opinion, the use of purely geometrical concepts induces a loss of the energetic information, and is thus less powerful concept when understanding the structure and transformations of a crystal (as mention before two nearly identical C-H…O

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contacts can have very different interaction energies2). Other authors,37 proposed to abandon the use of intermolecular bonds in the analysis of molecular crystals because they are very weak and flexible (that is, the can present a lot of structural minimum energy structures, see Figure 1). Therefore, they suggested that the analysis should be only done on terms of molecule-molecule interactions. In our opinion, although analyzing the crystal packing in terms of molecule-molecule interactions is a valid form of doing such analysis, it is a less powerful approach than when the intermolecular bonds are introduced, because ones looses many of the reasons behind the strengths and directionality of the molecule-molecule interactions. 5.5. TYPES OF INTERMOLECULAR BONDS

Using the fact that bonds are the dominant attractive intermolecular interactions, it is possible to classify them using the same criterion described above for intermolecular interactions, that is, according to the dominant energetic component (using, for instance, equations 1–7). However, some of these interactions (as the exchange-repulsion) are always energetically repulsive and thus, there cannot be bonds where they are the strongest component. In other cases, as with hydrogen bonds, they are traditionally considered as a separate type, despite the fact that their strong electrostatic nature (in many cases) would allow its classification as ionic interactions. Hereafter, we will respect the usual classification, also indicating that it is very close to the classification obtained by looking at the dominant energetic component of these bonds. All intermolecular bonds known up to now in molecular crystals can be classified within the following three main classes: (1) ionic bonds, (2) hydrogen bonds, and (3) van der Waals bonds. As we will see below, the division is not always exclusive, and some bonds could have been classified as mixed class or in more than one class. The properties of each of these types of bonds are described in detail in the following separate subsections. 5.5.1. Ionic Bonds The are found when one or the two interacting fragments are charged. The first case (X±…neutral bonds) interactions is found in ion-solvent interactions, while the second one (X+…Y– bonds) is found in Na+…Cl– interactions. They are dominated by their electrostatic components (in ionion interactions the leading term is the charge-charge term, while in ionneutral interactions is the charge-dipole term, or when no dipole is present, the charge-quadrupole term). Notice that when the two fragments have charges of the same sign the interaction is generally repulsive38 and we cannot talk about the existence of a bond.

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TABLE 2. Value of the energetic components of the interaction energy for the indicated systems, computed using the IMPT method. Eel, Eer, Ep, Ect and Edisp are, respectively, the electrostatic, exchange-repulsion, polarization and dispersion components. Etot is the sum of all energetic components. EMP2 is the BSSE-corrected interaction energy, shown to serve as reference to calibrate the quality of the IMPT calculation. The MP2 intermolecular optimum distance is also indicated (ropt). Distances are given in Å and energies in kcal/mol Eel Eer Ep Ect Edisp Etot EMP2a System ropt ionic bonds Na+…Cl– 2.412 –142.3 25.4 –10.5 –1.4 –35.5 –164.3 –128.0 HC2O4–…HC2O4– 1.537 25.4 31.4 –7.7 –4.2 –11.6 33.2 40.9b hydrogen bonds NH3CH2COOH+…SO4– 1.520 –155.1 31.4 –14.4 –6.2 –12.4 –156.6 –160.0 H3O+…H2O 1.202 –45.5 54.3 –27.4 –9.6 –31.7 –59.9 –31.8 H2O…F– 1.415 –38.3 30.6 –10.1 –4.3 –8.5 –30.6 –25.3 CH4…F– 1.873 –8.3 13.7 –6.7 –1.4 –4.0 –6.8 –5.8 FH…H2O 1.716 –16.3 12.2 –1.0 –0.6 –3.2 –8.9 –7.9 H2O…H2O 1.990 –6.7 5.0 –0.7 –0.5 –2.0 –3.9 –4.2 2.174 –4.1 2.6 –0.4 –0.2 –1.4 –3.5 –2.7 C2H2…H2O CH4…H2O 2.553 –0.9 1.5 –0.2 –0.1 –0.9 –0.6 –0.4 FH…Ar 2.634 –0.1 0.5 –0.2 –0.1 –0.4 –0.3 –0.4 van der Waals Ar…Ar 3.842 –0.04 0.15 0.00 0.00 –0.28 –0.16 –0.16 CO2…CO2 3.058 –1.7 1.9 –0.2 –0.1 –1.8 –1.8 –1.0 C6H6…C6H6 3.800c 1.2 2.7 –0.2 –0.2 –5.2 –1.7 –1.8 a BSSE corrected values. b The interaction is repulsive, and therefore cannot be a bond. It is only shown here for illustrative purposes. c Value obtained after a partial geometry optimization using frozen fragments.

Examples of ionic X+…Y– bonds are found in molecular ionic crystals, some of them within the family of molecular superconductors, and also in molecule-based magnets. Examples of ionic X±…neutral bonds are found in solvated ionic salts. However, when the solvent or the X fragments present A-H groups, in most cases short-distance A-H…X contacts are made, which are better classes as hydrogen bonds (in fact, they should be considered as charge-induced hydrogen bonds39). 5.5.2. Hydrogen Bonds A reformulation of Pimentel and McClellan original definition,40 consistent with the modern findings8,23,41,42,43 associated this name to any energetically stable A-H…B interaction presenting a H…B bond. The A-H is called the proton donor group, and the X atom (or group of atoms in some cases, as in π acceptors) is called the proton acceptor group. The stability of hydrogen bonds is usually attributed to the electrostatic component. In simple qualitative terms, the A-H group has a local dipole moment that points towards X, which is an electronegative atom (that is, a

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region of accumulation of electronic density). However, modern theoretical calculations indicate that the C-H…Ar bond found in the methane-argon complex is also a hydrogen bond. In these weak hydrogen bonds (C-H…Ar , or the C-H…O in the methane-water complex) the stability is not only due to the electrostatic component. It is also due to the dispersion component, which can be 50% of the interaction energy (see Table 2). Therefore, not all hydrogen bonds follow the same energetic properties. The main consequence is that not all of them present the same directionality (for instance, the dispersion component does not necessarily follow a trend towards colinearity that the electrostatic component presents). Three classes of hydrogen bonds are nowadays generally accepted, obtained according using the strength as main criterion:23,42,43 (1) weak hydrogen bonds42,43 have typical interaction energies in the –0.1 to –4 kcal/mol range, being the C-H…O hydrogen bond found in the methane-water complex a good prototype, (2) moderate hydrogen bonds,40 which have an strength in the –4 to –15 kcal/mol range, being the O-H…O found in a water dimmer a good prototype, and (3) strong hydrogen bonds,8,23 whose typical interaction energy in located in the –15 to –40 kcal/mol range, being a good prototype the O-H…O bond found in the water-OH– complex. Many of the strong hydrogen bonds can also be classified as charge-assisted hydrogen bonds,39 because their strength originates in the net charge that present the proton donor or acceptor group. Besides the charge-assisted hydrogen bonds, other specific classifications have also been used in the literature, based on a variety of properties. We just mention here, given their relevance, the resonance-assisted hydrogen bonds,44 and the low-barrier hydrogen bonds.41 All these new types can be classified within the weak, moderate, or strong classes (as mentioned before, such classification that fits all know examples of hydrogen bonds found up to now). The strongest known hydrogen bond, with an interaction energy (Eint ) of = –49.7 kcal/mol, is the O-H(+)…O bond found in the H3O+…H2O complex. Beyond around –50 kcal/mol, hydrogen bonds are considered to reach the so-called covalent limit, after which the H…B bond becomes mostly covalent. The prototypical excamples is the FH…F– complex (which is better described as [F-H-F]–). In this complex, instead of having a FH…F– structure, with one covalent F-H bond and one H…F- hydrogen bond, the system prefers to form two covalent H-F bonds. The covalent or hydrogen bond behavior of any A-H…B can be inferred from the symmetrical/nonsymmetrical position of the H respect to the A and B atoms. However, it is more rigorously recognized by looking at the properties of the BCP29

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connecting atoms H and B: when the BCP Laplacian is negative such bond is covalent (H-B bond), while when it is positive such bond is a hydrogen bond (H…B). For instance, the Laplacian is negative for the H-O bond of the H3O+…H2O complex and the H-F bond of the [F-H-F]– complex, but it is positive for the H…N of the NH4+…NH3 complex (hydrogen bond). Recent studies3,45 have indicated that the covalent limit is non-existent, because hydrogen bonds can also exist beyond the –50 kcal/mol limit, with all its usual properties (metrics, critical points, dominant electrostatic components, …). These very strong hydrogen bonds are only found when the two interacting fragments have net charges of opposite sign, that is in A-H+…B– and A-H–…B+ topologies. These net charges increase the value of the electrostatic component of the hydrogen bond, due to [q1q2/4πεor12] charge-charge term that adds to the usual dipole-dipole term. Only a few crystals presenting O-H…O bonds are currently in this situation, thus explaining why they were not found before. Finally, let us point that despite their differences, the electronic properties of hydrogen bonds change in a continuous form, as recently reported by various authors.30 ,46 Very strong hydrogen bonds also obey that trend. 3,45 5.5.3. Van der Waals Bonds These are intermolecular bonds that result from the direct overlap of regions of strong electronic accumulation (lone pairs, -orbitals) in atoms or molecules. Their main energetic component is the dispersion component (Table 2). Therefore, they are only observed when the electrostatic component is negligible (that is, when the charge, dipole, quadrupoles, … become zero or very small; then, the polarization component becomes also very small). Van der Waals bonds are usually indicated as A…B (for instance, Ar…Ar, or π…π), where A and B are the atoms (or group of atoms) whose lone pair electrons strongly overlap. In complex geometrical arrangements the AIM analysis helps to define the atoms participating in the bond, and also allow to distinguish between A…B bonds and A-H…B bonds made by between a A-H group and a B group of two interacting fragments. The electronic structure of the van der Waals bonds is characteristic: the only overlapping orbitals are doubly occupied orbitals, so the bonding and antibonding orbitals of the complex are all doubly occupied. 5.6. THE ENERGY SCALE OF INTERMOLECULAR BONDS

When one thinks about intermolecular interactions in solids there is a tendency to associate for them the 0 to 40 kcal/mol range of energies.23,42 However, these two limiting values result from neutral complexes. And the

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scale is much wider when one considers the real situation in molecular crystals. Van der Waals bonds are usually the weakest of all intermolecular bonds, although some strong van der Waals bonds can be stronger than some weak hydrogen bonds. Neutral hydrogen bonds are also weaker than ionic bonds, although strong and very strong hydrogen bonds can have comparable strengths. The energy scale (estimated from isolated complex calculations, as usually done in the literature) is much more wider. For instance, the molecule-molecule interaction energies computed for the complexes presenting the shortest O-H…O contacts in neutron diffraction crystals (deposited in the Cambridge Crystallographic Database47) spans over the +190 to -160 kcal/mol window3 (see Figure 7). Notice also that it includes attractive and repulsive interactions (thus proving that not all short-distance O-H…O interactions are attractive). 200

N···N ZW···ZW q···N q···q

E (kcal/mol)

100

0

-100

-200 1.2

1.4

1.6

1.8

2.0

rH ...O ( Å ) Figure 7. Interaction energy computed at the MP2/6-31+G(d) level for all dimers that present O-H…O contacts shorter than the sum of the O and H van der Waals radii. These dimers were located by systematically searching in subset of neutron diffraction crystals deposited in the Cambridge Crystallographic Database (see text for details). They are grouped by families, according to the charge in the interacting fragments (N = neutral, ZW = neutral zwitterions, q = charged fragments).

The interactions in Figure 7 are separated in four subgroups, according to the charge on the fragments that form the complex. We have distinguished the charge on each fragment according to three options: neutral (N), neutral zwitterion (ZW), and charged (q, irrespective of the

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value). Out of the six possible unique charge-charge combinations, the following groups were found in these neutron crystals (the range of interaction energies for the complexes in the group is given in parenthesis, after the group name): (1) N…N group (–3.4,–48.5); (2) N...ZW group (only one value, –36.0; (3) N…q group (–21.6,–50.8); (4) ZW…ZW group (–12.6, –27.0); (5) q…q group (190, –160). It is interesting to note that the q…q group contains interactions with the metric of O-H…O hydrogen bonds, but which are energetically unstable. These interactions cannot be considered as hydrogen bonds, according to our previous considerations. Obviously, these short-range repulsive interactions are found in crystals due to the existence in the crystal of attractive interactions whose sum is larger than that for the repulsive ones. Their origin and properties have been analyzed in detail in the original publications.2 Finally, it is also worth mentioning that when one molecule can make more than one hydrogen bond with nearby ones the strength of these bonds can become larger than that for each separate bond. This effect is called cooperativity and its origin is the polarization that the formation of an intermolecular bond induces in the electron density of the interacting molecules. Experimentally, the existence of polarization effects can be demonstrated by comparing the formation energy of an isolated water dimer (–5.44 kcal/mol,48 that is, 2.72 kcal/mol per water molecule) against the formation energy per water molecule in ice at 0 K (–11.3 kcal/mol49). However, not enough studies exist on this effect, particularly for nonneutral crystals. 6. Conclussions It has been shown that the use of intermolecular bonds provides a much deeper insight on the crystal packing than molecule-molecule energy interaction analysis. By combining short-contact analysis with quantum chemical computations, and analytical expressions that talk about the approximate strength of the intermolecular interactions and intermolecular bonds, it is possible to rationalize the crystal packing of any complex molecular crystals. The nature and properties of the intermolecular bonds found in molecular crystals have also been analyzed, paying particular attention to the concept of bond, and its physical meaning. 7. Acknowledgments The authors acknowledge the Spanish Science and Education Ministry (projects BQU2002-04587-C02-02 and CTQ2005-02329/BQU, and a

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Ph. D. grant to E. D’O.) and the Catalan DURSI (projects 2001SGR-0044 and 2005-SGR-00036). They also thank BSC and CESCA for allocation of CPU time.

References 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19.

20. 21. 22. 23. 24.

G. Desiraju, Crystal Engineering. The Design of Organic Solids, Elsevier, Amsterdam, 1989. D. Braga, F. Grepioni, E. Tagliavini, and J. J. Novoa, New. J. Chem., 755 (1998) E. D’Oria, J. J. Novoa, Cryst. Eng. Commun., 6, 367 (2004) See, for instance: F. Jensen, Introduction to Computational Chemistry, John Wiley, New York, 1998 A prototypical example where a large number of polymorphs are known is found in ROY. The first six forms are reported in: L. Yu, G. A. Stephenson, C. A. Mitchell, C. A. Bunnell, S. V. Snorek, J. J. Bowyer, T. B. Borchardt, J. G. Stowell, S. R. Byrn, J. Am. Chem. Soc. 122, 585 (2000) A. Gavezzotti, Acc. Chem. Res. 27, 309 (1994) A. I. Kitaigorodsky, Organic Chemical Crystallography, Consultants Bureau, New York, 1961 G. A. Jeffrey, W. Saenger, Hydrogen Bonding in Biological Structures, SpringerVerlag, Berlin, 1991 H.-B. Bürgi, J. D. Dunitz (Eds.), Structure Correlation, VCH, Weinheim, 1994 M. C. Etter, Acc. Chem. Res. 23, 120 (1990) G. R. Desiraju, Angew. Chem. Int. Ed. Engl. 34, 2311 (1995) R. Taylor, O. Kennard, J. Am. Chem. Soc. 104, 5063 (1982); G. R. Desiraju, Acc. Chem. Res. 24, 290 (1991) J. J. Novoa, B. Tarrón, M.-H. Whangbo, and J. M. Williams, J. Chem. Phys. 95, 5179 (1991) G. C. Maitland, M. Rigby, E. B. Smith, W. A. Wakeham, Intermolecular Forces. Their Origin and Determination, Clarendon press, Oxford, 1981; J. Israelachvili, Intermolecular and Surface Forces, 2nd edition, Academic Press, Amsterdam, 1992; A. J. Stone, The Theory of Intermolecular Forces, Clarendon Press, Oxford, 1996 A. Szabo, N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Macmillan, New York, 1982 J. D. Dunitz, A. Gavezzotti, Acc. Chem. Res. 32, 677 (1999) I. C. Hayes, A. J. Stone, J. Mol. Phys. 53, 83 (1984) B. Jeziorski, R. Moszynski, K. Szalewicz, Chem. Rev. 94, 1887 (1994) J. J. Novoa, P. Lafuente, R. Del Sesto, J. S. Miller, Angew. Chem. Int. Ed. 40, 2540 (2001); J. J. Novoa, P. Lafuente, R. Del Sesto, J. S. Miller, CyrstEngComm. 4, 373 (2002); R. Del Sesto, J. S. Miller, J. J. Novoa, P. Lafuente, Chem. Eur. J. 8, 4894 (2002). C. A. Coulson, Valence, Oxford University Press, Oxford, 1952 L. Pauling, The Nature of the Chemical Bond, 3rd edition, Cornell University Press, Ithaca, 1960. The first edition of this seminal book was published in 1939. V. G. Tsirelson, and R. P. Ozerov, Electron Density and Bonding in Crystals, Institute of Physics Publishing, Bristol, 1996. G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997 M. Born, J. E. Mayer, Z. Phys., 75, 1 (1932)

332 25. 26. 27. 28. 29. 30.

31. 32.

33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.

J.J. NOVOA AND E. D’ORIA A. J. Stone, Chem. Phys. Lett. 83, 233 (1981); A. J. Stone, M. Alderton, Molec. Phys. 56, 1047 (1985) P. K. L. Drude, The Theory of Optics, Longman, London, 1933. A. Gavezzotti, J. Phys. Chem. B, 107, 2344 (2003) A. Gavezzotti, CrystEngComm 5, 429 (2003) R. F. Bader, Atoms in Molecules. A Quantum Theory, Clarendon Press, Oxford, 1990 E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett., 285, 170 (1998); S. J. Grabowski, J. Phys. Chem. A, 105, 10739 (2001); I. Alkorta, J. Elguero, J. Phys. Chem. A, 103, 272 (1999) J. J. Novoa, P. Lafuente, F. Mota, Chem. Phys. Lett. 290, 519 (1998) It was first reported in: J. Cioslowski, S. T. Mixon, J. Am. Chem. Soc. 114, 4382 (1992). But has been found in various other cases (ionic crystals where anions and cations have very different sizes, …). See for instance: C. Gatti, E. May, R. Destro, F. Cargnoni, J. Phys. Chem. A, 106, 2707 (2002) V. G. Tsirelson, and R. P. Ozerov, Electron Density and Bonding in Crystals, Institute of Physics Publishing, Bristol, 1996 M. A. Spackman, Chem. Phys. Lett. 301, 425 (1999) G. R. Desiraju, Acc. Chem. Res., 35, 565 (2002) J. Dunitz, and A. Gavezzotti, Angew. Chem. Int. Ed., 44, 1766 (2005) The interaction between two anions or cations can be attractive when the charge is localized and the ions large enough (E. D’Oria, J. J. Novoa, et al., to be published). P. Gilli, V. Bertolasi, V. Ferretti, G. Gilli, J. Am. Chem. Soc. 116, 909 (1994) G. C. Pimentel, A. L. McClellan, The Hydrogen Bond, W. H. Freeman, San Francisco, 1960 S. Scheiner, Hydrogen Bonding. A Theoretical Perspective, Oxford University Press, Oxford, 1997 G. R. Desiraju, T. Steiner, The Weak Hydrogen Bond in Structural Chemistry and Biology, Oxford University Press, Oxford, 1999 T. Steiner, Angew. Chem. Int. Ed. 41, 48 (2002) V. Bertolasi, P. Gilli, V. Ferretti, G. Gilli, J. Am. Chem. Soc. 113, 4917 (1991) E. D’Oria, J. J. Novoa, submitted R. Parthasarathi, V. Subramanian, N. Sathyamurthy, J. Phys. Chem. A, 110, 3349 (2006) F. H. Allen, Acta Cryst. B, , 58, 380 (2002) K. Kuchitsu, Y. Morino, Bull. Chem. Soc. Jpn., 38, 805 (1965) E. Whalley, The Hydrogen Bond, (P. Shuster, G. Zundel, C. Sandorfy, Editors), NorthHolland, Amsterdam, 1976 (page 1427)

ON THE CALCULATION AND INTERPRETATION OF CRYSTAL ENERGY LANDSCAPES

SARAH L. PRICE Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, UK

Abstract. The energetically feasible crystal structures of a molecule can be computed for an increasing range of types of molecule, provided sufficient care is taken to ensure that their relative energies are calculated accurately and that an appropriate range of possible crystal structures are considered. The resulting crystal energy landscape demonstrates the packing possibilities of the specific molecule, showing, for example, which hydrogen motifs can close pack within the constraints of crystal symmetry. Some landscapes clearly predict the crystal structure of the molecule, whereas others provide insight into more complex solid state behaviour.

Keywords: Computer prediction; Crystal packing landscapes

1. Introduction The ideal computational tool for aiding the design of new materials would allow you to model a range of candidate molecules to find one which was predicted to crystallise in a structure which had the desired properties. This means that when computing the possible low energy crystal structures for each molecule under consideration, you would be searching for a crystal energy landscape like the one idealised in Figure 1a, where the desired crystal structure is so much more stable than any other possibilities that you can be confident that the molecule will reliably and controllably crystallise in the predicted structure.

333 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 333–349. © 2008 Springer.

Density

(b)

Energy

Energy

(a)

S.L. PRICE Density

(c)

Density

Energy

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Figure 1. Schematic examples of crystal energy landscapes. Each point denotes a crystal structure that is a local energy minimum, with the different symbols representing significantly different types of packing, such as different hydrogen bonding motifs. The experimentally known structures are denoted by open symbols.

Unfortunately, few molecules produce such landscapes where the energy gap between the known and other possible crystal structures is large. “Large” here is relative to the energy difference that may occur between polymorphs, and to the likely uncertainties in the computed energies. One of the largest reported1 energy gaps between the known and calculated hypothetical structures is over 12 kJ mol–1 for Pigment Yellow 74. If we look at the molecule (Figure 2), it is clearly one that it is unusually rigid for a molecule with large bumps and hollows in its van der Waals surface (Figure 3). The large calculated energy difference shows that the favourability of its crystal structure is quite specific in all three dimensions. It is plausible that the electrostatic interactions will allow only one stacking of the molecule, and that there is probably only one way of packing the bumps into the hollows to achieve dense packing in the plane of the molecule. The close packing principle is perhaps the dominant force in determining crystal structures,2 though it can be achieved by solvent molecules filling the voids. There are relatively few molecules that can be designed with such welldefined packing requirements as Pigment Yellow 74 in all directions. Hence we generally require much more accurate relative energies of the possible crystal structures to be confident of which structures are energetically feasible and their relative ranking. Thus, we first consider how to minimise the uncertainties in the relative energies of all the possible packings of the molecule in the crystal structure. This increases the confidence that the computed crystal energy packing landscape really represents the thermodynamically feasible crystal structures of the molecule. Then we consider how you interpret a crystal energy landscape that has more than one structure within the energy range of possible polymorphism, by contrasting various example landscapes with the range of known crystal forms. Figure 2 gives some idea of the range of molecules whose crystal energy landscapes are can currently be calculated. This chapter will be fairly general, and so

CRYSTAL STRUCTURE PREDICTION H3C

O H

O

335

CH3

N N HO

O

N

H2N

O

O

H O O 2N

CH3

N

O O

CH3

Pigment Yellow 74 H

aspirin

N

H

O

piracetam Cl

H

CH3

+

H

O

O

N

HN

-

H

Cl

H CH3

O

O

O

N H

H

5-azauracil monohydrate (R)-1-phenylethyl ammonium (R/S) 2-phenylpropanoate

NO2 H

2,3-dichloronitrobenzene O

H O

N H

S

O

O

Cl

pyridine

N H

hydrochlorothiazide

CH3

CN CH3

N

O

N

H NC

S

CH3

Cl

Cl

Cl Cl

chlorothalonil

O

progesterone

Figure 2. Molecular diagrams for some of the molecules whose crystal energy landscapes are mentioned in the text.

not discuss the next stage in the design of new materials with specific properties, which is the prediction of the desired property for all the structures that appear feasible on the crystal energy landscape. 2. Methodologies Available for Computational Crystal Structure Prediction Most of the methods that are currently used in crystal structure prediction have been tested in the international blind tests of crystal structure prediction,3 organised by the Cambridge Crystallographic Data Centre. The reports of these tests provide a route into the literature on the wide range of methods under development, which are also analysed in specialist books4,5 and considered in reviews that debate whether crystal structures are predictable.6,7,8,9 Most approaches at least begin with a search for the global minimum in the lattice energy. This would predict the structure if crystallisation was under thermodynamics control, and the energy appropriate to the crystallisation conditions could be approximated by the lattice energy calculated from a model for the forces acting within the crystals.

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Figure 3. Space filling diagrams for (a) Pigment Yellow 74, (b) 5-fluorouracil and (c) 3azabicyclo[3.3.1]nonane-2,4-dione. The bump that fits into the hollow in the crystal structure of Pigment Yellow 74 is indicated.

2.1. MODELS FOR THE INTERMOLECULAR FORCES

If we assume that the molecule is sufficiently rigid that it will adopt the same conformation in the crystals as in the gas phase (as modelled by an ab initio optimisation), then the lattice energy is obtained by simply summing over the intermolecular potential between every pair of molecules in the crystal. This potential is usually in the atom-atom form, and at the barest minimum must have a model for the repulsion between the atoms as their charge clouds overlap, and the universally attractive dispersion force which arises from the instantaneous correlation in the fluctuations in the electron density. A typical form for this is:

U = ∑ i∈M , k∈N Aικ exp (− Bικ Rik ) − Cικ / Rik6 where atom i in molecule M and k in molecule N are of atom types ι and κ respectively, and are separated by a distance Rik. Sets of potential parameters of this form have been empirically fitted10,11 to a wide range of crystal structures, and can prove very valuable for quick estimates of relative energies of crystals. However, in these potentials the electrostatic contribution has been effectively absorbed into the parameterisation. The electrostatic term can be attractive or repulsive and is sufficiently important for even non-polar molecules that it is usually modelled explicitly from the ab initio charge

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density of the specific molecule. Williams has carefully parameterised the exp-6 parameters for various atomic types12,13 for use in conjunction with a point charge electrostatic model that has been fitted to the electrostatic potential around the molecule. However, in order to reliably model the directionality of the electrostatic forces involved in hydrogen bonding, Williams had to use non-nuclear charges to represent the effects of the lone pairs and π electrons. These can be more effectively and automatically modelled14 by a distributed multipole model obtained by analysing the ab initio charge density of the molecule. A survey of the computed packing energy landscapes for 50 rigid molecules containing only C, H, N and O (with 64 known structures)15,16 concluded that the known structures were significantly more likely to be found at or near the global minimum in the lattice energy when a distributed multipole model was used rather than an atomic point charge model. This was particularly true for the molecules in the survey that were capable of hydrogen bonding. The prediction of crystal structures is providing a stringent test for the development of increasingly accurate models for their intermolecular forces.14,17 Certainly the quality of the predictions generally improves with the theoretical basis of the model for the intermolecular forces18 and future models will need to be less empirically based and include the induction effects, particularly where there are strong electrostatic fields around the molecules. 2.2. MODELLING MOLECULAR FLEXIBILITY

It is relatively easy to compute the crystal energy landscape if you can reasonably assume that the molecule is so rigid that it will have the same conformation in the gas phase and all crystal forms. Most molecules have sufficient flexibility that they can change their conformation within the crystal, paying an energy penalty ΔEintra, in order to improve their intermolecular interactions and hence lattice energy Ulatt, to give an overall more stable crystal structure with lower total crystal lattice energy Ecrys= Ulatt + ΔEintra. An atomistic force-field that included intramolecular distortion terms of the type commonly used in other molecular modelling applications, such as AMBER,19 should in principle be able to model the conformational distortions produced by the packing forces. However, Ecrys is very sensitive to the balance between the forces, and the prediction of a polymorph of aspirin with a planar molecular conformation20 and the distortion of the conformations of many flexible pharmaceutical model molecules on lattice energy minimisation,21 show that the force-field must be tested as adequate for the particular molecule first. Thus, the intramolecular energy penalty is more accurately calculated using quantum mechanics though unfortunately this can be very demanding of the correlated ab initio method used,22 particularly

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if there is a significant change in the intramolecular dispersion or any intramolecular hydrogen bonding between the conformations. One possible strategy is to perform rigid molecule crystal structure prediction searches with each of the conformational minima for the isolated molecule. The success of this strategy in predicting a crystal structure of aspirin23 that was later found as a metastable polymorph24 may have been due to the fortuitously good agreement between a B3LYP gas phase local minimum and the crystal structure conformation. For molecules where there are fairly shallow conformational wells, a range of conformations away from the minima need to be considered: over a hundred such searches were performed on piracetam in order to successfully predict25 the structure of a new conformational polymorph with only the information that it existed. Unfortunately, the relative crystal energies can be very sensitive to the exact conformation, particularly of the polar hydrogen atoms, where relatively small changes in the pyramidalisation of an amine group, for example, may have a significant effect on the geometry of the hydrogen bond. One approach to dealing with this is to specifically optimise ΔEcrys with respect to the key torsion angles as well as the otherwise rigid-body crystal structure parameters by shuttling between the ab initio and lattice energy minimisation programs.26 This DMAflex procedure significantly improves the relative structures of the three known and many hypothetical structures of (R)-1-phenylethyl ammonium (R/S) 2-phenylpropanoate and carbamazepine. It also suggests a way forward for reducing the number of rigid body searches needed for other flexible molecules, once the computational efficiency has been improved. 2.3. THERMODYNAMIC FREE ENERGIES

The comparison of total lattice energies, Ecrys, is completely neglecting the effects of temperature and pressure on the relative energies of the crystal structures. Although enthalpy differences dominate entropy differences in known polymorphs,27 the common occurrence of entropically related polymorphs28,29 shows that differences in entropy can mean that the free energy orders structures differently from the lattice energy.30 Currently, most entropy estimates are based on lattice dynamics calculations for rigid molecules.31 However, there are a few studies of organic crystals at normal temperatures by Molecular Dynamics32 and a successful application of the metadynamics method to exploring the free energy surface for benzene.33 These studies are so computationally demanding, that even in the future, they are only likely to be applied in special cases. Thus, although the crystal energy landscape should use free energies at the crystallisation temperature and pressure, the

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total lattice energy crystal energy landscape is generally a worthwhile first approximation. 2.4. THE SEARCH FOR POSSIBLE CRYSTAL STRUCTURES

Most of the older methods of generating trial crystal structures for lattice energy minimisation used crystallographic insight to try to effectively sample the huge range of possible crystal structures. They were therefore restricted to one molecule in the asymmetric unit cell (Z =1) and the most common space groups for organic molecules. In addition, PROMET,34 for example, looked for strong interactions between molecules related by the symmetry operators, and MOLPAK35 sought dense packings within common coordination patterns. As more extensive searches became possible, various types of simulated annealing to explore the lattice energy surface were introduced,36 and systematic searches grew in their ability to ensure a complete search in specified space groups and small defined values of Z . Analysis of the last blind test results37 suggests that the some recent computationally-demanding methods38 are close to ensuring a complete search of the approximated lattice energy surface for a wide range of specified space-groups and Z =1 or 2 for rigid molecules. It is important to note that the search effort increases very quickly with the number of conformational degrees of freedom (usually torsion angles), or independent units in the asymmetric unit cell, as this increases the dimensionality of the lattice energy surface. Most of the search methods that consider flexible molecules cannot be sure of crossing significant conformational barriers and so would be repeated starting from all the low energy conformational minima of the molecule. Searches for co-crystals, monohydrates, and salts, where there are necessarily two independent molecular fragments in the asymmetric unit are becoming feasible. A fairly general search method correctly predicted that the acetone solvate of dihydrocarbamazepine could be isostructural with that of carbemazepine.39 The more restricted approach of using a range of probable hydrogen bonded structures of the asymmetric unit cell contents to generate initial structures, and then allowing their relative positions to adjust on lattice energy minimisation, has been successfully applied to 5-azauracil monohydrate40 and simple diasteromeric salts.41 This approach could also be used to search for structures of molecular complexes where the relative position of the two molecules is known, for example because they are strongly associated in solution. Thus, the search technique has to be adapted to the problem in hand and the available computing resources. A Z =1 search would miss the increasing number of Z >1 crystal structures. This may not be important, if many of these are metastable polymorphs, that can be viewed as “fossil relics”42 or

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“arrested crystallisation” structures.43 Hence, the use of crystal structure prediction to guide the engineering of new materials may only require considerations of a few thousand of the more probable types of crystal structure. 2.5. HOW DO I CHOOSE THE COMPUTATIONAL METHOD?

The problem of choosing a computational model for a crystal structure prediction study is best illustrated by an example of the use of the same model for a range of isomers. Figure 4 overlays the crystal energy landscape44 generated by a MOLPAK search for Z =1 structures in common space groups for three isomers of dichloronitrobenzene. This landscape assumes that the molecular conformation of the dichloronitrobenzene corresponds to the MP2 6-31G(d,p) optimised isolated molecule geometry and that it interacts with the electrostatic forces from a distributed multipole representation of this charge density and an empirical isotropic atom-atom repulsiondispersion model. This approach appears quite adequate and successful for 2,3-dichloronitrobenzene, as the experimental structure is found at the global minimum, with sufficient of an energy gap to be consistent with no polymorphs being found in a manual polymorph search. However, the 3,5 isomer clearly cannot pack as well as it has a less stabilising lattice energy and there are many different structures that are almost as favourable as the only known structure. A more accurate model might well favour the known structure slightly more, but it is the molecule itself that prevents there being one really advantageous structure as found for the 2,3-isomer. The predictions for the unknown structure for the 2,4 isomer suggested that there were three quite favourable Z =1 structures – but the molecule found an even more favourable packing in Z =2 by distorting both nitro-torsion angles to differ by 27°! Hence, there is no easy recipe for what approach is adequate for an independent computational crystal structure prediction, even within a family of closely related molecules. It is essential that your model for the inter- and intramolecular forces reproduces the known crystal structures of that type of molecule well. The lattice energies should be reasonable compared with sublimation energies, and the differences between known polymorphs should be reasonable compared with the known or likely experimental differences,28 taking into account the computational approximations in the comparison.4,5 There should not be any hypothetical structures that are predicted to be more stable than is plausible for undiscovered polymorphs. However, even when you are using the most theoretically accurate feasible model which appears adequate against the available experimental data, you cannot be confident that using a reasonably exhaustive search method will allow you to predict the experimental crystal structures. The type of crystal energy landscape (c.f. Figure 1) depends on the specific molecule. Nevertheless,

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the calculation of the crystal energy landscape will certainly provide you with considerable insight into the solid state behaviour of the molecule, as shown by the following examples.

Figure 4. Overlay of the crystal energy landscapes for 3 isomers of dichloronitrobenzene (DCNB). The open symbols represent the experimentally known structures by the lattice energy minimum found starting from the experimental structure using the same computational model.

3. Interpretation of Crystal Energy Packing Landscapes A few possible idealised crystal energy packing landscapes are shown in Figure 1. The interpretation of each type is given below, assuming that the energy gaps between the lattice minima relative to the plausible energy differences between polymorphs are qualitatively accurate. 3.1. ONE CLEARLY PREFERRED STRUCTURE (FIGURE 1a)

This is the ideal type of landscape, as one structure is clearly predicted to be so thermodynamically preferred that the molecule should crystallise in this structure (provided it does crystallise in a structure covered by the search). If this crystal structure is obtained, such a crystal energy landscape would add confidence to a limited polymorph screen that there are unlikely to be any practically significant polymorphs.45 Such an energy landscape should arise when the molecules have been engineered to have strongly preferred directional interactions in all three dimensions that are capable of packing densely with translational symmetry.

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3.2. AN UNKNOWN STRUCTURE IS PREDICTED TO BE MORE STABLE (FIGURE 1b)

Such an energy landscape should motivate a careful polymorph screen to find the predicted polymorph, as the existence of a more stable polymorph has the potential to produce quality control problems in manufacture. Two

(a) H H

O

N N

F

H O

Form 2 Form 1

Alternate ribbon in solvate

(b) H H

N

The ribbon in 30 of the 33 lowest energy computed structures and in all 6 stable forms.

O N

F NH2

(c) O

NH2 N

low energy predicted

observed

observed

low energy predicted

observed

low energy predicted

(d) O

NH2 N

(e) O O

N H

Figure 5. Competitive hydrogen bonding motifs found in the crystal energy landscapes of (a) 5-fluorouracil, where the energy range of these motifs is 5.9 kJ mol–1 (b) 5-fluorocytosine, where all structures within 8 kJ mol–1 had this motif (c) carbamazepine, where the lowest chain structure was 2.2 kJ mol–1 more stable than the known dimer form III (d) dihydrocarbamazepine where the observed chain in forms 1 and 2 are the most stable predicted structures, but dimers are only 5 kJ mol–1 less stable (e) 3-azabicyclo[3.3.1]nonane-2,4-dione where dimer based structures are predicted to be slightly more stable than the observed catemer polymorphs.

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cases where the crystal energy landscape had more stable structures than the known Z =4 structure have resulted in the finding of a new Z =1 polymorphs. However, for neither pyridine46 nor 5-fluoruracil47 has the relative stability been definitely established. The new polymorph of 5-fluorouracil was crystallised from dry nitromethane, and Molecular Dynamics48 simulations showed how this solvent promoted the formation of the doubly hydrogen bonded dimer motif (Figure 5a), whereas water hydrated the molecule so strongly that it promoted the close F···F contacts in form 1. This exemplifies the idea49 that analyzing the variety of hydrogen bonding motifs in the low energy structures can suggest the choice of solvents to promote the crystallisation of each motif. Similarly, analysis of the targeted structure could suggest polymer, surface or additive templates that would be worth trying. 3.3. A RANGE OF LOW ENERGY STRUCTURES (FIGURE 1c)

When there are many crystal structures within a small energy range, then this is showing that there are many ways of packing the molecule that are energetically competitive. Which ones are actually seen will depend on kinetic factors that influence which structures can nucleate and grow most readily and not transform into a slightly more stable structure. There are many factors that experimentally can influence polymorphic outcome apart from temperature and pressure, ranging from controllable factors50 such as solvent, cooling rate, and initial supersaturation, to the less obvious such as impurity profile.51 Hence, it seems unlikely that computational modelling of kinetic factors could reliably pick out which crystal structures will be observed polymorphs from such a landscape. Comparisons with the crystal structures of closely related molecules may provide a route forward, and such datamining techniques are being developed.52 Despite the current lack of recipes, examination of the crystal packings of the low energy structures can give some insights when coupled with experimental polymorph screening. The type of crystal energy landscape in Figure 1c indicates that multiple or complex crystal forms are likely. It certainly shows that the molecule has a packing problem, which may be solved by solvate formation or polymorphism. For example, the low energy structures of 5-fluorocytosine all contain the same ribbon motif (Figure 5b) which is found53 in both polymorphs and the 4 stable solvates. Many of the wide range of hydrogen bonding motifs in the low energy landscape54 of hydrochlorothiazide appear in one or more of the polymorphs and solvates. Alternatively, the frustration of not having a well defined way of packing with itself may lead to the molecule forming incommensurate, high Z or disordered crystal structures. This is illustrated by chlorothalonil, where 5 structures within 1.25 kJ/mol of the global minimum have been related to the observed polymorphs:55 the ordered form 1

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corresponded to the global minimum, two predicted Z =1 ribbon structures could be recognised in the Z =3 form 3, and two Z =1 predicted layer structures rationalise the apparent disorder in form 2. The observation of aspirin crystallising as intergrowths of two “polymorphic” domains56 seems a reasonable reflection of the growth problems arising when two low energy structures on the crystal energy landscape23 correspond to different stackings of the same sheet. Nucleation is certainly the key to polymorph formation57, as only if it is not possible to create more than one type of nucleus, or they all rearrange to grow into the most stable structure, will there only be one form. Cases where the low energy structures contain more than one type of hydrogen bonding motif seem the most likely to give rise to polymorphism, as there is expected to be a considerable barrier to rearrangement. Two recent studies show that this argument can only be applied with care. Carbamazepine has four polymorphs, but all are based on the doubly hydrogen-bonded dimer motif (Figure 5c), whereas the predicted energy landscape has a chainbased structure as the global minimum.58 Extensive polymorph screening has generated a wide range of solvates, though the predicted chain of carbamazepine molecules has only been found in a solid solution with dihydrocarbemazepine,59 which is isomorphous with one of the predicted low energy structures. Since dihydrocarbamazepine crystallises in a chain structure in all 3 polymorphs, but dimer motif based structures are within the energy range of possible polymorphism (Figure 5d), it is clear that the effects that tip the balance as to which hydrogen bonding motif nucleates are quite subtle. It has been suggested that the slight differences in molecular geometry affect the ease of formation of the chain motif hydrogen bond in the two molecules,60 though this, like the relative energies, is sensitive to the limited conformational flexibility.61,26 A contrasting case is 3-azabicyclo [3.3.1]nonane-2,4-dione which was predicted by many participants of the 2nd blind test of crystal structure prediction to be a dimer based structure and actually forms a catemer (Figure 5e). An extensive search62 found two solvates, a Z =2 “fossil relic” chain-polymorph and a plastic phase. The latter implied that the barrier to disrupting the hydrogen bonding was very low, and computational modelling confirmed that the hydrogen bonding motif could readily change in small clusters. Thus, in this case, it appears that the chain motif is the most thermodynamically stable, and it is probably not possible to trap a dimer based motif as a metastable polymorph because of the weak barrier to rearrangement during nucleation and growth.

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4. Conclusions Many more experimental polymorph screening results need to be compared to the computed energy landscape before we can understand the factors that determine polymorphism, let alone predict the observed crystal structures, when the molecule has a packing problem. However, even in this case where the crystal energy landscape is complex (c.f. Figure 1c), the computed low energy structures are useful for showing the range of possible motifs. This can rationalise why an expected hydrogen bonding motif is not seen,63 or suggest possible starting points for solution of structures from powder Xray data. However, if we are aiming to design a new material with a controllable specific solid state structure, then ideally the desired structure should be markedly more stable than the alternatives (Figure 1a). Whether the application of crystal engineering principles can design such structures remains to be seen, though certainly contrasting the desired with alternative hypothetical structures should facilitate the process. Computer modelling could save the synthetic chemist from making molecules that are highly unlikely to crystallise in the desired way. We are slowly increasing the accuracy of the crystal energy landscapes to the point where we can have enough confidence in those energy landscapes that approximate Figure 1a to invest considerable experimental resources in making the predicted material. For example, we crystallised a few mg of the precious synthetic mirror image with the natural enantiomer of progesterone, to produce the predicted crystal structure of racemic progesterone.64 Crystal structure prediction currently has to be seen as a complementary tool to experimental studies, but it at least provides considerable insight into the range of possible crystal structures. The computer-aided design of new materials could become a reality provided experimentalists and theoreticians work together on generating and interpreting crystal energy landscapes of appropriate accuracy for their type of materials. 5. Acknowledgements Many members of ‘Control and Prediction of the Organic Solid State’ (CPOSS, www.cposs.org.uk) are thanked for their work and discussions that underpin this article, particularly Dr Louise Price who assisted in preparing the manuscript. The Basic Technology program of the Research Councils UK funded CPOSS. The computed crystal structures for all CPOSS studies are stored on CCLRC e-Science Centre data portal and are available on request.

