Spectroscopy and Structure (Advances in Metal and Semiconductor Clusters)

ADVANCES IN METAL AND SEMICONDUCTOR CLUSTERS Volume3

,,

1995

SPECTROSCOPY AND STRUCTURE

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ADVANCES IN METAL AND SEMICONDUCTOR CLUSTERS SPECTROSCOPY AND STRUCTURE

Editor: MICHAEL A. DUNCAN Department of Chemistry The University of Georgia

VOLUME3

9 1995

JA! PRESS INC. Greenwich, Connecticut

London, England

Copyright 91995 by JAI PRESSINC 55 Old Post Road, No. 2 Greenwich, Connecticut 06836 JAI PRESSLTD. The Courtyard 28 High Street Hampton Hill, Middlesex TWl 2 1PD England All rights reserved. No part of this publication may be reproduced, stored on a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, filming, recording, or otherwise, without prior permission in writing from the publisher. ISBN: 1-55938-788-2 Manufactured in the United States of America

CONTENTS

LIST OF CONTRIBUTORS

vii

PREFACE

Michael A. Duncan

ix

METAL ATOM-RARE GAS VANDERWAALS COMPLEXES

W. H. Breckenridge, Christophe Jouvet, and Benoit Soep SPECTROSCOPIC STUDIES OF LARGE-AMPLITUDE MOTION IN SMALL CLUSTERS

Eric A. Rohlfing

85

STUDY OF SMALL CARBON AND SILICON CLUSTERS USING NEGATIVE ION PHOTODETACHMENT TECHNIQUES

Caroline C. Arnold and Daniel M. Neumark

113

CRLAS: A NEW ANALYTICAL TECHNIQUE FOR CLUSTER SCIENCE

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally

149

METAL-CARBON CLUSTERS: THE CONSTRUCTION OF CAGES AND CRYSTALS

J. S. Pilgrim and M. A. Duncan INDEX

181 223

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LIST OF CONTRIBUTORS

Caroline C. Arnold

Department of Chemistry University of California Berkeley, California

W. H. Breckenridge

Department of Chemistry University of Utah Salt Lake City, Utah

Michael A. Duncan

Department of Chemistry University of Georgia Athens, Georgia

Christophe Jouvet

Laboratoire de Photophysique Mol~culaire Universit~ de Paris-Sud Orsay, France

Daniel M. Neumark

Department of Chemistry University of California Berkeley, California

A. O. O'Keefe

Deacon Research Palo Alto, California

J. B. Paul

Department of Chemistry University of California Berkeley, California

J. S. Pilgrim

Department of Chemistry University of Georgia Athens, Georgia

Eric A. Rohlfing

Sandia National Laboratories Combustion Research Facility Livermore, California vii

viii

LISTOF CONTRIBUTORS

R. ]. Saykally

Department of Chemistry University of California Berkeley, California

J. J. 5cherer

Department of Chemistry University of California Berkeley, California

Benoit 5oep

Laboratoire de Photophysique Mol~culaire Universit~ de Paris-Sud Orsay, France

PREFACE

In Volume 3 of this series, we focus on the complex issues which arise in the determination of the structures of gas phase clusters. Although some cluster systems can now be isolated in bulk (e.g., the fullerenes), cluster science began in the gas phase and there are still more varied examples of clusters in this medium. Breckenridge, Jouvet, and Soep provide a comprehensive review of metal-rare gas complexes, where the details of metal-ligand interactions, electronic structure, and their implications for geometric structure are revealed in detail. Rohlfing looks at small polyatomic systems, where large-amplitude motions are important, making the concept of structure more difficult to define. Arnold and Neumark as well as Scherer, Paul, O'Keefe, and Saykally describe the application of nontraditional spectroscopy techniques and their applications to the measurement of metal and nonmetal cluster structures. Finally, Pilgrim and I describe photodissociation studies of larger metal carbide clusters. Spectroscopy in these systems is not feasible, but it is nevertheless possible to obtain good evidence for cluster structures from their mass spectra and patterns in their dissociation channels. These varied studies illustrate the complexity and variety of structure determination for gas phase clusters. In future volumes, we will contrast this with studies of isolated clusters which can be studied with more traditional techniques leading to direct measurements of structure. Michael A. Duncan Editor

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METAL ATOM-RARE GAS VAN

OERWAALS COMPLEXES

W. H. Breckenridge, Christophe Jouvet, and Benoit Soep

I. II.

III.

IV.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 M . R G Diatomic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 B. Pure-l-I States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 C. Pure-A States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 D. Rydberg States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E. Spin-Orbit Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 E Ground States of M.RG Complexes . . . . . . . . . . . . . . . . . . . . . 51 M'(RG)n Polyatomic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . 55 A. HgArn Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 B. Mercury Atoms in Rare Gas Matrices . . . . . . . . . . . . . . . . . . . . 66 C. BaArn Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Direct, Time-Resolved Measurements of Metal-Rare Gas Dynamical Processes . . 70 A. Direct Dissociation in the B(f~ = 1) State of HgAr and HgNe . . . . . . . . 75 B. Vibrational Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Advances in Metal and Semiconductor Clusters Volume 3, pages 1-83. Copyright 9 1995 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-788-2

2

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

C. Direct Observation of Resonances in the fl = 1 Continuum of HgN2 . . . 78 D. Future Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

!. I N T R O D U C T I O N The interaction of rare gas atoms with ground state and electronically excited states of metal atoms has been an important area of study for many decades. From a fundamental point of view, such atom-atom van der Waals interactions are much simpler than those involving several atoms, yet allow interesting and informative variations of parameters such as metal atom identity, electronic state energy and symmetry, and rare-gas polarizability. Determination of accurate potential curves for specific M.RG ground- and excited-state interactions (M = metal atom; RG = rare gas atom) is also important in understanding simple dynamical processes such as scattering and electronic energy transfer. Finally, the long-range portions of M.RG potentials are good models for M-molecule interactions when the RG has a polarizability similar to the molecule. From a practical point of view, M.RG and M§ transients can also be important species in electrical discharges and laser systems. Our detailed knowledge of M.RG diatomic.potential curves has increased greatly in the last few years, due primarily to the synthesis and laser spectroscopic characterization of cold M-RG van der Waals complexes in supersonic jets. In this chapter, we review the work that has been published through June, 1993, and present some of our ideas about the bonding in such M.RG complexes. We also discuss experiments on M-(RG) n clusters, as well as direct, time-resolved measurements of dynamical processes in M.RG complexes.

!!. M , RG D I A T O M I C MOLECULES A. General Shown in Tables 1-3 are values of dissociation energies (De) and bond lengths (and relevant M+.RG) states studied to date. ~-65 Most of the data comes from direct spectroscopic studies of M.RG van der Waals molecules, but we have included values from theoretical calculations or from less direct experimental studies when such information was qualitatively important in illustrating ideas on M.RG bonding. Shown in Table 1 are the systems in which the M-RG bonding interactions can be thought of (only in a relative sense, of course) as "strong." These are all states that correlate with RG(1So) ground states and certain excited states of the metal atom M. The M.RG states listed comprise those for which:

(Re) for the diatomic M.RG

T a b l e 1.

Strongly Bound M.RG Excited States a n d M+-RG States a

M.He Metal Atom A t o m i c State

Molecular State

Li(2p 2p3/2)

2I'[3/2

Li(3d 2Dfl

2A5/2

Li(3s 2S1/2) Li+(ls 2 ISo)

2Y~'~/2 ly+

Na(3p

21"13/2

2p3/2)

Na+(2p6 ISo)

1~+

Ag(5p 2/)3/2) Be+(2S 2S1/2) Be+(2p 2p3/2) Mg(3s3p 3p1)

21"13/2 2~/2 21"I3/2 31-10+

Mg(3s3p IPl)

IH 1

De

1020 1 (868) 58 (894) 62 610 1 (549) 58 (486) 58 [596] 43 [570] 41 [593] 56 (601)52 (486) 62 [480] 3 [496] 65 (513) 62 [285] 56 (266) 40 (225) 62

(15) 63 (16) 64

M.Ne Re

1.781 (1.81) 58 (1.82) 62 1.861 (1.90) 58 (2.17) 58 [1.96] 43 [1.96] 41 [ 1.93] 56 (1.92)52 (2.01) 62 [2.3] 3 (2.30) 65 (2,34) 62 [2.41] 56 (2.41) 40 (2.41) 62

De

212 2 (270) 62

M.Ar Re

2.312 (2.4) 62

570 2 [920] 41 [968] 51 [ 1034] 57 (1001)59

2.172 [2.11] 41 [2.06] 51 [ 1.99] 57 (2.04)59

144 4~5 (131) 62

2.734,5 (2.83) 62

[520] 56 (508) 40 (580) 62

[2.49] 56 (2.48) 40 (2.48) 62

(4.2) 63 (4.2) 64 53 11

3.85 11

De

M.Kr Re

De

M.Xe Re

De

Re

[800]55

[3.1155

[1180155

[3.2]55

[1630155

[3.1155

[2173] 56 [2195] 53 [2520] 41 (2040)38 (2190) 42 5681)6

[2.40] 56 [2.43] 53 [2.42] 41 (2.42)38 (2.38) 42 2.91b6

[3183] 56 [3710] 41 (2490) 39

[2.42] 56 [2.45] 41 (2.56) 39

[4310] 41 [4434] 56

[2.54141 [2.51] 56

3.057

11208

3.228

[1504] 56 (1150)40 (1020) 38 (1450) 57 1234 19 41 O0 45 11,500 45 316 c1~

[2.70] 56 (2.86) 40 (2.88) 38 (2.71) 57 [2.8119 2.0945 1.9345 3.631~

[1778] 54 [1774] 56

[2.91] 54 [2.87] 56

[2079] 54 [2089] 56

[2.98]54 [3.11156

368 12

3.2712

7607

[5400] 46 [16,000] 46

2.2246 2.0746

1500 13

3.0713 (continued)

Table 1. (Continued) M.He Metal Atom Atomic State

Mg(3s4s 3S1) Mg+(3s 2Sl/2)

.Ix

Molecular State

De

M.Ne

g~

De

M.Ar Re

3z+ 2Y~/2

(73) 40

(3.57) 40

(169) 4o

(3.30) 4o

Mg+(3p 2p3/2) Ca(4s4p Ipl) Sr(5s5p IP I) Zn(4s4p 3p2) Zn(4s4p Ipl) Zn(4sSs 3Sl) Cd(5s5p 3P l)

2H3/2 IFIl

3Ho+

7720

3.6220

Cd(5s5p 3p2) Cd(5s5p IP l) Cd(5s6s 3Sl)

3H2 IH 1 3]~+

8922

3.6122

Hg(6s6p 3pI) Hg(6s6p 3p2)

31-1o+

8328

3.4728

IH 1 3H2 ll'll

3I:+

3n 2

2228

3.4628

M.Kr

De

Re

1127cl~ 1270 61 1187 61 (1073) 38 (1137) 40 (1045) 62 5486 61 134 14 136 14 487 cl5 706 16 1829cl5 32223' 32520

2.83 l~

435 c21 544 22 1253c21 1267c27 376 28 437 30

M.Xe

De

De

(2.88) 38 (2.89)40 (2.9) 62

3.2315 2.9716 2.6115 3.4520 3.3721 3.2822 2.8421 3.3628 3.313O

1466 17 [499] 24 513 20

2.7917

3241 18

[2.8] 18

1086 20

1036 22

629 29

[3.35] 29 1381 29

[3.15] 29

Hg(6s6p IP l) Hg(6s7s 3Sl) Hg+( 6s 2Sl/2)

In 1

3Z+ 2X+

B( 2s23s 2S1/2) B+(2s 2 IS0) AI(3s 2 4s 2S l/2) AI(3s 2 5S 2S 1/2) Al(3s 2 as 2s I/2) AI(3s 2 7s 2s I/2) AI(3s 2 6p) Al(3s 2 4d 2Dj) Al(3s 2 5d 2Dj) Al(3s 2 6d 2Dj) Al(3s 2 7d 2Dj) Al(3s 2 8d 2Dj) Al(3s 2 9d 2Dj) Al(3s 2 Al(3s 2 5d 2Dj) Al(3s 2 6d 2Dj) Al(3s 2 7d 2Dj) Al(3s 2 8d 2Dj) AI(3s 2 9d 2Dj) Al(3s 2 3d 2Dj) Al(3s 2 4d 2Dj) Al(3s 2 5d 2Oj) AI(3s 2 6d 2Dj)

2X+

21-I

2z+ 2x+ 2~+

2z+ 2z§ 21-I 2H 21-I 21-1 21-1 21-1 2A 2A

2a 2A

96 31

3.4131

542 31 3.2831 1430 30 2.7930 1840 + 3748 [1630 + 100] 47 [<2.87] 47 >1800 50 ca. 120083 2.16 83 (2150) 32 (2.45) 32 398 34 3.0533 (412) 62 (3.0) 62 731 34 815 34 863 34 826.34 312 34 494 34 704 34 806 34 84734 91434 686 34 712 34 802 34 883 34 927 34 943 34 557 34 826 34 931 34 941 34

1495 31

[2.93] 31 [3595] 31

3170 49

6033 49

1010 35 1262 35 1309 34 [ 1426]34

3.0335

[2.95] 31

1769 c36

3.1035

488 34 943 34 [ 1050134

1180 34 1239 34 1327 34

1175 1476 1527 1521

34 34 34 34

(continued)

Table 1. (Continued) M.He Metal Atom Atomic State

Al(3s 2 7d 2Dj) Al(3s 2 8d 2Dj) Al(3s 2 9d 2Dj) Al(3s 2 4f 2Fj) Al(3s 2 4f 2Fj) Al(3s 2 5f 2Fj) Al(3s 2 4f 2Fj) Al(3s 2 5f2Fj) Al+(3s 2 ISo) ln(5s 2 6s 2S 1/2) Si(3s23p 4s 3pj) Si+(3s23p 2pj) Si +(2s23p 3pj)

Molecular State

2A 2A 2A 2y+ 21"I 21-I 2A 2A IE+ 2•+ 3]-1 21-1 2y+

De

M.Ne Re

De

M.Ar Re

De

943 34 943 34 958 34 423 34 857 34 926 34 951 34 1004 34 1024 34 (865) 62 319 c6O 2111 c44 (2076)62 (319) 62

M.Kr Re

De

M.Xe Re

De

1372 34 1445 34 1577 34 (3.2) 62 3.2860

820 c37

(2.80) 62 (3.82) 62

Notes: a~'he M.RG excited states all have significant M-atom valence p~ (or d~) electronic character, or correlate with a Rydberg state of M. h2[ll / 2 Cprobably upper limits: possible maxima in 3~s or 2~ Rydberg-state potentials. ( ): From a theoretical calculation of potential curve. [ ]: Estimated value, a value that has been determined indirectly, or a value that we believe to be relatively uncertain.

1437 c37

Re

Table 2. Weakly Bound M.RG Excited States M.Ne Molecular

State

State

De

Re

25".+ 21-!

4,54.5

7.94.5

Na(3p 2P3/,,) Al(3s23d 2D.t) Zn(4s4p IPi)

"q

M.Ar

Metal Atom Atomic

Re

De

M.Xe Re

Ag(4d95s22Dj)

21-13/2 31-103F! I

De

Re

134 + 1218

[5.9] 18

18829

[4.47] 29

137 M

ix+

Cd(5s5p 3PI) Hg(6s~p 3p()) Hg(6s6p 3pI) Notes:

De

M.Kr

1923,212.5 152s

4.9228

99 + I019 5625,6023 ! 103o 6228

[4.15119 [5.0122.23 4.333o 4.7028

IAII have substantial po, do, dg, or s2 outer-shell M-atom valence electronic character. See text. [ ]: Estimates or uncertain values.

160124,722s 10529

[4.58] 29

Table 3. M-RG Ground States Molecular State

De

Re

Na(3s 2S I/2) Ag(5s 2S I/2) Mg(3s 2 Iso) Ca(4s 2 Iso) Sr(4s 2 Iso) Zn(4s 2 Iso)

2Z+ 2E+ IE+ IE+ IE+ i~E+

8.04,5

5.34'5

23 ll

4.40 II

Cd(5s 2 ISo)

IE+

3925, 3823

4.2622

Ig+ 21-11/2 2Fll/2 2[!1/2 3Fi0+.1

4628

3.9028

Hg(6s 2 ISo) B(2s22p 2Pl/2) AI(3s23p 2pI/2) ln(5s 2 5/9 2P!/2) Si(3s23p2 3pj)

Notes: aLarge uncertainties due to the uncertainties in upper-state De values.

bD0 = 176 :t: 5 cm-l. c~= 3.61 ,/~. [ ]" Estimates or uncertain values.

M.Xe

M.Kr

M.Ar

M.Ne Metal Atom Atomic State

Re

o~

gC

o~

nc

429 98 -I- 1019 [70] al2 [621 as4 [68] a14 75 _ 40 a16 I96] 17 10723,10625

5.019 [4.0] 19 4.4912

687

4.927

1178

4.958

[94] 13

4.5613

4.1816

[115] 17

16218

[4.4] 18

4.3122

14228 [ 120] a32 138 ~ 181 ]a37 13751a44

3.9928 3.57 c32 3.7933 4.136o

12922,1312.s [ 114] 24 17829

De

176 ~ [ 102]a37

4.217

183 b26 [4.07] 29

25429

3.8435

[329] a36 [238] a37

[4.25] 29

Metal Atom-Rare Gas van der Waals Complexes

9

1. There is a single excited valence p~ (or dS) orbital occupied on the metal atom, or 2. There is a single excited orbital on the metal atom that has a principle quantum number greater than that of the ground state (Rydberg states). The M§ states listed for comparison are all relatively strongly bound because of the ion-induced-dipole interaction. In Table 2 are the systems that correlate with electronically excited states of a metal atom but are nevertheless quite weakly bound. These are states that have a metal atom with an excited valence p 6 (or d6 or d~) orbital, or a metal atom with substantial p 6 character caused by spin--orbit mixing with E states that have the same value of f~ (see Section liE). There is also one example of an excited state of a metal atom with a filled valence s shell as the outermost orbital. In Table 3, M.RG ground states are listed, all of which are weakly bound, at least compared to the analogous excited states of the same M and RG listed in Table 1. Note that this appears to be true whether the ground-state configuration is Z or H in character. Before we consider the data in each of the individual tables in greater detail, one major bonding trend should be noted that is found for the data in all three Tables. For the same correlating electronic state of a metal atom, and the same molecular state symmetry, the values of the dissociation energies in virtually every case increase as one moves across a row, in the order RG = He, Ne, Ar, Kr, Xe. There are only two exceptions, Li(2p 2P3/2).He(21-I3/2) and Na(3p 2P3/2).He(21-I3/2), which are anomalous in many ways, and which we will discuss below in more detail (Section liB). This trend is not particularly surprising, since almost any kind of attractive force, such as fluctuating dipole-induced dipole (dispersion), quadrupole-induced dipole, or ion-induced dipole (see Section liB), will increase with the polarizability of the RG atom in the order indicated. However, a closer examination of the data shows that the variation in D e with RG polarizability is not always linear and may vary in form from state to state. Also, the R e values do not always show such consistent trends across a row. In fact, in some sets the bond distance increases as D e increases, whereas in others the bond distance decreases as D e increases across a row. These interesting observations are a challenge to interpret.

B. Pure-H States For states of Group 1, 2, 11, and 12 metal atoms with a valence p orbital as the excited electron on the metal atom, g alignment of this orbital results in much greater D e (and much smaller Re) values than 6 alignment. Shown in Figure 1 are experimentally determined 18 potential curves for the Zn(4s4p I P1).Xe(ll-I1) state (pure ~ alignment) and the Zn(4s4p IPl).Xe(IZ+ ) state (pure 6 alignment), which illustrate this point dramatically. At long range, the ~Z+ state is actually more

10

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP 47 500 qk 47

,

DIT-c"

i

000

46 500 46 000

o E

I 45 000 ~

~.

~

44 500

~

44 000

=

43 5o0 ~-

~

i

I I/

//

/

i /

ooo p 500

X,.T.,o.

~i

'

~

2.00

Zn ('S:) - Xe

,

I

3.25

J

!

:

!

4.50 5.75 R (Angstroms)

~,

;

,

i

7.00

Figure 1. Potential curves of the low-lying singlet states of the Zn.Xe van der Waals complex determined by laser-induced fluorescence or predissociation "action spectroscopy. "18 Note that the Re values of each state relative to the other states are known much more accurately (+ 0.1 A) than are the absolute Re values. attractive than the ~H~ state, but net attraction proceeds to much shorter distances in the l l-Il state, resulting in a bond strength which is twenty-four times larger, and a bond length which is 3.1,4, shorter, than in the IT,+state! This is quite remarkable, and leads us immediately to emphasize the important role of repulsive forces in producing such alignment effects. The p c orbital electron density is pointed towards the incoming RG atom, and the p a polarizability of the excited Zn(4s4p IP l) state is thus greater than the pr~ polarizability, accounting for the greater dispersive attraction at long range for the ~E+ versus the ~rI~ state. But that same directional p c electron density also produces electron-electron repulsiye forces that dominate at distances as large as 5,4, resulting in a very shallow potential well. On the other hand, although the long-range dispersive attraction is less for pn alignment, the Xe atom is approaching along the nodal axis of the Zn(4p_ l) orbital, and there is little electron-electron repulsion until the Zn(4s) electron core is approached. Thus the main reason that the ll-I~ state has a much larger bond strength than the IE+ state is, we believe, the minimization of repulsive forces.

Metal Atom-Rare Gas van der Waals Complexes

11

We now consider, in somewhat more detail, the attractive and repulsive forces in the bonding of the M(pn).RG-type states listed in Table 1. At very long range, the dominant interaction is likely to be dispersion, the leading term of which (fluctuating dipole, induced dipole) will vary as 1/R6 and be proportional both to the polarizability of the RG atom and the polarizability of the metal-atom state. [There will be, in addition, dispersion terms of fluctuating dipole, induced quadrupole or fluctuating quadrupole, induced dipole (1/RS); fluctuating quadrupole, induced quadrupole ( 1/Rl~ etc. 66] The M(pr0 atomic states also have substantial permanent quadrupole moments of-l/2, +1,-1/2 character, due to the diffuse excited p orbital, and the leading term at long range resulting from these quadrupole moments will be the permanent quadrupole, induced dipole interaction, which will be proportional to the polarizability of the RG atom and will vary as 1/RS. 66 Let us now consider the attractive interactions at s h o r t e r range, near R e, where repulsive forces will suddenly begin to dominate at internuclear distances less than R e. At least for the sake of argument, we assume that the internuclear distance at that point, R, is now comparable to the most probable distance, , of the valence np~ excited electron from the M nucleus, in the plane p e r p e n d i c u l a r to the internuclear axis. There will still be the I/R 6 dispersive interaction of the RG atom with the nprc orbital and the M + core electrons, but careful attempts by others to fit potentials for simple (filled-shell) atom-atom systems have shown that this attractive 1/R6 term must be "switched off" (damped) as the electron clouds begin to interpenetrate. These observations have led to model potentials such as those of Tang and Toennies. 67 Also important, however, is that the diffuse pn orbital quadrupolar (-1/2, + 1,-1/2) charge distribution interacting with the RG atom will at close r a n g e be the same as a net positive charge on the M § core, inducing a dipole moment on the RG atom, since the effective (-1/2) negative charges of the p orbital electron, roughly centered at in the pn plane, are now much further away from the RG atom than the center of positive charge at the M + core. Depending on the "size" of the p orbital, , and the internuclear distance R, then, the RG atom will undergo a net positive charge less than one centered at the M nucleus. This attractive potential energy term will vary as 1/R4 (at short range) and will depend on the polarizability of the RG atom and the effective charge Z on the M § core at a given R. Preliminary ab initio calculations of the quadrupole moments of atomic states such as Mg(3s3p IPl) and Na(3p 2pj), for example, indicate large effective values of nearly 3/~.62 Breckenridge and co-workers have therefore recently used an extremely oversimplified model function to analyze the potential curves of several M(pr0 states near their potential minima, 17 C12 V(R) = + R~---~

~

(1) 2R 4

12

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

where o~ is the polarizability of the RG atom, Z is the effective charge on the M atom, e is the unit charge, and C~2 is a constant. Equation (1) obviously cannot describe the potential at very large R, and probably not at very small R either, given the inflexible nature of the Lennard-Jones-type repulsive term. However, these workers were surprised to find that for several M.RG(px) states where R e and D e were both known (or well estimated), Equation (1) resulted in rational, consistent values of the effective charge Z. Reasonable predictions of the fundamental vibrational frequencies foe' which of course are sensitive measures of the shapes of the potential curves near their minimum R e values, were also made for several states with this ultrasimple potential. 17 Here we extend this simplistic analysis to a more complete data set (including Rydberg states and M§ states). By differentiating Equation (1) and setting the result equal to zero, it can be shown that:

(2)

Knowing 0~,D e, and Re, it is possible to calculate Z, the effective charge on the metal atom: 1

[De(cm-l)l~ Z = 5.08 x 10-3 L - ~ [Re(,~)]2

(3)

Shown in Table 4 are the calculated values of Z for all the complexes in Table 1 for which R e a n d D e have both been determined. These values will be discussed in Section IB. Furthermore, the fundamental frequency foe can be calculated for the model potential (1) by taking the second derivative of the potential at R e and setting it equal to the vibrational force constant for the molecular state. By algebraic manipulation: l

3 where B is the reduced mass. In Table 5 are shown the calculated versus observed values of foe for the states listed in Table 4 for which foe values have been determined experimentally. Although the values of Z and foe for the M.RG px states calculated from the assumption of Equation (1) should not be taken too seriously, we believe they provide a framework within which we can discuss the bonding in the px states and compare their character to those of states that should more reasonably be described as "ionic": M.RG Rydberg states and M+.RG states. Breckenridge and co-workers 62'68

Table 4. Calculated Values of Z, the Effective Charge on the Metal Atom Pure-Fl State

Z

Li(2p 2p3/2).He (21-[3/2) Li(2p 2p3/2).Ne (21"13/2)

1.15 0.62

Na(3p 2p3/2).He (2113/2) Na(3p 2p3/2).Ne (2113/2) Na(3p 2p3/2).Ar (2]'13/2) Na(3p 2p3/2).Kr(21I3/2) Na(3p 2p3/2).Xe (2]13/2)

[ 1.32] 0.72 0.79 0.83 0.88

Mg(3s3p3Ps).Ar(31Io+) Zn(4s4p 3p2).Ar (3112) Cd(5s5p 3Pl).Ne (31-1o§

Pure-I'l State

Mg(3s3p IPl).Ne (lI-il) [0.93]h Mg(3s3p IPI).Ar (Jl-!I) Mg(3s3p IPj).Xe (tl-ll) [0.931b Zn(4s4p IPj)-Ar (ll'li) Zn(4s4p IPl).Kr (ll-lt) 0.93 Cd(5s5p IPl)-Ne (ll-ll)

Z

0.87 0.82 0.90 0.93 0.97 0.99

Rydberg State

Z

Li(3d 2Dj).He (2A5/2) Li(3s 2St/2).Ne (212+)

0.97 0.90

Mg(3s4s 3Si).Ar (312+)

i.07

Zn(4s5s 3Si).Ar (312+)

!.16

Ionic State

Li+(Is 2 ISo).He (~Z+) Li+(ls 2 ISo).Ne (rE+) Li+(is 2 tSo).Ar (112+) Li+(is 2 JSo).Kr (I/2+) Li+(Is 2 ISo)-Xe (JZ+) Na+(2p6 ISo).He (I/2+) Na+(2p6 JSo).Ne (I/2+) Na+(2p6 JSo).Ar (t/2+) Na+(2p6 JSo).Kr (JY+) Na+(2p6 ISo).Xe (!/2+) Be+(2s 2Sj/2).Ar (2/2+) Be+(2p 2p3/2).Ar (21-13/2) Be+(2s 2St/2).Kr (212+) Be+(2p 2p3/2).Kr (21"13/2) Mg+(3s 2St/2).He (2/2+) Mg+(3s 2Sj/2).Ne (212+) Mg+(3s2Sj/2).Ar (2/2+)

Z

11.041 [!.061 [I .09] 11.111 [I.071 (I.09) (I.I I) (I.10) 11.15] 11.021 !.! ! 1.56 1.17 1.75 (I.22) (I.14) (I.12)

(continued)

Table 4. (Continued) Pure-Fl State

Cd(SsSp3e~)-Ar(3no§ Cd(Ss5p 3p2).Ar (31-12) Hg(6s6p 3Pl).He (31"ltr Hg(6s6p 3Pl).Ne (311o+) Hg(6s6p 3Pi).Ar (31Io§ Hg(6s6p 3p2).Ar (31"12)

Z

0.85 0.94 0.63 0.88 0.87 0.91

Pure-Fi State

Z

Cd(5s5p IPl).Ar (IFll)

0.99

Hg(6s6pIPl).Ne (IFll)

0.92

Hg(6s6pIPi)-Ar (IFll)

1.00

Rydberg State

Cd(5s6s 3Sl).Ar (2Z+)

Hg(6s7s 3Si).Ar (3L-7~) B(2s23s 2SI/2)-Ar (2Z+) Al(3s24s 2SI/2).Ar (2Z+) Ai(3s24s 2SI/2).Kr (2Z+) Al(3s25s2Si/2).Kr(2Z+)

Si+(3s23p).Ar (21-1) Si+(3s23p)-Ar (2Z+) Notes:

Z

Ionic State

I. 14

1.17 Hg+(6s 2S)-Ar (2E+) 0.64 B+(2s2 ISo).Ar(tZ+) 0.74 0.94 !.10 (I.32) (1.03)

nThe simple potential function V(R) = C ~ 2 / R 12 - o~(Ze)2/2R 4 is assumed to be valid near Re, from dala of Table I. The polarizability of the RG alom is a. bUpper limit, because D,, is probably overestimated. See Table !. ( ): From c a l c u l a t e d potential curve. [ ]: From potential curve parameters, at least one of which is considered somewhat uncertain.

Z

!!.32] (I.10)

Table 5. Comparisonof the oe Values

tOe(eSt.)~ Pure-ii State

tOe(obs.)

Li(2p 2p3/2).He (2Ii3/2) Li(2p 2_P3/2).Ne (2H3/2) Na(3p 2p3/2).Ne (_"113/2) Na(3p 2p3/2).Ar (2ii~/,)

452/357 111/108 54/48 86/84 86/85 94193

Na(3p 2p3/E)-KI (2ii~/") Sa(3p 2P3/2)-Xr (2H3/2)

Pure-il State

%(est.)/ toe(obs.)

Rydberg State

Li(3d 2Dfl.He (2A5/2) Li(3s 2Si/2).Ne (25,+)

tOe(eSt.)/ %(obs. )

Ionic State

tOe(eSt.)/ tOe(obs.)

335/278 194/150

Be+(2s 2~_S1/2).At (22;+)

455/363 814/583 Be+(2s ZSl/2).Kr (z2~+) 467/367 Be+(2p 2fi3/2).Kr (21"13/2) 862/555 Be+(2p2p3/2).Ar (2il3/2)

Mg(3s3p IpI)-Nr ll1) Mg(3s3p IPl)-Ar Ill) Mg(3s3PilPl).Xe lill) Zn(4s4p Pl).Ar Ill) Zn(4s4p lPl)-Kr ~1~) Cd(5s5p 91 Cd(5s5p IPl)-Ar !-I1) Hg(6s6p IPl).Ne Ill)

23/21 61/43 114/100 73/62 92/81 25/23 53148 27/27

Hg(6s6p IPl).Ar (Inl)

48/50

i

Cd(5s5p 3PI)-Ne (3I"1o+) Cd(5s5p 3pl)-Ar (3Ilo+) Hg(6s6p 3Pl).Ne (31-Io+) Hg(6s6p 3Pl).Ar (31Io+) Hg(6s6p 3pE)-Ar (31I2)

24/23 39/39 25/28 40/41 44/46

Mg(3s4s 3Sl)-Ar (3?E+)

123/127

Zn(4s5s 3SI).Ar (32;+)

133/142

Cd(5s6s 3Sl)-Ar (22;+)

931105

Hg(6s7s 3SI).Ar (3~+) B(2s23s 2Sl/2).At (2~-) Al(3s24s 2SI/2).At (22;+) Al(3sE4s 2Sl/2).Kr (22;+) Al(3sE5s 2Sl/2).Kr (2~+)

94/112 220/209 66/85 93/99 102/93 b

Hg+(6s 2S).Ar (22;+)

98/99

Notes: IEstimatedfrom the assumption that the simple potential V(R)= C12/R12- ot(Ze)2/2R4 is valid near Re (data from Table 1 ) to those toe values determined experimentally.

bpotential curve is anomalous because of strong avoided crossing with a repulsive valence state near potential minimum.

16

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

have begun to analyze those states for which RKR potentials are available, using more realistic electrostatic potentials, as well as quadrupole moments and exponential repulsive potentials based on ab initio calculations; the preliminary results are encouraging.

Group I and Group 11 Metal Atoms Let us first consider the Li.RG(2H3/2) and Na.RG(2H3/2) states, which correlate with Li(2p 2P3/2) and Na(3p 2P3/2). The diffuse Li(2pn;) and Na(3pn:) orbitals are m u c h larger than the filled-shell Li(ls2) § and Na(2p6) § core orbitals, 69 and there should be very little C6/R6 lowering of potential energy by dispersive interaction of the RG atom with the ionic cores, which have very low polarizability. This was shown to be true by realistic estimates of the Li§ and Na§ free-ion potentials by Tang, Toennies, and co-workers. 7~ Although there was a substantial attractive term that varied as 1/R61 and this term increased the well depth somewhat over that calculated with only the I/R 4 ion-induced-dipole expression, in the Li § and Na § systems this resulted mainly from the next higher order term in the induction expansion, 13~de2 Vi~d=---~-

~q e2 2-7-(...)

(5)

where ~d is the dipole polarizability and ~q is the q u a d r u p o l e polarizability of the RG atom. Thus, neglect of this ion-quadrupole induction term and of the damped C 6 / R 6 term (representing the dispersion interaction between the RG atom and the diffuse/m orbital at short distances) are the principal shortcomings of the attractive part of the simplistic Equation (1). Failure to include such terms will result in the calculated value of Z, the effective charge on the M-atom core, being too high. As can be seen from Table 4, for RG = Ne, Ar, Kr, Xe, quite reasonable (upper-limit) values of Z - 0.6-0.9 are obtained for Li-RG and Na-RG pn states. (The Lille and NaHe pn states are anomalous and will be discussed at the end of this section.) For the Na(pn) states, where R e and D e are known very accurately from high-resolution LIF studies of the van der Waals complexes, Z increases monotonically from Ne through Xe; this may be due to the increasing relative importance of the neglected ion-quadrupole polarizability term at the R e distances of each complex as one moves through the Ne, Am',Kr, Xe series. Saxon, Olson, and Liu 71 performed very high level ab initio calculations of the Na-Ar(EH) potential curve, and were able to reproduce the experimental D e and R e values fairly well. They also calculated the dipole moment of this state as a function of internuclear distance, and at their calculated R e value found a Na-Ar § dipole moment of 0.66 D. Using an effective Na charge of +0.80 (see Table 4), we calculate an induced-dipole moment on the Ar atom at their R e value of 0.68 D, which of course is Na-Ar § in direction. The agreement is excellent.

Metal Atom-Rare Gas van der Waals Complexes

17

Note also, in Table 5, that Equation (1) does a remarkably good job (probably too good!) of predicting the o e values of the known Li.RG and Na-RG pn states for

RG = Ne, Ar, Kr, and Xe. We also point out that the standard Lennard-Jones (6-12) potential function would result in predicted toe values some 23% higher than Equation (1), obviously inconsistent with experiment. On the other hand, it can be s h o w n that for a general t w o - t e r m p o t e n t i a l of the f o r m V(R) = t 2 + (C J R n) - (Cn,/Rn'), the force constant k = n.n (De~Re), and toe = (n'n') 1/2, so that a "soft" 6-8 potential (with n = 8, n" = 6) would predict these toe values just as well as the 4-12 potential of Equation (1), as would a 5-9 or 5-10 potential. In fact, when Zimmerman and co-workers 7'8 fit their high-resolution data on both the NaKr and NaXe pn states to a five-parameter Tang-Toennies model potential (two Born-Mayer exponential repulsion parameters and C6, C 8, C10 dispersion coefficients), the fits collapsed to give large negative values of C 8. The best fit was equivalent to a 6--8 potential, with the other two exponential repulsion parameters and the C~0 parameter serving as "fine-tuning" fitting coefficients. Of course, no 1/R4 close-range dependence, such as that postulated by our extremist equation [Eq. (1)], was allowed by the Tang-Toennies model potential used by these workers. Very recent MCSCF calculations of the repulsive portions of the NaAr(21-l) potential curve are fit best by a 1/R i~ function 68 (see Figure 2). Given the 1/R 6 and 1/R4 attractive terms that we postulate, perhaps a 5-10 potential is in fact the best two-term compromise near R e. Finally, let's examine the trends in R e values with RG atom for the pr~ states of Li and Na listed in Table 1. For Na, where the spectroscopic characterization of the states is of high accuracy, there is a clear trend of slightly increasing R e values as one moves across a row from Ne to Xe, and of c o u r s e D e also increases. This seems reasonable, based on our ideas of the attraction to a partially charged Na +~ core; as the RG atom gets larger, the value of R at which the repulsion with the Na § core (and the Na(p~) orbital) sets in also increases. On the other hand, the polarizability of the RG atom increases as well, so there is more attraction at the slightly larger R e distances as one moves from Ne to Ar to Kr to Xe. (Of course, we must admit at this stage that similar arguments could be made based on 6-8 potentials in which the major attractive terms were the Na(p~)-RG 1/R 6 dispersion terms.) We also ions very note, however, that the available information on the analogous Na§ nicely parallels that of the Na.RG(21-I) states. There is a smooth increase in R e values through the Ne to Xe series; for each particular Na+.RG, the R e is also smaller and the D e greater than the equivalent Na.RG(21-I) state, as expected. A similar trend is observed for the Li(pn)-RG states, although the experimental data for Ar, Kr, and Xe are indirect and far less accurate. As mentioned previously, the LiHe(21-l) and NaHe(21-l) states appear to be anomalous. They are much more strongly bound than their LiNe(21-l) and NaNe(21-I) counterparts, for example. Although that could perhaps be rationalized by the slightly smaller size of the He atom, which allows it to penetrate much more closely along the p~ orbital nodal axis (to the small Li § or Na § cores) before

18

W.H. BRECKENRIDGE,CHRISTOPHE JOUVET, and BENOIT SOEP

repulsion sets in, it is difficult to explain why the LiHe(2I-l) state apparently has a shorter bond length and much larger bond strength than even the free Li+.He ion. [A similar effect is noted for NaHe(21-l) versus Nat.He, but the data are either estimated indirectly or are from ab initio calculations.] One possibility, consistent with our ideas, is that compared to the LiNe(21-I) system, there is less r e p u l s i o n from the.Li(2pr0 orbital for the smaller He atom, allowing it to penetrate very close to the Lit(ls 2) core while still undergoing the I/R 6 Li(2p~).RG dispersive attraction. This extra attraction could allow the He atom to better overcome the Li§ core electron-electron repulsion than in t h e f r e e Lit-He ion. An early but high-level SCF calculation of the NaHe(2FI) and LiHe(2I-I) potential curves 72 showed them to be very similar to the calculated Nat.He and Lit.He curves near their R e values, and it was argued that the small He atom had essentially completely penetrated beneath the diffuse p-orbital electron density, so that the 21-Istates were Rydberg-like and the main attractive force was the Mt.He ion-induced-dipole term, similar to the free ion states. A later SCF calculation (near the SCF limit) 58 led to essentially the same conclusions: Li(2p 2P~).He(2I-I) has D e = 525 cm-1 and R e = 1.88/~; Lit.He(1Z § has D e = 554 crn-l and R e = 1.94/~. Of course, such calculations do not include correlation and would not reveal any extra dispersive attraction between the Li(2pr~) orbital and the He atom. In this unusual system, such interactions could persist to quite short internuclear distances owing to the lack of interpenetration of the diffuse Li(2p~) orbital by the Is-electron density of the small He atom. High-level CEPA calculations in the later study 58 are entirely consistent with this possibility, in that the Lit-He R e and D e values (601 crn-1 and 1.92/~) are similar to the SCF values, whereas the Li(2pn).He results (868 cm -1 and 1.81 /~) are strikingly different from the SCF values and closer to the experimental values of 1020 crn-1 and 1.78/~. A careful analysis by Jungen and Staemmler 58 of the total electron correlation energy in the CEPA calculation showed that the major contribution (ca. 400 cm -1 m o r e correlation energy at R e = 1.81/~ than at R = o,,) for the Li(2pn).He state resulted from correlation between the Li(2pr~) valence electron and the He atom (and Li t core) ls electrons. However, the great difference between the 2pn states of Li-Ne and Na.Ne versus those of Li.He and Na.He, respectively, cannot obviously be explained by the size of the RG atom alone, since various estimates show that the helium atom is n o t that much smaller than the Ne atom. For instance, < r l s > H e = 0.49/~ and Ne = 0.51 /~ from ab initio calculations. 73 Estimates of the "hard-sphere" radius of the helium atom are ca. 1.30/~ versus ca. 1.40/~ for the Ne atom. TMAs shown in Table 1, the estimated R e values for Lit.He and Nat.He aren't really that much smaller than those for Lit-Ne and Na§ respectively. One possible difference between the helium atom and the neon atom, of course, is the presence of two filled pr~ orbitals on neon, and Li(2pn)-Ne(2pn) 4 electron-electron repulsion may just rise more quickly as R is decreased than Li(2pn)--He(lst~) 2 repulsion. 68 (We thank Professor Jack Simons for this suggestion.)

Metal Atom-Rare Gas van der Waals Complexes

19

The only M.Rg(2H) state of a Group 11 metal atom that has been characterized is that of the Ag.Ar molecule. As can be seen from Table l, the bond strength is quite high, 1234 cm -1. The bond length value, R e - 2.8 +_0.4/~, is not known very accurately, because the simulations of the spectra were only sensitive to the change in R e value from ground-state AgAr(X2s +) to upper state AgAr(EH), so the bond length could actually be less than 2.8/~. The main difference between the Group 11 and Group 1 states, we believe, is that the M + cores will be (n - 1)d 1~ in nature rather than ( n - 1)p6. Because of the presence of low-lying configurations of ( n - 1)d9ns 1 character for the Group 11 M + ions, there is a possibility of sd hybridization, which (because of the "d-hole") can remove electron density from the direction of an incoming RG atom. For example, the Cu+(3da4s 1D2) and Ag+(4d 95s ID2) states lie at ca. 26,000 and ca. 46,000 cm -l above the ground-state ion energies, respectively; in contrast, the first similar excited state of Na +, the Na+(2pS3s 2p) state, lies ca. 265,000 crn-1 above the ground state. Calculations of Cu+-Ar versus Na+-Ar potential curves by Bauschlicher et al. 4~are consistent with this idea, since the D e value for Cu+-Ar is 3270 cm -1, nearly three times greater than that of Na+-Ar. The bond length, 2.37/~, is also substantially shorter than that of Na+-Ar, 2.86/~. This would not be predicted from a comparison of the value calculated for Na, 0.42/~, versus that of calculated for Cu, 0.53/~. The ab initio calculations show that there is important sdo hybridization in Cu+-Ar and Ar-Cu +Ar bonding. 73 Even though for Ag is calculated to be even larger, 0.74 ~, and the 4d orbital in Ag is relatively more stable than the 3d orbital in Cu, it appears that sd hybridization can still occur in the AgAr(EH) core, resulting in a D e value much larger than, and an R e value probably smaller than, the NaAr(2H) state. One final point is that from crystallographic data 75 of ionic solids, the self-consistent radii of Cu + and Ag + are 0.60/~ and 0.81/~ (for coordination number 2), whereas that for Na + is 1.13/~ (for coordination number 4; 1.16/~ for coordination number 6). G r o u p 2 a n d G r o u p 12 M e t a l A t o m s

We now move on to discuss the p~ states of the Group 2 (primarily Mg) and Group 12 (Zn, Cd, Hg) metal atoms with RG atoms. These states have been of great interest in our research groups, and the ideas presented here about M.RG interactions have evolved primarily from our interests in understanding LIF spectra for which such states were either the upper or the lower states. As can be seen from Table 1, the over-all data set is now much larger for Group 2 and Group 12 than for Group 1 and Group 11 M-RG(p~) states, largely owing to experiments in our laboratories (as well as those of Tsuchiya and co-workers). The major difference in Group 2 and Group 12 versus Group 1 and Group 11 M.RG(p~;) states, we believe, is that the M + core in the former has a valence ns electron that is larger, but is also much more polarizable than the lsE(Li), (n - 1)p6, or (n - 1)d10 cores of the Group 1 and Group 11 p~ states. For RG = Ne, which has a low polarizability, the MgNe(lHl) state is less bound and has a much larger R e

20

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

value than the NaNe(2II) state, largely owing to the much larger size of the Mg(3s) § core compared to that of the Na(2p6) § core. The MgAr(ll-Ii) state is also less bound than the NaAr(21-I) state (368 cm -l versus 568 crn-1), but the R e value of the MgAr(lIll) state is actually substantially less than the MgNe(1FI l) state (3.27 versus 3.85/~). A dramatic difference is also seen in the calculated Mg(3s3p 3PI)-He(3FI) potential curve, where Re= 20 cm -1 and De= 4 /~ versus the Na(3p 2P3/2). He(2II3/2) R e value of about 2.3 ~ and D e value of about 480 cm -1. It is obvious that the helium atom undergoes net repulsion from the Mg(3s) electron density at large distances, but in the Na system can penetrate much closer because of the absence of a 3s electron. The Ar atom is substantially more polarizable than the Ne atom (tx = 1.64/~3 versus 0.40/~3),76 and thus will have a substantially larger induced-dipole moment than the Ne atom as it moves towards the Mg § core. The Mg(3s) electron will be "back-polarized" by this -,+ dipole in the direction opposite to the incoming Ar atom. This will have two important effects in lowering the total energy: (1) The Ar atom will synergistically undergo a greater effective positive charge as the Mg 2§ ion core is less shielded. (2) Perhaps more importantly, the Mg(3s)-Ar repulsion will be reduced, allowing closer approach. Another way of looking at this is to examine what there is to be gained by the Mg(3s) electron polarizing away from the incoming RG atom (stronger ion-induced-dipole interaction with the more "exposed" Mg 2§ core) versus what is lost (the energy necessary to polarize the 3s electron density away from the nucleus). For a certain range of internuclear distances R, there is apparently more to be gained than lost for the more polarizable RG atoms. Although the MgKr(ll-ll) state has unfortunately not yet been characterized, the MgXe state is not only strongly bound (De= 1500 cm-l), but also has a substantially shorter bond distance of only 3.07 ]k. In fact, the NaXe(2FI) state is less bound (1120 crn-1) with a larger R e value than that of MgXe(ll-I1), an amazing reversal which of course is consistent with the above arguments, since Xe has a much larger polarizability (o~ = 4.04/It3). 76 Ab initio calculations by Bauschlicher et al. on Mg§ and Na§ ground states show exactly the same kinds of trends, consistent with these back-polarization ideas. 4~ As seen in Table 1, in the Na§ Na+.Ne, Na+.Ar sequence, both D e and R e values and Mg§ steadily increase. In contrast, the R e values for the Mg+.He, Mg§ sequence decrease substantially, and the D e values increase more rapidly than in the Na§ sequence. In fact, MgAr § and NaAr + have virtually identical calculated R e and D e values. The calculated wave functions show clearly that there is increased back-polarization of the Mg(3s) orbital to reduce repulsion in the sequence RG = He, Ne, Ar. In fact, the MgAr~ ion was shown to adopt a very nonlinear geometry so that the Mg§ orbital could back-polarize away from both Ar atoms, minimizing M§ total repulsion. 4~ MCSCF calculations, which have very recently been performed, of the repulsive portions of the potential curve for MgAr(ll-I) are also consistent with such back-

Metal Atom-Rare Gas van der Waals Complexes

21

polarization ideas. 62 Shown in Figure 2 arc such calculated repulsive curves for MgAr(lFll) and NaAr(21-l). As can be seen, the MgAr state is more repulsive at all distances because of the presence of the large 3s core electron, which is absent in the NaAr state. However, the repulsive curve (at lower energies) is much "softer" for MgAr(lrll) than for NaAr(2I-l). In contrast to the NaAr state, where the best-fit +UR n repulsive function yields n -- 10, for the MgAr(IFll) state the best fit gives n ~- 6.0--6.5! This softness is due to the continual back-polarization of the Mg(3s) orbital; the "harder" repulsive potential of the NaAr(2I-I) state at smaller R is expected, given the small size and very small polarizability of the Na(2p 6) core. Furthermore, within the context of a simple +(Cn/R" ) -(Cn,/R n') potential, the vibrational frequency toe of the MgAr(llI1) state would be severely overestimated by our simple 4--12 model potential, Equation (1). As can be seen in Table 5, the predicted frequency is in fact over 40% higher than the experimental one, a serious discrepancy. However, the frequencies predicted by 4-6 or 5--6.5 model potentials, for example, are 43 cm -1 and 50 cm -1, in much better agreement with the experimentally determined value of 43 crn-1. 8000 NaAr 6000

I

E 4000 0

2000

0 2.: :)

,

2.7 R (A)

3.2

Figure 2. MCSCF ab initio calculations 62 of the repulsive portions of the Mg(3s3p 1p1)-Ar(C1N1) and Na(3p2pj).Ar(A2U) potential curves, in order to better estimate only the lower energy repulsive part of the interaction potential, a basis set was used that had no polarization functions on the Ar atom, but allowed 3s or 3p orbital distortion and mixing on the metal atoms. The solid lines are best fits of the expression A.R-n where R is the internuclear distance. For the Na.Ar(2rl) data, n = 9.9. For the Mg.Ar(1H) data, n = 6.2.

22

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

By examination of Table 1, it can be seen that there are similar trends in Re for all the Group 12 M(pn)-RG states. There is a decrease in R e as RG is changed from Ne to Ar for the Cd.RG(3H0+), Cd.RG(IH), Hg.RG(3H0+), and Hg.RG(ll-I) states, and as RG is changed from Ar to Kr for the Zn.RG(III) states. This is, of course, consistent with the back-polarization idea. If we now turn to Table 4, the estimated effective charges Z of the Group 2 and Group 12 states are all somewhat higher, in general, than the analogous Na.RG(21-I) states, consistent with some back-polarization. We now compare the M.RG(II-II) states of Zn, Cd, and Hg to those of Mg. As can be seen in Table 1, the analogous M.RG(IIII) states of the Group 12 dements are all more strongly bound and have smaller (or comparable) bond lengths than the 1H l states of MgNe, MgAr, and MgXe. We attribute this mostly to smaller core ns orbital sizes of Hg +, Cd +, and especially Zn +, compared to that of Mg +. This is somewhat compensated for by the larger polarizability of the Mg+(3s) core electron compared to those of Zn+(4s), Cd+(5s), or Hg+(6s)electrons. M(ns 2) polarizabilities for ground-state neutral Mg, Zn, Cd, Hg, atoms are about 11, 6, 7, and 6 A3, respectively, 76 and the polarizabilities of the M+(ns) cores will be somewhat smaller but should scale roughly proportionately. Thus we believe that core back-polarization does occur in the Group 12 M.RG(1FII) states, but is less important in a relative sense than in Mg.RG(IFI1) states. The concept of back-polarization will be discussed further in the next section on Rydberg-type states. There are two examples where 1II1 states are not very strongly bound: CaAr and SrAr. The bond strengths, 134 and 136 crn-1, respectively, are substantially smaller than that of their lighter counterpart, MgAr(llIl), which has a D e of 368 crn-1. There may be two reasons for this. The Ca(4s) and Sr(5s) cores will be much larger than that of Mg(3s) [in contrast to the Zn(4s) and Cd(5s) cores, which are smallerowing to the d-shell shielding effect], and repulsion may just set in at larger internuclear distances. Also, the excited Ca(4s3d ID 2) and Sr(5s4d 1D2) levels are only 1803 crn-1 and 1548 cm -1 lower in energy than the asymptotic Ca(4s4p 1P1) and Sr(5s5p 1P1) levels. There will thus be 11I1 states resulting from M(dTt).RG interactions, which will probably not be so attractive. Avoided crossings (or at least strong mixing) may occur, leading to shallower potential wells in the higher lying M(prt)-RG states. 77 One final point can be made from the data on Group 2 and Group 12 pn states in Table 1. Where comparisons are possible, the pure-II triplet states (3F10+,3II2) all have smaller D e and larger Re values than their 1111analogues. This is to be expected since the higher energy M(nsnplP1) atomic states have larger and more diffuse p orbitals than the M(nsnp3pj) states. 22 The RG atoms can thus penetrate closer, because there is less npn-RG repulsion, as well as more effective attraction because of the larger pn quadrupole moment and C6 dispersion coefficient for the M(IP1).RG interaction. As seen in Table 4, except for the MgAr(llIi) state (which is probably anomalous because of its very soft repulsive potential, as discussed previously), the calculated effective charge Z is greater for the singlet pn states than for their triplet analogues.

Metal Atom-Rare Gas van der Waals Complexes

23

C. Pure-A States Only two valence dA states have been characterized, 34 Al(3s23d2D3/2) 9 RG(EA3/2), where RG = Ar, Kr. They are strongly bound (quite consistent with our ideas), because, in analogy to the pr~ states, the RG atom can approach along the nodal axis of the d• orbital. This allows close approach to the A1~ core as well as dispersive attraction to the 3dA electron cloud. In both cases, the bond energies of the valence ndA states are a substantial fraction of the AI§ binding energy: Ar, 557 cm-1 versus 1024 cm-1; Kr, 1175 cm-l versus 1577 cm-1.

D. Rydberg States

Group 2 and Group 12 Atoms A wide variety of M.Rg excited states have now been characterized that correlate with a metal atom that has an outer electron in an orbital with a principal quantum number greater than that of the outer electron in the ground atomic state: so-called Rydberg states. Many of these states are quite strongly bound, with D e values approaching those of the analogous free M§ ions. We present a simple model for the bonding in such complexes, then show that most of the results to date can be rationalized within the framework of that model. We use s orbital Rydberg states to illustrate the model. As an RG atom approaches an excited s Rydberg electron on a metal atom, there will be a strong dispersion-type attraction at very long range because of the large polarizability of the very diffuse Rydberg electron. However, at least for the lowest lying Rydberg states, as the RG atom begins to penetrate the outer lobe of the Rydberg electron, the electron-electron repulsion may exceed the attraction, and the potential energy can then begin to rise above the asymptotic energy of the separated atoms, even at large distances of 5 or

6A. When the RG atom approaches even closer, however, the repulsion will first maximize near the maximum radial electron density of the Rydberg orbital, then (depending on the Rydberg orbital and the size and polarizability of the RG atom) may decrease substantially as the RG atom passes through the region of the first radial nodeof the diffuse s orbital. The RG atom is now within a substantial fraction of the Rydberg s-orbital electron density and will undergo a strong ion-induceddipole attraction to the partially charged M ~+core. This attraction, which of course will depend on the polarizability of the RG atom, can then be much greater than repulsion, and there may be a second, much deeper minimum in the potential curve, which can mimic that of the free M+-RG ion potential at short R (especially for Rydberg states with higher principle quantum numbers). Thus these unusual states can have two minima and a barrier in their potential curves, but not because of an avoided crossing with another electronic state of the same symmetry, which is the usual cause of such double-minimum potential curves. The first direct experimental evidence for such a double-minimum Rydberg poten-

24

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

tial was obtained in 1985 at Orsay by laser double resonance experiments. 3~ Using the weakly bound HgAr(3Hl) state as a "stepping-stone" intermediate, we were able to access very large Hg-Ar internuclear distances that are not normally Franck-Condon accessible even from the weakly bound ground state. The results showed conclusively that the Hg(6s7s 3SI).Ar(3E+) state has a double-well potential curve with a potential maximum (above the asymptotic energy) of about 15 cm -1 at R = 5/~. The long-range shallow well of about 40 crn-1 reaches its minimum at R = 6.95/~, and the deep, Rydberg-type well of 1430 cm -1 minimizes at R e = 2.79 /~. The D e value is only 410 cm-l smaller than that of HgAr § 1840 cm-1,48'50 consistent with our arguments. Other similar (n + 1)s Rydberg type states of MgAr, ZnAr, and CdAr have since been characterized at Utah by LIF spectroscopy of M.Ar metastable 31-10-or 3I-I2 states. These states were synthesized by expanding M(nsnp 3P0,2) metastable atoms (from a laser vaporization source) into a pulsed, supersonic, free-jet expansion of argon gas. 1~ In all cases, as can be seen in Table 1, the M[ns(n + 1)s 3SI].Ar(3E) Rydberg states are found to be much more strongly bound and to have much shorter bond lengths than the M(nsnp 1P1).Ar(ll-I1) states discussed previously, as expected. No potential maxima were detected, but Franck-Condon overlap limitations (the 31-I spin-orbit states synthesized were all moderately bound) prevented access to the larger internuclear distances where such maxima might occur. For the Mg system, the bond strength and bond length of Mg+.Ar have been estimated in ab initio calculations by Bauschlicher and co-workers 4~ to be 1140 crn-1 and 2.89/~, respectively, very similar to the measured values for the Mg(3s4s 3S1).Ar(3~) states of 1127 cm -1 and 2.83/~. Very recent experimental estimates 61 of D e for Mg§ of 1187 and 1270 crn-1, are consistent with the ab initio calculations. Thus, the MgAr(3E+)/MgAr§ comparison is quite similar to that of HgAr(3E+)/HgAr +. Shown in Figure 3 is a plot of the radial electron density of the Mg(3s4s 3Sl) atomic state, from a high-level ab initio calculation. 79 To show how, in this case, the argon atom can "nestle" in the region of the first radial node of the 4s orbital, between the 4s maximum and the Mg(3s) + core, we draw a circle on the plot with a diameter equal to the hard-sphere diameter of the Ar atom, 3.43/~.74 The minimum in the Mg(3s4s 3Sl) electron density is calculated to be at 2.7/~, very close to the R e value for the Mg(3s4s 3S1).Ar(3L-q) state, 2.8/~, and consistent with our ideas. The electron density maximum due to the 4s orbital is calculated to be at 4.16/~, suggesting that the argon atom has, indeed, substantially penetrated the Rydberg orbital. However, the qualitative picture in Figure 3 should not be construed to mean that only RG size is important. For the first (n + 1)s Rydberg states there will always be a balance between repulsion and attraction. In states such as MgAr(3E), it appears that the M+-Ar attraction, and the increased attraction and decreased repulsion

Metal Atom-Rare Gas van der Waals Complexes

25

3.0

i

Argon atom

~"

2.0

n

1.5

...-, t/i

,.--4

1.0

0.5

0.0

.......

o.o

1. . . . . . . .

0.5

k _ _ _ _ l

1.o

........

I

1.,~ z.o

1

I

I

z.5

3.0

3.5

1

-1

410 4.5

I.

5o

5. f)

r (Angstroms)

Figure 3. The total radial electron density of an Mg atom in the 3s4s251 Rydberg electronic configuration, from a high-level ab initio calculation. 79 The Ar atom is shown as a sphere 3.43 ,~ in diameter z4 centered at 2.83 ,~, the value of re for the Mg(3s4s 351).Ar(3Z+) molecular state.

caused by the resultant back-polarization of the Mg(3s) § core, almost completely outweigh the net repulsion with the diffuse Mg(4s) orbital. In a recent double-resonance study of the Hg(6s7s3Sl).Ne(3E +) state, however, Tsuchiya and co-workers 8~ showed that there was indeed a double-well potential curve, but that the inner-well m i n i m u m was still somewhat above the Hg(6s7s 3S1) + Ne asymptotic energy (by about 60 crn-1). Two bound (metastable) inner-well vibrational eigenstates were observed, however, because the tunnelling rate through the substantial potential maximum of about 150 crn-~ was slow compared to the fluorescence rate. It appears that although Ne (~ = 2.8/~) is smaller than Ar (o = 3.4/~) and should presumably therefore experience less repulsion as it displaces a smaller volume of Hg(7s) electron density (1.8 times less), it also has a polarizability more than four times less than that of Ar. Thus both Hg+-Ne attraction and the resultant back-polarization of the Hg(6s) core electron are just not sufficient to result in a net overall bound state, only a moderately deep metastable potential well. These kinds of delicate balances should become more understood as the whole range of Rydberg M(n + 1)s-RG states, from He to Xe, are characterized in the future. Finally, we discuss the experimentally determined 45 '46 information about Be+Ar and Be+Kr, which further illustrates our back-polarization ideas and is consistent with the Mg+.RG ab initio results.a~ The Be+.Ar ground state is very strongly bound, D e = 4100 crn-l, and has an extremely short bond length, 2.09 A. This can be compared to several theoretical and experimental estimates of D e - - 2200 cm -1 and R e - - 2.4/~ for the Li+.Ar ground state (see Table 1). Of course, the ls 2 core for Li + is much smaller than the 2s electron core in Be +, with radius of only about 0.2 ~,

26

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

versus about 1.0/~ for Bet(2s), 73 so that there must be a great deal of back-polarization in the Bet-Ar system, leading to t w i c e the bond strength and a 0.3-/~ s h o r t e r bond length than in Lit.Ar. A similar comparison exists for the Bet.Kr and Lit-Kr ground states, although the estimated D e and R e values for Lit-Kr are fairly uncertain. The bond distance does increase from Bet-Ar to Bet.Kr, probably because in this system of very small ions, even for RG = Ar, the Be(3s) orbital has polarized so much that the Ar atom may already be close to interpenetrating the "hard" core (pardon the pun) of Be2t(ls 2) electron density. The Kr atom is larger and just can't get too much closer. The excited Bet(2pn).RG states are even more strongly bound and have slightly shorter R e values than the ground states, since the s orbital has been excited (polarized) in the/m direction, and the RG atoms can penetrate even closer to the Be2t(ls 2) core, undergoing an effective charge much greater than +1 (see Table 4). Coxon and co-workers also indicate that they can fit their Bet-Ar RKR potential curve quite well using a function of the form A e -bR - C n / R n, with a best-fit n = 4.4 + 0.4. This would be consistent with 1/R4 ion-dipole attraction with some admixture of 1/R 6 ion--quadrupole attraction, of course, but other functional forms were found to fit the potential as well. 45

Group 1 Atoms The only (n + 1)s Rydberg state characterized of a Group 1 or 11 metal atom is Li(3s 2S1/2).Ne(2Et ), for which the D e and R e values are 570 crn-1 and 2.17 .~,,2 compared to values of 900-1000 cm-1 and 2.05-2.10/~ estimated for the Lit-Ne ground-state potential (see Table 1). A definite maximum of >60 cm -1 in the potential curve was identified at large R. 2 The Li(3s 2S1/2).Ne(2s lower-state D e value was determined very accurately by observation of the onset of rotational predissociation. It was then possible to show that rotational levels of v' = 5 in the Li(3s 2S1/2).Ne(2Et ) Rydberg state were being accessed that were about 60 crn-1 above the Li(2p 2p) + Ne dissociation limit, clear evidence for a long-range maximum in the potential, as expected. The Li(3d 2Dj).He(2As/2) Rydberg state has a bond energy (610 cm -1) very similar to that estimated (and calculated) for the Li+.He ion, and a bond distance slightly less than that estimated for Lit.He (see Table 1). For the A orientation of the 3d orbital, the small He atom can approach along the nodal axis and easily penetrate to the Li t core. Unlike the unusual Li(2p).He(21-l) state, however, the 3d orbital may be so diffuse that additional dispersive Li(3dA).He interactions are minimal because the effective distance from He to is so much larger. On the other hand, the similarity in bond energy may just be due to a combination of Lit-He core attraction (which is slightly weaker than in the free ion) p l u s some Li(3dA).He dispersive attraction. Again, very high quality all-electron ab initio calculations should be possible on this state, and would be useful in understanding the bonding.

Metal Atom-Rare Gas van der Waals Complexes

27

Group 3 and Group 13 Atoms As can be seen from Table l, many Rydberg states of AI and In atoms have now been characterized by recent efforts of the Morse, 34 Breckenridge, 35 Lester, 81 and Hackett 82 research groups. Dagdigian, Alexander and co-workers have also very recently completed a joint experimental/theoretical study of the first Rydberg state of BAr, as well as of B+.Ar. 32'83 We first discuss the (n + 1)s Rydberg states of BAr, A1Ar, and InAr, which generally fit nicely into our model of the bonding expected in such states. There is now reasonable experimental evidence for a potential barrier at large relative internuclear distances in all three of these states, consistent with our ideas. Concerning the A1Ar system, an earlier Birge-Sponer-type determination of D~ for the AI( 3s24s 2S1/2)'Ar(2Z) state33 has been shown to be inconsistent with an accurate ground-state value of D~' = 122 + 4 cm -1 for A1Ar determined recently by Morse and c o - w o r k e r s . 34 The results can be reconciled if there is a small barrier to dissociation in the Al(3s24s 2S1/z).Ar(2s ) Rydberg state of about 40 cm -1. Fawzy et al. 82 very r e c e n t l y p o i n t e d out a s i m i l a r d i s c r e p a n c y for the In(5sZ6s 2SI/2).Ar(2E) state. Dispersed-fluorescence measurements of ground-state vibrational energies nearly to the dissociation limit yielded accurate dissociation energies for the two spin--orbit components of the In.ArCH) ground-state. These values are inconsistent with Birge-Sponer extrapolations for the upper state; however, the two measurements could be reconciled if there were an approximately 100-cm -1 barrier to dissociation in the In.Ar(2s Rydberg state. Finally, inconsistencies were also noted in high-resolution spectra of the BAr complex, 32 where an unreasonably high value of D~' for ground-state B.Ar(2H) was derived from a Birge-Sponer extrapolation of upper state vibrational eigenstate energies. This led the authors to propose that there was an approximately 200-crn -1 barrier to dissociation in the excited B(2s23s2S1/2).Ar(2Z +) state. High-level C ASSCF-CI calculations of this state were consistent with such a barrier.32 Ab initio calculations of the B+-Ar curve 83 were quite similar (in both shape and R e value) to the experimental RKR potential curve of the B(2s23s 2S1/2).Ar(2E+) Rydberg state, consistent with our expectations. The values of the ab initio calculated D e and R e for B§ shown in Table 1, are probably somewhat too small and too great, respectively. Dagdigian and Alexander, 83 however, argue that the lack of similarity between their theoretical B-Ar(2E+) and B§ Rydberg state potential curves shows the failure of a Rydberg orbital penetration-type model to explain the origin of the inner potential minimum, at least in the BAr system. Further, they also claim 32 that because there was no evidence of a potential well in their simple CASSCF calculations, which they believe should be of sufficient quality to adequately describe the distortions of the B(3s) Rydberg orbital (which in turn they claim must occur for B§ attraction to be effective), a penetration model is not useful. It should be noted in this regard that Simons and co-workers, 84 performing similar

28

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

CASSCF calculations, did find a "dip" in the analogous Be(2s3s 3Sl/z).Ar(3Z+) Rydberg state potential curve. Dagdigian and Alexander believe that "subtle interplay between the differential electron correlation and charge polarization effects" are responsible for the potential well in B(2sZ3s 2SI/2).Ar(ZZ+). Although such subtle effects are undoubtedly present (see below), we believe they are probably not responsible for the sudden, strong attraction observed experimentally. The size of the 3s Rydberg orbital, 3s, on the B atom can be estimated (see below) to be about 3.3/~.85 Since the experimentally determined distance of the Ar nucleus from the Be nucleus is only 2.16/~ (Re), it is obvious that the Ar atom has penetrated beneath a very substantial portion of the electron density of the atomic B(3s) orbital and therefore must have some attraction for the underlying, positively charged core. However, we do note one difference between the A1Ar and MgAr 4s Rydberg states that is relevant to this controversy. From Table 1, the binding energy for the Al(3s24s 2S1/2)-Ar state is only 398 cm -1, compared to the D e of AI-Ar+ (measured directly and accurately by Morse and co-workers), 34 which is 1024 crn-~. In contrast, the binding energy of the Mg(3s4s 3S1).Ar state is 1127 crn-1, ~~compared to the experimental value of D e of about 1230 cm -l for Mg+.Ar. 61 The Rydberg state binding energy is thus a much higher fraction of the free-ion energy for the MgAr state than for the AIAr state. As pointed out previously, a similar situation exists for Hg(6s7s3Sl).Ar(3Z+),De = 1430 cm -1, versus Hg+.Ar, D e = 1830 cm -1. No neutral BeAr data exist for comparison, but the D e for B(2s23s 2S1/2).Ar(2L'+)32 is about 1200 cm -1, compared to the calculated D e value for B+.Ar83 (probably somewhat too low) of about 2200 crn-1. Again, it appears that the Ar atom has more difficulty "fitting into" the region of the first radial node for Group 3 diffuse (n + l)s Rydberg orbitals than into those of Group 2 (or 12) diffuse (n + 1)s Rydberg orbitals. This could be due to two reasons: (1) The one-electron Group 2(12) M+(ns) core orbitals can more easily "back-polarize," decreasing repulsion and increasing the effective positive charge of the core seen by the Ar atom. (2) The Group 2(12) (n + 1)s Rydberg orbitals are more diffuse, and thus it is easier to fit into the region of the first node. The Al(3s2) + ion core should be somewhat smaller, but also less polarizable, than the Mg+(3s) ion core. Both 3s electrons must sp hybridize to effectively avoid the incoming Ar atom, and this may be a price too high to pay for the increased attraction to the ion core in the Al(3s24s 2S1/2)-Ar(2'~"+) system. Polarization of the two-electron Al+(3s2) core will require mixing of the Al+(3s3p) configuration at about 37,000 cm-1; in contrast, the one-electron Mg+(3s) core can be quite effectively polarized by mixing of the Mg+(3p) configuration at only about 26,000 cm -1. An analogous situation exists for B + and In § cores. We therefore believe that there is some truth to Dagdigian and Alexander's assertion 32 that subtle correlation and charge polarization effects are in play for the B(2sZ3s 2Sl/2)-Ar(2L'+) Rydberg state, in that the Ar atom has a difficult time nesting into a region of minimum B(3s)

Metal Atom-Rare Gas van der Waals Complexes

29

charge density because the two-electron B+(2s 2) core does not back-polarize as easily as do the one-electron M(ns) § cores of Group 2 and Group 12 atoms. The ultimate s o u r c e of the attraction, we believe, is still M+~Ar core-ion/induceddipole forces, however. It is possible to estimate from quantum defect theory 85 the mean radius of the 4s orbital in the Al(3s24s) state versus the Mg(3s4s) state: ns(au) = 3/2(n*) 2, which is the expectation value of r for a one-electron ns atom, with n replaced by n*= n - a, where a is the quantum defect for the state of interest; I P - E = R / ( n - a) 2, where IP is the ionization potential of the ground-state atom, E is the energy above the ground state of the state of interest, and R is the Rydberg constant (the IP of the H atom). (Note that for Rydberg atoms with 14: 0, will depend on /.86 We find that Al -- 3.81/~, and Mg = 4.27/~. Even though the Al+(3s 2) core will be somewhat smaller than that of Mg+(3s), an RG atom may still have less difficulty fitting within the first outer maximum of the more diffuse Mg(4s) Rydberg orbital than of the Al(4s) orbital, as observed experimentally. Similar quantum defect calculations for 3s Rydberg orbitals of Be versus B atoms, and of 5s Rydberg orbitals of Cd versus In atoms also show that the Group 2(12) (n + 1)s Rydberg orbitals are more diffuse than their Group 3 counterparts. As can be seen in Table 1, the In(5s26s 2S ).Ar(2L-'+) state is bound by only about 400 1/2 1 cm -1, whereas the Cd(5s6s 2SI/2).Ar(3E+) state is bound by about 1250 c m - . The bond strength of the Al(3s24s 2Sl/2).Kr(2L-'+) state is 1010 cm -1, which is a larger fraction of the AI+.Kr bond energy, experimentally determined 34 to be 1577 crn-l. Although Kr is slightly larger than Ar (about 17% more "volume"), 74 it is 51% more polarizable (0~ = 2 . 4 8 /~3).76 It appears, therefore, that this extra polarizability allows it to penetrate into the Al(4s) Rydberg orbital at less net expense, since the ion-induced-dipole attraction will be much greater, and more back-polarization of the Al+(3s2) core can also occur. The R e for this state is 3.03 /~, even slightly less than that ofthe Al(3s24s 2S1/2).Ar(2E+) state, 3.05/~, reflecting the reduction of core repulsion due to greater back-polarization by Kr. We now turn to the higher AIAr and AIKr Rydberg states, many of which have been characterized in a comprehensive study by Morse and c o - w o r k e r s . 34 One excitation spectrum of AIKr to a higher state has been rotationally resolved by Fu et al., 35 so we discuss this Al(3s25s 2S1/2).Kr(2E+) state first. As expected, since the Al(5s) orbital will be much larger and more diffuse (and thus easier to penetrate), the bond energy is greater (1262 cm -1 versus 1010 cm -1) for the Al(5s).Kr than the Al(4s)-Kr state. However, the Re value is a l s o slightly greater, rather than smaller, than the Al(4s).Kr value (3.10/~ versus 3.03/~), which was quite puzzling at first. The likely explanation, we believe, is that there is an avoided crossing with the strongly repulsive 2E§ state that correlates with the valence Al(3s23d 2D5/2) atomic level. This state lies above the Al(3s24s 2Sl/2) state and only 5252 cm -1 below that of the Al(3s25s 2S1/2) state.

30

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

-62

1. . . . . . . . . .

-279

I. . . . . . . . . . . . . . . . . . . .

!

1" .............

B

-495

-712

I::I

u..]

-929

-1145

-1362

.........

2.0

1 . . . . . . .

2.5

t

_

3.0

_t

.

3.5

t_

.

4.0

j_.

4.5

Internuclear separation

_t

. . . . .

5.0

i . . . . .

5.5

6.0

(,h.)

Figure 4. Superimposed potential energy curves 35 for the Al(3s24s 251/2).Kr(B2y'.+) and Al(3s25s 51/2).Kr(H2s +) states, in which each curve is plotted relative to the same asymptotic dissociation energy of E = 0.

Shown in Figure 4 are the RKR potential curves of the Al(4s).Kr and the Al(5s)-Kr states, where the zero energies for both curves have been normalized to the asymptotic atomic states at infinite distance. As expected, at large R, the Al(5s).Kr energy is much lower, since the Kr atom has essentially already penetrated the Al(5s) orbital outer lobe. On the inner wall, however, the repulsion is steeper for the Al(5s).Kr state than for the Al(4s).Kr state. The only reasonable explanation for the increased net repulsion at the same distance R for the higher Rydberg state is an avoided crossing with a repulsive 2s247 state high above its own asymptotic atomic states. The non-Rydberg 3dE state arising from the valence Al(3s23d figuration is the likely culprit. In the work of Morse and co-workers, 34transitions to more than 40 Rydberg states of A1Ar and AIKr, all the way to the ionization limits, were observed and assigned. The complete assignments were based on the assumptions that for a given atomic Rydberg configuration the bonding strength varied in the order A > H > E, and, for some of the congested spectra from transitions to the higher energy Rydberg states, that the bond energy of such a state would never exceed that of the corresponding AI§ ion. This is quite reasonable of course, from our view of the bonding, and 2 D 5 / 2 )

c o n -

Metal Atom-Rare Gas van der Waals Complexes

31

resulted in a very consistent set of bond energies for essentially all the states observed, as seen in Table 6. For the AI.Ar(2E § states that correlate with the Al(3s2ns) Rydberg atomic states, for example, the bond energies (after increasing by a large increment from n = 4 to n = 5, consistent with the above arguments) increase slowly as n rises to n = 7, where D e = 863 cm -1, approaching the De(AI§ = 1024 cm -1 value, as expected. A similar trend is observed for the AI.Kr(2E+) states correlating with Al(3s2ns) atomic states. Several transitions were also observed to molecular Rydberg states of s 11, and A symmetry that correlate with Al(3s2nd 2D) Rydberg atomic states because of the allowed nature of the Al(3s2nd 2D ~ 3s23p 2p) atomic transitions. As can be seen from Table 6, the same slow increase in D e for the series of Al(3s2nd 2D)-Ar(2'L"+) states is observed, approaching the D e of AI+.Ar as n ~ oo. Also, the D e for each particular Al(3s2nd 2D).Ar(2E+) state is less than that of the Al(3s2ns 2S).Ar(2E§ state with the same value ofn. This makes sense, because even when n is large, there may still be more electron density concentrated along the bond axis for dE alignment of an nd orbital than for an ns orbital (even though an nd Rydberg orbital will be overall more diffuse than an ns Rydberg orbital, because it is less penetrating). An nd s Rydberg atomic orbital is thus apparently more difficult to penetrate than an ns E orbital, but (as can be seen in Table 6), the difference becomes less and less as n increases. Similar results are seen for AIKr, although the data set is not so extensive. For the assigned ndA Rydberg states, even for relatively low values of n = 4 and n = 5, the bond energies are much greater than those of the nE and nH states of the same quantum number and are already close to the AI.Ar § and A1.Kr§ values. This is to be expected, since in the A configuration the RG atom is approaching along the nodal axis of the Al(nd) orbital, where the two nodal planes intersect, thus minimizing repulsion. Such ndA states probably have no potential barriers to penetration of the Al(nd) Rydberg orbitals. Of course, for larger n, as the nd orbitals become quite diffuse, the D e values of ndE, ndI-l, and ndA states with the same value of n become more and more similar (see Table 6). Very weak transitions to states correlating to atomic Al(3s2t~ Rydberg states were also observed, even though the nf ~ 3p transitions are electric dipole forbidden. 34 Complexation with the RG atom apparently provides sufficient perturbation that f E ~ pFl,fl-I ~ pl-I, andfA ~ pFl transitions in the molecules have some oscillator strength. As can be seen in Table 6, the D e information (although more limited) shows that even for n = 4, the nfA states are already approaching the AI§ bond energies. Of course, the 4f orbital has no radial node and penetrates to the nucleus very ineffectively, 34 so the RG atom may feel a high effective AI § core charge even for low n values. This may account for the relatively high D e values of the 4 f s 4fI-l, and 5fl-I states compared to their 4d and 5d counterparts, as well. (We thank Professor M. Morse for suggesting this possibility.) 87

32

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP Table 6. Bond Dissociation Values of AIAr and AIKr Excited States 34'3s in c m -1

Species

n

nff,

npH

nd~,

ndI'l

ndA

137

557

rife

nf H

nfA

AIAr

3(vaknce)

AIAr

4

398

--

312

686

826

423

857

951

AIAr

5

731

--

494

712

931

--

926

1004

AIAr

6

815

826

704

802

941

m

__

AIAr

7

863

~

806

883

943

m

~

AIAr

8

~

847

927

943

~

~

AIAr

9

~

914

943

958

m

AIAr

~ (AI+.A0

1024

1024

1024

1024

1024

1024

1445

1024

1024

AIKr

3 (valence)

AIKr

4

1010

~

488

1180

1476

--

1372

AIKr

5

1262

~

943

1239

1527

~

--

1309

AIKr

6

AIKr

7

AIKr

~(A~.Kr)

~

. 1577

~

~

-. 1577

1175

1327 .

. 1577

m

. 1577

1521 . 1577

~ .

~ .

1577

1577

1577

Group 14 Atoms The only state of this G r o u p that has been c h a r a c t e r i z e d is Si(3s23p4s 3Pj).Ar(3H).44 The bond strength of this state is quite high, 2111 cm -1. The atomic state is a Rydberg state, of course, so there should be a strong bond with the Si+(3s23pr0 core if the Ar atom can penetrate the Si(4s) Rydberg electron cloud effectively, which appears to be a difficult task (as discussed previously) for the analogous Al(4s) Rydberg orbital. From quantum defect theory, as for the Si(3s23p4s) state is in fact much smaller than that of the Al(3s24s) state, 3.27 ,~, versus 3.81/~. The effective Si+(3s23pn) core could also be much smaller than that of Al+(3s2); however, ~t~2 ..... = 1;,16/~ versus A~sj . . . . . = 1.26/~.73 Also, if the Ar atom can get close to the Sit (3s)" core, it may encounter a net positive charge of more than + 1, because it is approaching along the Si(3pn) nodal axis. The rotational band contour simulations were much more sensitive to the AB values than to absolute B v" values, 44 and the true R e value for Si(3s23p4s 3pj). Ar(3H) may be quite small. An R e value of less than 2.8/~ and/or an effective charge greater than +1 would appear to be required to adequately rationalize the 2100-cm -l bond strength with any sort of Rydberg electrostatic bonding arguments. We note in this regard that Rydberg state bond energies with the Ar atom can easily approach 2000 cm -1, since D e for the Zn(4s5s 3SI)-Ar(3~+) state is 1829 cm -1. However, this high bond energy is attained via a very short bond distance of 2.61 /~, where ion-induced-dipole forces (with a point charge of +1) can provide 2100 crn-1 of attractive energy, and the ion--quadrupole term proportionally more energy, as it is dependent on R -6 rather than on R -4. Because AB for the SiAr transition has been determined fairly accurately 44 (as confirmed by a successful Franck-Condon

Metal Atom-Rare Gas van der Waals Complexes

33

intensity simulation of the spectrum with AR = 0.9/~), this would require that the SiAr ground state bond distance be about 3.6/~. As about to be discussed, however, this is quite reasonable, because the SiAr ground state has a substantially stronger bond than A1Ar, where R e = 3.79/~. Very recent ab initio calculations 62 of the Si+.Ar ion ground state, Si+(3s23p 2Pj).Ar(2I-I), yield values of D e = 2076 cm -l, and R e = 2.80/~. These estimates are quite consistent with our view that the Si.Ar(31-I) state is Rydberg in character, with an Si.Ar § core surrounded by a diffuse 4s electron cloud, which may polarize away readily to take advantage of the energy lowering from the strong Si+-Ar bonding. It is also interesting to note the much greater bond strength of the Si+-Ar(2H) ion compared to the Mg§ and AI+.Ar ions, which are bound by only 1000-1200 cm -1 (see Table 1). This appears to be due not only to the expected smaller size of the Si § versus the Mg § and A1§ ion, but also to the preferred H alignment of the Si+(3p) outer-shell orbital. The potential curve of the Si+(3s23p 2Pj).Ar(2Z) state, wherein the Si+(3p) orbital is aligned in a t~ fashion with respect to the Ar atom, has also been calculated and shows a well depth more than five times smaller than that of the Si+.Ar(21-I) state, and an R e value about one /~ larger (see Table 1). Apparently, even though the p orbital is quite compact in this ground-state ion, approach of the Ar atom along the nodal axis reduces repulsion and allows the Ar atom to interact effectively with the Si 2§ core. There could also be mixing of other nearby Si excited-state configurations that either enable better effective penetration of the Si(4s) Rydberg orbital by the Ar atom, or allow a higher effective Si core charge (greater than + 1) to be experienced by the Ar atom at moderate distances, or both. The only triplet state that is even close in energy, however, is the valence Si(3s3p 3 3Oj) configuration, which is more than 5000 cm -l higher in energy. It is an intriguing configuration in that it corresponds to two spin-paired electrons in an l = 10t)p orbital, one in an l = 0(6) p orbital, and only one electron in an s orbital. For Ar approach along the z-axis, a 3A configuration would result that might be very favorable, as the approach would be along the p• nodal axis, and the s and p0(o) orbitals could hybridize to back-polarize out of the way. The 3I-I molecular state of SiAr, which would also correlate with Si(3s3p 3 3Oj) c a n be shown 87 to consist of equal contributions of 1 0 2 1 1 2 1 0 s (P0) (P+I) (P-l) and s (P0) (P+l) (P-l) configurations, and still have 1/3 P0, 2/3 P• character on average; any mixing of this valence 31-I configuration into the 3s2(3P+l)14s(3H) Rydberg state of SiAr might conceivably increase the effectiveness of the bonding with Ar. High-level ab initio calculations of all these states would be very interesting and useful.

Nonlinear Birge-Sponer Plots One other point should be made. Many of these (n + 1)s Rydberg states show linear Birge-Sponer plots over the midrange of v' values but then exhibit sudden negative curvature as dissociation is approached. For the only bound state for which a potential maximum has been characterized directly, Hg(6s7s 3SI).Ar(3Z+), the

34

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP 4

o

\

100

\

'4 \

\ Q

\

75

\

\

4"

>

\ \

\

50

\ t

25-

J

0

!

10

I.

2O

v

1

v

30

Figure 5. Birge-Sponer

plot of the vibrational eigenvalues of the Hg(6s7s 3S1).Ar(3y_,+) state, right up to the outer maximum in the potential curve. 3~

AG1/2 values in the Birge-Sponer plot very suddenly approach zero as shown in Figure 5. This is to be expected, since the shape of the potential curve near the "bump" maximum is convex, and the spacing of the vibrational eigenfunctions thus drops off extremely rapidly as v' increases compared to, for example, a Morse potential function or a Lennard-Jones potential function, where the outer-wing value of the potential approaches its asymptotic value quite slowly. Similar negative deviations from nonlinearity in B irge-Sponer plots have been observed 32'37'44 in several other systems (BAr, AlAr, A1Kr, SiAr) where the upper states correlate with (n + 1)s atomic states. This is consistent with our belief that M.RG states that correlate with Rydberg M*[(n + 1)s] atomic states have long-range maxima in their potential curves due to the net repulsion experienced by the RG atom as it passes through the outer lobe of the (n + 1)s electron density. It should be noted that linear Birge-Sponer plots were observed in studies of (n + 1)s (3Z+) Rydberg states of MgAr, ZnAr, and CdAr, but those measurements all

Metal Atom-Rare Gas van der Waals Complexes

35

involved excitation from moderately bound M(nsnp 3P).Ar(3H) pure-x states where v = 0, so that the upper-state v' levels (Franck--Condon accessed) were very far from the dissociation limit. 1~ Recent double-resonance experiments by Krause and co-workers, 27 in which h i g h e r v i b r a t i o n a l l e v e l s of the Cd(5s5p 3P1).Ar(3Ho§ ) state were used as intermediate states, allowed access to much higher levels of the Cd(5s6s 3S1)-Ar(3Z+) state, up to v' = 19; definite negative curvature in their Birge-Sponer plot was observed at high v', as expected.

E. Spin-Orbit Coupling For M.RG states that have both spin and orbital angular momentum, spin-orbit coupling can have important effects on their spectroscopic transitions, bonding, and possible predissociation. The spin-orbit operator can be represented, using oneelectron operators, as, 85 ^6^ i = aili.s

HSO = 9

r a^ i: l ^ l~[.s; ^ + ~l^i.s^i + liz.Siz/1

(6)

.

and,

aili = X K

K li K (, riK )

^

where o~ = e2/h c, and IlK is the orbital angular momentum of electron i about nucleus K, riK its distance from nucleus K, and Ze~jc is the effective charge of the K ~ nucleus (less than Z K because the spin-other-orbit part of Hso has the effect of the nuclear charge by 20-50%),85 and the sum is over all electrons i. The ^screening ^ lz.sZ term couples only states with^the^ sa~nevalues of ~, A, and Z, but S can either be the same or differ by +1. The/+.s- +/-.s + terms couple configurations with the same value of ~, but with AA = _+1, A~ = gl, and AS = 0,+1. For the Group 2 (or 12) excited configurations of valence nsnp character (which we use here to illustrate spin-orbit effects), there will be singlet states of 1H and I'L'+ character, but also triplet states of 317 + - and 3~;+_ character The f ;: o ,0,1,2 o ,l 9 z.Sz term results in (diagonal) coupling of each state with itself, thus splitting the 3H0,1,2 states [in the Hund's case (a) limit, where electrostatic interactions are much larger than Hso ] into three different energy levels, spaced by 1/2a n, where a n is the molecular spin--orbit parameter. However, the ll-I_'.l and 3H 1 states have the same orbital configurations (~ = l, A = l, E = 0), and ~"~z coupling between these states can affect somewhat the even spacings of the ~ = 0,1,2 multiplets in the 3H n states. Because the 1H1 and3H 1 states for the systems discussed in this review [from M(nsnp).RG configurations] are widely separated in energy at all R values, owing to the large difference in the quantum mechanical exchange interaction between the singlet and triplet states, this effect is usually minor.

36

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

The ~+.sA- + ~-.s% terms causes E-H coupling in those triplet states with the same value of Q and the same total parity (+ or-), 31"I0-/3Y:~- and 3II 1/3E~, and thus causes them to become "mixed" E-FI states as spin-orbit coupling increases. The 3II0+ and 3H 2 states do not couple via the spin-orbit interaction with the 3~+ states, and thus remain electrostatically pure-H in character no matter how large the spin-orbit coupling is (in a single-configuration approximation). Finally, the ~+.s- type terms can also couple the lIIi/3s and 1s states. Because, in the cases of interest here (see Figure 1), the higher energy 1E+ states are quite repulsive compared to the lower energy pure-H attractive 3H0+ states, coupling of the latter pair of states is unimportant for either the spectroscopy or the dynamics of these systems. On the other hand, as seen in Figure 1, the ll-I1 states can be quite attractive in nature. If the 3'L-~1state is sufficiently repulsive, the two states can come quite close in energy or even "cross," in a diabatic sense. If so, the ll-Il a n d 3~; states become fl = 1 "mixed states" near their crossing point, and the bound ll'I1 state can thus be predissociated by the repulsive 3E~ state. This is now discussed in more detail.

Mixed E--I'I States As indicated, for those states with spin angular momentum, H and s multiplet states with the same value of fl are really mixed states, and the degree of mixing

500

!

400

!

3E+ 1 3E+ ,~. O"

3p

2

3P 1

~ 300

3P 0

>

/ 3112

200

/~ 3110+

100 I10_ 0

I

2

3

~-/

l 4

I 5

R (Angstroms)

!

I

6

7

8

Figure 6. Potential energy curves of the Mg.Ar electronic states correlating with the Mg(3s3p 3pj) atomic multiplet statesJ ~

44 600

44 400

O

I

44 200

3P2 44 000

43 800

2

43 600 40 000

39 800 ID

~39 600 4)

3p

,oo t., e

39 200

39 000

(continued) Figure 7. Potential energy curves of the Hg.Ar electronic states correlating with the Hg(6s6p 3PI) atomic multiplet states. 3~ 37

38

W. H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

38 500

38 300

38 100

37 900

37 700

37 500

3P0 2

3

4

R(

Figure 7.

5

stro

)

6

7

8

(Continued)

will increase as the spin--orbit parameter increases in value. At one extreme [low spin-orbit coupling, Hund's case (a) limit], pi-state multiplets [Group 1(11), np 21-Its; Group 2(12), nsnp3I-l~; Group 3(13), ns2np 2I-1~, etc.] will be essentially uncoupled from the corresponding ~ states near their R e values. For example, shown in Figure 6 are the excited 3I-I0,1,2 and 3~-'§0,1potential curves of Mg.Ar estimated by an approximate treatment of spin--orbit coupling to be described below. Near R e for the 3IIa levels, these states are all essentially strongly bound and nearly pure-l-I in character, whereas the 3 ~ levels are nearly pure-E and repulsive in character. At the other extreme [high spin-orbit coupling, Hund's case (c) limit], the triplet "~" and "II" states with the same values of f~ are completely mixed near their R e values, and f~ is the only good quantum number. Shown in Figure 7 are potential curves for a system approaching that of Hund's case (c), Hg(6s6p 3ej)-Ar(3II,3~). The f~ = 0(+) and f~ = 2 levels remain pure-l-I and are (relatively) strongly bound, whereas all of the f~ = 0(-) and f~ = 1 levels are bound much less owing to the almost completely mixed E(repulsive)-H(bound) character of the states. Finally, shown in Figures 8 and 9 are the similarly constructed potential curves for the analogous 4s4p and 5s5p states of Zn.Ar and Cd.Ar. Near R e for the pure-Il states, these states are clearly between Hund's case (a) and case (c) limits, with ZnAr closer to case (a), and CdAr closer to case (c).

,

3000

,

,

,

,

2700 2400

=" 2too 1800

1500 1200 3P 2 "9

900

3P0[ 3P 1

6OO

0

,~-uo~s~- i 3 4

2

i

j

i

5

6

7

8

r (Angstroms)

Figure 8. Potential energy curves of the Zn.Ar electronic states correlating with the Zn(4s4p 3pj) atomic multiplet states./s

32 500

d3Z'0.

32 000

Cd ('P~) * A r ~

b3l']

= 31 500 >

-" 31 000 Cdl~P,) + Ar

_

Cd (3P o) + Ar

I

A3]'[o ,

30 500 a3rIo -

30 00n 5~176

X:s

~

1 Cd (=So) + A r I

o =

2.00

!

3.25

i

- I

z

,I

4.50 5.75 R (Angstroms)

;

!i

7.00

Figure 9. Potential energy curves of the Cd.Ar electronic states correlating with the Cd(5s5p 3p/) atomic multiplet states. 21'88 39

40

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

If one assumes that there are spin-free Vn and V~ electrostatic potentials for these kinds of doublet or triplet states (for ZnXe, for instance, the triplet Vn and V~. potentials would be similar to, but not the same as, the 1H l and lL.+potentials shown in Figure 1), it is possible to estimate the "true" potential curves for the f~ = 0(-) and f~ = 1 triplet states, knowing the spin--orbit coupling matrix elements and the magnitude of the spin--orbit coupling for the particular states of interest. It is usually necessary to assume that the molecular spin-orbit coupling constant remains unchanged from the R = oo value of the spin-orbit coupling constant of the atomic metal-atom multiplet state (multiplied by some constant fraction to transform from the atomic to the molecular frame). This is not always true (see below), so such a treatment will necessarily be only semiquantitative or even qualitative in nature. We illustrate the theory by applying it to the M(nsnp 3Pj)-RG(3I-Ifl, 3 ~ ) sets of states. ~~ Spin-orbit'interaction matrices ~5are shown below for the states arising from nsnp 3pj atomic states.

01 I I I - o~ ct

f~=0:

@

0

a

H-o~

f~=l: f~=2:

[lI + ct]

The quantity H represents the energy of the M atom pn orbital, and Z the energy of the M atom p a orbital, at some internuclear distance R of the M.RG state. (The nsnp IH and nsnp 1Z+ states are assumed to be much higher in energy near R e of the 3H~ states and are not included here). The factor ct (always positive) is set equal to half of the atomic spin-orbit coupling constant for the M(nsnp 3pj) states {et = 1/3[E(3P2) - E(3Po)] }. Near R e for these 31-IM.RG states, the value of H will be negative and that of Z positive. The energy levels of the six nondegenerate molecular states as functions of Z and l-I are predicted by solving det I Hik - ESik [ = 0 for each of the three matrices, where Sik = 8ik. The following expressions are found for the six levels in order ofincreasing energy [the zero of energy is exactly halfway between the M(3pI) and M(3P2) atomic energies]" El(3IIo) = (3a/2)[x + (21-I/3ct) - 1/3 - (x2 + 2x/3 + 1) 1/2] E2(3H~) = + H - 0~

E3(31-11)= (3~/2)[x + (21I/3~- (x2 + 4/9) I/2] E4(31-12)= ct + H

Metal Atom-Rare Gas van der Waals Complexes

41

E5(3~1-1)= (3ct/2)[x + (21-I/3ct) + (x2 + 4/9) 1/2] E6(3]~-) = (3(x/2)[x + (21-I/3(z) - 1/3 + (x2 + 2x/3 + 1) 1/2] Here x = ( Z - I-I)/(3(z) is a measure of the magnitude of the electrostatic energy versus that of the spin-orbit coupling. In the case (a) limit, x will approach infinity, and the splittings between the three 3I-I2,1,0 levels (see Figure 6) will approach (z. In the case (c) limit, x will approach zero: the 31-10+,0-splitting will approach ct, the 31-I0+,1 levels will become essentially degenerate, and the 3I-11,2 splitting will approach 2ix. (See Figure 7.) This sort of method, first applied by Callender et al. 36 to M.RG systems, has now been used in several examples to analyze spectroscopic data and predict multiplet potential c u r v e s . 10'15'19'21'29'37'44 It is also possible, of course, from I-I multiplet splittings in intermediate cases, to obtain approximate information about the (usually) unseen, repulsive, multiplet Z states.