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21. S. Brodersen, S. Wilke, F. J. J. Leusen, and G. Engel, A study of different approaches to the electrostatic interaction in force field methods for organic crystals, Phys. Chem. Chem. Phys. 5(21), 4923–4931 (2003). 22. T. van Mourik, P. G. Karamertzanis, and S. L. Price, Molecular conformations and relative stabilities can be as demanding of the electronic structure method as intermolecular calculations, J. Phys. Chem. A 110(1), 8–12 (2006). 23. C. Ouvrard and S. L. Price, Toward crystal structure prediction for conformationally flexible molecules: The headaches illustrated by aspirin, Cryst. Growth Des. 4(6), 1119– 1127 (2004). 24. P. Vishweshwar, J. A. McMahon, M. Oliveira, M. L. Peterson, and M. J. Zaworotko, The Predictable Elusive Form II of Aspirin, J. Am. Chem. Soc. 127(48), 16802–16803 (2005). 25. H. Nowell and S. L. Price, Validation of a search technique for crystal structure prediction of flexible molecules by application to piracetam, Acta Crystallogr., Sect. B 61 558–568 (2005). 26. P. G. Karamertzanis and S. L. Price, Energy Minimization of Crystal Structures Containing Flexible Molecules, J. Chem. Theory Comput. 2(4), 1184–1199 (2006). 27. A. Gavezzotti and G. Filippini, Polymorphic Forms of Organic-Crystals at Room Conditions – Thermodynamic and Structural Implications, J. Am. Chem. Soc. 117(49), 12299–12305 (1995). 28. J. Bernstein, Polymorphism in Molecular Crystals (Clarendon Press, Oxford, 2002). 29. H. G. Brittain, Polymorphism in Pharmaceutical Solids (2005). 30. J. D. Dunitz, G. Filippini, and A. Gavezzotti, Molecular shape and crystal packing: A study of C12H12 isomers, real and imaginary, Helv. Chim. Acta 83(9), 2317–2335 (2000). 31. G. M. Day, S. L. Price, and M. Leslie, Atomistic calculations of phonon frequencies and thermodynamic quantities for crystals of rigid organic molecules, J. Phys. Chem. B 107(39), 10919–10933 (2003). 32. S. L. Price, S. Hamad, A. Torrisi, P. G. Karamertzanis, M. Leslie, and C. R. A. Catlow, Applications of DL_POLY and DL_MULTI to organic molecular crystals, Mol. Simulat. 32(12–13), 985–997 (2006). 33. P. Raiteri, R. Martonak, and M. Parrinello, Exploring Polymorphism: The Case of Benzene, Angew. Chem., Int. Ed. 44, 3769–3773 (2005). 34. A. Gavezzotti, Generation of Possible Crystal-Structures from the Molecular- Structure for Low-Polarity Organic-Compounds, J. Am. Chem. Soc. 113(12), 4622–4629 (1991). 35. J. R. Holden, Z. Y. Du, and H. L. Ammon, Prediction of Possible Crystal-Structures For C-, H-, N-, O- and F-Containing Organic Compounds, J. Comput. Chem. 14(4), 422–437 (1993). 36. P. Verwer and F. J. J. Leusen, Computer Simulation to Predict Possible Crystal Polymorphs, in: Reviews in Computational Chemistry Volume 12, edited by K. B. Lipkowitz and D. B. Boyd (Wiley-VCH, New York, 1998). 37. B. P. van Eijck, Comparing hypothetical structures generated in the third Cambridge blind test of crystal structure prediction, Acta Crystallogr., Sect. B 61, 528-535 (2005). 38. P. G. Karamertzanis and C. C. Pantelides, Ab initio crystal structure prediction – I. Rigid molecules, J. Comput. Chem. 26(3), 304–324 (2005). 39. A. J. C. Cabeza, G. M. Day, W. D. S. Motherwell, and W. Jones, Prediction and observation of isostructurality induced by solvent incorporation in multicomponent crystals, J. Am. Chem. Soc. 128(45), 14466–14467 (2006). 40. A. T. Hulme and S. L. Price, Towards the prediction of organic hydrate crystal structures, J. Chem. Theory Comput. 3(4), 1597–1608 (2007). 41. P. G. Karamertzanis and S. L. Price, Challenges of crystal structure prediction of diastereomeric salt pairs, J. Phys. Chem. B 109(36), 17134–17150 (2005). 42. J. W. Steed, Should solid-state molecular packing have to obey the rules of crystallographic symmetry?, CrystEngComm 5(32), 169–179 (2003).

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43. D. Das, R. Banerjee, R. Mondal, J. A. K. Howard, R. Boese, and G. R. Desiraju, Synthon evolution and unit cell evolution during crystallisation. A study of symmetry-independent molecules (Z' > 1) in crystals of some hydroxy compounds, Chem. Commun. (5), 555– 557 (2006). 44. S. A. Barnett, A. Johnson, A. J. Florence, S. L. Price, and D. A. Tocher, A systematic experimental and theoretical study of the crystalline state of six chloronitrobenzenes, Cryst. Growth Des. submitted (2007). 45. S. L. Price, The computational prediction of pharmaceutical crystal structures and polymorphism, Adv. Drug Deliver. Rev. 56(3), 301–319 (2004). 46. A. T. Anghel, G. M. Day, and S. L. Price, A study of the known and hypothetical crystal structures of pyridine: why are there four molecules in the asymmetric unit cell?, CrystEngComm 4(62), 348–355 (2002). 47. A. T. Hulme, S. L. Price, and D. A. Tocher, A New Polymorph of 5-Fluorouracil Found Following Computational Crystal Structure Predictions, J. Am. Chem. Soc. 127(4), 1116– 1117 (2005). 48. S. Hamad, C. Moon, C. R. A. Catlow, A. T. Hulme, and S. L. Price, Kinetic Insights into the Role of the Solvent in the Polymorphism of 5-Fluorouracil from Molecular Dynamics Simulations, J. Phys. Chem. B 110(7), 3323–3329 (2006). 49. N. Blagden, W. I. Cross, R. J. Davey, M. Broderick, R. G. Pritchard, R. J. Roberts, and R. C. Rowe, Can crystal structure prediction be used as part of an integrated strategy for ensuring maximum diversity of isolated crystal forms? The case of 2-amino-4-nitrophenol, Phys. Chem. Chem. Phys. 3(17), 3819–3825 (2001). 50. T. Threlfall, Crystallisation of polymorphs: Thermodynamic insight into the role of solvent, Organic Process Res. Dev. 4(5), 384–390 (2000). 51. R. W. Lancaster, P. G. Karamertzanis, A. T. Hulme, D. A. Tocher, T. C. Lewis, and S. L. Price, The Polymorphism of Progesterone: Stabilization of a ‘Disappearing’ Polymorph by Co-Crystallization., J. Pharm. Sci. submitted (2007). 52. A. Dey, N. N. Pati, and G. R. Desiraju, Crystal structure prediction with the supramolecular synthon approach: Experimental structures of 2-amino-4-ethylphenol and 3-amino-2-naphthol and comparison with prediction, CrystEngComm 8(10), 751–755 (2006). 53. A. T. Hulme and D. A. Tocher, The Discovery of New Crystal Forms of 5-Fluorocytosine Consistent with the Results of Computational Crystal Structure Prediction, Cryst. Growth Des. 6(2), 481–487 (2006). 54. A. Johnston, A. J. Florence, N. Shankland, A. R. Kennedy, K. Shankland, and S. L. Price, Crystallization and crystal energy landscape of hydrochlorothiazide, Cryst. Growth Des. 7(4), 705–712 (2007). 55. M. Tremayne, L. Grice, J. C. Pyatt, C. C. Seaton, B. M. Kariuki, H. H. Y. Tsui, S. L. Price, and J. C. Cherryman, Characterization of complicated new polymorphs of chlorothalonil by X-ray diffraction and computer crystal structure prediction, J. Am. Chem. Soc. 126(22), 7071–7081 (2004). 56. A. D. Bond, R. Boese, and G. R. Desiraju, On the polymorphism of aspirin: Crystalline aspirin as intergrowths of two “polymorphic domains”, Angew. Chem. ,Int. Ed. 46(4), 618–622 (2007). 57. R. J. Davey, K. Allen, N. Blagden, W. I. Cross, H. F. Lieberman, M. J. Quayle, S. Righini, L. Seton, and G. J. T. Tiddy, Crystal engineering – nucleation, the key step, CrystEngComm 4(47), 257–264 (2002). 58. A. J. Florence, A. Johnston, S. L. Price, H. Nowell, A. R. Kennedy, and N. Shankland, An automated parallel crystallisation search for predicted crystal structures and packing motifs of carbamazepine, J. Pharm. Sci. 95(9), 1918–1930 (2006). 59. A. J. Florence, C. K. Leech, N. Shankland, K. Shankland, and A. Johnston, Control and prediction of packing motifs: a rare occurrence of carbamazepine in a catemeric configuration, CrystEngComm 8(10), 746–747 (2006).

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60. A. J. C. Cabeza, G. M. Day, W. D. S. Motherwell, and W. Jones, Importance of molecular shape for the overall stability of hydrogen bond motifs in the crystal structures of various carbamazepine-type drug molecules, Cryst. Growth Des. 7(1), 100–107 (2007). 61. A. J. C. Cabeza, G. M. Day, W. D. S. Motherwell, and W. Jones, Amide pyramidalization in carbamazepine: A flexibility problem in crystal structure prediction?, Cryst. Growth Des. 6(8), 1858–1866 (2006). 62. A. T. Hulme, A. Johnston, A. J. Florence, P. Fernandes, K. Shankland, C. T. Bedford, G. W. A. Welch, G. Sadiq, D. A. Haynes, W. D. S. Motherwell, D. A. Tocher, and S. L. Price, Search for a predicted hydrogen bonding motif - A multidisciplinary investigation into the polymorphism of 3-azabicyclo[3.3.1]nonane-2,4-dione, J. Am. Chem. Soc. 129(12), 3649–3657 (2007). 63. T. C. Lewis, D. A. Tocher, and S. L. Price, Investigating Unused Hydrogen Bond Acceptors Using Known and Hypothetical Crystal Polymorphism, Cryst. Growth Des. 5(3), 983–993 (2005). 64. R. W. Lancaster, P. G. Karamertzanis, A. T. Hulme, D. A. Tocher, D. F. Covey, and S. L. Price, Racemic progesterone: predicted in silico and produced in the solid state, Chem. Commun. (47), 4921–4923 (2006).

NMR CRYSTALLOGRAPHY AND THE ELUCIDATION OF STRUCTURE-PROPERTY RELATIONSHIPS IN CRYSTALLINE SOLIDS

SUSAN M. REUTZEL-EDENS Lilly Research Laboratories, Eli Lilly and Company Indianapolis, IN, 46285 USA

Abstract. SSNMR spectroscopy, an established technique for identifying crystalline polymorphs and solvates, can provide detailed structural information useful for rationalizing materials properties in terms of molecular and crystal structure. Contributions of solid-state NMR spectroscopy to the field of crystal engineering, which range from identifying polymorphs and solvates to providing detailed information on structure and dynamics in crystalline solids (NMR crystallography), are described.

Keywords: NMR crystallography, solid state, polymorph, hydrate, solvate, crystal engineering, structure-property relationships, dynamics, disorder

1. Introduction Crystal engineering, the design and synthesis of functional crystalline materials constructed from molecular building blocks, has significant implications for many fields, including catalysis, pharmaceuticals and materials science. Scientists continue to discover new ways of controlling molecular recognition events and crystallographic symmetry by exploiting both the directionality and strength of non-covalent interactions in the design of molecular crystals. Validating crystal engineering approaches, however, requires thorough solid-state characterization to ensure that the pre-designed molecular assemblies survive crystal nucleation and growth processes and that designed properties agree with the predicted structures. Crystallization performed under varying conditions can, of course, produce crystals in different forms (polymorphs, solvates), sizes and morphologies, as molecules or ions pack in different crystal structures at different rates to minimize their free energy. Polymorphs, i.e., different 351 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 351–374. © 2008 Springer.

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crystalline phases arising from different arrangements of a given molecule in the solid state1, and solvates can significantly complicate the rational design of crystalline solids from molecular components (the paradigm of molecular crystal engineering), since competing crystallization pathways, each with its own characteristic thermodynamics, crystal nucleation and growth kinetics and molecular recognition events, must be navigated in crystallization.2 Although many would argue that polymorphism is a nemesis to crystal engineering, this phenomenon, in allowing the material properties of a given compound to be fine-tuned, can be used to one’s advantage. The opportunity afforded to materials scientists and crystal engineers to modify particles to desired specifications and the challenges faced by those who wish to produce crystalline materials of consistent quality have prompted much interest in the characterization of structures, dynamics and energetics of molecular solids.3 Solid-state NMR (SSNMR) spectroscopy, which in many respects complements arguably the most powerful tool for structure determination, X-ray crystallography, has become an indispensable tool for the characterization of both structure and dynamics in molecular materials.4 This technique has the unique ability to probe electronic environments of specific nuclei in the solid state over a large timescale without the requirement of single crystal substrates or even homogeneous samples.5 Thus, not only is SSNMR spectroscopy well suited for identifying polymorphs and solvates, but this technique can also provide detailed structural information useful for both rationalizing materials properties in terms of molecular and crystal structure and needed to confirm structure solutions obtained from powder diffraction data. Continuous improvements in NMR hardware, new and optimized pulse sequences that increase the sensitivity, specificity and resolution of SSNMR spectra, and advances in the computational prediction of NMR chemical shifts and tensors, have dramatically expanded the role of NMR spectroscopy in structure determination, out of which the field of NMR crystallography has emerged.6 In this contribution, methods and applications of SSNMR spectroscopy, which provide direct, detailed structural information from which crystal engineering strategies may be advanced and structure-property relationships ascertained in molecular solids, are presented. As many of the applications are demonstrated for pharmaceutical compounds, for which selective or uniform isotopic labeling is for practical reasons, prohibitive, an emphasis is understandably placed on NMR techniques for the characterization of compounds at natural abundance. Thus, only the fundamental principles, which underpin the SSNMR spectroscopy of dilute spin-½ nuclei at natural abundance (without the requirement of isotopic labeling), are described. The discussion, though directed at solid-state 13C NMR spectroscopy, may

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also be applied to other relevant spin-½ nuclei, such as 15N, which is a dilute (low natural abundance) nucleus, and 31P, which has a high natural abundance, but is diluted in most organic solids. 2. CP/MAS NMR Spectroscopy of Spin ½ Nuclei Although the basic principles are the same for solution and solid-state NMR measurements, to obtain high-resolution solid-state spectra, the standard solution methods have been modified to specifically address two effects of the solid state on NMR, low sensitivity and severe line broadening. The sensitivity of the solid-state experiment, which for 13C is expected to be low based on its 1% natural abundance, is further diminished by long spinlattice (T1) relaxation times. Severe line broadening originates from both chemical shift anisotropy (CSA) and 13C-1H dipolar interactions. These anisotropic spin interactions, which are motionally averaged to zero by rapid molecular tumbling in solution, are not eliminated in the solid state where molecules are generally rigid. As a result, solid-state NMR spectra are very broad because the full effects of the orientation-dependent interactions are observed in the spectrum, Figure 1. CSA patterns of carbonyl and aromatic carbons may span ~200 ppm.

Figure 1. Solution (top) and solid-state (bottom) NMR spectra, contrasting the sharp transitions observed in solution due to the averaging of anisotropic NMR interactions by rapid molecular tumbling with the broad CSA pattern of a solid, where the orientationdependent (anisotropic) interactions are observed.

Three modifications: cross polarization (CP), magic angle spinning (MAS) and high-power 1H decoupling, have overcome the sensitivity and

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line broadening problems encountered with solids. The CP technique was introduced by Pines, Gibby and Waugh to address the low sensitivity associated with collecting NMR spectra of dilute spin-½ nuclei.7 The basic CP pulse sequence as shown for 13C-(1H) in Figure 2, entails bringing both the 1H and 13C spins into resonance by applying two spin-locking fields, the magnitude of which will satisfy the Hartmann-Hahn matching condition (γHB1H = γCB1C). When the correct spin-locking fields are chosen, thermal contact is established and polarization transfer occurs, wherein the rare (13C) spins take on the magnetization and relaxation behavior of the abundant (1H) spins. The net result is a sensitivity enhancement (up to fourfold based on the 1H and 13C magnetogyric ratios) and a reduction in the pulse repetition time. 90x

1H

13C

(spin lock)y

decouple

(Hartmann-Hahn)x

Figure 2. 13C cross polarization NMR pulse sequence.

The line broadening caused by strong 1H-13C dipolar interactions and the CSA of the 13C nuclei may be averaged by MAS and high power 1H decoupling. MAS involves mechanically rotating the sample at an angle of 54.7° (the ‘magic angle’) relative to the static magnetic field, Figure 3.8,9 Spinning a sample about the magic angle, which represents the body diagonal of a cube, forces the individual vectors from each nucleus to spend an equal amount of time along all three axes, thereby averaging out the CSA. When the MAS rate is comparable to the width of the 13C CSA, the anisotropy pattern can be averaged to its isotropic value and weak dipolar interactions averaged (or nearly so) to zero. When the sample spinning rates are insufficient relative to the shielding anisotropy of the nucleus, spinning sidebands appear, which are separated from the isotropic peaks (or centerbands) by integer multiples of the spinning rate (in Hz). These artifacts, which can be particularly significant at high magnetic fields or low spinning rates, can be eliminated from solid-state NMR spectra using the total suppression of spinning sidebands (TOSS) technique.10

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static

Figure 3. Left: Rapid sample spinning about the magic angle, θ=54.7°, with respect to the static magnetic field is a dynamic implementation of cubic symmetry, which averages anisotropic chemical shielding interactions and weak dipolar coupling. Right: The spectrum of a powder sample under magic angle spinning (polycrystalline glycine is shown) will depend on the spinning frequency; if the spinning frequency is lower than the width of the CSA pattern, spinning sidebands spaced at integer multiples of the spinning rate will appear. [Adapted from ref. 11]

Because static 1H-13C dipolar interactions can be quite strong, MAS speeds of 25–50 kHz may be required to average these effects. Only recently have MAS technologies (probe designs) and materials become available to consistently achieve these spinning speeds. Since many materials are unable to withstand such high MAS rates (frictional heating and pressure produced by MAS12), other approaches are required to average the 1H-13C dipolar coupling. The most effective method is to use high power 1 H decoupling, which entails irradiating a sample at a frequency that stimulates rapid 1H spin flips, so as to average the dipolar effect of 1H on 13 C. Two-pulse phase-modulated decoupling (TPPM) provides additional line narrowing with less decoupling power and is recommended for highly crystalline, rigid materials, where 1H-1H interactions are strong and dominate the linewidth.13 3. Solid Form Identification X-ray diffraction of powders and single crystals (from which powder patterns may be calculated) is generally considered the ‘gold standard’ through which polymorphism (and solvate formation) is demonstrated in

356

S.M. REUTZEL-EDENS

polycrystalline solids. Since Schaefer and Stejskal14,15 first combined CP, MAS and high power 1H decoupling to produce high resolution solid-state NMR spectra, not only has CP/MAS NMR spectroscopy emerged as an indispensable tool for chemical analysis, structure determination and studies of dynamic processes in the solid state, but it is also rapidly approaching the status (and acceptance) of XRPD as one of the most powerful tools for differentiating crystal forms.16 To illustrate the differences typically observed in the 13C CP/MAS NMR spectra of polymorphs and solvates, the spectra of several crystal forms of olanzapine (active ingredient in Zyprexa®), including anhydrous Form I, polymorphic dihydrates B and D, and a mixed EtOH-H2O solvate, are shown in Figure 4.17 Polymorphism or solvate formation may be inferred by the different isotropic chemical shifts of the equivalent 13C nuclei of olanzapine in the different spectra. EtOH 13C resonances are also observed in the EtOH-H2O solvate spectrum; however, water is observed only indirectly in the dihydrate spectra by its influence on the 13C environments of the molecular host. As each crystal form is characterized by its own physicochemical properties, the identification of polymorphs and solvates is arguably the most important industrial application of SSNMR spectroscopy, with significant implications for the production and commercialization of molecules in the form of crystalline materials. In the olanzapine example, the substantial differences between the crystal structures of the various nonsolvated and solvated forms were easily detected by a number of different analytical methods. Of course, no single technique can universally distinguish polymorphs and solvates; however, SSNMR spectroscopy has been used to demonstrate polymorphism when X-ray diffraction failed to show differences. In fact, SSNMR spectroscopy is uniquely suited to differentiate isomorphic solids, which are inherently difficult to distinguish by X-ray diffraction. Isomorphism occurs when structurally similar compounds crystallize in essentially the same three-dimensional crystal structure, different guest molecules are incorporated into the same crystal structure of a host molecule or the three-dimensional crystal structure of a parent solvate is retained (i.e., an isomorphic desolvate is formed) upon removing the solvent. Having established the similarity in three-dimensional packing by X-ray diffraction, SSNMR spectroscopy may be used to unambiguously identify each of these types of isomorphic crystal forms. The isomorphic dihydrates of structurally-related erythromycin A and B, for example, were readily differentiated by 13C CP/MAS NMR spectroscopy.18 The ability of SSNMR spectroscopy to differentiate isomorphic desolvates from their parent solvates, wherein only slight differences in crystallographic packing occur, has been demonstrated for LY334370 HCl19 and thiamine hydrochloride (vide infra)20.

NMR CRYSTALLOGRAPHY

357

anhydrous Form I

dihydrate B

dihydrate D

EtOH-H2O solvate

160

*

140

120

100

80

60

*

40

20

ppm

Figure 4. Solid-state 13C NMR spectra of olanzapine crystal forms. EtOH 13C resonances are denoted with asterisks (*).

The means by which solvents are retained in isostructural solvates can, in many cases, be elucidated by SSNMR spectroscopy. Most often, as the solvent composition is varied, the isotropic resonances of the parent compound will appear at slightly different chemical shifts due to specific interactions between the host and guest, slight changes to the unit cell parameters or both. The dramatic differences noted in the 13C chemical shifts of six solvated crystal forms of dirithromycin, for example, were taken as evidence that solvent was an integral part of each solvate crystal lattice and used to explain the structural collapse to a different crystal form upon desolvation.21 In cases where the SSNMR chemical shifts do not change with changes in solvent composition, the solvents are likely to be either retained nonspecifically or dynamically disordered in the crystal. 4. NMR Crystallography Single crystal X-ray crystallography is generally unparalleled in its ability to provide detailed structural information on molecular geometry, intermolecular

358

S.M. REUTZEL-EDENS

interactions and packing of molecules in a crystal, however, with the development of advanced SSNMR spectroscopy techniques, NMR crystallography is evolving into the derivation of precise bond lengths and angles within a molecule and the determination of intermolecular bond lengths and angles associated with packing patterns.22 Harris, in discussing many advances in NMR crystallography, has reviewed the types of crystallographic information that currently can be obtained from MAS NMR isotropic chemical shifts.23 NMR chemical shift tensors, spin diffusion and dipolar interactions have also been used to examine structures and conformations in polycrystalline solids, although isotopic labeling was required in many instances. Highlighted below are a number of examples wherein SSNMR spectroscopy of spin-½ nuclei has been used to extract detailed crystallographic information on molecular solids at natural abundance. 4.1. MOLECULAR STRUCTURE DETERMINATION

With extremely powerful solution-state NMR spectroscopy and single crystal X-ray diffraction tools widely available, there are two main reasons for the intense interest in high resolution SSNMR spectroscopy for structure elucidation. One is that SSNMR spectroscopy can bridge precisely determined molecular structures and conformations derived by X-ray diffraction to solution-state NMR spectra to identify conformational isomers and tautomers in solution. The second reason for the interest in this application of SSNMR spectroscopy is that molecular structures and conformations may be determined as they exist in the solid state for materials that are not amenable to study by X-ray diffraction (perhaps because suitable crystals cannot be grown) and in cases where the diffraction data is ambiguous (H atom positions, disorder, etc.). In an interesting example of structural characterization by SSNMR spectroscopy, Likar et al. determined that the keto ↔ gem-diol equilibrium of trospectomycin sulfate was impacted in the solid state by altering the water content in both the bulk drug and freeze-dried formulations, Figure 5.24 SSNMR spectroscopy has also been used to examine the ionization state of different functional groups in crystalline solids. While it is generally accepted that proton transfer will occur between an acid and base to form a salt in solution when the difference between their pKa values (ΔpKa) is greater than 2–3 units25, Steiner has pointed out that there is a gradual transition from hydrogen bonding to purely ionic interactions and that the exact hydrogen-bond geometry in the solid state cannot be predicted from ΔpKa values because pKa values are solution properties and the influence of the crystalline environment cannot be quantitatively predicted.26 One NMR approach to establishing the degree of proton transfer in the solid state is to

NMR CRYSTALLOGRAPHY

359

measure chemical shift tensor values, which are known to be especially sensitive to changes in ionization state.27 Proton transfer in acid-base complexes can also be established via isotropic chemical shifts and dipolar interactions. For example, Apperley et al. confirmed the site of proton transfer in sildenafil citrate, the active ingredient in Viagra®, using dipolar dephasing 15N CP/MAS NMR spectroscopy to identify the protonated and nonprotonated 15N centers.28 Li et al. examined the proton transfer of several acid-base complexes of an ErbB2 inhibitor using 15N chemical shifts and short contact time 15N CP/MAS spectral editing to distinguish protonated and nonprotonated nitrogens.29 In this work, protonation of the free base was shown to significantly shift (>80 ppm) the 15N resonances upfield. Interestingly, among the series of acid-base complexes, the degree of proton transfer correlated with the ΔpKa between the acid and base.

H

CH3 OH N O

HO H 3C

H

O N

H

CH3 OH N

HO H3C

O O

N

H

O

16.1% H2O

OH OH OH

O

<2.8% H2O

OH O

Figure 5. keto-diol equilibrium of trospectomycin sulfate. (Adapted from ref. 24)

4.2. CHARACTERIZATION OF THE SOLID STATE

SSNMR spectra will give the same number of isotropic chemical shifts, barring incidental peak overlap, as observed by solution NMR when the symmetry of the molecule itself is preserved, possibly by dynamic processes in the crystal. However, when molecules pack on general crystallographic positions, as they frequently do, their ideal point group symmetry may be lost. In cases where lower symmetry molecular conformations or rapidly interconverting isomers are ‘frozen’ in the solid

360

S.M. REUTZEL-EDENS

state, chemically-equivalent nuclei become crystallographically-inequivalent. The loss of molecular point group symmetry may be readily detected in SSNMR spectra by the appearance of multiple peaks for the chemicallyequivalent nuclei.

Figure 6. Refocused 13C-13C CP-INADEQUATE spectrum of α-testosterone, showing pairs of crosspeaks for each pair of bonded carbons in the two independent molecules of the asymmetric unit. (Adapted with permission from ref. 32; copyright 2006; Owner Societies.)

In a small, but significant, percentage (~8%) of crystal structures, molecules in the unit cell are not related by any symmetry operation, i.e., the asymmetric unit consists of two or more symmetry-independent (noncongruent) molecules.30 Identifying the number of molecules in the asymmetric unit (Z’) by SSNMR spectroscopy is usually straightforward with sufficient peak resolution, Z’ being equal to the number of peaks per unique atom. While the number of noncongruent molecules in a crystal structure can frequently be estimated by simply counting peaks in a onedimensional spectrum, assigning the peaks to a particular independent

NMR CRYSTALLOGRAPHY

361

molecule is not trivial. Only recently has the assignment of 13C resonances to two individual molecules in a unit cell been reported. In this work, Harris et al. used both the refocused CP INADEQUATE pulse sequence31 to establish 13C-13C connectivity based on J-couplings and first principles computation of chemical shifts to assign resonances in the SSNMR spectrum of the α form of testosterone, Figure 6.32 The ability of SSNMR spectroscopy not only to readily identify the crystallographic asymmetric unit, but also to extract structural information (from 13C chemical shifts) specific to independent molecules when Z’ >1 should be of great value to solving crystal structures from powder diffraction data. Generally, there is excellent agreement between the Z’ values deduced by SSNMR spectroscopy and identified by X-ray diffraction; however, in a few cases, the SSNMR and diffraction results appear to directly conflict with one another. For example, a single olanzapine molecule was confirmed in the asymmetric unit of its EtOH-H2O solvate determined by X-ray diffraction, yet two 13C resonances were clearly observed in the ambient temperature CP/MAS NMR spectrum (Figure 4, bottom) for many, if not most, of the carbons in the drug molecule.33 The discrepancy in the number of molecules identified in the asymmetric unit by SSNMR spectroscopy and the Z’ value determined by X-ray diffraction in this case is related to disordered EtOH in the crystal structure, Figure 7. Thus, the EtOH-H2O mixed solvate crystal structure was solved in a higher symmetry space group (C2/c) because over several unit cells, electron density for the EtOH molecules was located in two symmetry-related positions. In any given unit cell, however, the solvent occupies one site or the other, not both, causing the local symmetry to be lower than that of the whole crystal. The disorder

Figure 7. Site occupancy of EtOH in the ambient temperature crystal structure of olanzapine EtOH-H2O solvate, observed by X-ray diffraction (left) and SSNMR spectroscopy (right).

362

S.M. REUTZEL-EDENS

which caused the loss of local symmetry was readily detected by the splitting of the olanzapine 13C resonances. This system highlights an important difference between X-ray crystallography and SSNMR spectroscopy, namely the scale over which periodic systems may be studied. X-ray diffraction detects comparatively long-range order (>100 Å), while SSNMR spectroscopy is sensitive to local or short-range order (<5 Å). Variable temperature (VT) 13C CP/MAS NMR spectroscopy was used to resolve the seemingly conflicting SSNMR and X-ray diffraction data collected for the EtOH-H2O solvate of olanzapine. As shown in Figure 8, the lower temperature spectra were relatively unchanged from the RT spectrum (Figure 7, bottom), except for the increased resolution of the

54 ºC

*

45 ºC

*

28 ºC

*

6 ºC

*

-20 ºC

170

*

160

150

140

130

120

110

20

10 ppm

Figure 8. Variable temperature 13C CP/MAS NMR spectra of the EtOH-H2O mixed solvate of olanzapine. Asterisks (*) denote the EtOH resonances.

NMR CRYSTALLOGRAPHY

363

asymmetric doublets produced by residual dipolar coupling to quadrupolar 14 N.34 The comparable peak splitting suggests that at ambient temperature, EtOH is statically disordered in the mixed solvate. Upon raising the temperature, the olanzapine 13C resonances coalesced to single peaks and the EtOH 13C peaks (only the methyl resonance is shown) became noticeably broad. The high temperature spectra show that the local symmetry can be restored by breaking the hydrogen-bonding interaction between EtOH and olanzapine in the mixed solvate crystal structure. The appearance of broadened solvent peaks upon restoring the local symmetry in the olanzapine mixed solvate further revealed that the hydrogen-bonding interactions which restrict the mobility of the EtOH in the crystal lattice are broken prior to desolvation of the solvate. This study highlights the unique ability of VT SSNMR spectroscopy to probe static disorder (dynamic disorder that is slow on the NMR timescale) with site selectivity.35 By identifying the mechanism by which solvents are retained in (and lost from) solvated crystals, studies like these can be important for designing crystallization, solvent exchange and drying processes. SSNMR spectroscopy, which in the previous example was used to directly probe structural and dynamic aspects of hydrogen bonding, can provide unique insights into hydrogen bonding that are not easily obtained by other methods. For example, the hydrogen bonding topology in homochiral (enantiomorphic) and racemic crystal forms of tazofelone is clearly discernable by X-ray crystallography, Figure 9, yet the relative contribution of hydrogen bonding to stabilizing the structures was not obvious since the hydrogen bond donors of tazofelone paired with different acceptors and the geometry of the hydrogen bonds was quite different.36 Therefore, to evaluate the strength of hydrogen bonding in these structures, the carbonyl isotropic 13C chemical shifts, which are known to be particularly sensitive to hydrogen bonding37, were measured by 13C CP/MAS NMR spectroscopy. As shown in Figure 9, the carbonyl 13C peaks were significantly shifted (~5 ppm) downfield in the racemic form relative to the enantiomorph. The greater deshielding experienced by the carbonyl 13C in the racemic crystal was taken as qualitative evidence of stronger hydrogen bonding in this crystal form. The tazofelone amide 15N resonance in the 15N CP/MAS NMR spectrum of the racemic form was also shifted downfield (by ~12 ppm) from that in the enantiomorph (Figure 9). Based on previous studies of hydrogen bonding in peptides38, which showed that isotropic 15N chemical shifts of NH donors may be displaced downfield by as much as ~15 ppm, the tazofelone NH groups also appear to be more strongly hydrogen bonded in the racemic crystal. The solid-state 13C and 15N NMR results, combined with conformational energy and crystal packing analyses, were ultimately

364

S.M. REUTZEL-EDENS 2.812 Å (2.651 Å)

2.898 Å 2.898 Å

(H3C)3C

H

HO S

H

O

S

N

N H

(H3C)3C

C(CH3)3

O

OH

(H3C)3C

(H3C)3C H H

H O

H

H

S

C(CH3)3

O

O

O N

S H

C(CH3)3

C(CH3)3

N

H

2.943 Å (2.917 Å)

racemate II (RII)

enantiomorph (E)

13C

15N

RII

RII

Δ = 11.9 ppm

Δ = 5.3 ppm

E

E

1 8 0

1 6 0

1 4 0

1 2 0

1 0 0

8 0

6 0

4 0

Figure 9. Hydrogen bonding geometries (and heteroatom-to-heteroatom distances) identified by X-ray crystallography and 13C/15N CP/MAS NMR spectra of tazofelone racemic form II (RII) and enantiomorph (E). The hydrogen bonding in RII is stronger than in E, evidenced by the downfield shifted carbonyl 13C and amide 15N peaks in the RII spectra.

used to rationalize the greater thermodynamic stability of the racemic crystal form, providing a molecular basis for the thermodynamic stability relationship between the homochiral and racemic crystal forms of tazofelone. Though structural details of hydrogen bonding are clearly attainable from 13C and 15N SSNMR spectra, there theoretically should be no more sensitive a probe of hydrogen bonding distances and geometries than the 1H nucleus. Indeed, because hydrogen atoms are weak scatterers and difficult to accurately locate39 in crystal structures by X-ray diffraction methods, 1H NMR spectroscopy in the solid state is of particular interest for studying hydrogen bonding in molecular materials. Historically, high resolution 1H NMR spectra have been difficult to measure, however, owing to strong homonuclear 1H-1H dipolar coupling interactions that span 20–30 ppm (the isotropic chemical shift range of 1H is typically ~15 ppm), severely broadening 1H signals.40,41 As stated previously, only recently have advances in MAS technologies and materials allowed spinning speeds of >25–30 kHz to consistently be attained yielding high resolution 1H spectra. If the corresponding 13C NMR spectrum has been assigned, then magic angle spinning J heteronuclear multiple quantum coherence (MAS-JHMQC42,43), a 2D correlation experiment which uses magnetization transfer

NMR CRYSTALLOGRAPHY

365

based on scalar heteronuclear JCH couplings to provide isotropic chemical shift correlation between pairs of directly bonded 1H and 13C nuclei, can also be used to unambiguously identify 1H chemical shifts in powdered solids. If the 13C NMR spectrum cannot be completely assigned using onebond MAS-J-HMQC, longer evolution periods producing multiple-bond couplings in the correlation spectrum or less selective through-space techniques, such as 1H-13C dipolar heteronuclear correlation (HETCOR), may be used to complete the spectral assignment. Dipolar HETCOR spectroscopy, which uses through-space 1H-13C dipolar coupling interactions to correlate 1H and 13C spins, separating the 1H resonances according to the chemical shifts of neighboring 13C nuclei, can yield unambiguous 1H peak assignments provided that polarization transfer occurs for only a very short time.44 Shown in Figure 9 are the MAS-J-HMQC and CP HETCOR spectra of simvastatin (active ingredient in Zocor®).45 The additional correlation signals in the dipolar HETCOR spectrum represent intermolecular polarization transfer events. The interatomic contacts may be traced theoretically to 4–5 Å, although Spiess et al. have shown that with sufficient 1H spin diffusion, dipolar coupling interactions may be detected up to 200 Å.46 While the presence of long-range peaks in the dipolar HETCOR spectra can make the process of assigning 1H peaks much more difficult, the ability of dipolar HETCOR spectroscopy to detect long-range 1 H-13C polarization transfer to remote atoms is useful for structural studies. Through-bond and through-space 2D SSNMR correlation experiments were recently demonstrated for simvastatin. The 13C-13C connectivity was initially established for all but one linkage using refocused CP-INADEQUATE. Then, MAS-J-HMQC and a series of 1H-13C dipolar HETCOR experiments were used to complete the 1H and 13C assignments and to observe long-range (ca. 3.0–5.1 Å) heteronuclear polarization transfer, from which interatomic contacts were determined. This study showed that NMRderived 1H-13C and 1H-1H contacts, in conjunction with 13C and 1H NMR aggregation (δliq - δsol) shifts, could be used to determine both the conformation and the relative orientation of well-organized molecules within a crystal structure, Figure 11. Quantum-mechanical calculations of shielding parameters are being increasingly used to assign experimental SSNMR spectra. To accurately reproduce SSNMR spectra for molecular crystals, intermolecular effects can be explicitly accounted for using clusters, which simulate the shortrange order in the crystalline state.47 1H chemical shifts, for example, can be calculated for the molecular clusters and compared to experimentallydetermined values. Hydrogen-bonding distances may then be extracted from the cluster which best simulates the experimental chemical shifts.

366

S.M. REUTZEL-EDENS

18

17

11

10 1

8 13 5

14

3

2

4

6

9 16

15 20

19

12

7

24

25

22 23

21

ppm

0 1 2 3 4 5 6 7 ppm

180

ppm

135

70

ppm

40

35

30

25

20

15

10

ppm

Figure 10. 1H-13C MAS-J-HMQC (top) and 1H-13C CP HETCOR (bottom) spectra of simvastatin. (Reproduced with permission from ref. 45; copyright 2004; American Chemical Society.)

2.7 Å

3.4 Å

11

25

10

3.4 Å

12

3.8 Å

8

4.2 Å 2.2 Å

9

1

3.8 Å

6 17 16

13

2.7 Å

23

24

23

2 3.4 Å

3

2.1 Å

1.9 Å

20

2.9 Å

18

21

7 2.8 Å

14

15

3.3 Å

24

2.7 Å

5 4.6 Å 4

19

23’

15 11

16 10

22

22’ 21’

Figure 11. Left: Conformation of a single molecule of simvastatin, with interatomic 1H-13C contacts (marked by arrows) detected by refocused 13C-13C CP-INADEQUATE, 1H-13C CP HETCOR and 1H-13C MAS-J-HMQC NMR spectroscopy. Right: Molecular packing in crystalline simvastatin, with intermolecular contacts (marked by arrows) detected by 1H-13C CP HETCOR. Disorder of the terminal ester was proposed by X-ray diffraction. (Reproduced with permission from ref. 45; copyright 2004; American Chemical Society.)

NMR CRYSTALLOGRAPHY

367

Using this approach with L-histidine, the hydrogen-bonding distances obtained by SSNMR were found to be comparable to those from neutron diffraction.23 By comparison, the hydrogen-bond lengths given by X-ray diffraction can differ by more than 20% from results obtained by neutron diffraction.48 Recently, Yates et al. combined experimental SSNMR data with first-principles quantum mechanical calculations of 1H, 13C and 19F NMR shielding parameters to predict the structure of flurbiprofen using periodic boundary conditions to implicitly account for the intermolecular effects within the crystalline lattice.49 Single crystal X-ray diffraction is undoubtedly the most important technique for elucidating crystal and molecular structures. X-ray powder diffraction may also be used for structure determination; however, when three-dimensional diffraction data is compressed into a one-dimensional powder pattern, information is lost (obscured by peak overlap), which increases both the difficulty and uncertainty of structure solution from powders.50,51 Because crystallographic information can be identified by SSNMR spectroscopy, this technique has become a critical tool for ensuring that structure solutions f rom powders are correct. In the case of anhydrous theophylline, for example, 13C and 15N NMR spectroscopy was used to eliminate one of two possible hydrogen bonding configurations derived from X-ray powder diffraction data.52 Solid-state 13C NMR spectroscopy was also used to confirm structural disorder in the β-phase of (E)-4formylcinnamic acid that was suggested by the slightly better quality of fit to powder diffraction data attained when disorder was modeled in the refinement calculations.53 Indeed, crystallographic information attainable from SSNMR spectra is now being integrated into the structure refinement process in the form of structural restraints and penalty functions in the search algorithms.23 Middleton, et al. found that incorporating even a single restraint obtained by SSNMR spectroscopy could significantly improve the efficiency and reliability of crystal structure solution from powder diffraction data.54 The previous examples clearly illustrate how SSNMR spectroscopy is evolving for structure determination. Today, molecular structures and conformations, as well as intermolecular contacts, are now accessible from SSNMR spectra (with the help of computational chemistry, in some cases) with a high degree of accuracy. The successful application of SSNMR spectroscopy to characterizing close contacts is not surprising given the sensitivity of this technique to short-range order. There is no reason, however, to expect that SSNMR spectroscopy might also be useful for looking at long-range effects of crystal packing. In fact, SSNMR spectroscopy has been shown to be quite useful for probing, on a molecular level, one important phenomenon related to crystal packing: nonstoichiometric hydration.

368

S.M. REUTZEL-EDENS

SSNMR spectroscopy was used in conjunction with X-ray crystallography to probe the nonstoichiometric hydration of LY297802 tartrate.55 LY297802 tartrate (Form B) experiences a continuous uptake of up to 0.5 molar equivalents of water from 0 to 90% RH. 13C CP/MAS NMR spectra collected for samples of the nonstoichometric hydrate that were dried at different conditions to alter the water content showed significant, yet systematic, peak shifting, Figure 12. For the local chemical environments of the 13C nuclei to change without altering the packing motif (no changes were observed by XRPD), water had to be incorporated into the structure, presumably by hydrogen-bonding interactions. Indeed, the water of crystallization was located in the crystal structure, bound by two relatively long OH…O hydrogen-bonding interactions to the crystallographicallyinequivalent tartrate anions (Figure 12). The systematic peak shifting noted for the other signals in the SSNMR spectra also suggests that a conformational change in LY297802 is induced by water migration into the crystal lattice. The crystal structure of LY297802 tartrate revealed that this hydrate possesses one common feature of nonstoichiometric hydrates: channels. In this case, the channels are somewhat corrugated and appear to be just large enough to permit water molecules to migrate to their hydrogen bonding sites (Figure 11).56 SSNMR spectroscopy provided unique insights into both the progression of hydration in LY297802 tartrate and the mobility of the

60 °C, 12 hr 2.912 Å

2.892 Å

40 °C, 12 hr

ambient

180

175

170

165

160

155

ppm

Figure 12. Left: Hydrogen-bonding interactions that bind water molecules in the channel hydrate of LY297802 tartrate, along with a crystal packing diagram. The water molecules are omitted in the packing diagram for clarity. Right: 13C CP/MAS NMR spectra of the nonstoichiometric hydrate, showing systematic peak shifting as the water content is altered.