Mixing of RG Orbital Character into Nominally M% RG Wavefunctions As noted in the approximate treatment of spin-orbit coupling outlined above, it is often assumed that the coupling comes entirely from the M(nsnp) electronic configuration, which can be thought of as being perturbed electrostatically by the filled-shell 1S0 electronic configurations [s2(He) or p6] on the RG atom. However, if our quadrupole, "effective charge" model ofpn interactions is correct, then near R e or on the inner wall of the M(p~).RG potentials, the RG electron distribution will be severely polarized towards the M + core. From a quantum mechanical point of view, this means that high-energy electronic configurations of the RG atoms may be mixed into the M(pn).RG wavefunctions. Mixing of npS(n + 1) Rydberg state configurations of the RG atoms would allow polarization of the RG electron cloud towards the M + core; mixing of the RG[(ntm)a(npt~)l(n + 1)s l] configuration, for example, would yield np/(n + 1)s hybridization. 89 Even a very small admixture of such configurations could increase the apparent spin-orbit coupling constant for M-RG states such as Li(2p2p1/2,3/2).RG(2I-ll/2,3/2) or Na(3p2pl/2,3/2) 9 RG(2FII/2,3/2), where the inherent spin-orbit coupling constant due to the M(np) electron is very small" 0.23 cm -1 for Li, 11.5 crn-l for Na. This is because for all the RG atoms (except He, of course) the spin-orbit constant in these "p-hole" Rydberg states is fairly large and similar to that of the RG+(np 5) free ion.

Variation of Multiplet Splittings with Vibrational Level. FortheNa(3p 2P1/2,3/2).RG(21-I1/2,3/2) multiplets, where RG = Ar, Kr, Xe, it has been observed 7'8 that the splitting between the f~ = 1/2 and f~ = 3/2 levels (which is the molecular spin-orbit parameter A in these systems) is not only larger than predicted from the assumption that A = 2/3 {E[Na(aP3/2)]- E[Na(aPI/2)]} = 11.5 cm -l, but also increases as v' decreases (see Table 7). For NaAr, NaKr, and NaXe, the extrapolated values of A at the potential minima are ca. 20, ca. 50, and ca. 110 cm -1, respectively.

42

W.H. BRECKENRIDGE,CHRISTOPHE JOUVET, and BENOIT SOEP

Table 7. Variation of Spectroscopic Constants 7'8'9~of Na(3p 21-I1/2,3/2)"RG with Vibrational Quantum Number (cm -1) RG

v"

Av,a

Ar

7

14.79

--0.95 x 10-3

0.0861

Ar

8

14.29

-1.39 x 10-3

0.0794

Ar

9

13.87

-1.86 x 10-3

0.0726

Ar

10

13.48

-2.79 x 10-3

0.0660

Kr (84)

7

[32.8]

+3.40 x 10-3

0.0740

Kr

8

31.3

+3.23 x 10-3

0.0703

Kr

9

29.2

+2.87 x 10-3

0.0666

Kr

10

26.9

+2.50 x 10-3

0.0628

Kr

11

25.4

+1.93 x 10-3

0.0591

Kr

12

23.7

+1.20 x 10-3

0.0553

Kr

13

22.0

+0.10 x 10-3

0.0515

pv ,b

B v,

Kr

14

[20.5]

-1.37 x 10-3

0.0478

Xe (129)

11

64.1

+9.24 x 10-3

0.0597

Xe

12

60.1

+8.95 x 10-3

0.0574

Xe

13

56.1

+8.65 x 10-3

0.0550

Xe

14

52.3

+8.36 x 10-3

0.0526

Xe

15

48.5

+8.00 x 10-3

0.0502

Xe

16

[44.8]

+7.54 x 10-3

0.0477

Notes:

aValues in brackets are extrapolated. bThe value reported is actuaUy pc + 2qv, where qv' is the centrifugal portion of the lambda-doubling constant; we assume here that 2qv, << Pv', since qr is expected to be smaller than Pv" by approximately the ratio

Bv,/Av,?5

For the NaXe state, then, the observed spin--orbit coupling is (remarkably) about 10 times the value expected from the Na(2P1/2,3/2) spin--orbit coupling alone. An early suggestion by Smalley et al. 9~ that the increase in spin-orbit coupling in the NaAr case was perhaps due to perturbation (hybridization) of the Na(2p 6) core by the Ar atom (the 2p electrons would have a much higher spin-orbit constant because of their more efficient penetration to the nucleus) was shown by Cooper, in a quantum mechanical study, 91 to be quite unlikely. Mixing of excited configurations RG[npS(n + 1)s], RG[npS(n + 1)p], etc., where, owing to their valence "nphole" nature the spin--orbit splittings are several thousand wave numbers, might therefore be responsible for the large 21-I1/2/21113/2splitting near the bottom of their respective potential curves. The increase of t h e 3 1 1 1 / 2 / 2 1 1 3 / 2 splitting as v' decreases would just reflect the increased relative sampling of the inner-wall portion of the Na.Xe(21"I) potential curve (where there is a stronger interaction with the RG atom and thus greater mixing of RG* excited-state character) due to the anharmonic nature of diatomic potential curves. For the NaKr and NaXe cases, 7'8 the spin-orbit contribution from the excited Kr and Xe states would dominate. Because the excited Xe and Kr atomic states are all

Metal Atom-Rare Gas van der Waals Complexes

43

p-hole-type configurations, however, owing to the Xe(5pS) + and Kr(4pS) + cores, they are thus inverted: Ej=l/2 > Ej=3/2. Why, then, are the Na.Kr(2Hl/2,3/2) and Na.Xe(2I-ll/2,3/2) states apparently both regular [E(3/2) > E(1/2)]? The regular nature of the multiplets is confirmed by the high-resolution analysis, where, for example, only the lower lying 2I-I1/2 levels exhibit large N-dependent e/f splittings (lambda doubling), as expected (see below), and upper-state vibrational quantum number assignments from band-origin isotope splittings were done separately for 21-11/2 and 2I-I3/2 levels. 7'8 This is rather puzzling. Similar effects have been seen even for RG = Ne in the Li(2Pj) 9 Ne(2Fll/2,3/2), v ' = 0, state. 2 A doubling of levels was observed at low N, the magnitude of which decreased as N increased, which was interpreted as 21-I1/2/21-I3/2 splitting. [In this example, the spin--orbit splitting is comparable to the magnitudes of the rotational energies, and the molecular description goes from Hund's case (a) to Hund's case (b) quite rapidly as N increases.] The measured value of the spin--orbit splitting, 2.77 cm -1, is again much greater than that expected from the Li(2p) orbital alone, which would be 0.23 cm -1. Lee and Havey 2 have suggested, similarly, that mixing of higher energy Ne states, in which the Ne(3p 6) core is excited, could be responsible. No information on whether the 2II 1/2,3/2 multiplets were regular or inverted was given. In related studies, 92 even larger increases in the effective spin--orbit coupling constants of the Li(3p 2pj) and Na(3p 2pj) states excited in solid xenon matrices have been reported:-213 crn-l and -196 cm -1, respectively, derived from MCD (magnetic circular dichroism) spectra. However, in these systems the negative signs (derived unequivocally from the MCD spectra) can be readily and reasonably interpreted as indicating that the Xe atom p-hole (inverted) character dominates in the Li(2p) and Na(2P) cases, since the metal atomic states' spin-orbit coupling is so small. Also, for the Cs(6p 2pj) state excited in a Xe matrix, the effective spin-orbit constant is found to be positive. The spin-orbit coupling constant for the free Cs(6p 9pj) atomic states (+369 crn-1) is large, and therefore apparently dominates. 92'93 Similarly, for excitation of K(4p 2pj) in Kr and Xe matrices, 93 the effective spin-orbit constants have been found to be negative, but of smaller absolute magnitudes than the analogous Li and Na cases. Since the positive spin--orbit coupling for the K(2Pj) states is larger (+38.5 cm-l), this may just reflect some average spin-orbit interaction which, however, is still most influenced by the RG p-hole configurations. A theoretical treatment 94 of these matrix results [as well as of similar experimental results on excitation of Cu(2p) and Au(2p) states in RG matrices], in which the metal atoms were assumed to be in tetradecahedral sites (substituting in an RG atom site and thus surrounded by 12 equivalent RG atoms), was qualitatively successful in explaining both the signs and relative magnitudes of the effective spin-orbit constants observed in all the experimental studies. The theory assumed that mixing of valence RG(np) and Rydberg RG[(n + 1)p] character into the metal atom wavefunctions was responsible for the spin--orbit interactions observed. The matrix

44

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

results and their theoretical rationalization make the observations of regular 2H 1/2,3/2 multiplets for the NaKr and NaXe diatomic molecules even more puzzling. We propose thefollowing possibility, which could certainly be tested by careful, high-level ab initio calculations. As pointed out by Pellow and Vala,94 although the (n + 1)p Rydberg orbitals of RG atoms are very high in energy compared to the ground-state np electrons, with regard to an RG + + e- energy scale they are at energies o f - 2 to-2.5 eV (for RG = Ar, Kr, Xe). Similarly, when the energy of the excited Na(3p) orbital is referenced to an Na § + e- energy scale, it is a t - 3 eV. This means that Na(3p) and RG[(n + 1)p] orbitals are similar in energy (and size, both being quite diffuse) and could thus readily overlap and mix at smaller internuclear distances R. Thus the nominally Na(3p) atomic orbital could simply acquire more and more RG[(n + 1)p] character as the Na.RG internuclear distance R decreases. This would not be a two-electron configuration interaction mixing of Na(3s).RG[npS(n + 1)p] states (where the spin--orbit character would be dominated by the inverted np5 p-hole contribution) but rather a simple one-electron mixing of Na(3p•).RG(np6) and [Na§ + 1)pn:] character into the pn one-electron wave-function. The advantage of such a proposal in rationalizing the NaXe and + 1)pn:] configuration will be NaKr experimental results is that the Na§ regular, not inverted. The disadvantage is that because the RG[(n + 1)pn] orbital is Rydberg in nature, its spin-orbit interaction constant will be much less than that of RG[(npS)(n + 1)s] p-hole configurations. The spin--orbit constants 94 for such RG[(n + 1)p] orbitals are several hundred cm -1 rather than several thousand cm -l, which requires that the admixture of formally Na§ + 1)p] character must in fact be fairly high to explain, for example, a ten-fold increase in the expected spin--orbit constant for the NaXe(2H) state near its Re value. On the other hand, let's examine the further advantages of this sort of electronic mixing in terms of the electrostatic arguments we discussed above for strong M(pn).RG van der Waals bonding. As, for instance, a Xe atom approaches the Na(3p~) state, attraction to the Na + core can be maximized if the Na(3pn) orbital can somehow become more diffuse (in the limit, become the Na + ion). One way of doing that would be to mix in Rydberg Na(4pn) character, for example, allowing the Xe atom to more readily penetrate the Na(p~) orbital and approach closer to the Na § core. However, this would decrease rather than increase the apparent rI1/2~3/2 spin-orbit interaction, contrary to observation. On the other hand, Na+.Xe-(5p~ character being mixed into the wave function will provide the sameelectrostatic advantages, and, in fact, at shorter internuclear distances R, the state will more and more resemble an Na+.Xe ion surrounded by a Xe "6p" Rydberg electron, i.e., a strongly-bound Rydberg-type molecular state! (See Section IID.) The quantum mechanical calculations of Cooper 91 on the Na.Ar(2H) state appear to be consistent with this postulate, since he observes an increasingly positive spin--orbit coupling as R decreases. Very recent ab initio results (R. Buenker, private communication, August, 1995) (received at the "proof" stages of

Metal Atom-Rare Gas van der Waals Complexes

45

this review) indicate that at least for the LiAr[2H] excited multiplet states, our postulated mechanism appears to be correct. As R decreases, the "Li(2pn)" M.O. acquires more and more diffuse "Ar(4px)" character, and this correlates directly with a remarkably large increase in the (regular) S.O. splitting (up to 30-fold), consistent with experimental observations (B. Bruhl and D. Zimmerman, Chem. Phys. Lett. 1995, 233, 455).

Lambda Doubling. There is another spin-orbit-related aspect of the data on the Na(3p 2Pj)-RG(EH) states (RG --- Kr, Xe) that is also unusual and puzzling. For 2H states, a rotationally induced splitting can occur between the two degenerat e levels of e and f symmetry 85 if there is a nearby state of 2Z+ symmetry. For the + state is coupled only by the/-uncoupling operator, 85 so 21"I3/2component, the 2Zl/2 the effect is small and often difficult to detect except at very high J. For the 2I-I1/2 component, however, which is spin-orbit coupled directly to the 2~/2 state (Af~ 0) with the same asymptoti c metal atom np configuration, there is a cross term in the square of the coupling matrix element, involving the spin-orbit constant, that is different for the e andfcomponents. If the spin-orbit interaction is large compared to the rotational constant, this term dominates the J-dependent coupling, 85 AEf,e = p(J + 1)

(8)

where, p=

2.Av.Bvl(l+ 1) (En - er)

=

4Av.Bv

(9)

(En - Er)

under the Van Vleck "pure precession" hypothesis (Av = spin-orbit constant, Bv = rotational constant). Shown in Table 7 are the values ofp observed for NaAr, NaKr, and NaXe. For NaAr, p is negative and increases with v' as the dissociation limit is approached. This is consistent with coupling with a 2Z+ state above the 21-I1/2 state, which becomes closer in energy as E n increases. This is also exactly what is state will be only 17 c m -1 expected, ofcourse. The repulsive Na(3p away at dissociation, because it correlates with Na(3p 2P1/2) + Ar. On the other hand, for Na(3p 2P1/2).Xe(2I-I1/2) the value of p is not only large but positive and decreases in magnitude as v' increases. This is entirely unexpected and is consistent in a simple pure precession model with coupling with a EL+ state lower in energy than the 2ri1/2 state! o f course, there is a 2E+ state lower than the 21-I1/2 state, namely, the Na(3s 2S1/2).Xe(2~'+ ) ground state. If the ground state were to retain its formal Na(3s)-Xe character, however, there would be no spin-orbit constant cross term, and the lambda doubling from coupling to the ground 2~+ state would be weak. The Na(3s) orbital is likely to be severely distorted by the presence of the Xe atom, however, on the repulsive wall of the NaXe(X2~~+) ground state, and will 3s3p hybridize out of the way of the Xe atom to minimize repulsion. That

2P3/2).Ar(2~l/2)

46

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

means there could be a substantial amount of Na(3po) character in the wavefunction, which of course will allow the spin-orbit cross-term to come into play, 87 However, dispersed fluorescence measurements from high-lying vibrational levels of the NaXe(2H) state 8 indicate that the repulsive NaXe(X2E +) potential curve is more than 12,000 crn-1 lower in energy than the NaXe(2H) potential curve, even at internuclear distances as short as 2.7/~ on the inner limb of the 21-Icurve. This casts considerable doubt on the above possibility, so it appears that the positive values of the constant p in Table 7 for NaXe(2H) and NaKr(2H) vibrational levels must somehow be linked with the anomalously large Av, spin-orbit values for those levels; there certainly appears to be a rough correlation. Again, careful ab initio calculations of these states and their interactions would be very informative and interesting.

Spin-Orbit-Induced Predissociation In Table 1, the D e value for Cd(5s5p 3Pl).Xe(3I10+) is listed as 1036 cm -1, which is a reasonably high bond energy. Under the same conditions with which it was possible to obtain good LIF spectra for excitation of this state of the Cd-Xe complex [to the red of the spin-forbidden Cd(3pI ~ Is0) transition], no fluorescence could be observed 26 for excitation to the red of the strongly allowed Cd(1p1 ~ iS0) transition, where, by analogy with the CdNe, CdAr, and CdKr complexes, the Cd(5s5p lPl).Xe(ll-ll) state should have been excited. 22 When the frequency of a second laser pulse, delayed by about 10 ns, was fixed onto the Cd(5s6s 3S1 ~ 5s5p 3P2) atomic transition, and the excitation laser was then scanned to the red of the Cd(5s5p 1P 1 ~ 5s5s 1So) transition, it was determined that the Cd(5s5p lP1).Xe(ll-II) state was predissociating very efficiently to produce Cd(5s5p 3P2) exclusively. 26 [No Cd(5s5p 3P1) or Cd(5s5p 3P0) predissociation products could be detected by tuning of the probe laser to similarly allowed LIF transitions.] In the Cd(5s5p 3P2) predissociation action spectrum for the CdXe(lI-Ii <---Xls § transition, the vibrational transitions, by analogy with the similar transition to the CdKr(ll-ll) state, 22 should exhibit complex rotational structure because of the overlapping P,Q,R branches of the many CdXe isotopomers with different band origins. Even at high resolution, however, the bands show absolutely no structure and have a Lorentzian shape. 22 Simulations of the bands (with Morse curves, D' = 2500 ern-1, 0~e = 88 em -1 , D e, = 1 8 7 c m -1 ,o~e- = 1 4 c r n -1,andAR e = 1 . 2 9 / ~ ,e estimated from trends in the other Group 12 M-RG states) could best reproduce the band shapes by assignment of a bandwidth of about 7 crn-1 to each rotational line, with convolution of the many isotopic transitions. This corresponds to a predissociation lifetime of about 0.8 ps, or roughly one vibrational period of the Cd.Xe(1Hl) state in the Franck--Condon-accessed region of the potential curve. It had been postulated several years earlier by Breckenridge and Malmin 95 that spin-forbidden collisional deactivation of the Cd(5sSp 1P l) atomic state by RG atoms (or even filled-shell molecules such as CH 4, which might mimic Kr at long

Metal Atom-Rare Gas van der Waals Complexes

47

range because their polarizabilities and hard-sphere radii are similar) could occur via these same Cd(5s5p 1Pl).RG(ll-ll) potential curves. It was suggested that the repulsive Cd(5s5p3P2).RG(3E~) potential curves could cross the bound Cd(5s5p IPI)-RG(II-II) p~teAntial curves. Near the crossing, the coupling of these f~ = 1 states induced by the l+.s- terms in the spin-orbit operator could be large [given the large spin-orbit coupling in the Cd(5s5p) atomic configuration], resulting in predissociation of Cd.RG(IIII) states to produce the Cd(5s5p 3P2) multiplet state preferentially. The Cd.Xe( IH l) "half-collision" predissociation action spectrum is clear evidence that this mechanism is correct. A subsequent measurement of the cross section for the full collision deactivation of Cd(5s5p 1Pl) by Xe [to produce Cd(5s5p 3P2) exclusively] 26 resulted in a value of 25 + 5 A2, consistent with a very efficient process occurring at nearly every collision. Of course, this is to be expected, since the bound CdXe(ll-ll) state predissociates in only one vibration. Finally, we believe that the reason the analogous Cd.RG(llll)states, where RG = Ne, Ar, Kr, do not predissociate has nothing to do with the external heavy atom Xe, since model calculations 96 indicate that the Cd(5s5p) states themselves provide more than sufficient spin-orbit coupling for such efficient 1Fll/3E~ state mixing and predissociation. Rather, it is because, for the smaller, less polarizable RG atoms, the 11-11states are less bound and the 3E1 states less repulsive: the two potential curves do not cross in the energetically accessible region. Similar observations were made for the ZnXe complex. 18 No fluorescence was observed to the red of the Zn(4s4p 1P 1 ~ 4s4s ISo) atomic transitions under conditions where ZnXe was present, under which LIF spectra of ZnAr and ZnKr were readily obtained. 16'17However, a strong Zn(4s4p 3P2) action spectrum was recorded of ZnXe in this spectral region, as shown in Figure 10. In this case, clear isotopic band-head structure could be observed at high resolution, and an unambiguous assignment of the upper-state Zn-Xe(1 l-Il) vibrational states was possible by spectral simulation. The rough, best-fit Lorentzian linewidth for each rotational line of 1 crn-1 for the simulations was much larger than the laser linewidth, however, and indicated a predissociation lifetime of about 5 ps [about 7 vibrations of the Zn.Xe(IH1) state]. This is consistent with the much lower spin-orbit coupling constant for the Zn(4s4p) states, 382 cm -1, versus that of the Cd(5s5p) states, 1142 cm-1, the effective mixing of the 3E'~and 1H1 states (and thus the predissociation rate, roughly) being proportional to the square of the spin-orbit coupling constant. 85 Using the CdXe half-collision versus full-collision analogy, Breckenridge and co-workers 18 predicted that the cross section for collisional deactivation of Zn(4s4p 1P1) by Xe should be in the 2-5 ~2 range. The cross section was subsequently measured by Umemoto and co-workers 97 to be 3.4 ,~2. Wallace et al. 18were also able to detect (see Figure 1) the excitation of the pure-s state, Zn(4s4p 1P1)-Xe(1E§ by laser-induced fluorescence to the blue of the Zn(4s4p 1P1 ~-- 4s4s 1S0) atomic transition. 97 The fact that this state is long lived is also consistent with the idea that only spin-orbit-induced 1I-I1/3E 1 coupling, and n o t 1E~/31-I0§coupling, will be effective inthese systems, since the bound 3H0+curve

i w

-

9

|

|

9

=,

|

9

u

'v' 41 3? 34 31 28 l'l'l I I I " I ' I" I" i "I I' I i

I 4'7180

46885

46590

4 62 95

46000

Enercy (wavenurnber~) Figure 10. The Zn(4s4p3p2) predissociation action spectrum of Zn-Xe to the red of the Zn(4s4plP1 ~ 4s4s 15o) atomic transition: lower panel, experimental; upper panel, simulation. 18

48

Metal Atom-Rare Gas van der Waals Complexes

49

never approaches the higher energy repulsive 1]~ curve. In the language of full-collision dynamics, these half-collision experiments have shown conclusively and dramatically that n-alignment of the Zn(4p) orbitals is effective in deactivation of Zn(4s4p IP1) by Xe, whereas ~ alignment is not. In contrast to the Cd.Xe(~l-ll) results, where Cd(5s5p 3P2) was the exclusive predissociation product, a small (10-- 15%) yield of Zn(4s4p 3P1) in addition to the Zn(4s4p 3P2) product was observed from Zn-Xe(ll-ll) predissociation. 18 The Zn(4s4p 3P1) action spectrum was identical to the Zn(4s4p 3P2) action spectrum shown in Figure 10. It was postulated that the Zn(4s4p 3P1) population resulted from coupling of the repulsive Zn(4s4p3P2).Xe(3Z~) state with the Zn(4s4p 3P1).Xe(31-I1) state, induced by the high radial relative nuclear velocity of the dissociating 3Z~ state. This non-Born--Oppenheimer radial-type coupling will maximize at large R where the 3E[ and 31-I1states are closest in energy and the Zn-Xe relative nuclear velocity is highest. 18Similar yields of Zn(4s4p 3P1) were observed in the full-collision deactivation of Zn(4s4p 1P1) by Xe, and a quantum mechanical close-coupling calculation 97 has confirmed the suggestion 18 that 3]~]/3H1 radial coupling is responsible. No Cd(5s5p 3PI) is produced in the Cd.Xe(1Fll) predissociation because such radial coupling depends quite sensitively on the ratio of the relative velocity of the dissociating state (about the same in both cases) to the asymptotic 3]~~/3I-Ilenergy difference (much greater for Cd, because the spin-orbit splitting of the 3P2/3P l asymptotic levels is about 3 times larger owing to the greater spin-orbit splitting). A recent theoretical study by Alexander 98 of the analogous full-collision process Ca(4s5p 1P1) + He ~ Ca(4s5p 3pj) + He, studied experimentally by Leone and co-workers 99 has shown that the primary product is Ca(4s5p 3P2), produced by a lI-ll/3E] curve crossing of the type originally proposed by Breckenridge and Malmin, 95 and that the Ca(4s5p 3P1) state is produced by 3]~'/31-11 radial coupling in the exit channel, as suggested by Wallace et al. 18 to explain the ZnXe results. The analogous Mg(3s3p 1P1)-Xe(11-I1) state has been observed readily by strong laser-induced fluorescence, and careful studies have shown that there is no predissociation to form the Mg(3s3p 3pj) states.13 Thus the predissociation lifetime of Mg(3s3p 1Pl).Xe(lI-ll) is probably greater than about 2 ns, the radiative lifetime of this state. There are two possible ways to explain this result. The MgXe(1Hl) state is much less bound than the ZnXe(1HI) state, 1500 cm-1 versus 3241 crn-1. It is possible that the (less?) repulsive Mg(3s3p 3P2).Xe(3Z~) state does not cross the Mg.Xe(llIl) bound state until above the Franck--Condon accessible energies (or even above its dissociation limit). Consistent with this possibility, the quenching cross section of Mg(3s3p 1P1) by Xe is quite small. 13 The other possibility is that, because of the low spin--orbit coupling of the Mg(3s3p) states (about 40 cm-1), the 1H1/3El- coupling strength is so small that fluorescence occurs before predissociation. However, this seems rather unlikely because, if the predissociation lifetime is inversely proportional to the square of the atomic spin-orbit coupling constants, one can predict [from the Zn.Xe(1Hl) lifetime] an Mg.Xe(1H1 ) predissociation

50

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

lifetime on the order of about 500 ps, which is much less than that necessary to explain the observations. Also, given the NaXe results discussed previously, any mixing of Xe excited-state character into the wavefunction could actually increase the spin--orbit coupling in the Mg(3s3p) system relative to that of Zn(4s4p) (where the spin--orbit coupling is already reasonably high). Very recent ab initio calculations 69 of the Mg(3s3p 3P2)-Xe(3~+) repulsive potential curve [as well as the analogous Zn-Kr(3Z§ and Zn.Xe(3Z§ repulsive curves] have shown that high-level CI calculations with very good basis sets are necessary to accurately describe the energies of such states near the bound l lI 1 state energies. In the MgXe system, as the quality of the ab initio calculation is continually improved, the 3Z§ state becomes progressively less repulsive. For the highest level calculation, the Mg(3s3p 3P2)-Xe curve still crosses the RKR experimental Mg(3s3p 1P1).Xe potential curve 13 high on the inner wall, but, given the less and less repulsive character of the 3Z§ curve as the level of ab initio calculation is improved, it is quite possible that the true 3Z+ curve actually crosses the l I-ll curve in a higher, energetically inaccessible region. A similarly high-level CI calculation 69 of the Zn(4s4p 3P2).Kr(3~+) repulsive state also shows a crossing with the RKR experimental Zn(4s4p IPI)-Kr(IHI) potential curve, 17 high on its inner wall. However, because there is no question that the larger spin--orbit coupling is sufficient for ll-I1/3Z+ predissociation to occur in the Zn(4s4p) states (given the ZnXe results), it is virtually certain that the true Zn.Kr(3Z§ potential curve does not cross the Zn.Kr(ll-II) curve until higher energies, as the Zn.Kr(ll-Ii) state does not predissociate. I7 We therefore believe that the true Mg.Xe(3E§ repulsive curve does not cross the Mg-Xe(ll-ll) potential curve in the energy regions experimentally accessible. We now turn to the initially puzzling case of Hg(6s6p 1P1).Xe(lI-ll), where spin-orbit coupling is extremely high, but where at least a few of the Hg.Xe(ll-ll) vibrational states have been detected by laser-induced fluorescence! 31 Again, as with Mg.Xe(llI1), it may be that the repulsive Hg(6s6p 3P2).Xe(3'E]) potential curve does not cross the Hg.Xe(l I-I1)curve in an energetically accessible region. However, unlike Mg-Xe(1H1), the Hg-Xe(ll-I1) state is even more strongly bound than the Zn.Xe(ll-Ii) state, with a D e of about 3600 cm -1. Furthermore, as can be seen from Table 1, the other Hg-RG states are very similar to their Cd-RG analogues with regard to both D e and R e values. Also, owing to the greater spin--orbit splitting of the Hg(3pj) multiplets, the 6s6p 3P2 level is only about 10,000 cm -l away from the 6s6p 1P 1 level, whereas in cadmium the 5s5p 3P2/5s5 p 1P 1 energy gap is about 11,900 cm -1. Thus it seems quite likely that the 1H1 and 3E~ curves do cross in the HgXe system. The probable reason that the HgXe ll-I1/3Z1 coupling is so low is, ironically, that the spin-orbit coupling for the Hg(6s6p) states is too large! With a spin-orbit coupling constant of 4265 crn-l, the two diabatic molecular states will mix so strongly that they will avoid each other completely in the crossing region, forming two well-separated f~ = 1 adiabatic states (in the appropriate Hund's case (c)

Metal Atom-Rare Gas van der Waals Complexes

51

description). Thus the Hg-Xe "IHI" state will, indeed, have 11-11character on its outer limb, but essentially 3~ repulsive character on its inner limb. 85 The Hg.Xe ,,3v+,,,.,lrepulsive state will have 3 ~ character at large R, IFll character at small R. The two adiabatic f~ = 1 potential curves will always be well separated in energy, so the bound f~ = 1 state which is initially excited will not "hop" to the repulsive f~ = 1 state, but instead will eventually fluoresce back to the Hg-Xe (f~ = 0 +) ground state. It should be noted that the full-collision results are again consistent with these half-collision spectroscopic observations. The cross section for collisional quenching of Hg(6s6p 1PI)by Xe has been shown to be very low (< 1/~2).100

E Ground States of M'RG Complexes

Experimental Determination of Spectroscopic Constants and Dissociation

Energies Shown in Table 3 are the R e and D e values obtained experimentally for the (relatively) weakly bound M.RG ground electronic states. Although laser excitation of ground-state M.RG complexes that have been synthesized and cooled in supersonic jet expansions has been very successful in characterizing the potential curves of electronically excited states of M.RG complexes, it has given us much less direct information about the ground-state potential curves. This is because the very effect that simplifies and facilitates the analysis of spectra of jet-cooled M.RG molecules, namely the efficient cooling to the lowest (v" = 0) state of the complex (with J'" distributions characteristic of 2-15 K effective temperatures), hides virtually all detailed information about the ground-state potential curve. It appears to be generally true that the jet conditions that favor synthesis of ground-state M.RG complexes also favor essentially complete simultaneous vibrational cooling (perhaps because the M.RG vibrational spacings are so low and close to the energies of the collisions in the expansion, even at very low temperatures). Thus, "hot" bands are rarely seen in M.RG spectra, and even if they do appear, the only vibrational state populated is usually v" = 1. Most of the information on the ground states (see Table 1) is therefore indirect (D~' values from upper-state D~ values), incomplete (R~" values only, even from completely rotationally resolved spectra) or of low resolution (dispersed fluorescence measurements). (More detailed knowledge of the ground-state potential curves could be gained by techniques like stimulated emission pumping.) For example, because of the relatively weakly bound nature of even excited-state M-RG complexes, it is often quite easy to ascertain the asymptotic dissociation energy of an excited M*-RG state just by knowing the energies of the excited M* atomic states relative to the ground-state M atom. If it is possible to determine (or estimate) D~, therefore, and determine (or estimate by extrapolation) v0.0, one can estimate Dt~' by Equation (10):

52

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP #/

D O+

p

VM,M~ -- D O + VO,0

(10)

where v0,0 is the (0,0) band origin, and VMM. is the difference in energy between the excited atomic state M* and ground-state M. There are several problems with this procedure, however. First of all, in most cases, owing both to the lack of hot bands and to the fact that most upper states are more strongly bound than the ground state, Franck--Condon overlap restricts the examination of v' levels to a narrow window (the v" = 0 vibrational wavefunction centered at r~'), which is usually nowhere near vd orV'dissoc.. Thus two extrapolations must be made, even if band origins can be determined accurately from rotationally P p resolved spectra: to v 0 and to Vdissoc.. Barfing something unusual (like an avoided crossing near the bottom of the upper-state potential curve), the former extrapolation is expected to be more reliable than the latter. Many of the spectra show linear Birge-Sponer plots at low v' [two-term (toe, to~e) power series are sufficient to describe the vibrational eigenvalues], and it is reasonable to assume that the plot will remain linear to v' = 0. On the other hand, nonlinear B irge-Sponer behavior near dissociation is quite common, so any long extrapolation to the dissociation limit can be more hazardous. Even though such small nonlinearities may result in only a small percent error in D~, there will often be a much larger percent error in the (usually much smaller) value of D~'. As discussed previously, there can also be errors in D~ determinations if the upper state has a maximum at large R in its potential curve, since Birge-Sponer (or even higher power series) extrapolations will be to the wrong (higher) dissociation limit, and this will lead to overestimated Dd" values. This may be a problem in all spectra to (n + 1)s Rydberg upper states, for example (Section liD), unless the height of the potential maximum can be characterized directly. 3~ The most reliable data obtained by the use of Equation (10) are those for transitions to upper states which are more weakly bound than the ground state, so that v' levels are accessed (on the inner limb of the potential curve) very near the dissociation limit. In fact, when the sharp onset of a dissociation continuum is observed in such a case, application of Equation (10) is not even necessary, because subtraction of VMM.from the energy of this onset yields D~' directly and accurately. One must still assume that there is no long-range maximum in the upper state potential curve, of course, but this should be true for all valence pure-Z or mixed Y:-II states, which are weakly bound, we believe. In Table 3, ground states for which Dt~' was estimated by the observation of such a dissociation limit (or a very short extrapolation thereto), and thus for which D e' estimates are fairly accurate, are: Na.Ne, Zn-Xe, Ag.Ar, Cd.RG (RG = Ne, Ar, Xe), Hg.RG (RG = Ne, Ar, Kr, Xe), AI.Ar, and A1.Kr. Careful dispersed fluorescence measurements for the molecules NaAr, NaKr, and NaXe have also reduced the uncertainties in their D e' values considerably. The D e" for NaAr is also known to within one wave number, since Aepfelbach et al. 9 were able to observe weak hot bands, at high resolution, nearly to the ground-state dissociation limit.

Metal Atom-Rare Gas van der Waals Complexes

53

On the other hand, since B O' is what has been determined when there has been a rotational analysis, the R e' values are more reliable in most cases than the D e values. When it is necessary to perform computer simulations of incompletely resolved rotational (and isotopic) band structure to extract rotational constants, however, it is often possible to extract AB values with a much greater accuracy than absolute B v and B~' values. Thus Re"-R e is more reliably determined in most cases than is R~'. Furthermore, the Franck-Condon pattern of intensities of the (v',v" = 0) bands is very sensitive to Re'--R~ (but not to either of their absolute values), so FranckCondon simulations can provide a double check on the Re"--Re reliability. pp

Bonding Trends In these weakly bound ground states, attractive dispersion forces will dominate at long range (and probably fight up to where repulsion suddenly sets in). This will be true even for those states with outer-shell M(npr~) character, since the pro orbitals will be compact and not much larger than the M(ns 2) electrons. But for such Group 3(13) atoms, pn approach of the RG atom along the P• nodal axis will result in less repulsion than pff approach, since the Po electron density is directed along the axis of the incoming RG atom. Experimental and theoretical results show, indeed, that the 21-11/2states are the ground states for the B.RG, AI-RG, and In.RG complexes studied to date. (See Table 3.) Furthermore, strong lambda doubling of the 2II1/2 states (induced by spin-orbit coupling; see Section IIE) is consistent with the pff(2E§ states being a few hundred crn-1 higher in energy (and thus repulsive) at the R e" values of the 2II1/2 ground states. Given the same line of reasoning, the fact that the Si(3s23p 2 3Pj)-Ar ground state is apparently of 3s symmetry is expected. Shown in Figure 11 are two possible RG atom approaches to the ground Si(3s23p 2 3pj) atomic state, which has two unpaired electrons in Px'Py orbitals. Approach along the nodal axis of the p orbitals

$i

Tr

Figure 11. Pictorial representation of the p orbitals in the Si(3s23p2 3P/).Ar states.

54

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

Table 8. Comparison of <ms> Values z3 with the Re' Values of the M.RG Ground States (see Table 3) M.RG

<ms > (it)

Re'(M.RG)(A)

/(R e' (M-RG))

Mg.Ne Cd.Ne Hg.Ne

1.72 1.64 1.50

4.40 4.26 3.90

0.391 0.385 0.385 0.387 + 0.04

Mg.Ar Cd.Ar Zn.Ar Hg.Ar

1.72 1.64 1.51 1.50

4.49 4.31 4.18 3.99

0.383 0.381 0.361 0.376 0.375 + 0.14

is obviously most favorable for minimizing repulsion, yielding a 3•-rather than a 31-Iground state. As discussed previously, a probable long-range barrier in the upper state Rydberg potential curve means that the D e' value listed in Table 3 is probably somewhat overestimated, but the true De', Re' values (about 250 crn-l and 3.6/~?) would still be quite consistent with the smaller size and (pn) 2 nature of the Si atom ground state versus the (pn) 1 AI atom ground state. We now turn to the data in Table 3 on ground states of Group 1(11) or Group 2(12) metal atoms, which have outer-shell (ns) 1or (ns) 2 configurations. Their M.RG ground states must therefore be completely symmetric (2Z~n or l T_~ symmetry, respectively). In contrast to the strongly bound, excited H states in Table 1, the R e values (where data is available) for all Group 2(12) M.RG states increase (slightly) as one moves through the series RG = Ne, Ar, Kr, Xe. Although the attraction is now totally dispersive, correlated polarized motion of the two-electron M(ns 2) cores may be more difficult than for the H state M+(ns) cores, even as the RG polarizability is increased. Essentially the opposite is observed for the Na.RG ground states; in contrast to their excited 21-I states (see Section liB), R e" drops in the series Ne > Ar > Kr ~- Xe. Correlated, polarized motion of the single ns electron cloud may again be easier to accomplish. Finally, we point out one interesting trend in the R e values of Group 2(12) M.Ar and M.Ne ground-state values, where there exist the most reliable R e' data. Shown in Table 8 are the ab initio ns values of each state calculated with relativistic pseudo-potential techniques (important especially for Hg, where the 6s orbital is quite contracted owing to efficient penetration to the very high nuclear charge of the Hg nucleus), as compared to the M.Ar and M-Ne R e' values. As can be seen, R~' (M.RG) for a common RG atom correlates quite well with ns, given the subtle interactions between electron correlation and Pauli repulsion that must be in play for these weakly bound states.

Metal Atom-Rare Gas van der Waals Complexes

55

Iil. Mo(RG)n POLYATOMIC MOLECULES In contrast to the many detailed studies of several electronic states of M.RG diatomic molecules that have now been carried out, as discussed in Section II, very few experiments on M.(RG) n polyatomic clusters have yet been reported. Such studies could be of great interest, of course, since in principle they would provide fundamental information about the progressive solvation of a simple metal atom to reach finally the equivalent of liquid- or solid-state conditions. Several points can be made with regard to such progressive solvation processes: 1. When the interactions of an atomic metal-atom chromophore and inert solvent molecules like RG atoms are modeled, it is often convenient to assume that the atom-atom potentials are additive, i.e.; the M.(RG) n potentials are constructed from known M.RG and RG.RG interatomic potential functions, ignoring three-body or higher order interactions. This assumption has been widely used in model studies of rare gas clusters or mixed molecule/rare gas clusters. 1~176 Does this approximation hold for the ground and excited states of metal atom/rare gas clusters? 2. From the isolated to the fully solvated metal atom, how many rare gas atoms are needed in an M(RG) n cluster to reach the spectroscopic properties of the metal atom M isolated in a solid RG matrix? 3. What does "solvation" of a neutral atom in a cluster really mean? It might seem, for instance, that solvation has occurred when the atom has been surrounded by at least a full solvation shell of solvent species. Or perhaps full solvation can be considered to have been attained only when a particular measurable property has reached the same asymptotic value as in a liquid solution or solid matrix. Of course this injects ambiguity, because solvation may then be reached at different cluster sizes, depending on the radial extension of the particular property one chooses.

A. HgArnClusters Studies of HgAr n clusters are a logical first step in addressing the above points. There is good spectroscopic information on both the ground-state and several excited-state potential curves of the HgAr diatomic molecule (see Refs. 28-31, and Refs. therein). At the other extreme, Hg atoms embedded in solid argon matrices have also been carefully studied spectroscopically. 1~176 In the energy region of the Hg(6s6p 3p]) excited atomic state, as shown in Figure 7, there are two states of HgAr, an f~ = 0(+) state and an f~ = 1 state. As discussed previously (Section IIE), because of large spin--orbit-induced mixing, the f~ = 1 state actually has mixed t~-~ character. It is therefore relatively weakly bound (D e = 62 cm -1) and has a long bond length (R e = 4.70/~). The f~ = 0 (§ state [31-10. in Hund's case (a) notation] remains pure-~ in nature, and thus has a substantially

56

W.H. BRECKENRIDGE,CHRiSTOPHEJOUVET, and BENOIT SOEP

stronger bond (D e = 376 cm -1) and shorter bond length (R e = 3.36/~). It is useful, as we discuss the spectroscopy of the larger HgAr n clusters, to visualize the p-electron density of the Hg(6s6p 3PI) state (J = 1) as a torus of electron density. If the Ar atom approaches the torus symmetrically along its axis, then the ~2 = 0(+) (pure-rt) state results. However, if the Ar atom approaches in the plane of symmetry of the toms, the f~ = 1 (50% 7t, 50% c) state results. [We note that such a picture is only strictly true for the limiting case of very high spin-orbit coupling (Hund's case (c) behavior), but this should be a reasonable approximation for these Hg(6s6p3pj).Ar states, because the s p i n - o r b i t coupling p a r a m e t e r for Hg(6s6p 3pj) is more than ten times greater than the bond strengths.] The HgAr ground state, Hg(6s6s IS0).Ar(lY-+), f~ = 0(+), has a D e value of 142 cm -1 and an R e value of 3.99/~. It is therefore slightly more bound than the f~ = 1 excited state but much less bound than the pure-n f~ = 0(+) excited state. The ground-state Ar 2 molecule has a D e value of 97 cm -1, slightly less than that of HgAr. We begin our discussion of structures of ground-state HgAr n clusters, then, by assuming that all bonding interactions in the ground-state clusters can be described by additive pair potentials that are the same as those for the Hg-Ar and Ar-Ar molecules. For example, simple simulations show immediately that the most stable form of ground-state HgAr 2 has C2v symmetry, with the two Ar atoms "touching" to reach the lowest possible energy compared to Hg + Ar + Ar. Experimental observations of the Hg(Ar) n clusters 1~176 have involved mainly the determination of the changes in the absorption spectra of the complexes at frequencies near the Hg(6s6p 3P 1 ~ 6s6s 1So) asymptotic atomic transition as the number of atoms n of Ar is increased from n = 1 to higher values. As n is increased, the absorption to the red [associated with the transition to the pure-re f~ = 0(+) state in diatomic HgAr] dies out very quickly, and is essentially gone by n = 4. In contrast, the spectrum to the blue of the atomic line (associated with the transition to produce the mixed a - ~ state, f~ = 1) appears to become more intense and progressively shifts to the blue as n increases. However, for the largest n investigated, the HgAr n spectrum has not yet reached that of Hg atoms isolated in solid argon, where there is no absorption to the red but an absorption even further shifted to the blue of the atomic transition. ~~176

HgArz The HgAr 2 cluster has been studied by both laser-induced fluorescence 105 ' 106 and mass-resolved multiphoton ionization. 1~ Vibrationally well resolved transitions have been observed, both red- and blue-shifted from the Hg(aP1 ~ 1So) atomic transition (see Figure 12). In the C2v symmetry of HgAr 2, the transition to the f~ = 0(+) state of HgAr to the red becomes A 1 ~ X A l, but the transition to the blue, to the f~ = 1 state in HgAr, splits into two transitions, to HgAr 2 states of B~ and B 2 symmetry (similar to C2v HgH 2 or CdH 2 complexes, which correlate with atomic 3P 1 spin-orbit levels). 1~176

57

Metal Atom-Rare Gas van der Waals Complexes ll/,Ar z

i

-150

i

t

~

I

-I00

Ibm B2 r

100

. . . . . . . . . . . .

150

.,;taLc.

A l

l

I.------L

i

1

l

|

!

-50

IIgAr., '" !

! .......

200 c m -I

!

0 ~'!

B, ~ . . . . . . . . . . .

250

I

300

Figure 12. (a) Mass-resolved resonance-enhanced two-photon ionization spectrum of HgArn clusters recorded at mass 200 amu (Hg). I~ The spectral features are mainly assigned to HgAr2 dissociating in the ionic state. (b) ExcitatiOno~pectrum of HgAr2 recorded through laser-induced fluorescence by Okunishi et al. I (Note that we use the opposite convention with regard to BI, 82 symmetry labels as that in Ref. 107. In the convention used here, B2 transforms to A' as the symmetry is changed from C2v to Cs.~~176

The vibrational structure of the transition to the most strongly bound A 1 state has been observed and analyzed by Okinushi et al. 1~ All the bands can be assigned by use of a combination of the three expected modes (v~ symmetric stretch, v 2 bending, and v3 asymmetric stretch). The B 2 state has also been characterized spectroscopically by the same group 1~ and by van Zee et al. 1~ The vibrational structure has been assigned by use only of a combination of the bending and symmetric stretching modes. 1~ It has also been shown 1~ that this state undergoes predissociation to HgAr(0 § + Ar, presumably facilitated by the breakdown of C2v into C s symmetry, since the A~ and B2 states both become A' states in the C s point group.

58

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

The transition to the B l state, only weakly observed in the LIF spectra, ~~176 can be clearly characterized via the MPI spectra 1~ (see Figure 12). This is the first direct experimental evidence of a sufficient perturbation of the mercury atomic (f~ = 1) electron density by a noncylindrically symmetric species (C2v Ar 2) to induce B~/B 2 splitting. The HgAr 2 potential surfaces, in the ground and excited states, have been modeled theoretically by Roncero et al., 11~assuming the additivity of the individual interatomic potentials. Given this assumption, the experimental knowledge of the D = 1 and f~ = 0(+) states of HgAr allows a model calculation of the full potential energy surface. Recent quantum mechanical calculations of the HgAr 2 vibronic spectra, ill performed by the same group, fit the experimental data very well for transitions to the B2 and B 1 states, but some minor discrepancies have been found for those to the A~ state. It is possible that this is a deviation from the additivity approximation for the A 1 state in HgAr 2.

II! II [ il

cm

-1

Figure 13. Mass-resolved resonance-enhanced t w ~ h o t o n ionization spectrum of HgArn clusters recorded at mass 240 amu (HgAr). 1~ (Backing pressure around 2

atmospheres, hv2 = 44,550 cm -1 .) The strong peaks are due to excitation of the HgAr D. = 0(+) and D. = 1 states.

Inset:. Enlarged view of the spectral region lying above the HgAr dissociation limit, where transitions to HgAr2 can be seen.

Metal Atom-Rare Gas van der Waals Complexes

59

MPI Spectra of HgAr~_5 Shown in Figures 13 and 14 are MPI spectra 1~ at masses 240 (HgAr+), 280 (HgAr~), 320 (HgAr~), and 360 (HgAr~). As can be seen in Figure 13, most of the HgAr + signal can be assigned to the known HgAr diatomic electronic transitions, but there are also HgAr 2 transitions resulting from loss of an Ar atom (HgAr~ ---) HgAr + + Ar; see inset in Figure 13). Similarly, in Figure 14, the spectra at masses 280, 320, and 360 can be interpreted as superpositions of direct MPI of HgAr n, as '

'

'

1

'

'

'

1

'

'

9

1

'

'

'

1

'

'

'

"! -1

mass: 280 amu

l

i

i

800

i

i

I

600

I

|

HgAr2*

,

i

i

,

4-00

I

t

A1,

i

,

200

,

,-1

i

0

-200

-I c m

HgAr4+-)HgAr~ ++Ar

mass: 320 amu

: B 1 and 82

F

,

800

,

=

1

600

,

A1

,

,

,

:

400

!,

200

,

:

,

0

'

'-'-

-200

-1 c m

gAr5 + - )

800

600

H Ar4+§ .~

mass: 360 amu

400

200

0

:

-200

-I c m

Figure 14. Mass-resolved resonance-enhanced two-photon ionization spectrum of HgArn, the masses selected being 280 amu (HgAr2), 320 amu (HgAr3), 360 amu (HgAr4). 1~

60

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

well as MPI with loss of a single Ar atom. 1~ The interpretation of the spectra is supported by the determination of ground-state structures for these clusters from molecular mechanics (see below) and by calculations of the vertical transitions to the excited states using the model of Roncero et al. tl~ Calculations on larger clusters (up to HgArl2 ) have been performed in order to get some feeling for the evolution from the 1"1 complex to the matrix-isolated Hg atom. The excitation spectrum observed at the HgAr 3 mass (320 amu, Figure 14) exhibits a broad band peaking at about +300 cm -1 with a shoulder at about +80 crn-1. When the argon pressure is increased, a new band peaking at about +400-500 cm -l appears, causing the spectrum to extend further towards the blue. It should be noticed that there is no longer any red-shifted absorption. At a mass of 360 amu (HgAr4), the spectrum (Figure 14) shows one broad blue-shifted band (maximum absorption at about +500 cm-1). Rare gas matrices can be considered to be a limiting case of Hg(RG)n where n ---) oo. Spectroscopic studies of mercury in matrices show that, for argon and krypton, only one spectral feature, blue shifted with respect to the gas phase, is observed. 13A4 As the cluster size increases, the formation processes in the jet and the finite temperatures of the clusters may lead to the formation of several isomers. In order to understand the HgAr n spectra, it is very important to know what kind of isomer may be populated. This information can be estimated from calculations using molecular dynamics simulations.