NMR CRYSTALLOGRAPHY

369

water in the corrugated channels. At sub-stoichiometric water compositions, only a fraction of the water sites can be occupied at any one time. Therefore, if the water is statically disordered on the NMR timescale, both hydrogen-bonded and non-hydrogen bonded tartrate carbonyl groups should be observed, i.e., the 13C resonances should be split. In fact, no peak splitting is observed, revealing that all particles are “hydrated” at the same time, and to the same extent, as water is absorbed into the polycrystalline solid. The observation of a single solid-state environment for each carbonyl 13 C at the various water compositions further reveals that the water molecules are highly mobile, hopping rapidly (on the NMR timescale) between hydrogen bonding sites along the corrugated channels. The gradual shifting of the carbonyl 13C resonances (175-177 ppm) simply reflects the differences in the average occupancy of water in the hydrogen bonding sites as the water composition is changed. A similar investigation of water-solid interactions was recently reported for the nonstoichiometric hydrate of sildenafil citrate.28 As previously observed for LY297802 tartrate, the appearance of one set of sildenafil citrate 13C resonances, which systematically shifted as the water content was altered, was interpreted in terms of rapid water migration into the crystal structure. Whereas nonstoichiometric hydration in sildenafil citrate caused its 13C resonances to systematically shift, the 15N resonances of this drug responded differently to changes in water content. Specifically, the directly-bonded nitrogens of the sildenafil pyrazole ring did not show the characteristic asymmetric doublet produced by dipolar 14N-15N coupling when the sample was stored at a high relative humidity. The loss of the residual dipolar coupling (i.e., the collapse of the pyrazole ring nitrogen signals) was attributed to enhanced relaxation caused by water migration in the crystal structure (the water protons act as efficient relaxation sinks). Hydration has been shown to affect other relaxation processes in the solid state as well.57 In the case of β-estradiol hemihydrate, the dominant relaxation mechanism between 77 and 260 K is C3 reorientation of a single methyl group; water is presumed to be static on the NMR timescale. Above 260 K, however, water migration is sufficiently rapid to generate dipolar relaxation.58 While water absorption can facilitate relaxation, Te et al. used SSNMR spectroscopy to show that the water of hydration in thiamine hydrochloride (vitamin B1) hydrate reduced molecular mobility.20 In this study the crystal structures of thiamine hydrochloride hydrate and its isomorphic desolvate were examined, revealing a decrease in the unit cell volume, but a slight increase in the free volume as water was removed from the hydrate crystal. The changes in molecular mobility accompanying the increase in free volume were established by 1H and 13C T1 relaxation measurements. The T1H values measured for the isomorphic desolvate were found to be lower (1.8 v. 11.2 s) than those of the hydrate which suggested an increase in

370

S.M. REUTZEL-EDENS

TABLE 1. T1C Values (in seconds) for Thiamine Hydrochloride Monohydrate and Dehydrated Thiamine Hydrochloride (Adapted from ref. 20)

H3C

2’

H Cl + N

6’

N 4’

5’

NH2 carbon atom α β 5 4 4-CH3 2 5’-CH2 5’ 4’, 2’ 6’ 2’-CH3

N

Cl

β

S

2

5

+

OH

α

4

CH3

monohydrate 7.44 ± 0.43 4.17 ± 0.30 84.69 ± 4.60 103.45 ± 7.99 6.56 ± 0.11 85.46 ± 13.31 89.36 ± 7.45 84.22 ± 4.01 148.12 ± 13.31 106.52 ± 22.03 14.70 ± 0.17

dehydrate 0.38 ± 0.03 0.12 ± 0.01 21.83 ± 2.50 51.95 ± 6.19 5.45 ± 0.10 22.66 ± 0.80 26.13 ± 1.54 52.18 ± 8.80 56.95 ± 6.53 40.40 ± 3.41 12.96 ± 0.16

T1C (hyd)/T1C (dehy) 19.6 34.8 3.9 2.0 1.2 3.8 3.4 1.6 2.6 2.6 1.1

molecular mobility upon dehydration. The specific motions which dominated the relaxation process could not be determined by T1H measurements, however, because rapid spin diffusion resulted in a single T1 value for all of the protons in the sample. Therefore, since common spin temperatures do not exist for dilute nuclei, e.g., 13C, T1C measurements were undertaken to identify the specific groups most affected by the loss of water. While all of the T1C values were shorter for the dehydrated form, those of the hydroxyethyl carbons decreased to the greatest extent, Table 1. Hydrogen bonding arguments were made to explain the T1C results in terms of localized motions of the hydroxyethyl side chain; it is the hydroxyl group that hydrogen bonds to the water in the hydrate. Both the hydrogen-bonding interactions to the water and the lower free volume (relative to the desolvate) likely limited the mobility of the thiamine in the hydrate crystal. Recently, Vogt et al. published a comprehensive SSNMR analysis of the isomorphic dehydration of CXCR2 antagonist, N-(3-aminosulfonyl)-4chloro-2-hydroxyphenyl)-N’-(2,3-dichlorophenyl) urea, trihydrate.59 In lieu of X-ray crystal structure analysis of the dehydrated phases, multinuclear (1H, 13C, 15N and 23Na) MAS NMR and static 2H and 17O NMR spectra (using isotopically-labeled water) were used along with the trihydrate

NMR CRYSTALLOGRAPHY

371

crystal structure, variable temperature/RH powder X-ray diffraction patterns and Raman spectra to examine the structural changes induced by the uptake of water vapor. Monitoring six NMR-active nuclei throughout both the dehydration and exchange processes was shown to provide complementary structural and dynamic information beyond that available from diffraction methods.

References 1. 2.

3.

4.

5. 6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16.

W. C. McCrone, Physics and Chemistry of the Organic Solid State (Wiley Interscience, New York, 1965) S. M. Reutzel-Edens, Achieving Polymorph Selectivity in the Crystallization of Pharmaceutical Solids: Basic Considerations and Recent Advances. Curr. Opin. Drug Dis. & Dev. 9, 806–815 (2006) L. Yu, S. M. Reutzel and G. A. Stephenson, Physical Characterization of Polymorphic Drugs: An Integrated Characterization Strategy. Pharm. Sci. Tech. Today 1, 118–127 (1998) M. C. Etter, R. C. Hoye and G. M. Vojta, Solid-State NMR and X-Ray Crystallography: Complementary Tools for Structure Determination. Cryst. Rev. 1, 281–338 (1988) D. E. Bugay, Solid-State Nuclear Magnetic Resonance Spectroscopy: Theory and Pharmaceutical Applications. Pharm. Res. 10(3), 317–327 (1993) R. K. Harris, Applications of Solid-State NMR to Pharmaceutical Polymorphism and Related Matters. J. Pharm. Pharmacol. 59, 225–239 (2007) A. Pines, M. G. Gibby and J. S. Waugh, Proton-Enhanced NMR of Dilute Spins in Solids. J. Chem. Phys. 59, 569–590 (1973) E. R. Andrew, A. Bradbury and R. G. Eades, Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation. Nature 183, 1802–1803 (1959) I. J. Lowe, Free Induction Decays of Rotating Solids. Phys. Rev. Lett. 2, 285–287 (1959) O. N. Antzutkin, Sideband Manipulation in Magic-Angle Spinning Nuclear Magnetic Resonance. Prog. NMR Spectrosc. 35, 203–266 (1999) D. D. Laws, H.-M. L. Bitter and A. Jershow, Solid-State NMR Spectroscopic Methods in Chemistry, Angew. Chem. Int. Ed. 41, 3096–3129 (2002) J. Brus, Heating of Samples Induced by Fast Magic-Angle Spinning. Solid State Nucl. Magn. Res. 16, 151–160 (2000) A. E. Bennett, C. M. Rienstra, M. Auger, K. V. Lakshimi and R. G. Griffin, Heteronuclear Decoupling in Rotating Solids. J. Chem. Phys. 103, 6951–6958 (1995) J. Schaefer and E. O. Stejskal, Carbon-13 Nuclear Magnetic Resonance of Polymers Spinning at the Magic Angle. J. Am. Chem. Soc. 98, 1031–1032 (1976) E. O. Stejskal, J. Schaefer and J. S. Waugh, Magic-Angle Spinning and Polarization Transfer in Proton-Enhanced NMR. J. Magn. Reson. 28, 105–112 (1977) D. E. Bugay, Characterization of the Solid-State: Spectroscopic Techniqes. Adv. Drug Del. Rev. 48, 43–65 (2001)

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17. S. M. Reutzel-Edens, J. K. Bush, P. A. Magee, G. A. Stephenson and S. R. Byrn, Anhydrates and Hydrates of Olanzapine: Crystallization, Solid-State Characterization, and Structural Relationships. Cryst. Growth Des. 3(6), 897–907 (2003) 18. G. A. Stephenson, J. G. Stowell, P. H. Toma, R. R. Pfeiffer and S. R. Byrn, Solid-State Investigation of Erythromycin A Dihydrate: Structure, NMR Spectroscopy, and Hygroscopicity. J. Pharm. Sci. 86(11), 1239–1244 (1997) 19. S. M. Reutzel-Edens, R. L. Kleemann, P. L. Lewellen, A. L. Borghese and L. J. Antoine, Crystal Forms of LY334370 HCl: Isolation, Solid-State Characterization, and Physicochemical Properties. J. Pharm. Sci. 92(6), 1196–1205 (2003) 20. R. L. Te, U. J. Griesser, K. R. Morris, S. R. Byrn and J. G. Stowell, X-Ray Diffraction and Solid-State NMR Investigation of the Single-Crystal to Single-Crystal Dehydration of Thiamine Hydrochloride Monohydrate. Cryst. Growth Des. 3(6), 997–1004 (2003) 21. G. A. Stephenson, J. G. Stowell, P. H. Toma, D. E. Dorman, J. R. Greene and S. R. Byrn, Solid-State Analysis of Polymorphic, Isomorphic, and Solvated Forms of Dirithromycin. J. Am. Chem. Soc. 116, 5766–5773 (1994) 22. M. C. Etter and G. M. Vojta, The Use of Solid-State NMR and X-Ray Crystallography as Complementary Tools for Studying Molecular Recognition. J. Mol. Graphics, 7, 3– 11 (1989) 23. R. K. Harris, NMR Crystallography: The Use of Chemical Shifts. Solid State Sci. 6, 1025–1037 (2004) 24. M. D. Likar, R. J. Taylor, P. E. Fagerness, Y. Hiyama and R. H. Robins, The 3’-KetoDiol Equilibrium of Trospectomycin Sulfate Bulk Drug and Freeze-Dried Formulation: Solid-State Carbon-13 Cross-Polarization Magic Angle Spinning (CP/MAS) and High Resolution Carbon-13 Nuclear Magnetic Resonacne (NMR) Spectroscopy Studies. Pharm. Res. 10, 75–79 (1993) 25. A. T. Serajuddin and M. Pudipeddi, Handbook of Pharmaceutical Salts: Properties, Selection, and Use (Wiley-VCH, Weinheim, 2002) 26. T. Steiner, The Hydrogen Bond in the Solid State. Angew. Chem. Int. Ed. 41, 48–76 (2002) 27. C. Gardiennet-Doucet, B. Henry and P. Tekely, Probing the Ionisation State of Functional Groups by Chemical Shift Tensor Fingerprints. Prog. Nucl. Magn. Reson. Spect. 49, 129–149 (2006) 28. D. C. Apperley, P. A. Basford, C. I. Dallman, R. K. Harris, M. Kinns, P. V. Marshall and A. G. Swanson, Nuclear Magnetic Resonance Investigation of the Interaction of Water Vapor with Sildenafil Citrate in the Solid State. J. Pharm. Sci. 94(3), 516–523 (2005) 29. Z. J. Li, Y. Abramov, J. Bordner, J. Leonard, A. Medek and A. V. Trask, Solid-State Acid-Base Interactions in Complexes of Heterocyclic Bases with Dicarboxylic Acids: Crystallography, Hydrogen Bond Analysis, and 15N NMR Spectroscopy. J. Am. Chem. Soc. 128, 8199–8210 (2006). 30. J. W. Steed, Should Solid-State Molecular Packing Have to Obey the Rules of Crystallographic Symmetry? Cryst. Eng. Comm. 5, 169–179 (2003) 31. A. Lesage, M. Bardet and L. Emsley, Through-Bond Carbon-Carbon Connectivities in Disordered Solids by NMR. J. Am. Chem. Soc. 121, 10987–10993 (1999). 32. R. K. Harris, S. A. Joyce, C. J. Pickard, S. Cadars and L. Emsley, Assigning Carbon-13 NMR Spectra to Crystal Structures by the INADEQUATE Pulse Sequence and First Principle Computation: A Case Study of Two Forms of Testosterone. Phys. Chem. Chem. Phys. 8, 137–143 (2005) 33. S. M. Reutzel-Edens, J. K. Bush and J. Brus, Solid State Characterization of Pharmaceuticals (Pergamon, Poland, 2006)

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34. A. C. Olivieri, Effects of Solid Proton Transfer of the [13]C,[14]N Residual Dipolar Coupling in CPMAS NMR. Implications for the Shape of the Potential Energy Function. J. Chem. Soc. Perkin Trans. 2, 85–89 (1990) 35. J. R. Lyerla, C. S. Yannoni and C. A. Fyfe, Chemical Applications of VariableTemperature CPMAS NMR Spectroscopy in Solids. Acc. Chem. Res. 15, 208–216 (1982) 36. S. M. Reutzel-Edens, V. A. Russell and L. Yu, Molecular Basis for the Stability Relationships Between Homochiral and Racemic Crystals for Tazofelone: A Spectroscopic, Crystallographic, and Thermodynamic Investigation. J. Chem. Soc. Perkin Trans. 2, 913–924 (2000) 37. M. C. Etter, S. M. Reutzel and G. M. Vojta, Analysis of Isotropic Chemical Shift Data from High-Resolution NMR Studies of Hydrogen-Bonded Organic Compounds. J. Mol. Struct. 237, 165–185 (1990) 38. A. Naito, S. Tuzi and H. Saito, A High-Resolution 15N Solid-State NMR Study of Collagen and Related Polypeptides. The Effect of Hydration of Formation of Interchain Hydrogen Bonds as the Primary Souce of Stability of the Collagen-Type Triple Helix. Eur. J. Biochem. 224, 729–734 (1994) 39. F. H. Allen, A Systematic Pairwise Comparison of Geometric Parameters Obtained by X-ray and Neutron Diffraction. Acta Crystallogr. B42, 515–522 (1986) 40. S. P. Brown and H. W. Spiess, Advanced Solid-State NMR Methods for the Elucidation of Structure and Dynamics of Molecular, Macromolecular, and Supramolecular Systems. Chem. Rev. 101, 4125–4155 (2001) 41. A. E. Aliev and K. D. M. Harris, Structure and Bonding Volume 108 (Springer-Verlag, Berlin, 2004) 42. A. Lesage, D. Sakellariou, S. Steuernagel and L. Emsley, Carbon-Proton Chemical Shift Correlation in Solid-State NMR by Through-Bond Multiple Quantum Spectroscopy. J. Am. Chem. Soc. 120, 13194–13201 (1998) 43. A. Lesage, P. Charmont, S. Steuernagel and L. Emsley, Complete Resonance Assignment of a Natural Abundance Solid-Peptide by Through-Bond Heteronuclear Correlation Solid-State NMR. J. Am. Chem. Soc. 122, 9739–9744 (2000) 44. D. Burum, Encyclopedia of Nuclear Magnetic Resonance Volume 4 (John Wiley & Sons, New York, 1996) 45. J. Brus and A. Jegorov, Through-Bonds and Through-Space Solid-State NMR Correlations at Natural Isotopic Abundance: Signal Assignment and Structural Study of Simvastatin. J. Phys. Chem. A108, 3955–3964 (2004) 46. M. Wilhelm, H. Feng, U. Tracht and H. W. Spiess, 2D CP/MAS 13C Isotropic Chemical Shift Correlation Established by 1H Spin Diffusion. J. Magn. Reson. 134, 255–260 (1998) 47. R. K. Harris, P. Y. Ghi, R. B. Hammond, C. -Y. Ma and K. J. Roberts, Refinement of a Hydrogen Atomic Position in a Hydrogen Bond Using a Combination of Solid-State NMR and Computation. Chem. Commun. 2834–2835 (2003) 48. G. A. Jeffrey, An Introduction to Hydrogen Bonding (Oxford University Press, Oxford, 1997) 49. J. R. Yates, S. E. Dobbins, C. J. Pickard, F. Mauri, P. Ghi and R. K. Harris, A Combined First Principles Computational and Solid-State NMR Study of a Molecular Crystal: Flurbiprofen. Phys. Chem. Chem. Phys. 7, 1402–1407 (2005) 50. K. D. M. Harris, M. Tremayne and B. M. Kariuki, Advances in the Use of Powder XRay Diffraction for Structure Setermination. Angew. Chem. Int. Ed. 40, 1626–1651 (2001) 51. K. D. M. Harris and E. Y. Cheung, How to Determine Structures When Single Crystals Cannot Be Grown: Opportunities for Structure Determination of Molecular Materials Using Powder Diffraction Data. Chem. Soc. Rev. 33, 526–538 (2004)

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52. E. Smith, R. B. Hammond, M. J. Jones, K. J. Roberts, J. B. O. Mitchell, S. L. Price, R. K. Harris, D. C. Apperley, J. C. Cherryman and R. Docherty, The Determination of the Crystal Structure of Anhydrous Theophylline by X-Ray Powder Diffraction with a Systematic Search Algorithm, Lattice Energy Calculations and 13C and 15N SolidState NMR: A Question of Polymorphism in a Given Unit Cell. J. Phys. Chem. B 105, 5818–5826 (2001) 53. S. Meejoo, B. M. Kariuki, S. J. Kitchin, E. Y. Cheung, D. Albesa-Jové and K. D. M. Harris, Structural Aspects of the β-Polymorph of (E)-4-formylcinnamic Acid: Structure Determination Directly from Powder Diffraction Data and Elucidation of Structural Disorder from Solid State NMR. Helv. Chim. Acta 86, 1467–1477 (2003) 54. D. A. Middleton, X. Peng, D. Saunders, K. Shankland, W. I. F. David and A. J. Markvardsen, Conformational Analysis by Solid-State NMR and its Application to Restrained Structure Determination from Powder Diffraction Data. Chem. Commun. 7, 1976–1977 (2002) 55. S. M. Reutzel and V. A. Russell, Origins of the Unusual Hygroscopicity Observed in LY297802 Tartrate. J. Pharm. Sci. 87, 1568–1571 (1998). 56. S. M. Reutzel-Edens and A. W. Newman, Polymorphism in the Pharmaceutical Industry (Wiley-VCH, Weinheim, 2006) 57. C. L. Jackson and R. G. Bryant, Carbon-13 NMR of Glycogen: Hydration Response Studied by Using Solids Methods. Biochemistry 28, 5024–5028 (1989) 58. E. R. Andrew and M. Kempka, Molecular Motions in Solid Estradiol by Nuclear Magnetic Resonance Spectroscopy. Solid State Nucl. Magn. Reson. 4, 249–253 (1995) 59. F. G. Vogt, J. Brum, L. M. Katrincic, A. Flach, J. M. Socha, R. M. Goodman and R. C. Haltiwanger, Physical, Crystallographic, and Spectroscopic Characterization of a Crystalline Pharmaceutical Hydrate: Understanding the Role of Water. Cryst. Growth Des. 6, 2333–2354 (2006)

ORGANIC MATERIALS FOR NONLINEAR OPTICS

M. BLANCA ROS Química Orgánica. Facultad de Ciencias. Universidad de Zaragoza-Instituto de Ciencia de Materiales de Aragón. 50009-Zaragoza (Spain)

Abstract. Interest in nonlinear optics has grown continuously since these phenomena first emerged and the field now encompasses fundamental studies of the interaction of light with matter and the development of new materials and applications. The field is interdisciplinary and expertise is required in subjects such as physic, materials science, chemistry, mathematics and engineering. In addition, as further progress is made in this area, nonlinear optical organic materials will be the key to future photonic technologies. This review chapter provides an introduction to the basic concepts of nonlinear optics and related effects and also covers different strategies for the design of new organic materials for nonlinear optical applications, all from an organic chemist’s point of view.

1. Introduction Photonic processes involve the use of photons instead of electrons to perform the same functions as the latter but at a much faster speed and in an easier and “cleaner” way. Such processes also offer new applications that are not suitable for electronic systems. Indeed, such processes represent the technology of the XXI century. The ability to manipulate light has enormous scope for technological applications and these include optical processing, lasers, optical filters and optical recording. The origin of these new properties and possibilities lies in the way in which light and matter interact with each other. In the so-called nonlinear optical materials this interaction occurs in such a way that as soon as the electromagnetic field of a laser interacts with the electric charges of the material, dramatic changes occur in the propagation properties of the incoming light and this modifies properties such as frequency, phase and polarization. Nonlinear optics can therefore be considered as the study of the interaction of intense laser light with matter.1–8,10,11

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Applications for nonlinear optical materials vary from modulation of optical signals to sensing, imaging or microfabrication. In the first case these applications are mediated by different effects, many by the electrooptic effect. The second ones are facilitated by multiphoton absorption, wherein molecules simultaneously absorb at least two photons of light. However, in order to control light in a suitable way for the target applications, appropriate materials that allow the modulation or combination of photons to give precise and rapid responses are needed. Progress in the field of nonlinear optics (NLO) in terms of photonics is approached through interdisciplinary research involving a range of specialists. Nonlinear optical processes of technological interest result from the interactions of the electromagnetic field of a laser with certain materials and the questions that clearly arise are: Why and how do these effects occur? In this respect a qualitative approach to the situations at both the microscopic (atomic or molecular) and the macroscopic levels should be considered. The electric field of light (E) stimulates the atomic or molecular charges and this gives rise to a force F (F = q.E). This induced force, which is timedependent, leads to polarization of the electronic density of the atoms or molecules, which in turn creates induced dipolar moments (µ), even in cases where a permanent molecular moment was not present (Figure 1).

Figure 1. Cartoon showing the molecular polarization of linear and nonlinear materials as a function of time under irradiation with light (top). Plots of the induced polarization waves (red) and the electric field of the applied light wave (blue) as a function of time, and induced polarization versus applied field, for both linear and non-linear materials (bottom).

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For low intensity electric fields, this polarization is proportional to the applied field. In other words, the frequency of both the electric field and the polarization will be the same and in phase. This situation is expressed by equation (1), where αij(ω) is a tensor of the linear polarization at a frequency ω. Polarization = µ (ω) = αij (ω) • Ε (ω)

(1)

If one considers the material as a whole rather than an isolated molecule, the polarization (P) of this material can be expressed by equation (2), where χij is called as the linear susceptibility of the material. P (ω) = χij (ω) • Ε (ω)

(2)

All materials that show this kind of response with light are termed linear optical materials. The movement of charge leads to the reemission of radiation without modifying the frequency of the incoming light. However, the induced polarization causes changes in the speed of the incoming light, generating optical phenomena related to variations in the refractive index such as refraction or birefringence. When very intense radiation (i.e. a laser) interacts with a molecule or a material, the electronic densities are polarized in such a way that the induced electrical polarization gives rise to many unusual and very attractive properties that are optically nonlinear because they depend on the asymmetric movement of the electronic density (Figure 1). In this case both microscopic and macroscopic polarizations can be represented by equations (3) and (4) respectively µ = µo + αij•Ε + βijk •Ε •Ε + γijkl •Ε •Ε •Ε + ...

(3)

P = Pο + χij(1)•Ε + χijk(2)•Ε •Ε + χijkl(3)•Ε •Ε •Ε + ...

(4)

where µo is the original dipolar moment, αij is the linear polarizability and β and γ are called the first and second order hyperpolarizabilities. At the macroscopic level, Pο is the original polarization of the material and χ(n) are the susceptibilities of order n, which are all tensors of order n+1. For this reason these materials are called nonlinear optical materials (NLO materials). Terms that are higher than first order are responsible for the nonlinear optical effects. Some representative nonlinear second order effects are second harmonic generation (SHG), which enables the frequency of the incoming light to be doubled, and optical rectification (OR) or the electro-optic effect, also known as Pockels effect, which allows the

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refractive index to be modulated by an electric field (Figure 2). There are also interesting third order effects and these include third harmonic generation (THG), optical phase conjugation and optical limiting. It is known that nonlinear polarization is more significant at both the microscopic and macroscopic levels on applying a more intense electromagnetic field. For this reason, only a few nonlinear optical effects were observed prior to the development of the laser. In fact, all materials can exhibit these kinds of nonlinear optical responses but their applicability for nonlinear optics depends on the magnitude of the responses, which are governed by the molecular and material coefficients β (and γ) or χ(n), respectively. ω

ω1 ω2

NLO MATERIAL

2ω

NLO MATERIAL

ω3 = ω1 + ω2

FM NLO MATERIAL

ω1

AM

V Figure 2. Schematic representation of important nonlinear optical and electro-optic effects.

2. Materials for Nonlinear Optics The field of nonlinear optics is now forty years old, taking into account the first observation of SHG by Franken and co-workers in 1961. Research on NLO has mainly focussed on second and third order effects, which are suited to different applications and also have different structural requirements.1–12 NLO responses (namely SHG) were first described for inorganic salts such as KDP, BBO or LiNbO3, which are alternatives to semiconductors that are still providing high challenges to the field, especially in the form of epitaxially grown confined structures (GaAs, GaSb). Both kinds of materials have been studied widely and both have various applications. However, in the last few decades a great deal of effort has been focussed on

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organic materials and this area has opened up new possibilities and challenges in the field.28 The ideal material for applications in NLO devices should have a combination of physicochemical properties that is very often difficult to achieve: appropriate values for given parameters, high damage threshold, high mechanical strength and thermal stability, fast response, processability, ease of fabrication and optical transparency. Compared with inorganic NLO materials, organic materials can fulfil many of these requirements and, furthermore, they have attracted the interest of researchers because they offer broad possibilities in terms of design. Fortunately this characteristic can also help to overcome some of the drawbacks associated with NLO systems, such as low mechanical strength, environmental stability or variable performance at low or high temperature. Nevertheless, some of these limitations – along with the often complex set-ups required for proper evaluation of the nonlinear optical response have slowed progress in the field. Interestingly, however, these aspects have enriched the field by inspiring many different and clever approaches to the design of this type of material. Thus, depending on the target phenomena (second or third order effects) or the area of research interest, either at the molecular or at macroscopic level, a wide variety of approaches have been exploited and reported in books and reviews.1,4,5,7,9,10,14,17 3. Organic Materials for Second Order NLO Applications 3.1. MOLECULAR DESIGN

In order to develop organic materials for second order NLO effects, an appropriate molecular design should be planned. In this respect one of the most successful and widely used strategies involves highly polarizable structures in which an asymmetric change in the electronic density should be produced by light. The most prevalent approach to provide high β values through chemical structures involves the incorporation of an electron-donating group (D) and an electron-withdrawing one (A) connected by a π-system. In this respect pnitroaniline can be considered as a model (Figure 3). The total β value is the sum of two contributions, βadd resulting from the interactions between the substituents and the conjugated structure and βCT arising from the donor-acceptor charge transfer contribution. The latter contribution is the most important. These NLO-moieties are called NLOchromophores or NLO-phores and they are easily identified in many materials for nonlinear optics.

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A Electronwithdrawing group

e

O2N

D

NH2

Electrondonating group

π-system Figure 3. Typical molecular structure for second-order nonlinear optical materials.

Nevertheless, in spite of the wide adoption of this approach, a great deal of activity is still devoted to this type of structure, not only in order to improve the NLO response but also to establish a deeper understanding of the structure-activity relationships. There is a desire to open new structural alternatives and in this sense theoretical calculations can be applied, an approach that helps to provide more rapid and less arduous progress.5,10 Calculations in nonlinear optics have been claimed to lead to “a rethinking of paradigms now used to design molecules. The theoretical results are useful to the device engineer as a guide for understanding the best material properties that can be achieved, to the chemist as a metric of the usefulness of a particular synthetic paradigm and to the physicist for an understanding of how complex material structures could be used to obtain as much out of a materials as is fundamentally possible”. A great deal of synthetic work has been carried out and the NLO properties of novel molecules must be characterized; this is mainly achieved using the EFISH method.1,4,5 All of these studies allow trends to be established as far as the chemical structure-NLO activity is concerned. On the basis of these studies some factors that affect β values have been proposed. For example, structural changes in the strength of electron donor and acceptor substituents and their conformations, the nature of the conjugated bonds and the length and aromaticity of π-systems have all been investigated. 1,3,4,5,7,9,10,12,14 Organic chemists are providing a wealth of new structures for these studies. In an effort to the increase further the number of organic molecules that incorporate new electron-donating or electron-withdrawing groups, the incorporation of metal atoms through the use of coordination complexes has opened up new possibilities for the design of materials, both from the electronic and structural points of view. These metal-containing compounds were expected to exhibit large molecular hyperpolarizabilities due to the transfer of electron density between the metal atom and the ligands, as well as to increase the design possibilities through the use of different central metal atoms with diverse oxidation states, coordination geometries and ligands (Figure 4).1,5,6,10,11,14,16,24

ORGANIC MATERIALS FOR NONLINEAR OPTICS O

381 R N

S N

O N CH3

R

O

N

β : 1000 x 10 esu (1,90 µm) -30

β : 2169 x 10 esu (1,06 µm) -30

NO2 Ph3P

Ru

C4H9 N C4H9

N

PPh3

β : 1455 x 10 (1,06 µm)

-30

esu

β : 152 x 10 esu (1,34 µm)

Cl Zn Cl N

-30

H3C

Figure 4. Chemical structures and first order hyperpolarizabilities of some representative 1D NLO-phores.

Furthermore, to the most commonly reported monodimensional A-π-D structures one can add 2D and 3D-systems to the variety of new molecules for NLO that chemists have explored recently and which can be advantageously associated with other components of β tensor (Figure 5).5,6,7,10,14 Generally, this tensor has two irreducible components, one dipolar and other octupolar. It is therefore possible to design molecules where a nonzero βoct is compatible with a zero dipole moment. In this respect, the development of experimental techniques such as HRS, 1,4,5 which is used to measure the molecular parameter β for ionic and octupolar molecules, was very important. 3.2. MATERIAL ENGINEERING

Applications based on NLO effects require materials rather than molecules. Thus, even though progress at the molecular level has offered very good starting points, a great deal of effort has been devoted to provide materials that allow these molecules to be processed in a suitable way for applications. In the case of second order effects, a serious problem arises at the macroscopic level as molecules with large β values alone are not sufficient. According to equation (4), second order nonlinear optical phenomena only occur when χ(2) has a value other than zero, so the molecular disposition within the material must be non-centrosymmetric.

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CH3CH2NH

NC

NHCH2CH3

CN

O

CN

O

NO2

O2N

β : 10 x 10 esu (1,06 µm) -30

NO2 H2N

NH2

O2N

NO2

NC

β : 193 x 10 esu (1,06 µm) -30

NH2

H3C

N

CH3

β : 30 x 10 esu (1,06 µm) -30

N(CH3 )2

N

β : 159 x 10

-30

N

esu

C H3C

CH3 N CH3

N CH3

β : 560 x 10 esu (1,06 µm) -30

Sn N (H3 C)2 N

N

N(CH3 )2 N

N N N N(CH3 )2

Figure 5. Chemical structures and first order hyperpolarizabilities of some representative 2D and octupolar NLO-phores.

This limitation, along with processing and thermal and chemical stability of the materials, has had a major influence on the advances and the strategies as far as material design are concerned. Different alternatives have been developed for the attainment of non-centrosymmetric order and alignment of the NLO-phores. 4,5,7,10,14,17 Single crystals are among the most attractive materials because of their typically large macroscopic nonlinearities, high packing densities, superior long-term orientational and photochemical stabilities and their optical quality. Inorganic single crystals are currently used in a variety of NLO photonic applications and, in a similar way, organic crystals were expected to be used in industry. However, considering that roughly 75% of nonchiral organic molecules crystallize centrosymmetrically, many NLO-phores that are active at the molecular level do not show any nonlinear optical activity. Thus, noncentrosymmetric orientation in the bulk is one of the most important issues for this approach. Numerous authors have incorporated into their designs stereogenic centers or/and hydrogen bonded systems as “tools” to induce polar order. The former possibility guarantees crystallization in one of the noncentrosymmetric groups. On the other hand, non-covalent interactions are used to define the tridimensional structure of the crystal (Figure 6).

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Alternatively, the use of strong coulombic interactions, for example by changing the counterions in organic salts, has also proven to be a simple and highly successful strategy to obtain materials with large χ(2) values (Figure 7).4,5,14,15,29

Figure 6. Different strategies followed to orient NNP (N-(4-nitrophenyl-(L)-prolinol) for second order nonlinear optical responses: single crystals (top),5 where molecules are arranged head to tail by intermolecular H-bonding and as intercalated materials (bottom).

Figure 7. Packing drawing of DAST (N,N-dimethylamino-N´-methylstilbazolium ptoluenesulfonate) showing the non-centrosymmetric order within the single crystal15 and powder second harmonic generation efficiencies for different salts based on the same cationic NLO-phore.

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The use of single crystals does, however, have some limitations related to the size and mechanical stability and processing. As a result, many different approaches to overcome such drawbacks have been developed by researchers in this field. Intercalated materials have been proposed to control the mobility and order of the NLO-phores within their cavities (Figure 6). With this aim in mind, matrices that are different in nature and morphology (e.g. zeolites, cyclodextrins, silicates, …) have been investigated and in this respect the sol-gel methodology has opened very attractive possibilities.21,27 The increased interest in thin films in electronics, nonlinear optics and related new technologies has focussed interest on developing organic materials that have easily controlled film thickness and highly ordered micro- or nanostructures.13,17,23,25,26,30,31 In this area the Langmuir–Blodgett technique is one of the most powerful ways to obtain films with uniformly oriented close packing and controlled thickness. As a result, the Langmuir–Blodgett technique has been identified as a very suitable approach to prepare non-centrosymmetric materials that give large NLO-parameters. Indeed, a number of classical Dπ-A structures have been incorporated into designs that combine the hydrophobic-hydrophilic characteristics that allow the preparation of this type of film (Figure 8).1,4,5,6,7 Alternatively, promising results have also been reported for non-covalent films prepared by PVD techniques.25 With the same general aim, a very closely related design strategy has been introduced and this involves building materials through covalent interactions. It is thought that this approach could overcome some limitations inherent in this type of non-covalent film. The application of an appropriate sequence of chemical reactions can create non-centrosymmetric self-assembled multilayers that give rise to NLO-materials with good mechanical properties and a high degree of order (Figure 8).14,17

Figure 8. Different strategies followed to prepare thin films for second order nonlinear optical responses: Langmuir-Blodget films and covalent self-assembled multilayers.

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All of the strategies outlined above have helped to advance the field in many different respects, but one of the most successful lines of research in NLO materials concerns the use of polymers.1,3–7,10,14,17,18,19,28 Numerous research groups (both academic and industrial) have concentrated their efforts on this type of material. Polymers combine a number of outstanding characteristics to add to large nonlinearities, including the possibilities of design and processing, that make them difficult to equal. From the structural point of view, different kinds of polymers have attracted the interest of researchers. The systems studied to date range from simple blends of commodities such as PPMA with NLO-phores -the so called guest-host systems-, to side-chain polymers, main-chain polymers, cross-linked polymers and networks, or ferroelectric materials (Figure 9). This kind of material offers the possibility of altering the glass transition temperature not only to process the material but also to orient the NLOmoieties using an external stimulus such as an electric or magnetic field by using “poling” techniques. A suitable structural design of the polymer enables a wide variety of materials to be developed and it is envisaged that the non-centrosymmetric order could be retained below the Tg for long periods of time (Figure 9).

Figure 9. Different polymer-based materials designed for second order nonlinear optical applications (top) and one of the strategies used to orient the NLO-moieties by electric poling (bottom).

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Furthermore, interest for polymers in nonlinear optics has significantly increases due to their potential as photorefractive materials.3–7,10,19 The photorefractive effect is defined10 “as spatial modulation of the index of refraction due to charge distribution in an optically nonlinear material”. As a result of the combination of several effects -photoconductive and electrooptic- refractive index gratings are created in this kind of material. Such photorefractive gratings can efficiently diffract a reading light beam and are the basis for various optical processing and data storage systems. Finally, in this short review of the strategies used to develop NLOmaterials for second order effects one must also mention liquid crystals.1,2,5,6,20 These materials are characterized as a unique state of matter that combines both order, which provides anisotropic properties as in the solid state, and fluidity as in the liquid state. These characteristics not only provide the possibility of ordering the NLO-phores with a non-centrosymmetric polar order but also allow them to be processed as thin films or fibres. Of the large number of different liquid crystal arrangements (or mesophases), very few have been used to order and orient NLO-phores (Figure 10). For example, the less ordered and viscous nematic phase has often been used to pole polymers under electric or magnetic external fields. Nevertheless, ferroelectric mesophases have been considered as a very attractive alternative because weaker electric fields could be used to achieve the polar order in the ferroelectric chiral SmC phase (SmC*). From the structural point of view, the majority of these studies have been developed on calamitic structures (1D NLO-phores) but in recent

Figure 10. Liquid crystalline phases used for second order nonlinear optical applications and the different molecular designs proposed to orient the NLO-moieties within the noncentrosymmetric polar order of the mesophase.

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years very promising alternatives have been considered for liquid crystals. For example, the use of V-shaped materials the so-called bent-core or banana-shaped liquid crystals,32,33 provides mesophases with non-centrosymmetric polar order. These new materials are 2D NLO-structures that exhibit a significant increase in the nonlinear activity in comparison to the classic ferroelectric mesogenic materials. Interestingly, and in order to diminish the relaxation of the polar order with time, some approaches developed for polymers have also been assessed with these materials, e.g. cross-linked polymers have been prepared by using in situ-polymerization methods. Liquid crystal monomers that are non-centrosymmetrically aligned in the mesophase can subsequently be photopolymerized in the non-centrosymmetric mesophase to give high molecular weight materials that retain the polar order from the mesophase at room temperature.22,26 4. Organic Materials for Third Order NLO Applications Third order nonlinear optical effects have been developed to a lesser extent than the second order systems, particularly as far as the design is concerned. The structural requirements at the microscopic level are not well understood and the number of studies in this line is significantly lower in comparison to those developed for second order materials. Third-order nonlinear optics imposes no symmetry requirements for the effects to occur. But in contrast to second-order nonlinear optical materials, there are few rational strategies for optimizing this kind of response for materials.1,3,4,5,7,9,10 Acentricity strongly enhances the third-order nonlinear optical properties of molecules. The presence of conjugated systems connecting donor and acceptor structures favours this type of NLO response. Furthermore, certain combinations of parameters also used for molecular electronic are welcome for these materials, even though no direct correlation between high conductivity and χ(3) values has been observed. A range of very different compounds such as phthalocyanines,24 cyanines, tetrathiafulvalenes or fullerene-derivatives have been characterized as third order NLOphores (Figure 11). Nevertheless, the majority of work and interest in this area concerns conjugated polymers. Examples are polydiacetylenes, poly-pphenylenevinylene or polythiophenes. The polymer chains should pack as closely as possible to maximize the χ(3) values. Alternatively, polyalkylsilanes are non conjugated polymers that contain no π electrons in the polymer backbone, but χ(3) values have been reported for some polysilanes.

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CH3O CH3O CH3O

S

N

N

S

γ : 140 x 10-34 esu

OCH3

(1,39 µm)

OCH3 OCH3

S

S

S

S

S

S

S

S

R

. I3

(3)

Χ : 5 x 10

--8

R n

esu R

n

S

R

S

Χ(3) ~ 10 -9 esu Χ(3) : 2700 x 10 -10 esu

Figure 11. Chemical structures and non-linear responses of some representative NLO-phores designed for third-order responses.

Since third-order effects do not require bulk order, all materials, including solids as crystalline materials, amorphous polymers, glassy materials or multilayer films, as well as liquid crystals can be used for this purpose. On the other hand, cascaded second-order nonlinearities provide an attractive alternative to obtain third-order nonlinearities. Cascading is a process where lower-order effects are combined to contribute to a higherorder nonlinear response.5,6,34 Therefore the development of materials with large χ(2) values are also pursuit for cubic nonlinear optics. In the last year interest in both the optical phenomena controlled by χ(3) as well as the characterization and development of materials for third order NLO-responses have increased markedly and have attracted further interest in this field. 5.

Aknowledgements

This work was supported by project MAT2006-13571-C02 (CYCITFECER) from Spain-UE and by the Aragón government (Spain).