Ground-State Geometriesand Binding Energiesof HgArn Clusters Molecular dynamics simulations have been performed to find the favored HgAr n equilibrium geometries in the ground state. 1~ The potential surfaces are built using the two-body, atom-atom potentials of HgAr and Ar2.11~ The potential surfaces have been explored by use of the usual molecular dynamics procedure. 1~ To one particular isomer, kinetic energy is added (about 30% of the binding energy in order to overcome the potential barriers between the different isomers without evaporating the Ar atoms). After a delay of 10 or 20 ps, allowing the energy to be shared into all degrees of freedom, a quench procedure is performed every one or two ps; periodically, along the trajectory, a quenching force is added in order to cool the cluster, which is then trapped in a local minimum on the surface. This method allows the exploration of a whole set of local minima. In fact, the dynamical quench process allows the cluster to be trapped only in minima that correspond to the deepest valleys. The statistical appearance frequency of an isomer over many quench procedures gives some idea of which isomer is preferentially populated in the jet. The binding energies of the HgAr n isomers, relative to the separated atoms, are given in Table 9 and the most stable isomers are shown in Figure 15. For HgAr 2, the ground-state structure is obviously T-shaped (the binding energy being 373 cm -1). For the HgAr 3 cluster, the most stable structure corresponds to a symmetrical

Metal Atom-Rare Gas van der Waals Complexes

61

Table 9. Comparison between Calculated and Experimental Spectral Shifts1~ cm -1

Cluster HgAr 2

Ground State Number of Number of Shifts Shifts Binding 1 Hg-Ar Ar-Ar (calculated) (experime.nml) Isomer Energy (cm- ) Bonds Bonds Symmetry (cm-l) (cm-l) 1

-373

2

1

Czv

HgAr 3

1

-709

3

3

C3v

HgAr 4

1

- 1051

4

5

C2v

-106 (A1) 162 (B2) 270 (B1) -105 (A l) 300 (E) -25 (A 1) 141 (B2) 542 (B l)

2

-1021

3

6

C3v

1

-1410

4

8

C4v

2

-1400

5

7

Cs

3

-1370

4

8

Cs

H gAr 6

1

- 1841

6

10

Csv

HgAr 7

1

-2195

7

12

Cs

2

-2168

6

13

Cs

HgArl2 Matrix: 12 neighbors

1

-4212

12

24

Oh

- 1 5 ( a l) 322 (E) 92 (A') 249 (A') 483 (A") -49 (A') 239 (A') 421 (A") 216 (A) 388 (E) 264 (A') 373 (a') 526 (A") 199 (A') 373 (A') 379 (A") 850 (Tlu)

1

-4158

12

Oh

903 (Tlu)

18 neighbors

2

-6958

18

Oh

811 (Tlu)

HgAr 5

-80 a

160 230 0 230

80 300

-127 (A 1) 289 (E)

= 500

1250 b

Notes: aSeealso Ref. 105. bRefs. 103, 104.

(C3v) geometry, the mercury being in symmetric contact with all three argon atoms (the binding energy is 709 cm-1). For HgAr 4, two different conformations with nearly the same binding energy are found. As shown in Table 1, the most stable geometry is the symmetrical (C2v) structure in which the four argon atoms are all in symmetric contact with the

62

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET,and BENOITSOEP

.~,

0 <:.)

IqgAr2 (C2v)

e~'.

HgAr3 (C3v)

I,~,1).~.

H.qAI5

(C4V)

-

,

) :)

"~ (Cs)

HgAr4. (C2v)

I( (Cs)

(C3v)

).,

-~'. ~:'~

),

(

Figure 15. HgArn (n = 2 to 5) ground-state structures calculated with atom-atom

potentials.1~ (Theblack sphere is the mercuryatom.) mercury atom, but on only one side of the Hg atom (with a binding energy of 1051 crn-1). A C3vgeometry, consisting of a triangle of argon atoms bound to the fourth argon atom on one side and to the mercury atom on the other side (binding energy of 1021 crn-1) is also found. From a series of different trajectories and quench procedures, it can be established that the probability of being trapped in the potential well corresponding to the C2vform is greater (90%) than the probability of being trapped in the C3v potential well. The C3v geometry corresponds to a "surface cluster" in that the Hg atom sits on a tetrahedral Ar4 cluster, whereas in the C2v geometry the presence of the mercury atom induces a deformation of the Ar 4 cluster. For HgAr 5, there are three reasonably stable isomers, all of which are also "one-sided" (or "oyster-on-the-half-shell") structures, in that the Hg atom is bare on one side, with all the Ar atoms in shell-like structures on the other side. This is because more is to be gained from the increased additional number of Ar-Ar contacts (which require small Ar-Ar distances) than from the slightly more attractive Hg-Ar contacts in more centrosymmetric "solvated" structures, which one might naively assume would be most stable. As the number of argon atoms increases, of course, the ground-state cluster potential surface becomes more and more complicated, with an increasing number of minima in the same energy range. For the HgAr n clusters with n > 4, we do not present all the isomers but only the most significant ones, grouped into different classes according to the number of Hg-Ar and Ar-Ar bonds. Hg-Ar and Ar-Ar linkages are considered to be bonded if the interaction energy represents 80% of the binding energy of the pair potential. For a cluster of a given size, the total

Metal Atom-Rare Gas van der Waals Complexes

63

number of van der Waals bonds is constant for all the most stable isomers, but the number of Hg-Ar bonds is an indicator of the mercury atom solvation, the first solvation shell being achieved for HgAq2, with 12 Hg-Ar bonds. In order to compare the jet and matrix results, the geometry and binding energy of the HgAq2 cluster has been calculated: the fully solvated Oh isomer has 12 Hg-Ar bonds, 24 Ar-Ar bonds, and is bound by 4213 cm-1.

Interpretation of the MPI Spectra of HgArn Clusters The observed MPI spectra are governed mostly by the geometry of the clusters in their ground state and by the Franck-Condon vibrational overlap factors in the excitation process, which do not favor excitations near the minima of the excitedstate potential surfaces. The spectral shifts can be estimated by calculating the vertical energy difference between excited- and ground-state potential energy surfaces at the local minimum equilibrium geometry of the ground state (8 approximation). For such a 8 approximation, the ground-state vibrational wavefunction is concentrated near the equilibrium geometry. The calculations can at least, then, give an estimate of the energy of the most intense band in the excitation spectrum. The procedure used for the calculation of the ground-state surfaces can be adapted for excited states with appropriate axis rotations applied to the nonspherical electron distributions, using the model developed by Roncero et al. 1l0 for HgAr 2. This model is based on the additivity of the potentials and the following assumptions: 1~ 9 The Ar-Ar potential is the same in the calculation of the ground and excited state. 9 All the Hg-Ar interactions are equivalent in the excited state. However, the nonspherical character of the Hg(3PI) state is taken into account by projection of the f~ = 0(+) and t2 = 1 Hg-Ar potentials obtained from experiment onto each Hg-Ar bond axis in the cluster. 9 These calculations are performed with the geometry of the ground state at a temperature of 0 K as a basis. No corrections have been made to take into account the zero point energies. The results are summarized in Table 9.

The MPi Spectra of HgAr3_s Experiments at different ionization wavelengths 1~ show that the spectra recorded for a given mass depend on the fragmentation processes occurring in the ion when an excess of energy is given to the system. For such conditions, a spectrum recorded at the HgAr n mass generally corresponds to the superposition of the absorption spectrum of the HgAr n cluster and of the HgArn+1 cluster, which dissociates to HgAr~+ + Ar. To disentangle such spectra it is necessary to start with spectra from smaller clusters, where the transitions have been assigned, then ascribe the extra features to HgArn§ l and its fragmentation. From the theoretical calculations and our knowledge of the HgAD absorption spectra, the HgAr 3 transition to the A l state [relative to the Hg(3p1 ~ 1So) atomic

64

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

transition] is found to be at about 0 crn-l, and the transition to the E excited state at +230 crn-l (see Figure 14). In the same way, a comparison of the spectra shown in Figure 14 with those in Figure 13 leads to the assignment of two bands to HgAr4: the first one at about +80 cm -l and the second, very broad band peaking at about +300 crn-1. These bands might be assigned to the A 1 and BI,2 states of HgAr 4 (C2v isomer) or to theA and E states (Cavisomer) (see Table 9). Although the calculations seem to show that the C2,.isomer is more probable, we cannot exclude the possibility that this spectrum consists of a superposition of spectra of both isomers. Finally, the very broad spectrum recorded at 360 amu could be a superposition of the HgAr 4 and HgAr 5 spectra. The bluest part of the spectrum around +500 cm -1 probably results from HgAr 5 (perhaps from several isomers; see Table 9). The general tendency as n increases is an overall blue shift of the transitions of HgAr n clusters. The simple atom-atom additive potentials model leads to qualitative agreement with the experiments. As the size of the clusters increases, the degree of solvation increases, and the blue shift of the excitation spectrum becomes larger. However, a major discrepancy between experiment and the model appears in the case of HgAr 3, where the A l state is blue shifted, although calculations predict the same red-shifted absorption as for HgAr 2. Since the spectral shift is calculated at 0 K, warmer clusters may have different spectral shifts. Indeed, a change in the Hg-Ar equilibrium distance of only a small amount can alter this shift markedly. Molecular dynamics calculations can give us some insight into this problem. Starting from the equilibrium geometry ofHgAr 2 or HgAr 3, we let clusters evolve on the ground-state potential surface with an excess energy that corresponds to a temperature of about 30 K. Periodically, we calculate the spectral shift of interest. This kind of simulation gives us an idea of which part of the excited-state surface is explored upon absorption of a photon by the ground-state neutral clusters in the jet. No significant difference in the shifts has been observed for HgAr 2, nor for HgAr 3, which appears to rule out the hypothesis that a very particular surface of HgAr 3 or a strong dependence of the spectra on the temperature is responsible.

Possible Failures of the Pairwise, Atom-Atom Potential Function Approximation The main approximation in the potential energy surface calculations is the additivity of the pair potentials. This assumption seems to be quite reasonable for the ground state. For ionic clusters, possible charge-induced dipoles on the polarizable rare gas atoms must obviously be taken into account. However, even in the neutral excited-state potential energy surfaces considered here, it is possible that the additivity assumptions are false. In the recent work of Zuniga et al., 111 it has been shown that quantum mechanical calculations that give the vibrational levels by using the additive potentials are in very good agreement with experiment for the B2 state. However, for the A l state a difference of about-20 crn-~ has been found, and assigned to the nature of the potential.

Metal Atom-Rare Gas van der Waals Complexes

65

Although there is no net charge on the mercury atom in the excited state, it has been proposed by Breckenridge (see above) that, for a (6s6p) H state, much of the binding energy between the metal and the rare gas is due to the interaction of the Hg ~ core with the argon. This leads to a polarization of the Ar atoms (induction of a dipole moment), especially in the A 1 states of the molecules correlating with Hg(6s6p 3P1). The effective 8+ charge for HgAr [f~ = 0(+)] has been estimated as 0.87 au (see Table 4). In HgAr 2 the repulsive interaction between the approximately parallel induced dipoles on each argon atom must therefore be taken into account: a crude estimate of this effect using the usual electrostatic interaction formula 74 shows a destabilization of the complex by about 30 cm -l for the A l state (RHg_Ar = 3.35/~, RAr_Ar= 4/~). Although this model is only a rough estimation of the non-additive part of the potentials, it allows us to understand the difference between experiment and calculation. ~~176 For the B 1and B2 states, since the Ar atoms are at a much larger internuclear distance from the Hg core, the effect will be much smaller. However, this simple estimate does not pretend to take into account all the non-additive effects (which are only accessible through more accurate theoretical calculations, such as quadrupole interactions and/or back-polarization effects of the mercury atom). Assuming that the polarization correction is of the order of 30 crn-1 for the A l state of HgAr 2, one can expect that for HgAr 3 this effect will be on the order of three times greater (three approximately parallel induced dipoles mutually interacting in the C3vsymmetry) and will move the calculated A-state shift from -105 crn-1 to about 0 crn-1, similar to what is observed experimentally (see Table 9). For larger clusters, this kind of effect should also be present, but cannot easily be evaluated.

Progression to Solvation: HgArn Clusters with High n From the calculated cluster geometries, one can see in Table 9 the evolution of the spectral shift from HgAr to HgArl2. For HgArl2, the first solvation shell is completed, and the blue shift reaches 850 cm -1. The matrix shift is calculated with the assumption that there is no distortion of the matrix in the ground state when an argon atom is replaced by a mercury atom. The first twelve nearest neighbors being taken into account leads to a 900-cm -1 shift. This calculation, as already discussed, only gives the fight trend for the experimental blue shifts. In the case of Hg in an Ar matrix, where the solvation is complete, only one transition with a strong blue shift of 1250 cm -1 is observed. 1~176 On the other hand, the spectroscopy of the smallest HgAr and HgAr 2 clusters is clearly characterized by a single red-shifted transition. The blue shift of the transitions as n increases may then be taken as an indication of Hg solvation. The largest characterized cluster in our case is HgAr 4. Nonetheless, even for such small aggregates, there remain no red-shifted bands but only an overall blue shift of the spectra. Although this blue shift is still far from what is observed in the matrix, it appears to mimic the onset of the solvation process. This is consistent with the calculated geometries, which show that even in the HgAr 4 cluster the Ar4 moiety is distorted by the metal.

66

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

B. Mercury Atoms in Rare Gas Matrices A mercury atom in a rare gas matrix can be considered to be the limiting case of a Hg-RG n cluster as n goes to infinity. The comparative study of the metal atom isolated in matrices and in small R a clusters is aimed at determining 1. The effects of the symmetry, from the C** symmetry of the 1:1 complex to the O h symmetry of the substitution site in the fcc lattice of the rare gas crystal, for example. 2. The additivity or non-additivity of the Hg-RG pair potentials. 3. The relative importance of the short-range, nearest-neighbor, versus the long-range, bulk polarization interactions. Absorption and emission spectra of mercury atoms isolated in RG matrices at low temperatures have been recorded recently by Cr6pin and Tramer 1~ in the vicinity of the Hg(6s6p 3P 1 ~ 6s6s ISo) atomic transition. These metal atom absorption spectra, shown in Figure 16, are broad structureless blue-shifted bands except for the xenon matrix, which displays a triplet feature characteristic of the excitation of metal atoms in matrices into np I and nslnp 1 excited states 92'11~The bands for Ar and Kr, which are homogeneously broadened, have been assigned 1~ to phonon bands with a missing zero phonon line. The emission spectra for Ar and Kr, displayed in Figure 16, are essentially mirror images of the absorptions. These observations, together with the absence of significant inhomogeneous broadening, are explained by the facile adaptation of the mercury atom to the substitution sites, especially in Kr matrices. The band shifts in absorption for the (3P 1 <----IS0) bands in the rare gas matrices result from (1) the long-range dielectric effect of the medium (which accounts only for a small red shift of 50 cm-l), and (2) the immediate neighbors in the Hg-RG12 cage, which is the dominant effect. Calculations based on a simple model ll~ of additive pairwise potentials, Vx and Vn, reproduce qualitatively the spectroscopic observations of the Hg atom in all the rare gas matrices. A slight blue shift is predicted in Ar and Kr. The argon and krypton atoms in the lattice maintain the same symmetrical position in the excited states as in the ground states, but encounter an increased repulsion owing to the more diffuse nature of the mercury 6p orbital. This blue shift agrees with cluster work discussed previously in this section, where the Hg-Ar 3 spectrum is dominated by a blue-shifted broad band. On the other hand, Hg in Xe matrices (see Figure 16) is affected by Jahn-Teller distortion in the excited state (where the favorable p-orbital alignment becomes unsymmetrical), and the Hg atom can approach as close as 3.45/~ to the nearest Xe atom, only 0.2 ~ more than the equilibrium distance in the 1:1 Hg-Xe complex. This "quasi-dimer" conformation results in the removal of the degeneracy of the orbital alignment within the cage. Also, the much smaller Hg*-Xe distance yields a more red-shifted emission onto the ground-state repulsive surface than in the argon

Hg/Ar

Hg/Kr

40000

38000

36000

34000

CiE"1

Figure 16. Absorption and emission (red-shifted) spectra of Hg atoms isolated in pure argon, krypton, and xenon matrices. 1~ 67

68

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

and krypton matrices. Finally, the unsymmetrical position of the excited Hg state in Xe matrices results in less electron-phonon coupling, and thus sharper bands. In closing this Section, we point out an important difference between clusters and matrices" in the latter, the metal atom electronic state has to accommodate itself to the matrix, whereas the contrary may be true for the cluster.

C. BaArnClusters The transition to the condensed phase has also been explored by Visticot and co-workers in a recent series of clever experiments on clusters formed by the "pick-up" entrainment of barium atoms into argon clusters. 112'113 These experi-

Wavelength (nm) 570

560

550

_

540

530

i

t~

-

Ba(1S-:P)

[iExperiment t

-

'

-

- ~S

7e60

~

~8000 k

~84o0

~8800

( c m -1)

Figure 17. Molecular dynamics simulations of BaArn absorption spectra. 112'113 The "surface" simulation is for a Ba atom at the surface of a large Arn cluster, and the "volume" simulation is for a Ba atom at the center of the same cluster.

69

Metal Atom-Rare Gas van der Waals Complexes

ments allow spectroscopic characterization of larger Ba-Ar n clusters. In addition, these workers have been able to conduct micromatrix isolation experiments, whereby a scavenger is also added to the clusters. This can be a quencher of fluorescence (xenon, methane) or a reactive species (N20). A new procedure has thus been created that does not have the drawbacks of the secondary effects in matrices but has the convenience of clusters. The systems studied reveal the surface location of the barium atom. The fluorescence excitation spectrum shown in Figure 17 is composed of two main bands, one shifted by 400 cm -1 to the blue of the Ba(6s6p 1P 1 ~ 6s6s 1So) transition and a second to the red. The resulting fluorescence has been dispersed and shown to be composed of a single band shifted by 200 cm -1 from the atomic barium line. The

1.85xi04 1.84 1.83 T

B~-Ar

1.82

(BE)

o

B

1.81

Ba(1P1)

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200

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o -I00 -200

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Figure 18. Atom-atom potentials used in molecular dynamics simulations of the absorption spectra of BaArn clusters.14'110'112-114

70

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

existence of blue- and red-shifted absorption bands has been interpreted as indicating a surface location for the metal atom on the cluster, for which some directionality of the p orbital can be preserved on excitation, in contrast to excitation of Hg(6s6s 3P1) in larger Ar n clusters (as discussed previously). The confirmation of this hypothesis is given by molecular dynamics simulations using pairwise potentials, known or estimated, as displayed in Figure 18. (Note that the Ba-Ar ground-state interaction is assumed to be slightly weaker than the Ar-Ar interaction, whereas the reverse is known to be true in the HgAr case.) To simulate the excitation spectrum, the pairwise additivity has been extended to the excited nonspherical 6s6p 1P 1 state of barium. At each step of the ground-state interatomic movement, three excitation frequencies are calculated (by solving a 3 x 3 hamiltonian) and are binned in a table. After a few nanoseconds of evolution, this table yields the calculated spectrum. In Figure 17 the experimental results are compared with two calculated simulations where the barium atom is (1) at the surface of a large argon cluster, and (2) at the center of the same cluster. "Volume" clusters generate a triplet, blue-shifted spectrum, whereas "surface" clusters produce (without adjustment of the potentials) a spectrum very close to the experimental one. The observation of surface clusters can be intuitively expected given the pick-up, entrainment experimental method used, but the attractive forces in the ~P~ excited state could have sucked the metal atom into the cluster. The results show that the metal should occupy cuplike sites at the surface and hence be quite mobile, as is clear from fluorescence-quenching experiments. ~~2,113

IV. DIRECT, TIME-RESOLVED MEASUREMENTS OF

METAL-RARE GAS DYNAMICAL PROCESSES Time-resolved experiments are providing new insights into the spectroscopy and dynamics 115-12~of van der Waals clusters. The inclusion of the word spectroscopy may at first seem surprising to some readers. However, spectroscopic information can be obtained by the direct observation of molecular movements, both on bound and dissociative potential surfaces. The essence of the experimental method, principally developed by Zewail, is the localized excitation by ultrashort (pump) laser pulses, thereby defining the distances of the atoms at the time t = 0. The molecular system can thus be excited in a non-equilibrium geometry, and the subsequent nuclear movement is analyzed by another short light pulse (the probe). The durations of these pulses (pump and probe) must be shorter than the characteristic movements of the atoms. The typical movements to be probed are the dissociations (dynamics) or the periodic vibrations (structure) of the excited molecules. The characteristic times lie typically below 100 femtoseconds (10 -13 s) for light atoms chemically bound in molecules and below picoseconds (10-12 s) for weakly bound van der Waals molecules. Analysis of such movements can be made in a survey manner by the classical mechanics of

71

Metal Atom-Rare Gas van tier Waals Complexes

probe

~

....

aD1

probel on

B

res.I

-pump

' i

~

/So

....

~__lJ Figure 19. Schematical potential energy diagram of the Hg-Ar pair.121 The pump pulse excites the complex from the ground X state to the intermediate B(D = 1) state and the probe pulse to the repulsive D(s state. Depending upon the pump frequency, the excited Hg-Ar pair is prepared either in a superposition of bound states and starts to oscillate or is promoted on the repulsive wall of the B state and dissociates directly. It is seen in the Figure that the repulsivity of the D potential curve allows for the selection of a small range of internuclear distances with the probe laser frequency.

point masses, but the rapid experimental development of these methods has spurred the use of time-dependent wave packet techniques. The latter methods provide an ideal comparison of quantum theory and experiment in the same directly perceptible way as in classical dynamics. Of course, short-pulse excitation will be of great interest in determining the time decay of selected predissociative levels in states such as CdXe(ll-I) or ZnXe(lrl), discussed previously in this chapter. The time-dependent spectra have a direct frequency correspondence that can be characterized by calculations of the propagation of the excited quantum wave packet. As a simple example, consider the coherent excitation of two levels of a harmonic oscillator with energies t~,, and t~,,+l. The difference in the inverse of any two oscillation periods within the potential curve of the oscillator corresponds to the frequency separation of these levels.

72

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP

_

V~5

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d

'.U~ ',j '

_

~'~

_

,m~.,

ga,_ . . . .

9 ~

~r

--

"; " .

g

0 4

(continued)

Figure 20. (a) Double-resonance (bound-bound, bound-free) spectra ofthe HgAr B(D = 1) state.The first laser is tuned to excite various v' levels of the B(D = 1) state (as labeled), and a second laser is scanned through the frequency region indicated (see Figure 19). Atomic emission from the Hg(6s6d 3D 1) states is detected on a time-scale of several nanoseconds. (b) Simulation of the bands in (a) by use of the calculated vibrational eigenstates of the well-characterized HgAr[B(D = 1), v') levels and the single upper state potential curve that was found empirically to best reproduce the experimental spectra. (c) The empirical, single repulsive potential curve of the upper state that best reproduces the experimental spectra. The maximum in the potential near R = 4 ~ was necessary for a satisfactory simulation of the experimental spectra. The present interest in such experiments does not mean that time-domain experiments will supersede those performed in the frequency domain. They are complementary methods, however, since slow movements will appear more clearly in the time domain and the converse in the frequency domain. The study of weakly bound complexes is therefore especially attractive close to the

73

Metal Atom-Rare Gas van der Waals Complexes

~-

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Figure 20. (Continued)

dissociation limit where, as we shall see, the separation between vibrational levels can become exceedingly small, even smaller than their rotational energy variations. When the photoinduced process occurs on the flat potential energy surfaces of van der Waals systems, whose characteristic frequencies may lie as low as the 10-cm -1 frequency domain, the time period is 3.3 x 10-12 S, i.e., a few picoseconds. The resulting oscillations (vibrational recurrences) have proved to be a sensitive tool to accurately determine the 3B potential in I2ll9 over a wide region of internuclear separations. They should also help to unravel the congested spectra of weakly bound van der Waals molecules. The large excursion along the van der Waals coordinate will show up as recurrences if the upper and lower potentials in the probe absorption spectrum are noticeably different along this coordinate. It was shown first that short-pulse picosecond laser excitation of Hg complexes results in the spatial localization of the atoms, and that the subsequent movements

74

W.H. BRECKENRIDGE,CHRISTOPHEJOUVET, and BENOIT SOEP 800

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Figure 20. (Continued)

can be probed. 121 The bound motion in the same complexes 121 was then described, and finally evidence of trapped, quasi-bound motion above the dissociation limit of the Hg-N 2 complex was shown. 122 The dissociation of the Hg-Ar (B,~2 = 1), Hg-Ne (B,fl = 1), Hg-N 2 (B) excited states has been observed and analyzed, as well as the vibrational recurrences associated with nuclear motion in the bound portions of the potentials of these states. ~21'122 The curves relevant to this experiment are sketched in Figure 19. TM The pump laser excites the f~ = 1 (mixed (s-n) state of Hg-Ar. Vertical excitation accesses both bound vibrational states and the dissociation continuum leading to excited Hg(3p1) + Ar. In the Figure, one can see that the excited state (f~ = 1) potential is displaced by about 0.7/~ to longer internuclear distances than the ground state [f~ = 0(+)]. Therefore, the short-pulse excitation will prepare a narrow wave packet, localizing the atoms on the inner wall of the B(f~ = 1) potential curve. The dynamics of the subsequent nuclear motion is probed by a second laser pulse, which was chosen to have a frequency near to that of the (6s6d 3Dj ~-- 6s6p 3P1) mercury atom transitions. When the motion of the atoms is localized in a narrow wave packet, we see from the sketch in Figure 19 that the absorption occurs when the probe laser is resonant with the potential curve separation at the distance R, in the simplest stationary-phase approximation. Hence the probe will have greatest

Metal Atom-Rare Gas van der Waals Complexes

75

spectral sensitivity to the distance R(Hg-Ar) when the two potential curves are most different, as in the case of a lower attractive and an upper repulsive curve. This should be the case for the 63D ~ 63p1 transitions with 6s6d~ character. The full characterization of the many potential curves of the Hg(6s6d 3Dj).Ar states has not yet been achieved, but bound-free nanosecond absorption measurements have resulted in spectra that can be rationalized by simulations with a single empirical potential curve (3~-~) correlating with Hg(6s6d 3D.~). The spectra, their simulations, and the resulting potential appear in Figure 20.12f A. Direct Dissociation in the B(fl = 1) State of HgAr and HgNe When excited above 39,540 cm -1 (~ < 2529/~), the HgAr(f~ = 1) complex encounters repulsive forces and dissociates into an excited mercury atom (3P1) and argon. 121 The free mercury atom state, observed after a certain delay, can be monitored with a probe laser resonant with the 63D1 ~ 63P1 transition at 3131 A. This is shown in Figure 21, where the excited mercury appears with approximately a 3-ps delay with respect to the reference curve (uncomplexed atom). In the region of the continuum that is accessed, this delay is not found to vary considerably (<1 ps) with up to 50 crn-1 of excess energy in the excitation, since the Hg-Ar molecule with even zero excess energy will already be driven by the bound potential, 50 crn-1 in depth. Hence, at low excess energies, the dissociation time is found to be close to half of the round-trip time within the last levels in the potential well, determined as follows. When the probe laser is set at a fixed frequency away from the atomic resonance transition, a transient signal is observed with a delay that decreases with increasing frequency of the probe, as seen in Figure 21. [Undispersed, delayed fluorescence is monitored in the spectral region of the Hg(6s6d 3Dj ~-- 6s6p 3P2) transitions.] This can be understood in terms of the vertical excitation of the dissociating complex, wherein the probe laser frequency matches the potential energy difference, within a narrow range of Hg-Ar distances. Looking at Figure 19, one can see that at shorter times the absorption of the probe corresponds to the highest potential difference and will be in the blue part of the spectrum, and the converse is true at longer times. The time profiles of the probe laser absorption have been simulated, using classical mechanics, as described in Reference 123: the separating atoms are taken as classical particles starting a trajectory at the turning point of the potential, and the absorption by the probe equals the potential difference, VD - V B, within a 20-cm -1 width. The calculated time signals are convoluted for the finite pulse widths (1.5 ps FWMH) of the lasers. The simulations account satisfactorily for the observed waveforms. Although the formation of the free mercury atom is only described approximately (for experimental reasons), the calculated transients are well reproduced in peak position and width. This is most important, since this simple model gives a precise picture of the time evolution of the dissociating

76

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP ,

,

,

.~

9

- r - ~ - ~

r --

-T ....

v ....

T -

-v

....

-r-.--] /

HG re/L/ '//"'// .....'---

1

t ~-..f~ ......

J 3131

..........................

-5

0 Delay

5

(ps)

-5

0 Delay

//./

- ~/,,,~

5

(ps)

Figure 21. Pump-probe observation of the Hg-Ar transients after excitation of the continuum of the B state.121 The left part displays the variations of the laser-induced fluorescence intensity as a function of the delay between pump and probe pulses for various excitation conditions. The upper curve corresponds to the pump and the probe 9 ~ in resonance with the Hg atomic transitions, 1 So- 3 P1 (2537 A) and 3 P1- 3 D1 (3133 A), providing the time resolution of the present experiment (reference curve). The five other curves correspond to the pump tuned to 2527 A in the continuous, dissociative part of the absorption to the B state. From top to bottom the probe wavelength is decreased starting from the atomic transition at 3131 A, to 3120, 3110, 3100, and 3090 A. The right part displays the results of the classical calculations for the corresponding wavelengths.

complex. There is a direct correspondence between the position of the classical particles and the probe laser frequency, and this allows us to use this spatial localization even in soft van der Waals potentials to characterize the bound motion in the well.

B. Vibrational Recurrences When the complex is excited below the dissociation limit, a bound-free probe laser transient signal from the complex can still be observed 121 [again, by observa-

Metal Atom-Rare Gas van der Waals Complexes

77

,~,,l,,,r-l,i-,,l',,,',~l,,,',l,,',,i,,J'i

3 4 5 6 7

Freq. (cm -t)

0

10 20

30 40 50 Lime (ps)

60 70

Figure 22. Pump-probe observation of the Hg-Ar recurrences121 after the coherent excitation ofthe bound states in the B state potential. The left part displays the observed recurrences (top) for a pump wavelength of 2531 ~ and a probe at 3104 ~,, and the results (bottom) of the quantum simulation. The right hand side insert presents the Fourier transform of the experimental spectrum.

tion of d e l a y e d f l u o r e s c e n c e in the spectral region of the Hg(6s6d 3Dj ~ 6s6p 3P2) transitions]. Here, as in the preceding experiment, the atoms start to separate from the inner limb of the potential, but are reflected back at the outer limb, resulting in oscillatory nuclear motion (temporal recurrence). The pump laser coherently excites several levels in the B state at wavelengths greater than the onset of the continuum at 2529/~. The probe is then set off-resonance at 3104/~, where the inner turning point of the B potential is mainly probed. A beat pattern is observed, as is shown in Figure 22, for 2531-/~ excitation. In this spectrum, the main beat period is 6.4 ps, but other periods are conspicuous in the time-spectrum. These periods correspond to wave-packet motion within the B potential well, and indeed a Fourier transform of the spectrum shows three main frequencies at 4.02, 5.21, and 6.52 cm -1, centered about the observed 28 frequency for the v = 4, v = 5 level separation, as shown on the left hand side of Figure 22. The signal can be simulated by the motion of the excited wave-packet I W> = IpX> within the B well. The packet I W> has been projected from the ground state, IX>, and is not a stationary solution of the molecular hamiltonian. Therefore the full simulation describes the subsequent evolution of this packet on

78

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

the B potential and its excitation by the probe. The major assumption is that of a nonrotating complex, but in accordance with Gruebele and Zewai1119 this would cause a shift of the frequencies by only Av = -O~ekT/B ~- 0.2 crn-l for Hg-Ar (B) at T = 5 K, a rather small value. The results of the calculation reproduce the experimental spectrum rather well, as shown in Figure 22. All the individual maxima contained in the calculated spectrum also appear in the experimental one, but the experimental spectrum is slightly broader. This feature can be ascribed to the non-Fourier transform pulse shape of the lasers. The beat period is, as expected, very sensitive to the level positions, and it was in fact necessary to modify slightly the published spectroscopic constants to fit the beat pattern that results from the coherent excitation of four levels with three frequency separations given by the Fourier spectrum. The new values for the B potential, toe = 11.2 and toe Xe = 0 . 6 c m -1, lie within the error limits of the spectroscopy values? 8 The calculations also show that, in agreement with the experiment, the beat pattern and period are not very sensitive to the pump average frequency but are very sensitive to the probe frequency. This is due to the fairly wide extension of the wave packet within the B potential owing to the modest resolution of the laser: the absorption probability for the probe laser radiation varies considerably with the excited B-state level. Nonetheless, the beats happen to be best observed for the actual laser temporal resolution! Pulses that are too long do not excite the levels coherently, and pulses that are too short produce complex patterns owing to the large anharmonicity of the levels with respect to their vibrational frequencies. Although the experimental curves are presently quite noisy, an important fact can be stressed that is characteristic of the temporal method: the values given by the Fourier transformation do not result (as in frequency spectra) from a single line measurement but the average of n beat periods. Hence the side frequencies show up in the Fourier transform even though they are barely perceptible in the time evolution spectra. Similar experiments have been performed on Hg-Ne complexes 122 where the B(f~ = 1) potential is so shallow (15 cm -1) that all the levels can be coherently excited within the coherence width of the laser. The results reproduce the known frequencies differences, 28 but also identify a new 0.65-cm -1 frequency resulting from two levels very near the dissociation limit.

C. Direct Observation of Resonances in the ~ = 1 Continuum of HgN2 The dissociation dynamics in the B(f~ = 1) state repulsive continua of HgAr and HgNe are, as we could predict and have observed, quite simple and are determined by the potential curves of the electronic states of the diatomic molecule studied. In contrast to the situation with vibrational recurrences, as discussed previously, the time evolution does not add great precision in the determination of the potential.

Metal Atom-Rare Gas van der Waals Complexes -i-,',,|

. . . .

i , , i , - i

. . . .

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w i , ~

79

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.

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25

Figure 23. Pump-probe observation of the Hg-N2 complex. The pump laser is tuned to a "resonance" in the B(D. = 1) continuum transitions above the B(E2= 1) dissociation limit. Top: Time evolution of probe signal when free Hg(6s6p 3p]) is being monitored. Bottom" Time evolution of probe signal when the probe laser is monitoring the excitation and decay of the long-lived B(D. = 1) resonance state. The simulations to the right were both constructed assuming a lifetime of 5 ps for the resonance state.

The case of the triatomic Hg-N 2 molecule is different, however, in that two movements, the Hg-N 2 stretch and the Hg-N 2 bend, can contribute to dissociation. The fluorescence excitation spectrum of this molecule 124 to the B(f~ = 1) state reveals a complex spectrum merging into a continuum where diffuse (but quasiregular) bands appear that become increasingly broad at higher energies. It has been shown that these bands lie above the dissociation limit of the Hg.N 2 excited electronic state, and that their excitation leads to Hg(3pl) + N 2. Krim et al. 122 have recently excited these transitions with a picosecond laser and have observed an excitation-dependent lifetime that is inconsistent with a direct, pseudo-diatomic, repulsive dissociation to form Hg(3pl) and N 2. Instead, the trajectories are longer and involve the formation of a transient that decays with the same time constant as that with which free Hg(3p1) appears, as shown in Figure 23. These diffuse bands are ascribed to rotational resonances, whereby the nitrogen molecule is rotationally

80

W.H. BRECKENRIDGE, CHRISTOPHE JOUVET, and BENOIT SOEP

excited above the dissociation limit and the anisotropy of the "hindered-rotor" potential couples the "rotation" to the dissociation coordinate. Here, in a different manner, time-resolved experiments show that diffuse structures in spectra can be used to identify and characterize long-lived transient species.

D. Future Experiments The present time-resolved approach should apply to reactive systems and other polyatomic van der Waals systems, where the interplay between van der Waals modes is often difficult to assign.

ACKNOWLEDGMENTS We gratefully acknowledge support of our ongoing research programs by the National Science Foundation (WHB), the Petroleum Research Fund (WHB), and the Centre Nationale du Recherche Scientifique" (CJ and BS). We are particularly grateful for a U.S.-France Binational Travel Grant, jointly funded by NSF and CNRS, which has allowed us to continue our collaborative research efforts and our fruitful, synergistic exchange of ideas. We acknowledge stimulating and useful conversations with M. Morse, Jack Simons, D. Funk, S. McCaffrey, P. Dagdigian, M. Alexander, A. Beswick, C. Dedonder-Lardeux, D. Solgadi, N. Halberstadt, A. Trainer, J.M. Mestdagh, J.-P. Visticot, L. Krim, Q. Peixia, S. Martrenchard-Bara, and C. Cr6pin. We also thank the many scientists in this area who responded to our requests for reprints and preprints of their work.

REFERENCES A N D NOTES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Lee, C. J.; Havey, M. D.; Meyer, R. P. Phys. Rev.A 1991, 43, 77. Lee, C. J.; Havey, M. D. Phys. Rev. A 1991, 43, 6066. Havey, M. D.; Frolking, S. E.; Wright, J. J. Phys. Rev. Lett. 1980, 45, 1783. Lapatovich, W. E; Ahmad--Bitar, R.; Moskowitz, E E.; Renhorn, I.; Gottscho, R. A.; Pritchard, D. E. J. Chem. Phys. 1980, 73, 5419. Gottscho, R. A.; Ahrnad--Bitar, R.; Lapatovich, W. E; Renhom, I.; Pritchard, D. E. J. Chem. Phys. 1981, 75, 2546. Tellinghuisen, J.; Ragone, A.; Kim, M. S.; Auerbach, D. J.; Smalley, R. E.; Wharton, L.; Levy, D. H.J. Chem. Phys. 1979, 71, 1283. Briihl, R.; Kapetanakis, J.; Zimmerman, D. J. Chem. Phys. 1991, 94, 5865. Baumann, E; Zimmerman, D.; Brtihl, R. J. Mol. Spectrosc. 1992, 155, 277. Aepfelbach, G.; Nunneman, A.; Zimmerman, D. Chem. Phys. Lett. 1983, 96, 311. Bennett, R. R.; McCaffrey, J. G.; Breckenridge, W. H. J. Chem. Phys. 1990, 92, 2740. Wallace, I.; Breckenridge, W. H. J. Chem. Phys. 1993, 98, 2768. Bennett, R. R.; McCaffrey, J. G.; Wallace, I.; Funk, D. J.; Kowalski, A.; Breckenridge, W. H. J. Chem. Phys. 1989, 90, 2140. McCaffrey, J. G.; Funk, D. J.; Breckenridge, W. H. J. Chem. Phys. 1993, 99, 9472. Kowalski, A.; Funk, D. J.; Breckenridge, W. H. Chem. Phys. Lett. 1986, 132, 263. Bennett, R. R.; Breckenridge, W. H.J. Chem. Phys. 1990, 92, 1588. Wallace, I.; Bennett, R. R.; Breckenridge, W. H. Chem. Phys. Len. 1988, 153, 127. Wallace, I.; Ryter, J.; Breckenridge, W. H. J. Chem. Phys. 1992, 96, 136. Wallace, I.; Kaup, J. G.; Breckenridge, W. H. J. Phys. Chem. 1991, 95, 8060.

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0. Hackett, E A.; Balfour, W. J.; James, A. M.; Shetty, B. J.; Simard, B. J. Chem. Phys. 1993, 99, 4300. 61. Pilgrim, J. S.; Yeh, C. S.' Duncan, M. A. Chem. Phys. Lett. 1993, 210, 322. 62. Bililign, S.; Gutowski, M.; Simons, J.; Breckenddge, W. H., to be published. 63. Chalasinski, G.; Simons, J. Chem. Phys. Lett. 1988, 148, 289. 64. Pouilly, B.; Lengsfield, B. H.; Yarkony, D. J. Chem. Phys. 1984, 80, 5089. 65. Pascale, T. Technical Report, Service de Physique des Atoms et des Surfaces (C. E. Saclay), as quoted in: deVivie-Riedle, R.; Driessen, J. E J.; Leone, S. R. J. Chem. Phys. 1993, 98, 2038. 6, Buckingham, A. D.Adv. Chem. Phys. 1967, 12, 107. 67. Tang, K. T.; Toennies, J. E J. Chem. Phys. 1980, 80, 3726. 68. Bililign, S.; Gutowski, M.; Simons, J.; Breckenridge, W. H.J. Chem. Phys. 1994, 100, 8212. 69. Bililign, S.; Gutowski, M.; Simons, J.; Breckenridge, W. H. J. Chem. Phys. 1993, 99, 3815. 70. Ahlrichs, R." B6hm, H. J.; Brode, S.; Tang, K. T." Toennies, J. E J. Chem. Phys. 1988, 88, 6290. 71. Saxon, R. E; Olson, R. E.; Liu, B. J. Chem. Phys. 1977, 67, 2692. 72. Krauss, M.; Maldonado, E" Wahl, A. C. J. Chem. Phys. 1971, 54, 4944. 73. Desclaux, J. E Atomic Data and Nuclear Tables 1973, 12, 311. 74. Hirschfelder, J. O.; Curtiss, C. E; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964. 75. Shannon, R. D. Acta Chrystallogr. 1976,A32, 751. 76. Handbook of Chemistry and Physics, 71st ed.; Lide, D. D., Ed; CRC: Boca Raton, 1990. 77. This was first suggested to us by J.-E Daudey (private communication). 78. The possibility of an RG atom penetrating a Rydberg orbital was first suggested by King (King, D. S. J. Chem. Phys. 1985 82 3629) to explain his observation that the major product of 2 + . . ' ' NO(A E ).Ar predlssocmtion was ground-state NO, presumably from a potential curve crossing of the ground NO.Ar state with the inner wall of the deeply bound NO.Ar Rydberg state, which has NO+.Ar character. This observation appears to have been essentially ignored by other workers in the area. See Heaven, M. C. Ann. Rev. Phys. Chem. 1992, 43, 283. 79. Anchell, J.; Taylor, H.; Nichols, J.; Simons, J., private communication. The basis set was chosen to reproduce the Mg(3s4s 3S1) energy accurately. 80. Okunishi, M.; Yamanouchi, K.; Onda, K.; Tsuchiya, S. J. Chem. Phys. 1993, 98, 2675. 81. Gardner, J. M.; Lester, M. I. Chem. Phys. Lett. 1987, 137, 301. 82. Fawzy, W. M.; LeRoy, R. J.; Simard, B.; Niki, H.; Hackett, E A. J. Chem. Phys. 1993, 98, 140. 83. Dagdigian, E; Alexander, M., private communication. 84. Boatz, J. A.; Bak" K. L.; Simons, J. Theor. Chim. Acta 1992, 83, 209. 85. Lefebvre-Brion, H.; Field, R. W. Perturbations in the Spectra of Diatomic Molecules; Academic: Orlando, 1986. 86. Ref. 85, p 207. 87. Morse, M., private communication. 88. Wallace, I. Ph.D. Thesis, University of Utah, 1991. 89. Simons, J., private communication. 90. Smalley, R. E.; Auerbach, D. A.; Fitch, E S. H.; Levy, D. H.; Wharton, L. J. Chem. Phys. 1977, 66, 3778. 91. Cooper, D. L. J. Chem. Phys. 1981, 75, 4157. 92. Rose, J. L.; Smith, D.; Williamson, B. E.; Schatz, E N.; O'Brien, C. M. J. Phys. Chem. 1986, 90, 2608. Mowery, R. L.; Miller, J.; Krausz, E. R.; Schatz, P. N.; Jacobs, S. M.; Andrews, L. J. Chem. Phys. 1979, 70, 3920. Bailing, L. C.; Havey, M. D.; Dawson, J. E J. Chem. Phys. 1978, 69, 1670. 93. Samet, C.; Rose, J. L.; Schatz, E N.; O'Brien, M. C. M. Chem. Phys. Lett. 1989, 159, 567. 94. Pellow, R.; Vala, M.J. Chem. Phys. 1989, 90, 5612. 95. Breckenridge, W. H.; Malmin, O. K. J. Chem. Phys. 1981, 74, 3307. 96. Bililign, S.; Morse, M. D.; Breckenridge, W. H.J. Chem. Phys. 1993, 98, 2115.

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97. Umemoto, H.; Ohnuma, T.; Ikeda, H.; Tsunashima, S.; Kuwahara, K. J. Chem. Phys. 1992, 97, 3282. 98. Alexander, M. H. J. Chem. Phys. 1992, 96, 6672. 99. Leone, S. R. In Selectivity in Chemical Reactions; Whitehead, J. C., Ed.; Kluwer Academic: Dordrecht, 1988; p 245, and references therein. 100. Umemoto, H.; Kasakura, A.; Kikuma, J.; Sato, S. BulL Chem. Soc. Jpn. 1987, 60, 2343. 101. Leutwyler, S.; B6siger, J. Chem. Rev. 1990, 90, 489. 102. Shalev, E.; Ben-Horin, N.; Even, U.; Jortner, J. J. Chem. Phys. 1991, 95, 3147, and references therein. 103. Chergui, M.; Cr6pin, C.; Hebert, T.; Tramer, A. Chem. Phys. Lett. 1992, 197, 467. 104. Cr6pin, C.; Tramer, A. J. Chem. Phys. 1992, 97, 4772. 105. Okunishi, M.; Yamanouchi, K.; Tsuchiya, S. J. Chem. Phys. 1992, 97, 2305. 106. van Zee, R. D.; Blankespoor, S. C.; Zwier, T. S. Chem. Phys. Len. 1989, 158, 306. 107. Martrenchard-Barra, S.; Dedonder-Lardeux, C.; Jouvet, C.; Solgadi, D. J. Chem. Phys. 1993, 98, 528. 108. Wallace, I.; Funk, D. J.; Kaup, J. G.; Breckenridge, W. H. J. Chem. Phys. 1992, 97, 3135. 109. Bernier, A.; Millie, P. J. Chem. Phys. 1988, 88, 4843. 110. Roncero, O.; Beswick, J. A.; Halberstadt, N.; Soep, B. In Dynamics of Polyatomic van der Waals Complexes; Halberstadt, N; Janda, K., Eds.; NATO ASI ser B; Plenum: New York, 1990, Vol. 227, p471. 111. Zuniga, J.; Bastida, A.; Requena, A.; Halberstadt, N.; Beswick, J. A. J. Chem. Phys. 1993, 98, 1007. 112. Visticot, J. P.; Berlande, J.; Cuvellier, J.; Lallement, A.; Mestdagh, J. M.; Meynadier, P.; de Pujo, P.; Sublemontier, O. Chem. Phys. Lett. 1992,191, 107. Visticot, J. P.; de Pujo, P.; Mestdagh, J. M.; Lallement, A.; Berlande, J.; Sublemontier, O., Meynadier, P.; Cuvellier, J. J. Chem. Phys. 1994, 100, 158. 113. de Pujo, P.; Mestdagh, J. M.; Visticot, J. P.; Cuvellier, J.; Meynadier, P.; Sublemontier, O.; Lallement, A.; Berlande, J. Z. Phys. D. 1993, 25, 357. 114. Barker, J. A. In Rare Gas Solids, Klein, M. L.; Venables, J. A., Eds.; Academic: New York, 1976; p212. 115. Dantus, M.; Rosker, M. J.; Zewail, A. H. J. Chem. Phys. 1988, 89, 6128. 116. Rose, T. S.; Rosker, M.J.; Zewail, A. H. J. Chem. Phys. 1989,91, 7415. 117. For a review see Zewail, A. H. Science 1988, 242, 1645. 118. Gruebele, M.; Roberts, G.; Dantus, M.; Bowman, R. M.; Zewail, A. H. Chem. Phys. Lett. 1990, 166, 459. 119. Gruebele, M.; Zewail, A. H. J. Chem. Phys. 1993, 98, 883. 120. Baumert, T.; Engel, V.; R6ttgermann, C.; Strunz, W. T.; Gerber, G. Chem. Phys. Lett. 1992, 191, 639. 121. Krim, L.; Qiu, P.; Jouvet, C.; Lardeux-Dedonder, C.; McCaffrey, J. G.; Soep, B.; Solgadi, D.; Benoist d'Azy, O.; Ceraolo, P.; Dai Hung, N.; Martin, M.; Meyer, Y.; Visticot, J. P. Chem. Phys. Len. 1992, 200, 267. 122. Krim, L.; Soep, B.; Visticot, J. P.; Onda, K.; Yamanouchi, K.; Janvet, C.J. Chem. Phys. 1995,103, in press. 123. Bersohn, R.; Zewail, A. H. Ber. Bunser~ Phys. Chem. 1988, 92, 373. 124. Yamanouchi, K.; Isogai, S.; Tsuchiya, S.; Duval, M.-C.; Jouvet, C.; Benoist d'Azy, O.; Soep, B. J. Chem. Phys. 1988, 89, 2975.