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References Books and monographs: 1. P. N. Prasad, D. J. Williams. Introduction to nonlinear optical effects in molecules and polymers. (Wiley Interscience, New York, 1991). 2. I-C. Khoo, S-T. Wu. Optics and nonlinear optics of liquid crystals. (World Scientific, Singapore, 1993). 3. J. Zyss. Molecular nonlinear optics: Materials, physics and devices. (Academic Press, New York, 1994). 4. Ch. Bosshard, K. Sutter, Ph. Prêtre, J. Hulliger, M. Flösheimer, P. Kaatz., P. Günter. Organic nonlinear optical materials. (Gordon and Breach, Basel, 1995). 5. H. S. Nalwa, S. Miyata. Nonlinear optics of Organic Molecules and polymers. (CRC Press, Boca Raton, 1997). 6. I-C. Khoo, F. Simoni, C. Umeton. Novel optical materials and applications. (John Wiley and Sons, New York, 1997). 7. P. Günter. Nonlinear optical effects and materials. (Springer-Verlag, Berlin, 2000). 8. Y. R. Shen. The principles of nonlinear optics. (Wiley-Interscience, New Jersey, 2003) and R. W. Boyd. Nonlinear optics. (Academic Press, Amsterdam, 2003) 9. R. G. Denning, “Chromophores for nonlinear optical materials”. In Spectroscopy of new materials. Chap. 1. Eds. R. J. H. Clark, R. E. Hester, (John Wiley and Sons, Chichester, 1993). 10. Chem. Rev. Vol. 94, (1994). This issue provides a detailed look at the uses of optical nonlinearities in chemistry. 11. Ed. D.W. Bruce, D. O´Hare, “Metal-containing materials for nonlinear optics”. In Inorganic materials. Ed. S. R. Marder. (John Wiley and Sons, Chichester, 1997). 12. J. J. Wolff, R. Wortmann, “Organic materials for second-order non-linear optics”. Adv. Phys. Org. Chem., 32, 121–217 (1999). Reviews and papers of interest: 13. R. Dorn, D. Baumns, P. Kersten, R. Regener, “Nonlinear optical materials for integrated optics: Telecommunications and sensors”. Adv. Mater., 4, 460–473 (1992). 14. S. R. Marder, J. W. Perry, “Molecular materials for second-order nonlinear optical applications”. Adv. Mater., 5, 804–815 (1993). 15. S. R. Marder, J. W. Perry, C. P. Yakymushym, “Organic salts with large second-order optical nonlinearities”. Chem. Mater., 6, 1137–1147 (1994). 16. N. J. Long, “Organometallic compounds for nonlinear optics: The search for en-lightenment!”. Angew. Chem. Int. Ed. Engl., 34, 21–38 (1995). 17. T. J. Marks, M. A. Ratner, “Design, synthesis and properties of molecule-based assemblies with large second-order optical nonlinearities”. Angew. Chem. Int. Ed. Engl., 34, 155–173 (1995). 18. L. R. Dalton, A. W. Harper, B. Wu, R. Ghosn, J. Laquindaum, Z. Liang, A. Hubebel, C. Xu. “Polymer electro-optic modulators: Materials synthesis and processing”. Adv. Mater., 7, 519–540 (1995). 19. Y. Zhang, R. Burzyns, S. Ghosal, M. K. Casstevens, “Photorefractive polymers and composites”. Adv. Mater., 8, 111–125 (1996). 20. F. Simoni, “Non-linear optics in liquid crystals: basic ideas and prespectives”. Liq. Cryst. 24, 83–89 (1998). 21. F. Chaumel, H. Jiang, A. Kakkar, “Sol-gel materials for second-order nonlinear optics”. Chem. Mater., 13, 3398–3395 (2001). 22. C. Artal, M. B. Ros, J. L. Serrano, N. Pereda, J. Etxebarria, C. L. Folcia, J. Ortega. “SHG characterization of different polar materials obtained by in situ photopolymerization”. Macromolecules, 34, 4244–4255 (2001). 23. A. N. Rashid, C. Erny, P. Günter, “Hydrogen-bond directed orientations in non-liner optical thin films”. Adv. Mater., 15, 2024–2027 (2003).

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24. G. De la Torre, P. Vázquez, F. Agulló-López, T. Torres, “Role of structural factors in the nonlinear optical properties of phthalocyanines and related compounds”. Chem. Rev., 104, 3723–3750 (2004). 25. A. Facchetti, E. Annoni, L. Beverina, M. Morone, P. Zhu, T. J. Marks, G. A. Pagani, “Very large electro-optic responses in H-bonded heteroaromatic films grown by physical vapour deposition”. Nature Materials, 3, 910–917 (2004). 26. J. A. Gallastegui, C. L. Folcia, J. Etxebarria, J. Ortega, N. Gimeno, M. B. Ros, “Fabrication and nonlineal optical properties of monodomain polymers derived from bent-core mesogens. J. Appl. Phys., 98, 083501–1/4 (2005) 27. P. Innocenzi, B. Lebeau, “Organic-inorganic hybrid materials for non-linear optics”. J. Mater. Chem. 15, 3821–3831 (2005). 28. S. R. Marder, “Organic nonlinear optical materials: where we have been and where we are going”. Chem. Commun. 131–134 (2006). 29. A. Datta, S. K. Pati, “Dipolar interactions and hydrogen bonding in supramolecular aggregates: understanding cooperative phenomena for 1st hyperpolarizability”. Chem. Soc. Rev. 35, 1305–1323 (2006). 30. R. U. A. Khan, O-P Kwon, A. Tapponnier, A. N. Rashid, P. Günter, “Supramolecular ordered organic thin films for nonlinear optical and optoelectronic applications”. Adv. Funct. Mater., 16, 180–188 (2006). 31. R. U. A. Khan, O-P. Kwon, A. Tapponnier, A. N. Rashid, P. Günter, “Supramolecular ordered organic thin films for nonlinear optical and optoelectronic applications”. Adv. Funct. Mater., 16, 180–188 (2006). 32. R. A. Reddy, C. Tschierske, “Bent-core liquid crystals: polar order, superstructural chirality and spontaneous desymmetrisation in soft matter systems”. J. Mater. Chem., 16, 907–962 (2006). 33. H. Takezoe, Y. Takanishi, “Bent-core liquid crystals: their misteriousand attractive world”. Jap. J. Appl. Phys., 45, 597–625 (2006). 34. C. Bosshard, “Cascading second-order nonlinearities in polar materials”. Adv. Mater., 8, 385–397 (2006).

BUILDING CONDUCTING MATERIALS FROM DESIGN TO DEVICES

CONCEPCIÓ ROVIRA Departament de Nanociència Molecular i Materials Orgànics, Institut de Ciència de Materials de Barcelona (CSIC), Campus Universitari de Bellaterra, 08193 Cerdanyola, Barcelona (Spain)

Abstract. The electronic and structural characteristics of organic molecules that generate materials with conducting properties will be analyzed, emphasizing specially the design of the material and the methodology for its preparation. We will follow the way to create the material from the molecule and how the material can be used to prepare devices, particularly field effect transistors.

1. Introduction In the search for functional molecular materials with a specific physical property, the election of the suitable building block having adequate electronic, functional and structural characteristics is critical to achieve the appropriate supramolecular organization giving rise to the desired property. To reach this goal it is first necessary to know why the property of choice is produced. What is needed to have a conducting material is a free movement of valence electrons within the material when an electrical field is applied. It is then required the formation of electronic bands and the generation of charge carriers. The basic characteristics that molecular building-blocks should fulfill in order to reach these requirements are: a) molecules with LUMO and HOMO orbitals that interact strongly in the solid state to form energy bands and b) at the same time those molecules should be able to produce persistent and stable free radicals to include the charge carriers and produce stable materials. Due to space restrictions, we will develop the lecture only with one type of molecules.

391 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 391–405. © 2008 Springer.

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2. TTF as Building Blocks TTF derivatives are versatile building blocks to form supramolecular aggregates in the solid state with interesting conducting and also magnetic properties. As stated in the introduction, those properties are associated with specific interactions between molecules having none or one unpaired electrons and the control of the intermolecular interactions permits modification of the bulk properties of the material. In fact, low dimensional molecular charge transfer salts based on TTFs present a wide scope of electronic and magnetic properties ranging, as far as conducting properties are concerned, from semiconductors to metals and superconductors, and in regard to magnetic properties, from Pauli like paramagnetism and BonnerFisher, spin-ladder or Heisenberg behaviors to spin Peierls, antiferromagnetic or canted ferromagnetic ground states.1 The reason why TTF derivatives have been widely used as building blocks of molecular conductors and magnets lies in their electronic and structural characteristics. Thus, TTFs are strong π-electron donors that form thermodynamically stable open-shell species by transferring one π-electron from the HOMO. The dication derivative can be sequentially formed and is also stable due to the gain in aromaticity.

On the other hand these molecules have planar shapes that promote their stacking and as a consequence the π-π orbital overlap. Sulfur Sulfur interactions also promote electronic coupling and formation of electronic 2D structures. Depending on the packing of the molecules in the solid the intermolecular electronic interaction, described by the transfer integrals,

Figure 2. Schematic representation of the supramolecular characteristics of TTF derivatives, as well as of the most common interactions in their supramolecular organizations.

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varies and therefore the bulk electronic and magnetic properties of the molecular solid can be modified. In addition, it is synthetically available the introduction of a large number of substituents in the 2, 3, 6 and 7 positions of the TTF core2 modifying in that way not only the electronic (HOMO tuning) but also the supramolecular characteristics of the TTF derivative.

3.

Crystalline Materials

When the TTF molecules pack in a crystal, have a great tendency to form alternated layered structures of donors and anions. The packing pattern in the donor layer is responsible for the formation of energy bands that depend on the molecular overlap (Fig. 3). The electronic properties of the material are determined by the molecular overlap and the position of the Fermi energy level, EF that depends on the oxidation (doping) degree (Fig. 4).

Figure 3. Crystal structure (up) and associated band structure and Fermi surface (down) of (TMTSF)2CIO4.

Figure 4. Energy diagram of (a) A metal with a small work function. (b) An n-type semiconductor. (c) An insulator. (d) A p-type semiconductor. (e) A metal with a large work function.

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One characteristic of the molecular crystalline conductors is their anisotropy in electronic structure and softness. Their elastic stiffness constant is one order of magnitude smaller that those of conventional semiconductors and metals. Therefore intermolecular distance in the crystals, and consequently the transfer integrals, can be largely modified by moderate pressures to show dramatic changes in electronic properties.8b A typical example is the promotion of superconductivity by applying pressure. The first discovered organic superconductor, (TMTSF)2PF6, shows at ambient pressure a metal-insulator transition at about 12K due to an instability characteristic of one- dimensional electronic systems, giving rise to spin-density waves. Hydrostatic pressure of about 6 kbar suppressed the insulating state and induced superconductivity. Crystalline charge transfer salts are prepared either by electrocrystallization3 or by chemical oxidation, and a characteristic of TTF charge transfer salts is the strong tendency to polymorphism. Polymorphs of the same salt can be obtained by changing the preparation conditions or simply in the same experiment.4 Since in each polymorph the packing of the molecules is different the electronic bands formed are also different deriving in the variation of the physical properties. Thus, it is possible to have for the same salt electronic properties as divergent as insulator or superconductor. This is the case of Bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF)2 I3 salt where κ and β phases are superconductors at low temperature whereas α phase is an insulator below 135 K.4

κ

β

α

Figure 5. Schematics of the arrangement of the BEDT-TTF molecules in three different polymorphs of the (BEDT-TTF)2 I3 salt.

In fact, (BEDT-TTF) salts containing trihalide ions form a very interesting family of molecular solids that not only shows a rich polymorphism (at least eight crystalline modifications) along with a large variety of physical properties but also many electronically and structurally reversible phase transitions which can be induced by changes of pressure and/or temperature. As an example the salt (BEDT-TTF)2Br1.3I1.1Cl0.6 exists in three crystalline polymorphic forms (α’-, α’’’-, β’’-phases)5 and, surprisingly, is able to adopt the same metal-like β’’-phase both at low (T<185 K) and high (T>395 K) temperatures.6 An schematic representation of the process is given in Figure 6.

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Figure 6. Schematic representation of the temperature driven transitions in the (BEDTTTF)2Br1.3I1.1Cl0.6 salt.

Polymorph α’ can be converted in polymorph α’’’ that in turn is converted in the metallic β’’ phase at low and high temperature. The phase transitions are clearly seen not only by the variation of the crystallographic cell volume with temperature but also in the physical properties as conductivity and magnetism (Fig. 7). (a)

(b)

2.6 70

V (lm)

2.4 2.2

60

2.0 1.8

50 40

1.6 1.4

30

1.2 1.0

20 10

0.8 0.6 100

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R (Ω)

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10

400 300 200 300

320

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360 T(K)

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400

1 120 140 160 180 200 220 240 260 280 300 T(K)

Figure 7. Temperature dependence of cell volume (a) ESR signal intensity (b) and conductivity (c) and (d) of the (BEDT-TTF)2Br1.3I1.1Cl0.6 salt.

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Subtle changes in the donor molecule as the replacement of sulphur by selenium promotes large differences in the transport properties as can be observed in Figure 8 for tetramethyl tetrathiafulvalene (TMTTF) and tetramethyltetraselena fulvalene TMTSF salts. Also small changes in the size and shape of the counterion used to form the ion-radical salt with a given TTF derivative promote variations in the physical properties. Figure 8 illustrates the case of TMTSF salts in which ClO4 counterion gives a superconductor at low temperature whereas PF6 gave an insulator at low temperature.7 Donoranion interactions through weak hydrogen bonds are also responsible of changes in properties.

Figure 8. Resistivity versus Temperature curves for different TMTTF and TMTSF salts.

It is also possible to combine different properties in the same crystal lattice by using anions with specific properties as for example the case of magnetic anions that gave rise to compounds that are paramagnetic superconductors, and metallic ferromagnets.8 Since there are almost infinite possibilities of change both in the organic molecule and in the counterion it is possible to prepare molecular conductors with tailored electronic properties. Therefore, such electronic molecular materials are very promising in the field of electronics since one can achieve control over the property of materials and the performance of the electronic devices based on them. Nevertheless the materials described above are obtained in small quantities as tiny and fragile crystals (Fig. 9) which is a drawback for their technological applications.

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Figure 9. Photograph of a homemade holder that allows measuring R(T) for two samples simultaneously: two plate-like crystals are attached to platinum electrodes, a typical length of crystals is 0.5÷1.5 mm. Ccourtesy of V. Laukhin.

4. Conducting Bilayered Films To overcome the technological limitations of single crystals of organic conductors, it is of great interest the preparation of conducting bi-layer composite films (BL films)9 that consist of a polymeric matrix with a conducting surface layer formed by a nanocrystalline network of organic conductors. One great advantage of this method of preparation of electronic materials is that it results in a material that combines the unusual electronic properties of molecular metals (e.g. metallic conductivity, superconductivity) together with the favourable properties of a polymeric matrix (e.g. flexibility, transparency, low density). Furthermore, BL-films can be produced with different sizes and shapes, which could be of technical interest. The conducting topmost layer comprising crystallites of the TTF-based organic conductor is prepared by treatment of the surface layer of a polymer film which contains 2 wt% of the TTF-based donor with vapours of a halogen or interhalogen and an organic solvent. At this point donor molecules which are embedded in the polymer film, as well as the halogen and solvent molecules, diffuse to the surface layer of the film. Diffusion of solvent molecules results in swelling of the surface layer of the film in which the crystalline conducting topmost layer of the TTF-based organic conductor is formed. Two main processes are responsible for this: 1) formation of the molecular-conductor building blocks by oxidation of a fraction of donor molecules by (inter)halogen (I2, Br2 , IBr, ICl) and 2) crystallization of the TTF-based organic conductor as a well developed conducting topmost layer.

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Choosing the appropriate donor and by establishment of optimum conditions for the step of the BL-film preparation, that implies the reaction between a TTF derivative and halogen, it is possible to generate a very transparent film containing a layer of highly oriented and well-connected nanocrystals as in the example of salt θ-(BET-TTF)2Br·3H2O (Fig. 10).10

Figure 10. a) SEM image of the surface layer of a BL film showing the network of θ -(BETTTF)2Br·3H2O nanocrystals. b) View through the metallic BL film.

The transport properties of the films are the same as in the single crystals being possible, by choosing appropriately the donor and the halogen, the tuning of conductivity from semiconducting to metallic behaviour and, even superconducting films have been achieved.9a Interestingly, these films can be patterned by direct writing with a heat source, like a laser beam, what permits to remove the halogen from the salt. In such a way, the treated areas are non conducting and electronic circuits can be drawn (Fig. 11).11

Figure 11. Electronic circuits in which the BL films before patterning (left) and after patterning (right) are used as micro-resistors. The light zones in the right figure correspond to the laser writing path and are insulating.

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5. Organic Field Effect Transistors In the field of organic electronics,12 organic field – effect transistors (OFETS) are technologically interesting because they could serve as the main component in large-area, low cost, and flexible electronic circuits. Major possible applications that are getting close to being brought to the market are RF-ID tags and flexible displays.13 A field-effect transistor can be described as a three terminal device in which the current through a semiconductor linked to two terminals (namely source and drain) is controlled at the third terminal (called gate) by a voltage. A typical organic field-effect transistor (OFET) configuration is shown schematically in Figure 12. The voltage applied to the gate (VG) induces an electric field through the dielectric and causes the formation of an accumulation layer of charges at the interface of the semiconductor deposited above. This field causes a shift in the HOMO and LUMO energy levels in the organic semiconductor. Depending on the work function of the electrodes relative to the HOMO/LUMO levels, electrons will either flow out of the HOMO into the electrodes (leaving behind holes) or flow from the electrodes into the LUMO, forming a conducting channel between a source and drain. Then, by applying a source-drain voltage (VSD) it is possible to measure current between the source and the drain (ISD).

Figure 12. Schematic drawing of an OFET. This device is biased the way a p-type semiconducting OFET would be. The source is grounded and a negative voltage is applied to the drain and the gate to induce holes in the semiconducting channel.

In a transistor device the organic semiconductor is doped applying voltage through the gate electrode, and more charge carriers are produced as the voltage is increased. The material used as semiconductor should not only permit a high mobility of the charge carriers but also should have stability under ambient conditions as well as easy processing. These characteristics can be achieved with the same building blocks of the above

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reviewed charge-transfer salts in which the doping is promoted by chemical or electrochemical redox processes. The example of TTF derivatives applies also for OFETs. As mentioned before, the crystallisation of TTF derivatives is governed by the π-π stacking, which permits, together with the S···S interactions, an intermolecular electronic transfer responsible for their transport properties. TTF derivatives are generally soluble in various solvents, are easily chemically modified, and are good electron donors producing upon oxidation stable cation-radicals in air. As a consequence, TTF derivatives are also good molecules for the preparation of OFETs due to the possibilities of synthesising tailored derivatives, and in the last three years TTF based OFTEs with high device performance have been described.14 OFET devices have been prepared by evaporation, spin coating or drop casting. The best performance have been achieved for devices based on dithiophene tetrathiafulvalene DT-TTF single crystal grown from solution by drop casting, a very simple method. 15 The electrical measurements performed on the DT-TTF crystals are typical of a p-type semiconductor, as a more negative VG is applied, more holes are induced in the semiconductor and the conductivity increases (Fig. 13b). The maximum mobility achieved so far has been of 3.8 cm2/Vs, with an on/off ratio > 106, which is the highest mobility reported for an organic semiconductor which is not based on pentacene derivatives, and is of the order of that of amorphous silicon that is widely used in solar cells and flat screen displays. With the aim of establishing a correlation between crystal structure and charge carrier mobility, we recently prepared OFETs based on various a)

b) -1200

S

-1000

Isd / nA

VG = -40 V

S

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-800 VG = -20 V -600 VG = -10 V -400 VG = 0 V

-200

100 μm

0 0

-5

-10

-15

-20

-25

-30

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-40

Vsd / V

Figure 13. a) DT-TTF crystal formed on microfabricated electrodes b) ISD versus VSD at constant VG for a single-crystal OFET based on DT-TTF.

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neutral TTF crystals grown from solution.16 We studied eigth different TTF derivatives, namely bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF), (ethylenethio)- (ethylenedithio)-tetrathiafulvalene (ETEDT-TTF), bis(ethylenethio)-tetrathiafulvalene (BET-TTF), (ethylenethio)-(thiodimethylene)tetrathiafulvalene (ETTDM-TTF), dithiophene-tetrathiafulvalene (DT-TTF), dibenzo-tetrathiafulavlene (DB-TTF), (thiophene)(thiodimethylene)-tetrathiafulvalene (TTDM-TTF) and (ethylenethio)-(thiophene)-tetrathiafulvalene (ETT-TTF). Taking, thus, into account the crystal packing in which these molecules are arranged, this family of compounds can be classified into three groups. BEDT-TTF and ETEDT-TTF belong to the first group. Their supramolecular organisation consists of dimers sustained by hydrogen bonds, forming chains along a due to lateral S···S interactions (Fig. 14a). The chains are arranged perpendicularly to each other avoiding therefore the formation of stacks. In the second crystal structure group, BET-TTF and ETTDM-TTF crystallise forming chains of quasi planar molecules along the a axis interacting side-by-side (Fig.14b). These chains stack into layers giving rise to a bi-dimensional electronic structure. Finally, the molecules from group 3, DT-TTF, DB-TTF, TTDM-TTF, and ETT-TTF, crystallise forming uniform stacks of almost planar molecules along the b axis (Fig. 14c). The interplanar distance between molecules of one stack is very short (3.56–3.66 Å).

Group 1 S

S

S

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S

S

S S

S

S S BEDT-TTF S S

S S ETEDT-TTF

S S

S S

S

S

S

S BET-TTF S S

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S DT-TTF

S S

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(a)

(b)

c 0

b

0 c

a

a

b

c b

a

0 a c

(c)

0 a

b

c

c

0 a

Figure 14. Crystal structures of the dissymmetric donors (a) ETEDT-TTF representative of Group 1 (b) ETTDM-TTF representative of Group 2 and (c) TTDM-TTF representative of Group 3.

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A trend in mobilities through the different crystal structures is observed. Among the structures studied, the herringbone crystal structure of group 3 molecules, DT-TTF, DB-TTF, ETT-TTF and TTDM-TTF is the most suitable for preparing OFETs. The devices made with some molecules of this group exhibit the highest mobilities found for solution-processed materials, and are also among the highest reported for OFETs. Group 3 based devices exhibit mobilities at least two order of magnitude higher than those of group 1 that is the worse one. The differences in mobilities within each crystallographic group could be influenced by respective slight differences in S···S distances. However, we should note that the devices based on the molecules which present more disorder in their crystal structure due to the lower symmetry of molecules exhibit poorer mobilities. Indeed, within group 3 the increase in disorder (DT-TTF < TTDM-TTF < ETT-TTF) diminishes the mobility values found. A similar tendency is observed for the molecules within groups 1 and 2. At room temperature, the charge mobility of semiconducting materials is often described by a hopping transport process, which is determined by two major parameters: i) the electronic coupling between adjacent molecules (transfer integral), which needs to be maximised and ii) the reorganisation energy, which needs to be small for efficient charge transport. We performed calculations of these two parameters and we found that the experimental results were in agreement with the calculations; that is, the materials showing higher mobility, have lower reorganisation energy and larger transfer integral.16–17 This result is of great importance for the future design of new promising materials. In addition, further calculations demonstrated that the reorganisation energy values strongly depend on the crystal structure and, thus, investigating the role of the intermolecular interactions on TTF crystals is crucial to understand their transport properties.17 A step further has been the preparation of high performance OFET based on large areas of aligned films of TTF derivatives, namely, tetrakis(octadecylthio)-tetrathiafulvalene (TTF-4SC18) and the analogous C22 compound. The films were prepared from solution by zone-casting, a simple technique that does not require the use of preoriented substrates.18 Despite the fact the use of TTF derivatives in OFETs is still at its infancy compared to the vast amount of work carried out with pentacene and oligothiophenes, the recent progress on TTF-based OFETs have already shown their potential and versatility, and high mobilities (of the same order as or higher that their parent compounds acenes and thiophenes) have already been achieved. Certainly, their high performance and facile processability guarantee these materials a privileged position in the field of organic fieldeffect transistors.

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6. Acknowledgments This work has been possible due to the valuable collaboration of many students and co-workers of the department and other institutions. Most of them appear in the references, but I want to express a special acknowledgment to M. Mas-Torrent, E. Ribera, J. Tarrés, E. Laukhina, V. Laukhin, J. VidalGancedo, X. Ribas, S. Bromley, P. Hadley, K. Wurst, and J. Veciana. The financial support of different agencies through the following grants is also acknowledged, DGI Spain CTQ2006-06333/BQU, EU 6FP NAIMO IP nº NMP4-CT-2004-500355 and DGR Catalonia, 2005SGR00362 and XERMAE.

References 1. a) Williams, J. M.; Ferraro, J. R.; Thorn, R. J.; Carlson, K. D.; Geiser, U.; Wang, H. H.; Kini, A. M.; Whangbo, M-H. Organic Superconductors (Including Fullerenes) Synthesis, Structure, Properties, and Theory, (Prentice Hall, Englewood Cliffs, New Jersey, 1992). b) Ishiguro, T.; Yamaji, K.; Saito, G. Organic Superconductors, (Springer-Verlag New York, 1998) c) Veciana, J.; Rovira C.; Amabilino, D. B. Supramolecular Engineering of Synthetic Metallic Materials: Conductors and Magnets, (Kluwer Academic Publishers, Dordrecht, 1999) d) Chem. Rev. 104 (nº 11) (2004) special issue on molecular conductors. 2. J-I Yamada, T. Sugimoto TTF Chemistry, Fundamentals and Applications of Tetrathiafulvalene. (Kodanska-Springer 2005). 3. P. Batail, K. Boubekeur, M. Fourmigué, J.-C. P. Gabriel, Chem. Mater, 10, 3005 (1998). 4. a) Saito, G. in Organic Superconducting solids, edited by Jones, W., CRC Press, Boca Raton New York, 1997, Chap. 10. b) Avramenko, N. V.; Zvarykina, A. V.; Laukhin, V. N.; Laukhina, E. E.; Lubovskii, R. B.; Shibaeva, R. P. JETP Lett., 48, 472 (1988). 5. E. Laukhina, J. Vidal-Gancedo, S. Khasanov, V. Tkacheva, L. Zorina, R. Shibaeva, J. Singleton, R. Wojciechowski, J. Ulanski, V. Laukhin, J. Veciana, C. Rovira, Adv. Mater., 12, 1205 (2000). 6. E. Laukhina, J. Vidal-Gancedo, V. Laukhin, J. Veciana, I. Chuev, V. Tkacheva, K. Wurst, C. Rovira J. Am. Chem. Soc., 125, 3948 (2003). 7. D. Jerome, Science, 252, 1509 (1991). 8. E. Coronado, P. Day, Chem. Rev, 104, 5419 (2004). 9. a) Laukhina, E. E.; Merzhanov, V. A.; Pesotskii, S. I.; Khomenko, A. G.; Yagubskii, E. B.; Ulanski, J.; Kryszewski, M.; Jeszka, J. K. Synth. Met. 70, 797 (1995). b) Laukhina, E. E.; Ulanski, J.; Khomenko, A. G.; Pesotskii, S. I.; Tkachev, V.; Atovmyan, L.; Yagubskii, E. B.; Rovira, C.; Veciana, J.; Vidal-Gancedo J.; Laukhin, V. J. Phys. I France, 7, 1665 (1997). 10. a) Mas-Torrent, M.; Laukhina, E.; Rovira, C.; Veciana, J.; Tkacheva, V.; Zorina, L.; Khasanov, S. Adv. Funct. Mater. 11, 299 (2001), b) Mas-Torrent, M.; Ribera, E.; Tkacheva, V.; Mata, I.; Molins, E.; Vidal-Gancedo, J.; Khasanov, S.; Zorina, L.; Shibaeva, R.; Wojciechowski, R.; Ulanski, J.; Wurst, K.; Veciana, J.; Laukhin, V.; Canadell, E.; Laukhina E.; Rovira, C. Chem. Mater. 14, 3295 (2002) c) E. Laukhina, V. Tkacheva, , S. Khasanov, L. Zorina, J. Gómez-Segura, A. Pérez del Pino, J. Veciana, V. Laukhin, C. Rovira ChemPhysChem., 7, 920 (2006).

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11. M. Mas-Torrent, E. Laukhina, V. Laukhin, C. M. Creely, D. Petrov, C. Rovira, J. Veciana. J. Mater. Chem. 16, 543 (2006). Patent application ES200501879. 12. a) Hagen Klauk. Organic Electronics, materials, manufacturing and applications WileyVCH Verlag GmbH & Co. Weinheim, 2006 b) Chem. Rev. 107 (nº 4) (2007) special issue on organic electronics and optoelectronics. 13. a) S. E. Burns et al. J. Soc. Inf. Disp.. 13, 583 (2005) b) G. H. Gelink et al. J. Soc. Inf. Disp. 14, 113 (2006). 14. M. Mas-Torrent, C. Rovira J. Mater. Chem., 16, 433 (2006). 15. M. Mas-Torrent, M. Durkut, P. Hadley, X. Ribas and C. Rovira, J. Am. Chem. Soc. 126, 984 (2004). 16. a) M. Mas-Torrent, P. Hadley, S. T. Bromley, X. Ribas, J. Tarrés, M. Mas, E. Molins, J. Veciana and C. Rovira, J. Am. Chem. Soc., 126, 8546 (2004) b) M. Mas-Torrent, P. Hadley, S. T. Bromley, N. Crivillers, J. Veciana and C. Rovira, Appl. Phys. Lett., 86, 012110 (2005). 17. S. T. Bromley, M. Mas-Torrent, P. Hadley and C. Rovira, J. Am. Chem. Soc., 2004, 126, 6544. 18. P. Miskiewicz , M. Mas-Torrent, J. Jung, Sylwia Kotarba, I. Glowacki, E. Gomar-Nadal, D. B. Amabilino, J. Veciana, B. Krause, D. Carbone, C. Rovira, J. Ulanski and J. Mater. Chem. 18, 4724 (2006).

HYDROGEN BONDING AND CONCURRENT INTERACTIONS

URSZULA RYCHLEWSKA Dept. of Chemistry Adam Mickiewicz University 60-780 Pozna , Poland

Abstract. The lecture deals with the various forms of interactions with dominant electrostatic component. It points to dipole/dipole interactions as strong structure determining factor that often accompanies hydrogen bond and halogen bond interactions, and becomes the major structure determining factor when hydrogen bond donor groups are no longer available. It illustrates a combined use of hydrogen bond, halogen bond and dipolar interactions for engineering of reliable layer motifs.

Keywords: hydrogen bonding, parallel and antiparallel local dipolar interactions, halogen bonding, tartaric acid derivatives, NH-oxalamides, maleimides

1. Introduction Given a proliferation of publications on hydrogen bonds in the crystallographic literature, another version could be hard to justify. Nonetheless, hydrogen bonds in the presence of other structure determining interactions seem like an interesting subject for study. With this in mind, we have selected groups of relatively simple organic compounds that possess different hydrogen bond functionalities and are capable of forming, besides hydrogen bonds, other types of interactions. The studied systems represent both flexible and rigid molecules, and have been chosen from chiral and achiral objects. Specifically, they are derivatives of optically active tartaric acid (1), diamides of oxalic acid (2), and di-substituted maleimides (3). The studied groups of compounds are well known due to their countless applications: tartaric acid is one of the most important chiral compounds,1 oxalamide moiety attracts attention as a substitute of peptide amide bond,2 as a ligand in metal complexes,3,4,5 and is utilized as a building block in crystal engineering,6 while maleimides are used as electron transfer photoinitiators7, as bifunctional linkers8, and as intermediates in organic syntheses,9. In each of these groups we shall search for the structure determining factors and establish their relative importance. 407 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 407–427. © 2008 Springer.

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Hydrogen Bonding and Local Dipolar Interactions Stabilize the Structure of Chiral Tartaric Acid Derivatives

Molecules possessing singly-bonded, four-atom carbon chain are of special interest as models to study the effects of substituents on population of conformers, commonly designated as T, trans and G, gauche. Both steric and electronic effects contribute to the stability of these conformers, and usually both G and T conformers are found in the crystal structures.

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Scheme 2. Three basic conformers of (R, R) tartaric acid derivatives. Arrows mark antiparallel local CH and CO dipoles.

However, a search of the CSD10 carried out for all possible derivatives and salts of optically active tartaric acid resulted in 493 observations of which 97% of cases corresponded to the T-conformer, with carbon chain in a fully extended conformation and only 3% of cases corresponded to the bent carbon chain conformers G – and G + (Scheme 2, Figure 1). Closer inspection reveals that the few G – conformers, being preferred by N,Ndisubstituted tartrdiamides, also appear as a result of coordination to the metal ion, and in specific cases, this conformation appears as a result of an intramolecular hydrogen bond. In a very few structures containing the G +

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conformers the T isomers are also present, which indicates that they appear to enable an extended intermolecular hydrogen bonding network to be built.

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Figure 1. (b) Scattegram illustrating population of T, G – and G + conformers among R,R and S,S configurational isomers (X-axis: O–C*–C*–O; Y-axis C–C*–C*–C torsion angles).

The T conformation of the carbon main chain is invariably accompanied by the co-planar arrangement of the hydroxyl substituent and the proximal carboxyl, ester or amide functional group (Figure 2). More specifically,

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hydroxycarboxyl and hydroxyester moieties show tendency to place the neighboring C=O/C–O bonds in synperiplanar (syn) orientation, while αhydroxy-NH-amides adopt a conformation in which the hydroxyl group takes the antiperiplanar (anti) orientation with respect to the carbonyl oxygen. 180 160 140 120 100 80 60 40 20 180

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Figure 2. Scattegram showing distribution of the values of the O–C*–C=O torsion angles around two Csp3–Csp2 bonds in chiral tartaric acid derivatives possessing an extended carbon chain (T) conformation.

2.1. IN QUEST FOR FACTORS RESPONSIBLE FOR UNIQUE CONFORMATIONAL PREFERENCES OF TARTRATES AND TARTRAMIDES

The well pronounced preferences towards T,syn and T,anti conformations of tartaric acid esters and amides can be explained by the stabilizing role of intramolecular hydrogen bonds of the O–H…O(=C) type (acid, ester) and N–H…O(–C*) type (amide), which close the five-membered ring (the S(5) motif11) (Figures 3a, b and c). These intramolecular hydrogen bonds in specific cases become three-center, with one component intermolecular or totally switch to intermolecular. Therefore, in a search for factors responsible for conformational preferences of chiral tartaric acid derivatives we have eliminated, by substitution, all possible hydrogen bond donors, so that no stabilization could come form this type if interaction. It appeared that dimethylester of (R,R)-O,O’-dibenzoyl tartaric acid (Figure 4a) as well as (R,R)-O,O’-dibenzoyl tartaric acid mono (N,N-dimethylamide) monomethyl ester (Figure 4b) adopted the usual T-conformation, indicating that the hydroxyl group substitution had little effect on conformation and thus

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eliminating a possibility of intramolecular hydrogen bonding as the key factor stabilizing molecular conformation.

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c Figure 3. Perspective view of selected (R,R)-tartaric acid derivatives. The T conformation of the main carbon chain is accompanied by either syn/syn (a), syn/anti (b) or anti/anti (c) conformation around the C(sp2)–C(sp3) bonds. All structures are stabilized by intramolecular hydrogen bonds of the OH…O and NH…O type, forming the S(5) motifs.

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Figure 4. Extended carbon chain conformation (T) observed in the crystal structures of (R,R) tartaric acid derivatives lacking the ability of hydrogen bond formation, (a) dimethyl (R,R)O,O’-dibenzoyltartrate, (b) (R,R)-O,O’-dibenzoyltartaric acid mono(N,N-dimethylamide) monomethylester. Arrows and shaded areas mark local CO/CH dipolar interactions. The only hydrogen atoms shown are those taking part in dipolar interactions.

Then, we reasoned that perhaps substitution of the hydroxyl groups with bulky tert-butyl or trialkylsilyl groups could shift the conformational equilibrium towards G+, in which the hydroxyl groups, substituted by bulky groups, would be in trans orientation (Scheme 2). Dimethyl (R,R)-O,O’-ditert-butyltartrate, dimethyl (R,R)-O,O’-di-(tert-butyldimethylsilyl)tartrate (Figure 5a) and (R,R)-N,N’-dimethyl-O,O’-di-tert-butyltartramide (Figure

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5b) were chosen to serve as tools for probing conformational stability of tartaric acid derivatives.12 As previously, the molecules invariably adopted in the solid state the extended (T) conformation, supporting the presumption that there must exist some other factors that stabilize the conformation of tartaric acid derivatives and salts.

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Figure 5. Extended carbon chain conformation (T) observed in the crystal structures of dimethyl tartrate (a) and N, N’-dimethyl tartrdiamide (b) substituted at O,O’ by bulky tertbutyldimethylsilyl and tert-butyl groups, respectively. Hydrogen atoms constituting methyl groups have been omitted for clarity. Arrows and shaded areas mark local CO/CH dipolar interactions. Hydrogen bonds are denoted as dashed lines.

By inspecting visually hundreds of derivatives retrieved from the CSD we have noticed that among chiral tartaric acid derivatives and salts possessing the T-conformation, mutual disposition of the CH and CO dipoles situated in the 1,3-position with respect to each other was very consistent. Namely, the two dipoles were inclined with respect to each other at roughly 60 or 180o, depending on which of the two carboxylate CO bonds had been taken into account (Figure 6), but the CH bond was always placed in an antiparallel orientation with respect to one of the two carboxylate CO bonds (see Figures 3, 4 and 5). We interpreted this finding as an indication of the existence of 1,3-dipolar CO/CH interactions. Since there are two such CO/CH bond arrangements in each tartrate molecule, the stabilizing effect of these dipolar interactions might be substantial. Distribution of the angular values describing mutual disposition of the CO and CH dipoles in 1,3-position in 473 tartaric acid derivatives and salts (946 fragments) deposited in the CSD is shown in Figure 6. Concentration of all values in the region of 60 and 180o is a good illustration of consistency of data and thus indicates the importance of such interactions for the conformational stability and preference.

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Figure 6. Scattegram illustrating distribution of angles formed between pairs of 1,3 CH/CO dipoles in 473 optically active tartaric acid derivatives and salts (there are two such pairs in an average tartrate molecule).

If the assumption about the role of 1,3-CH/CO dipoles in stabilizing the molecular conformation of R,R-tartaric acid derivatives was indeed correct one would expect that systems deprived of either CH or CO dipoles should display different conformational preferences. The CSD search revealed several optically active tartaric acid derivatives in which methyl groups replaced the H-atoms at chiral centers. In some of these crystals the molecules adopted the G+ conformation, highly unpopular among (R,R)tartaric acid derivatives (Figure 7a.)13.

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Figure 7. (a) Bent carbon chain conformation of (R,R)-tartaric acid derivatives resulting from (a) replacement of C*–H dipoles by C*–CH3 bonds; (b) replacement of the terminal carboxylates by cyano groups. Atoms constituting the carbon main chain are represented as spheres.

Final support came from our own X-ray investigations of (2S,3S)-2,3dibenzoyloxy-2,3-dicyanoethane (the analogue of R,R-tartaric acid, in which terminal carboxylates have been replaced by the cyano groups, Figure 7b). It turned out that in the crystal these molecules also adopted the

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G conformation, which allowed them to place the bulky benzoyloxy substituents in trans orientation14. One further point concerning local dipolar interactions in chiral tartaric acid derivatives deserves a comment. Some O,O’-dibenzoyloxy derivatives display a tendency towards nonplanariy of the O–C–C*–O molecular fragments, which limits their ability for dipolar interactions involving terminal CO groups15. However, as these interactions become geometrically less favorable, the C*–H dipoles situated at chiral centres tend to orient nearly parallel to the carbonyl groups belonging to benzoyloxy substituents. This creates geometrical conditions favoring dipolar interactions between C*–H dipoles located at chiral centres and benzoyloxy carbonyls attached to the same chiral atom, as illustrated in Scheme 3.

Scheme 3. Antiparallel arrangement of CH/C=O(Bz) dipoles in (R,R)-O,O’-dibenzoyltartaric acid esters and amides.

We have established that simultaneous realization, by the same C*–H bond, of both types of dipolar interactions is rarely achieved, and dipolar interactions with terminal CO groups are favored over the analogous interactions with the benzoyloxy carbonyls. However, as the former type of dipolar interactions becomes difficult to achieve due to e.g. steric reasons, the second type of dipolar interactions begins to operate still within the same T conformation of carbon chain. 2.2. INTERMOLECULAR HYDROGEN BONDS FORCE CHANGE IN MOLECULAR CONFORMATION OF (R,R)- TARTRDIAMIDES, A TASK DIFFICULT TO ACHIEVE BY SIMPLE CHEMICAL SUBSTITUTION

We shall now demonstrate that, in specific cases, interactions at supramolecular level can be more effective in changing the molecular conformation than the chemical modifications are. The molecules of (R,R)O,O’-dibenzoyl tartardiamide adopt in their crystals the expected T,anti conformation and are hydrogen bonded to form a ladder motif, typical for

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diamides (Figure 8)16,17. The ladder consists of R 22 (14) rings formed when neighboring molecules, related by a single translation along the crystallographic axis with a repetition period of approximately 5Å, join together with pairs of NHtrans…O=C hydrogen bonds (the C(4) motif11). The two C(4) chains that take part in the formation of the ladder run in the same direction, as required by the two-fold symmetry operation relating the two symmetrical halves of the molecule. The benzoyloxy substituents are situated on the front and back-side of the ladder. Hence, further extension of the ladder motif into layer by means of NHcis…O hydrogen bonds, is possible only in the plane of the ladder. As the layer is build, structural voids are created (around the R 24 (8) motif), which are filled by solvent molecules, e.g. THF, pyridine, dioxane, loosely connected to the host16.

Figure 8. Packing of (R,R)-O,O’-Dibenzoyltartrdiamide molecules in T conformation. The 2 highlighted area marks the R 2 (14) ladder, build of two parallel C(4) chains.

This uniform picture of the mode of packing of (R,R)-O,O’-dibenzoyltartrdiamide molecules, which could have been predicted by crystal engineers on the basis of the well known rules that govern the association of primary amides18, was recently perturbed by our discovery that inclusion of an aggressive type of guest molecule, such as DMSO, changes the molecular conformation of dibenzoyltartrdiamide from highly populated T to a drastically less populated G– form (Figure 9).19 What stimulates the conformational change? There are two strong driving forces that influence the packing of (R,R)-O,O’-dibenzoyl tartardiamide molecules. First, the amide trans hydrogen tends to form NHtrans …O=C hydrogen bonds between molecules related by a unit translation of approximately 5Å (the

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C(4) motif). This motif is reproduced persistently in all symmetrically substituted tartrdiamides so far investigated, both primary and secondary, despite the presence of other hydrogen bond functional groups in these structures. The second driving force is the competition between the strongest hydrogen-bond acceptors for the strong NHcis amide donor. The list of possible acceptors includes the amide carbonyl oxygen (in which case solely the amide hydrogen bonds build the host matrix) and the oxygen atom from the guest molecule in which case the hydrogen bonds are used as host/guest connectors. Since in the formally zwitterionic DMSO the oxygen atom is known as a strong H-bond acceptor, the N-H groups would be expected to form H-bonds with that O atom above the carbonyl O atoms. In contrast to this, in the structures with included THF, pyridine and dioxane molecules neither THF and dioxane O atoms nor pyridine nitrogen atom are preferred to the carbonyl O atoms, so no host…guest hydrogen bonds are formed. How this change affects the packing mode? The basic supramolecular building block, that is the R 22 (14) ladder motif, is again present in the crystal, although in a slightly modified form. It differs from the previous one in that the two C(4) hydrogen bond chains that take part in the formation of the ladder run in opposite directions, as a result of conformational change within the molecule. The benzoyloxy substituents are now situated on one side of the ladder and so the ladder clearly gains its hydrophobic and hydrophilic sides. Two neighboring ladders have their hydrophilic sides directed inwards. In this way, the DMSO molecules take part in building double molecular layers that are roughly parallel to the (110) plane (Figure 9).

Figure 9. Packing of (R,R)-O,O’-Dibenzoyltartrdiamide molecules in G– conformation. The highlighted area marks the R 22 (14) ladder motif, consisting of two antiparallel C(4) chains.

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Was the conformational change of tartramide necessary? The observation, that in the presence of the sulfoxide group the host molecule is forced to change its molecular conformation to the high energy form, can be accounted for by the presence of two strong structure determining factors: one is a need to preserve hydrogen-bond ladder motifs, the other is to generate the hydrophilic sides accessible for the DMSO molecules. Underlying this explanation is the assumption that, in condensed media, formation of a polyamide supramolecular ladder motif is far more important than the maintenance of the preferred molecular conformation. With respect to packing of tartramide molecules, one further point deserves a comment. In the two ladder motifs the approach of the carbonyl oxygen by N–H hydrogen bond donor group is realized in a different way. In the ladder motif formed by parallel C(4) chains, the hydrogen approaches the carbonyl oxygen from the direction of one of its lone pairs (the average (N)–H…O=C angle amounts to 134(9)o), while in the ladder motif, build of antiparallel C(4) chains, the N–H and C=O vectors are nearly co-linear, giving the average (N)–H…O=C angle of 163(1)o. This observation brings about a question about the variation of hydrogen bond parameters and factors responsible for such variation. Owing to the softness of this kind of bonds and enormous variety of functional groups that possess the hydrogenbonding capability, differences in values of geometrical parameters that describe this type of bonding are to be expected. However, in cases where the functional groups involved in hydrogen bond interactions are chemically the same, the corresponding geometrical parameters might be expected to cluster around the same mean values. We shall further discuss this issue as we move to the next subtopic, which concerns concurrent hydrogen bond and dipolar interactions in NH-oxalamides 3. Hydrogen Bonds and Concurrent Dipolar Interactions in NH Oxalamides NH-oxalamides are capable of forming strong hydrogen bonds and robust cyclic motifs and contain highly polar functional groups, so we looked for concurrent hydrogen bond and local dipolar interactions as the prominent structure determining factors in this group of compounds20. We first examined conformational preferences of oxalic acid and its derivatives by inspecting the values of O=C–C=O torsion angles and the angles between CH/CO and NH/CO dipoles within one molecule. Distribution of the absolute values of the O=C–C=O torsion angle are illustrated in Figs. 10a to c in a form of histograms. Unlike oxalic acid and oxalates, which display variety of conformational rotamers along the C–C bond (Fig.10a), oxalic acid primary and secondary amides adopt only one type of conformation in which the carbonyl oxygens are trans (Fig. 10b). In tertiary oxalamides the

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situation is again more complex, as the absolute values of the O=C–C=O torsion angle cover the range from 80 to 140° (Fig. 10c).

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Figure 10. Distribution of the absolute values of the O=C–C=O torsion angles in oxalic acid its esters and salts (a), in N–H oxalamides (b) and in –NR2 xalamides (c).

All these observations clearly indicate that the coplanar arrangement of two carbonyl bonds, which are part of the oxalate skeleton, is not specific to all oxalic acid derivatives but only to oxalic acid NH amides. This can be explained by a tendency of NH oxalamides to form intramolecular NH…O hydrogen bonds that close five membered ring (the S(5) pattern designator)11. There might be two such hydrogen bonds in one oxalamide molecule (Figure 11). This type of interaction must have a strong electrostatic component coming from interactions between two pairs of antiparallel NH/CO dipoles. The angle between such dipoles is in the range 150 to 180° with an average value of 171 (3)°. Moreover, secondary oxalamides that possess CH group bonded to the nitrogen atom display a

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tendency to situate these CH dipoles antiparallel with respect to the CO dipoles in the 1,3-position. (Figure 11).

Figure 11. Multiplication of intramolecular dipole-dipole interactions (dipoles marked by arrows) resulting from favourable antiparallel arrangement of local NH/CO and CH/CO dipoles, as observed in JAGXOV21.

In the crystal, oxalamides form two types of hydrogen bond cyclic motifs, the well known. R 22 (8) amide motif and the R 22 (10) oxalamide motif (Figure 12).

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Figure 12. R 2 (8) and R 2 (10) hydrogen bond motifs in oxalamide crystal.

Aleman and Casanovas pointed out22 that the two types of hydrogen bonds display different geometrical characteristics. We have therefore performed a CSD search10 for the two specific ring motifs. The hydrogen bonds were characterized by three sets of angles: the angle on the hydrogen atom, the angle on the oxygen acceptor and the angle between dipoles

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formed along the hydrogen bond. The R 22 (8) motif formed by primary amides, appeared 1353 times in the CSD. The average N–H…O(=C) angle was 168(6)° (Figure 13a) while the angular distribution of proton donors around the carbonyl acceptor, i.e. the (N)H…O=C angle was approximately 121(5)° (Figure 14a). The R 22 (10) motif formed by oxalamides (68 hits) had the N-H…O(=C) angle less linear, the mean value being 153° (6) (Figure 13b) but the angle on the carbonyl acceptor, i.e. the (N)H…O=C angle, adopted nearly the same mean value of 158 (6)° (Figure 14b). 1400

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Figure 13. Distribution of the values of the NH…O(=C) angle in the amide R 2 (8) (a), and 2 the oxalamide R 2 (10) (b) ring motifs.

70

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Figure 14. Distribution of the values of the (N)H…O=C angle in the amide R 2 (8) (a), and 2 the oxalamide R 2 (10) (b) motifs.

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However, what distinguished the two systems of hydrogen bonds the most, was the mutual orientation of N–H and C=O dipoles formed along the same hydrogen bond. The mean value of the angle between the two dipoles summed 63(5)° (Figure 15a) and 10(4)° (Figure 15b) in R 22 (8) and R 22 (10) motifs, respectively. 1600

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Figure 15. Distribution of the values of the angle between N–H and C=O dipoles formed 2 2 along the hydrogen bond in the amide R 2 (8) (a), and the oxalamide R 2 (10) motifs (b).

Hence, when it comes to the intermolecular interactions, geometrical parameters describing the hydrogen bonded R 22 (10) dimer (built up of two N-Htrans…O=C hydrogen bonds running in opposite direction) differ from those describing typical R 22 (8) amide dimer in the angle on the accepting oxygen and in the angle between dipoles formed along the hydrogen bond. The observed difference in geometry between analogous pairs of hydrogen bonds, formed by the same functional groups has prompted us to ask the question about the nature of the two types of interactions. As the two vectors formed along the interacting N–H and O=C groups are parallel in the case of the R 22 (10) oxalamide ring motif, and that electron density favors the dipole formation along these bonds, the driving force for the formation of oxalamide type of dimer seems to be the dipole-dipole interaction. The value of the angle between dipoles lying along the hydrogen bond is a very sensitive measure if two vectors (bonds) are parallel – much more sensitive than (pseudo) torsional angles or angles measured with each atom being a vertex. We may conclude this part by stating that the dominance of local dipolar interactions rationalizes the adoption of the extended T conformation by NH-oxalamides and formation of the oxalamide R 22 (10) dimers. All these findings point to the dominant role of

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local dipole-dipole interactions in the stabilization of molecular conformation and supramolecular association of N-H oxalamides in a form of parallel layers. 4. Halogen Bonds and Dipolar Interactions Compete with Hydrogen Bonds in Formation and Stabilization of Layers in Crystals of Dihalo-Substituted Maleimide Derivatives Halogen bonding is much less recognized as a widely occurring type of noncovalent interaction than hydrogen bond. Organic halogen fragments (C-Hal) form halogen bonds most commonly with organic bases, e.g. N or O (but potentially also with other halogens) and geometry of this interaction is commonly described by the same set of parameters as a hydrogen bond. Hassel and Romming23,24 first established the existence of attractive interactions between bonded halogen and oxygen atoms in molecular complexes. As to the nature of these interactions, they considered them as a charge transfer between an electron pair donor (O, N, S) and an electronpair acceptor (halogen). Politzer and co-workers25 provided explanation for the occurrence of halogen bond in terms of the presence of regions of positive electrostatic potential on the outermost portions of covalently bonded halogen atoms. Metrangolo, Pilati and Resnati stressed that due to the highly anisotropic electron density around the Cl, Br and I nucleus, these atoms exhibit electrophilic character along the C–Hal bond (partially positive charge along the sigma bond) and nucleophilic character along direction perpendicular to this bond26. A search of the Cambridge Crystallographic Data Base performed by Allen and co-workers27 illustrated the directionality of this type of interaction and lead Nyburg and Faerman28 to postulate an elliptic effective van der Waals radius for F, S, Cl, Se, Br and I bonded to carbon, with the effective atomic radius being smaller along the C–Cl bond and longer in the direction perpendicular to this bond. We have investigated 2,3-dichloro and dibromomaleimides by X-ray crystallography and compared the obtained results with the quantum chemical calculations performed by Hoffmann29. The combined approach of crystal structure analysis and quantum chemical calculations has proven to be extremely powerful in investigating non-bonded interactions20,30,31. In 2,3-dihalomaleimides the carbon bound halogen atoms are close to the imide cabonyl oxygens, so in fact they are situated in strong electron withdrawing environment. This results in an overall strong attractive halogen…oxygen interaction in which chlorine or bromine atoms are involved. The electrostatic potential around F, Cl, Br and I in 2,3dihalomaleimides is illustrated in Figure 16.

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Figure 16. The B3LYP/SDD computed electrostatic potential around molecules of 2,3difluoro, 2,3-dichloro- and 2,3-dibromo- and 2,3-diiodomaleimide29. Color ranges from red most negative to blue most positive.

As can be seen from this Figure, F atom behaves differently form other halogens, as it does not exhibit positive electrostatic potential along the C–F sigma bond. In the other halogens the positive electrostatic potential increases in the order Cl, Br, I, indicating an increase of the ability of halogen bond formation. In the crystal, strong attractive halogen…oxygen interactions, in which chlorine or bromine atoms are involved, compete with strong NH…O(=C) hydrogen bonds. There might be a variety of ways, in which the formation of hydrogen and halogen bond, and packing requirements are satisfied. This is well seen in the case of 2,3-dichloromaleimide, which displays concomitant polymorphism. The two forms differ in crystal symmetry and chirality. Monoclinic crystals of 2,3-dichloromaleimide (space group P21/c) display layered packing, very similar, but not identical, to the packing found in 2,3-dibromomaleimide crystals (Figure 17).

Figure 17. Layered motif found in the monoclinic crystals of 2,3-dichloro- and 2,3dibromomaleimide. The layer is build of concurrent hydrogen and halogen-bonds. Shaded area marks the tape motif build solely of halogen bonds.

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In monoclinic 2,3-dichloro- and 2,3-dibromomaleimide crystal structures, the N–H…O=C hydrogen bonds and C–Hal…O=C interactions operate within molecular layer and form two types of supramolecular tapes, fused together: one constituting solely of halogen bonds and the other of mixed hydrogen and halogen bonds. In between the layers operate dipolar C=O/C=O and C=O/C–Cl interactions.

Figure 18. Part of the supramolecular motif found in tetragonal crystals of 2,3-dichloromaleimide. The halogen-bonded tape motifs (shaded area) are connected in a helical manner by N–H…O(=C) hydrogen bonds.

The other of the 2,3-dichloromaleimide polymorphs provides chiral crystals (space group P41212), in which the halogen bonded molecules form tapes, hydrogen bonded in a helical manner (Figure 18). Surprisingly, the dibromo analogue does not exhibit any indications of polymorphism. Kumar et al.32 described similar behavior of chloro- in contrast to bromo- derivatives. Observed in both polymorphic forms of dichloromaleimide antiparallel or nearly antiparallel arrangement of pairs of C–Cl/C=O and C–Cl/C–Cl bonds brings additional support to the concept that, at least in some cases, mutual orientation of molecules is dictated by local dipolar interactions. 4.1. HALOGEN/METHYL EXCHANGE

The structure-determining role of halogen bonds is convincingly illustrated by comparing the crystal structures of 2,3-dihalomaleimides with that of 2,3-dimethylmaleimide. Chlorine and methyl substituents have similar size (21 vs 19 Å3, respectively) so it seems plausible that Cl/methyl interchanged molecules will form similar crystal structures, if the close packing principle33 is the one that dominates the packing. It turns out that 2,3-dimethylmaleimide crystals, which lack the ability to form halogen bonding, display different packing from both dihalogen derivatives (Figure 19). This is an indication that different electronic properties of methyl and halogen substituents are more important than the close packing principle.

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Figure 19. NH…O(=C) hydrogen bonds (thin lines), face stacking (shaded areas) and C=O/C=O dipolar interactions (atoms represented as spheres, dipoles marked by arrows) stabilize the crystal structure of 2,3-dimethylmaleimide.

5. Conclusions We have demonstrated that local dipolar interactions may play a key role in understanding conformational preferences of molecules and in designing the hydrogen bonded supramolecular assemblies. Additionally, the structurally defining role exerted by halogen bonding interactions has been documented. Presented examples illustrate that concurrent hydrogen and halogen bonds, and local dipolar interactions constitute essential driving forces in the formation of extended layered crystal structures although in specific cases may lead to diverse recognition patterns and hence to polymorphism.

References 1.

J. Gawro ski, K. Gawro ska, Tartaric and Malic Acids in Synthesis, A source Book of building Blocks, Ligands, Auxiliaries, and Resolving Agents, J. Wiley & Sons. INC, New York, 1999.

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U. RYCHLEWSKA F.J. Martinez-Martinez, I.I. Padilla-Martinez, M.A. Brito, E.D. Geniz, R.C. Rojas, J.B.R. Saavedra, H. Hopfl, M. Tlahuextl, and R. Contreras, Three-center intramolecular hydrogen bonding in oxamide derivatives. NMR and X-ray diffraction study, J. Chem. Soc., Perkin Trans. 2, 401–406 (1998). F.A. Cotton, C.Y. Liu, C.A. Murillo, D. Villagran, and X. Wang, Modifying Electronic Communication in Dimolybdenum Units by Linkage Isomers of Bridged Oxamidate Dianions, J. Am. Chem. Soc. 125, 13564–13575 (2003). M.D. Santana, G. Garcia, M. Julve, F. Lloret, J. Perez, M. Liu, F. Sanz, J. Cano, and G. Lopez, Oxamidate-Bridged Dinuclear Five-Coordinate Nickel(II) Complexes: A Magneto-Structural Study, Inorg. Chem. 43, 2132–2140 (2004). M.F. Rastegar, E.K. Todd, H. Tang, and Z.Y. Wang, A New Class of Near-Infrared Electrochromic Oxamide-Based Dinuclear Ruthenium Complexes, Organic Lett. 6, 4519–4522 (2004). T.L. Nguyen, F.W. Fowler, and J.W. Lauher, Commensurate and Incommensurate Hydrogen Bonds. An Exercise in Crystal Engineering, J. Am. Chem. Soc. 123, 11057– 11064 (2001). J. von Sonntag, W. Knolle, Maleimides as electron-transfer photoinitiators: quantum yields of triplet states and radical-ion formation, J. Photochem. Photobiol. A: Chemistry 136, 133–139 (2000). H. D. King, Facile synthesis of maleimide bifunctional linkers, Tetrahedron Lett. 43, 1987–1990 (2002). S.G. Bodige, M.A. Méndez-Rojas, W.H. Watson, Structure and properties of Nphenylmaleimide derivatives, Journal of Chemical Crystallography 29, 57–66 (1999). F.H. Allen, The Development, Status and Scientific Impact of Crystallographic Databases, Acta Cryst. A54, 758–771 (1998). J. Bernstein, R.E. Davis, L. Shimoni, N.L. Chang, Graph-Set Analysis of HydrogenBond Patterns in Organic Crystals, Angew. Chem. Int. Ed. 34, 1555–1575 (1995). J. Gawro ski, A. Długoki ska, J. Grajewski, A. Plutecka, U. Rychlewska, Conformational Response of Tartaric Acid to Derivatisation: Role of 1,3-Dipole–Dipole Interactions, Chirality, 17, 388–395 (2005). M. Yamashita, K. Okuyama, I. Kawasaki, S. Ohta, Stereoselective dimerization of keto amides using samarium diiodide, Tetrahedron Lett. 37, 7755–7756 (1996). J. Gawro ski, K. Gawro ska, N. Wa ci ska, A. Plutecka, U. Rychlewska, Tartaronitriles – the Derivatives of Tartaric Acid with a Bent Conformation, Polish J. Chem. in press. U. Rychlewska, B. War ajtis, Interplay Between Dipolar, Stacking and Hydrogen Bond Interactions in the Crystal Structures of Unsymmetrically Substituted Esters, Amides and Nitriles of (R,R)-O,O’-Dibenzoyltartaric Acid, Acta Cryst. B57, 415–427 (2001). U. Rychlewska, B. War ajtis, Isostructuralism in a Series of methylester/Methylamide Derivatives of (R,R)-O,O’-Dibenzoyl Tartaric Acid; Inclusion Properties and GuestDependent Homeotypism of the Crystals of (R,R)-O,O’-Dibenzoyltartaric Acid Diamide, Acta Cryst. B58, 265–271 (2002). W.D.S. Motherwell, G.P. Shields, F.H. Allen, Graph-set and packing analysis of hydrogen-bonded networks in polyamide structures in the Cambridge Structural Database, Acta Cryst. B56, 857–871 (2000). J. Bernstein, M.C. Etter, L. Leiserowitz, The Role of Hydrogen Bonding in Molecular Assemblies, in Structue Correlation, H.B. Bürgi, J.D. Dunitz Eds. VCH Verlagsgesellshaft, mbH, Wienheim, v. 2, pp 431–507, 1994

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19. U. Rychlewska, B. War ajtis, Inclusion Properties of (R,R)-O,O’-Dibenzoyltartrdiamide: Influence of the Guest on the Molecular Conformation of the Host, J. Mol. Struct. 647, 141–150 (2003). 20. M. Hoffmann, U. Rychlewska, B. War ajtis, The Role of Multiple Parallel and Antiparallel Local Dipoles for Molecular Structure and Intermolecular Interactions of Oxalamides, CrystEngComm 7, 260–265 (2005). 21. Z. Stefanic, B. Kojic-Prodic, Z. Dzolic, D. Katalenic, M. Zinic, A. Meden, Hydrogen bonding in N,N'-bis[(1S)-2-azido-1-(2-methylpropyl)ethyl]oxalamide: twofold symmetry of R 22 (10) hydrogen-bonded dimers connected into an -network, Acta Cryst. C59, 0286-0288 (2003). 22. C. Alemán, and J. Casanovas, Analysis of the oxalamide functionality as hydrogen bonding former: geometry, energetics, cooperative effects, NMR chemical characterization and implications in molecular engineering, J. Mol. Struct.: THEOCHEM 675, 9–17 (2004). 23. O. Hassel, Chr. Rømming, Direct structural evidence for weak charge-transfer bonds in solids containing chemically saturated molecules, Q. Rev. Chem. Soc. 16, 1–18 (1962). 24. O. Hassel, Nobel Lecture (June 9, 1970) http://nobelprize.org/nobel_prizes/chemistry/ laureates/1969/hassel-lecture.html 25. P. Politzer, P. Lane, M.C. Concha, Y. Ma, J.S. Murray, An overview of halogen bonding, J. Mol. Mod. 13, 305–311 (2006). 26. P. Metrangolo, T. Pilati, G. Resnati, Halogen bonding and other noncovalent interactions involving halogens: a terminology issue, CrystEngComm, 8, 946–947 (2006). 27. J.P. Lommmerse, A.J. Stone, R. Taylor, F.H. Allen, The Nature and geometry of Intermolecular Interactions between Halogens and Oxygen or Nitrogen, J. Am. Chem. Soc. 118, 3108–3116 (1996) and references therein. 28. S.C. Nyburg, C.H. Faerman, A Revision of van der Waals Atomic Radii for Molecular Crystals: N, O, F, S, Cl, Se, Br and I Bonded to Carbon, Acta Cryst. B41, 274–279 (1985). 29. M. Hoffmann, Halogen Bonding, Lithium Bonding and Dipole Dipole Interactions: Usefulness of Quantum Chemical methods in Studies of Weak Interactions, Adv. Chem. Info. 1, 29–42 (2007). 30. M. Hoffmann, A. Plutecka, U. Rychlewska, Z. Kucybala, J. Paczkowski, I. Pyszka, New Type of Bonding Formed from an Overlap between Aromatic and * C=O Molecular Orbitals Stabilizes the Coexistence in One Molecule of the Ionic and Neutral meso-Ionic Forms of Imidazopyridine, J. Phys. Chem. A 109, 4568–4574 (2005). 31. V. Patroniak, A.R. Stefankiewicz, J.-M. Lehn, M. Kubicki, M. Hoffmann, SelfAssembly and Characterization of Homo- and Heterodinuclear Complexes of Zinc(II) and Lanthanide(III) Ions with a Tridentate Schiff-Base Ligand, Eur. J. Inorg. Chem. 1, 144–149 (2006). 32. V.S.S. Kumar, F. Ch. Pigge and N. P. Rath, Polymorphism in 1,3,5-triaroylbenzenes: structural characterization of concomitant polymorphs obtained from 1,3,5-tris(4chlorobenzoyl) benzene, CrystEngComm, 6, 102–105 (2004). 33. A.I. Kitajgorodskij, Molecular Crystals and Molecules (Academic Press, New York, 1973).

SIGNALLING BY MODULATION OF INTERMOLECULAR INTERACTIONS

JANET L. SCOTT* School of Chemistry, Monash University, Wellington Road, Clayton, Victoria 3800, Australia; [email protected] KOICHI TANAKA Department of Applied Chemistry, Faculty of Engineering & High Technology Research Center, Kansai University, Suita, Osaka 564-8680, Japan

Abstract. The importance of intermolecular interactions in the solid-state for modulation of material properties useful for signaling is discussed. Specifically, the genesis of crystalline solvatochromism; crystalline fluorescence and crystalline photochromism is considered.

Keywords: solid-state chromogenicity; solid-state fluorescence; photochromic crystals; intermolecular interactions; crystal structure

1. Introduction Spectral changes in response to an event, including guest binding/ dissociation, or external stimulus, such as change in temperature, are a form of signal transduction. In particular, changes that lead to simple read-outs, such as modulation of colour or luminescence, are of interest in sensor development,1,2 as well as having applications in information storage and optical switching, to name just a few applications.3 Sensor systems that rely on a simple colour change, to signal an event, are preferred over more complex reporting mechanisms such as mass changes detected by specialist instruments (for example, quartz crystal microbalance (QCM) systems4), for ease of application, particularly in “field” or labelling applications. Spectral changes in solution, due to binding events with analytes or guests, including fluorescence enhancement5,6 (or fluorescence quenching7) or colour changes8 are frequently used in sensing applications, but such 429 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 429–447. © 2008 Springer.

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phenomena are rarer in the solid-state. Various possibilities exist for effecting chromogenic responses in crystalline solids and these may be classified according to the phenomenon leading to the effect, as eloquently described by Favaro et al.9 They include responses to both physical (heat, light pressure, electric field) and chemical (complexing agents, pH change) stimuli – thus an effect due to heating is “thermochromism”, one due to light, photochromism and so on.9 While such phenomena have been widely described for metal coordination complexes10 and metal ion containing host:guest systems,11 here we will focus on some specific examples of colour or luminescence changes in organic crystalline materials due to: • host:guest complex formation leading to crystalline solvatochromism,* • host:guest complex formation leading to crystalline fluorescence, and • single crystal-to-crystal photochromism. Weak intermolecular interactions are of great importance in these systems and, in the latter two, specific interactions that are significant only in the crystalline state, are required for a noticeable effect. 2. Responsive Crystals 2.1. CRYSTALLINE “SOLVATOCHROMISM”

Solvatochromism, the phenomenon whereby a compound changes colour according to its environment, specifically the solvent, has been widely used to probe polarity.12 Specific “solvatochromic probes” that allow an estimate of relative polarity by consideration of colour of the analyte (probe) have been widely applied.13 Azobenzenes tend to be highly coloured, with the position of λmax dependent on substituents,14 hydrogen-bonding and geometry.15 Colour changes associated with cis/trans isomerism, effected by irradiation with visible light,16 have been employed in a plethora of “switching” or “signalling” applications,17 however, this transition, requiring gross molecular motion, is usually suppressed in the crystalline form. The electronic transitions of coloured trans-azobenzene compounds have been widely studied and the lowest energy absorption is ascribed to a (formally forbidden) n→π* transition18 which, Robin and Simpson suggest, gains intensity by mixing with the strong, low frequency azo-dye ‘colour’ band.19 The transition energies, and hence colour, are determined “primarily by the local symmetry *

Described as “coordination-chromism” by Favaro,9 we prefer “crystalline solvatochromism” as this phenomenon closely parallels solution phase solvatochromism.

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of the azo group”20 and an increase in π electron conjugation is reflected in N-C(aromatic) bond contraction and N=N bond expansion or a decrease in double bond character of the azo bond.21 Protonation to yield the azonium cation also results in significant shifts to longer wavelength, although steric factors are also important.22 A group of azobenzene based “dogbone” host compounds have been prepared by coupling of dibromoazobenzenes with 1,1-diphenylprop-2-yn1-ol. Ortho 1, meta 2 and para 3 hosts all exhibit wide ranging formation of host:guest complexes (Table 1) and, in each case, the guest free host crystals are yellow while inclusion complexes are orange to orange-red in colour.23,24,25 Thus these host compounds exhibit “crystalline solvatochromism” (Figure 1), which mirrors that noted in solution. This solution phase colour change may be used to screen for suitable guests and, to date, no inclusion complexes have been isolated from solutions that retain the host alone yellow colour upon guest addition.25 This phenomenon indicates that the effect is more specific than a simple indication of polarity or hydrogen-bond acceptor capacity of the added guest but instead is indicative of association of host and guest in solution, the first step in the chain of events leading to nucleation and growth of an inclusion complex crystal.

Figure 1. The crystalline inclusion complex of 3 with pyridine (left) is bright orange/red while the desolvated material (right) is yellow.

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Colour changes, from orange/red to yellow (Figure 1), may be effected by desolvation on heating, Table 1, or from yellow to orange/red on absorption of guest vapours from a saturated atmosphere.23 This solid-phase solvatochromism is reflected in solution, providing a rapid screening mechanism for the likely formation of host guest complexes.25 TABLE 1. Coloured host:guest complexes of trans-azobenzene “dogbone” hosts 1 Guest

H:G

– THF dioxane

2 colour

colour

1:2 1:2

yellow orange orange

1:1 1:2

orange orange

yellow

CH3CN cyclopentanone

3

H:G

H:G

colour yellow

γ-butyrolactone DMF DMSO

1:2 1:2

red red

1:2 1:2 1:1

orange orange orange

1:2 1:2 1:2

orange red orange

pyridine

1:2

orange

1:2

orange

1:3

orange

3-acetylpyridine

1:1

4-acetylpyridine morpholine piperazine MeHN(CH2)2NHMe

1:1 1:1:(2)* (PhMe)

Me2N(CH2)3NMe2 N-methylimidazole 2,2,6,6-tetramethylpiperidine

1:2

orange/red

1:1:(1) (DCM) 1:2

orange/red

1:1

orange

orange

orange

Me2NCH2NMe2 Me2N(CH2)2NMe2

orange *

1:2

red

1:1:(1)* (DCM) 1:2

orange orange

1:2

orange

1:2

orange/red

1:2

orange

1:2

orange/red

* number of moles of the 2nd guest (solvent), the identity of which is provided in parentheses.

Single crystal structure analysis of guest-free host crystals and various H:G complexes reveals vastly different packing modes, (and guest release temperatures, Table 2) even in similar complexes (Figure 2), but it is the distinct differences in molecular geometry and intermolecular interactions, rather than gross packing effects (which frequently serve to maximise the occurrence of phenyl embraces, such as those described by Scudder and Dance26), that are responsible for colour changes.

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All molecules, which act as guests in these complexes, are H-bond acceptors and form H-bonded complexes with the host OH group. In the absence of H-bond acceptor guests the N=N group acts as an H-bond acceptor (Figure 3) leading to small, but significant, changes in bond lengths and angles of the azobenzene core. TABLE 2. Guest release temperature for a range of H:G complexes Host 1 1 2 2 2 2 2 2 2 2 3 3 3 3

guest DMF DMSO THF dioxane CH3CN cyclopentanone γ-butyrolactone DMF DMSO pyridine γ-butyrolactone DMF DMSO pyridine

T/°C 173 142 87 91 105 93 131 94 154 102 93 93 130 81

c

a

0

0

b

b

Figure 2. Different packing modes of meta host inclusion complexes. 2•DMSO (left) forms H-G-H- H-bonded tapes and 2•2DMF (right) forms discreet G-H-G H-bonded units. Guests are accommodated in channels in both structures (inserts, bottom right). New J. Chem., 2002, 26, 1822-1826 - Reproduced by permission of The Royal Society of Chemistry.

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The most obvious effect on molecular geometry is in the twist angle of the azobenzene core i.e. the dihedral angles between the azo core and aromatic rings. Analysis of a large number of crystal structures reveals that the twist angle for the host alone is always greater than for inclusion complexes and there appears to be some correlation between twist angle and N=N bond length, indicating differing degrees of conjugation, Table 3.24 The colour change however, appears to be due to the double H-bond acceptor nature of the azo group in the host alone structures. The formation of hydrogen bonds to the azo group may be considered as the first step along the continuum to the formation of azonium cations and, as such, would be expected to yield a shift to longer λ in the absorption spectrum.22 Oddly, the converse is seen, indicating that the colour change is a subtle interplay of degree of conjugation and degree of protonation. O1-H1…N1: O1...N1 = 2.921 ; O1-H1O = 1.13; H1O...N1=1.797; OHO = 170 º Tors: N=N-C(Ar)-C(Ar) = 155 º

1.428 Å 1.262 Å 114.3 º

1.423 Å 1.270 Å 114.1 º O1-H1…N1: O1...N1 = 3.019 Å; O1-H1O = 0.94 Å; H1O...N1=2.110 Å; OHO = 162 º Tors: N=N-C(Ar)-C(Ar) = -162 º

Figure 3. Hydrogen bonding to the azo core as seen in crystal structures of 1 and 3 (solventfree crystals of 2 suitable for crystal structure analysis have not been obtained). Bulky endgroups have been omitted in the acceptor molecules for clarity. TABLE 3. Comparison of geometric parameters and twist angles (defined by N=N-C-C(Ar) torsion angle) of the azo core for 1, 3 and DMF inclusion complexes of each

1 1•2DMF 3 3•2DMF 3•2DMFa a

d N=N/Å

d N-C/Å

∠ N=N-C/º

∠ N=N-C-C/º

1.262 1.251 1.270 1.257 1.262

1.428 1.421 1.423 1.432 1.424

114.3 113.7 114.1 113.2 114.0

30.3 20.9 21.5 16.5 12.6

two ½ hosts in the asymmetric unit

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The azobenzene core of the ortho host is planar in some cases (e.g. ortho host with 2-N-methylimidazole) and staggered in others (e.g. ortho host with DMF), and, indeed, staggered and flat in the same structure (e.g. ortho host with 2DMSO). That of the para and meta hosts tend to be staggered to greater or lesser degrees, as reflected by the torsion angle N=N-C(Ar)-C(Ar). HO

HO Ph

N

N

Ph Ph

Ph 4

Subtle intermolecular interactions and changes in geometry of the azobenzene core are also apparent in the simpler chromogenic host 427 and these have been probed by consideration of features contained in Hirshfeld fingerprint plots, derived from Hirshfeld surfaces, computed using the programme Crystal Explorer.28 (For a clear discussion of the use of such “fingerprint” plots see Spackman et al. 29) The Hirshfeld surface, a 3-D isosurface, effectively defines the molecular volume in the crystal.30,31 In the plots presented here, the distance from the surface to the closest atom outside the surface, de, is mapped with “cold” colours representing longer values of de, and “hot” colours short values of de - thus, red “hotspots” indicate close contacts with neighbouring molecules. Intermolecular interactions such as the OH···N hydrogen bond of the non-solvate crystal is clear, as is the CH···π interaction between pyridine guest and diazobenzene aromatic ring, detailed in Figure 4.32 a

b

x

y1

N N

y2

N N

z

Figure 4. Hirshfeld surfaces for 4 in a) the non-solvated crystal and b) the 4·2pyridine crystal, viewed perpendicular to the azobenzene core. The orientation of Ar-N=N-Ar groups is represented by molecular diagrams overlaid in black with the H-bonded OH group (neighbouring host) and pyridine guest molecules depicted in “stick” mode. Redder surface coloration indicates close contacts, thus the OH···N H-bond (labeled x) is clearly visible. In (b) a CH···π interaction of the pyridine guest with the diazobenzene Ar ring and one terminal phenyl ring is clearly visible (labeled y1 and y2). The subtle “spoked wheel” shape, labeled z, in (a) is indicative of an overlaid Ar ring and, indeed, molecules of 4 are π-stacked with each azobenzene group offset from that below (inset). Reproduced with permission from Cryst. Grow. Des., 2007, 7, 1049–1054. Copyright 2007, American Chemical Society.

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Hirshfeld fingerprint plots, generated as 2-D representations of the quantities di (distance from the surface to the closest atom internal to the surface) and de30 allow direct comparison of intermolecular interactions. Fingerprint plots for the entire molecule of 4 in each crystalline environment and two guests, pyridine and dioxane, are presented Figure 5. The plots for molecules of 4 in host:guest lattice inclusion complexes provide information about specific types of intermolecular interactions: the long “horns” in Figure 5a indicate hydrogen-bond interactions: in 4 alone, both acceptor and donor groups are part of the unsolvated molecule 4, but, in the solvate crystals the host OH group acts as the hydrogen-bond donor, a

4 unsolvated

b

d

4 pyridine solvate

c

4 pyridine solvate

e

4 dioxane solvate

4 dioxane solvate

Figure 5. Hirshfeld fingerprint plots for 4 (a-c) and guests (d,e) in the non-solvate crystal, pyridine solvate crystal and dioxane solvate crystal. Reproduced with permission from Cryst. Grow. Des., 2007, 7, 1049-1054. Copyright 2007, American Chemical Society.

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while the guest N or O atoms are acceptors. Considering host and guest fingerprint plots side by side makes this quite clear. For example in Figure 5b the long “horn” due to the OH donor is reflected in the pyridine guest (in the crystal) as a similar feature denoting the acceptor interaction. While hydrogen bond donor/acceptor type interactions may be anticipated and thus are readily detected by examination of close contacts, other, more subtle intermolecular interactions, are often more difficult to discern. Specific features in the fingerprint plots point to these: in the pyridine fingerprint, the small feature indicated by an arrow in Figure 5d, when examined, yields information about a CH···N interaction (ortho C-H to neighbouring pyridine guest), which might have gone undetected otherwise. In the host plot, Figure 5b, the double “wings” on the acceptor side (di>de) indicate two different types of CH···π acceptor interactions. Similarly, the plot for the 1,4-dioxane guest, exhibits a “wing” on the donor side (de>di), which, on examination, proves to relate to CH···π interactions between methylene H-atoms and host aromatic rings. This in a crystal structure that, at first, seems to show a lack of optimized (Ar)CH···π interactions and certainly none of the phenyl embraces that one might predict in crystal structures of molecules such as 4. 2.2. CRYSTALLINE FLUORESCENCE

A subset of “crystalline solvatochromism” is crystalline fluorescence and a class of fluorene/fluorenone based host compounds 5 and 6 have been prepared by Pd(II)-catalysed coupling reactions33,34 in similar fashion to the hosts described above. These compounds also exhibit guest dependent colour changes, Figure 6, but similar to Ogawa’s observation of fluorescence in salicylideneanilines,35 the colour changes are due to changes in solid-state fluorescence rather than changes in absorption spectra. Thus the colours are modulated from bright acid-yellow, through orange-yellow to orange, reflecting highly fluorescent materials to those that are nonfluorescent, Figure 7. It is noteworthy that 5, 6a and 6b are not fluorescent in solution at ambient T but that the crystalline fluorescence is quite marked. Crystals are effectively ultra-pure phases which, if free of porous channels or similar, preclude fluorescence quenching by quenchers such as oxygen. Changes in fluorescence must therefore be due to changes in the molecular environment within the crystal. 5 (fluorenone based) is found to form fluorescent crystals where strong intermolecular interactions such as H-bonding are absent and it is postulated that hydrogen-bonding to the fluorenone core, Figure 8, provides a non-radiative degradation mechanism, analogous to that seen in ROH solutions,36 leading to non-fluorescent, orange crystals.

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Figure 6. a) Spectral changes on guest complexation of 5 reflecting the colour of the crystalline complexes; b) reflected in the colours of the complexes with EtOAc (left), middle (no guest), pyridine (right).

Figure 7. Enhanced fluorescence of 5 on complexation of guests is reflected in a) the fluorescence spectrum of crystalline 5 with no complexed guest and of the inclusion complex of 5 with pyridine and b) in the colours and fluoresecence exhibited by the crystalline solids. Top crystalline complexes of TMEDA (left); ethyl acetate (middle) and pyridine (right) under white light (top) and UV light (bottom). (Solutions of the host are not fluorescent). New J. Chem., 2004, 28, 447–450 - Reproduced by permission of The Royal Society of Chemistry (RSC) on behalf of the Centre National de la Recherche Scientifique (CNRS).

Removal of the carbonyl H-bond acceptor, as in hosts 6a and b (fluorene based), yields hosts which cannot accept strong intermolecular interactions to the fluorene core. These compounds shows variable wavelength solidstate fluorescence (Figure 9), in a range of crystalline complexes (Table 4). The non-fluorescent complexes, such as that formed between 6b and ethyl

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acetate, do not exhibit excimers, formed by stacking of the fluorene cores, thought to be responsible for fluorescence in these complexes, Figure 10.37 All fluorescent crystalline materials examined exhibit aromatic/ aromatic interactions of the fluorene cores and the modulation in colour of fluorescence is ascribed to the differences in Ar/Ar registration and interplanar distances of these moieties.

Figure 8. 5·ethyl acetate complex showing H-bonding to the fluorenone core, which may provide a non-radiative decay mechanism leading to fluorescence quenching in the ethyl acetate complex.

Figure 9. Photographs of clusters of crystals of the 6a·DMF complex (left) and 6a (right) under a) ambient light and b) 254 nm light. Reprinted with permission from Bull. Chem. Soc. Jpn., 2004, 77, 1697–1701. TABLE 4. Host:guest ratio and fluorescence of inclusion complexes of 6a and 6b Guest methanol acetone dioxane N,N-dimethylformamide N,N-dimethylacetamide dimethylsulfoxide pyridine

6a:G 1:1 1:1 1:1 1:1 1:2 1:1 1:3

fluorescence blue blue yellow yellow blue blue blue

6b:G – 2:1 1:1 1:1

fluorescence – no blue blue

1:1 1:1

no blue

triethylamine N-methylpyrrolidine

– 1:2

– blue

1:1

no

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3.6 Å

3.5 Å

Figure 10. Intermolecular interactions in crystals of 6b with ethyl acetate (non-fluorescent) (left); 6a alone (top right) and 6a with complexed DMF (bottom right). The stacked pairs of fluorene moieties are absent in the non-fluorescent ethyl acetate complex of the host bearing bulky end groups.

2.3. CRYSTALLINE PHOTOCHROMISM

Photochromism, the development of colour on exposure to light, is relatively common in organometallic38 or hybrid organic/inorganic materials.39 If irreversible, this may represent write/read/store data storage, while reversible systems are write/read/erase systems. All organic systems are of interest in information storage, electronic display systems, optical switching devices and ophthalmic glasses, to name but a few applications.40 Most commonly photoresponse in such compounds is due to specific, detectable changes in structure or conformation including: bond forming/breaking reactions, as in fulgides,41 diarylethenes42 or spiropyrans;43 keto/enol tautomerisation, as in ohydroxy Schiff bases44 and pyrazolone derivatives;45 or one of these accompanied by ionization46 or radical formation,47 Scheme 1. Consequently, the photochromic response is often common to both solution and solid phases.48 R1

R1

O

O

Ph O

O

O

R3 R4

O

R3

R4

O

N

CF2

F 2C

O

ON+

N N

N+ S

S

S

Ar Cl

Cl CF2

-O S

NH Ar

F2 C

F2 C F 2C

O H

O Cl

Cl

O N

N+

-O

Scheme 1. Examples of photochromic systems: fulgides; diarylethenes; spiropyrans; ohydroxy Schiff bases; and nitroso ionic dimer/radical monomer.

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Some members of the families of propargylallenes 7 and 8, exhibit reversible photochromism in the solid-state but not in solution.49,50,51 As the photoresponse is limited to some compounds (indeed, some crystal forms!) a series of crystal structures of solvates and non-solvated crystals were examined with the goal of correlating structure and activity. Compounds 7a, 7b, 7e and 7f and many of 8 with e-donating Ar substituents (8b and 8d to 8g) exhibit rapid colour change from colourless or pale yellow to green or blue/green on exposure to light, Figure 11. The photoresponse is reversible, with fading times dependant on substitution of Ar rings, but in all cases bleaching may be substantially speeded by warming to ca 60ºC. In some cases no bleaching is noted at ambient temperature and the colour change is effectively irreversible unless the temperature is raised. Z3

C Z4 ArOC

Z1

COAr

Z2

7

Ar=Ph

a b c d e f g h

Z1, Z2, Z3, Z4 Cl, Cl, H, H Br, Br, H, H, H, H, Cl, Cl H, H, Br, Br Cl, H, Cl, H Br, H, Br, H Cl, Cl, Cl, Cl Br, Br, Br, Br

8 Z1=Z2=Z3=Z4=H a b c d e f g h i j

Ar C6H5 2-MeC6H4 3-MeC6H4 4-MeC6H4 2-MeOC6H4 3-MeOC6H4 4-MeOC6H4 2-ClC6H4 3-ClC6H4 4-ClC6H4

C

COPh

PhOC

Figure 11. Upon irraditation, many of the propargylallenes exhibit reversible thermochromism, changing from colourless or pale yellow to green.