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SPECTROSCOPIC STUDIES OF LARGE-AMPLITUDE MOTION IN SMALL CLUSTERS

Eric A. Rohlfing

I.

II. III. IV. V.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Carbon Trimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Dicarbide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laser-Induced Grating Spectroscopy . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85 89 98 105 109 110 110

i. INTRODUCTION In the past decade, new molecular-beam sources have enabled scientists to probe the physics and chemistry of an ever-increasing variety of atomic and molecular clusters. We have used one of these sources, based on the laser vaporization of a substrate into a pulsed expansion, to generate jet-cooled clusters for spectroscopic studies. Our emphasis has been on the spectroscopic characterization of large-am-

Advances in Metal and Semiconductor Clusters Volume 3, pages 85-111. Copyright 9 1995 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-788-2

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plitude motion on the ground-state potential energy surface (PES) in small clusters, principally triatomic molecules such as the copper trimer, ! the carbon trimer, 2-5 and silicon dicarbide. 6 These systems are all strongly covalently bound and thus differ from weakly bound van der Waals clusters in that the floppy degree of freedom is not coupled to the dissociation coordinate. In fact, for triatomic systems the floppy degree of freedom is always in a bending-type motion. Our efforts to characterize the rovibrational states of floppy triatomics share common themes with current studies of high-lying vibrational states of normal (i.e., stiff) molecules. In both cases the character of the rotational and vibrational motion is quite different from our customary picture of the rigid rotor-harmonic oscillator, and the density of rovibrational states is quite high. The experimental characterization and theoretical understanding of the internal dynamics on highly anharmonic regions of potential surfaces, whether near the minimum of a flat surface or at high energies on a "normal" surface, is a problem of much current interest. The copper trimer represents a classic example of the dynamical Jahn-Teller effect 7 in the simplest system that can display such behavior, i.e., an X 3 molecule with nominal D3hsymmetry. In the case of Cu 3, the Jahn-Teller stabilization energy (the difference between the O3hcusp and the C2v minima) is rather large; however, the barriers between the three equivalent C2vminima are small. Thus large-amplitude pseudoration is relatively facile on the ground-state PES. 8'9 The carbon trimer has long been held as a canonical example of large-amplitude bending motion in a nominally linear molecule. In C 3, the bending potential is so fiat that it more closely resembles a square well than the usual quadratic function. The harmonic bending frequency is only 62 cm -1 and the "turning points" of the bending potential occur at such large deviations in bond angle that C 3 can be accurately described as a "molecular hinge." Finally, SiC 2, although isoelectronic with C 3, is nominally a cyclic (C2v) molecule but possesses a low-lying linear isomer. The isomerization barrier is negligible, and thus SiC 2 displays large-amplitude motion that can best be thought of as hindered rotation of the C 2 moiety within the molecule. To obtain spectroscopic data on the rotation-vibration level structure supported by the ground-state PES, we use techniques that are based on rovibronic transitions in electronic band systems. There are several other spectroscopic approaches that are currently being applied to the characterization of small clusters in free jets, including high-resolution microwave and diode-laser IR spectroscopies. For the floppy systems that interest us, electronic spectroscopy is a powerful technique because there is usually a large frequency change in the floppy vibrational mode (and sometimes a significant change in molecular geometry) upon electronic excitation. This leads to favorable Franck--Condon factors for vibronic transitions that span a wide range of vibrational levels in the ground state and thus map extensive portions of the PES. Figure 1 illustrates an overall systematic approach designed to elucidate the PES from spectroscopic data and theory. Our portion of the data acquisition begins with a laser-induced fluorescence (LIF) excitation spectrum of a particular band system

Large-Amplitude Motion in Small Clusters

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Figure 1. A systematic approach, combining spectroscopic data with theory, to the determination ofthe potential energy surface of a small molecule. The first three boxes on the left illustrate the experimental progression used in our studies; these are complemented by the use of model Hamiltonians.

(preferably one that is already known) of the molecule of interest. Because we obtain all our spectra under jet-cooled conditions, LIF excitation spectra do not provide much information on high-lying vibrational levels inthe ground state. Some very useful data can be obtained via analysis of hot bands; however, this approach is usually limited to low-lying vibrational levels. The LIF excitation spectrum provides vibronic band positions and assignments for the upper electronic state that we use in the next step, in which we disperse the fluorescence from a selected vibronic level in the upper state. These dispersed fluorescence (DF) spectra, which are also known in the literature as single vibronic level (SVL) fluorescence spectra, provide a low-resolution mapping of the full range of FranckCondon-allowed vibrational levels in the ground state. The DF spectra serve as guides for the final step in our data collection sequence: the acquisition of rotationally resolved stimulated emission pumping (SEP) spectra. SEP is a now wellestablished technique in which one laser (the PUMP) excites a single rovibronic line, and a second laser (the DUMP) is tuned to downward transitions that terminate on the ground-state rovibrational levels of interest. In its usual implementation, the SEP DUMP resonances are detected by monitoring of the depletion in spontaneous fluorescence due to stimulated emission. SEP spectra provide more precise values

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for vibrational term energies and, more importantly, yield rotational level structure that is often very sensitive to large-amplitude vibrational motion. Through the LIF --~ DF ~ SEP spectroscopic sequence we obtain a database of vibrational and rotation-vibration term energies for states that span a wide range of the PES. None of the systems that we study can be accurately described by use of the customary approaches of molecular spectroscopy, i.e., small anharmonic deviations from a rigid rotor-harmonic oscillator. Floppy molecules exhibit strong coupling between the stiff vibrations (small-amplitude motions that can be described as harmonic oscillations) and the large-amplitude vibration. In addition, there is strong interaction between the floppy vibration and molecular rotation. In order to interpret the complex rovibrational level structure of these molecules, and ultimately use the spectroscopic database in order to determine the PES, one needs more accurate descriptions of the rovibrational Hamiltonian. These come in two somewhat distinct flavors and, although it is much beyond the scope of this article (not to mention the expertise of the author) to delve into theoretical details, I shall give an experimentalist's view of the two classes of techniques. The first type of approach employs a model Hamiltonian that provides a better description, in the perturbation theory sense, of the true rovibrational Hamiltonian. The aim of these so-called bender models (nonrigid bender, semirigid bender, etc.) is to treat the large-amplitude motion and its coupling to rotation in a more exact way while leaving the high-frequency modes to be treated in the usual (i.e., harmonic oscillator) approximation, l~ The net result is a model that provides physical insight into the internal dynamics, via effective bending potentials, and gives some predictive capability. An advantage of the model-Hamiltonian approach is that it is not computationally intensive and is thus amenable to use in nonlinear least-squares fitting of experimental data. The second class of theoretical approaches is more rigorous. These begin with the exact rovibrational Hamiltonian and seek solutions to the SchrOdinger equation through a variety of methods, including variational calculations 12-14 and semiclassical dynamics. 15 These methods have the advantage of being "exact"; however, they tend to suffer from being so computationally intense (even for triatomics) that iteration between theory and experiment to refine the PES is generally not feasible. For example, variational approaches tend to suffer convergence problems because of the large number of basis wavefunctions required to describe high-lying bending states. All theoretical approaches to the rovibrational SchrOdinger equation for floppy molecules are greatly aided by ab initio quantum chemistry calculations of the PES. The increasing accuracy of high-level quantum chemistry techniques make these ab initio surfaces excellent starting points for iterations between experiment and theory that converges toward the true PES. The remainder of this chapter is organized as follows. I shall present progress reports on our studies of large-amplitude motion and the characterization of the PES for two molecules, C 3 and SiC 2, in Sections II and III, respectively. The discussion will be heavily oriented toward the experimental data we have acquired

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89

but will also include the results of recent theoretical analyses. In Section IV I shall make a brief digression to discuss a laser-induced grating approach to double-resonance spectroscopy that holds great promise for several spectroscopic applications, including background-free SEP spectroscopy. Finally, in Section IV I shall summarize our results and briefly discuss future research directions.

II. THE CARBON TRIMER The C 3 molecule has long been a prototype for the study of large-amplitude motion and rotation-vibration coupling in nonrigid linear molecules. 16Until the flurry of recent experimental studies, the spectroscopic database for C a consisted largely of the data obtained from the analysis of the only electronic transition assignable to gas-phase C3, the ,~ lII,,- ~" leg band system whose origin lies at 405 nm. This system was first observed in the spectra of comets more than a century ago. 17 The analysis of the laboratory spectrum, by Gausset et al. 18 and subsequently by Merer, 19 was greatly complicated by the floppiness of the molecule, which gives rise to large /-type doubling in the ground state, and a strong Renner-Teller interaction in the excited state. Lemire et al. 2~ found a new, vibronically induced band system, or systems, of C a in the 266-302-nm region using mass-selective resonant two-photon ionization (R2PI) in a cold molecular beam. The two possible electronic states that could give rise to the UV system(s) are the 1Au a n d 1FIustates, calculated to lie at 4.13 and 4.17 eV, respectively. 21 Rotational analyses reveal that most of the bands in the UV system have E~+ symmetry in the upper vibronic level, but vibrational assignments have not been made because of the complex nature of the vibronic coupling and interleaving of the two excited states. Prior to the recent DF and SEP spectra obtained by us 2-4 and by Sears and + ground state co-workers, 22-24 our knowledge of the rovibrational levels in the 1~Eg was limited to the original analysis of the cometary system, 18 which gave bending levels up to v 2 = 6, and high-resolution spectra of the fundamentals of the antisymmetric stretch 25and bend. 26 Despite the lack of spectroscopic data over a wide range of energies, C a has continued to be a favorite molecule of theoretical descriptions of large-amplitude motion. Jensen and co-workers published a series of papers 27-29 in which either the nonrigid bender (NRB) Hamiltonian 1~ or a Morse oscillatorrigid bender (MORBID) Hamiltonian 3~ was used to fit the available experimental data and an ab initio PES calculated by Kraemer et al. 31 The results of these studies revealed a PES that had a very small barrier to linearity, ! 6.5 cm -1, and thus C a was thought to be "quasilinear." In addition, the effective bending potentials change dramatically with excitation of either of the high-frequency stretching motions. Upon excitation of the symmetric stretch, a9l, C 3 becomes stiffer; excitation of the antisymmetric stretch, ~3, produces effective potentials with significant barriers to linearity, i.e., C 3 becomes effectively bent. Our initial foray into the spectroscopy of C a began with an LIF/DF study of both the cometary band system and the UV system. 2 In these (and all other) experiments

90

ERIC A. ROHLFING

we generate C 3 by pulsed-laser vaporization of graphite into the helium flow through a channel following a pulsed valve. Subsequent free-jet expansion into vacuum produces rotationally cold C 3 that is crossed at fight angles by an excitation laser beam some 10-20 nozzle diameters downstream from the source orifice. Fluorescence is collected perpendicular to both the expansion and the laser beam and is imaged onto either a bandpass filter/PMT combination or onto the entrance slit of a 0.75-m monochromator. The monochromator is used for excitation scans of selected fluorescence bands and for DF spectra. DF spectra are obtained either by scanning of the monochromator (with PMT detection) or through the use of an optical multichannel analyzer (OMA) system. Because C 3 is stable under the high-temperature conditions in the vaporization region, C a produced from the source is often vibrationally hot. This is especially true for the high-frequency stretches, which are ineffectively cooled by collisions with helium, and we often observe hot bands in both 1)1 and 1)3.2,4 By contrast, the low-frequency bend, like rotational motion, is effectively cooled in the expansion, and bending hot bands are never observed. The LIF excitation spectra of the UV system provided further identification (but not assignment) of its vibronic bands, including bands with 1-I, vibronic symmetry in the upper level and hot bands in the symmetric stretch. The strong vibronic coupling in the excited electronic state(s), although greatly complicating the excitation spectrum, produces extraordinarily rich DF spectra that extend to energies up to 17,000 cm -1 in the ground state. Figure 2 shows an example of one of the DF spectra from the UV system. Because the electronically excited states of C 3 are much stiffer than the ground state, the DF spectra exhibit long progressions in the low-frequency bend for each stretching state (designated by v 1 and v3). In the UV system, transitions from Zu+ upper states are dipole allowed to ground-state levels with Eu+(12= 0) and I-Ig(/2 = 1) symmetries. The former occur whenever both v 3 and v 2 are even, for example, the 0v~ progression labeled in Figure 2, and the latter occur whenever both v 3 and v 2 are odd, for example the 0v~l progression labeled in Figure 2. (The notation for vibrational states in terms of the three vibrational quantum numbers and bending vibronic angular momentum, 12, is VlV~-'v3.) The spectrum in Figure 2 is representative of both the richness (or diabolical complexity) of the DF spectra of the UV system and of the bizarre intensity distribution in which strong fluorescence bands are always seen at the red end of the spectrum. For one vibronic band of the UV system (at 33,589 cm -1) these high-energy bands are by far the brightest in the DF spectrum and can be assigned to short bending progressions built on highly excited stretching states, the strongest of which is the 6v~l progression. 3 The intensity of these bands is difficult to reconcile by simple Franck-Condon factors alone, even for substantial increases in C-C bond length in the excited state. This anomalous intensity must be derived from a dramatic increase in transition moment with variation in bond length, probably through mixing with vibronic levels in the high-lying IZ~ state? 1

Large-Amplitude Motion in Small Clusters

91

m

t~ tom Or)

oo

Ov

-,~

a

I

(1) 0 t-" r 0 oo

Ov',l

L__

0 U_ ,

,

,

I

4000

,

,

,

I

,

,

,

1

8000 12000 F r e q u e n c y Shift (cm -1)

,

,

,

1

16000

Figure 2. The DF spectrum obtained upon excitation of the P(2) line of the T_,+u- 000 T_,~ovibronic band of the UV system of jet-cooled C3 at 36,443 cm -I . Regions containing the Ov~1 and 0v121 progressions are indicated.

In sharp contrast, the DF spectra for the cometary system show the regular Franck--Condon intensity patterns one expects for a stiffer upper state with roughly the same bond length as the ground state. In Figure 3 we display the DF spectrum obtained upon excitation of the (unresolved) Q branch of the 020 1-I~) - 0 0 0 L~g band of the cometary system. Perpendicular transitions are allowed from the I1(,,+) upper state to E~ (12 = 0) states for v 2 = 0 and to Z~ (l 2 = 0) and Ag (l 2 = 2) states for v 2 = 2, 4, 6 ..... etc. In addition, transitions are only allowed to states with even quanta in the antisymmetric stretch. With the exception of the v 3 = 2 and v 3 = 4 states, the resolution in the DF spectra are insufficient to resolve the splitting between the Z; and A levels. The pure bending progression in Figure 3 shows the anharmonic nature of the bending potential. The level spacing increases with increasing v 2, a pattern consistent with the square-well nature of the bending potential but just the opposite of a conventional anharmonic oscillator, in which the level spacing decreases with v 2. Not so clearly revealed in Figure 3 is the unusual level structure in the 0v22 progression, which becomes even more pronounced in the 0v24 progression. 2 This pattern is indicative of the fact that, in these antisymmetric stretching states, the effective bending potential develops a substantial barrier to linearity and supports bending levels localized at bent geometries. Analysis and assignment of our DF spectra yielded an enormous number of vibrational term energies for the ground state of C 3. In all, term energies were assigned to some 144 levels that cover the range 0 < v I < 8, 0 < v 2 < 37, and 0 < v 3 < 4. 2 The bending progressions for the symmetric stretch-bend progressions can be fit to the usual simple polynomial expansions in v 2 and show that the effective bending frequency increases with increasing v 1. In other words, the molecule becomes stiffer with excitation of the symmetric stretch. It is impossible to fit all the observed vibrational term energies to the standard Dunham-type expansion; the anharmonicities involved in the bend-stretch interaction are too

92

ERIC A. ROHLFING Ov20 ,

r-F-T--.....I T - T - - ] :

i

xlO u

c c~

Ova2

CO 9 o c-(1) o or) (1)

lirr I T iT' !

i,

i-,.

0

z

U..

I

-500

500

L

,

~

I

1500

........

_L

....

2500

Frequency

~_.~

Z .......L. . . . . . . . . . _l___J____t__ _~_____k

3500

4500

._.L__.

5500

S h i f t ( c m -1)

Figure 3. The DF spectrum obtained upon excitation of the unresolved Q branch of the 020 rl(u+) - 000 ~ band of the cometary system of jet-cooled C3 at 25,528 cm -1 . Ground-state progressions (I = 0) indicated are: 0v20 (v2 = 0,2,4, ...,18) and 0v22 (v2 = 0,2,4 ..... 16).

strong to be accounted for in this simple manner. As we shall discuss, more sophisticated theoretical approaches are required to characterize the vibrationallevel structure in C 3. In order to probe the nuances of the internal dynamics of C 3 in more detail, we performed rotationally resolved SEP spectroscopy. 3'4 Besides offering higher resolution of the vibrational band origins, such spectra give rotational constants for each vibrational level that provide a direct measure of the average nuclear configuration of that state. The SEP experiments were performed by crossing the C 3 expansion with a second tunable laser and monitoring the loss in fluorescence due to stimulated emission when the DUMP laser hit a downward resonance. The DUMP laser is delayed in time from the PUMP laser in order to provide a reference fluorescence signal that is used to normalize the fluorescence dip. Without such a normalization scheme, the shot-to-shot fluctuations in the C 3 source would swamp the fluorescence dips. 4 In Figures 4 and 5 we display rotationally resolved SEP spectra for the 0v22 and 0v24 progressions, respectively. In each case we show DUMP spectra of the first few bending levels for different rotational lines of the PUMP. These spectra are assigned in two notations: a linear molecule with doubly degenerate bend and

Large-Amplitude Motion in Small Clusters vb, K v, I ,

0,0 0,0 .

93

0,2 2,2

j'Le~,~u,,

1,0 2,0

.

:,

'.

vl! I!

'

p(lo)

1

475.8

~

I

476.2

,

1

476.6 Dump

,

1

L

477.0 Wavelencjth

I

477.4

~

I

477.8

~

I

478.2

(nm)

Figure 4. Rotationally resolved SEP spectra of the first three features in the 0v2 bend-stretch progression of C3, assigned in notation appropriate for a bent molecule (Vb, K) and a linear molecule (v,/), where v = 2Vb + K and K = I II. The pump band is 020 rl(u- ) - 000 Y_,~,and each spectrum is normalized to the largest fluorescence loss" 13% for P(6), 21% for P(8), and 21% for P(12).

vibronic angular momentum, (V2,/2) or just (v,/), and a bent molecule with nondegenerate bend and a-type rotational levels, (v b, K a or just K). The transformation between the two is given by: v 2 - 2v b + K a and K a = Ill. Because ofnuclear spin statistics in 12C3, the l(Ka) = 0 levels support only even J states; these appear as P and R branch lines in the spectra in Figures 4 and 5. For l(Ka) = 2 levels, both even and odd J are allowed and we observe P, Q, and R branch lines. However, only one of the l(Ka)-type doublets is allowed for each rotational level. The positive-oriented features in the spectra in Figure 4 are fluorescence signals induced by the DUMP laser on the 020-002 hot band. This illustrates the high degree of vibrational excitation often observed for C a generated in the laser-vaporization source; in some cases the effective vibrational temperature in the antisymmetric stretch is as high as 2400 K.4 We obtain a complete mapping of the low-lying (J _< 12) rovibrational levels in the 0v22 and 0v24 by taking SEP spectra for each of the rotational lines in the PUMP transition. From high-resolution diode laser spectroscopy of the antisymmetric stretch fundamental, 25 the rotational constants of the ground and 001 states were found to be: B(000) - 0.430579(17) crn-1 and B(001) = 0.435704(19) cm-1. The slight

94

ERIC A. ROHLFING 0,0 0,0

v b, K v,I

0,2 2,2

'...

"..... '.. P(4)

"".,

'.,, P(8) ,, ". 9: .. 'v.

I

,

583.5

,

,

~

1

'l

t

L

t

~ ~

,

/~. p(12)

z

t

I

t

584.0 584.5 585.0 D u m p Wavelength (nm)

,

~

l

585.5

Figure 5.

Rotationally resolved SEP spectra of the first two features in the 0v4 bend-stretch progression of C3, assigned in notation appropriate for a bent molecule (Vb, K) and a linear molecule (v,/), where v = 2Vb + K and K = I II. The pump band is 020 I1(o- ) - 000 s and each spectrum is normalized to the largest fluorescence loss" 20% for P(4), 22% for P(8), and 19% for P(12).

increase in B was taken as evidence of quasilinear behavior, i.e., a small barrier to linearity in the 001 state. From our SEP spectra, we determined rotational constants for the 002 and 004 states: B(002) = 0.4621(58) cm -1 and B(004) = 0.5090(36) cm -1. The huge increase in B as v 3 increases above one is because the barrier in the effective bending potential becomes large enough to support bending states localized at nonlinear geometries, i.e., C 3 is effectively bent in the 002 and 004 states. As the bend excitation in either the 002 or 004 states is increased, the barrier to linearity is exceeded and the rovibrational levels take on the character of a linear molecule. Thus, neither a rigid asymmetric rotor model nor a linear molecule model, which includes variation of the/-doubling with v2 ,22'23 is appropriate to describe the rotation-bending levels of the 002 and 004 states. Concurrent with our work on C 3, Northrup and Sears obtained SEP spectra of C3 .22'23 By mutual agreement, they focused their efforts on the pure bending levels and symmetric stretch-bend levels and we pursued the antisymmetric stretch-bend levels described above. The net result of this recent SEP work, combined with the previous data from electronic ]8 and IR spectra, 25'26 is a substantial database of rotation-vibration term energies that span a wide range of the ground-state PES. In

Large-Amplitude Motion in Small Clusters

95

order to analyze this data set we employed 5 the semirigid bender (SRB) model Hamiltonian developed by Bunker and Landsberg. 32 Although this model does not attempt to deduce the true multidimensional PES, it is relatively easy to apply and does provide strong physical insight into the variation of the bending potential as the stretching modes are excited. The basic approach in the SRB (and all other bender models) is to separate the high-frequency, small-amplitude stretches from the large-amplitude bending and rotational degrees of freedom. In the SRB model one solves a rovibrational Hamiltonian for each stretching state (defined by v 1 and v 3) that includes an effective bending potential function (usually expressed in a power series in the complement of the bond angle). In addition, the bond length averaged over a particular stretching state is allowed to vary with bond angle. In Figure 6 we display the effective bending potentials and low-lying bending levels determined from our SRB fits 5 to the C 3 data for three stretching states: (v 1 = v 3 = 0), (v 1 = 3;v 3 = 0), and (v 1 = 0; v 3 = 4). For the zero-point stretching level the splitting of the l = 0 and l = 2 levels is very small and decreases with increasing v 2. The effect of stretching excitation is illustrated dramatically by the potentials for the (v I = 3; v 3 = 0) and (v 1 = 0; v 3 = 4) states. Symmetric stretch excitation produces a much stiffer and more harmonic bending potential. Also, the ordering of the l levels is reversed from the (v 1 = v 3 = 0) state and the splitting increases with v 2. Excitation of the antisymmetric stretch gives rise to substantial barriers to linearity; the barriers are 78 cm -1 and 271 crn -l, with bond angles of 133 ~ and 125 ~, for the 002 and 004 states, respectively. The level structure shown for the v 3 = 4 state in F i g u r e 6 shows the bent to linear t r a n s i t i o n (v 2 = 2v b + K a and K a = l/I). For bending levels well below the barrier the l ( K a) level splitting increases roughly quadratically with K a, as expected for a rigid bent molecule. Well over the barrier the behavior is typical of a linear molecule, in which there is a small splitting between I levels with a common v 2. The dependence of the SRB effective bending potential with stretching excitation can be qualitatively understood through the angle-dependence of the G-matrix elements as described by Bunker in the case of C302 .33 This analysis shows that the symmetric stretch harmonic frequency increases as the molecule is bent, i.e., the molecule is straightened by excitation ofx)~. By contrast, the antisymmetric stretch frequency decreases as the molecule is bent, i.e., excitation of a93 raises the barrier to linearity. Simple predictions based only on the changes in G-matrix elements do not accurately reflect the angle dependence that is extracted from the SRB fits, 5 indicating that the force constants are also angle dependent. Finally, from the SRB effective potentials we can estimate an equilibrium bending potential. This potential retains a minimum at the linear geometry and thus C 3 is not quasilinear, as earlier results had suggested, but is truly a linear molecule. Although the SRB analysis provides an excellent intuitive picture of the internal dynamics of C 3, the SRB effective potentials are not to be confused with "cuts" through the true multidimensional PES. Indeed, the SRB potentials specifically include effects unrelated to the PES, such as the angle dependence of the kinetic

96

ERIC A. ROHLFING

400

200

'E

400

t=,.

c.U..I

200 v2-O

~=4

400

=3

200 Vb= 0

80

120 160 200 240 Bond Angle (degrees)

280

Figure 6. A comparison of the effective bending potentials determined from SRB fits to the s p e c t r o s c o p i c data for t h r e e different s t r e t c h i n g states of C3 1L~g:vl = 3, v3 = 0 (top), vl = v3 = 0 (middle), and vl = O, v3 = 4 (bottom). The bending levels in the top and middle frames are labeled appropriately for the linear configuration (v2) and the levels in the bottom frame are labeled in bent notation (vb). Different values of/(K) are indicated: I ( = K) = 0 are solid lines, I ( = K) = 1 are dotted lines, and I ( = K) = 2 are dashed lines. energy operator noted previously. Motivated by the opportunities afforded by the new spectroscopic database for C 3, Jensen et al. 34 have recently performed ab initio calculations of the PES (and dipole moment surface) of C 3 using the full valence complete active space self-consistent field (CASSCF) method with a very large basis set. We display the C2v portion of this surface, as a function of bond angle and

Large-Amplitude Motion in Small Clusters

97

Figure 7 . A portion of the CASSCF potential energy surface of C3 X' 1~. The C2v portion of this ab initio surface (from Ref. 34) is shown as a function bond angle and R+, which is the sum of the C-C bond lengths. Note the extreme flatness of the potential along the bending coordinate.

R+ (the sum of the C--C bond lengths), in Figure 7. Note the remarkable flatness along the bending coordinate; conversely, symmetric distortion (along R+) produces the customary rapid increase in energy. On the basis of the CASSCF surface, Jensen et al. 34 have calculated the low-lying rotation-vibration energies usingthe MORBID method. 29 The agreement between the CASSCF/MORBID calculation and experiment is semiquantitative and illustrates that the ab initio PES has the correct degree of floppiness and appropriate bend-stretch couplings. In addition, the CASSCF equilibrium bending potential is in good agreement with that derived from our SRB analysis. 5 However, the CASSCF/MORBID calculations do not

98

ERIC A. ROHLFING

accurately reproduce all of the experimental rotation-vibration term energies in the low-energy range and calculations of higher lying states have not yet been attempted.

III.

SILICON DICARBIDE

Silicon dicarbide, SiC 2, shares much in common with the carbon trimer. The two molecules are isoelectronic, both are detected in the astrophysical environment, and, most importantly for us, both exhibit large-amplitude motion on a highly anharmonic ground-state PES. The green band system of SiC 2 has been observed in carbon-rich stars 35 and, in analogy with C3, was initially assigned as a ll-1-1]~+ transition in a linear molecule. 35-38 However, rotational analysis of the origin band of this system at 498 nm 39'40 proved conclusively that SiC 2 is cyclic, with CEv symmetry in both states of the reassigned ,4 IB 2 - X 1A1 transition. The geometry and inertial axes of ground-state SiC 2 are shown in Figure g; the molecule can be described as having a short C-C (triple) bond and long Si-C (single) bonds. Based on ab initio calculations, 41-44 the linear isomer of SiC 2, with the cummulene-type structure Si---C=C, is believed to lie only 300-1700 crn-1 higher in energy than the cyclic form. Although only limited theoretical work has been done to elucidate the full PES, the isomerization barrier is predicted to be negligible. In addition, it is not clear from existing calculations whether the linear structure is a true minimum or simply a saddle point on the PES. In the cyclic geometry the three normal modes are a high-frequency C-C stretch, ~l (al), a stretch between Si and the C 2 moiety, ~)2 (al), and a low-frequency antisymmetric bending-type vibration, ~3 (b2)" The minimum-energy isomerization path corresponds to the silicon atom being "swung" around to one end of the C 2 fragment. However, because Si is comparable in mass to C 2, the large-amplitude motion that connects the cyclic and linear geometries is best thought of as a hindered rotation of the C 2 fragment in conjuction with a slight wobble of the silicon atom. This vibrational motion corresponds

! !

Si !

rc_c = 1.265 ,/k L_

rsi.c 1.836 ,/k

__

-

C-Si-C

C

,, !I

= 40.29 ~

C

! a

Figure 8. The geometry of SiC2 with the a- and b-inertial axes indicated. Bond lengths and angles are given for the ~" 1A1 ground state (from Ref. 40).

Large-Amplitude Motion in Small Clusters

99

roughly to the antisymmetric normal mode at the bottom of the cyclic well but must include mixing with the Si--C 2 stretching mode at higher energies. Our experimental strategy for studying large-amplitude motion on the groundstate PES of SiC 2 is identical to that used for C 3. The experimental approach is also identical, except that silicon carbide is used as the vaporization substrate. Our first step involved a more detailed look, and subsequent reassignment, of the gas-phase LIF excitation spectrum of the ,4 1B2-X 1Al band system. 6 Bondybey 38 had previously studied this spectrum in the gas phase at 77 K, but his vibronic assignments were incorrect because they were based on the assumption that SiC 2 was linear. In Figure 9 we display our LIF survey spectrum, with vibronic band assignments, of the first 2000 cm -1 above the origin. The cold rotational temperature (and consequently narrow rotational envelopes) achieved in the free jet allows us to resolve some weak bands that were obscured in Bondybey's warmer spectrum. In particular, the weak 3~ band is the key to the rest of the vibronic assignments. [The vibronic band notation is mode number(s) with vibrational quantum numbers ..... 9

"

I

9

-

SiCz ~lB2

-

l

"

"

9

l

"

"

"

l

9

"

"

- ]~l]dkl

0~

30

/o 311 0

-- - . . . . . . .-200 9

9

9

I

1 1 2031 .

.

.

+ ....

400

9

-

-

,-~.'

n "';

600

I

"

"

"

I

800 9

"

"

1000

I

9

"

9

lo20 20 30 1

331 . . . . . .

1000

___& ....

1200

11o ,31~

2

23

21

o, o 1 !

201 3 ,

1400

.

.,--r ----k-

1600

y~ 1

2232 ,

,

1800

2000

Relative Frequency (cm -~) Figure 9. LIF excitation survey spectrum of the ~, 1B2 - ~' 1A1 system of jet-cooled SiC2 in the range 0-2000 cm -1 above the origin 4~ at 20,065.5 cm -1. Vibrational assignments are indicated. The spectrum is a composite of scans over several laser dyes and is normalized for laser power variations.

100

ERIC A. ROHLFING

for ground and excited states as subscripts and superscripts, respectively.] This band is formally dipole forbidden because it entails one quantum of the antisymmetric stretch in the excited state, but can be vibronically induced through mixing with other 1A1 electronic states. The assignment of the 3~ band is proven conclusively by the rotational structure of this band, which is of the A 1-A1 parallel type. 6 With the assignment of the antisymmetric fundamental, the assignments of all the excited-state fundamentals is complete, and most of the rest of the spectrum is assigned to overtones and combination bands. 6 This is straightforward because the A state is much more harmonic at the cyclic minimum than the ground state. The survey spectrum in Figure 9 also shows hot bands that correspond to one quantum of excitation in the antisymmetric stretch, such as the 3 [ band. These bands are strong because they are dipole allowed in the 2B2-1Al transition, not because there is significant population in the v 3 = 1 level in the ground state. From rotational analysis of the 3~ and 31 bands 6 we determine the fundamental frequency in the ground state, 93 = 196.37(4) cm -1. There is a huge shift in the antisymmetric stretch fundamental between the gas phase and an Ar matrix, in which a93 = 160.4 cm-1. 45 SiC 2 is a highly ionic molecule (dipole moment 2.393 D 46) of the form Si+(C2 ). In fact, the C-C bond length and C--C stretch harmonic frequency and anharmonicity in SiC 2 are nearly identical 6 to those of free C~. Clearly, the polarizable Ar matrix greatly distorts the true PES of the floppy, ionic SiC 2, perhaps by lowering the barrier between the cyclic and linear forms. In order to investigate the vibrational-level structure in the ground state, we have taken DF spectra for ten of the bands in the,4 IB2 _ ~, 1A1 sYstem'6 As was the case for C 3, the electronically excited state of SiC 2 exhibits substantial frequency changes (in both ~2 and ~3) from the ground state and thus good Franck--Condon factors exist to a wide range of levels in the ground state. Analysis of our DF spectra yields vibrational term energies for 43 levels in the ground state, including a progression in the bending-type mode up to v 3 = 16. In Figure 10 we display the low-energy region of the DF spectrum obtained from excitation of the 2~ band. Assignments are given in the notation (v 1, v 2, v3) and only transitions to levels with even v 3 (i.e., totally symmetric states) are dipole allowed. The spectrum in Figure 9 is typical of the higher resolution DF spectra of B2-A 1 excitations in which the rQ0 band (all J) is excited. It shows resolution of the two Q branches terminating on K a = 0 and K a = 2, the rQo and PQ2 branches, respectively. For 12C3, nuclear spin statistics dictate that A l vibrational levels support only even Ka; B 2 levels support only odd K a. The 2~ DF spectrum shows short progressions in the low-frequency, antisymmetric mode, both in (0,0,v 3) and (0,1,v3). The spacing between adjacent levels is greater for (0,1,v3) than it is for (0,0,v3), indicating a strong coupling between the Si--C2 stretch and the bending-type mode. This coupling is also manifested in the form of Fermi resonances between the levels of two different (0,v2,v 3) progressions, for example the (0,0,6) and (0,1,0) levels shown in Figure 10.

Large-Amplitude Motion in Small Clusters

101 iii

9

I

.

.

.

.

I

'

'

'

1,0,0

2~ Band r

p

0,2,0

0,0,2 I

.

.

.

I

780

880 / J x\

z ~x

z / z

L J~ .

300

.

.

.

.

.

I

800

,

,

9

..,

I

,

1300

..,

,

i

1800

Relative Frequency (cm -1) Figure 10. The low-energy region of the DF spectrum obtained upon excitation of the rQo branch ofthe 2~ band (B2 - A1)in the ~ 1/32 - ~' 1A1 system ofjet-cooled SIC2. The abscissa is the frequency relative to the exciting line and the ordinate is in arbitrary units. Individual bands are labeled vl,v2,v3. The inset shows an expanded view of the (0,0,6) and (0,1,0) bands and indicates the resolution of the two Q branches, rQo and ~

1 Figure 11 displays the DF spectrum for excitation of the 2o3 o2 band. Excitation of this type of combination band produces a very rich DF spectrum because of favorable Franck-Condon factors to a broad range of ground-state levels. The 1 2 2030 DF spectrum gives term energies for the (0,0,v 3) levels with even v 3 up to v3= 14. The region of this spectrum beyond about 1400 cm -1 is quite congested and contains many weak, unassigned bands. There are many possible combinations in this region, including (0,1,v3) with large v 3 and (0,2,v3) with small v 3, but the high density of bands and the lack of any regular pattern makes assignment impossible. In addition, it is in this energy region that one might expect to observe largeamplitude bending states above the isomerization energy, i.e., hindered C 2 rotor states. We can assign the regular series of bands in the 1700-3100 cm -1 region to the (1,0,v3) levels, which have a predictable energy level pattern because the coupling between the C--C stretch and the bend is weak. In keeping with our expectations, the ground-state vibrational term energies cannot be fit to the usual Dunham-type expansion; the bending mode is too

102

ERIC A. ROHLFING l

I

i

!

[

i

i

!

'

'

I

'

'

O,O,vs 0

[ i I

I

1 2

4

6

1

1

2

2030 Band

8 10 12 14

0,2,0 O,l,vs

I

I

2

1,O,v 3

I

4

1 I I

0

2

4

6

Ii

8

10 12

.L I

-200

I

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anharmonic and exhibits strong coupling with the Si--C 2 stretch. By contrast, the observed vibrational terms in the A state are well described by the usual approach, with reasonable anharmonicities. We plot the energy difference between adjacent levels in the (0,0,v3) progression, AG = G(0,0,v 3 + 1) - G(0,0,v3), versus vibrational energy in the antisymmetric mode in Figure 12. The rapid drop in AG at low v 3 demonstrates the high degree of anharmonicity near the bottom of the cyclic minimum and provides indirect evidence for large-amplitude motion. The data in Figure 12 also show evidence for the Fermi-resonant mixing between various (0,0,v 3) and (0,1,v3) states. For example, AG for v 3 = 5 is too small and that for v 3 = 6 is too large because the (0,0,6) level interacts with the (0,1,0) level. A more sensitive measure of large-amplitude motion is provided by the energy separation between the rQo andPQ2 branches (see Figure 10). This splitting is a measure of the energy difference between K,~ = 0 and K a = 2 rotational states (unresolved in J) for each vibrational level and thus provides information on the vibrationally averaged inertial moment about the symmetry axis (the a axis in Figure 8). This inertial moment decreases rapidly with internal rotation of the C 2 fragment, becoming zero at the linear geometry. Much as in C 3, the K-type

Large-Amplitude Motion in Small Clusters

103

Figure 12. A plot of the spacing between adjacent vibrational levels, AG (black circles), and the frequency difference between Q-branches, (PQ2-rQo)/4 (stay squares), as a function of the vibrational energy of the (0,0,v3) levels of SiC2 ,~"A1. Representative v3 are indicated.

rotational structure in the cyclic isomer is transformed into vibrational structure in the degenerate bending mode of the linear molecule. In Figure 12 we plot the energy difference between rQo and PQ2 branches, given as (PQ2 - rQo)/4 for the (0,0,v 3) levels with even v 3. The dramatic increase in the Q-branch splitting with increasing v 3 is direct evidence of large-amplitude internal rotation that samples the linear region of the ground-state PES. Our final phase of spectroscopic characterization, the acquisition of rotationally resolved SEP spectra, has just begun for SiC 2. Ultimately, we intend to use the increased resolution of SEP to help sort out the vibrational assignments in the congested spectral regions (see Figure 11). Initially, however, we have concentrated our efforts on the (0,0,v3) levels; we show rotationally resolved SEP spectra of the (0,0,12) level in Figure 13. Silicon dicarbide poses a greater experimental challenge than C 3 because laser vaporization is less effective at making SiC 2 and the signal-to-background ratio for the SEP spectra of SiC 2 is generally poorer. (In the following section we discuss a laser-induced grating technique for SEP spectra that addresses this problem.) In addition, the rotational structure of SiC 2 is more complex because it is an asymmetric top (rotational levels denoted by Jra,rc). This

104

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makes rotational selection in the PUMP more difficult because of greater spectral congestion and also makes interpretation of the DUMP spectra more challenging. Nonetheless, we have successfully obtained and assigned SEP spectra for (0,0,v 3) levels up to v 3 = 12. In collaboration with Ross, who has previously used the SRB approach to analyze the rovibrational levels in the HCN/HNC system, 47 we have begun to analyze the vibrational level data from the DF spectra and the rovibrational term energies from the SEP Spectra using the SRB model. 48 In our initial fits, we have considered only the one-dimensional hindered rotation that connects the cyclic and linear isomers and have attempted to extract the corresponding potential for this large-amplitude motion. This approach gives good fits to the DF and SEP data for the (0,0,v 3) levels and gives a large-amplitude potential that has no isomerization barrier and apparently no minimum at the linear geometry. The isomerization energy is found to be about 1600 crn-1, in good agreement with ab initio estimates. 41 As noted previously, the turning points in the large-amplitude potential are particularly sensitive to the vibrationally averaged moment of inertia about the C2v symmetry axis. Thus, SEP data that fully resolve levels with K a = 0 (which are largely unaffected by largeamplitude motion) and levels with K a ~ 0 (which are strongly affected) are vital to

Large-Amplitude Motion in Small Clusters

105

an accurate determination of the SRB potential. Our SRB results should be regarded as tentative. It is particularly hazardous to extrapolate the current fits, which describe levels below the isomerization energy, to higher levels that sample the linear geometry. Thus we cannot conclude, without further data for levels at and above the isomerization energy, that there is no minimum at the linear geometry.

IV. LASER-INDUCED GRATING SPECTROSCOPY There is currently a burgeoning interest in resonant four-wave mixing techniques, which can also be described via laser-induced gratings, as sensitive and coherent probes of molecules in the gas phase. 49 Of particular interest to chemists is the application of these techniques to molecular spectroscopy and dynamics. Zhang et al. 5~ have demonstrated the use of degenerate four-wave mixing (DFWM) as a background-free method of detecting SEP spectra. In a similar vein, Buntine et al. 51 showed that two-color laser-induced grating spectroscopy (LIGS) could also be used to obtain SEP-like spectra. We became motivated by these results to perform resonant four-wave mixing techniques on jet-cooled transient molecules, namely C 3 and SIC2.52 Of particular interest to us is the use of two-color LIGS to obtain background-free SEP spectra of SiC 2, which, as mentioned previously, has proven less amenable than C a to conventional SEP detection by fluorescence depletion. Two-color LIGS is particularly easy to describe by use of induced gratings; 53 this viewpoint is illustrated schematically in Figure 14. Two laser beams at kl are crossed at a shallow angle in the sample medium, and the interference between

Figure 14. Schematic picture of the formation of a laser-induced grating via interference of two crossed beams at %1. Diffraction from the induced grating occurs when the probe beam at ~.2 senses the spatial variation in either the real refractive index, An, or the absorption coefficient, Acx.

106

ERIC A. ROHLFING

these two beams forms a spatially modulated intensity pattern. If to~ is tuned to a molecular transition, absorption creates a spatial modulation (grating) in the populations in the ground and excited states connected by the transition. The induced grating is probed by a second laser beam at ~ that senses the spatial modulation in both the real refractive index, An, (a phase grating) and the absorption coefficient, Ao~ (an amplitude grating). In the absence of collisional effects, the diffraction efficiency, and thus the intensity of the signal, is due entirely to the pure population grating. In other words, when the probe laser frequency, to2, is resonant with a transition from either of the levels involved in the grating transition, then the probe beam "sees" a spatially modulated absorption and diffracts off the ground- or excited-state population grating. However, in high-density environments (i.e., dense gases or condensed phases), collisional relaxation of the state excited by the grating laser can drive thermal and acoustic variations in density that produce phase (An) gratings. These thermal gratings are generally undesirable because they produce nonresonant scattering of the probe beam. Thermal gratings, and the nonresonant background they produce, are absent in the collision-free region of a fully expanded free jet. Thus, a free-jet expansion provides an excellent medium for laser-induced grating spectroscopy.

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Large-Amplitude Motion in Small Clusters

107

Clearly, two-color LIGS is a true double-resonance technique since (detectable) signal generation requires that both co1 and o)2 be resonant with a molecular transition. In Figure 15 we display energy level schematics for our applications of DFWM to the origin of the cometary system of C 3 and of two-color LIGS to the ,4 1B2 - X 1A1 system of SiC2 .52 The DFWM spectra obtained for C 3 offer no real advantage over conventional LIF excitation spectra; however, the success of our application of DFWM to C 3 proves that resonant four-wave mixing techniques have sufficient sensitivity to detect jet-cooled transient molecules at number densities of about 1012 cm -3 per quantum state. In our two-color LIGS spectroscopy of SiC 2, the probe laser excites downward transitions from the excited state to higher ground-state vibrational levels; i.e., it diffracts off the excited-state grating (Figure 15). In this case, the two-color LIGS spectrum yields the same spectra! information as an SEP spectrum detected by the conventional method of fluorescence depletion. The huge advantage that LIGS offers over fluorescence depletion is that there is no LIGS signal in the absence of both resonances, i.e., LIGS is a zero-background technique. Figure 16 displays a comparison of SEP spectra obtained by two-color LIGS and the fluorescence-dip technique for the,~ 1B2 - ~" 1A1 system ofjet-cooled SiC 2. The fluorescence-dip SEP spectrum was obtained using the time-delayed normalization scheme mentioned previously for C 3. In the fluorescence-dip spectrum we pump the rR2(2)e o line of the 2~ band; for the two-color LIGS spectrum we pump the same line of the ~202band. The DUMP laser probes the Fermi-resonant pair of levels in the 9

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108

ERIC A. ROHLFING

ground state: (0,0,6) and (0,1,0). For each vibrational level, two strong lines are observed that terminate on the unresolved 220,21 and 440,41 rotational levels. As is customary in fluorescence depletion, in order to obtain reasonable signal-to-background the intensity of the DUMP laser is high and the fluorescence-dip spectrum shows clear signs of saturation. The strong lines are significantly broadened and much weaker rotational lines, terminating on the 322,21 and 422,23 levels, are observed. In contrast, the two-color LIGS spectrum was obtained by saturating the PUMP transition but with probe (DUMP) intensities well below saturation. This results in laser-limited linewidths for the strong lines; the weak lines can be observed by increasing the intensity of the probe laser. In the fluorescence dip technique, the ability to detect SEP lines is determined by the ratio of the signal (dip) to the fluctuations in the non-zero background (S/B). The spectrum in Figure 16 is typical of our SEP spectra of SiC 2 obtained by use of fluorescence dip (see also Figure 13); it has S/B --- 4, which is significantly worse than similar spectra of C 3 (see Figures 4 and 5). The production of SiC 2 via laser vaporization of silicon carbide requires higher laser intensities than the generation of C 3 from graphite. Thus the amplitude and temporal fluctuations of the source are much larger for SiC 2 than for C 3, and the fluorescence signal in the absence of a DUMP resonance is less constant. In two-color LIGS, detection of SEP lines depends on the ability to generate signal in excess of the background from probe-laser scatter. We take great care, through the use of a nonplanar beam geometry and spatial filtering of the probe and signal beams, 52 to reduce background scattering. For the spectrum in Figure 16, we estimate that about 200 photons per laser shot arrive at the photomultiplier for the strongest line. Because of the near-zero scattered light background (about 1 photon/shot), the two-color LIGS spectrum has S/B -~ 170, a 40-fold improvement over the fluorescence-dip spectrum. Like all four-wave mixing processes, two-color LIGS is subject to a phase-matching constraint. For spectroscopic applications with a fixed geometry this imposes a phasematching bandwidth, which we define as the full width at half-maximum of the diffraction efficiency, on the tuning range of either the grating or probe lasers. 52'54In our experiments, we employ very shallow angles (about 2 ~ full angle for the grating beams) that, coupled with the short path length in the free jet (about 1 cm), produce large phasematching bandwidths. For example, the bandwidth for tuning the probe (DUMP) laser for the spectrum in Figure 16 is calculated to be about 1460 cm -l. Thus, phasematching does not critically impact the applicability of two-color LIGS for spectroscopic applications. 54 Finally, laser-induced grating techniques show great promise in other areas of spectroscopy and dynamics. For example, one of the great advantages of a technique like two-color LIGS is that it depends only on molecular absorption and is thus applicable to nonfluorescing molecules. We have recently demonstrated this use of two-color LIGS by obtaining double-resonance excitation spectra of jetcooled NO 2 above its predissociation threshold. 54 A variation of two-color LIGS,

Large-Amplitude Motion in Small Clusters

109

based on resonant diffraction off a photofragment grating created by crossed photolysis beams, can be used to study photodissociation dynamics. We demonstrated this photofragment grating technique on the NO grating produced from the photolysis of jet-cooled NO2.55 Scans by the probe laser give spectra that reveal fragment-state populations, and scans by the grating laser, with the probe laser monitoring a specific fragment state, produce photofragment excitation (PHOFEX) spectra. Most significantly, the temporal behavior of the photofragrnent grating provides a quantitative measurement of the speed and translational anisotropy of the state-selected fragment.