The fluorene moiety is essential for photoresponse and crystals of 9 exhibit no colour change on exposure to light. Examination of a series of crystalline complexes reveals that, in all photoresponsive crystals the packing arrangement leads to parallel overlap of electron rich (allene terminus) and electron poor (alkyne terminus) fluorene moieties as

9

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442 a

b

c

d

e

f

Figure 12. Different packing motifs of photochromic and non-photochromic crystals. Electron rich (allene) fluorene moieties are coloured green and electron poor (alkyne) fluorene moieties are coloured red, terminal ArC=O groups have been removed for clarity and allene and alkyne moieties are represented as heavy bonds. a) 8f (photochromic) forming two types of infinite 1D ribbons with side-to-side, opposite end overlap; b) 8g: (photochromic) exhibiting 1D ribbons with opposite end-to-end overlap; c) 8d DMSO solvate (non-photochromic) side-to-side, opposite end overlap – pairs are isolated from each other and ribbon formation is frustrated; d) 8j (non-photochromic) “same end” overlap with unusual host conformation; e) 8j acetone solvate (non-photochromic) same end overlap and f) 8c DMSO solvate (non-photochromic) exhibiting overlap of alkyne terminus fluorene moieties yielding dimers isolated from each other by solvent molecules. Reproduced (in part) with permission from Cryst. Growth Des., 2005, 5, 1209–1213. Copyright 2005 American Chemical Society.

illustrated in Figure 12. In all cases infinite ribbons of opposite end overlap occur either in the most commonly seen end-to-end arrangement, or a side to side pattern as in Figure 12a. These 1-D strands of alternating but overlapping electron rich and electron poor fluorene moieties appear in all photochromic materials, even where inclusion complexes with solvents are formed. It is postulated that this allows for the formation of charge-transfer type interactions upon excitation with visible light. It is interesting to note that the colours and bleaching times of the same propargylallene host with different guest molecules may differ, but insufficient data, in the form of comparative crystal structure analyses, are available to discern whether this is due to modulation of Ar/Ar distances, degree of overlap, or direct interaction with the entrapped solvent. 2.4. THERMOCHROMISM

Many examples of transformations from solid starting materials to solid products exist and these have frequently been termed solid-solid reactions. This term should be taken only to mean that solid reagents are transformed into solid products although, analogous to the solid-solid reaction between 2 (or more) starting materials,52,53,54 the possibility of intervention of molten

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(albeit transient) or plastic intermediate phases should always be considered. While measuring the melting points of a series of propargylallene host compounds 7 and 8, sharp and distinct colour changes were noted. The colourless prisms of the propargylallenes converted, in an apparent crystal to crystal transformation to dark blue or brown crystals of 10. The reaction and accompanying phase change results in a large exotherm measured by Differential Scanning Calorimetry (DSC) analysis, Figure 13.55

ArOC Δ

Ar

O

C COAr 8

a b c d

Ar C 6 H5 4-MeC6H4 4-ClC6H4 4-MeOC6H4

Ar

O 10

The conversion of 7 or 8 into 10 is easily followed by infrared spectroscopy of powdered samples,55 but the hope that this represented a single crystal to single crystal transformation (such as the remarkable rearrangements accompanied by large molecular motions noted by Atwood and Barbour56) was dashed by the observation that the single crystal of 7 or 8 begins to show evidence of the development of a powder once a partial transformation to 10 has occurred. The arrangement of molecules in the crystals of 8a and 10 makes it appear that an intermolecular mechanism may compete with an intramolecular one, but experiments with unsymmetrically brominated molecules 7b and 7d yield only 11 implying an intramolecular mechanism as per the solution phase reaction.57

a b c d

Figure 13. DSC thermogram (left) showing large exotherm corresponding to the transformation of the propargylallene into the furofuran 10. The solid-solid transformation is also evident in the IR spectra (right), which evolve over time from a to d. Reprinted with permission from Eur. J. Org. Chem., 2003, 2035–2038.

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X1 Ph Δ

X1 C

O

O

COPh

PhOC

X2

X2

Br

Ph Br

7b 7d

X1 = Br; X2 = H X1 = H; X2 = Br

11

3. Conclusion The host compounds described (so-called because they have a distinct tendency to form inclusion complexes) exhibit varied visible readouts of guest binding or guest loss events as well as response to light or heat. In some cases the transformation is reversible, as in bleaching of photochromic crystals of propargylallenes 7, 8 and 9, but these may be combined with readouts of thermal events or, indeed, thermal history. Consider, for example, an inclusion complex or solvate, that exhibits photochromism in the solvated form, which upon conversion to a desolvated crystalline form loses the ability to develop colour in response to visible light: if this desolvation event occurs at a temperature lower than that required for relaxation or bleaching we have a tamperproof indicator for prior exposure to visible light (as in when a package has been opened and resealed). Any attempt to bleach the green colour by application of heat (the reversible photochromic response) will result in desolvation, yielding a non-photochromic material. Thus a newly received sealed package may be opened and the crystalline propargylallene indicators exposed to light – if no green colour develops, the package has (intentionally or coincidentally) been exposed to temperatures above the desolvation T (and the bleaching T). If combined in a label or bar code with a series of solvates that fluoresce (with desolvated phases that do not, or vice versa), e.g. some examples of complexes of 5 and 6, a combination of uv and visible light visualization may even provide a measure of what temperature a package has been exposed to, depending on which complexes are degraded by guest loss. A number of such combinations may be envisaged to provide very simply read “colour coded” history for a sample, product or package. Similarly, colour development in the presence of amines (by absorption to a differently coloured H:G compound as in compounds 1 to 4) may be a

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useful basis for detecting malodour arising from decomposition of some foodstuffs. In summary, signaling may be achieved, in a very simple manner, by modulation of intermolecular interactions of host compounds that “respond” to light by either absorption (colour) or emission (fluorescence and colour), or that develop charge complex interactions upon absorption of energy.

References 1. 2. 3. 4.

5.

6.

7. 8. 9. 10.

11.

12. 13. 14. 15.

For example: a) T.J. Novak, V.D. Henderson, J.A. Parsons, Anal. Lett., 1991, 24, 925– 934; b) T.J. Novak, V.D. Henderson, J.A. Parsons, Anal. Lett., 1990, 23, 169–182. Z. Fei, N. Kocher, C. J. Mohrschladt, H. Ihmels, D. Stalke, Angew. Chem. Int. Ed., 2003, 42, 783–787 M. Irie, Chem. Rev., 2000, 100, 1685. a) K. Matsuura, K. Ariga, K. Endo, Y. Aoyama, Y. Okahata, Chem. Eur. J., 2000, 6, 1750 and references therein.; b) Z. Cao, K. Murayama, K. Aoki, Anal. Chim. Acta, 2001, 448, 47. Cation sensing review: a) B. Valeur and I. Leray, Coord. Chem. Rev., 205, 3 (2000); recent examples: b) W-L. Wong, K-H. Huang, P-F. Teng, C-S. Lee, and H-L. Kwong, Chem. Commun., 2004, 384; c) T. Kawese, K. Tanaka, Y. Seirai, N. Shiono, and M. Oda, Angew. Chem. Int Ed., 42, 2003, 5597; d) A. Prasanna de Silva, G.D. McClean, and S. Pagliari, Chem. Commun., 2003, 2010; e) K.J. Wallace, J.W. Belcher, D.R. Turner, K.F. Syed, and J.W. Steed, J. Am. Chem. Soc., 125, 2003, 9699; f) Y. Kubo, M. Yamamoto, M. Ikeda, M. Takeuchi, S. Shinkai, S. Yamaguchi, and K. Tamao, Angew. Chem. Int Ed., 42, 2003, 2036. Recent examples: a) F.P. Cossio, A. Arrieta, V.L. Cebolla, L. Membrado, J. Vela, R. Garriga, and M.P. Domingo, Org. Lett. 2, 2000, 2311; b) M. Narita, F. Hamada, I. Suzuki, and T. Osa, J. Chem. Soc., Perkin Trans. 2, 1998, 2751. For example: Y. Takenaka, M. Higashi, and N. Yoshida, J. Chem. Soc., Perkin Trans. 2, 2002, 615. For example: A.I. Oliva, L. Simon, F.M. Muniz, F. Sanz, C. Ruiz-Valero, J.R. Morán, J. Org. Chem., 2004, 69, 6883–6885. P.L. Gentili, M. Nocchetti, C. Miliani, G. Favaro, New J. Chem., 2004, 28, 379–386. For example: a) D.B. Qin, X.S. Zeng, Q.S. Li, F.B. Xu, H.B. Song, Z.Z. Zhang, Chem. Commun., 2007, 147–149; b) E.J. Fernández, J.M. López-de-Lzuriaga, M. Monge, M.E. Olmos, J. Pérez, A. Laguna, A.A. Mohamed, J.P. Fackler, Jr., J. Am. Chem. Soc., 2003, 125, 2022–2023. For example: a) Z.F. Chen, X.Y. Wang, J.W. Chen, X.L. Yang, Y.Z. Li, Z.J. Guo, New J. Chem, 2007, 31, 357-362; b) A. Caballero, V. Lloveras, D. Curiel D, A. Tarraga, A. Espinosa, R. Garcia, J. Vidal-Gancedo, C. Rovira, K. Wurst, P. Molina, J. Veciana, Inorg. Chem., 2007, 46, 825–838. C. Reichardt, Chem. Rev., 1994, 94, 2319–2358. C. Reichardt, Solvent Effects on the Absorption Spectra of Organic Compounds 3rd Ed, Wiley VCH Verlag GmbH & Co. KGaA, Weinheim, 2003. M.G. Hutchings, Dyes Pigments, 1991, 17, 227–240. S. Millefiori, A. Millefiori, F. Guerrera, Spectrochim. Acta, 1980, 835

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16. K. Janus, K. Matczyszyn, J. Sworakowski, Mol. Cryst. Liq. Cryst., 2001, 361, 143–148. 17. For example: P. Ahonen, D.J. Schiffrin, J. Paprotny, K. Kontturi, Phys. Chem. Chem. Phys., 2007, 9, 651–658. 18. H.H. Jaffe, S-J. Yeh, R.W. Gardner, J. Mol. Spectrosc., 1958, 2, 120. 19. M.R. Robin, W.T. Simpson, J. Chem. Phys., 1962, 36, 580. 20. H. Rau, Angew. Chem., Int. Ed. Engl., 1973, 12, 224. 21. N. Biswas, S. Umapathy, J. Phys. Chem. A, 2000, 104, 2734. 22. J. Griffiths, B. Roozpeikar, J. Thomasson, J. Chem. Res. (S), 1981, 302. 23. K. Tanaka, M. Asami, J. L. Scott, New J. Chem., 2002, 26, 378–380. 24. J.L. Scott, M. Asami, K. Tanaka, New J. Chem., 2002, 26, 1822–1826. 25. J.L. Scott, A.P. Downie, M. Asami, K. Tanaka, CrystEngComm, 2002, 4, 580–584. 26. M. Scudder, I. Dance, J. Chem. Soc., Dalton Trans., 1998, 155. 27. J.L. Scott, A. Almesaker, Y. Sumi, K. Tanaka, Cryst. Growth & Des., 2007, in press. 28. CrystalExplorer 1.52, S.K. Wolff, D.J. Grimwood, J.J. McKinnon, D. Jayatilaka, M.A. Spackman, University of Western Australia, 2005, http://www.theochem.uwa.edu. au/CrystalExplorer/ 29. a) McKinnon, J. J., Mitchell, A. S.; Spackman, M. A., Chem. Eur. J. 1998, 4, 2136; b) Spackman, M. A.; Byrom, P. G., Chem. Phys. Lett. 1997, 267, 215. 30. Spackman, M. A.; McKinnon, J. J. CrystEngComm, 2002, 4, 378. 31. McKinnon, J. J.; Spackman, M. A.; Mitchell, A. S. Acta Cryst. B, 2004, B60, 627. 32. As Spackman emphasizes: Hirshfeld surfaces are difference functions and thus are specific for a molecule in the crystal. The coloration on these surfaces, therefore reflect close contacts and inter- and intra-molecular interactions in a specific crystalline form. 33. K. Tanaka, M. Asami, J. L. Scott, J. Chem. Res. (S), 2002, 483–484. 34. J.L. Scott, T. Yamada, K. Tanaka, Bull. Chem. Soc. Jpn., 2004, 77, 1697–1701. 35. K. Ogawa, T. Fujiwara, J. Harada, Mol. Cryst. Liq. Cryst. A, 2000, 344, 169–178. 36. a) S. A. Rani, J. Sobhanadri, T. A. P. Rao, J. Photochem and Photobiol. A: Chemistry, 1996, 94, 1–5; b) L. Biczók, T. Bérces, H. Inoue, J. Phys. Chem. A, 1999, 103, 3837– 3842. 37. a) J.L. Scott, T. Yamada, K. Tanaka, New J. Chem., 2004, 28, 447-450; b) A.H. Matsui, Pure Appl. Chem., 1995, 67, 429–436. 38. For example: H. Konaka, L.P. Wu, M. Munakata, T. Kuroda-Sowa, M. Maekawa, Y. Suenaga, Inorg. Chem., 2003, 42, 1928-1934; H. Nishimura, N. Matsushita, Chem. Lett., 2002, 319, 930–931. 39. K. Matsuda, K. Takayama, M. Irie, Chem. Commun., 2001, 363–364. 40. B. V. Gemert, in Organic Photochromic and Thermochromic Compounds, Ed. J. C. Crano, R. J. Guglielmetti, Plenum Press, New York, 1999 41. a) S. Kobatake, M. Irie, Chem. Lett., 2004, 33, 904–905; b) Y. Yokoyama. Chem. Rev., 2000, 100, 1717–1739. 42. M. Morimoto, S. Kobatake, M. Irie, J. Am. Chem. Soc., 2003, 125, 11080–11087 and references therein. 43. a) O. Godski, U. Peskin, M. Kapon, Y. Eichen, Chem. Commun., 2001, 2132–2133; S. Bénard, P. Yu, Adv. Mat., 2000, 12, 48–50; b) R. Guglielmetti, Photochromism, Molecules and Systems, Elsevier, Amsterdam, 1990, ch 8.; c) S. Iyengar, M.C. Biewer, Chem. Commun., 2002, 1398–1399. 44. H. Fukuda, K. Amimoto, H. Koyama, T. Kawato, Org. Biomol. Chem., 2003, 1, 1578– 1583. 45. L. Liu, D.-Z. Jia, Y.-L. Ji, K.-B. Yu, J. Photochem. and Photobiol. A, 2003, 154, 117– 122.

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46. H. Vančik, V. Šimunic-Mežnaric, I. Ćaleta, E. Meštrović, S. Milovac, K. MlinarićMajerski, J. Veljković, J. Phys. Chem. B, 2002, 106, 1576–1580. 47. T. Ishida, M. Murakami, H. Yoshikawa, S.-I. Nishikiori, Internet Electron. J. Mol. Des. 2003, 1, 14–23, http://www.biochempress.com 48. H.-J. Suh, W.-T. Lim, J.-Z. Cui, H.-Soo Lee, G.-H. Kim, N.-H. Heo, S.-H. Kim, Dyes and Pigments, 2003, 57, 149–159. 49. K. Tanaka, A. Tomomori, J.L. Scott, CrystEngComm, 2003, 5, 147–149. 50. K. Tanaka, A. Tomomori, J.L. Scott, Bull. Chem. Soc. Jpn., 2005, 78, 294–299. 51. J.L. Scott, K. Tanaka, Cryst. Growth Des., 2005, 5, 1209–1213. 52. G. Rothenberg, A.P. Downie, C. L. Raston and J.L. Scott, J. Am Chem. Soc., 2001, 123, 8701–8708. 53. G.W. V. Cave, C.L. Raston, J.L. Scott, Chem. Commun., 2001, 2159–2169. 54. W.H. Correa, S. Papadopoulos, P. Radnidge B.A. Roberts, J.L. Scott, Green Chem., 2002, 4, 245–251. 55. K. Tanaka, A. Tomomori, J.L. Scott, Eur. J. Org. Chem., 2003, 2035–2038. 56. J.L. Atwood, L.J. Barbour, A. Jerga, B.L. Schottel, Science, 2002, 298, 5595. 57. F. Toda, M. Yamamoto, K. Tanaka, T. C. W. Mak, Tetrahedron Lett., 1985, 26, 631– 634.

BIOMINERALIZATION OF ORGANIC PHASES ASSOCIATED WITH HUMAN DISEASES

JENNIFER A. SWIFT Department of Chemistry, Georgetown University, 37th and O Sts NW, Washington, DC 20057-1227 (USA)

Abstract. Crystal deposition diseases are a type of biomineralization process. Most reviews of pathological crystallization events focus on the formation of inorganic phases (e.g. calcium carbonates, calcium phosphates), but a number of organic crystals are common in physiological systems. Herein we review the structural and mechanistic aspects of formation of three of the most common organic materials observed in physiologic deposits – cholesterol, uric acid and hemozoin. 1. Introduction The formation of crystals within biological systems is prevalent throughout a wide range of organisms. Such precipitation processes are referred to as biomineralization, and result in structures that serve a variety of functions essential to life. A common example is the protective shell of mollusks which are composed of crystalline forms of calcium carbonate. In humans, bones and teeth are notable products of biomineralization. Generally such crystallization events are carefully regulated by the organism through complex pathways balancing solute concentration fluxes, pH, ionic strength, and the presence of growth-modulating organic species. However, certain unregulated crystal formations occur outside of normal conditions with deleterious effects. In physiologic environments, this can result in damage to surrounding tissue and lead to a number of disease states. Examples include the formation of gallstones, kidney stones, atherosclerotic plaques, joint diseases and even malaria. Crystal deposition diseases have long been of interest to the medical community whose focus is typically on the clinical aspects of the disease. Over the past few decades, it has become increasingly clear that crystalbased diseases also provide a number of fascinating questions and opportunities for solid state chemists. Studies on the initial nucleation and crystal growth processes of the relevant crystal phases and the associations 449 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 449–475. © 2008 Springer.

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between these crystals and other components present in the physiologic environment can lead to new understandings of key steps in the disease progression and possibly new strategies to address disease treatment and/or prevention. A variety of crystalline materials are associated with different crystal deposition diseases. The purpose of this manuscript is not to provide a comprehensive review of all crystal-based diseases and their associated crystal phases but rather to focus on some of the more recent insight gathered from solid state studies on three organic molecular systems – cholesterol, uric acid and hemozoin (Figure 1). It is hoped that this essay will provide a more general sense for how various aspects of crystal deposition diseases have been approached from a solid state chemistry perspective. CH3

(a)

COOH

HOOC

CH3

HO CH3

H3C O H

H

Fe(III)

N

N

(b)

O O

N H

N

N

N

N

N

CH3

H CH3

(c)

Figure 1. Molecular structure of (a) cholesterol, (b) uric acid and (c) heme.

2. Cholesterol Cholesterol is the most ubiquitous steroid in the human body – it is found in all tissues with high concentrations in the brain, spinal cord, fats, and oils. It can be obtained either from the diet, or it can be synthesized enzymatically in vivo from small molecule precursors such as acetate. Within cell membranes it serves an essential structural purpose stabilizing the fluidity of cells. It also plays important roles in cell membrane transport processes and signal transduction, [1] and the biosynthesis of many hormones, Vitamin D, and bile acids. [2] Its early identification with gallstone formation is indicated by its original name, cholesterin, which is derived

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from the Greek words for bile, chole, and hard, stereos. In addition to gallstone formation, the pathogenic crystallization of cholesterol is also implicated in cardiovascular disease and Schnyder’s corneal dystrophy. [3] 2.1. CHOLESTEROL BASED DISEASES

2.1.1. Gallstones The earliest known human gallstone was discovered in an Egyptian mummy from ~1000 BC, and the first medical observation of calculi within bile ducts was given in the 5th century. Today it is estimated that about 1 in 12 people in the USA are afflicted with gallstones. [4] Of these, the great majority are “silent stones” found serendipitously in asymptomatic patients undergoing unrelated medical tests. Symptomatic gallstone attacks occur when gallstones become lodged in and block the ducts that transport bile, resulting in inflammation of the gallbladder, pancreas, or liver. Cholecystectomy, or the removal of the gallbladder, is one of the most commonly performed abdominal surgical procedures in the Western hemisphere. [5] Gallstones are by nature heterogeneous composite materials. When viewed in cross-section, they usually show multiple concentric layers of crystalline material formed around a central nidius. Based on the composition of their major components, they are typically classified into two major types – cholesterol stones and pigment stones. Cholesterol gallstones are far more common in North American and European populations. [4] They typically contain more than 80–90% cholesterol by weight, [6] with the remaining mass attributed to calcium containing minerals (carbonates and phosphates) and a pigmented organic matrix (mostly mucin glycoproteins) which holds the heterogeneous composite together. Most cholesterol stones are light brown in color, 2–30 mm in diameter and can appear smooth or faceted. [6] Cholesterol monohydrate (ChM) is the sole crystalline form of cholesterol found in human gallstones as confirmed by light microscopy and X-ray diffraction. [7] Anhydrous cholesterol has been suggested as a minor component of cholesterol gallstones, [7] but this has been disputed as a consequence of specimen drying. [8] Pigment stones are composed of more than 40% of the unconjugated form of the bile pigment bilirubin and are black or brown in color. [4, 9] Black stones typically occur in patients with pancreatitis or cirrhosis. Brown stones are associated with bacterial infections, such as from Escherichia coli [10] or liver flukes. [11] Pigment stones are usually 2–5 mm in diameter, with either smooth or irregular exterior surfaces. [6, 12]

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2.1.2. Atherosclerotic Plaques The narrowing of the arteries is characterized by the accumulation of cholesterol, cholesterol esters, and phospholipids [13] forming plaques along arterial walls. Within the core of these plaques there is also an increased presence of macrophages containing significant amounts of lipids. Most of the lipids in arterial plaque including cholesterol are in the amorphous or non-crystalline form, however, in the core regions of advanced arterial plaques and lesions, plate-like ChM crystals are observed along with vesicular lipids and oily droplets under electron microscopy. [14] The mineral component deposited through the calcification stage of the lesions has been identified as hydroxyapatite, [15] though it has been suggested that the deposition of minerals may occur at a later stage in the pathogenesis. [16] 2.2. BILE SOLUTION & CHOLESTEROL PRECURSOR PHASES

Cholesterol is readily soluble in organic solvents, but highly insoluble in water. [17–19] In vivo cholesterol is solubilized into lipid bilayers, micelle and vesicle carrier systems with the assistance of bile salts, or with lipoproteins in blood serum. Supersaturation is a necessary but not exclusive prerequisite for crystal nucleation and growth. The cholesterol concentration can exceed the capacity of the solubilizing agents either when the organism experiences a marked increase in cholesterol concentration or a decrease in the solubilizing lipid concentrations. [20] Gallstones form within bile solution, the main components of which are water, electrolytes, and dissolved organic components (cholesterol, bile acids, and phospholipids). [21] The physical properties of native and model bile solutions have been characterized with a wide variety of techniques including light scattering, small angle x-ray and neutron scattering, and cryo-TEM. [22–33] There is significant evidence that ChM growth in vivo occurs via the transformation of other metastable crystalline intermediates. A variety of cholesterol carriers (e.g. micelles, vesicles, multilayer vesicles, bilayers) and metastable intermediates including filaments, needles, ribbons and tubular crystals are observed to precede the formation of the final platelike crystals of ChM. The needle-like crystals observed in native and model bile solutions were originally thought to correspond to an anhydrous cholesterol phase [34, 35] due to their similar morphology and density. [27, 36] More recently, Leiserowitz et al. [37] identified and structurally characterized this metastable phase, “Cholesterol II,” by grazing incidence X-ray diffraction (GIXD) using synchrotron radiation. Cholesterol II consists of crystallites organized in bilayers corresponding to a rectangular unit cell with a =

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10.07Å and b = 7.57Å, with a disordered cholesterol multilayer showing the stable triclinic monohydrate phase lying above it. Talmon and coworkers [38] simultaneously identified and characterized the same metastable “Cholesterol II” intermediate phase using cryo-electron diffraction. 2.3. CHOLESTEROL MONOHYDRATE

ChM crystallizes in a bilayer-type structure (P1: a=12.39, b=12.41, c=34.36, α=91.9o, β=98.1o, γ=100.8o) [39] in which bilayers measuring 33.9Å in height are stacked along c (Figure 2). The long axes of the molecules are nearly parallel and are tilted by ~17o from the normal to the (001) plane. At the bilayer interface, the C3 hydroxyl groups and water molecules form a slightly puckered 2-dimensional hydrogen bonded network.

Figure 2. (left) ChM packing diagram constructed from fractional coordinates obtained from ref. 39. Oxygen atoms attached to C-3 are red; water oxygens are blue. Hydrogen atoms are omitted for clarity. (right) ChM crystal grown from model bile solution prepared according to ref. 30. Scale bar = 0.1mm.

ChM crystals grown from model bile and/or aqueous organic solutions adopt a plate-like morphology. The large plate face is the c face, (001), which is consistent with faster growth within the bilayer plane (stronger intermolecular interactions) than growth between bilayers. The side faces correspond to (100) and (010). A small (011) chamfering face and a (1 1 0) facet are predicted by theory [40] but not always observed experimentally.

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The surface topography of ChM (001) was analyzed with in situ atomic force microscopy (AFM) under both aqueous and organic solution conditions, and found to be terminated with bilayers. [41] Adhesion force measurements obtained with chemically modified tips showed that the 3hydroxyl end of cholesterol is exposed on (001) in aqueous media, while alkyl tail groups terminate the surface in organic solutions. In aqueous solutions with bile acid concentrations exceeding the critical micelle concentration, the (001) surface of ChM can be chemically heterogeneous, presenting monolayer features as the smallest topographical feature. [42] This changing topography is notable, because ChM crystals appear in different physiological environments which can vary quite significantly in their composition. Dissolution studies on lab-grown single crystals of ChM also provide a view of the extensive defects present in the system. [43] 2.4. CHOLESTEROL INHIBITORS & PROMOTERS

2.4.1. Soluble Species A number of clinical studies have demonstrated that cholesterol supersaturation is not the sole prerequisite for ChM crystal deposition. [20, 44] Some patients with high cholesterol levels that meet the clinical definition of supersaturation do not develop gallstones, while others who do not appear to meet the prerequisite saturation levels can exhibit cholesterol deposits. This clinical evidence suggests that the presence of nucleating agents or growth inhibitors may play a fundamental role in ChM deposition under physiologic conditions. The presence of nucleating agents in the bile of gallstone formers was first suggested in the early 1980s when samples of gallbladder bile from stone formers were added to that of healthy control groups, resulting in a reduction in the crystal observation time. [45] Though it is not known exactly which molecules might regulate cholesterol crystallization in vivo, a number of studies have examined the effect of bile components such as mucin, [46] assorted glycoproteins, [47– 54] and metal ions [55, 56] on cholesterol nucleation and growth rates. These studies demonstrate an effect, but the experimental methods employed generally do not provide molecular-level specifics of how nucleation and/or growth are altered by these agents. Such detail has been provided through studies by Addadi et al. [57] on the recognition between ChM surfaces and monoclonal antibodies. The detailed effects of phospholipids on the nucleation of cholesterol films has also been reported by Leiserowitz and Lahav et al. [58, 59]

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2.4.2. Insoluble Species Microstructure studies on gallstones using light microscopy, infrared spectroscopy, [60] X-ray diffraction [61] and scanning electron microscopy [62] have identified various calcium carbonate (calcite, vaterite, aragonite) and calcium phosphate (hydroxyapatite, brushite) phases. The role that preexisting mineral seeds might play in the crystallization of cholesterol has been a subject of speculation since the 1960s, when Lonsdale first hypothesized that geometric matching between the surface lattices of different crystal phases may be a factor in gallstone formation. [63] EpiCalc [64] was used as a systematic screening tool to identify the ChM surfaces which epitaxially match the naturally abundant faces of calcium carbonate and calcium phosphate phases present in the pathogenic deposits. [65] A large number of geometrically matched ChM-mineral interfaces were identified, the best of which was found between the (001) plate-face of ChM and the natural cleavage face of calcite, (10–14). The nucleation and epitaxial growth of ChM from model bile solutions on calcite (10–14) was later demonstrated using in situ atomic force microscopy (AFM) in the orientation predicted by calculations. [40] Other matches have not to our knowledge been demonstrated experimentally. 3. Uric Acid Karl Wilhelm Scheele isolated a substance called lithic acid from urinary calculi in 1776. [66] The compound was later renamed uric acid near the turn of the 19th century. [67] It is now known that uric acid is a normal constituent of human urine and one of the final products of purine metabolism formed by the enzymatic conversion from xanthine. The kidneys shoulder the burden of removing uric acid from the body, with an average daily output of 600 mg. [68] Typical concentrations in serum and urine are 0.37 mM and 2 mM, respectively. Increased consumption of foods rich in proteins and nucleic acids, [69] increased cell turnover rates (e.g. during chemotherapy), [70] or other metabolic uric acid regulation problems can lead to elevated serum uric acid concentrations (hyperuricemia) which can result in the subsequent precipitation of uric acid in the joints or kidneys. Uric acid, a weak acid with a pKa of 5.27 at 24°C, [71] exists in equilibrium with its ionized urate form in physiologic solutions. Urate results from dissociation of the proton at N3, as determined by spectrophotometric titrations of N-methylated derivatives [72] and the crystal structure of its sodium salt. [73] Further dissociation of a second proton at N9 occurs at high pH (pKa2 = 10.3), though the dianion is considered negligible under normal physiologic conditions. [74] Uric acid is

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only slightly soluble in water and effectively insoluble in all organic solvents. Its aqueous solubility increases with temperature, [71] but at a fixed temperature, remains constant over a range of ionic strengths (0.15M to 0.30M) and even in standard artificial urine solutions. [75] Uric acid is considered to have a fixed solubility over the whole pH range, though urate solubility increases significantly with pH. Therefore, the total (uric acid + urate) solubility also increases with pH. Sodium is the principal cation in extracellular fluids (pH 7.4 – 7.0). Solutions with a pH and sodium content equivalent to serum are considered saturated with urate at 6.4 mg/dL at 37°C, though the measured solubility of urate in human plasma is slightly higher (7 mg/dL). [76] There is a strong correlation between the degree of hyperuricemia and the prevalence of gouty arthritis and uric acid kidney stone formation. Although hyperuricemia is usually regarded as a necessary prerequisite, additional environmental factors (e.g. temperature, pH, presence of crystal growth promoters, absence of growth inhibitors, seed crystals) are presumed to play a role in determining how and where uric acid/urate crystal precipitation occurs in vivo. 3.1. CRYSTAL PHASES

At least five different phases of uric acid and/or urate are known to form in physiologic solutions. These include anhydrous uric acid (UA), uric acid dihydrate (UAD), uric acid monohydrate (UAM), monosodium urate monohydrate (MSU) and ammonium acid urate (AAU). Their unit cell parameters appear in Table 1. Other urate complexes are known (e.g. hexaaqua magnesium (BADTEX), octa-aqua magnesium, [77] guanidinium (XANDEV), and methylene blue (UGEXIN) salts), but these phases are likely not physiologically relevant. TABLE 1. Unit cell parameters of different uric acid & urate phases formed under physiologic conditions

UA UAD UAM MSU AAU

Cell parameters

Ref.

P21/a: a=14.464, b=7.403, c=6.208 Å, β=65.10° P21/c: a=7.237, b=6.363, c=17.449, β=90.51°. P21/c: a=4.786, b=16.812, c=8.598, β =90.13° P-1: a=10.888, b=9.534, c=3.567, α=95.06˚, β=99.47˚, γ=97.17˚ a=17.356, b=3.528, c=11.285, β=94.23˚

[78] [79] [80] [73] [81]

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3.1.1. Uric Acid Phases Under low pH conditions, uric acid most commonly precipitates in either an anhydrous form (UA) or as a less stable dihydrate (UAD). Both UA and UAD phases have been identified in kidney stone deposits and can be readily prepared in the laboratory. [82] UAD is known to undergo an irreversible phase transformation to UA in solution by a presumed dissolution-recrystallization mechanism. [83] The crystal structure of UA was first reported in 1966 [78] although its optical properties had been investigated much earlier (Figure 3). [84–86] Layers within the bc plane consist of parallel ribbons of uric acid molecules hydrogen-bonded head-to-head (O2…H-N1: 1.826Å, 175.0°) and tail-to-tail (O8…H-N7: 1.734Å, 155.8°), with the ribbon plane perpendicular to the b-c plane. There is no hydrogen-bonding between ribbons within a layer, although ribbons in adjacent layers are hydrogen-bonded to one another and offset by ~ 62°. Synthetic UA crystals deposit as clear rectangular plates, with large (100) faces bounded by (210), (201), (001), and sometimes smaller (121) facets. [82, 87] Initial diffraction studies of UAD crystals were carried out in the 1990s on avian samples. [88, 89] An orthorhombic structure for UAD was originally proposed, but was later revisited by Parkin [79] using synthetic crystals and found to be monoclinic. Comparison of the packing diagrams of UA and UAD shows the 1-D ribbon and 2-D layer motifs to be quite similar, although the registry between adjacent layers and the interlayer distances are necessarily different, owing to the addition of a 2-dimensional hydrogen-bonded water layer in UAD. Synthetic UAD crystals deposit as clear rectangular plates, with large (001) faces bounded by (011), (102) and infrequently (210) faces. [82] Only recently, Shubert et al. [80] reported the existence of a new uric acid monohydrate phase, which was observed in only 0.015% of more than 100,000 urinary stones analyzed. The structure of UAM, solved by refinement of powder X-ray data, consists of continuous layers formed from uric acid and water molecules and is quite different from that of UA and UAD. Interestingly, the authors note that all the UAM samples analyzed also contained a high percentage of amorphous material present. 3.1.2. Urate Phases Under neutral and basic pH conditions, uric acid exists predominantly in solution as urate, so precipitates tend to be urate salts. The two most frequently observed in physiological deposits are monosodium urate monohydrate (MSU) and ammonium acid urate (AAU). Both MSU and AAU are found as minor components in human kidney stones, though AAU is a common constituent of urinary deposits in some domestic pets. [90, 91]

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The classic clinical symptom of gout is the presence of MSU crystals in the interstitial fluid surrounding joints. The single crystal structure of MSU was solved by Mandel in 1976. [73] MSU crystals are composed of one dimensional stacks of purine rings, which are coordinated to sodium ions through short Na…O contacts. The purines are also coordinated to the oxygen atoms of the included water molecules by O-H…O and N…H-O hydrogen bonds. MSU crystals grown in vitro and in vivo typically develop as flat needles (≤ 200 μm) elongated about the crystallographic c axis with (010), (100) and (1 1 0) side faces and (001) end faces. Four additional theoretical stable faces have been predicted, [92] although these surfaces are typically not observed on in vitro crystals. Comparatively little has been reported on the physical properties of AAU. The monoclinic unit cell dimensions obtained from powder diffraction studies are known, [81] though a single crystal structure has not yet been reported to our knowledge.

Figure 3. (left) Packing diagram of UA constructed from fractional coordinates obtained from ref. 78. (right) Uric acid crystals (possibly different phases) grown in vivo exhibit a variety of morphologies. Reproduced from ref. 93, copyright 1965 McGraw-Hill Book Company.

3.2. URIC ACID BASED DISEASES

3.2.1. Kidney Stones Human kidneys have two basic functions – to excrete metabolic waste products and other foreign chemicals, and to regulate fluid volume, osmolarity, acidity and mineral composition in order to maintain normal concentrations in the extracellular fluid. Impaired kidney function can lead to the deposition of a number of different precipitates throughout the renal

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tract and contribute to kidney stone formation. The major mineral species identified with urinary deposits is calcium oxalate monohydrate, otherwise known as whewellite. A recent review by Wesson and Ward addresses many of the physico-chemical properties of this material. [94] A variety of other calcium phases (hydroxyapatite, brushite, weddelite), magnesium phosphates (struvite, newberyite), and organic molecular crystals (cysteine, various drug metabolites) have also been identified as minor components urinary precipitates. Kidney stones are heterogeneous composites of aggregated crystals held together by an organic matrix and can reach several millimeters in size. They can consist of principally one crystalline component, or as mixture of two or more components present in significant quantities. Compositional analysis of kidney stones across the globe [80, 95–101] show that the occurrence of uric acid stones varies significantly. In all cases, the frequency of UA is typically higher than that of UAD. 3.2.2. Gout Perhaps the oldest known type of arthritis, gout was first described as early as the 5th century by Hippocrates. [102] Once known as the “disease of kings,” gout afforded a level of social advantage in the 18th and 19th centuries, as it was thought to afflict only the wealthy. Sir Alfred Baring Garrod was the first to attribute gout to urate crystal formation in 1849. However, his theory did not become widely accepted until the 1960s when polarized light microscopy was used to examine synovial fluid. [103] Two key steps in the pathogenesis of gout are the crystallization of monosodium urate monohydrate (MSU) in tissues, and the subsequent inflammation response induced. Neither process is currently well understood on the molecular-level. Precipitation often occurs first in the big toe, and it has been suggested that the preference for this site may be due to the fracture of a single parent crystal into many smaller seed crystals. Symptoms of acute attacks include severe pain with reddening and swelling of the afflicted joint(s) while those of chronic gout can result in loss of cartilage and bone erosion. [104] Approximately 23% of gout sufferers also suffer kidney stones. [105] 3.3. NUCLEATION & GROWTH OF URIC ACID

3.3.1. Nucleation The common coexistence of different crystalline phases in physiological deposits, and the observation that the nucleus of a stone is often chemically different than the material in subsequent layers, led Lonsdale [63] to suggest in 1968 that epitaxial relationships between these crystalline phases

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may be an important factor contributing to their formation. Theoretical calculations on epitaxial interfaces typically examine the percentage of misfit (up to 15%) of various interfacial lattice alignments. [63, 106] A more recent epitaxy search [107] for uric acid/uric acid and uric acid/ mineral interfaces of the major kidney stone components identified four commensurate matches and over two hundred coincident epitaxial matches. Most of the experimental studies examining epitaxial growth in these systems have sought evidence for heterogeneous nucleation by introducing seeds of one phase (most often MSU, UA or calcium oxalate) into supersaturated inorganic solutions of another constituent and looking for changes in the overall nucleation rate. [108–114] Experimental studies by Boistelle and Rinaudo [83] showed more specifically that UA (100) nucleates preferentially on UAD (001) surfaces, in an orientation predicted by epitaxy calculations. [107] Others have also observed this phenomenon. [115] A similar study [116] found epitaxial growth in solutions simultaneously supersaturated with both newberyite and uric acid. 3.3.2. Growth Molecular-level growth on single crystal UA (100) surfaces was investigated in pure aqueous solutions as a function of supersaturation over a pH range of 3.9 – 5.2. [117] Mechanistically, growth was found to be initiated at screw dislocation sites and proceed bilayer-by-bilayer with highly anisotropic rates. Uric acid crystals grown in vivo tend to adopt a wide variety of morphologies and are usually colored (Figure 3). [93] Investigations into the crystallization of uric acid in the presence of impurities began as early as the 19th Century when it was first noted that uric acid crystals precipitated from urine or inorganic solutions containing safranine violet or aniline yellow were colored. [84] Gaubert in the 1930s [118] and later Kleeberg in the 1970s [119, 120] made many observations on the growth of uric acid from solutions containing assorted dyes. Although the presence of some dyes led to novel morphologies or colored crystals, in much of this early work, the existence of multiple uric acid phases was generally overlooked, so it is difficult to know with certainty which phase(s) the authors examined. More recent work [82, 121, 122] examined the molecular recognition of assorted dyes during UA and UAD growth. A number of urine components (e.g. mucine, escin, glycerrhizic acid, Nacetyl-L-cysteine, pentosan polysulfate, and chondroitin sulfate) have been reported to inhibit or delay uric acid crystallization times at different concentrations. [123] Others have considered whether some of the components of the matrix, [124–129] the relatively small amount of amorphous organic material present in kidney stones, plays a role in the nucleation or

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growth modulation of the microcrystals or heps mediate epitaxy between different crystalline forms. [130] The exact identity of the compound(s) resulting in stone coloration is still uncertain, but urochrome, a broad category of pigments found in the urine, are likely candidates. 3.4. NUCLEATION & GROWTH OF MONOSODIUM URATE

3.4.1. Nucleation While an elevated urate level is usually regarded as a necessary prerequisite for the onset of a gout attack, considerably higher serum urate supersaturation levels (> 50mg/dL) have been observed in some patients without gouty deposits. [70, 102] Additional environmental factors (e.g. temperature, pH, presence of crystal growth promoters, absence of growth inhibitors, seed crystals) must play a major role in determining how and where MSU crystal precipitation occurs in vivo. When synovial fluid of gout patients was added to in vitro urate solutions, it was found that nucleation proceeds much more rapidly than when fluids of rheumatoid arthritis patients are added. [131] A number of in vitro studies have examined the binding of various synovial fluid proteins to MSU crystals in an attempt to elucidate the role of potential nucleating factors. [132–139] In general, these experiments provide some guidance as to which macromolecular agents may (or may not) play a role in the crystallization process, though they do not typically provide insight into the specific mechanism(s) of crystal surface recognition events. One notable exception is the study by Perl-Treves and Addadi, [137] where specificity was demonstrated in the binding of albumin to select MSU surfaces. Insoluble seed crystals are a second class of potential nucleating agents. It is well known that the addition of MSU seed crystals to supersaturated urate solution results in its immediate precipitation. [140] A number of in vitro studies have examined heterogeneous seeding experiments in the context of kidney stone formation, [106, 107, 110, 115, 116, 141] although epitaxial relationships between MSU and other crystalline species commonly found in synovial fluid [142] have not been systematically examined experimentally to our knowledge. 3.4.2. Growth A number of different methods for preparing MSU crystals in vitro are described in the literature. [143] Most yield needle-like crystals that are <200μm long, similar to those formed in vivo. An alternative spherulitic MSU morphology is also occasionally observed in synovial fluid. [144] The relationship between spherulites and needles in vivo is unclear, though the

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former has been suggested as a possible metastable precursor to the latter. [144] A few mechanistic studies on MSU growth from inorganic solutions has also been reported, [131, 140, 145–148] sometimes generating conflicting interpretations of the growth mechanism. Lam Erwin and Nancollas [140] reported that the growth kinetics of MSU followed the square of the relative supersaturation, indicating a spiral growth mechanism, while a similar study by Calvert et al. [147] concluded that the growth rate better correlated with a 2D-island growth model, which is fundamentally different in a mechanistic sense. Additional studies are necessary to resolve this discrepency. 4. Malaria Pigment Malaria is caused by protozoan parasites, affects hundreds of millions around the globe and results in over one million fatalities per year. [149] There are 5 protozoa parasite species that infect humans, the most prevalent and virulent of which is Plasmodium falciparum. Two stages (liver and red cell) define growth and division of the parasites within the human body, with all clinical symptoms of malaria (e.g. fever, anemia, coma, etc.) due to the red cell stage. A key step in the parasite lifecycle within the red blood cell is the digestion of hemoglobin into free amino acids and free heme (Fe2+-protoporphyrin IX). Heme above a few micromolar is toxic to the cell, but is rendered less so by further one-electron oxidation to hematin (Fe3+protoporphyrin IX), which precipitates as micron-sized crystals of the highly pigmented compound hemozoin. The visual confirmation of this pigment in red blood cells is one of the classic clinical diagnostics for identifying malaria-infection. Until the late 1990s, hemozoin was widely thought to be a polymer, however with its crystal structure now firmly established, hemozoin formation is now considered a true biomineralization process. Many of the chemical and structural aspects of hemozoin formation have been recently reviewed previously by Egan. [150] 4.1. HEMOZOIN STRUCTURE & MORPHOLOGY

Hemozoin crystals can be isolated from infected red blood cells, though in general, characterization methods that require large sample sizes can be impractical given the number of parasites required. Noland et al. [151] used scanning electron microscopy to compare the size and shape of hemozoin crystals synthesized by different Plasmodium species and found that the crystals isolated from mammalian cells are of similar size (~300–500 nm in largest dimension) and morphology (flat faced rectangular prisms).

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Hemozoin crystals have also been characterized by various spectroscopic methods [152–155] including IR, ESR, EXAFS and Mössbauer, however, no single crystal structure of the parasite-made material has been reported. Most structural work on malaria pigment uses a synthetic version of hemozoin, β-hematin, which can be prepared from different methods. The most reliable appears to be via the dehydrohalogenation of hemin (Cl-Fe3+protoporphyrin IX) [156] which results in a microcrystalline powder that is of a single crystalline phase. [157] The powder x-ray pattern and spectroscopic profile of the parasite-made and synthetic versions are identical, so the two are considered to be isostructural. The structure of β-hematin was solved by Pagola et al. [158] from powder x-ray diffraction using synchrotron radiation (Figure 4). The pattern indexed to a triclinic cell (P-1: a=12.196, b=14.684, c=8.040, α=90.22o, β=96.80°, γ=97.92°). The structure consists of centrosymmetric head-to-tail heme dimers linked through Fe-carboxylate bonds (Fe1-O41) and hydrogen O-H…O=C hydrogen bonds (O36…O37). The size (200 to >1600nm in length) of synthetic β-hematin crystals is somewhat more variable than the naturally derived hemozoin.(151) Synthetic crystals typically grow as needles which sometimes have tapered ends. [157, 159] The theoretical growth morphology based on the powder x-ray structure and crystal attachment energies also predicts needles elongated along the c-axis, with (100) and (010) side faces, smaller (011) faces, and a minor (001) face. [160] 4.2. β-HEMATIN GROWTH STUDIES

Most of the growth studies performed to date on malaria pigment have focused on β-hematin. Egan et al. [161] investigated the formation of βhematin formation from acetate solution as a function of pH, temperature, acetate concentration and seeding. Using a combination of IR, X-ray diffraction and SEM, they reported that the process occurred via the rapid precipitation of amorphous (or nanocrystalline) material followed by the slow conversion to the known crystalline phase. This amorphous to crystalline transformation is similar to that proposed in the biomineralization of other calcium phases. [162] Others have suggested the presence of an intermediate phase, B-hematin, [163, 164] in the precipitation process which possibly corresponds to either a phase with a different hydration state or a mixture of hematin (monomer) and β-hematin. Studies have also examined the effect of a variety of biological molecules potentially related to β-hematin formation in vivo. Evidence suggests that hemozoin formation can be nucleated by Plasmodium falciparum histidine rich protein II (HRP II) [165] and/or lipids. [166] The

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mechanism by which crystallization is promoted is not firmly established, though Goldberg et al. [167] observed that hemozoin crystals formed in the digestive vacuole of intact parasites appear aligned relative to one another. It has been hypothesized that this alignment may be ascribed to nucleation of β-hematin on the lipid membrane surface. Nucleation under simulated physiological conditions such as those at lipid-water [168] and air-water [159] interfaces support this hypothesis. Measuring crystallization rates within living parasites is difficult, but recent spinning disk confocal microscopy work by Gligorijevic et al. [169] demonstrated that it is possible to quantitatively estimate the rate of hemozoin production in 3D within living parasites in real time.

Figure 4. (left) Packing diagram of β-hematin constructed from coordinated in ref. 158. (right) FEISEM image of extensively purified hemozoin courtesy of David J. Sullivan, Jr. (Johns Hopkins). [151] Scale bar = 100 nm.

4.3. β-HEMATIN & ANTIMALARIAL DRUGS

The mechanism by which antimalarial drugs function within a cell has been a topic of interest for several decades. At least three hypotheses have been proposed. These include (a) sequestering one of more forms of the protoporphyrin in solution to reduce the local concentration, (b) reducing the growth rate by binding to one or more growing crystal faces, (c) destabilizing preformed hemozoin through some other mechanism, or some combination of these. Previous experimental work has demonstrated the importance of both the size of the aromatic moiety [170] and the flexible amine side chain [171] in the efficacy of quinoline-type drugs. Buller et al. [160] calculated the binding energies of various quinoline drugs to the fastest growing (001) surface of β-hematin. The trends observed in the surface binding

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calculations support the hypothesis that quinoline drugs inhibit hemozoin formation through surface binding. A more recent study examined the crystal observation time and morphological changes of β-hematin grown in the presence of quinoline additives. [159] In chloroform solutions containing 10% quinine or chloroquinine, the crystal observation time increased 4-fold relative to “pure” solutions. Crystal morphology also changed to tapered needles in the presence of additive such that β-hematin crystals now exhibited large stepped (001) or (011) stepped surfaces. Attempts to measure the crystal mosaic domain size with micro-Raman and XRPD suggest that the β-hematin crystals grown in the presence of additives are more strained than their pure counterparts, and that some additives may have been occluded in the growth process. The action of other antimalarial drugs has been explained as an effect of binding heme in solution, [172] though the mode of action may be subject to reinterpretation. [159] 5. Acknowledgements The author is grateful for the financial support provided by Georgetown University, the Henry Luce Foundation, the Camille & Henry Dreyfus Foundation, and the National Science Foundation. The author also thanks the many talented researchers past and present who have made contributions to the biomineralization studies pursued in her laboratory. References 1. 2. 3.

4. 5. 6. 7. 8.

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136. Cherian, P. V., and Schumacher Jr, H. R. (1986) Immunochemical and ultrastructural characterization of serum proteins associated with monosodium urate crystals (MSU) in synovial fluid cells from patients with gout, Ultrastruct. Path. 10, 209–219. 137. Perl-Treves, D., and Addadi, L. (1988) A structural approach to pathological crystallizations. Gout: the possible role of albumin in sodium urate crystallization, Proc. R. Soc. Lond. B 235, 145–159. 138. McGill, N. W., and Dieppe, P. A. (1991) The role of serum and synovial fluid components in the promotion of urate crystal formation, J. Rheumatol. 18, 1042–1045. 139. Ortiz-Bravo, E., Sieck, M. S., and Schumacher Jr., H. R. (1993) Changes in the proteins coating monosodium urate crystals during active and subsiding inflammation, Arthritis Rheum. 36, 1274–1285. 140. Lam Erwin, C.-Y., and Nancollas, G. H. (1981) The crystallization and dissolution of sodium urate, J. Cryst. Grow. 53, 215–223. 141. Grover, P. K., and Ryall, R. L. (1997) Effect of seed crystals of uric acid and monosodium urate on the crystallization of calcium oxalate in undiluted human urine in vitro., Clin. Sci., 205–213. 142. Schumacher, H. R., and Reginato, A. J. (1991) Atlas of Synovial Fluid Analysis and Crystal Identification, Lea & Febinger, Philadelphia. 143. Fam, A. G., Schumacher, H. R., Clayburne, G., Sieck, M., Mandel, N. S., Cheng, P.-T., and Pritzker, K. P. H. (1992) A comparison of five preparations of synthetic monosodium urate monohydrate crystals, Journal of Rheumatology 19, 780–787. 144. Fiechtner, J. J., and Simkin, P. A. (1981) Urate spherulites in gouty synovia, JAMA 245, 1533–1536. 145. Allen, D. J., Milosovich, G., and Mattocks, A. M. (1965) Crystal growth of sodium acid urate, J. Pharm. Sci. 54, 383–386. 146. Khalaf, A. A., and Wilcox, W. R. (1973) Solubility and nucleation of monosodium urate in relation to gouty arthritis, J. Cryst. Grow. 20, 227–232. 147. Calvert, P. D., Fiddis, R. W., and Vlachos, N. (1983) Crystal growth of monosodium urate monohydrate, Colloids and Surfaces 14, 97–107. 148. Kaneko, K., and Maru, M. (2000) Determination of urate crystal formation using flow cytometry and microarea X-ray diffractometry, Anal. Biochem. 281, 9–14. 149. Greenwood, B., and Mutabingwa, T. (2002) Malaria in 2002, Nature 415, 670–672. 150. Egan, T. J. (2002) Physico-chemical aspects of hemozoin (malaria pigment) structure and formation, Journal of Inorganic Biochemistry 91, 19–26. 151. Noland, G. S., Briones, N., and Sullivan Jr., D. J. (2003) The shape and size of hemozoin crystals distinguished diverse Plasmodium species, Mol. Biochem. Parasit. 130, 91–99. 152. Slater, A. F. G., Swiggard, W. J., Orton, B. R., Flitter, W. D., Goldberg, D. E., Cerami, A., and Henderson, G. B. (1991) An iron-carboxylate bond links the heme units of malaria pigment, Proc. Natl. Acad. Sci. USA 88, 325–329. 153. Bohle, D. S., Dinnebier, R. E., Madsen, S. K., and Stephens, P. W. (1997) Characterization of the products of the heme detoxification pathway in malarial late trophozoites by X-ray diffraction, J. Biol. Chem. 272, 713–716. 154. Bohle, D. S., Debrunner, P., HJordan, P. A., Madsen, S. K., and Schulz, C. E. (1998) Aggregated heme detoxification byproducts in malarial trophozoites: β-hematin

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CRYSTAL STRUCTURE DETERMINATION FROM X-RAY POWDER DIFFRACTION DATA

MARYJANE TREMAYNE School of Chemistry, University of Birmingham, Edgbaston, Birmingham, United Kingdom, B15 2TT

Abstract. Many crystalline materials cannot be prepared in a suitable form for conventional single-crystal diffraction studies, and hence the successful structure characterisation and rationalisation of these materials and their properties often relies on the ability to gain this information from powder diffraction data. Although the refinement stage of the structure determination process can be carried out fairly routinely, structure solution is associated with several intrinsic difficulties. However, the recent development of direct-space structure solution methods has enabled the study of a wide range of materials using powder diffraction data, many of structural complexity only made tractable by these advances in methodology. This paper aims to guide you through the structure determination from powder diffraction process, highlighting the application of direct-space methods (and the global optimisation techniques on which they are based), including experimental and structural considerations, and examples illustrating the impact that powder diffraction has had on the structural study of both organic and inorganic materials.

1. Introduction Powder diffraction data is most commonly used in the qualitative identification of crystalline phases or compounds, as each crystalline substance has a characteristic powder pattern that can be used as a fingerprint. Fortunately, the last decades of the 20th century saw considerable progress in the development of ab initio crystal structure determination from powder diffraction data. Advances in instrumentation and software for data analysis have brought about a rapid evolution in this field, and new developments in crystal structure solution methods in recent years (particularly direct-space techniques)

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have had a significant impact in the area of molecular crystallography, particularly in the study of pharmaceuticals, pigments, polymorphic systems, coordination complexes and compounds used in the study of intermolecular networks [1–3]. These developments have equipped us with tools and techniques that enable us to tackle structures of size, complexity and in numbers not thought possible twenty years ago. 2. Methods and Strategy The aim of structure determination from either single-crystal or powder diffraction data is to establish the distribution of electron density in the unit cell, and this requires the extraction of information in the form of diffraction intensities from the experimental data. Single-crystal and powder diffraction data contain essentially the same structural information, but whereas in the former case the diffraction intensities are distributed in three-dimensional space, in the latter, the three-dimensional data are ‘compressed’ into one dimension. As a consequence, individual peaks in the powder diffraction pattern overlap and information on the individual diffraction intensities is obscured. In general terms, a single-crystal data set may contain thousands of unique individual intensities that can be used to determine a crystal structure, but even a high-resolution powder data set may contain only a few hundred intensities most of which can still be partially overlapped and hence ambiguous. It is this severe ‘loss’ of data that constitutes the main reason for the difficulties encountered and the limitations in complexity and size of the structures that can be determined from powder diffraction data. In the case of molecular species in which the majority of the atoms in the structure are weak X-ray scatterers, the situation is made even more problematic with little intensity information at high diffraction angle. The process of structure determination from powder diffraction data consists of several discrete steps: (i) the pattern is indexed to give lattice parameters, crystal system and space group, (ii) structure solution is carried out to produce an approximate structural model that is used as a starting point for (iii) Rietveld refinement and completion of the structure determination process. Although any attempt at crystal structure determination from powder diffraction data relies on the successful completion of the first step, the most significant progress over recent years has resulted from the development of new ‘direct space’ methods of structure solution. The aim of structure solution is to derive an approximate description of the crystal structure, starting from no knowledge of the actual arrangement of atoms, ions or molecules in the

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unit cell. If the approximate structure solution is a sufficiently good representation of the true structure, a good quality structure may then be obtained fairly routinely by Rietveld profile refinement [4–6]. In general, correct structure solution from powder diffraction data is a significantly greater challenge than structure refinement. 2.1. UNIT CELL DETERMINATION

The first stage of crystal structure determination is determination of the unit cell. Unfortunately, difficulties encountered at this stage are often the limiting step in the structure determination process. As already discussed, experimental powder diffraction patterns typically have considerable peak overlap and sometimes peak displacements, which can lead to failure of indexing. Certain peaks which may be crucial for correct indexing may be obscured or completely unresolved because of peak overlap. Other problems arise when an impurity phase (or second polymorph) is present in the powder sample, or if there is a significant zero-point error or poor definition of peak positions because of poor sample crystallinity or poor instrumental resolution. The most common method used for indexing is to apply a range of indexing programs which consider the measured positions of the peak maxima for a number (usually about 20) of selected peaks. Several of the most widely used methods are contained within the CRYSFIRE package [7]. Other methods have been developed which attempt to make the indexing process more reliable when the powder data are not ‘ideal’; these include a whole-profile fitting genetic algorithm approach in which potential unit cells are assessed against the whole profile [8], and methods based on the traditional dichotomy approach but developed to be relatively insensitive to impurity peaks and large diffractometer zero-point errors [9,10]. After a unit cell has been identified, the space group must be assigned by identifying the conditions for systematic absences. This is not always a straightforward process as peak overlap can also obscure this information. If the space group cannot be assigned uniquely, structure solution is carried out for each of the plausible space groups. Knowledge of the unit cell volume, space group and density considerations should allow the contents of the asymmetric unit to be established, and this information used in the structure solution process. Information obtained from other experimental techniques such as solid-state NMR may be particularly helpful in confirming the number of molecules and/or structural units in the asymmetric unit or the presence of any crystallographic symmetry in the molecule [11]. Before structure solution can be attempted, further analysis of the powder diffraction profile is required using pattern decomposition methods such as the LeBail [12] or Pawley [13] techniques. These methods involve fitting

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the complete powder diffraction profile to establish both the intensities of each of the underlying diffraction maxima, and reliable values of the instrumental profile parameters. Some structure solution techniques use these extracted intensities to assess the quality of structural models (using χ2) whereas others are based on a profile-based figure-of-merit (such as Rwp). However, reliable comparison between calculated and experimental data in the structure solution stage still requires accurate fitting of the instrumental parameters. This process should involve refinement of the unit cell parameters, background distribution, zero-point, peak width and peak shape parameters, with the use of arbitrary peak intensities (i.e. without using any structural model to determine peak intensities). Careful analysis of the experimental data in this way ensures that the profile parameters used in the subsequent structure solution calculations provide a reliable description of the experimental powder diffraction pattern. 2.2. DIRECT-SPACE STRUCTURE SOLUTION METHODS

Direct-space methods differ considerably from the traditional reciprocal space approach to structure solution that is used routinely in single crystal diffraction studies and to a lesser extent still used in structure solution from powder diffraction data. In the direct space strategy, trial crystal structures are generated independently of the experimental diffraction data by movement of a structural model (e.g. a single molecule of the compound under

Figure 1. A two-dimensional section through an R-factor hypersurface.

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consideration) around a pre-defined unit cell, exploiting the information available from knowledge of chemical structure. The suitability of each trial structure is then assessed by direct comparison of the powder diffraction pattern calculated for the trial structure and the experimental diffraction data. This is quantified by a crystallographic R-factor or figure-of-merit (e.g. R wp or χ2). Structure solution aims to find the trial crystal structure that has the lowest R-factor (the best fit between the calculated and experimental data). This is equivalent to locating the global minimum on a multi-dimensional hypersurface, the shape of which depends on the structure and the parameters used to define the problem. Figure 1 shows a simple representation of a two-dimensional section through an R-factor hypersurface. The surface clearly shows both peaks (high R-factor) and troughs (low R-factor). The deep minimum corresponds to the correct structure solution, but the plot clearly shows the existence of another significant local minimum. 2.2.1. The Structural Model For structure solution by traditional methods, the complexity of the problem is generally judged on the number of atoms to be located in the asymmetric unit. For direct space methods, the complexity and hence the number of parameters or dimensionality of the global optimization problem, depends more on the number of variables required to define the structure. Thus, the direct-space solution of a molecule that is large but essentially rigid is generally more straightforward than the structure solution for a molecule that is small but completely flexible. The use of prior structural knowledge in terms of molecular geometry (intramolecular connectivity and typical bond lengths and angles) in direct-space methods means that each trial crystal structure need only be defined by variables representing the position, orientation and intramolecular conformation of the molecule within the unit cell. For a general rigid molecule (e.g. benzene or pyrene), six variables are required to define movement of the structural model through translation (x,y,z) and variation of the orientation (θ,ϕ,ψ) of the molecule (a six-dimensional hypersurface). However, if part of the intramolecular geometry cannot be pre-defined i.e: in the case of an alkyl side chain, conformational flexibility is introduced to the model by the variation of a number of torsion angles (τ1,τ2,…,τN), increasing the number of variables required and the complexity of the optimization calculation. E.g. Triethyl-1,3,5-benzenetricarboxylate (Figure 2a) is defined by a total of 15 variables (including 9 variable torsion angles) [14]. If there was any crystallographic symmetry within the molecule i.e. a three-fold axis such that each side chain was equivalent and the position and orientation were constrained (e.g. triethyl-1,3,5-triazine-2,4,6tricarboxylate) [14], the number of variables needed would be reduced to four (Figure 2b). In cases with multiple molecules or multiple components

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Figure 2. Structural models for (a) triethyl-1,3,5-benzenetricarboxylate, (b) triethyl-1,3,5triazine-2,4,6-tricarboxylate, (c) 1,2,3-trihydroxybenzene:hexamethylenetetramine (1/1) and (d) bis(3,5-dihydroxybenzoate)nickel(II)cyclam. Dashed lines indicate part of the structure related by symmetry. Arrows show the variable torsion angles used in the direct-space structure solution calculation.

in the asymmetric unit, the number of variables needed increases, making the optimisation significantly more complex. I.e. for a binary cocrystal with rigid molecular components such as 1,2,3-trihydroxybenzene: hexamethylenetetramine (1/1) (Figure 2c) [15], a set of independent parameters for position and orientation are required for each component; in this case 12 variables were used. Definition of an appropriate structural model for structure solution can become even more complicated when considering metal complexes. When solving these materials, assumptions must often be made about symmetry constraints and coordination geometry in constructing the structural model. Consider the nickel (II) cyclam complex bis(3,5-dihydroxybenzoato)-1,4,8,11tetraazacyclotetradecane nickel (II) (Figure 2d) [16]. This structure is typical of many inorganic systems and molecular complexes; although the connectivity is known, bond lengths and angles are often not as well-defined as in organic systems, especially when considering bonds between ligands and metal centres. In this case, it was clear from density considerations that the nickel lies on a crystallographic inversion centre. So for direct-space structure solution, the structural model must be described either by constraint of interatomic distances and angles to mean values by comparison with related systems (four degrees of freedom), or by consideration of multiple units (nine degrees of freedom, or 21 degrees of freedom if the metal centre is not

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on an inversion centre). The first approach can result in the failure of structure solution if the correct structure deviates significantly from the mean geometry, whilst the second introduces additional complexity to the structure solution by increasing the number of degrees of freedom. The incorporation of some degree of flexibility in the molecular model (e.g. consideration of ligands and metal centres as individual fragments that are constrained to lie within a certain distance from each other) attempts to reduce the computational cost whilst enabling successful structure solution [16]. It is clear that there are many ways in which the structural model can be defined, each one defining a different hypersurface to be explored. In most cases, the common practice is to define the structural model using as much chemical knowledge as possible, but to also be aware of the limitations of structure solution from powder diffraction data, and to adapt the structural model accordingly. In all the above examples, only hydrogen atoms in known configurations were included in the calculation, i.e. CH2 groups in (a),(b) and (c), whereas hydrogen atoms whose position could not be defined relative to the rest of the model i.e. hydroxyl Hs in (c) and (d) were omitted until refinement. Reliable hydrogen atom positions may be obtained with very high quality synchrotron powder data or with neutron powder data, but not from laboratory X-ray powder data. By omitting these atoms in the structure solution stage, the number of torsion angles required is reduced and the optimization is made significantly easier. In most cases these hydrogen atoms are then introduced at the refinement stage in positions consistent with possible hydrogen bonding networks or in staggered conformations. One example of this is the structure solution of 2,4,6-triisopropylbenzenesulfonamide from powder diffraction by Monte Carlo methods [17]. This material was solved as part of a study of the supramolecular aggregation of a series of arenesulfonamides and arenesulfonylhydrazines [18]. The structural model used in the direct-space structure solution is shown below (Figure 3a); hydrogen atoms in fixed positions (such as those attached to the benzene ring) were included, as were those at the base of the substituent chains (given the significant R-factor discrimination during rotation of these groups). During refinement all 18 methyl hydrogens were inserted in staggered conformations, and both amide hydrogens placed at positions consistent with a reasonable hydrogen bonding scheme (Figure 3b). A subsequent single-crystal study not only confirmed the results of the powder structure including the torsion angles about the benzene-substituent bonds, but also confirmed the hydrogen atom positions that had been postulated on the basis of their intermolecular contacts [19]. If no prior knowledge of connectivity is available, the structure solution calculation can be run considering each atom in the material as an independent entity, so-called ‘shake-and-bake’ methods [20,21]. However, success is limited as the resulting structure solution (that with lowest R-factor) is

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Figure 3. (a) Structural model used in the structure solution of 2,4,6-triisopropylbenzenesulfonamide. Arrows indicate flexible torsion angles. (b) View of part of the crystal structure of 2,4,6-triisopropylbenzenesulfonamide showing the hydrogen-bond network as dashed lines and the thin lines representing bonds to carbon.

often a collection of atomic positions that makes no chemical sense. This approach tends to be more successful when applied to structures containing strong scatterers. 2.2.2. Search Methods In principle, any global optimization technique can be used to explore the resulting hypersurface and locate the lowest point, and it is this aspect of method development that has attracted the most interest. With a multidimensional hypersurface often containing numerous false local minima (corresponding to incorrect structures) as well as the global minimum, this is a relatively complex optimization problem that requires highly efficient search methods so that the structure solution calculation is not unnecessarily computationally expensive. The most straightforward approach is based on a grid search procedure in which the structural model is moved systematically around the unit cell so that all possible packing arrangements and conformations are assessed. Such an exhaustive approach guarantees that the global minimum is found (given that a fine grid is used), but is inefficient and computationally demanding, making complex problems (with a large number of variables) intractable in a reasonable timeframe. In such cases, more efficient optimisation techniques based either on sequential or evolutionary algorithms have been more successful.

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The first optimization algorithms to be developed for crystal structure solution, Monte Carlo (MC) [22] and simulated annealing techniques (SA) [23–25], are based on the physical principles of heating and cooling. Both these methods involve the generation of a sequence of structures for consideration as potential structure solutions. In the MC method, each trial structure is generated from the previous one in the sequence by random movement of the molecule. The new structure is then accepted in the sequence if it has a lower R-factor than the previous structure or with a fixed probability if it has a higher R-factor. In this way, the algorithm performs a random walk that explores the hypersurface by avoiding the peaks (areas of high Rfactor) and giving emphasis to the regions of low R-factor, but with the ability to escape from local minima. The level of probability used in the MC method operates in a manner analogous to temperature, and it is in the way that this ‘temperature’ factor is used that the MC and SA techniques differ. In the MC method this is fixed or varied manually, whereas SA invokes an annealing schedule to systematically reduce the ‘temperature’ of the system and converge on the global minimum. An alternative but closely related approach is that of parallel tempering, in which a number of parallel optimizations are made each with a different temperature, with periodical exchange of trial structures between the parallel runs [21]. The MC approach has also been combined with features of molecular dynamics in a hybrid approach (HMC) [26]. This method considers each trial structure as a particle that is assigned a momentum to travel over the hypersurface. As the total energy of the system must be conserved, promising structures with low potential energy (low R-factor) have a high kinetic energy allowing the particle to escape from any local minima. Evolutionary search algorithms have also been applied to the structure solution problem. These are based on the Darwinian principles of natural evolution and involve the processes of mating, mutation and natural selection. Unlike sequential algorithms that operate on a single trial structure, these evolutionary strategies maintain a population of trial structures (or members) each with a genetic code defined by the structure model parameters (x,y,z, θ,ϕ,ψ,τ1,τ2,…,τN) that are mutated and recombined together over a number of generations. By natural selection, the fittest members of the population (those with lowest R-factor) will survive and procreate, leading to improved individuals in subsequent generations until the population evolves to a point where one or more members locate the global minimum. Evolutionary techniques are highly efficient optimizers and have been implemented for structure solution in the form of genetic algorithms (GA) [27,28] and differential evolution (DE) [14,18,29]. These methods differ in the way the mutation and recombination processes are invoked, and in the selection process used to progress from parent to child and generate the new population.

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2.2.3. Efficiency and Reliability With the development of this range of global optimization techniques for structure solution, there are inevitably comparisons made regarding efficiency and reliability. The success of each technique is judged predominantly on the complexity of problem solved (in terms of the number of variables used to define the structure), the number of structures generated in order to achieve solution, and the amount published. However, such a straightforward comparison is not truly indicative. The shape of the hypersurface can differ significantly not only for apparently similar structures, but by the choice of R-factor used for calculation or by the way a structure has been defined (e.g. the exact values of the bond lengths and angles used to construct the model, or any limitation in conformational flexibility). An apparently simple structure in terms of number of variables can give rise to a hypersurface that contains many local minima and an ill-defined global minimum. In addition, the inherent random nature of these techniques (except in the case of a grid search) means that it is highly unlikely that two calculations will result in the global minimum being located via the same optimization route or by the same number of moves or generations. The performance of each technique is also highly dependent on the parameters used to control the optimization. It is clear that the efficiency of a grid search depends on the size of the grid used; even a small change towards a finer mesh can result in a combinatorial explosion! The efficiency of the ‘physical’ techniques is controlled by temperature. In a MC calculation, this must be low enough so that the sequence is not essentially a random walk over all areas of the surface, but high enough to prevent becoming trapped in a local minimum. The HMC approach is controlled in a similar way using the kinetic energy. In the case of SA, it is primarily the different choice of annealing schedule (e.g. reduction at a preset rate or use of R-factor fluctuation) that affects the performance of the various implementations of this method. However, the selection of cooling scheme is an optimisation problem in itself, as the optimal cooling rate is infinitely slow (to prevent the algorithm getting trapped in a local minimum). Despite a recent direct comparison of the SA and HMC techniques (using a consistent hypersurface and multiple calculations) in which the latter was found to be more efficient [26], SA is the most widely used optimization technique and has been developed by several groups [25,30–34] and is implemented in several programs e.g. DASH [35], ENDEAVOUR [32], PSSP [31], PowderSolve [30] and ESPOIR [20]. The performance of the evolutionary algorithms depends on population size, and either the type of crossover and number of structures used for mating and mutation operations (in the case of GA), or the levels of recombination

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and mutation (in DE). Although an increase in population size and hence an increase in the number of trial structures per generation may appear to reduce efficiency, the astute use of mating and mutation operations often speeds up convergence on the global minimum requiring less generations and hence increasing performance [36]. The reliability of all these techniques is often addressed by performing multiple optimization calculations using the same hypersurface and control parameters. Repeated convergence on a particular structure solution implies that it represents the global minimum, but this practice clearly impacts on the efficiency of the techniques with many more structures than is often necessary generated to achieve solution. The progress of these structure solution calculations can be followed by plotting the R-factor of each structure versus the number of moves or generations in the calculation. Figure 4 shows the results for a simulated annealing calculation with 80 structure solution attempts [33]. The target value χ2 for a successful structure solution is ~100. It is clear that many of the runs locate the global minimum in less than a million moves, but that others become trapped in false minima at the two plateau regions χ2 = 175 and 350. Figure 5 shows an n evolutionary progress plot used to follow a DE structure solution calculation. In a similar way to a simulated annealing calculation, it clearly shows structure solution calculations converging to the global minimum (Rwp ~ 10%), while a few others become trapped in false minima (Rwp > 15%). As with other evolutionary techniques, the aim is to choose the correct combination of optimization parameters to prevent this premature convergence, but to ensure optimum efficiency by quick convergence to the global minimum. This example shows multiple DE calculations run using different

Figure 4. Correlated integrated intensity versus the number of SA moves for the structure solution of famotidine form B.

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Figure 5. DE progress plot showing the evolution of Rwp for the best structure in the population (line) and the average value of Rwp for the structures in the population (circles).

a optimization control parameters, and the effect of the mutation factor on this particular calculation [18]. The efficiency of any of these global optimization methods will obviously be affected by reducing the search area, i.e. restricting the search to low-lying regions of the hypersurface. However, there is always the danger that introducing constraints can disrupt natural optimization pathways. The most common route to imposing structural constraints is through limiting molecular conformation using data from similar materials deposited on a crystallographic database, but this does not take account of possible atypical behaviour of a powder sample. A more robust approach is to incorporate information from other experimental methods such as solid-state NMR which can be used for conformational analysis [37]. An alternative approach is to use the optimization technique itself to provide information about structural parameters as the calculation progresses. This approach has been used very successfully recently by incorporation of cultural evolution principles to the DE technique and the use of dynamic parameter boundaries to drastically improve the efficiency of the calculation [38]. 2.3. RIETVELD REFINEMENT

Once a suitable structure solution has been generated, the structure determination process is completed by Rietveld refinement. In Rietveld refinement, every point in the digitized powder diffraction profile is considered as an individual intensity measurement. The calculated powder diffraction pattern is then compared, point by point, with the experimental powder diffraction pattern, and selected parameters defining the structural model and/or the

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profile are adjusted by least-squares methods to obtain an optimal fit between the experimental and calculated powder diffraction patterns. Several criteria can be used to assess the agreement between the experimental and calculated powder diffraction patterns, and the most common figure-of-merit is the weighted profile R factor Rwp. Some commonly used programs for Rietveld refinement are GSAS [39], FULLPROF [40] and TOPAS [10]. For successful Rietveld refinement, the initial structural model (from structure solution) must be a sufficiently good representation of the correct structure. In most cases, Rietveld refinement will be straightforward if all atoms are within 1.0Å of their final refined positions. In the case of triethyl1,3,5-benzenetricarboxylate (Figure 6) it is clear that the majority of the atoms positions obtained from the structure solution are close to their final refined positions. However, the carbon atoms at the end of two of the side chains have adopted the incorrect conformation. This is caused by the presence of significant preferred orientation in the sample and its effect on the relative intensities in the powder data. Corrections can be made in refinement by variation of a preferred orientation parameter, and hence the global minimum in refinement is essentially different than that defined in structure solution. In this example, the atoms of concern moved significantly during refinement.

Figure 6. Comparison between the position of the molecule obtained from the DE structure solution calculation and the corresponding atoms in the refined crystal structure of triethyl1,3,5-benzenetricarboxylate [14].

As Rietveld refinement can often suffer from problems of instability, it is generally necessary to use geometric restraints (soft constraints) based on standard molecular geometries to bias the refinement towards structurally reasonable results and to prevent excessive shifts in the atomic positions. In general, the introduction of restraints allows more parameters to be refined than would be possible in unrestrained refinement from the same experimental data, and indeed refinement is often successful only if appropriate

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restraints are imposed. Figure 7 shows the results of a typical Rietveld refinement. A successful refinement must show a combination of a good fit (as below), a reasonable R-factor value (i.e. an Rwp or χ2 close to that obtained by LeBail or Pawley refinement) and a crystal structure that makes structural sense.

Figure 7. Final observed (circles), calculated (solid line) and difference (below) X-ray powder diffraction profile for the final refinement of α-methyl-α-propylsuccinimide [38]. Reflection positions are also marked.

3. Concluding Remarks The propensity of many materials to occur only as crystalline powders makes this an essential tool in any area in which structure in the solid state is important. Continued advances in structure determination techniques and continual improvements in data collection should extend the current boundaries towards larger and more challenging problems. In molecular crystallography, this clearly points to the continued development and optimization of the efficiency and reliability of the direct space methods or indeed the application of new algorithms. No matter how the advances in data analysis and instrumentation are achieved, the limiting factor to structure determination from powder data may prove to be the inherent lack of data observations that can currently be obtained from a powder pattern. The advantages of incorporating additional observations in the structure determination process are clear, and whether through the use of molecular structure (chemical knowledge) in a direct space structure solution calculation, extensive stereochemical restraints, spectroscopic data or theoretical calculations, proper utilization of all the structural information that is available, will allow us to go beyond the bounds of what has currently been achieved. Although not an ab initio

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structure determination, the demonstration of the structure solution and refinement of a protein structure from powder diffraction data [41] has confirmed the arrival of powder diffraction in the biological arena and given us a glimpse of future possibilities. Alternative approaches based on crystal structure prediction by minimization of lattice energy and comparison of simulated and experimental powder patterns are also being developed to overcome the reliance on the success of indexing before structure determination can be continued. In these cases, essentially both the indexing and structure solution stages are carried out without reference to the powder data, and the resulting structure used as the starting point for Rietveld refinement [42–45]. The current state of the crystal structure determination from powder diffraction data is comparable to that of single-crystal methods several decades ago. We can predict with optimism that the future state of this technique may mirror that of single-crystal diffraction today. 4. Acknowledgments MT would like to thank the Royal Society for the award of a University Research Fellowship.

References 1. K. D. M. Harris, M. Tremayne and B. M. Kariuki, Contemporary advances in the use of 2. 3. 4. 5. 6. 7. 8.

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powder X-ray diffraction for structure determination. Angew. Chem. Int. Ed. 40, 1626– 1651 (2001) W. I. F. David, K. Shankland, L. B. McCusker and Ch. Baerlocher (Eds.), Structure determination from powder diffraction data (Oxford University Press, Oxford, 2002) M. Tremayne, The impact of powder diffraction on the structural characterization of organic crystalline materials. Phil. Trans. R. Soc. Lond. A. 362, 2691–2707 (2004) L. B. McCusker, R. B. VonDreele, D. E. Cox, D. Louer and P. Scardi, Rietveld refinement guidelines. J. Appl. Cryst. 32, 36–50 (1999) R. A. Young (Eds.), The Rietveld Method (Oxford University Press, Oxford, 2002) H. M. Rietveld, A profile refinement method for nuclear and magnetic structures. J. Appl. Cryst. 2, 65–71 (1969) R. Shirley, The CRYSFIRE System for Automatic Powder Indexing (University of Surrey, UK) (1999) B. M. Kariuki, S. A. Belmonte, M. I. McMahon, R. L. Johnston, K. D. M. Harris and R. J. Nelmes, A new approach for indexing powder diffraction data based on whole-profile fitting and global optimization using a genetic algorithm. J. Sync. Rad. 6, 87–92 (1999) M. A. Neumann, X-Cell; a novel indexing algorithm for routine tasks and difficult cases. J. Appl. Cryst. 36, 356–365 (2003) A. A. Coehlo, Indexing of powder diffraction patterns by iterative use of a singular value. J. Appl. Cryst. 36, 86–95 (2003)

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11. M. Tremayne, B. M. Kariuki and K. D. M. Harris, Structure determination of a complex organic solid from X-ray powder diffraction data by a generalized Monte Carlo method: The crystal structure of red fluorescein. Angew. Chem. Int. Ed. Engl. 36, 770–772 (1997) 12. A. LeBail, H. Duroy and J. L. Fourquet, Ab initio structure determination of LiSbWO6 by X-ray powder diffraction. Mat. Res. Bull. 23, 447–452 (1988) 13. G. S. Pawley, Unit-cell refinement from powder diffraction scans. J. Appl. Cryst. 14, 357–361 (1981) 14. S. Y. Chong, C. C. Seaton, B. M. Kariuki and M. Tremayne, Molecular vs crystal symmetry in tri-substituted triazine, benzene and isocyanurate derivatives. Acta Cryst. B62, 864–874 (2006) 15. M. Tremayne and C. Glidewell, Direct-space structure solution from laboratory powder diffraction data of an organic cocrystal: 1,2,3-trihydroxybenzene-HMTA (1/1). Chem. Comm. 2425–2426 (2000) 16. M. Tremayne, C. C. Seaton and C. Glidewell, The use of differential evolution in structure solution from powder diffraction data. ACA Trans. 37, 35–50 (2002) 17. M. Tremayne, E. J. Maclean, C. C. Tang and C. Glidewell, 2,4,6-Tri-isopropyl benzenesulfonamide: Monte Carlo structure solution from X-ray powder diffraction data for a molecular system containing four independent asymmetric rotors. Acta Cryst. B55, 1068–1074 (1999) 18. M. Tremayne, C. C. Seaton and C. Glidewell, Structures of three substituted arenesulfonamides from X-ray powder diffraction data using the differential evolution technique. Acta Cryst. B58, 823–834 (2002) 19. J. Caleb Clark, M. L. McLaughlin and F. R. Fronczek, 2,4,6-Triisopropylbenzenesulfonamide from single-crystal data. Acta Cryst. E59, 2005–2006 (2003) 20. A. LeBail, ESPOIR: A program for solving structures by Monte Carlo analysis of powder diffraction data. Mat. Sci. Forum 378, 65–70 (2001) 21. V. Favre-Nicolin and R. Cerny, FOX, ‘free objects for crystallography’: a modular approach to ab initio structure determination from powder diffraction. J. Appl. Cryst. 35, 734–743 (2002) 22. K. D. M. Harris, M. Tremayne, P. Lightfoot and P. G. Bruce, Crystal structure determination from powder diffraction data by Monte Carlo methods. J. Am. Chem. Soc. 116, 3543–3547 (1994) 23. J. M. Newsam, M. W. Deem and C. M. Freeman, Direct space methods of structure solution from powder diffraction data. Accuracy in Powder Diffraction II, NIST Special Publication 846, 80–91 (1992) 24. Y. G. Andreev, P. Lightfoot and P. G. Bruce, A general Monte Carlo approach to structure solution from powder diffraction data: application to poly(ethyleneoxide)3 :LiN(SO2CF3)2. J. Appl. Cryst. 30, 294–305 (1997) 25. W. I. F. David, K. Shankland and N. Shankland, Routine determination of molecular crystal structures from powder diffraction data. Chem. Commun. 931–932 (1998) 26. J. C. Johnston, W. I. F. David, A. J. Markvardsen and K. Shankland, A hybrid Monte Carlo method for crystal structure determination from powder diffraction data. Acta Cryst. A58, 441–447 (2002) 27. B. M. Kariuki, H. Serrano-Gonzalez, R. L. Johnston and K. D. M. Harris, The application of a genetic algorithm for solving crystal structures from powder diffraction data. Chem. Phys. Lett. 280, 189–195 (1997) 28. K. Shankland, W. I. F. David and T. Csoka, Crystal structure determination from powder diffraction data by the application of a genetic algorithm. Z. Krist. 212, 550–552 (1997) 29. C. C. Seaton and M. Tremayne, Differential evolution: crystal structure determination of a triclinic polymorph of adipamide from powder diffraction data. Chem. Commun. 880– 881 (2002)

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30. G.E. Engel, S. Wilke, O. Konig, K. D. M. Harris and F. J. J. Leusen, PowderSolve – a complete package for crystal structure solution from powder diffraction patterns. J. Appl. Cryst. 32, 1169–1179 (1999) 31. S. Pagola, P. W. Stephens, D. S. Bohle, A. D. Kosar and S. K. Madsen, The structure of malaria pigment β-haematin. Nature 404, 307–310 (2000) 32. H. Putz, J. C. Schon and M. Jansen, Combined method for ab initio structure solution from powder diffraction data. J. Appl. Cryst. 32, 864–870 (1999) 33. K. Shankland, L. McBride, W. I. F. David, N. Shankland and G. Steele, Molecular, crystallographic and algorithmic factors in structure determination from powder diffraction data by simulated annealing. J. Appl. Cryst. 35, 443–454 (2002) 34. A. J. Florence, N.Shankland, K. Shankland, W. I. F. David, E. Pidcock, X. Xu, A. Johnston, A. R. Kennedy, P. J. Cox, J. S. O. Evans, G. Steele, S. D. Cosgrove and C. S. Frampton, Solving molecular crystal structures from laboratory X-ray powder diffraction data with DASH: the state of the art and challenges. J. Appl. Cryst. 38, 249– 259 (2005) 35. W. I. F. David, K. Shankland, J. Cole, S. Maginn, W. D. S. Motherwell and R. Taylor, DASH User Manual. (Cambridge Crystallographic Data Centre, Cambridge, UK) (2001) 36. S. Habershon, K. D. M. Harris, R. L. Johnston, G. W. Turner and J. M. Johnston, Gaining insights into the evolutionary behaviour in genetic algorithm calculations, with applications in structure solution from powder diffraction data. Chem. Phys. Lett. 353, 185–194 (2002) 37. D. A. Middleton, X. Peng, D. Saunders, K. Shankland, W. I. F. David and A. J. Markvardsen, Conformational analysis by solid-state NMR and its application to restrained structure determination from powder diffraction data. Chem. Commun. 1976– 1977 (2002) 38. S. Y. Chong and M. Tremayne, Combined optimization using cultural and differential evolution; application to crystal structure solution from powder diffraction data. Chem. Comm. 4078–4080 (2006) 39. A. C. Larson and R. B. Von Dreele, Generalized Structure Analysis System. Los Alamos Natl. Lab. Rep. LA-UR-86–748 (1987) 40. J. Rodriguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction. Physica B 192, 55–69 (2003) 41. R. B. Von Dreele, P. W. Stephens, G. D. Smith and R. H. Blessing, The first protein crystal structure determined from high-resolution X-ray powder diffraction data: a variant of T3R3 human insulin-zinc complex produced by grinding. Acta Cryst. D56, 1549–1553 (2000) 42. M. Tremayne, L. Grice, J. C. Pyatt, C. C. Seaton, B. M. Kariuki, H. H. Y. Tsui, S. L. Price and J. C. Cherryman, Characterization of complicated new polymorphs of chlorothalonil by X-ray diffraction and computer crystal structure prediction. J. Am. Chem. Soc.. 126, 7071–7081 (2004) 43. L. Vella-Zarb, M. Tremayne, A. D. Bond, T. C. Lewis, D. A. Tocher and S. L. Price, The elusive crystal structure of adenine: a single-crystal, powder diffraction and theoretical prediction study. In preparation (2007) 44. M. U. Schmidt, M. Ermrich and R. E. Dinnebier, Determination of the structure of the violet pigment C22H12Cl2N6O4 from a non-indexed X-ray powder diagram. Acta Cryst. B61, 37–45 (2005) 45. M. U. Schmidt, D. W. M. Hofmann, C. Buchsbaum and H. J. Metz, Crystal structures of pigment red 170 and derivatives, as determined by X-ray powder diffraction. Angew. Chem. Int. Ed. 45, 1313–1317 (2000)

SURFACE PROPERTIES OF THE BINARY ALLOY THIN FILMS

ILONA ZASADA Solid State Physics Department, University of Lodz, ul. Pomorska 149/153, 90263 Lodz, (Poland)

Abstract. The theory of order-disorder phenomena of different physical nature in binary alloy thin films of AB3 type is considered. The investigations are based on the model of the samples with restricted dimension when it requires the construction of a thermodynamically inhomogeneous system consisting of homogeneous subsystems. The main idea of the present description was introduced by Valenta in the approach showing the thin film in the form of monoatomic layers parallel to the surfaces and treated in the sense of Néel sublattices.