V. SUMMARY In this chapter I have attempted to illustrate, through progress reports o n C 3 and SiC 2, our approach to the spectroscopic investigation of large-amplitude motion on the ground-state PES of small clusters. The recent flurry of spectroscopic studies of C 3, by us and others, have made this molecule one of the most well-characterized nonrigid triatomics in existence. The vast spectroscopic database for C 3, which covers a broad range of the PES, provides a unique basis for testing modern theoretical descriptions of large-amplitude motion. The recent calculation of a high-level ab initio PES for C 3 provides an excellent starting point for iterations between theory and experiment toward the true PES. Although the spectroscopic database for C 3 is indeed substantial, there are still a large number of unassigned vibrational bands in our DF spectra, particularly for the UV band system (see Figure 2). Hopefully, with theoretical guidance, we shall be able to assign these states and, if useful for further refinements in the PES, perform high-resolution SEP spectroscopy upon them. Concerning SiC 2, we have not progressed as far in the spectroscopic investigation of large-amplitude motion. However, our DF spectra show conclusive evidence for large-amplitude hindered rotation of the C 2 fragment, and we are in the process of obtaining rotationally resolved SEP spectra to more completely characterize states near, and hopefully above, the isomerization energy. The SEP spectroscopy of SiC 2 will be greatly facilitated through the use of the background-free, two-color LIGS technique. As in the study of C 3, iteration with theoretical efforts, already begun with the SRB model, shall guide our future experimental studies of SiC 2. Despite the fact that the molecules described here are only triatomics, the highly anharmonic nature of their potentials gives rise to rovibrational motion that cannot be described using the conventional, perturbation-based tenets of molecular spectroscopy. Because they are small molecules, however, the challenge of calculating their rotation-vibration states is amenable to more sophisticated theoretical approaches. We have demonstrated that model Hamiltonians, particularly the semirigid bender, can be used to gain physical insight into large-amplitude dynamics and to provide predictive capability for these molecules. However, such approaches do not lead to the ultimate goal: the true multidimensional PES. More and

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more sophisticated approaches to the rovibrational Schrtidinger equation, incorporating advances in coordinate system and basis set methodology, 56 should make it possible in the near future to perform nonlinear least-squares fits of experimental data with nearly exact theoretical methods. High-quality ab initio potentials will be critical initial inputs to such attempts to determine the true PES. Finally, the knowledge gained from a better understanding of the rovibrational dynamics at low energies on the highly anharmonic potential surfaces of floppy molecules should be applicable to other areas of current interest in chemical physics, including the dynamics of highly excited rigid molecules and reactive transition states.

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division. I am grateful for fruitful collaborations with John Goldsmith, Trevor Sears, Tom Butenhoff, and Stephen Ross and for the expert technical assistance of Dan Ferko and Russ Hanush. In addition, I thank Celeste Rohlfing, Jan Almlt~f, and Per Jensen for permission to display a portion of their CASSCF potential surface of C3. Finally I thank several of my colleagues at the Combustion Research Facility, including Dave Chandler, Carl Hayden, Larry Rahn, Roger Farrow, Rick Trebino, and Dave Rakestraw, for our many useful discussions on laser-induced gratings.

REFERENCES AND NOTES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Rohlfing, E. A.; Valentini, J. J. Chem. Phys. Lett. 1986, 126, 113. Rohlfing, E. A. J. Chem. Phys. 1989, 91,4531. Rohlfing, E. A.; Goldsmith, J. E. M. J. Chem. Phys. 1989, 90, 6804. Rohlfing, E. A.; Goldsmith, J. E. M.J. Opt. Soc. Amer. 1990, B7, 1915. Northrup, E J.; Sears, T. J.; Rohlfing, E. A. J. Mol. Spectrosc. 1991, 145, 74. Butenhoff, T. J.; Rohlfing, E. A. J. Chem. Phys. 1991, 95, 1. Longuet-Higgins, H. C. Adv. Spectros. 1961, 2, 429. Thompson, T. C.; Truhlar, D. G.; Mead, C. A. J. Chem. Phys. 1985, 82, 2932. Truhlar, D. G.; Thompson, T. C.; Mead, C. A. Chem. Phys. Len. 1986, 127, 287. Zwanziger, J. E; Whetten, R. L.; Grant, E. R. J. Chem. Phys. 1986, 90, 3298. Bunker, P. R. Ann. Rev. Phys. Chem. 1983, 34, 59. Jensen, P. Comp. Phys. Rep. 1983, I, 1. Carter, S.; Handy, N. C. Mol. Phys. 1986, 57, 175. Carter, S.; Handy, N. C. Comp. Phys. Rep. 1986, 5,115. Tennyson, J. Comp. Phys. Rep. 1986, 4, 1. Ba~r Z.; Light, J. C. J. Chem. Phys. 1986, 85, 4594. Light, J. C.; BaSiC, Z. J. Chem. Phys. 1987, 87, 4008. Ba~i~, Z.; Whitnell, R. M.; Brown, D.; Light, J. C. Comp. Phys. Comm. 1988, 51, 35. Koszykowski, M. L.; Rohlfing, C. M.; Noid, D. W. Chem. Phys. Lett. 1987, 142, 67. S~rensen, G. O. In Topics in Current Chemistry; Boschke, F. L., Ed.; Springer-Verlag: Heidelberg, 1979; Vol. 82, p. 96. Huggins, W. Proc. Roy. Soc. 1882, 33, 1. Gausset, L.; Herzberg, G.; Lagerqvist, A.; Rosen, B.Astrophys. J. 1965, 142, 45. Merer, A. J. Can. J. Phys. 1967, 45, 4103. Lemire, G. W.; Fu, Z.; Hamrick, Y. M.; Taylor, S.; Morse, M. D. J. Phys. Chem. 1989, 93, 2313.

Large-Amplitude Motion in Small Clusters 21. 22. 23. 24.

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. 50. 51. 52. 53. 54. 55. 56.

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R6melt, J., Peyerimhoff, S. D.; Bunker, R. J. Chem. Phys. Lett. 1978, 58, 1. Northrup, E J.; Sears, T. J. Chem. Phys. Lett. 1989, 159, 421. Northrup, E J.; Sears, T. J. J. Opt. Soc. Amer. 1990, B7, 1924. Smith, R. S.; Anselment, M.; DiMauro, L. F.; Frye, J. M.; Sears, T. J. J. Chem. Phys. 1987, 87, 4435. Smith, R. S.; Anselment, M.; DeMauro, L. E; Frye, J. M.; Sears, T. J. J. Chem. Phys. 1988, 89, 2591. Matsumura, K.; Kanamori, H.; Kawaguchi, K.; Hirota, E. J. Chem. Phys. 1988, 89, 3491. Kawaguchi, K.; Matsumura, K.; Kanamori, H.; Hirota, E. J. Chem. Phys. 1989, 91, 1953. Schmuttenmaer, C. A.; Cohen, R. C.; Pugliano, N.; Heath, J. R.; Cooksy, A. L.; Busarow, K. L.; Saykally, R. L. Science 1990, 249, 897. Jensen, P. Coll. Czech. Chem. Commun. 1989, 54, 1209. Jensen, P.; Kraemer, W. P. J. Mol. Spectrosc. 1988, 129, 172. Beardsworth, R.; Bunker, P. R.; Jensen, P.; Kraemer, W. P. J. Mol. Spectrosc. 1986, 118, 50. Jensen, P. J. Mol. Spec. 1988, 128, 478; J. Chem. Soc., Faraday Trans. 1988, 2, 84. Kraemer, W. P.; Bunker, P. R.; Yoshimine, M. J. Mol. Spectrosc. 1984, 107, 191. Bunker, P. R.; Landsberg, B. M. J. Mol. Spectrosc. 1977, 67, 374. Bunker, P. R. J. Mol. Spectrosc. 1980, 80, 422. Jensen, P.; Rohlfing, C. M.; Alml6f, J. J. Chem. Phys. 1992, 97, 3399. Kleman, R. Astrophys. J. 1956, 123, 162. Verma, R. D.; Nagaraj, S. Can. J. Phys. 1974, 52, 1938. Weltner, W., Jr.; McLeod, D., Jr. J. Chem. Phys. 1964, 41,235. Bondybey, V. E. J. Phys. Chem. 1982, 86, 3396. Michalopoulos, D. L.; Geusic, M. E.; Langridge--Smith, P. R. R.; Smalley, R. E. J. Chem. Phys. 1984, 80, 3556. Bredohi, H.; Dubois, I.; Leclercq, H.; M61en, E J. Mol. Spectrosc. 1988, 128, 399. Grev, R. S.; Schaefer, Henry E, III. J. Chem. Phys. 1984, 80, 3552. Oddershede, J.; Sabin, J. R.; Diercksen, G. H. F.; Gruner, N. E. J. Chem. Phys. 1985, 83, 1702. Fitzgerald, G.; Cole, S. J.; Bartlett, R. J. J. Chem. Phys. 1986, 85, 1701. Sadlej, A. J.; Diercksen, G. H. F.; Oddershede, J.; Sabin, J. R. Chem. Phys. 1988, 122, 297. Presilla--M~rquez, J. D.; Graham, W. R. M.; Shepherd, R. A. J. Chem. Phys. 1990, 93, 5424. Suenram, R. D.; Lovas, E J.; Matsumura, K.Astrophys. J. 1989, 342, LI03. Ross, S. C.; Bunker, P. R. J. Mol. Spectrosc. 1983, 101, 199. Ross, S. C." Butenhoff, T. J.; Rohlf'mg, E. A.; Rohlfing, C. M.J. Chem. Phys. 1994, 100, 4110. Farrow, R. L.; Rakestraw, D. J. Science 1992, 25, 1894. Zhang, Q.; Kandel, S. A.; Wasserman, T. A. W.; Vaccaro, P. H. J. Chem. Phys. 1992, 96, 1640. Buntine, M. A.; Chandler, D. W.; Hayden, C. C. J. Chem. Phys. 1992, 97, 707. Butenhoff, T. J.; Rohlfing, E. A. J. Chem. Phys. 1992, 97, 1595. Eichler, H. J.; Gunter, P.; Pohl, D. W. Laser-Induced Dynamic Gratings; Springer-Verlag: BerSn, 1986. Butenhoff, T. J.; Rohlfing, E. A. J. Chem. Phys. 1993, 98, 5460. Butenhoff, T. J.; Rohlfing, E. A. J. Chem. Phys. 1993, 98, 5469. Ba~id, Z.; Light, J. C. Ann. Rev. Phys. Chem. 1989, 40, 469.

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STU DY OF SMALL CARBON AN D SILICON CLUSTERS USING NEGATIVE ION PHOTODETACHMENT TECHNIQUES

Caroline C. Arnold and Daniel M. Neumark

I. II. III.

IV.

V.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negative Ion Photodetachment Studies o f Carbon Clusters . . . . . . . . . . A. Photoelectron Spectroscopy o f C n (n = 2 - 11) . . . . . . . . . . . . . . B. Threshold Photodetachment Spectra o f C~ and Cg . . . . . . . . . . . . Negative Ion Photodetachment Studies o f Silicon Clusters . . . . . . . . . . . A. SiS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Si3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Si4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Metal and Semiconductor Clusters Volume 3, pages 113-148. Copyright 9 1995 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-788-2

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CAROLINE C. ARNOLD and DANIEL M. NEUMARK

I. I N T R O D U C T I O N A primary objective in the field of atomic and molecular clusters is to understand the evolution of physical and chemical properties of clusters as a function of size. In particular, small carbon and silicon clusters have been the focus of a recent upsurge in both experimental and theoretical work because of their relevance in several fields of study; carbon clusters have been found to be important species in combustion, 1 small silicon clusters have been shown to be involved in CVD processes, 2 and both have importance in astrophysics. 3 One of the more intriguing aspects of these two systems is that although carbon and silicon are in the same periodic group, the structures of their small clusters (less than 10 atoms) are predicted to be remarkably different. All of the carbon clusters are predicted to form linear chains, with several having close-lying monocyclic structures. 4 On the other hand, ab initio calculations predict more dramatic geometry changes for silicon clusters as a functiori of size, with the clusters larger than four atoms having three-dimensional structures. 5 The motivation of the work presented in this chapter is the determination of vibrational frequencies and the energetics of the low-lying electronic states of these elusive species as an important step towards their characterization. Spectral studies of carbon clusters have been ongoing for one hundred years, 6 but more recent work of note has been the high-resolution IR absorption spectra obtained by Saykally and co-workers, characterizing the geometries and the highest frequency asymmetric stretch mode of linear C 3 through C 7 and C9.7 Substantially lower resolution negative ion photodetachment studies have given electron affinities for these linear structures, 8-1~ as well as several ground-state vibrational frequencies, which will be discussed in this chapter. Interest in silicon clusters has been less historic, and most information regarding their structural and bonding properties other than for the dimer 11 has been primarily limited to ab initio calculations 12-15and several negative ion photodetachment studies, including those in this chapter. 16-21 In spite of the relatively low resolution of negative ion photodetachment techniques, however, these methods of study afford certain advantages over conventional absorption techniques. Negative ions are inherently mass selectable. Since most cluster sources simultaneously generate numerous ionic and neutral species of all sizes, the ability to mass select prior to spectroscopic investigation is important in eliminating ambiguity in species identification. Additionally, the selection rules for photodetachment are different from those of optical spectroscopy. Neutral states that are forbidden in emission or absorption experiments can often be accessed from the anion, generally giving a direct measurement of their excitation energies. As in electronic absorption, totally symmetric modes are usually most active in the spectrum, so the vibrational frequencies obtained for the neutral ground electronic state are complementary to those obtained by use of IR absorption techniques.

Small Carbon and Si#con Clusters

115

The focus of this chapter is the application of two cooperative negative ion photodetachment techniques for the study of small carbon and silicon clusters. "Fixed frequency" photoelectron spectroscopy is used to map out the vibrationally resolved electronic structure of the clusters, and the higher resolution threshold photodetachment (also known as zero kinetic energy electron, or ZEKE) spectroscopy is capable of resolving fine-structure, lower frequency vibrational modes, closely spaced sequence bands, etc. We have thus far obtained vibrationally resolved photoelectron spectra C n (n = 2 through 11)22and Sin (n = 2 through 4), 18'19 and threshold photodetachment spectra for C~,23 C6 ,24 and Sin (n = 2 through 4). 18'2~ The spectra presented and discussed below reflect the differences between carbon and silicon clusters; the carbon cluster spectra are primarily composed of linear anion to linear neutral transitions, whereas the silicon cluster spectra reflect greater electronic complexity and substantial geometry changes between the anion and multiple, close-lying neutral states. Carbon and silicon clusters have been investigated by others using negative ion photodetachment techniques. Ultraviolet photoelectron spectra have been obtained for Sin (n = 3 through 12) 16and C~ (n = 2 through 29) 8 by Smalley and co-workers. The resolution of the apparatus was not adequate to resolve individual vibrational transitions, but it did serve to determine electron affinities and electronic band structures. Considerably higher resolution (60--100 cm -1) photoelectron spectra were obtained for C 2 and C 3 by Lineberger and co-workers, 9 and for Si2 by Ellison and co-workers. 17 Additionally, negative ion photodetachment techniques have been successfully applied to the investigation of metal clusters. 25 The organization of this chapter is as follows. In Section II, the experimental techniques are briefly described. Section III discusses the results of the photoelectron spectra of C 2 through C~1 and threshold photodetachment spectra of C 5 and C 6, and Section IV discusses the results of the photoelectron and more recently obtained threshold photodetachment spectra of the small silicon clusters. These sections will be summarized with concluding remarks in Section V.

Ii. EXPERIMENTAL METHODS Both the fixed frequency photoelectron and the threshold photodetachment techniques involve the generation of an internally cold, mass-selected negative ion beam, but different photodetachment and electron detection schemes are employed. The two instruments will be discussed briefly in this section; more detailed descriptions may be found elsewhere. 26 In photoelectron spectroscopy, the negative ions are photodetached with a fixed-frequency laser, and the kinetic energy distribution of the ejected photoelectrons is measured. In our case. this is achieved with an electron time-of-flight analyzer. The photoelectron kinetic energies (eKE) are given by, eKE = hv - EA - T O+ ~

- E ~ + E~)

(1)

116

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

where hv is the detachment laser photon energy, EA is the neutral electron affinity, T O and T O are the term values of the specific neutral and anion electronic states, respectively, and E ~ and E~ are the vibrational energies with respect to the zero point energies of the neutral and anion states, respectively. The electron kinetic energy distribution therefore shows peaks from transitions between anion and neutral levels. The energy resolution of the electron time-of-flight analyzer in our spectrometer is 8 meV at 0.65 eV eKE and degrades as (eKE) 3/2 at higher electron kinetic energies. Although adequate to resolve most symmetric stretch progressions in the neutral carbon and silicon clusters, this is insufficient to discern rotational structure and lower frequency modes that may be active in the spectra. Figure 1 shows a schematic of the negative ion photoelectron spectrometer used in these studies. The negative ions are produced in a laser vaporization/pulsed molecular beam source (1) similar to that developed by Smalley and co-workers. 27 A XeC1 excimer laser is focused onto a rotating and translating graphite or silicon rod. The resulting plasma is entrained in a pulse of He from a pulsed solenoid valve and expanded through a channel into the source vacuum chamber. This configuration generates sufficient quantities of cluster anions, precluding the need of an electron gun as further means of attaching electrons to neutral clusters. A Wiley-

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5mall Carbon and Sificon Clusters

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MacLaren time-of-flight mass spectrometer 28 is used to mass select the ion of interest prior to photodetachment. The cluster anions are extracted from the source region by applying a pulsed field to the electrode (2) perpendicular to the molecular beam axis. The ions are then further accelerated to 1 keV and allowed to separate out by mass in the 1.4-m flight tube. The pulsed photodetachment laser crosses the molecular beam at (3) just prior to their detection, and is timed so that it interacts with the ion of desired mass. The spectra shown in Sections III and IV were obtained by use of the third harmonic (355 nm, 3.493 eV)or fourth harmonic (266 nm, 4.661 eV) output of a Nd:YAG laser, or an H 2 Stokes-shifted energy thereof. The small fraction of the photoelectrons ( 10-4) that pass through a series of baffles (4) and hit the electron detector (5) found at the end of the 1-m field-free drift tube are then energy analyzed. Considerably higher resolution spectra can be obtained by use of threshold photodetachment spectroscopy. This method involves photodetaching the negative ions with a tunable pulsed laser and detecting only those photoelectrons produced with nearly zero kinetic energy as a function of detachment wavelength. The electron signal plotted against the detachment wavelength therefore consists of peaks, each corresponding to transitions between levels of the anion and levels of the neutral, since nearly zero kinetic energy electrons will be produced only when the photon energy is equal to such a transition. This method of detection in which discrimination against energetic electrons is employed is similar to techniques developed by Miiller-Dethlefs et al.29 for threshold photoionization of neutrals. A schematic of the threshold photodetachment spectrometer is shown in Figure 2. Again, the ions are generated in a Smalley-type cluster source (1). For all of the threshold spectra shown in the following Sections, save the Si 2 spectrum, the second harmonic output of a Nd:YAG laser was used rather than the XeCI excimer laser for laser vaporization. An added modification to the cluster source for the production of Si3 and Si4 was use of a piezoelectric valve 3~ in lieu of the solenoid type valve, which greatly enhanced cluster cooling. The negative ions that pass through a 2-mm skimmer are collinearly accelerated to 1 keV. Mass selection is achieved with a 1-m long beam-modulated time-of-flight mass spectrometer. 3~ The massseparated ions then enter the detection region where they are photodetached in the region labeled (2) by a (pulsed) excimer-pumped dye laser 60 cm upstream of the ion (3) and electron (4) detectors (the electron detector is located out of the plane above the | The selective detection of zero kinetic energy (threshold) photoelectrons is achieved by photodetaching the anions when the interaction region (2) is initially field-free. A weak extraction pulse is then applied along the ion beam axis 200-300 ns after photodetachment occurs. The delay between detachment and extraction allows the higher kinetic energy electrons to spatially separate from the nearly zero kinetic energy electrons. Energetic electrons that scatter perpendicular to the ion beam axis are blocked upon extraction by the apertures (5) located between the detachment region and the electron detector, whereas those that scatter along the

Threshold Photodetachment Spectrometer

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Small Carbon and Silicon Clusters

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ion beam axis will emerge from the extraction region with different kinetic energies than the threshold electrons, giving them different arrival times at the detector. Discrimination against the energetic electrons is then achieved by gated integration of the threshold electrons. This combination of spacial and temporal filtering gives an energy resolution of as good as 3 cm -1. For several of the spectra presented in the following Section, particularly the Si~ and Si 3 spectra, resolution was sacrificed to increase the electron signal. The resolution of the apparatus as it was employed for these two species is estimated to be about 10 to 15 crn-~. The apparatus also has the capability of collecting all of the photoelectrons as a function of photon energy when the ions are detached immediately adjacent to the electron detector (| The information gained in this mode, which maps out the total photodetachment cross section of the ion, is useful for a more precise determination of where thresholds lie. It is also instrumental in the observation of transitions to excited anion states, if they exist, by means of two-photon detachment or autodetachment through the excited anion state. Such transitions appear as sharp features in the total photodetachment cross section spectrum, as they did for C6 .24

!11. NEGATIVE ION PHOTODETACHMENT STUDIES OF CARBON

CLUSTERS

A. Photoelectron Spectroscopy of Cn (n = 2 - 11 )

General Considerations In photoelectron spectroscopy, the intensity of transitions from a particular vibronic level of the anion to different vibrational levels within an electronic state of the neutral, x)" and x)', respectively, is assumed proportional to the Franck-Condon factors: Intensity o~ [ <x)"

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If the anion and neutral are of the same symmetry, transitions between the ground vibronic state of the anion to totally symmetric vibronic levels in the neutral will be the most intense in the spectrum. Moreover, geometry differences between the anion and neutral can be estimated by simulating the observed vibrational progressions. This can be achieved most simply by approximating the anion and neutral vibrational wavefunctions as products of harmonic oscillator wavefunctions. The displacement of the anion wavefunction along the appropriate neutral coordinate can then be varied until the simulated progression profiles match the spectrum per Equation (2). In some cases, the displacements obtained in this manner can be transformed into actual bond distance and angle differences between the anion and neutral geometries. Another analytical tool of photoelectron spectroscopy is the use of laser polarization to discern between overlapping electronic transitions. As many of these

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Small Carbon and Silicon Clusters

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elemental clusters are open-shell species, overlapping transitions are likely problem. However, photoelectrons detached from different molecular orbitals of the anion (which allows access to the different neutral electronic states) will generally have different angular distributions with respect to the laser polarization. The intensity of a particular electronic band in the spectrum will therefore change relative to other electronic bands at alternative polarizations.

Results and Discussion of the Cn PhotoelectronSpectra The description of the photoelectron spectra of C n (n = 2 - 11) will be brief, qualitative, and primarily concerned with general trends. Slightly more emphasis will be placed on the spectra of C~ and C 6 for the purpose of comparison with the threshold photodetachment spectra of these two molecules, presented in Section IIIB. The 266-nm photoelectron spectra of C 2 through C~i are shown in Figure 3. The even-numbered clusters are shown in the left column on a 0.0 to 2.0 eV scale and the odd-numbered clusters are shown in the fight column on a 0.0 to 3.0 eV scale. Note that, from Equation (1), the lowest kinetic energy electrons correspond to transitions from the anion to the highest neutral levels energetically accessible by the photon energy. Several things are immediately obvious from the spectra. First, most of the spectra are qualitatively very similar. Except for the C~0 spectrum, which exhibits only a mass of unresolved signal, and the C 2 and the C 3 spectra, which show contributions from several electronic transitions, the spectra are dominated by a single, intense peak that represents the electron affinity of the neutral cluster. Second, these peaks are found at lower eKE for the even-numbered clusters than for the odd-numbered clusters. This leads to the conclusion that the spectral features are due to linear neutral <---linear anion transitions. The odd-even alteration of the electron affinities for the linear species was predicted over thirty years ago by Pitzer and Clementi, 32 and is due to the odd-numbered linear clusters being closed-shell species (Iz~), whereas the even-numbered linear clusters are open-shel!(3E~). Also, as cluster size increases, the electron affinities increase. The linear electron affinities for n = 2 through 9 and 11 are summarized in Table 1. The lower intensity peaks seen in the spectra can in almost all cases be attributed to either vibrational progressions of the neutral or to "hot bands." The photoelectron spectra of C~ and C 3 show distinct transitions to multiple neutral electronic states. Several features in the spectra of C 4 through C 8 may also be due to low-lying neutral excited states, but, for these molecules, assignment of features to excited neutral states is less certain. Discernment between electronic bands in the C 2 and C 3 spectra was aided by variation of the laser polarization with respect to the direction of electron collection. The two lowest lying electronic states of the carbon dimer, the A" 1E~and the 31-I,states, have previously been characterized by Lineberger and co-workers 33 who used negative ion photodetachment, and most of the high kinetic energy peaks in the C~ spectrum can be attributed to transitions

122

CAROLINE C. ARNOLD and DANIEL M. NEUMARK Table I. Electron Affinities of Linear C2-11 from Fixed-Frequency Negative Ion Photoelectron Spectra Molecule

Electron Affinity(eV)

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4.185 (0.006)

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to these two states from the ground 2~g anion state, as they are labeled on the spectrum. Peak c, however, is an electronic hot band originating from the first excited 2IIu anion state. The less intense structure found at lower eKE's was not energetically accessible in previous photodetachment experiments. These include transitions between both anion states and the higher lying IH u neutral state. The lower intensity transition to the ground electronic state of C 3 (as in all odd-numbered linear clusters, it has a 1L'~gground state) exhibits floppiness evidenced by the poorly resolved shoulders of the origin transition, which are attributed to excitations in the bend mode. The sharp and intense peak at very low eKE marks the first determination of the excitation energy of the first excited ~ 3H u neutral state in gas phase: 2.118 _+0.026 eV. This value is nearly identical to those obtained in matrix studies. 34 Transitions to only the lowest electronic states of the linear clusters were observed inthe 4.66-eV photoelectron spectra of C a, C 6 and C 8 owing to the high electron affinities of the neutral species. However. in the case of C a , evidence for vibronic coupling was seen from the appearance of transitions to odd quanta in a bend mode. By symmetry arguments, transitions from the totally symmetric ground level of the anion are allowed to only even levels of the non-totally symmetric modes (but any level in a totally symmetric mode), but this can be overcome if vibronic coupling lends symmetric character to an odd level. The lower eKE peak E in the spectrum was tentatively assigned to the 1As neutral state because the spacing between it and the origin of the 3s transition (2000 crn-1) did not match any predicted vibrational frequency. Structure observed in the C 6 spectrum is more sparse. Peaks B and C, which are poorly resolved shoulders found about 200 and 480 cm -l to the low eKE side of the main transition, are attributed to a sequence band and a transition to the lowest frequency symmetric stretch (v3) of the neutral. The latter assignment has been

Small Carbon and Sificon Clusters

123

made in spite of the poor agreement with the calculated value (673 crn-1), although the possibility was raised that is could be a transition to two quanta in the v 7 (r~g bend) mode. The more intense peak 1), located 1315 cm -1 to lower eKE from the origin, was assigned to a transition to the fundamental v 2 level, again in disagreement with the ab initio frequency, 1759 cm -1. The possibility that it could be the lAg + e-<---2Hu origin was also considered, as the 1Ag-3~g splitting for the even-numbered neutral clusters is predicted to decrease as cluster size increases. However, upon comparison with the threshold spectrum (see Section IIIB), this possibility was rejected. The remaining structure, peak E, is due to a hot band. The C 8 spectrum only exhibited two distinct peaks: the origin and a less intense peak 565 cm -1 to lower eKE, which was tentatively assigned to transition to the lowest frequency symmetric stretch (v4) although, again, it may be due to the lAg neutral state. Also present in the spectrum is a fairly intense, structureless tail, which will be discussed in relation to the C~0 and C~l spectra. The 266-nm photoelectron spectra of the odd-numbered clusters, C 5 through C 9, did not reveal any more structure than the even clusters, in spite of their lower electron affinity. Aside from the linear neutral (IL'~g)~-- linear anion (either 2Hg or 2I'lu) transition origin, most peaks in the spectra are only partially resolved. For C 7, it is believed that the presence of excitation in low-frequency bend modes (C 7 is believed to be quite floppy, as is C a) contributes to the blurring of the spectrum. Peak B is assigned to the low-frequency symmetric stretch (v3). whereas peaks C and l) could be assigned to either double quanta in a bend and antisymmetric stretch modes, or to an excited electronic state of the neutral. The spectrum of C 9, on the other hand, is interpreted as showing excitation only in symmetric stretch modes. The 355-nm photoelectron spectrum was obtained for C~ (and shall be presented in Section IIIB, Figure 4) in addition to the 266-nm spectrum shown. It reveals better resolved transitions to (presumably) even quanta in all three bend modes of the neutral. Notably, only the lowest frequency symmetric stretch (v 2) appears to be active. The 355-nm spectrum also reveals low intensity and very irregular structure to lower eKE, which possibly could be attributed to a low-lying excited neutral state. The spectra of C~0 and C~l are startlingly different to the other spectra. They both exhibit an intense unresolved mass of signal, although the Cll spectrum shows some sharp structure that, in analogy to the smaller odd-numbered clusters, may be due to activation of the lowest frequency symmetric stretch mode of the linear neutral. (It is possible that similarly sharp structure would be observed in the C~0 spectrum if the photon energy were greater; the linear electron affinity for Cl0 should be greater than for C 8, which barely shows up on the 266-nm spectrum.) The broad signal mass, on the other hand, suggests considerable geometric rearrangement between the anion and neutral. It is believed to be due to either cyclic neutral ~-linear anion or cyclic neutral <-- cyclic anion transitions. Transitions of this type may also be responsible for the high eKE tails seen in the C 6 and C 8 spectra.

124

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

In summary, the photoelectron spectra of the odd-numbered clusters reveal excitation primarily in the lowest frequency symmetric stretch mode as well as in the bend modes, which is not a usual feature of photoelectron spectra. This suggests a very small overall length difference between the anion and neutral species, but a large difference in the bend potentials in conjunction with mode coupling in the neutral species. The even-numbered clusters (excluding C 2 and Cl0) exhibit structure which could not definitively be assigned. The C 4 spectrum shows evidence of vibronic coupling with a higher lying state (not directly observed) by the appearance of a fundamental level in a bend mode. The vibrational frequencies extracted from the C 6 spectrum cannot be reconciled with the calculated frequencies. The C 8 spectrum reveals very limited structure owing to its high electron affinity. Although the photoelectron spectra leave many questions regarding the vibrational properties of the ground and excited electronic states of the neutral, they have served to determine to a better degree of accuracy the electron affinities of the linear structures as well as to confirm that the linear anions are very similar in geometry to the linear neutrals. More definitive information regarding the C 5 and C 6 species has been extracted from the higher resolution threshold photodetachment spectra of the anions.

B. Threshold Photodetachment Spectra of C~ and C~ General Considerations Although it is desirable to obtain the higher resolution threshold photodetachment spectra for all of the carbon clusters studied using photoelectron spectroscopy, the ability to acquire threshold photodetachment spectra is contingent on the photodetachment cross section near threshold. The Wigner threshold law 35 gives that, near threshold, the photodetachment cross section for an atomic system goes as, (~ or (I0(Ehv

_~

q+l/2

"thresholdJ

(3)

where Ehv-EthresholdiS the difference between the detachment photon energy and the transition energy between an anion and neutral level, and l is the angular momentum imparted upon the photoelectron. For l = 0 (s-wave detachment) the cross section rises sharply above threshold, but for l > 1 (p, d...-wave detachment), the cross section is very small near threshold, making this technique insensitive to transitions other than those involving s-wave detachment. Reed et al. 36 extended the threshold law to polyatomic anions with the end result that s-wave photoelectrons are those detached from orbitals that transform as x, y, or z in the anion symmetry. This limitation confines our studies to only those carbon clusters in which the neutral ~ anion transition involves the removal of a ~u electron, i.e., C~, C~, C 6, C 9, etc. Since C2/C 2 have already been exhaustively

Small Carbon and Sificon Clusters

125

studied, we have focused our attention on C~ and C 6 (we have not yet been successful in our attempts to obtain the C 9 threshold photodetachment spectrum).

Results and Discussion of the C~ Threshold Photodetachment Spectrum The threshold photodetachment spectrum of C~ (solid line) superimposed onto the 355-nm photoelectron spectrum (dotted line) is shown in Figure 4. There are two distinct bands labeled X and a in the threshold spectrum; they are distinguished from each other both by their different vibrational structure and peak profiles. The threshold band X, which unquestionably corresponds to band X in the photoelectron spectrum, comprises a dominant double exhibiting a 22-crn -1 splitting, as well as irregularly spaced lower intensity doublets found primarily at higher photon energies. For each distinct doublet, the lower energy peak is less intense than its higher energy counterpart. The appearance of band a is somewhat startling. Although there is some structure found in the corresponding energy range in the photoelectron spectrum that has been conjectured as being due to an excited neutral state, neither the intensity nor the positions of the congested peaks come close to

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126

CAROLINE C. ARNOLD and DANIEL M. NEUMARK ....

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matching the intensity of this band in the threshold spectrum. (The 266-nm photoelectron spectrum shown in Figure 3 exhibits almost no structure in this energy region.) Moreover, the broadness of the features (about 100 cm -1 FWHM) in the threshold spectrum and the unusual peak intensiiy distribution prevent us from confidently assigning the band to a linear neutral <---linear anion transition. More can be said about band X, however. Figure 5 shows the threshold photodetachment spectrum of band X of C~ obtained under colder ion source conditions. As discussed in Section IIIA, calculations on both the anion and neutral linear structures indicate a very small difference in geometry between the two. The most u transition intense peak, AI, has therefore been assigned to t h e l ~ g - I - e - ~ - - - 2 H origin, as in the photoelectron spectrum. The doublet structure of the transition is due to the spin-orbit splitting in the anion, where the most intense peak in the doublet (Al) is from transitions from the ground 21-I1/2spin-orbit level and the less intense peak (A2) is due to transitions from the 2H3/2 spin-orbit excited state. This energy interval between A 1and A 2, 22 cm -1, is the 21-Iuspin-orbit splitting. Transitions to the low-frequency bend levels (peaks B, C, and Dl, 2) and the symmetric stretch level (peak El,2) in the neutral are much better distinguished in the threshold spectrum relative to the photoelectron spectrum. Their positions give

5mall Carbon and Sificon Clusters

127

the following neutral frequencies: v 5 = 216 cm -1, V 6 = 535 cm -1, V 7 = 106 cm -1, and v 2 = 779 cm -1. These frequencies are in good agreement with ab initio calculated frequencies. 37 Also observed in Figure 4 are hot bands, al, 2 and bl, 2, which should be due to population of the lowest frequency (v 7) fundamental level of the anion. Peak a I is only 91 cm -l from the origin, which is too small for a 1 to be due to the 70 transition. Instead. it is most likely the 71 transition, giving an anion v 7 frequency of 200 crn-1. This large change between the anion and neutral frequencies (i.e., the anion and neutral bend potentials) allows for overlap between the ground vibrational wavefunction of the anion and the neutral v 7 overtone wavefunction. Peaks B and C are much broader than the peaks in the A or E doublets. This is believed to be due to anharmonicity. Peak D, because of its position, is assigned to a combination level of two quanta in each of the two lowest frequency bend modes (72502): If this assignment is correct, the peak is unusually intense and well resolved relative to peaks B and C. This could be the result of a Fermi-type resonance, in which the component of the 2v 7 + 2v 5 level with X; symmetry and vibrational angular momentum l = 0 can couple with the v 2 = 1 (symmetric stretch, peak El, 2) level, lending more intensity to the transition to the particular X;, l = 0 level. In summary, the threshold photodetachment spectrum of C~ is very similar to the photoelectron spectrum except for the unexplained appearance of band a. The threshold spectrum reveals fine structure due to spin-orbit splitting in the anion (further evidence that we are observing linear to linear transitions). The geometry change between the anion and neutral is confirmed to be small by virtue of the low degree of excitation in the symmetric stretch mode. Considerable activation of the bend modes was observed, however, which occurs because the bend potentials of the anion and neutral are so different. The neutral frequencies obtained are in good agreement with ab initio calculations.

Results and Discussion of the C~ Threshold Photodetachment and Total Photodetachment Cross Section Spectra The threshold photodetachment spectrum of C 6 is shown in the upper panel of Figure 6. The peak profiles in this spectrum are similar to those in the C~ spectrum. The doublet structure again reflects the spin--orbit splitting in the 21-Iuanion state. The overall profile of the electronic band, however, is very different. The C 6 threshold photodetachment spectrum shows the intense origin transition (A1,2), as in all of the other C~ spectra, and relatively intense transitions (DI, 2, G1, 2 and 11,2) to levels in three different vibrational modes of the neutral. There are no lower intensity features apparent in the spectrum, but the signal-to-noise ratio of the spectrum is such that lower intensity transitions, such as those observed in the C~ photodetachment spectrum, would be obscured. In spite of the significant excitation of bend modes seen in the carbon cluster anion photoelectron spectra and the C 5 threshold spectrum, it is still expected that the most intense transitions would be to fundamental levels in the totally symmetric

128

CAROLINE C. ARNOLD and DANIEL M. NEUMARK .

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Small Carbon and Sificon Clusters

129

fundamental levels) to perform simulations within the Franck--Condon approximation (Section IIIA). The vibrational wave functions are taken to be the product of three harmonic oscillator wave functions corresponding to the three symmetric stretches. By simulating the experimental intensities, we obtain normal mode displacements that can in turn be transformed to bond length differences. From our simulations, we have determined that the outer bond in the anion is only 0.005/~ greater than for the neutral, whereas the center bond is shorter in the anion by 0.057 .~ and the intermediate bond is 0.057/~ longer in the anion. These bond distance changes are reconcilable with the orbital from which the electron is detached; the n, orbital is bonding for the central and outer bonds, and is antibonding for the intermediate bond. 39 However, these geometry changes should be treated with caution, since their determination included making several approximations. The disparity between the calculated and experimentally determined symmetric stretch frequencies presents a compelling problem. The antisymmetric stretch frequencies determined from a combination of gas-phase and matrix IR absorption studies have been in excellent agreement with the calculated frequencies. 4~It would seem that the unexpectedly low symmetric stretch frequencies would be accompanied by at least one unusually low antisymmetric stretch frequency, since all of the modes are determined from the same C = C bond force constants. This, however, is apparently not the case. Clearly, this matter requires further attention. Although the threshold photodetachment spectrum of C 6 is provocative, the total photodetachment cross section of C 6 has also proven to be very interesting. Unlike the total photodetachment cross section spectrum of C 5, which exhibited only the sharp photoelectron signal increases at threshold, the total photodetachment cross section spectrum of C 6, shown in the bottom panel of Figure 6, reveals groups of sharp and intense peaks found at slightly lower energy relative to the linear neutral linear anion transitions. Also observed are several less intense but equally sharp features that do not correspond (apparently) to any direct detachment transitions. The presence and nature of the sharp structure in the total photodetachment cross section spectrum indicates the existence of a loosely bound excited anion state that is virtually identical (vibrationally) to the neutral ground state. From the position of the apparent origin of the sharp structure, it appears that this state is bound only by 43 c m-1 with respect to the detachment continuum, making any vibrationally excited levels of the excited anion subject to vibrational autodetachment. The autodetachment features fall into groups of peaks comprising an intense peak that is insensitive to ion source conditions found at the high-energy end of the group, and less intense peaks that appear to be either vibrational or spin--orbit hot bands. The position of the sequence bands relative to the cold transition indicates that the frequencies of the excited anion state are less than those of the ground anion state for the lowest frequency bend modes. The nature of this excited anion state is uncertain. Its similarity to the neutral state and proximity to the detachment continuum are characteristics of an electrostatically bound state. If the r~-system of the C 6 neutral core is polarizable enough,

130

CAROLINE C. ARNOLD and DANIELM. NEUMARK

the outermost electron could conceivably form an image-charge-bound state, as with Au~.41 On the other hand, C 6 is an open-shell anion with an electron affinity high enough to support a bound valence state. Several bound excited states have been predicted to lie below the detachment continuum, 42 and this same phenomenon has been observed for C~.a3 These arguments suggest that the that the (C6)* we observe in our spectrum is a valence state, and we are more inclined to believe this than that it is an electrostatically bound state. Coincidentally. as both C~ and C~ have shown resonances in the total photodetachment cross section spectra owing to excited anion states, so have Au~ 44 and Au 6. These resonances, however, have not been observed in the total photodetachment cross section spectra of Si~ or Si 6.

IV.

NEGATIVE I O N P H O T O D E T A C H M E N T STUDIES OF SILICON CLUSTERS

The organization of this section is different than that of the last. The photoelectron and threshold photodetachment spectra for each silicon cluster will be simultaneously discussed, the reason for this being the importance of the interplay between the two spectra in gaining a better understanding of the clusters. The analysis of the congested Si~ photoelectron spectra were greatly facilitated by comparison with the higher resolution threshold photodetachment spectra. By that same token, of all the electronic transitions congesting the silicon cluster spectra, quite a few involve p-wave transitions (or, as in the case of Si 3, s-wave transitions that were so weak as not to appear in the threshold photodetachment spectrum), rendering the threshold photodetachment spectra of these clusters incomplete. Hence, the two types of spectra shall be presented and discussed together.

A. Sii The silicon dimer has been studied spectroscopically for thirty years, 11 but the energetics of the many low-lying excited neutral (and anion) states have been determined only recently by use of the combination of photoelectron spectroscopy and threshold photodetachment spectroscopy of Si~. 18The silicon dimer neutral has 3 and x u.4 Two nearly three low-lying molecular orbital configurations: ~ x2, degenerate triplet and four singlet states resulting from these configurations are predicted to lie within 1.5 eV of each other, with the singlet states lying above the two triplet states. The 3Z~gstate (o~gx2u)has long been accepted as the neutral ground 1 3 state. The 3 rIu state (t~gn;u) has been predicted to lie very close in energy, but no direct emission or absorption between the two states has been seen. Emission between two of the four singlet states had been observed, 45 but, owing to optical selection rules, no transitions between the singlet states and the lower lying triplet states are allowed, precluding the ability of conventional optical techniques to determine the excitation energies of the 31-Iuand the four singlet states.

(~g~'u'l

Small Carbon and Silicon Clusters

131

d~Y~

c Y_, blH~

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Figure 7. Low-lying excited states of Si~ and Si2, and the one-electron transitions between them. It would seem that this is the ideal system for photodetachment studies, but photodetachment spectra of the dimer anion are complicated by the presence of two 23 14 nearly degenerate anion states, 2Hu (ash:,,) and 2 ~ (asrcu). One-electron transitions to all six low-lying neutral valence states are possible from either one or the other anion state, and in some cases, both. Figure 7 depicts the anion and neutral states in the order in which they are predicted to lie (which has subsequently been confirmed). The one-electron transitions between the states are indicated by the vertical arrows. Two-electron transitions between the anion and neutral levels (e.g., between t h e 2~g anion and 3E-~sneutral) will be too weak to be observed in the spectra. Figure 8 shows the 416-nm (2.977-eV) photoelectron spectrum (dotted line), which primarily accesses the neutral triplet states. The threshold photodetachment spectrum is shown as well (solid line); it will be discussed shortly. The difference between Figure 8a and Figure 8b is only the angle of the laser polarization with respect to the electron collection for the photoelectron spectrum. From the differences between the two photoelectron spectra obtained by use of different polariza-

132

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

90 = 90 ~

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Figure 8. Threshold photodetachment spectrum of the triplet band of Si~ with the 416-nm photoelectron spectra (dotted line) obtained using (a) horizontal and (b) vertical polarization superimposed onto the detachment wavelength scale. tions, it is appears that at least peaks C, D, and d are due to different electronic transitions, but a more specific assignment is difficult. By varying ion source conditions, it was found that peaks B and A were transitions from vibrationally excited levels of the anion, so peak C represents the lowest energy transition from a vibrationally cold anion level. Ellison and co-workers also obtained photoelectron spectra of Si~, 17 but their resolution was not adequate to resolve peaks D and d.

Small Carbon and Sificon Clusters

133

By superimposing the threshold and photoelectron spectra, it becomes apparent that peak d is conspicuously missing from the threshold spectrum. This is answered by consideration of the Wigner threshold law (see Section IIIB). Detachment from a x u orbital results in an s-wave photoelectron, whereas an electron detached from a o+ orbital departs as a p-wave. The only one-electron allowed p-wave transition is 3~,, + e- +-- arI,,, which leads us to unambiguously assign peak d to this transition. Also, with the higher instrumental resolution, the threshold spectrum resolves peak D seen in the photoelectron spectrum into a triplet, with peaks labeled D 1 , D 2, and D 3. Peak C is also resolved into a doublet labeled C 1 and C 2. Likewise, peaks E and B are resolved into a triplet and doublet, respectively, and they are labeled appropriately on the spectrum. The triplet structure of O1,2,3, is consistent with what is expected for a 3H <----nx; transition, where the spacing between the individual peaks reflects the spin-orbit splitting of the upper state (in this case, approximately 60 cm -1). Likewise, the C1,2 doublet is consistent with the 35".g+ e- +-- 2H u transition suggested previously, and the energy interval between C 1 and C 2 is a direct measure of the spin-orbit splitting in the 21-1u anion state, as it was with C~ and C 6. The difference in intensity between the transitions from the ground 2II3/2 level (el) and those from the excited 21I1/2 level (C2) gives the spin-orbit temperature of the anion to be approximately 125 K. From the above discussion of the triplet band, a great deal of information regarding the anion can be extracted. First, since the 31-Iu + e-<---2Z'~8 transition requires the most energy of the three allowed transitions within the triplet manifold, the ground state of the anion must be the 2X;gstate (see Figure 7). Moreover, it is confirmed that the ground state of the neutral is in fact the 3X~ state. The T e of the 2IIu state is determined by the energy interval between peaks d and D on the photoelectron spectrum, which is 25 + 10 meV (200 + 80 cm-1). Anion frequencies for the two states can be determined from the hot bands. The temperature-dependent doublet B1,2 has the same profile as Cl, 2 but is found lower in energy than el, 2 by 533 + 5 cm -1, a frequency typical of the silicon dimer, which suggests that it is a transition from the fundamental level of the 2H u anion state. Similar hot bands for D1,2,a, are partially obscured by Cl, 2, but the anion frequency for the 2Xg + state can be estimated with less certainty as 528 + 10 cm -l. The anion bond lengths can also be approximated by use of Franck-Condon analysis (see Section IIA). The bond distances and vibrational frequencies of the 31-Iu and the 3Z~ states are well characterized from high-resolution work done previously, and the anion frequencies have been determined from these spectra. The remaining parameters, anion bond distances and vibrational temperature, are then adjusted until the simulation matches the spectrum. The results of the fits are listed in Table 2. New information regarding the neutral triplet states can be extracted from the spectrum as well. Because the neutral ground state cannot be accessed from the anion ground state by a one-electron transition, the electron affinity can only be determined by consideration of the excitation energy of the 21-Iu state, which is determined by the energy interval between peaks d and D on the photoelectron

134

CAROLINE C. ARNOLD and DANIEL M. NEUMARK Table 2. Summary of Spectroscopic Constants of the States of Si2 and Si2 Investigated by Photodetachment Techniques State Si2 a

die + 1,,..8 c Z,g

bll-lu alAg D3FIu Si2

Notes:

Te (eV)

Bond Length (ft)

1.152 + 0.010

--

Harmonic Frequency (cm-1)

0.586 :t: 0.010 0.544 + 0.010

-2.160 + 0.005

540 + 10

0.435:1:0.002 0.041 _ 0.010

2.290 _+0.010 2.155 b

486 -+ 10 536 + 5

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509 +- 10

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533 + 5 528 --+ 10

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aEA = 2.201 :!:0.010 bSee Ref. 11.

spectrum, 25_+ 10meV (200_+ 80 cm-1). The energy o f t h e 3]~g + e- ~-- 21-lutransition plus the Eli u excitation energy yields the electron affinity, 2.201 _+0.010eV. Another goal of these photodetachment studies was to determine the excitation energy of the neutral 3Flu state. This excitation energy is equal to the energy interval between peaks C and d on the photoelectron spectrum (it is helpful to refer to the energy level diagram in Figure 7), which is 41 _+ l0 meV (330 _+80 cm-1). Analysis of the singlet band is similar to the procedure described for the triplet band, but it is more straightforward given the new knowledge regarding the anion states. As with the triplet band, several peaks in the photoelectron spectrum are not present in the threshold spectrum, which is shown in Figure 9 for the singlet manifold. The 355-nm photoelectron spectrum in the energy region of the singlet manifold (dotted line) is superimposed onto the threshold photodetachment wavelength scale for reference. It is worthwhile to note that the doublets (indicative of transitions from the 21-Iuanion state) labeled Carl,2, H ~ , and M1,2 marked the first observation of transitions to the IA_g neutral state, which has been predicted to be the lowest lying of the singlet states, 46 in agreement with our spectrum. The vibrational progression formed by these peaks is more extended than the others, indicating that the difference in bond distance between the lag neutral state and the 2Hu anion is more dramatic than for the other states. This again is consistent with the calculations. 47 The excitation energies of all of the singlet neutral states can be determined from the peak positions and consideration of the 25-meV excitation energy of the 21-Iu anion state. These are summarized in Table 2 with the other spectroscopic constants determined from our spectra. The electronic structure of this molecule is remarkably complex and the spectrum is still not completely understood. Peak L in Figure 9 cannot be attributed to

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transitions between any of the anion and neutral valence states discussed, yet it energetically fits neatly into the singlet manifold. A possible explanation for the appearance of this peak is that it is due to a transition from Si 2 trapped in an electronically excited state. More theoretical work is required to determine whether this is a feasible explanation.