Keywords: thermodynamics of inhomogeneous systems, thin films, alloys, phase transitions

1. Introduction An interdependence between the order parameters of different physical nature observed in binary alloy thin films is considered in the context of their mutual relations. The theory is based on the model consisting of atomic interactions between nearest neighbour atoms belonging to the sublattices in the form of the monoatomic layers parallel to the surface. The main idea of the present description was applied at first by Valenta and Sukiennicki [1] in the case of permalloy films for their order-disorder characterisation. The equilibrium values of the considered order parameters are obtained by minimizing the free energy of the system. The study of thin films is interesting because of the size effects. A thin film has to be treated rather as the 2D system while the semi-infinite system is of 3D character. One can expect that there is a crossover between the two-dimensional behaviour of ultra-thin films and films thick enough when they behave similarly to three-dimensional systems. The crossover phenomena means a different behaviour of the order parameters for thin and thick films. The finite sample geometries lead to the distribution of the alloy component 495 J.J. Novoa et al. (eds.), Engineering of Crystalline Materials Properties, 495–513. © 2008 Springer.

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concentration in the direction perpendicular to the surface. This distribution depends on the temperature. In the thin films structure we observe the symmetric distribution in the film thickness direction while the concentration profile is of the film thickness dependence. Moreover, the priority for the investigations of thin films is connected with the development of modern growth technologies where the layer by layer geometry is realized in natural way. First of all the surface melting and surface disordering are discussed [2, 3]. The physical nature of melting is extremely different from the lattice disordering behaviour. We can, however, observe the interdependence between the order and crystallinity parameters. In the case of the lattice ordering parameter behaviour the lattice structure is preserved while the atoms move only around their equilibrium positions. The disorder concerns then a random occupation of the regular lattice sites by the atoms of two different kinds. In contrast, the melting described by the crystallinity parameter consists in a destruction of the lattice, which means that the atoms leave the lattice sites and they wonder in space of the sample volume interacting between them. The interactions in the liquid phase change then their character with respect to the interactions appearing in the crystalline structure, however, they conserve the nature of van der Waals interatomic forces. The surface melting is discussed in terms of three densities: (i) the crystallinity order parameter which characterizes a topological deviation of the liquid structure from the crystalline one, (ii) the lattice order parameter which describes a degree of the ordering of components in alloy and (iii) the nonordering density identified with the deviation of the local concentration in planes parallel to the surface from the average concentration. All three densities have their own temperature-dependent profiles across the film. The crystallinity parameter influences the local concentration profiles and the lattice order parameter which describe the alloy structure in a different way for different surface orientations. Next, the ferromagnetic and lattice order-disorder phase transitions in thin films of the binary alloy are considered [4]. The interdependence between these two kinds of the disordering processes is discussed. We defined the new order parameter describing the magnetic processes, namely: the ferromagnetic order-disorder parameter determined in the film layer i which corresponds to the random occupation of the lattice sites with respect to the magnetic moment orientations independently of the kind of atoms situated in arbitrary lattice sites. We discuss the behaviour of magnetisation in the binary alloy thin films with respect to their lattice disorder and the relative concentration of alloy components. Among others, we can see an interesting fact when the magnetic order appears for the lattice disorder, i.e. for higher temperatures while there is no magnetisation for the lattice ordered state. The application of this description can be connected with the interface alloying and magnetisation distribution at the

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neighbourhood of the junction of two components. The ultra-thin Fe film of the 3 monoatomic layers grown on a clean Pd (001) surface [5] is a good example for such a kind of application. In the light of the present result it seems that the magnetic order can be expected in such an interface even if it is of the lattice disordered state. In the bulk geometry the phase transitions connected with different order parameters characterising different properties of a sample take place consecutively in some specific order determined by the phase transition temperatures. In the thin film geometry this process can run differently and it depends on the concentration distribution across a film reflecting a strong influence of surface states. We can observe, for example, the surface melting before the surface disordering or the surface magnetic order in the case when the sample is in lattice disordered state. These phenomena is of great interest for multiple applications going towards the nanotechnology. 2. Basic Concepts The thermodynamic considerations in the case of thin films concern of course the systems in which the role of finite size effects in the rigorous definitions of the thermodynamic functions should be taken into account. The formulations reported by Hill [6] in the context of small particles can be applied to the film structure when we treat a thin film as a system divided into subsystems equivalent to two-dimensional monoatomic layers parallel to the surfaces [7]. The film thickness d is then the characterisation of a sample and it can be expressed by the number n of monoatomic layers, d = na , with a standing for the average spacing between the neighbouring layers. In real films the separations between layers at the surfaces change with respect to their values inside a sample. This effect can be introduced by the surface energy terms usually appearing in the current models of thin films [1]. Thus, the thermodynamic functions which describe the relations for the considered thin film structure are not rigorously extensive, i.e., they are not proportional to the number of elements, but they satisfy the relations including size effects. According to the considerations presented by Hill [6] an arbitrary thermodynamic function G can be written in the form: ⎛_ 1 ⎞ G = N 2 n ⎜ G + G′ ⎟ n ⎠ ⎝

(1)

where N2 stands for the _number of atoms in the plane while n is the number of monoatomic layers. G and G ′ refer to the mean value of G when the system is homogeneous and to the difference between the two-dimensional and three-dimensional average value of G [6], respectively.

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The evident example confirming the Hill procedure is connected with the behaviour of the order-disorder phase transition temperature Tt = Tt ( d ) [1,8] as well as the melting temperature Tm = Tm ( d ) with respect to their thickness dependences [9] which has been clearly demonstrated by experiments [10]. Moreover, the application of Hill’s procedure to the van der Waals equation of state was a subject of calculations leading to the relation Tm ( d ) in terms of reduced variables with the reducing parameter dependent on the sample thickness [11]. By this fact we can state that the Hill procedure for the phase transition temperature leads to the result which is qualitatively equivalent to that obtained by means of the approach in terms of molecular field approximation used for the description of thermodynamic subsystems and interactions between them. This approach is frequently applied in thin films physics. Originally introduced by Valenta [7], from the physical point of view based on the Néel sublattices idea, the model was successfully used by Valenta and Sukiennicki [1] in order to calculate the lattice orderdisorder phase transition temperature. Let us notice that the expected dependence of the order-disorder temperature on the film thickness can be then obtained due to the boundary conditions, first of all, given by the lack of nearest neighbours for the surface atoms; secondly by the appearance of the surface roughness reflected by surface potential [12]. The thermodynamic relation: F ( d ) = U ( d ) − TS ( d )

(2)

between the thermodynamic potential F, the internal energy U and the entropy S are apparently the same in the case of thermodynamic limit and for the systems with restricted dimensions. In particular, this relation is satisfied for each subsystem i ∈ (1, n ) , i.e. Fi = U i − TSi . Therefore, the thermodynamic potential F ( d ) as one of the thermodynamic functions G(d) given by (1) can be calculated on the standard way by means of (2) [12]. However, for the sake of simplicity, it is convenient to consider sometime the thermodynamic potential F ( d ) in its total form, not separated into two parts U and S. This fact takes its place for the description of melting phenomena in terms of the Landau-Ginzburg model for inhomogeneous systems [12]. For these reasons, assuming constructions the most frequently used in literature for given phenomena we take into account different description in the case of ordering and melting effects. We describe the ordering in terms of the internal energy U and the entropy S when calculated with respect to the boundary conditions. The melting is described in terms of the

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thermodynamic potential F considered in the most convenient form of two intersecting parabolas [9]. 2.1. THEORY

Let us now analyse an infinite thin film of fcc binary alloy AcB(1-c) with film thickness of n monoatomic layers having the (111) surface orientation. In order to describe the lattice long-range order, the fcc lattice is divided into two sublattices, α and β. In the perfectly ordered case, all α sites are occupied by A atoms and the β sites are occupied by B atoms. In the completely disordered case, the probabilities to find an A atom in α and β sites are the same. The lattice order parameter t(i), describing the difference in concentrations between the α and β sublattices is defined by [7]: t (i ) = p αA (i ) − p βA (i ) = p Bβ (i ) − p Bα (i )

(3)

γ

The symbols pC (i ) denote the probability of finding an C atom in the γ sublattice. These probabilities are normalised by [7]: p αA (i ) + p Bα (i ) = 1,

p Bβ (i ) + p βA (i ) = 1

(4)

The concentration of atoms A in the monoatomic layer i is given by: x(i ) = p αA (i ) Fα + p βA (i ) Fβ

(5)

while the concentration of atoms B in the same layer is written as: y (i ) = 1 − x(i ) = p Bα (i ) Fα + p Bβ (i ) Fβ

(6)

where Fα and Fβ are the relative numbers of α and β sites, respectively. With all these definitions it is possible to write the layer dependent probabilities as functions of the layer dependent concentration x(i) and the lattice order parameter t(i): pαA (i ) = x(i ) + Fβ t (i )

(7)

β

p A (i ) = x(i ) − Fα t (i ) pBβ (i ) = 1 − x(i ) + Fα t (i ) pαB (i ) = 1 − x(i ) − Fβ t (i )

The equilibrium values of t(i) and x(i) are obtained by minimising the free energy F given by (2) for our system with respect to of t(i) and x(i):

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∂F = 0, ∂t (i ) ∂F = λ, ∂x(i )

i = 1,2,..., n

(8)

i = 1,2,..., n

with λ standing for Lagrange factor which assures the condition:

∑ x(i) = nc

(9)

i

where c denotes the average concentration of the atoms A in stoichiometric composition of the alloy. In order to calculate the free energy F = F ( x, t ) we consider the terms connected with the internal energy U = U ( x, t ) and the entropy S = S ( x, t ) . In the Bragg-Williams approximation, which corresponds to the molecular field approximation (MFA) procedure [10], the internal energy U is given as the average over the energies corresponding to a given long-range order and for the film consisting of n layers can be written as follows: n

ii U = − N 2 ∑∑ ⎣⎡ QCC ′ ii VCC ′ + QCC ′ i =1 CC ′

ii +1

ii +1 VCC ′ + QCC ′

ii −1

ii −1 ⎤ VCC ′ ⎦

(10)

for C, C’ = A or B. In the present case, we consider only the nearest neighbours interactions and the mean number of nearest neighbour pairs in a given layer and in the neighbouring layers are given by: QCC ′ QCC ′ QCC ′

1 ii ii ⎡ Fα pCα ( i ) ( rαα pCα ′ ( i ) + rαβii pCβ ′ ( i ) ) + Fβ pCβ ( i ) ( rβα pCα ′ ( i ) + rββii pCβ ′ ( i ) ) ⎤⎦ 2⎣ 1 ii +1 α ii +1 α pC ′ ( i ) + rαβii +1 pCβ ′ ( i + 1) ) + Fβ pCβ ( i ) ( rβα pC ′ ( i + 1) + rββii +1 pCβ ′ ( i + 1) ) ⎤⎦ = ⎡⎣ Fα pCα ( i ) ( rαα ii +1 2 1 ii −1 α ii −1 α pC ′ ( i ) + rαβii −1 pCβ′ ( i − 1) ) + Fβ pCβ ( i ) ( rβα pC ′ ( i − 1) + rββii −1 pCβ ′ ( i − 1) ) ⎤⎦ = ⎡⎣ Fα pCα ( i ) ( rαα ii −1 2 ii

=

(11) In the above equations, we have used rγγii ′ for denoting the number of the nearest neighbours located at sites γ’ of an atom situated at a site γ in the same layer and rγγii ±′1 if two neighbouring atoms belong to different layers. The boundary conditions for the symmetrical situation at both surfaces requires that: QCC ′

nn +1

= 0, QCC ′

10

=0

(12)

The entropy S of the state with a given distribution of concentration and the long-range order parameter can by written as:

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n

S = − k B N 2 ∑∑ Fγ pCγ ( i ) ln pCγ ( i )

(13)

i =1 γ C

where the summation over C runs over A and B and the summation over γ should be taken over α and β. Let us notice that the summation in (10) and (13) concerns the homogenous subsystem in each plane i and then leads to the factor N2 when we compare (10) and (13) with (1) while the summation over i ∈ (1, n ) appears instead of n due to the construction for small number n of subsystems. 2.1.1. Surface Melting and Surface Disordering Usually, in the case of binary alloy theories we assume that the quantities ii ii ±1 VCC ′ and VCC ′ appearing in the equation (10) represent the interaction energies between two atoms. In the Bragg-Williams approximation, they are parameters of the theory characterising the solid phase in its average density state representation. In the present model the interpretation of these quantities is extended so that they describe the interaction energies between two atoms embedded in the medium characterised by its crystallinity. This fact can be reflected by introducing the interaction energy dependent on the crystallinity parameter ii ii ±1 and VCC by m(i).Thus, in the equation (10) we should replace VCC ′ ′ ii ii ±1 VCC ′ ( m ( i ) ) and VCC ′ ( m ( i ) , m ( i ± 1) ) , respectively.

Taking into account the model of solid-liquid phase transition discussed in [13] we can see that in general, the bulk melting behaviour can be described by means of van der Waals equation of state in its modified form. ii ii ±1 In this case VCC ′ ( m ( i ) ) and VCC ′ ( m ( i ) , m ( i ± 1) ) can be treated as the thermodynamic Gibbs free energy functionals with respect to the crystallinity parameter m(i). The most interesting analytical solutions seem to be those reported in [14] and [15] in terms of the density ρ = ρl + (ρc – ρl)m, where the behaviour of ρl (T) and ρc (T) are determined then by the conditions: 1. for ρl ⎛ dVccii′ ⎞ (14) ⎜ dm ⎟ = 0 ⎝ ⎠m=0 2. for ρc ⎛ dVccii′ ⎞ (15) ⎜ dm ⎟ = 0 ⎝ ⎠ m =1 ii ±1 and, for VCC ′ ( m ) , respectively.

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ii ±1 ii In order to derive the potentials VCC ′ ( m ) and VCC ′ ( m ) we apply, according to [13], the method reported by Reif [16] in the case of the van der Waals equation of state discussion. However, we modify the model by introducing the idea of different mean-field behaviours for solid and liquid phases (e.g. [17], [14]). The ab initio calculations performed for the thermodynamic potentials in the case of aluminium samples confirm their different shape describing both the phases [18]. The idea developed in [15] is based on the assumption that the liquid phase is well described by the van der Waals equation of state and the Gibbs energy which corresponds then to this van der Waals equation. The method is applied to determine an effective medium potential for the solid phase [15]. The van der Waals theory is next extended by introducing a modification of the entropy parameters in analogy to the prediction proposed in [14]. Taking into account the equations of state (14) and (15) we can develop ii ii ±1 and VCC into series with the functionals VCC ′ ( m ( i ) , m ( i ± 1) ) ′ ( m (i ))

respect to (1 – m), namely: 2 2 1 1 s ii VCC α CC ′ (1 − m ( i ) ) + α CC ′ ( m ( i ) ) = VCC ′ ( m = 1) + ′ ( m ( i ) ) ( δ1i + δ1n ) (16) 2 2

for the solid phase of a thin film and into series with respect to m, namely: 2 2 1 1 s ii α CC ′ ( m ( i ) ) + α CC VCC ′ ( m ( i ) ) = VCC ′ ( m = 0 ) + ′ ( m ( i ) ) ( δ1i + δ1n ) 2 2

(17)

for the liquid phase of a thin film. Similarly, the interaction energies between the atoms lying in neighbouring layers are expressed by: ii ±1 ii VCC ′ ( m ( i ) ) = VCC ′ ( m ( i ) ) −

1 J CC ′ m ( i ) Δm ( i ) 2

Δm ( i ) = m ( i + 1) + m ( i − 1) − 2m ( i )

(18) ii ii for both crystal ( VCC ′ ( m ( i ) ) given by (16)) and liquid ( VCC ′ ( m ( i ) ) given by (17)) phases, respectively. The appearance of the second order difference Δm ( i ) reflects the influence of the boundary conditions for m (1) and m ( n ) introduced by the lack of nearest neighbours at the surface (cf. (12)). The term Δm ( i ) corresponds to the gradient term in the Landau-Ginzburg functional and integrated over all the sublattices is equivalent to the term G’ in the Hill formulation (cf. (1)). The present forms of (16) and (17) correspond to the potentials of two intersecting parabolas which are very well known in literature and frequently used [11,13]. Moreover, the analysis of this type of the potential

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shows that it is very convenient for calculations and its results are quite precise [14]. For these reasons we reduce any potential to its parabolic s shape when it is described only by parameters α CC ′ and α CC ′ considered as the parameters of the theory. Of course, taking into account one of the forms for the van der Waals potential discussed in [13], we can precisely determine these parameters but it seems that the theory is more flexible when they remain free parameters. The parameters J CC ′ stand for the material constants characteristic for a given sample. s In the particular case α CC ′ = 0 , α CC ′ = 0 and J CC ′ = 0 the present model can be reduced to the standard form of the alloy description in terms of Bragg-Williams approximation for interaction energies which are given by VCC ′ ( m = 1) . Thus, they can be determined by the low temperature behaviour of the energy. In the present version of the model extended to the melting area the relation between the energy VCC ′ ( m = 1) in the solid phase and the energy VCC ′ ( m = 0 ) in the liquid phase is given by: VCC ′ ( m = 0 ) = VCC ′ ( m = 1) + Λ

(19)

⎛ T ⎞ Λ = Lm ⎜1 − ⎟ ⎝ Tm ⎠

(20)

where

is valid for arbitrary temperature T close to Tm with Tm and Lm standing for the bulk melting point and the latent heat for melting per unit volume, respectively. The relation (19) follows the thermodynamic considerations connected with the phase transition description [11,13]. In this case VCC ′ ( m = 1) and VCC ′ ( m = 0 ) belong to the internal energy term (10) while the entropy is given by (13). However, for the reasons explained above the potentials (16) and (17) contains the terms for α CC ′ which is a contribution of two kinds. Formally, we can write that α CC ′ = α CC ′ (U ) + α CC ′ ( S ) where α CC ′ (U ) denotes a contribution to the internal energy due to the change of the crystallinity parameter while α CC ′ ( S ) is a contribution introduced by the crystallinity parameter to the entropy S(m(i)) (cf. [12]}. Of course, we do not divide the coefficient α CC ′ into two parts in practice, taking into account the fact that the functional F ( x ( i ) , t ( i ) , m ( i ) ) is derived by means of the potentials (16) and (17) with (18) given in the convenient form of two intersecting parabolas (cf. [9]). Thus, substituting (16) and (17) with (18) into (10) we calculate the functional F for which we obtain the condition:

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∂F (21) = 0, i = 1, 2,..., n ∂m(i ) which now, together with the solutions of (8), leads to the equilibrium values of m(i) with respect to x(i) and t(i) considered simultaneously.

2.1.2. Ferromagnetic Properties The ferromagnetic order-disorder description requires the introduction of 8 probabilities pCγ s (i ) connected with the magnetic moment orientations s at the site described by the indices ( γ ,C ) . The index s can be defined by the direction of the spin component S Czγ (i ) . In particular, when we assume the 1 spin value S = , we have s = +1( ↑ ) or s = −1( ↓ ) . The probabilities 2 pCγ s (i ) are normalised then by: pCγ (i ) = pCγ ↑ (i ) + pCγ ↓ (i )

(22)

and they allow us to introduce the magnetic order parameter by following definition:

σ ( i ) = ∑ Fγ xC pCγ ( i )σ Cγ ( i )

(23)

pCγ σ Cγ ( i ) = pCγ ↑ (i ) − pCγ ↓ (i )

(24)

Cγ

and

which characterises the shape for the inhomogeneous distribution of local contributions σ Cγ ( i ) to the magnetic behaviour of the considered alloys. By means of equations (3) – (6) and (22) – (24) it is possible to write the layer dependent site probabilities as functions of the layer dependent concentration x ( i ) , long-range order parameter t ( i ) and magnetic order parameter σ Cγ (i ) : 1 pαA ↑ (i ) = ( x(i ) + Fβ t (i ) ) (1 + σ αA (i ) ) 2 1 pαA ↓ (i ) = ( x(i ) + Fβ t (i ) ) (1 − σ αA (i ) ) 2 1 p Aβ ↑ (i ) = ( x(i ) − Fα t (i ) ) (1 + σ Aβ (i ) ) 2

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1 ( x(i) − Fα t (i) ) (1 − σ Aβ (i) ) 2 1 pBβ ↑ (i ) = (1 − x(i ) + Fα t (i ) ) (1 + σ Bβ (i ) ) 2 1 pBβ ↓ (i ) = (1 − x(i ) + Fα t (i ) ) (1 − σ Bβ (i) ) 2 1 pαB ↑ (i ) = (1 − x(i ) − Fβ t (i ) ) (1 + σ Bα (i ) ) 2 1 pαB ↓ (i ) = (1 − x(i ) − Fβ t (i ) ) (1 − σ Bα (i ) ) 2

p Aβ ↓ (i ) =

505

(25)

The equilibrium values of t ( i ) , x ( i ) and σ Cγ (i ) are obtained by minimising the free energy of the system given by equation (2) with respect to of t ( i ) , x ( i ) (see (8) ) and σ Cγ (i ) : ∂F (26) = 0, i = 1, 2,..., n ∂σ Cγ (i ) The entropy term of the free energy F given by (2) can be calculated in the usual way [8] taking into account that: S = −k B N 2

∑ γ

pCγ s ( i ) ln pCγ s ( i )

(27)

C , , s ,i

where the probabilities pCγ s ( i ) are expressed by (25). The internal energy term U is a linear combination of two kinds of interactions, namely: (28) U = Ul + U f where the lattice order disorder part is given by (cf. [1]): 1 ii ′ ⎤ U l = − N ∑∑∑∑ Fγ ⎡⎣ pCγ s ( i ) rγii→′ γ ′ pCγ ′′s′ ( i′ )VCC ′⎦ 2 CC ′ γγ ′ ss′ ii′ while the ferromagnetic part is taken in the form:

(29)

1 ii ′ (30) U l = − N ∑∑∑∑ Fγ ⎡⎣ pCγ s ( i ) rγii→′ γ ′ pCγ ′′s′ ( i′ ) J CC ′ ss ′ ⎤ ⎦ 2 CC ′ γγ ′ ss′ ii′ where the summation over i′ runs over i′ = i − 1, i, i + 1 . ii ii ±1 The energies VCC ′ and VCC ′ in equation (29) describe the interaction between two atoms C and C’ in the sense of the Bragg-Williams approximation [8] lying in one monoatomic layer or in two neighbouring

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monoatomic layers, respectively. In a similar way the magnetic part of the ii ii ±1 energy can be characterised by J CC ′ ss ′ and J CC ′ ss ′ in equation (30) which describe the magnetic dipole interaction of two dipoles belonging to the atoms C and C’ when mutual orientations of interacting magnetic moments are introduced by the product ss′ factor. The explicit form of the internal energy term becomes: 1 γ γ′ ii ′ ii ′ ⎤ (31) U l = − N ∑ ∑ Fγ ⎡⎣ pCγ ( i ) rγii→′ γ ′ pCγ ′′ ( i′ ) (VCC ′ + J CC ′σ C ( i ) σ C ′ ( i ′ ) ) ⎦ 2 CC ′ γγ ′ii′ where the summation over i′ runs over i′ = i − 1, i, i + 1 . It is worth while to notice that in the case of inhomogeneous distribution of magnetizations σ Cγ (i ) with respect to i , the internal energy can be considered in two parts. One of them describing the internal energy additive for the internal energies of the subsystems i and its second part proportional to the second difference Δσ Cγ (i ) which is responsible for the size effect appearance. The simultaneous solution of equations (8) and (26) with condition (12) can be found numerically. On this basis the properties of the ordering alloys around two phase transition points, i.e. the order-disorder phase transition and the magnetic phase transition, are discussed. 3. Numerical Results

As an example we will consider the thin film of the AB3 alloy with (111) surface orientation. In this case the α sublattice consists of all corner sites and the β sublattice consists of all the face-centre sites. All α sites have six β sites as nearest neighbours in the plane while all β sites have two α sites and four β sites as nearest neighbours in the plane. In the next plane, all α sites have three β sites as nearest neighbours while all β sites have one α site and two β sites as nearest neighbours. The quantities Fγ , rγγii ′ , rγγii ±′ 1 appearing in the relation for internal energy U and entropy S take the following values: 1 3 ii ii ii ±1 ii ±1 Fα = , Fα = , rαα = 0, rαβii = 6, rββii = 4, rβα = 2, rαα = 0, rαβii ±1 = 3, rββii ±1 = 2, rβα =1 4 4 The considered system is described by the pairwise interactions of two kinds, lattice and magnetic, both taken in the nearest neighbours approximation. The lattice interactions are defined by three parameters VAA ,VBB and VAB = VBA . We also define (cf. [8]) the quantity 1 V = VAB − (VAA + VBB ) which take a positive value for ordering alloy and a 2

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negative value for the segregating one. We confine our considerations to the ordering alloys and we keep all the potential interaction parameters constant chosen in the way that the lattice order-disorder phase transition take place in the proper temperature for a given film thickness. We also assume that our sample is composed of nickel and iron atoms forming the FeNi3 alloy with the bulk lattice order-disorder phase transition temperature Tt(∞) = 779K and the bulk meting temperature 1748K. 3.1. SURFACE MELTING AND SURFACE DISORDERING

The three parameters VAA ( m = 1) , VBB ( m = 1) and VAB ( m = 1) = VBA ( m = 1) (see equation (16)) considered in the nearest neighbours approximation are nothing else then the interaction energies used in our paper [8] for describing the order-disorder phenomena in binary alloy thin films without taking into account the other phenomena appearing in the sample with temperature changes. In the present considerations the interaction energies are more complicated functions allowing the melting phenomenon and the values of these parameters have to be changed in the way which ensure that the order-disorder phase transition take place at the proper temperature for the considered alloy composition.

Figure 1. Layer-dependent long-range order parameter t(i) and crystallinity parameter m(i) vs. reduced temperature calculated for the film when its surface layers are in liquid phase [2].

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We discussed here the properties of the ordering alloys around the two phase transition points. The first one is characteristic for the order-disorder phase transition while the second one is connected with surface melting event. All the characteristics are found by simultaneous minimisation of the total free energy with respect to the lattice order parameter, concentration and crystallinity parameter (see equations (6)) for the thin film with thickness n = 9. Figure 1 presents the temperature dependence of the long-range order parameter t(i) and the crystallinity parameter m(i) calculated for the case of thin film with surface melting allowed. The results in this figure clearly indicate that the considered thin film exhibits first the surface disordering, next the global lattice disordering and after the important interval of temperature the surface melting is observed and finally the whole sample is melt. As mentioned above both kind of phase transitions discussed here depends on surface state. All interactions energies were the same for whole sample and the observed surfaces effects were connected exclusively with the boundary conditions (12).

Figure 2. Layer-dependent long-range order parameter t(i) and crystallinity parameter m(i) vs. reduced temperature calculated for the film with surfaces interactions enhanced when their melting is allowed [2].

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In Fig. 2 we present the same kind of curves but calculated for the film with the enhanced surface interactions. It is clearly seen that the considered thin film exhibits first the middle layer disordering, next the surface melting and then the surface and global lattice disordering followed by the sample melting. The surface layer melts before being disordered in the sense of the lattice distribution of components. In the considered case we can observe the melting at the surfaces while the lattice disorder is still different from zero. From the physical picture point of view it means that in the interval of temperature (Tsm , Tst ) we should expect that the surface liquid layer is inhomogeneous composition of the islands consisting the same kind of alloy components. At the temperature Tst the surface liquid layer becomes homogeneous. We considered here an interdependence between the surface melting and the surface disordering observed in binary alloy thin films in the context of their mutual relations. The present discussion allows us to extend the diagram of phase transitions to the case when the crystallinity parameter behaviour influences the local concentration profiles and the lattice order parameter describing the alloy structure. In particular, the surface induced disorder is described when the crystal structure is preserved and, in contrast, when the surface melting is expected for partially disordered samples. It is worth while to notice that the crystallinity parameter influences the local concentration profiles and the lattice order parameters which describes the alloy structure in different ways for different surface orientations. The detailed considerations of this phenomena are presented in [3]. 3.2. FERROMAGNETIC PROPERTIES

The three parameters J AA , J BB and J AB = J BA (see (31)) characterise the magnetic interactions. We discuss here the properties of ordering alloys with different values of the magnetic interaction parameters and we show the simultaneous influence of the magnetic and lattice ordering for the thin film of 5 monoatomic layers thickness. By choosing the appropriate values of the relative parameters we can obtain several physical pictures. Figure 3 shows the phase diagram for the case Tσ < Tt with Tt and Tσ denoting the transition temperatures for the lattice and magnetic order phase transition, respectively. This picture can be realised when we choose the set of relative parameters in the following J J J J way AA = 1 , BB = 2 and AB = BA = 0.23 . For x ≤ 0.15 and x ≥ 0.9 the VAA VBB VAB VBA magnetic interactions enhance magnetic order-disorder phase transition temperature with respect to the lattice order-disorder phase transition

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temperature. For 0.15 < x < 0.9 lattice ordering enhances Tt over Tσ . The case when two magnetic phase transition temperatures are notified can be realised by choosing the magnetic interaction parameters as J AA = 4, J BB = 1 and J AB = J BA = 0.2 .

Figure 3. Phase diagram for a fcc(111) alloy thin film with two magnetic component. The thick and thin lines represent the normalized transition temperatures Tt and Tσ , respectively [4].

Fig. 4 shows the phase diagram for the considered case and it can be interpreted in a similar way as in the case of semi-infinite sample [19] although the present diagram is more complex. For example, we can find a sequence of phases for x = 0.25 , namely: with increasing temperature one observe ordered ferromagnetic state, ordered paramagnetic state, disordered ferromagnetic state and disordered paramagnetic state. It is particularly interesting that the ferromagnetic phase can be observed in the region of lattice disordering which can be understood that the average surrounding of considered magnetic moment consist the nearest neighbours with strong magnetic interaction while in the ordered state this surrounding consist atoms B whose magnetic interaction is much smaller. In such a case, ferromagnetic order is, obviously favoured for the amorphous structure. We can also notice that the disordered ferromagnetic state appears for a restricted region of Fe-concentration - 0.2 ≤ x ≤ 0.4 .

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Figure 4. Phase diagram for a fcc(111) alloy thin film with two magnetic component. The thick and thin lines represent the normalized transition temperatures Tt and Tσ , respectively [4].

4. Final Remarks

The considerations concerning the long-range order behaviour are based on the model applied by Valenta and Sukiennicki [1] which takes into account the Valenta approach [7] to the description of thin films in the form of monoatomic layers parallel to the surfaces and treated in the sense of Néel sublattices. This assumption leads to the single-site entropy term which is factorised with respect to the order parameter in the monoatomic planes. In this case we can apply the approach to the samples with the restricted dimension, including thin films, based on the thermodynamic construction of the thermodynamically inhomogeneous system consisted of homogeneous subsystems [2,6]. It is possible, however to extend the model discussed here to the case when the short-range order behaviour is taken into account. The short-range order behaviour is considered in terms of the pair entropy term whose calculations are given for thin films in [20]. The pair entropy contribution is formulated by means of the pair probability standing for the number of possible configurations for a given distribution of concentration of two

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kinds of atoms. Each configuration is described by the probability of the nearest neighbouring sites occupation with respect to the central site. Then, the particular probabilities allow us to define the long-range order and first of all, the short-range order parameter which is related to the pair correlations. These probabilities describe also the internal energy term. In particular, the correlations at the surface are interesting from their physical applications in the case of the low-energy electron diffraction considerations. The correlation effects connected with different surface texture are used in diffuse LEED (DLEED) calculations in order to determine the local structure of the disordered surface. It is worth while to notice that the conditions for DLEED are of static character contrary to the conditions for surface melting which exhibits a dynamical nature of the process with respect to the temperature dependence. Finally, we would like to underline that it is possible to compare the experimental data for the concentration profiles with the conclusions obtained in the frame of theoretical model describing the surface properties in terms of the order parameters. The interpretation of the theoretical results in the context of measurements performed by means of various experimental techniques shows that the simultaneous description of the concentration profile and the long-range order parameters is rather difficult to agree the experimental behaviour. We show, however, that a very good agreement can be achieved when the interaction constants are consider to be temperature dependent [21].

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

L. Valenta and A. Sukiennicki, phys. Stat. Sol. 17, 903 (1966) L. Wojtczak, I. Zasada, A. Sukiennicki and F. L. Castillo Alvarado, Phys. Rev. B70, 195416 (1–9) (2004) L. Wojtczak, I. Zasada and T. Rychtelska, Surf. Sci. 600, 851–860 (2006) A. Sukiennicki, L. Wojtczak, I. Zasada and F. L. Castillo Alvarado, JMMM 288, 137– 145 (2005) K. Lee, J. S. Kim, B. Kim, Y. Cha, W. K. Han, H. G. Min, Jikeun Seo and S. C. Hong, Phys. Rev. B65, 014423 (2001) T. L. Hill, J. Chem. Phys. 36, 3182 (1962) L. Valenta, Chech. J. Phys. 7, 127 (1957) F. L. Castillo Alvarado, A. Sukiennicki, L. Wojtczak and I. Zasada, Physica B 344, 477 (2004) H. Sakai, Surf. Sci. 348, 387 (1996). L. Wojtczak sol. stat. phys. B23, K163 (1967); Thin Solid Films 4, 229 (1969) S. Romanowski, J. H. Rutkowski and L. Wojtczak, Bull. Soc. Sci. Letters (Lodz) Rech. Deform. 27, 103 (1999) A. Maritan, G. Lengie and J. O. Indekeu, Physica A 170, 326 (1991) F. L. Castillo Alvarado, J. Ławrynowicz, J. Rutkowski and L. Wojtczak, Bull. Soc. Sci. Letters (Lodz) Rech. Deform. 35, 7 (2001)

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14. A. Daanoum, C. F. Tejero and M. Baus, Phys. Rev. E 50, 2913 (1994) 15. T. Balcerzak and L. Wojtczak, Bull. Soc. Sci. Letters (Lodz) Rech. Deform. 29, 27 (1999) 16. F. Reif, Fundamentals of Statistical and Thermal Physics, Mc Grow-Hill (1985) 17. T. Coussaerd and M. Baus, Phys. Rev. E 52, 862 (1995) 18. G. K. Straub, J. B. Aidun, J. M. Wills, C. R. Sanchez-Castro and D. C. Wallace, Phys. Rev. B 50, 5055 (1994) 19. E. López-Chávez and F. L. Castillo Alvarado, JMMM 237 (2001) 7; JMMM 263, 182 (2003) 20. I. Zasada, A. Sukiennicki, L. Wojtczak and F. L. Castillo Alvarado, Phys. Rev. B74, 205402 (1–12) (2006) 21. I. Zasada, L. Wojtczak and S. Mróz, “Layer dependent composition of AuCu3(100) in the semi-infinite and thin film geometry”, to be published.

SUBJECT INDEX Conducting bilayered films 397 Conducting molecular materials 391 engineering 182 Conformational polymorphism 99 Contacts-interactions-bonds 324 Coordination frameworks 158 synthesis 158 CP/MAS NMR spectroscopy of spin ½ nuclei 353 Crystal Data File database 34 Crystal engineering 131 bio-inspired 1, 17 history 133 where to? 151 Crystal Lattice Structures database 34 Crystal packing landscapes 333, 341 Crystal packing prediction methods 309, 333 Crystal polymorphism 87, 136 Crystal transformations 144 Crystalline circular birefringence 255 Crystalline circular dichroism 255 Crystalline conducting materials 59, 393 Crystalline metals 59, 393 Crystalline solvatochromism 430 Crystallization at the air-water interface 271 Crystallization in supercritical fluids 146 Crystallization on self-assembled monolayers 17 Crystallographic databases 33 CRYSTMET database 34

A Activated intermolecular interactions 65 Alloy films 497 Amorphization 203 Amorphous assemblies structure 193 Amorphous mineralized structures 4 Amorphous structures 193 Amorphous-to-crystalline transitions 27 B Biological Macromolecule Crystallization database 34 Biomineralization 1 organic phases 449 Bonds 320 bond critical point 321 halogen bonds 62 hydrogen bonds 166, 326 intermolecular and intramolecular bond critical points 323 intermolecular 319 ionic 325 physical meaning 324 van der Waals 328 Bottom-up synthesis on self-assembled monolayers 26 C Cambridge Structural Database (CSD) 34 Chiral crystals 254 formation 254 macroscopic chiral anisotropy 255 Chiral discrimination and crystallization 264 Chiral polyoxometalates 187 Chiral tartaric acid derivatives 408 Chirality crystal-only 260 Cholesterol based diseases 451 Clathrates 112 Close packing principle 39 Co-crystals 51 Complementarity in host-guest compounds 111 Computer prediction of crystal structures 333 Concomitant polymorphs 90, 98

D Databases in crystal engineering 33 Desorption kinetics 122 Detection of multiple crystal forms 105 Dielectric hydrogen bonded materials 231 Diffusion-controlled crystal growth 29 Direct-space structure solution methods 480 Disapperaring polymorphs 89, 98 Disorder in crystalline metals 80 E Electrocrystallization 66 Electron Diffraction Database 34 515

516

SUBJECT INDEX

Enantioselective reactions in crystals 263 Enantiotropic polymorphs 92 Enclathration kinetics 122 Energy in crystal packing analysis 308 Energy-based crystal analysis 307 F Ferroelectric hydrogen bonded materials 231 Ferromagnetic properties of alloy films 504, 509 G Grazing Incidence X-ray diffraction (GIXD) 271 Grinding 144 Guest storage in coordination frameworks 164 H Halogen bonds 61 and concurrent dipolar interactions 417 Host-guest compounds 111 Hybrid molecular conductors 182 Hydrogen bonded zwitterionic metals 67 Hydrogen bonds 166, 326 and concurrent dipolar interactions 417 coordination 70 in crystalline metals 59 types 327 Hyperpolarizabilities 380 I Inclusion compounds 111 Induced nucleation of ice 277 Inorganic Crystal Structure database 35 Inorganic Structure Database 35 Insulator 393 Interface-induced crystal nucleation 276 Intermolecular bonds 319 energy 328 types 325 Intermolecular interactions energy components 313, 315 inventory 61 types 315 Ionic bonds 325

K Kagome topology in metals 73 Kneading 145 Knowledge-based applications 53 L Langmuir monolayers 272 Local dipolar interactions 408 M Magnetic molecular materials 174 types 291 Magnetic phenomena types 291 Magnets connected via covalent bonds 297 Magnets with spins in p and d orbitals 294 Magnets with spins in p orbitals 294 Making crystals from crystals 131 Malaria pigment based diseases 462 Measurement of chirality in crystals 255 Mechanical preparation of crystals 146 Metal-organic frameworks (MOF) 158 Metals 394 Methodologies for computational crystal packing prediction 335 Metrics of intermolecular interactions 46 Micropatterned single crystals 26 Milling 144 Models for the intermolecular forces 336 Molecular dynamics simulation of ice formation 280 Molecular dynamics simulation of monolayers 280 Molecular flexibility modelling 337 Molecular polarization 376 Molecular self-density 41 Molecular shape 39 Molecular size 39 Molecule-based magnetic materials 291 models 293 Molecule-molecule interaction analysis 318 Monitoring crystal nucleation by GIXD 282 Monotropic polymorphs 93 Multifunctional materials bimetallic approach 174 Multifunctional molecular materials 173

SUBJECT INDEX N Nanoscience 157 Nanostructures 166 Nature of the intermolecular interactions 311 Networks 132 NIST chemistry webbook 36 NMR characterization of the solid state 359 NMR crystallography 351, 357 NMR molecular structure determination 358 Non-crystalline structures 193 Non-equivalent hydrogen sites 240 Non-linear optical materials 378 Non-linear optics (NLO) molecular materials 375 engineering 381 second order 379 third order 387 Non-selectivity in host-guest compounds 118 Nucleation ice nucleus critical size 289 oriented 19 Nucleic Acids database 35 O Organic conducting devices 391 Organic field effect transistors (OFETs) 399 Organic host compounds 112 Organic phases associated with human diseases 449 P Patterns 49 Phase transformations 100 in organic conductors 395 Phase transitions in binary alloy films 497 Photochromic crystals 431, 442 Polarization properties 237 Polymorphism 50, 87, 136 conformational 99 in organic conductors 394 kinetics 95 relevance 101 thermodynamics 90 Polymorphs relative stability 94 Polymorphs concomitant 89, 98

517

disappearing 89, 98 enantiotropic 92 monotropic 92 Polyoxometalates 182 Powder Diffraction File database 35 Poycrystalline mineralized structures 9 Protein Data Bank database 35 Q Quantum theory of atoms-in-molecules (AIM) 321 Quarter-filled band Mott isolator 69 R Racemic crystals formation 252 Racemic mixtures separation 273 Rigidity 203 S Seeding 145 Selectivity in host-guest compounds 115 Self-assembled monolayers (SAMs) 17–18 Self-assembling by local rules 197 Semiconductor 393 Serendipity 102, 153 Single crystal mineralized structures 6 Solid-gas reactivity 141 Solid-solid reactions 131, 140 Solid-state chromogenicity 431 Solid-state fluorescence 431, 439 Solvates 51, 88 Solvatomorphism 136 Space groups abundance 43 Spectrometers to measure chirality 256 Spontaneous optical resolution 252 Statistical methods of crystal analysis 52 Structural Classification of Proteins database 35 Structural freedom 203 Structure-property relationships 351 Supramolecular synthons 37, 50 Surface melting and surface disordering in alloy films 501, 507 Surface self-assembly 166 Surface sensitive X-ray methods 285 Surface Structure database 35 T Tartaric acid derivatives crystals 408 Ternary crystalline metals 83

518

SUBJECT INDEX

Thermochemical and Physical Properties database 35 Thermochromic crystals 442 Thermodynamics of binary alloy films 497 Tolopogical analysis by local cluster 209 Topological approach to structural analysis 217 Topology of atom assemblies 195 U Uric acid based diseases 455

V van der Waals bonds 328 W Wallach’s rule 42 X X-ray powder diffraction crystal determination 477 methods and strategy 478 Rietvelt refinement 488 unit cell determination 479