B. Si~ The silicon trimer has been the focus of exhaustive ab initio efforts, 13'15 most of which conclude that the ground state is the 1A1[" .. (al)2(al)2(bl)2(b2) 2] isosceles triangle that results from Jahn-Teller distortion of the 1g" [...(2al')2(la2")E(2e') 2] state. The stability of this state is attributed to second-order Jahn-Teller interaction with a higher lying (undistorted) 1Al' state. However, the D3h 3A2' state, which has the same configuration as the IE' state (but with parallel spins in the two e' orbitals),

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of Si]. 136

137

Small Carbon and Silicon Clusters

]'able 3.

Summary of Excitation Energies of the Low-Lying Excited States of Si3 a

Band D C B A X

Neutral State IB 1 3B l 3A1 IB 1 IA 1, 3A2'

Te (eV) 1.67 1.10 0.89 0.45 0

Note: aEA= 2.300+ 0.001 eV.

is predicted to be nearly degenerate with the ~A~ state. The anion ground state is inferred by adding an electron to the 3A2' (or 1E' configuration), resulting in a 2E' state, which is also subject to Jahn-Teller distortion to (C2v) 2,41 [...(b2)2(al) l] and 2B2 [...(b2)l(al) 2] components. 13Higher level calculations predict that the 2A1 state represents the minima and 2B2 the saddle point on the Jahn-Teller distorted D3h potential. The barrier to pseudorotation is calculated to be only 160 cm -1. The 355-nm and 266-nm photoelectron spectra of Si3 are shown in the upper and lower panels, respectively, of Figure 10. In the 266-nm spectrum, there are at least five distinct bands, labeled X, A, B, C, and I), all within 2 eV of each other. The lower photon energy spectrum (upper panel) accesses only bands X, A, and B, although band A is hardly discernible from the noise. The inset on this spectrum shows band X on an expanded ordinate (dotted line) with the threshold photodetachment spectrum (solid line) superimposed onto the photoelectron spectrum energy scale. This was the only region for which we were able to obtain a threshold photodetachment spectrum; the photodetachment cross section near threshold seemed particularly small for this molecule. The assignment of the photoelectron spectrum was aided by the calculations of Rohlfing and Raghavachari; 13 their high-level (QCISD(T)/6-31G*) calculations included geometry optimizations and frequencies for the 2,41 anion and the 3A2' and ~AI states, as well as other excited neutral states formed by promotion of an electron to the a 1 LUMO from the HOMO and lower lying valence levels. A summary of the band assignments based on the experimentally determined excitation energies and several frequencies observed in the photoelectron spectrum is given in Table 3. Qualitatively, the profile of the Si~ photoelectron spectrum is very different from that of the Si2 spectrum. The 266-nm Si3 spectrum exhibits at least five bands varying greatly in intensity and profile strewn throughout the energy range accessible by the photon energy. The difference in relative intensities of bands X and A to band B between the two spectra taken at different photon energies indicates a fairly strong photodetachment cross section dependence on detachment wavelength. The threshold spectrum exhibits an evenly spaced 337-cm -1 progression but

138

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

is also congested with lower intensity peaks cluttering the baseline between the progression members. By comparison of the extent of band X in the photoelectron spectrum with that in the threshold photodetachment spectrum, it is apparent that the band comprises at least two different electronic transitions. This supports the ab initio result of the 3A2" state being nearly degenerate with the ~A1 state. The frequency of the progression observed in the threshold spectrum indicates that the structure is due to the 3A2' + e- ~ 2A1 transition. At the QCISD(T)/6-31 G* level, the e' mode frequency is calculated to be 285 crn-l, ~3 but density functional studies predict it to be closer to 340 crn-l. 48 The remaining, unresolved structure observed in the photoelectron spectrum is therefore attributed to the IA l + e- ~-- 2Al transition. Geometry calculations predict a Si-Si-Si bond angle of 80 ~ for the neutral lA l state and 65 ~ for the 2Al anion state. The IA l + e- ~---2Al transition is therefore expected to produce a more extended vibraiional progression than the 3A2' + e- ~ 2A1 transition. Moreover, the active mode in the former transition is calculated to be only 148 cm -l, so it is not surprising that the progression is not resolved in the photoelectron spectrum. It is not entirely obvious why the lAl+e-~---2Al transition does not appear in the threshold spectrum, however. This transition involves removal of an electron from an a I orbital, whereas the 3A2' + e- ~ 2Al transition entails the removal of a b 2 electron, but both should produce s-wave photoelectrons. It appears that in the case of the singlet state transition, the total photodetachment cross section near threshold, a 0 from the Wigner threshold law [Eq. (3), Section IUB] is much smaller than for the triplet state transition. It is interesting to note that band B, which is very intense in the photoelectron spectra, was not intense enough to be observed in the threshold photodetachment spectrum. The transition to which it has been assigned, 3Al + e- ~ 2A1, also involves the removal of an electron from a (deeper-lying) a 1 orbital. Although it appears from the profile of band X in the photoelectron spectrum that the 3A2' state actually lies lower in energy than the IA l state, this is not necessarily the case. The origin of the IA l + e- ~-- 2Al transition may have too little intensity owing to the large geometry difference between the anion and neutral to appear in the spectrum. We cannot definitively assign which is the ground state without higher resolution spectra including both states. A closer look at the threshold photodetachment spectrum of Si 3, shown on an expanded scale in Figure 11 reveals additional structure. The peaks labeled 0, 1, 2, 3, and 4 constitute the 337-crn -I progression in the V2a(e') mode of the neutral, and b l, I~, and b a are to levels in the v I (al) mode, or combination bands of one quanta in the v 1mode with V2a vibrational quanta. These give frequencies of 501 + 10 crn-1 and 337 + 10 crn -1 for v I and v2a, respectively, which are in good agreement with the density functional calculations. The remaining structure found at lower photon energies from the origin and the peaks labeled n' and a n are due to vibrational hot bands. The position and intensity of 0', found approximately 385 cm -1 to the red of peak 0, suggests that it is a hot band transition to the ground vibrational level of the neutral, originating from the fundamental level of the symmetric bend (v 2) of

Small Carbon and Silicon Clusters

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Detachment Wavelength (nm) Figure 11. Threshold photodetachment spectrum of band X of Si~.

the anion. Peak b may similarly be a transition from the v 1 symmetric stretch fundamental, yielding an anion frequency of approximately 565 cm -l for this mode. With these anion frequencies, however, simulations of the spectrum approximating the anion vibrational wavefunction as the product of harmonic oscillators (Section IIIA) could not reproduce the positions and intensities of the remaining structure in the spectrum, e.g., peaks n" and an. Because the anion is Jahn-Teller active, then this approximation is inadequate. A more satisfactory fit of the spectrum was achieved by assuming that the Jahn-Teller distorted components of the anion are vibronically coupled via the e" mode, which reduces to the symmetric a I and antisymmetric b 2 bends upon distortion from O3htO C2vgeometry. If the distortion in the anion is adequately large with little to no barrier to pseudorotation, the vibrational energy level pattern can be described by the familiar equation for a freely pseudorotating molecule, 1

1

E = h0) l (Dl + ~) + h0)2 (132 + 2) +

Aj2

(4)

where 0)~ and 0)2 are the symmetric and undistorted e' frequencies with the quantum numbers ul and ~2, respectively, and A is the rotor constant that is inversely proportional to the reduced mass and the square of the distortion, h2/21ap 2, andj is

140

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

a half integer. The selection rule for transitions between the distorted anion and the

D3hneutral is l =j + 1/2, where I is the vibrational angular momentum of the neutral vibrational level. With Eq. (4), the sequence band structure in the threshold photodetachment spectrum can be matched assuming A = 45 cm -1. From this, the sequence band structure can be explained in the following way: the excited anion level principally responsible for peaks 2', 3' . . . . is the 0,0,3/2 level, where the first and second indices are a; 1 and a92, respectively, and the third index is j; similarly, the 0,0,5/2 level of the anion generates peaks a~, a 2, etc. Note that from the selection rules, transitions from this level to the neutral ground vibrational level or the fundamental level of the e" mode are not allowed, and this is consistent with the spectral structure. A spectral simulation (dotted line) assuming the fluxional anion is shown superimposed onto the experimental spectrum in Figure 11. A detailed discussion of the simulation has been given elsewhere, 21 but, very briefly, the simulation was generated by solving the electronic Hamiltonian with the Jahn-Teller interaction terms included:

I

H0 - E 1 _,.,2...-2i~

kP i'~ + ~sv ~

kpeir + 2gp2e2i~

(5)

HQ- E

Here, k is the linear coupling constant related to the magnitude of the distortion, g is the quadratic coupling constant, which generates a barrier to pseudorotation, p and ~ are the coordinates of the two-dimensional isotropic harmonic oscillator in cylindrical coordinates, and ~• are expansions in the undistorted two-dimensional isotropic harmonic oscillator for the degenerate E' state. The solution of this equation gives the eigenvalues and eigenfunctions in terms of the undistorted vibrational frequency and wavefunctions of the degenerate mode, which can then be applied directly to the simulation. For the simulation shown, k = 2, g = 0.005, and the undistorted harmonic frequency is scaled such that the spacing between the origin and peak O' is matched. Although the threshold photodetachment spectrum of Si 3 was not as extensive as that of Si 2, very interesting information about the trimer anion and the lowest lying neutral states was extracted. A striking comparison between electronic features in the Si2 and Si3 spectra are the singlet-triplet splittings of the neutral states, which appe~ 0n the order of about 0.55 eV for the multiple states of both Si 2 and Si 3. Therefore, in spite of Si 2 and Si 3 being very different species with very different negative ion photodetachment spectra, it appears that there is a certain electronic theme maintained at least between these two clusters.

C. Si~ The 355-nm and 266-nm photoelectron spectra of Si 4 are shown in the upper and lower panels of Figure 12. The 266-nm photoelectron curve in the lower panel is

355 nm

0.0

0.5

1.0

1.5

z .0

0 Electron Kinetic Energy (eV)

Figure 12. 355-nm (upper panel) and 266-nm (lower panel) photoelectron spectra of Si~.

141

142

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

represented by a dotted line, and the threshold photodetachment spectrum is shown (solid line) superimposed onto the photoelectron energy scale. Both the 355-nm and the 266-nm photoelectron spectra show a fairly sharp band (X) isolated at high eKE (notably absent in the threshold photodetachment spectrum). The 266-nm spectrum, in particular, reveals that from about 1.65 eV to lower eKE, however, the spectrum is congested with long and perhaps overlapping progressions, although the 355-nm spectrum shows that band A is a fairly well resolved progression of about 300 crn-1. Again, the assignment of the spectrum was aided by the QCISD(T)/6-31G* calculations performed by Rohlfing and Raghavachari (the neutral state assignments are included in the Figures). 13 With four silicon atoms, the possibility of a three-dimensional (tetrahedral or distorted tetrahedral) structure arises. However, almost all ab initio considerations of this cluster predict a lAg ground state (rhombus, D2h geometry) with the valence orbital occupation ...(b3g)2(b3,,)2(as)2(blu) 2. The lowest lying excited electronic states of Si4 result from promoting an electron from the first few occupied orbitals to the b2g LUMO. The ground state of the anion is inferred by adding an electron to the b2g orbital, resulting in a 2B2gstate. 13The absence of band X in the threshold photodetachment spectrum (Figure 13b) is therefore easily explained; the groundstate anion to ground-state neutral transition involves removal of a b2g electron, which does not depart via s-wave. Band A, on the other hand, has been assigned to the 3B3u + e- (---.2B2g transition in which a bl~ electron (s-wave) is removed. The threshold photodetachment spectrum of band A is shown on an expanded scale in Figure 13. The progression spacing is more accurately determined to be 312 +_2 c m - l , in very good agreement with the calculated 306 c m -1 V 2 frequency. 13 The inset shows how each member of the progression is actually a group of peaks consisting of an intense peak (labeled by number) with less intense peaks shading to higher and lower photon energies, those at higher energies being more pronounced. All of the side peaks are dependent on ion source conditions, and their presence implies a considerable amount of vibrational excitation in the anion. An interesting feature of these sequence bands is the peak labeled g explicitly for peak 3 in the inset of Figure 13. It is fairly intense near the origin, but becomes increasingly less intense above n = 3 until 5 and 6, after which its intensity increases again. The extended appearance of the progression in the v 2 mode can be explained by comparison of the ab initio anion and neutral geometries, shown in Figure 14. The anion has two electrons in the blu orbital whereas the neutral only has one, causing the neutral r b bond to be longer. The form of the v 2 mode is shown below the geometries; clearly the transition involves a displacement along this normal mode coordinate. From a simple, uncoupled harmonic oscillator Franck-Condon analysis of the spectrum (Section IIIA), the progression in band A can be matched given a v 2 normal coordinate displacement of 0.219/~(amu) l/2, which is again in excellent agreement with the normal mode displacement determined from the difference

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Figure 13. Threshold photodetachment spectrum of band A of Si~. between the ab initio anion and neutral geometries and the form of the normal mode coordinate. 13The simulation of the progression, considering the v 2 mode along with three other modes that will be discussed below, which is shown in Figure 15, also explains the interesting behavior of the g sequence bands. Such an intensity pattern is observed for sequence bands in modes with substantial normal coordinate displacement. The position of g relative to the cold transition gives a v 2 anion frequency of 365 + 5 cm -l, which is in good agreement with the calculated value of 383 crn-1. The long string of sequence bands shading to higher photon energies, peaks a through e (Figure 13), is not so consistent with the calculated frequencies, however. For each mode of Si4/Si 4, the anion frequency is predicted to be greater than the neutral frequency, which would give sequence bands shading only to lower photon energy, as in the case of the autodetachment sequence band structure of C 6. In the Si 4 spectrum, the higher energy sequence bands appear to be progression in two modes, one of which is spaced by 50 crn-1 (b, d, e) and another which is spaced by approximately 30 crn-1 (a, e). The two lowest frequency modes in the anon are predicted to be v 5 and v 6, also shown in Figure 14. It is not intuitively obvious from molecular orbital considerations why these frequencies should be lower in the anion than in the neutral. These two modes are included in the simulation shown in Figure 15. We have assumed the calculated neutral frequencies to be correct (v 5 = 177 crn-1 and v 6 = 159 cm-1) 13 and have varied the anion frequencies (v 5 = 125 cm -1 and v 6 = 132 crn-l) to fit the sequence band structure.

2Beg anion ~

2 : b 1o rb ital

3B 3u neutral ', / / ~

'~,,

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~!9 ....... r~...... \'".3 ,%,. 7/,

---

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i

, 2.544

V6

3

~t 7

Vs

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'g/ Figure 14. Ab initio geometries of the SJ4 ground state and first excited state of SJ4 as well as normal modes of the neutral.

144

Small Carbon and S//icon Clusters [ ....

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Detachment Wavelength (nm)

Figure 15. Franck-Condon simulation of band A in the threshold photodetachment spectrum of Si~. Band B in the photoelectron spectrum (Figure 12) has been assigned to the

3Bg (C2h) + e- (--- 2B2gtransition, which involves removing an ag electron (p-wave). However, structure is seen in the threshold photodetachment spectrum in the energy region corresponding to the rising edge of band B in the photoelectron spectrum. This is not completely unexpected; there are three states, ]B3u, 1B2g, and 3B~g,other than the 3Bg predicted to lie roughly in the energy range of band B. Of these four states, only the IB3u state involves an s-wave photoelectron. Assuming this is the accessed state, the singlet-triplet splitting for the B3u state is 0.55 eV. This energy interval is remarkably similar to the singlet-triplet splittings exhibited by Si2 and Si3. Band B in the threshold photodetachment spectrum is much shorter than band A, and the intensity distribution exhibited by the members of the progression is not typical of a harmonic Franck--Condon envelope. Moreover, there are irregularities in the peak spacings. The profile of the band is most likely perturbed by the presence of the other close-lying states, which are accessible via p-wave. Band C in the threshold photodetachment spectrum could only be obtained with very poor resolution owing to low detachment power and small photodetachment cross section. However, that we could observe it at all lends support to the assignment by Rohlfing and Raghavachari 13 to the 3Blu -I- e- (s-wave) (-- 2B2gtransition.

146

CAROLINE C. ARNOLD and DANIEL M. NEUMARK

Table 4. Summary of Excitation Energies of the Low-Lying Excited States of Si4 a Band C B (photoelectronspectrum) B (threshold spectrum) A X Note:

State

Te (eV)

3Blu 3Bg,3Big, IB2g? IBlu 3B3u lAg

2.01 5-0.02 1.37 5-0.01 0.815 5-0.010 0

aEA-- 2.17 + 0.01.

A summary of the band assignments and the excitation energies of the neutral Si4 states can be found in Table 4.

V. SUMMARY This chapter has given an overview of our studies of small carbon and silicon clusters using the combination of photoelectron spectroscopy and threshold photodetachment spectroscopy. As predicted, the spectra presented indicate very different structures for the two elements. Even the dimers of carbon and silicon are electronically very different: C 2 has a 1Zg+ (~:4) ground state whereas Si 2 has a 3~g (~g~:,) 2 2 ground state. The spectra of the small carbon clusters, which revealed the odd-even alternation of electron affinities, indicated very small differences in geometry between the anion and neutral species for the clusters with fewer than 10 atoms. The photoelectron spectra of CTo and CTI gave evidence of cyclic structures contributing to the photoelectron signal. The neutral frequencies extracted from the threshold photodetachment spectrum of C 5 are in good agreement with ab initio calculated frequencies, whereas those from the C 6 spectrum clearly call for further investigation. The spectra of the small silicon clusters were more complicated with multiple and overlapping electronic transitions. Only through comparison with extensive ab initio studies could the spectra be assigned. Although the structures and spectra of the three silicon clusters discussed here were very different, the singlet-triplet splittings determined from the spectra are similar. Spectra of the larger clusters are desired for continued comparison.

ACKNOWLEDGMENTS We would like to gratefully acknowledge Drs. Krishnan Raghavachari and Celeste McMichael Rohlfing for enlightening discussion. Moreover, we would like to recognize Don W. Arnold and Theofanis N. Kitsopoulos for their data acquisition and analysis. This research is supported by the National Science Foundation under Grants No. CHE8857636 and No. DMR-920115.

Small Carbon and Silicon Clusters

147

REFERENCES 1. Gerhardt, P.; Loftier, S.; Homann, K. H. Chem. Phys. Lett. 1987, 137, 306. Edwards, J. B. Combustion, Formation, and Emission of Trace Species; Ann Arbor Science: Ann Arbor, 1974. Heath, J. R.; O'Brien, S. C.; Curl, R. F.; Kroto, H. W.; Smalley, R. E. Comments Condensed Matter Phys. 1987, 13, 119. Kroto, H. W.; McKay, K. Nature 1984, 331,328. 2. Ho, P.; Breiland, W. G.App. Phys. Len. 1986, 44, 51. 3. Douglas, A. E. Nature 1979, 269, 130. Knake, R. F. Nature 1979, 269, 132. Kroto, H. W.; Heath, J. R.; O'Brien, S. C.; Curl, R. F.; Smalley, R. E.Astrophys. J. 1987, 314, 352. Hinkle, K. H.; Keady, J. J.; Bernath, P. E Science 1988, 241, 1319. Merrill, P. W. Publ. Astron. Soc. Pac. 1926, 38, 175. Sanford, R. E Astrophys. J. 1950, 111,262. Kleman, B. Astrophys. J. 1950, 123, 162. 4. Raghavachari, K.; Whiteside, R. A.; Pople, J. A. J. Chem. Phys. 1986, 85, 6623. Raghavachari, K.; Binkley, J. S. J. Chem. Phys. 1987, 87, 2191. Parasuk, V.; Almof, J. J. Chem. Phys. 1989, 91, 1137. 5. Raghavachari, K.; Logovinsky, V. Phys. Rev. Len. 1985, 55, 2853. Raghavachari, K. J. Chem. Phys. 1986, 84, 5672. Pacchioni, G.; Kouteck~,, J. Chem. Phys. 1986, 84, 3301. Maluendes, S. A.; Dupuis, M. Int. J. Quant. Chem. 1992, 42, 1327. 6. See, for example, Huggins, W. Proc. R. Soc. London 1882, 1, 33. For a historical account of work done on carbon clusters up until 1989, see Weltner, W.; Van Zee, R. J. Chem. Rev. 1989, 89, 1713. 7. C3: Schmuttenmaer, C. A.; Cohen, R. C.; Pugliano, N.; Heath, J. R. Science 1990, 249, 897. C4: Heath, J. R.; Saykally, R. J. J. Chem. Phys. 1990, 94, 3271. C5: Heath, J. R.; Cooksy, A. L.; Grubele, M. H. W.; Schmuttenmaer, C. A.; Saykally, R. J. Science 1989, 244, 564. C6: Hwang, H. J.; Van Orden, A.; Tanaka, K.; Kuo, E. W.; Heath, J. R.; Saykally, R. J.; in press, 1993. C7: Heath, J. R.; Van Orden, A.; Kuo, E.; Saykally, R. J. Chem. Phys. Lett. 1991, 182, 17. Heath, J. R.; Saykally, R. J. J. Chem. Phys. 1991, 94, 1724. Heath, J. R.; Sheeks, R. A.; Cooksy, A. L.; Saykally, R. J. Science 1990, 249, 895. C9: Heath, J. R.; Saykally, R. J. J. Chem. Phys. 1990, 93, 8392. 8. Yang, S.; Taylor, K. J.; Craycraft, M. J.; Conceicao, J.; Pettiette, C. L.; Cheshnovsky, O.; Smalley, R. E. Chem. Phys. Lett. 1988, 144. 9. Ervin, K. M.; Lineberger, W. C. J. Phys. Chem. 1991, 95, 1167. Polak, M.; Gilles, M.; Lineberger, W. C. unpublished C3 data. 10. Arnold, D. W.; Bradforth, S. E.; Kitsopoulos, T. N.; Neumark, D. M. J. Chem. Phys. 1991, 95, 5479. 11. Douglas, A. E. Can. J. Phys. 1955, 33, 801. Verma, R. D.; Warsop, P. A. Can J. Phys. 1963, 41, 152. Dubois, I.; Leclerq, H. Can J. Phys. 1971, 49, 3053. Davis, S. P.; Brault, J. W. J. Opt. Soc. Am. B 1987, 4, 20. 12. Raghavachari, K.; Rohlfing, C. M. J. Chem. Phys. 1991, 94, 3670. Rohlfing, C. M.; Raghavachari, K. Chem. Phys. Lett. 1990, 167, 559. Raghavachari, K. Z. Phys. D. 1989, 12, 61. Raghavachari, K. J. Chem. Phys. 1986, 84, 5672. Raghavachari, K.; Logovinsky, V. Phys. Rev. Lett. 1985, 55, 26. 13. Rohlfing, C. M.; Raghavachari, K. J. Chem. Phys. 1993, 96, 2114. 14. Fournier, R.; Sinnott, S. B.; DePristo, A. J. Chem. Phys. 1992, 97, 4149. Li, S. D.; Johnston, R. L.; Murrell, J. N. J. Chem. Soc., Faraday Trans. 1992, 88, 1229. Dai, D. G.; Balasubramanian, K. J. Chem. Phys. 1992, 96, 3279. Adamowicz, L. Chem. Phys. Left. 1992,188, 131. Adamowicz, L. Chem. Phys. Lett. 1991, 185, 244. Kiatircioglu, S.; Erkoc, S. Chem. Phys. Len. 1991, 184, 119. Balasubramanian, K. Chem. Phys. Left. 1987,135, 283. Pacchioni, G.; Koutecky, J. J. Chem. Phys. 1986, 84, 3301. 15. Dixon, D. A.; Gole, J. L. Chem. Phys. Lett. 1992, 188, 560. Balasubramanian, K. Chem. Phys. Lett. 1986, 125, 400. Sabin, J. R.; Oddershede, J.; Diercksen, G. H. F.; Gruner, N. E. J. Chem. Phys. 1986, 84, 354. Slanina, Z. Chem. Phys. Len. 1986, 131,420. Raghavachari, K. J. Chem. Phys. 1985, 83, 3520. Grev, R. S.; Schaefer, H. F. Chem. Phys. Lett. 1985, 119, 111. Jones, R. O. Phys. Rev. A 1985, 32, 2589.

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CAROLINE C. ARNOLD and DANIEL M. NEUMARK

16. Cheshnovsky, O.; Yang, S. H.; Pettiette, C. L.; Craycraft, M. J.; Liu, Y.; Smalley, R. E. Chem. Phys. Lett. 1987, 138, 119. 17. Nimlos, M. R.; Harding, L. B.; Ellison, G. B.J. Chem. Phys. 1987, 87, 5116. 18. Kitsopoulos, T. N.; Chick, C.J.; Zhao, Y.; Neumark, D. M. J. Chem. Phys. 1991, 95, 1441. Arnold, C. C." Kitopoulos, T. N.; Neumark, D. M. J. Chem. Phys. 1993, 99, 766. 19. Kitsopoulos, T. N.; Chick, C. J.; Weaver, A.; Neumark, D. M. J. Chem. Phys. 1990, 93, 6108. 20. Arnold, C. C.; Neumark, D. M. J. Chem. Phys. 1993, 99, 3353. 21. Arnold, C. C.; Neumark, D. M. J. Chem. Phys., submitted. 22. Arnold, D. W.; Bradforth, S. E." Kitsopoulos, T. N.; Neumark, D. M. J. Chem. Phys. 1991, 95, 8753. 23. Kotsopoulos, T. N.; Chick, C. J.; Zhao, Y.; Neumark, D. M. J. Chem. Phys. 1991, 95, 5479. 24. Arnold, C. C.; Zhao, Y.; Kitsopoulos, T. N.; Neumark, D. M. J. Chem. Phys. 1992, 97, 6121. 25. For example, see Taylor, K. J.; Pettiette, C. L.; Cheshnovsky, O.; Smalley, R. E. J. Chem. Phys. 1992, 96, 3319. Ho, J.; Ervin, K. M.; Lineberger, W. C. J. Chem. Phys. 1990, 93, 6987. Eaton, J. G.; Sarkas, H. W.; Arnold, S. T.; McHugh, K. M.; Bowen, K. H. Chem. Phys. Left. 1992, 193, 141. Gandtfor, G.; Gausa, M.; Meiwesbroer, K. H.; Lutz, H. O. Faraday Disc. Chem. Soc. 1988, 86, 197. Gandtfor, G.; Gausa, M.; Meiwesbroer, K. H.; Lutz, H. O. Z. Phys. D 1988, 9, 253. Casey, S. M.; Villalta, P. W.; Bengali, A. A.; Cheny, G. L.; Leopold, D. G. J. Am. Chem. Soc. 1991, 113, 6688. 26. Metz, R. B.; Weaver, A.; Bradforth, S. E.; Kitsopoulos, T. N." Neumark, D. M. J. Phys. Chem. 1990, 94, 1377. Arnold, D. W.; Bradforth, S. E.; Kitsopoulos, T. N.; Neumark, D. M. J. Chem. Phys. 1991, 95, 8753. Kitsopoulos, T. N.; Waller, I. M.; Loeser, J. G.; Neumark, D. M. Chem. Phys. Lett. 1989, 159, 300. Kitsopoulos, T. N.; Chick, C. J.; Zhao, Y.; Neumark, D. M. J. Chem. Phys. 1991, 95, 1441. 27. Cheshnovsky, O.; Yang, S. H.; Pettiette, C. L.; Craycraft, M. J.; Smalley, R. E. Rev. Sci. Instrum. 1987, 58, 2131. 28. Wiley, W. C.; Maclaren, I. H. Rev. Sci. lnstrum. 1955, 26, 1150. 29. Miiller-Dethlefs, K.; Sander, M.; Schlag, E. W. Z. Naturforsch 1984, 39a, 1089. Miiller-Dethlefs, K.; Sander, M.; Schlag, E. W. Chem. Phys. Lett. 1984, 12, 291. 30. Proch, D.; Trickl, T. Rev. Sci. Instrum. 1989, 60, 713. 31. Bakker, J. M. B. J. Phys. E 1973, 6, 785. Bakker, J. M. B. J. Phys. E 1974, 7, 364. 32. Pitzer, K. S.; Clementi, E. J. Am. Chem. Soc. 1959, 81, 4477. 33. Ervin, K. M.; Lineberger, W. C. J. Phys. Chem. 1991, 95, 1167. Lineberger, W. C.; Patterson, T. A. Chem. Phys. Len. 1972, 13, 40. 34. Weltner, W., Jr.; McLeod, D., Jr. J. Chem. Phys. 1964, 40, 1305. Bondybey, V. E.; English, J. H. J. Chem. Phys. 1978, 68, 4641. 35. Wigner, E. P. Phys. Rev. 1948, 73, 1002. 36. Reed, K. J.; Zimmerman, A. H.; Anderson, H. C.; Brauman, J. I. J. Chem. Phys. 1976, 64, 1368. 37. Raghavachari, K.; Binkley, J. S.J. Chem. Phys. 1987, 87, 2191. 38. Martin, J. M. L.; Francois, J. P.; Gijbels, R. J. Chem. Phys. 1990, 93, 8850. Martin, J. M. L.; Franqois, J. P.; Gijbels, R. J. Comput. Chem. 1991, 12, 52. The tabulated frequencies were performed at the MP2/6-31G* level. 39. Parasuk, V.; Almtif, J.J. Chem. Phys. 1989,91, 1137. 40. See Ref. 7 for C6, and Kranze, R. H.; Graham, W. R. M. J. Chem. Phys. 1993, 98, 71. 41. Gantefor, G. E; Cox, D. M.; Kaldor, A. J. Chem. Phys. 1992, 96, 4102. 42. Adamowicz, L. Chem. Phys. Lett. 1991, 182, 45. 43. Hefter, U.; Mead, R. D.; Schulz, P. A.; Lineberger, W. C. Phys. Rev. A 1983, 28, 1420. Mead, R. D.; Hefter, U.; Schulz, E A.; Lineberger, W. C. J. Chem. Phys. 1985, 82, 1723. 44. Gantefor, G. E; Cox, D. M.; Kaldor, A. J. Chem. Phys. 1991, 94, 854. 45. See Davis and Brault in Ref. 11. 46. McLean, A. D.; Liu, B.; Chandler, G. S. J. Chem. Phys. 1984, 80, 5130. 47. Raghavachari, K." Rohlfing, C. M. J. Chem. Phys. 1991, 94, 3670. 48. See Fournier et al. in Ref. 14 and Dixon and Gole in Ref. 15.

CRLAS: A NEW ANALYTICAL TECHNIQUE FOR CLUSTER SCIENCE

J. J. Scherer, J. B. Paul, A. O'Keefe, and R. J. Saykally

I. II. III. IV.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . History of the CRLAS Method . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity of the CRLAS Method . . . . . . . . . . . . . . . . . . . . . . . Applications of CRLAS to Pulsed Molecular Beams . . . . . . . . . . . . . . A. The Copper Dimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. The Copper Trimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Metal-Rare Gas Complexes . . . . . . . . . . . . . . . . . . . . . . . . V. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149 151 160 170 171 173 176 178 179 179

I. INTRODUCTION The measurement of electronic spectra of atomic and molecular clusters is of central importance in the quest to understand the evolution of structure and bonding in systems of finite size. Moreover, electronic spectroscopy presents a sensitive route for detecting gas-phase clusters in analytical applications. The established ap-

Advances in Metal and Semiconductor Clusters Volume 3, pages 149-180. Copyright 9 1995 by JAI Press Inc. All Hghts of reproduction in any form reserved. ISBN: 1-55938-788-2

149

150

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

proaches for making such measurements are laser-induced fluorescence (LIF) and resonance-enhanced multiphoton ionization (REMPI). Both have been employed in studies of a variety of cluster systems. However, both methods usually fail for clusters containing more than a few atoms, owing to either rapid internal conversion or predissociation. Even for dimer and trimer systems, the vibronic band intensities are contaminated by the associated intramolecular relaxation dynamics; hence, these techniques cannot be used for reliable intensity measurements. For clusters that exhibit rapid photofragmentation, depletion spectroscopy can be employed quite effectively to measure their vibronic structure, but again, dynamical effects complicate the interpretation of spectra. It would often be preferable to measure electronic spectra of clusters in direct absorption, as this approach is the most straightforward and accurate means of ascertaining absolute vibronic band intensities and for accessing states that are invisible to LIF or REMPI. The problem, of course, is that direct absorption methods are generally orders of magnitude less sensitive than the competing methods, and therefore are very difficult to apply to transient species, such as clusters. In this chapter, we describe a new direct absorption technique which we have developed for measuring electronic spectra of jet-cooled clusters with both high sensitivity and high resolution. The method is based on measurement of the time rate of decay of a pulse of light trapped in a high-finesse optical cavity; we call it cavity ringdown laser absorption spectroscopy (CRLAS). The basic idea is presented in Figure 1. An approximately 15-ns pulse of light from a dye laser is injected

ii ul|

ii

time Figure 1. In the short pulse limit, discrete pulses of light spaced 2L/c apart exit the cavity. The peak intensities of the successive pulses are fit to a first-order exponential. Typical ringdown decays consist of ten thousand such pulses.

CRLAS: A New Analytical Technique

151

into a cavity formed by a pair of highly reflective (R > 99.9%) mirrors. Owing to the pulsed nature of the injected light, the cavity does not act as an etalon, i.e., standing waves are not established in the cavity. Instead, the light pulse acts like a particle as it makes many (ca. 10,000) traversals of the cavity. A fast (ns) detector placed after the exit mirror sees a series of pulses, spaced by the transit time of the cavity. The intensity envelope of these pulses ideally exhibits a simple exponential decay. The time required for the resonator to decay to 1/e of the initial output pulse is called the "cavity ringdown" time. Ideally, the ringdown time is a function of only the mirror reflectivities, cavity dimensions, and the sample absorption. Absolute absorption intensities are determined by subtracting the baseline losses of the cavity, which are determined when the laser wavelength is off resonance with all molecular transitions. Every laser pulse constitutes an independent measurement; hence the method is not seriously degraded by the large intensity fluctuations common to pulsed lasers. With state-of-the-art data collection methods, a fractional absorption of less than 1 x 10-6 per pass can be measured with a single laser shot; signal averaging can be employed to improve this figure. Though currently implemented in the optical and near infrared regions, the CRLAS method is limited in wavelength coverage primarily by the availability of the highly reflective mirrors that constitute the resonator, and could be extended to both longer and shorter wavelength regions. In this paper we present a detailed account of the history, theory, and applications of the CRLAS method. It is anticipated that this review will serve as a useful guide for the rapidly increasing number of researchers from various fields seeking to implement this powerful new spectroscopic tool.

!1. HISTORY OF THE CRLAS METHOD The history of the cavity ringdown technique dates back to the pioneering work of Herbelin et al. in the early 1980s. l In their first paper, they describe the apparatus, which was primarily used to characterize highly reflective optical coatings, and coin the acronym CAPS for cavity-attenuated phase shift method. In the CAPS technique, the lifetime of a photon in a high-finesse optical resonator is inferred from the measured phase shift at the exit mirror of the resonator. From this photon lifetime, the resonator mirror reflectivities are easily deduced, given the mirror spacing. With this approach, Herbelin et al. were able to determine reflectivities to within 100 parts per million (ppm). However, this represents at least two orders of magnitude less sensitivity than the current CRLAS method. To understand the reasons for this difference we must look more closely at their novel approach and trace the developments which have led to the current CRLAS technique. A block diagram of the CAPS experiment is shown in Figure 2, for a simple two-mirror resonator. Continuous wave laser light is passed through a piezooptical birefringent modulator, producing a time-varying linearly polarized beam which is modulated as:

152

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY Detector

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Two channel lock-in

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Figure 2. CAPS experimental schematic: frequency-modulated CW laser light is coupled into the resonator at mirror 1 and detected outside mirror 2, where it is shifted in phase. Standard lock-in schemes can be employed to measure the resultant phase shift.

sin2(2~ft +_O) wherefis the modulation frequency and 9 is the initial phase shift, usually set equal to 0. The modulated light is then coupled into the resonator through mirror 1 and detected after exiting the resonator outside mirror 2, where it is now shifted in phase by an amount o~. This phase shift is related to the photon lifetime in the resonator through the simple expression, l tan ~ = 4~ft where the photon lifetime (t) corresponds to a fixed number (n) of round-trip passes inside the resonator, 2Ln t = nt'

-

c

and where t' is the time required for the photon to complete one round trip (2L/c). The number of round trips (n) made by the photon for a two-mirror resonator with reflectivities R 1 and R2 is given by (for high reflectivity),

1t

n=~

1 - RIR2

/

therefore, t a n o~ =

4,Lt RIR2) c

1 -RIR 2

(1)

153

CRLAS: A New Analytical Technique

If R l is known, R 2 can be determined from the above expression by measurement of the phase shift cz. Similarly, molecular absorption A between the two mirrors can be incorporated into Equation (1) (for A << 1)

4~L[ R,(I-__A)ZR2]

tan @ - - ~

c

1 -RI(1 - A)ZR2J

A more complete derivation of the above expressions can be found in Ref. 1. In practice, the phase shift can be determined with various arrangements, although it can most efficiently be obtained by directly measuring tan o~ with a two-channel lock-in amplifier in the following manner: first, the modulator is placed outside of mirror R 2 and both channels of the two-channel lock-in are adjusted in phase to null out signals on both channels A and B; next, channel B is shifted by 90 ~ and the modulator is placed before mirror R 1. In this arrangement, channel A is directly proportional to sin cz and channel B is proportional to cos o~. With the use of a ratiometer, A/B = tan o~ can be obtained directly. A plot of tan cz versus L for different resonator lengths or of tan o~ versusf for various modulation frequencies provides a means of determining either the unknown reflectivities or molecular absorption. From the above description, the factors that determine the CAPS sensitivity become evident. Uncertainties in modulation frequency, cavity length, and phase shift lead to practical limits in the attainable sensitivity that prevent the technique from ever reaching the theoretical limit. Fluctuations in the modulation frequency, although small for the range of frequencies used in their apparatus (10-20 kHz), will lead to a linear correction in the above expression. These fluctuations can be eliminated by the taking of measurements at several modulation frequencies and fitting of the points to a straight line. In this manner, the uncertainty is reduced to a fraction of a percent, leading to a negligible correction in the reflectivity. Because the measurements are recorded on time scales on the order of 0.1 seconds, fluctuations in the cavity length due to thermal drift and acoustic vibrations are averaged out and again lead to a small correction to the reflectivity or absorption. In fact, these fluctuations can be desirable in that they can increase the longitudinal mode coupling between the laser and cavity owing to the decreased phase coherence of the circulating pulse. The limiting factor in attaining high sensitivity in the CAPS technique arises from the fluctuations in and the ability to measure the phase angle itself, with errors on the order of 5 to 10 degrees being reported} These fluctuations are caused by many factors, including laser noise and optical dephasing due to scattering, but are primarily caused by the erratic mode matching that occurs between the laser and resonator cavities. This dynamic mode matching is a complex convolution of laser wavelength, linewidth, mode quality, and phase coherence coupled to the cavity mode spacing, linewidth, and stability. A qualitative discussion of mode-coupling phenomena can be found in Refs. 1 and 2 and will be discussed in Section III, but it is currently sufficient to recognize that both phase

154

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

lame 1. Theoretical Sensitivity Limit of the CAPS Technique (dR~R) as a Function of Phase Angle Uncertainty for Different Pairs of Mirrors Rl

0.999 0.9995 0.99995 0.999975

MirrorR = R l

0.998 0.999 0.9999 0.99995

2

dRiRfor• o

2.4"10-4 1.5"10-4 1.6"10-5 8.0*10-6

dR/R f o r •

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o

dR/R f o r • 1 ~

7.0"10-5 3.3"10-5 3.5"10-6 1.5"10-6

angle uncertainty and mirror reflectivity combine to set an upper limit on the experimentally achievable sensitivity. To best illustrate this point, consider the error in determining a reflectivity (i.e., d R ~ R ) for pairs of mirrors (with increasing reflectivities) for various uncertainties in the phase angle about the value tx = 45 ~ (the situation gets worse for larger or smaller values of or). These data are given in Table 1 for values of R ranging from R = R 1 R 2 = 0.998 to 0.99995. Owing to the nature of the denominator in the expression for tan 0t, small increases in the value of R lead to large gains in sensitivity, whereas decreases in phase angle uncertainty scale almost linearly with sensitivity, as shown in the Table. Even if it were possible to determine accurately the phase shift to within 1~ from a set of mirrors with R 1 = R 2 = 99.9975%, one could achieve an ultimate absorption sensitivity of roughly 2 ppm. Although capable of higher levels of sensitivity in theory, the CAPS technique's reliance upon the phase angle measurement proved to be its greatest weakness. The next major step in the development of the cavity ringdown technique was made by Anderson, Frisch, and Masser in 1983. 3 Instead of relying on the imprecise phase shift measurement, Anderson et al. directly measured the photon lifetime in the resonator by monitoring the intensity decay that occurred when the light source was quickly shut off with a fast optical switch. A diagram of the apparatus is shown in Figure 3. In practice, CW laser light is coupled into the cavity through the input mirror and the longitudinal modes of the laser gradually overlap with longitudinal modes of the cavity. During this "buildup", the light exiting the output mirror is monitored with a fast photodetector. When the intensity reaches a preset threshold level, the Pockels cell is switched and the transient response or "ringdown" of the cavity is recorded. In this fashion, problems arising from spurious mode matching between the laser and cavity axial modes are greatly reduced. If the switching time of the Pockels cell is on the order of one cavity round-trip time, the intensity at the detector decays exponentially according to the simple first-order expression, l ( t ) = Io e - ' / t

where t c is the ringdown time of the cavity. The ringdown time is related to the mirror reflectivity via:

CRLAS: A New Analytical Technique

155

Pockers I

laser

~ - - - - ~

detector

. . . . . . . . . . . . . . .

comparator

~

Vref

Figure 3. Early ringdown apparatus of Anderson et al.: 3 continuous wave laser light is mode matched into the cavity and switched off with a Pockels cell. The resultant intensity decay of the cavity is monitored at the output mirror with a fast photodetector and fit to a first-order exponential, from which the mirror reflectivities are determined.

tc=

1

where L is the mirror separation, c is the speed of light, and R = R1R2 is the reflectance for a two-mirror configuration. In the above expression, a round-trip optical phase shift equal to 2n and a TEM mode coupling coefficient equal to unity are assumed. A more detailed derivation of the above expressions can be found in Ref. 3. In contrast to the approach of Herbelin et al., ~ the measured quantities in Anderson and co-workers' apparatus are cavity length and time, and it is this difference that allows a greater level of sensitivity to be achieved. Provided fast detectors and fast electronics are employed, the ringdown time of the cavity can be measured with nanosecond precision. With this arrangement, Anderson et al. were able to achieve a time resolution of 10 ns with a corresponding absorption sensitivity of approximately 5 ppm, at least an order of magnitude increase over the CAPS method. Owing to the exponential time dependence of the intensity decay, constraints on the determination of the time constant are greatly relaxed, as illustrated in Table 2. These data should be compared to those of Table 1. For example, determination of the time constant to within 1% for a set of mirrors with R = 99.99% in the ringdown approach is more than one order of magnitude more sensitive than the CAPS method for a 5-degree uncertainty in the phase angle. Yet, this 1% error in the time constant is still orders of magnitude larger than the theoretical limit, which will be discussed later. Although this new approach represented a significant improvement over the CAPS technique, the use of a CW light source required that sufficient axial mode coincidence occur between the laser and cavity resonators. Even with the use of threshold triggering techniques, this longitudinal mode coupling led to amplitude fluctuations, which set an upper limit

156

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY Table 2. Theoretical Sensitivity Limit of the Early Ringdown Method a as a Function of Uncertainty in the Decay Time, for Different Pairs of Mirrors b

Mirror Reflectivity

Number Oef Passes to l

lime Constant to 1%

l~me Constant to 2%

lime Constant to 3%

~ m e Constant to 10%

0.9950 0.9990

100 500

:t:5.05"10 -5 1.1"10 -5

+1.02"10 -4 2.04"10 -5

+1.5"10-4 3.0"10 -5

+_5.5"10-4 1.1"10 -4

0.9995 0.9999

1,000 5,000

5.05"10 -5 1.1"10 -6

1.02"10 -5 2.04"10 -5

1.5"10 -5 3.0"10-6

5.5"10 -5 1.1"10 -5

0.99995

10,000

5.05"10 -7

1.02"10-6

1.5"10-6

5.5"10-6

0.99999

50,000

1.1"10 -7

2.04"10 -7

3.0"10 -7

1.1"10-6

Notes: aRef.3 bThese figures should be compared to those in Table 1.

on the experimentally achievable sensitivity. Additionally, continuous scanning of the laser wavelength was not possible owing to the necessity to adjust the optical switch for each new wavelength, and this would pose a serious problem in spectroscopic applications. To address these drawbacks, O'Keefe and Deacon combined pulsed laser sources with fast waveform digitization to bring the ring'down technique to a higher level of performance. 4 By employing pulsed lasers with coherence lengths much shorter than the cavity dimensions, O'Keefe and Deacon were able to achieve stable frequency coupling into the resonator with each laser pulse, without the use of fast optical switches or threshold triggering schemes, thus allowing continuous wavelength scanning. In addition, digitization of the exponential cavity decay combined with fast (direct memory access) data transfer to a computer allowed for a rigorous real-time analysis of the data to be performed. With this new approach, a fractional absorption sensitivity of 10-6 per laser shot was easily achieved. Derivation of the ringdown decay expression is now easily understood, as the light pulse that is injected into the cavity can be visualized as being essentially particle-like in nature. Because the amount of light that exits the resonator is proportional to both the cavity transmissivity and the intensity of the trapped pulse, the time derivative of the output pulse is, dl/dt = -IcT/2L

where T is the transmission coefficient for the two-mirror configuration, c is the speed of light, and L is the mirror separation. The solution to this equation is: I = loe-rC(t-to )/2L

This expression can be rearranged to yield the total loss per pass (F) experienced by the light pulse while traversing the resonator:

CRLAS: A New Analytical Technique

i

157

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N2Pumpedl Laser] D~ye

Mirr~~

i

!

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I

m

Excimer I Figure 4. First-generation Berkeley CRLAS apparatus" a laser-vaporized pulsed molecular beam of metal clusters is generated in an evacuated chamber and perpendicularly intersected by the ringdown laser pulse. The ringdown decay is timed to coincide with the transient molecular beam and is monitored with a photomultiplier. The decay waveform is digitized and transferred to a PC for calculation of the molecular absorption at each laser wavelength.

I" = 1 -- e ( 2 L / c ) t

A plot of cavity loss verses wavelength allows one to extract either the transmission curve for the two mirrors or the absorption spectrum for a sample located between them. Again, the sensitivity of the technique is primarily dependent on the mirror reflectivities and the accuracy with which one can determine the cavity decay time constant. The high sensitivity of the apparatus constructed by O'Keefe and Deacon was explicitly demonstrated by measurement of the absorption spectrum of the doubly forbidden 1Y_,g-3Zs transition in molecular oxygen, and found to be roughly 1-ppm fractional absorption per shot.4 This represented nearly an order of magnitude improvement over Anderson's apparatus. The next advance in the development of the cavity ringdown technique occurred in 1990 when it was applied for the first time to molecular beam spectroscopy by O'Keefe, Scherer, and Saykally at Berkeley. 5 A diagram of the experiment is shown in Figure 4 and represents a combination of the ringdown design employed by O'Keefe and Deacon with the molecular beam machine built by the Saykally group for the study of infrared spectra of laser-vaporized clusters. 6 Briefly, a supersonic molecular beam of clusters is formed by vaporization of a sample rod that continuously rotates and translates in a stainless steel housing while a pulsed valve backed with 300 psi of argon is fired. The mixture expands through a nozzle into the evacuated chamber, forming a Campargue-type expansion of supersonically cooled molecules. Simultaneously, the molecular beam is intersected by the ringdown laser pulse at the cavity waist of the resonator. With proper timing, the transient molecular

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J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

beam can be tailored to temporally coincide with the ringdown event, which is typically tens of microseconds. The ringdown is monitored with a fast dynode photomultiplier detector, amplified, digitized, and transferred to a PC for analysis. The total cavity losses are deconvoluted from the measured cavity decay time. Molecular absorption intensities are then obtained by subtracting the baseline losses of the cavity, which are determined while the beam is off. Typically, several laser shots are averaged per wavelength, primarily to reduce the noise caused by molecular beam fluctuations. The first generation apparatus was capable of running at 20 Hz. When this endeavor first began, it was not clear whether the transient nature of the molecular beam would pose a problem in the extraction of accurate absorption intensities. Additionally, owing to the delicate nature of the cavity alignment, the extent to which alignment would be affected by refraction and scattering in the beam region was uncertain. However, it was found that with careful cavity alignment, source placement, and timing, these effects could be reduced to the point of limiting sensitivity to 5 to 20 ppm, depending on the particular cluster species and source conditions. In this first application, optical absorption spectra of several different species were obtained, including the Swann bands of C 2, rotationally resolved spectra of NbO and AIO, the B-X and C-X systems of Cu 2, and the 2A-2Esystem of Cu3 .5 Of particular interest in these initial studies were the results of the copper trimer system, which will be discussed in detail in Section IV. These results constituted the first direct absorption gas-phase data ever obtained for a polyatomic metal cluster. Since other state-of-the-art techniques, such as R2PI or LIE can suffer significantly from the effects of internal conversion or predissociation, the ringdown technique would now offer an alternative and complementary means of studying polyatomic cluster species. The large shot-to-shot fluctuations that occur in laser-vaporized sources combined with the high degree of optical scattering encountered as the light travels through the plasma renders conventional absorption techniques difficult or impossible to implement in this spectral region. Additionally, power fluctuations in pulsed lasers, which would normally render them useless in conventional absorption schemes, do not significantly limit the sensitivity in the ringdown approach. In fact, the primary source of noise in both our previous and current work is the noise introduced by the laser-vaporized molecular beam. Our initial results from employment of the ringdown technique were so encouraging that we have since designed and built a new, more sophisticated apparatus, depicted in Figure 5. Improvements in data handling, laser resolution, and molecular beam production have been made, resulting in a significant increase in instrument performance. One of the improvements that were made included modification of the data acquisition system, by replacement of the 100-MHz 8-bit digitizer with a 20-MHz 12-bit unit, effectively doubling the number of data points used in fitting the decay curve. Data processing was also improved by employment of a faster computer, leading to an increased repetition rate of over 65 Hz. Laser power and resolution

CRLAS: A New Analytical Technique

EXCIMEI~ EXCIMEI~ 308 nm 248 nm

159

EXCIMEI~ 193 nm

Chevron MCP detector ! I I

1

1

I

Dye Laser (.04 cm")

!I I

O

o),,~

ID

I'~ O

I

IOptics' ]

I

I ~ !

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!M

Digitizer Computer

Figure 5. Second-generation Berkeley CRLAS apparatus: pulsed molecular beams of laser-generated clusters are spectroscopically probed with the ringdown technique. Neutral species in the molecular beam are monitored with a differentially pumped time-of-flight mass spectrometer. The design allows in situ mass spectrometric measurements to be made while absorption spectra are monitored, as well as allowing resonance or depletion techniques to be performed for aid in spectral assignment of congested vibronic bands.

were increased from tens of microjoules at 1 cm -1 to over 10 mJ at 0.04 cm -l, leading to proportionate gains in absorption intensities where rotational resolution was achieved. The net result of our efforts translated to an apparatus with a sensitivity of roughly 2 x 10-7 fractional absorption per laser shot, while the scanning speed was increased by nearly an order of magnitude. Additionally,

160

J.J. SCHERER,J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

improvements in source design have led to five-fold increases in cluster absorption signal, due to increased species concentration in the probe region. Since our work in 1990, we have measured additional bands in the 2A-2Esystem of Cu 3 and have obtained rotationally resolved spectra of C 3, AIAr, Cu 2 and a variety of other diatomic species, including recently acquired data on Nb 2. Vibrationally resolved spectra have also been measured for a variety of polyatomic aluminum- and niobium-containing species and are currently under analysis. Coupled to the cavity ringdown laser absorption spectrometer (CRLAS) is a time-of-flight mass spectrometer (TOFMS), which combines laser photoionization and perpendicular extraction to achieve a mass resolution of 1/500 amu. The use of the mass spectrometer aids significantly in optimizing the production of specific clusters. With in situ mass spectrometric measurements made possible, resonanceenhanced photoionization or photodepletion experiments can be performed in suitable systems without alteration of the CRLAS apparatus, These methods can aid in assignment of the carriers of vibronic bands that are not rotationally resolved with the absorption apparatus owing either to severe lifetime broadening or to spectral congestion. Our primary interest, however, is in obtaining the highest possible combination of sensitivity and resolution in our direct absorption experiments. This leads us currently to a discussion of the ultimately achievable absorption sensitivity of the CRLAS technique.

i11. SENSITIVITY OF THE CRLAS M E T H O D Of critical importance in the discussion of CRLAS sensitivity is the model used in derivation of the first-order exponential expression for the photon lifetime in the resonator. In this model, the laser pulse injected into the cavity is assumed to be particle-like, leading to discrete pulses being transmitted through the cavity with each round trip. Figure 6 illustrates this situation, where the multiple reflections occurring in the cavity during the decay are represented by displaced arrows. In this picture, the intensity measured at the photomultiplier will be a series of pulses of decreasing intensity spaced in time by 2L/c, provided the pulse length is less than the cavity round-trip length. These pulses are treated as discrete steps that are fit to an exponential decay envelope, from which the cavity losses are determined. This smoothing of the decay to fit a simple exponential limits the accuracy in the determination of the time constant, which, in turn, sets a theoretical upper limit in the absorption sensitivity for a given set of mirrors. In this first-order picture, longitudinal and transverse mode matching coefficients are assumed to be unity. In practice, longitudinal and transverse oscillations in the cavity, which can lead to nonexponential decays, occur as a function of many competing factors including specific cavity geometry, laser wavelength, linewidth, pulse length, and cavity stability. Some of these contributions will be discussed later in this section, but for now we will accept that inclusion of these effects can lead to nonexponential decays that tend to decrease the attainable sensitivity. Therefore, for a given set of

CRLAS: A New Analytical Technique LASER

161

~..

f~

11

~.. 12 ~ , MIRROR 1

-,

13 ...I(t)

MIRROR 2

Figure 6. First-order model of ringdown decay: discrete pulses of laser light leak out of the cavity with each pass. The reduced intensity of each successive pulse is described by a smooth exponential expression.

mirrors, the ultimate sensitivity will depend explicitly on the ratio of the uncertainty in the number of round-trip passes of the light pulse to the total number of round trips that occur during the measured ringdown time. For example, if we construct a resonator with mirrors having reflectivities R 1 = R 2 = 99.995% (for a specific spectral region) and spaced one-half meter apart, we would measure a 1/e decay time of 33 Its, during which the light pulse would make 10,000 round trips, as shown previously in Table 2. In this case, if it were possible to determine the time constant to within a single round trip (1 part in 10,000), this would translate into a spectrometer absorption sensitivity of 5 parts per billion! For this level of sensitivity to be achieved, the length of the laser pulse (lft/ns) must be less than the round-trip length of the cavity. Otherwise, the uncertainty in the decay time would be greater than one round trip, as the ability to discriminate individual transmitted light pulses would be lost. For example, an excimer-pumped dye laser with a 15-ns FWHM pulse would undergo a total of roughly five round trips in a 0.5-m resonator during the length of the pulse, thus limiting the ringdown decay time accuracy to 5 parts in 10,000. This, in turn, would translate to an ultimate sensitivity of 2 x 10-8 (fractional absorption). Regardless of the accuracy of the electronics or the extent of signal averaging employed, the spectrometer sensitivity would converge to this figure but could never exceed it. This is because beyond this limit our model breaks down, as we have defined the ringdown time in terms of round-trip events. There is no observable event in our overlapping light pulse beyond the total number of round trips that the wavepacket undergoes, and therefore there is no physical meaning to a time constant beyond this resolution. If it were possible to discriminate the individual features of each pulse and fit the ringdown time by use of the same portion of each pulse (e.g., peak intensity), then the cavity decay constant could be determined with extremely high accuracy, increasing the attainable sensitivity. For example, if ultrashort laser pulses were combined with large cavity dimensions and fast detection, allowing the cavity time constant to be determined to subnanosecond

162

J.J. SCHERER,J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

accuracy, unparalleled levels of sensitivity could be achieved, provided an equal degree of precision could be obtained in the intensity measurement. From this discussion, it is clear that extremely high levels of sensitivity can be reached with the CRD technique; in practice, however, there are many factors that limit the experimentally achievable sensitivity. Contributions from finite data acquisition and analysis capabilities, laser and detector noise, cavity alignment, and mode competition combine to degrade the sensitivity by orders of magnitude. One of the first concerns in the construction of the CRLAS at Berkeley was the choice of waveform recording instrumentation. Our decision to continue to use a digitization format over analog methods was based on several considerations. Digitization of the decay allows fast, accurate acquisition of the entire decay and provides a versatile format for data manipulation (e.g., signal averaging), but the primary advantage is that it allows us to quantitatively monitor the ringdown during the alignment procedure. Although this last point may appear trivial, it is, in reality, extremely critical. In choosing the proper digitizer, two factors must be considered: sampling rate and analog-to-digital conversion resolution. These quantities can be tailored to a specific cavity geometry and detection scheme to give the largest number of points with the highest degree of precision. Because modern digitizers employ fast flash-converter circuits, they typically possess clock accuracies of 10--20 ps. Therefore, the sampling interval need only be considered in terms of the limitation that it places on the number of points that will be used in the fit of the ringdown signal. The A-D conversion, on the other hand, is critical because it will limit the precision of these points. For example, a 100-MHz 8-bit digitizer used in conjunction with a 0.5-m resonator with a 33-l.ts ringdown time would lead to a sampling capability of several thousand points in time but would suffer significantly from the A-D resolution of only 1 part in 254. In contrast, a 20-MHz 12-bit unit would not only double the number of meaningful points acquired but would also increase their precision by nearly a factor of 20. With this modification, we have found that only one-fourth the number of laser shots are needed with the 20-MHz unit to achieve the same level of sensitivity as with the 100-MHz unit. Although the extent of laser and detector noise will vary according to the specific equipment, the manner in which these noise sources contribute to CRLAS sensitivity can be easily demonstrated with reference to a 0.5-m sample cavity. More specifically, we must separately examine the effects of both the noise present in a single laser pulse and pulse to pulse power fluctuations in the laser. The issue of single pulse noise is treated by a comparison of the noise in the detection apparatus with the theoretical photon counting limit, and ascertainment of how this noise contributes to the determination of the cavity decay time constant. Consider the case of an excimer-pumped dye laser, which produces a 10-mJ, 15-ns pulse of narrowband light at 500-nm, that is injected into a 0.5-m, 33-l.ts ringdown resonator and is detected with a photomultiplier that possesses a 2-ns risetime. This laser pulse contains ca. N = 2.5 x 1016 photons, of which only 1 part in 108 are transmitted through the cavity to reach the photocathode during the first 15 ns. At the 1/e decay

CRLAS: A New Analytical Technique

163

time, there will be roughly 108 photons striking the photomultiplier in a 15-ns interval. If the quantum efficiency of the PMT is high and the dark current low, the photon-counting limit associated with this pulse, which scales as N -1/2, would limit the precision of the intensity measurement to I part in 104. This uncertainty is much lower than both the A-D resolution given previously and the theoretical limit calculated earlier, assuming the ringdown time resolution to be 5 x 10-4. From this example, it is clear that photon counting statistics are only critical in the case of extremely low laser fluence or when relatively noisy detectors are used. In fact, because a least-squares fitting program is implemented in the fitting of the exponential ringdown decay, random intensity fluctuations such as those from detector noise tend to average out in the fit, contributing very little to the overall precision in the determination of the decay time constant. One of the advantages inherent in using high-power lasers is the ability to run the photomultiplier at low voltages (100-200 volts), which greatly reduces the dark current and thermionic emission of the tube. Large shot-to-shot fluctuations in the laser, on the other hand, can noticeably decrease sensitivity. There are two primary mechanisms through which this type of noise can affect the determination of the decay time constant. The first and simplest mechanism has to do with the fact that large intensity fluctuations can both reduce the number of points used in the fit of the cavity decay profile and can shift the decay region being fit. In the case where only a single laser shot per wavelength is used, these intensity fluctuations can lead to large baseline fluctuations. If signal averaging is employed, shot-to-shot noise can reduce the precision of the fit as the varying intensities tend to blur out the decay features. Even if the laser is extremely stable, another type of amplitude variation may be observed at the detector. This variation is much more complex, and involves the phenomenon of longitudinal mode coupling between the laser and resonator cavities. The following considerations are of paramount importance in achieving the highest degree of sensitivity from the CRLAS apparatus. The two dimensions in which cavity resonances occur will be treated separately from both a CW and pulsed perspective, with a semiquantitative analysis of the grey region that links the two regimes. As a complete treatment of these phenomena is clearly beyond the scope of this paper we will only focus on the more salient features that pertain to CRLAS. In particular, we will address the issue of how well CW concepts, such as axial mode spacing, apply in the case of unstabilized high-finesse resonators injected by pulses of laser light. In the previous discussion of the data acquisition and digitization of the ringdown, decay signal, the importance of accurate monitoring of the decay profile was stressed. A cavity that either is injected with short-pulse laser light of poor TEM mode quality or is poorly aligned can exhibit large oscillations in the ringdown decay as well as multiexponential decays. Figure 7 shows examples of what one sees during a typical alignment procedure. In Figure 7a, large amplitude fluctuations in the decay arise from the off-axis beam walk of a poorly aligned cavity or from a properly aligned cavity with poor TEM laser mode quality. Laser modes

164

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

O~"~ r162

~D

time

0,--'d

O~"d

time Figure 7. Mode competition in the cavity. In Figure 7a, oscillations in the cavity are evident owing to the TEM mode competition. In Figure 7b, the multiexponential character of the decay is illustrated, though exaggerated for the sake of example.

other than TEM 00 possess larger cross-sectional areas with nodes and therefore sample a larger area of the mirrors as they walk in and out of the cavity waist. Different TEM modes can exhibit different ring-down times, which will typically decrease with increasing mode order. In Figure 7b these oscillations are averaged to reveal the multiexponential character of the decay, which is exaggerated for the sake of example. Attempts to fit this event to a single exponential result in large uncertainties in the decay time constant, which, in turn, translate to reduced spectrometer sensitivity. To eliminate these problems, two steps can be taken. When the laser light is passed through one or more spatial filters, such as a two-lens telescope with a precision pinhole, two goals can be achieved simultaneously. First, the transverse profile of the light can be brought to nearly pure TEM 00. This will greatly reduce the periodic amplitude fluctuations and nonexponential decays.

CRLAS: A New Analytical Technique

165

Secondly, the laser can be mode matched to the ringdown cavity, i.e., the laser spot size can be tailored to match the TEM 00 beam waist of the cavity. For a two-mirror stable resonator configuration where both mirrors have the same radius of curvature (R), and are separated by a distance (d), the beam waist radius (D) can be calculated from the expression: 7 D 2 = 2-~[d(2R - d)] 1/2 Therefore, a particular cavity geometry will lead to a specific beam waist that will vary with the square root of the wavelength. This waist should be designed for the particular application of the apparatus, especially in the case of molecular beam applications. For example, the beam waist radius of our CRLAS apparatus is approximately 1 mm at 500 nm. This allows excellent spatial overlap with the molecular beam. Confocal geometries, although stable, can produce extremely small beam waists. Mismatch of the laser spot size with the cavity waist will hinder efficient energy coupling into the resonator, although this effect is less noticeable as the laser pulse length is decreased. The telescope should be adjusted to bring convergent light into the resonator and tailored to overlap at least 100% of the cavity waist. Even after the mode quality of the laser has been spatially filtered and matched to the cavity, oscillations can still be evident during alignment, although to a much lesser extent. These remaining oscillations are primarily due to poor cavity alignment and can be removed by taking advantage of the digitization scheme previously discussed. If the entire ringdown decay is recorded with a transient digitizer, it is straightforward to fit two or more different regions and compare the respective decay times. If the losses calculated for the two fitted regions vary by more than a fraction of a percent, one can simply readjust the input mirror until all regions (excluding the earliest part of the decay) yield the same value. Differences in the decay time constant up to a few percent, though invisible to the naked eye, are easily discerned by the computer. Therefore, monitoring of the decay with an oscilloscope during the alignment procedure is not an adequate test of the single exponential quality of the ringdown. Similarly, detection schemes that fit only a small portion of the decay, or that fit segments and assume single exponential character, are clearly less accurate and should be avoided. In this discussion of transverse resonances we have treated the circulating light as being particle-like in the axial dimension and two-dimensional in the transverse dimension, except for the treatment of the beam waist, where we have assumed sufficient axial overlap. In the CW case, the concept of beam walk-off due to higher order TEM modes will still apply, but detection of this phenomenon can be difficult or impossible to separate from the comparably large amplitude fluctuations that accompany the longitudinal mode resonances. In this respect the TEM mode quality is more important when pulsed lasers with pulse lengths less than the cavity dimensions are used. As the laser temporal and

166

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

coherence length are increased, there will exist a competition between these two effects. This leads us to a discussion of longitudinal mode competition in high-finesse resonators, with emphasis on pulsed laser light. Longitudinal resonances in a laser-injected resonator occur as a function of several coupled factors. These resonances typically become more pronounced with increasing cavity finesse, laser pulse length, and laser coherence length. In both stabilized and unstabilized resonators, laser qualities and cavity dimensions will dictate the extent of axial mode buildup and competition. The ultimate sensitivity of the CRLAS method will at some point be hindered by the combination of the long coherence lengths (c/Aw) that accompany high-resolution laser light and the ultrahigh finesse of the resonator that is required for high sensitivity. As both the coherence length and temporal length of the laser light become longer than the resonator dimensions, the CRLAS resonator will essentially become an etalon that may no longer exhibit a ringdown that can be fit to a single exponential. In the intermediate cases, where numerous longitudinal modes are established in the cavity, the different modes can possess different decay times that, again, can cause deviations from the single exponential model. The simplest case of longitudinal cavity resonances is treated from a CW perspective, wherein we assume that interferometric models adequately describe the mode buildup, in the limit of strict periodicity. In this case, the modes established in the cavity are determined by the overlap of the injection laser modes with the resonant modes of the cavity, assuming that losses are negligible and that the cavity is motionless. This is the limit associated with Fabry Perot theory. 8 For example, a 0.5-m, 33-I.ts cavity would have a mode spacing of 2L/c = 300 MHz with an associated linewidth given by dv = (2mc)-1 = 5 kHz. In this system, the total number of axial modes excited in the cavity is determined from the ratio of the injection laser bandwidth to the 300-MHz mode spacing of the cavity. In the limit of CW single-mode operation, the circulating light pattern inside the cavity would be constant in amplitude and frequency, with an indefinite number of round trips. If the number of laser modes increases or if the cavity is dithered, the extent of coupling will depend on the number of mode matches that occur over the time interval of the measurement. For example, a 300-MHz cavity undergoing small acoustic vibrations of 5-10 kHz would not experience a substantial increase in the number of mode matches on a microsecond time scale, but would over a millisecond time interval. If the number of available laser modes is large, the number of mode matches will be large, regardless of the cavity stability. In the CW ringdown techniques discussed previously, both sensitivity and wavelength tuning were severely hampered by random mode coincidence. These random mode coincidences led to large amplitude fluctuations, which, in turn, caused the aforementioned problems. In the CRLAS pulsed laser approach, the issue of longitudinal mode competition involves many interdependent factors. Cavity stability, cavity length, laser pulse length, coherence length, and laser mode number and spacing all must be consid-

CRLAS: A New Analytical Technique

167

ered to accurately predict the mode competition that will occur in the optical cavity. In many instances, the ability to predict cavity resonances will be very limited owing to either the complex profile of the input pulse or the finite number of times the pulse overlaps itself in the cavity. Cavity motions, in the case of an unstabilized resonator, will decrease the ability of standing waves to become established in the cavity only when the mirrors undergo motions that are significant over the roundtrip time of the resonator. When this is the case, the circulating wavefront will no longer be coherent with itself as it overlaps, thus hindering the formation of longitudinal resonances. For example, a mirror spacing of 0.5 m will produce a round-trip time of ca. 3 ns. If the cavity undergoes small displacement vibrations on the order of acoustic frequencies (e.g., 10 kHz), the period of the mirror motion will be much longer than the round-trip time of the cavity, leading to a negligible dephasing of the circulating light. In its current form, the CRLAS method employs dye lasers that produce pulses of multimode laser light, with the result that the energy coupled into the cavity can look more like random noise with a bandwidth approaching that of the laser. To treat this case quantitatively, we will first make several assumptions about the input laser pulse and then study deviations that can occur as these assumptions become invalid. Suppose the input pulse consists of an envelope of modes with a spacing that is much less than the bandwidth of the total pulse and has a spatial length of several cavity round trips. Since the cavity finesse is extremely high, the amplitude of the wavepacket will be essentially constant over several round trips. If the coherence length of the pulse is on the order of several cavity round-trip lengths, we may partition the input pulse into sections equivalent to the cavity length. In this manner, the overlapping input pulse can be approximated by N number of pulses E(t) equal in length to the cavity length and applied at intervals of the cavity round-trip time (T). The intensity monitored at the output mirror in the frequency domain can be obtained by taking the Fourier transform of the field intensity inside the resonator in the time domain. For the case of two pulses injected into the cavity, the time variation of the electric field will be, Et2)(t) = E(t) + E(t- T) the Fourier transform of which is:

E(w) + exp(-iTw) *E(w) Therefore, the normalized Fourier transform of the two-trip signal is, EtZ)(w) = (1/2)[ 1 + exp(-iTw)]*E(w) = E(w)cos(Tw/2)exp(-iTw/2) with a corresponding intensity: /(2)(W) = IE(2)(w)l2 = I(w)cos2(Tw/2)

168

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

This signal is the single period spectrum modulated by a cos z term, causing it to be twice as large in amplitude at frequencies where w = Wq= (q2~/T), and dropping to zero halfway in between. Extension of this case to N successive repetitions of the signal E(t), which are delayed by T, yields, N-1

EN(t) = Z E(1 - nT) n=0

the Fourier transform of which is: N-1 1 -- e -iTwN

EN(w) = E e-inrw= E(w) =

.E(w). 1 - e-iTw

n=O

Therefore, the power spectral intensity is:

IN(w) = IEN(w)I2_ 1 -- COSNTw

- l--~os -~.l(w).

From this treatment, 9 it can be seen that the fixed time delay between successive round trips gives rise to the axial mode buildup in the cavity. As the number of round trips is increased, the frequency bandwidth of the cavity will sharpen, with a width on the order of Awq = Wax/N. The total number of axial modes in the cavity will essentially be the spectral width of the single pass signal E(t) divided by the axial mode spacing of the cavity, regardless of the number of round trips. For example, a dye laser pulse with a bandwidth (Aw) of 0.04 cm -1 would give n = 4 for a 0.5-m cavity if n were calculated using AW/Wq.However, this figure does not account for the limited coherence length of the laser pulse, which is roughly 4 cm. This 4-cm coherence length represents a fluctuation with a period of about 0.2 ns, which, using the formula for n, would give n = 22. In the preceding analysis, it was assumed that the input laser light pulse length was equal to the cavity length and applied periodically at intervals of the cavity round trip time. This assumption was made to mimic the case wherein the input laser light has a coherence length on the order of a few times the cavity dimensions but a pulse length many times that of the cavity. In practice, the input pulse periodicity may be many times the cavity length or some non-integral value of it. For example, a 15-ns light pulse would overlap itself nearly five times in a 0.5-m cavity. During this overlap, both the phase and amplitude of the pulse would be varying. In effect, the circulating pulse would be at best quasiperiodic within the round-trip time of the cavity, and this would decrease the extent of axial mode buildup. In this case, the previous analysis would break down as there is no longer a simple periodicity to E(t). For cases where a multimode dye laser pulse is used,

CRLAS: A New Analytical Technique

169

the axial mode buildup in the resonator can be essentially random. This random resonance will lead to amplitude variations in the ringdown signal that will increase as the pulse length and coherence length of the input pulse increase with respect to the cavity dimensions. Consider, this time, a 0.5-m cavity injected with narrow band light from a pulse-amplified CW dye laser system. If the laser produces a 50-MHz, 15-ns pulse, the coherence length of the light is now nearly twice as long as the cavity, whereas the pulse length is five times that of the cavity. In this case, we would expect a high degree of interference in the cavity with a small degree of energy coupling between the laser and ringdown cavities. In fact, we would expect to couple only a single laser mode into the cavity. From this, we would expect the amplitude monitored at the exit mirror of the cavity to fluctuate significantly on the timescale of the round-trip time. In the worst case, the exponential decay of the ringdown would be masked by the effects of constructive and destructive interference. The exact point at which these resonances would tend to deteriorate CRLAS sensitivity is a complex convolution of the above phenomenon. In order to avoid the ill effects associated with axial resonances in the CRLAS apparatus, several steps may be taken. The first and simplest measure is to design the cavity such that the spatial length of the input pulse is less than the cavity dimensions. In this configuration, the light has no chance of establishing standing waves in the cavity. This solution, however, is not practical in many applications and is overkill in the case where low-resolution laser light is used. More important is to design the cavity so that its dimensions are longer than the coherence length of the input pulse. In this fashion, the light is much less likely to undergo periodic interference, as the phase of the pulse is no longer preserved with successive round trips. Another possible solution is to dither one of the cavity mirrors with a period on the order of the cavity round-trip time. This would effectively destroy the coherence of the light, but would prove difficult to implement with existing technology, except in the case of very large resonator dimensions. From this discussion, it is evident that high resolution applications of the CRLAS technique can be implemented, if the above constraints are carefully considered. If good TEM laser mode quality is achieved and the light is properly coupled into the resonator, one need only tailor the cavity dimensions to the input light coherence and pulse length. Of course, the detection must also be optimized for the cavity finesse and dimensions. Additionally, the timescale of the event to be probed must be considered, as in the present applications to pulsed molecular beams. One final consideration in this discussion of CRLAS sensitivity is the role of the cavity mirrors beyond the previous consideration of maximum reflectivity. The mirrors employed in the cavity ringdown technique comprise highly polished quartz substrates with multiple-layer dielectric coatings. As many as 40 layers of

170

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY .

~'-

~/

15% bandwidth 9 al)

~

wavelength Figure 8. Typical reflectivity curve for multilayer dielectric mirror with layers of alternating ind ices of refr,~ction. At the wings of the curve, oscillations in the reflectivity value occur, due to the wavelength specificity of the coatings.

metal oxide coatings are applied to the substrate. The high reflectivity achieved in these optics is obtained through constructive interference of the multiple reflections from the many layers of the optic. Figure 8 shows a typical reflectivity curve for the case of layers of alternating high and low indices of refraction. 1~At the wings of the reflectivity curve, where the reflectivity drops off, oscillations in the r value are evident. These oscillations will also be present in the smooth part of the curve, although to a much lesser extent. As higher levels of sensitivity are desired in the cavity ringdown technique, these oscillations will require background subtraction. Even with the implementation of background subtraction, a point will be reached where the uncertainty associated with the mirror reflectivity will set an upper limit on the attainable sensitivity, regardless of the precision of the cavity decay time measurement. As the only method currently available to determine the reflectivity of such high quality mirrors is the ringdown method itself, this poses the added difficulty of separation of the error associated with mirror phenomena from errors associated with the other factors described here.

IV. APPLICATIONS OF CRLAS TO PULSED MOLECULAR BEAMS The first application of the cavity ringdown technique to the study of molecular spectroscopy was accomplished by O'Keefe and Deacon in 1988.4 By construction of simple gas cells whose windows consisted of kinematically mounted high~ reflectivity mirrors, a direct absorption ringdown spectrometer was assembled. High sensitivity was initially demonstrated by measurement of doubly forbidden optical transitions in molecular oxygen. Although these experiments established the capabilities of the CRLAS method, they did not exploit the fast timescale of the

CRLAS: A New Analytical Technique

171

ringdown event, which is typically tens of microseconds. In 1990, our group at the University of California at Berkeley, in collaboration with O'Keefe, applied the CRLAS method for the study of molecular beams. 5 In this work, pulsed supersonic beams of laser-generated metal clusters were probed, advantage of the similar timescales of both the ringdown event and the transient molecular beam being taken. Our initial work focused on the obtaining of vibronic spectra of metal clusters that had been previously observed with other techniques such as resonant two-photon ionization (R2PI) and laser-induced fluorescence (LIF). Comparison of our direct absorption data with those of other techniques clearly demonstrated the advantages of the CRLAS method.

A. The Copper Dimer Owing to the large volume of experimental and theoretical work on optical transitions in small copper clusters, we decided to target the dimer and trimer systems as a starting point, beginning with the dimer. Analogous to alkali atoms, the copper atom is the simplest of the transition metals and has therefore been the easiest to model in theoretical studies, ll From a theoretical perspective, the filled d-orbital atomic configuration of the copper atom (Ar3dl~ l) allows the extent of closed-shell contributions to bonding in metal clusters to be investigated. The copper dimer is perhaps the most thoroughly studied of the transition-metal diatomics. A wealth of experimental data has been obtained in the last decade, allowing a direct test of theoretical models of the bonding. In the first-order picture, d-orbital contributions to bonding in dicopper are ignored. In this approximation, two ground-state atoms (1S1/2) combine to form the 4st~2 bond of the leg ground state. Theoretical studies based on this simple picture, however, do not correlate well with experimental data. 12 Inclusion of d-orbital correlation in the calculations of Bauschlicher et al. 13 and Raghavachari et al. 14 effectively reduces the d--d core electron repulsion and leads to an increase in the ground-state binding energy of roughly 0.8 eV. Additionally, contributions from 4sa electron correlation have been calculated by inclusion of (4sty) 2 to (4pn,) 2 excitation, due to the near degeneracy of the 4s and 4p atomic orbitals. 13 Studies by Ziegler et al. suggest a significant relativistic correction to the bonding in dicopper that leads to an increase in the binding energy of nearly 500 crn-1, shortening the bond distance by nearly 0.03 /~.15 Although these corrections are important, the ground-state bonding in dicopper is primarily of 4so character. Comparison of the results obtained for dicopper with those of the NiCu diatomic, wherein the Ni atom possesses a d-hole (3d84s2), supports the dominant role of the s-electrons in the bonding, with these two species exhibiting similar force constants and bond lengths. 16 The first two excited states in dicopper are due to a 3d-4s promotion in one of the atoms, at the asymptotic limit. This produces a 3d94s 2 configuration that leads to 2D3/2 5 states. In Hund's case (a) coupling, these 2D states could combine with the 2S~/'2 /2 atom to produce a total of twelve possible E, H, and A states. Of these

172

J.I. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

possible states, only the lE u and ll-Iu would be dipole allowed from the ground state. Earlier work on dicopper attributed the A and B states to these lII, and 1s u states, respectively. 17a8 Later experiments, wherein rotational resolution was achieved, showed these assignments to be incorrect and postulated that these states could be explained in terms of a Hund's case (c) coupling scheme, m In addition to the A and B states, which were now assigned to both be of E symmetry, a new C state was measured at slightly higher energy than the B state. In two independent studies, LIF and R2PI spectra of the C state were obtained, though neither achieved the rotational resolution necessary for a positive spectral assignment. 2~ In our initial Cu 2 CRLAS spectra, data on the C state were obtained but proved to be relatively featureless owing to the 1-cm-1 probe laser resolution employed in that early work. 5 One of our first goals upon completion of the new CRLAS apparatus was to rotationally resolve the C-X bands to determine the state symmetry. Figures 9 and 10 show rotationally resolved CRLAS spectra for both the B - X and C - X rovibronic band systems. Inspection of the B - X system clearly demonstrates our improved linewidth (0.04 cm -1) and source stability. Of particular interest is the obvious Q-branch evident in the C-X band, indicating that the C state is of I1 symmetry. Additionally, the relative intensity of the C-X band compared to that of the B - X system suggests that it is also a singlet state. Just prior to our CRLAS measurements

P(18) P(19)P(20)

600

-

500

-

400

-

300

--

P(21) P(22) P(23)

63Cu63Cu 63Cu65Cu

CL &w

c~ o

~

o ~D 200

-

459.71

I

I

I

I

I

I

459.78

459.84

459.91

459.98

460.04

460.11

wavelength (nm) Figure 9. CRLAS rovibronic spectra of the 0-0 band of the Bls163 system of the copper dimer. The inset shows a blowup of the tail of the p-branch, where the rotational isotope effect is resolved. The beam rotational temperature is ca. 7 K and the bandwidth of the probe laser is 0.04 cm -1.

CRLAS: A New Analytical Technique 320

--

300

-

280

-

260

-

240

-

220

-

200

--

I 457

I .70

457

I .7 5

457 .81

173

I 457.86

I 457.91

I 457.97

, 458.02

Figure 10. CRLASrovibronic spectra of the 0--0 band of the C1Flu--Xls band system of the copper dimer obtained with a laser bandwidth of 0.04 cm -1. The obvious Q-branch indicates that the C state is of H symmetry. This system has also been rotationally resolved as described by Ref. 19. of the C state, Page and Gudeman had also obtained rotationally resolved LIF spectra of the C state. 19 In that work, features near the origin were less resolved, owing to the higher internal temperatures generated in the sputtering source compared to those of laser vaporization molecular beams. The absence of vibrational hot bands in our spectra also allowed features in the tail of the p-branch to become resolved. The inset in Figure 9 shows an expansion wherein the rotational isotope effect is evident. From the two naturally abundant isotopes of atomic copper, three diatomic species may be formed in the following proportions' 63Cu2, 47%; 63Cu65Cu, 43%; 65Cu2, 10%. These ratios are evident in our CRLAS spectral intensities, together with the 5:3 intensity alternation expected for the rotational lines of a homonuclear diatomic molecule with a nuclear spin of 3/2. Also of specific interest is the comparison of our intensity ratios for the B-X and C-X systems to those obtained in the R2PI work of Powers et al. 2~ In that work, the C-X band was measured as having nearly twice the intensity of the B-X system. In our CRLAS direct absorption experiments, the C-X system band intensity is only ca. 50% of the B-X system intensity, indicating a smaller oscillator strength. From our copper dimer spectra, the high sensitivity and accurate relative absorption intensities demonstrate the power of the CRD technique for the study of pulsed metal cluster beams.

B. The Copper Trimer The copper trimer is the most widely studied transition metal trimer, both theoretically and experimentally. Early experiments include the matrix isolation

174

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

work of Moskovits and Hulse 22as well as the jet-cooled R2PI experiments of Morse et al. 23 In Morse's R2PI and photodepletion experiments, twelve vibronic bands were measured in the 525-545-nm region and assigned to transitions from the 2E' ground vibronic state to an excited state of 2E" symmetry. Later experiments conducted by Rohlfing and Valentini provided evidence for a reassignment of the upper state to 2.4' symmetry, because additional fluorescence bands were observed when a vibrationally excited level of the upper electronic state was pumped. 24 In our initial Cu 3 experiments, data for the 530-nm band system were obtained with many interesting results. 5 Before presenting these results, a brief review of bonding in the copper trimer system is in order. As in the copper dimer, the first-order picture of bonding in the ground state of the copper trimer involves inclusion of only the 4s electrons. In this approximation, three Ar3dl~ copper atoms combine to form a 4sa'24se n electronic configuration. Early extended Huckel calculations by Anderson 25 as well as the SCF calculations of Bachmann et al. 26 predicted a linear 25".u ground state. In contrast, the ab initio calculations of Walch and Laskowski 27and Bauschlicher et al. 28predict a D3h ground-state structure of2E ' symmetry. In the work of Walch and Laskowski, inclusion of the 3d electron correlation leads to a nonnegligible bond contraction, with a net Cu-Cu bond length of 4.60 a 0. Additionally, the predicted symmetric stretch frequency of 224 cm -1 suggests that the 4se" orbital of the 4sa'24se 'l configuration is essentially nonbonding. Of special interest in the copper trimer is the fluxional nature of the Jahn-Teller active ground state. In the case of a strong Jahn-Teller distortion, the 2E' state, which is a maximum on the potential surface, is split into lower energy 2A1 (acute) and 2B2 (obtuse) states with CEvsymmetry. 27 According to Bauschlicher et al., these two minima are calculated to be nearly degenerate. 28 For an e' vibration of a 2E' electronic state, the addition of one quantum in the doubly degenerate bend leads to states of 2E', 2A(, and 2A~ symmetry. For the case of D3hsymmetry, these levels are degenerate. In the presence of a strong Jahn-Teller effect, this degeneracy is lifted, leading to two degenerate A states and a higher energy E state. In the work of Morse et al., 23 the 2Al and 2,42 states were measured to be roughly 15 cm -1 above the 2E' ground state. In the limit of strong Jahn-Teller stabilization, this energy difference would represent the tunneling splitting between the three equivalent C2v minima. This assignment has been verified by our CRLAS data, including two new previously unobserved transitions originating from the 2A' state, which lies 15 crn-1 above the ground state. Vertical excitation energies have been calculated for Cu 3, indicating a possible assignment for the 540-rim system. In the work of Walch and Laskowski, 27 two types of excited states were considered. The first type consisted of configurations wherein the 3d core remained intact, with excitations from the 4se" orbital to various virtual orbitals considered. The second class of excitations involved 3d-4s promotions. Both classes were treated with SCF methods as well as singles and doubles CI to determine excitation energies. Of the many excited states, the best candidate

CRLAS:A New Analytical Technique

175

for the 540-nm system was the dipole-allowed 2A~-2E transition, with an origin predicted at roughly 580 nm. Inclusion of relativistic effects shifted this origin to roughly 554 nm. Supporting this assignment was the calculated upper-state symmetric stretch frequency of 222 cm -l. The LIF data of Ref. 24 with subsequent reexamination of all Cu 3 databy Morse 29 supports this assignment. In Ref. 29, Morse postulated a curve crossing from the 2A~ state to near-lying 3d-4s states as a mechanism for the excited-state predissociation observed in his photodepletion spectra. 23 Comparison of the CRLAS spectra shown in Figure 11 with the R2PI work of Ref. 23 clearly reveals the advantages associated with a direct absorption probe. As a result of upper-state predissociation, the intensities of band 5 and 7 in the R2PI work are substantially lower than that of band 2. In contrast, the measurements obtained in our CRLAS study show similar intensities, with peak 5 being the strongest. These CRLAS intensities accurately reflect the relative transition probabilities for excitations out of the 2E' ground state. Accurate transition intensity measurements are important in ascertaining oscillator strengths and Frank--Condon 330

'I

I

I

~

I

J

I

~

I

I

,21

I

L_

320 -

Cu 3

I

-

2A,1_2 E,

-

5

_

I

a. I,...

_

Q. co t

o

i

310

300

-

290

-

4

_

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_

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o

7'

0

m 280 <

.Q

270 260 ti

530

-J

I

532

I

I

534

i

I

536 Wavelength

I

,I

538

I

I

I

540

(nm)

Figure 11. CRLAS vibronic spectra of the 2A-2E band system of the copper trimer. The energy defect between bands 4 and S and bands 7 and 7' is ca. 14 cm -1 . In the case where the zero point energy of Cu3 is greater than the barrier to pseudorotation, this 15-cm -1 gap measures the tunneling splitting of the Jahn-Teller active ground state. These data are to be compared those of Ref. 23 and Ref. 24.

176

J.I. SCHERER,J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

factors for vibronic transitions, and provide a direct comparison for theoretical models. A second point of interest involves the band labeled 7' in Figure 11. This band does not appear at all in the R2PI work of Morse et al., 23 owing to the poor signal-to-noise ratio obtained in that spectral region. If this additional band originated from the vibrationally excited ground state, a second band at 538.4 nm. would be expected, with reasonable intensity. This band would correspond to excitation from the singly excited v 1 level of the ground state to the triply excited doubly degenerate bend of the upper state. The absence of a band at this wavelength, presumably due to a lack of population in the ground state, argues against this assignment. An alternative assignment for this band is that it involves a transition from the Jahn-Teller active 2A' state located 15 cm -I above the ground state. The energy difference between bands 7 and 7' is precisely this 15-cm -1 value, the same as the energy difference between bands 4 and 5. Since the vibronic species of band 7 are A [ and E', excitations from the Jahn-Teller active 2A' state to the 2v12A[ are fully allowed. Since our initial work, results from our improved apparatus have yielded additional bands which correspond to 3vI2A/-2E ' and the 3v 12A[-2A' bands, also with the expected 15-crn-I splitting. Measurement of these additional Cu 3 bands supports our previous assignment.

C. Metal-Rare Gas Complexes The final species to be discussed in this paper is in a separate category from the covalently bound, pure metal clusters already discussed, viz., metal-rare gas van der Waals complexes. Metal-rare gas (MRG) clusters are particularly interesting owing to their very different ground- and excited-state properties. As in the case of AIAr, MRG complexes often exhibit a large increase in binding energy upon excitation into higher electronic manifolds. 3~This is due to the fact that bonding in the ground state is primarily of a van der Waals nature, in contrast to the excited state, which may be of ionic or covalent character. Two previous studies have obtained both low- and high-resolution rovibronic spectra for the A1Ar complex. In the one-color REMPI experiments of Gardner and Lester, 31 low-resolution spectra for the 2s band system were obtained consisting of a dominant vibrational progression in the upper electronic state. Several years later, McQuaid et al. obtained rotationally resolved spectra for this same band system with their LIF apparatus. 32 The relatively large A1Ar signal obtained in our mass spectrometer 9prompted us to search for this same band system in an effort to both compare our direct absorption data with the results from previously applied methods and to characterize the source conditions needed to produce MRG species. The ground state of AIAr is obtained by a combination of the ground 2 state of the AI atom with the IS0 state of the Ar atom. The lone p-electron in the Ne3s23p l AI atom can contribute to either a pt~ or pn bond, with better overlap expected for theprc orbital. As expected, a 211 ground state results and is best described in Hund's case (a), where the electron spin couples to the inter nuclear axis. The first excited

2P1/

CRLAS: A New Analytical Technique

8,.

1800

--

1600

--

1400

-

1200

-

i000

-

177

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A1 2S 1/2 -

5-0

A1 251/2

3-o 0

800

-

600

-

I

392.7s

~93.7s

I

394.7s

I

~gs.Ts

I

396.7s

wavelength (nm)

Figure 12. CRLASvibronic spectra of the 2Z-21-I band system of AIAr van der Waals complex. The two strongest peaks are due to the two spin-orbit components of the strong 25--2Ptransition in the AI atom. This low-resolution scan was performed with a laser bandwidth of ca. 0.35 cm -1 with a total acquisition time of 5 minutes. state involves promotion of the lone 3p electron of the AI atom to a 4s orbital, leading to a 2:[: state for the excited complex. This state is strongly bound as compared to the ground state, with an experimentally determined vibrational frequency of roughly 85 cm -1 and a well depth of roughly 400 cm -1.34 Because the 2s band essentially obtains its oscillator strength from the intense 2S-2P1/2 A1 atomic transition, it is expected to also be intense and red shifted with respect to the atomic line. Figures 12 and 13 show the low- and high-resolution CRLAS A1Ar spectra obtained with our apparatus. By systematically varying source conditions, we found that relatively low laser fluence and long time delays between the vaporization and probe lasers produced the most intense signal. In agreement with Ref. 31, we found maximum Frank--Condon overlap for the 4-0 vibronic band, indicative of the large decrease in bond length upon electronic excitation. Because of the excellent signal-to-noise ratios obtained, we were able to discern features previously postulated as being due to AIAr 2 in Ref. 32, with no evidence to support this suggestion. Of particular interest is the absence of the other spin--orbit component of the AIAr complex. Since the 2P3/2-2PI/2 energy separation in the atom is 112 cm -l, we would expect the S-O splitting of the complex to be less than this amount and therefore to occur within the same spectral region. We have observed an absence of higher energy spin--orbit components due to extreme cooling in other diatomic spectra; 33 however, we have no concrete evidence that this is indeed the case for AIAr. Also of interest is the absence of vibrational hotbands, even though

178

J.J. SCHERER, J. B. PAUL, A. O'KEEFE, and R. J. SAYKALLY

2500

~.

2000

O

1500

g

--

j

J

I000

I

I

I

I

I

393.05

393.10

393.15

393.20

393.25

wavelength (rim)

Figure 13. CRLAS rovibronic spectra of the 5-0 band of the 2E.--21-Iband system of AIAr. In this scan, the probe laser bandwidth is 0.04 cm -1 and the total acquisition time is roughly 10 minutes.

attempts were made to create hotter source conditions (e.g., more vaporization energy or less backing pressure for the carder gas). Although estimates have been made for the lower state well depth, 32 hot band measurements would greatly assist in determining its value. With source conditions maximized for A1Ar production, rigorous scans have been performed extending several thousand wave numbers to the red in search of larger AIAr n clusters. Although no bands attributable to AIArn have been observed, several other vibronic band systems of aluminum-containing species have been measured and are presently being analyzed.

V. SUMMARY In this chapter we have presented an overview of the theory and practice of the CRLAS technique, with emphasis on theoretical and practical sensitivity limits. As a direct absorption method, the CRLAS technique is relatively free from the complications associated with molecular internal conversion and excited-state predissociation, provided the lifetime broadening of the species is not much greater than the inhomogeneous broadening in the molecular beam. Although currently used primarily in the visible region, the availability of ultraviolet and infrared optics will permit the extension of the technique into new wavelength regimes. With the development of more sophisticated detection schemes, technique sensitivity can be further improved, provided careful consideration is given to the effects of transverse and longitudinal mode competition in the resonator.

CRLA5: A New Analytical Technique

179

Results for several species generated by laser vaporization in supersonic jets have been presented. The advantages of CRLAS for the study of pulsed molecular beams lies in the similar timescales of the ringdown and transient molecular beam events. In the copper cluster spectra presented here, the advantages of the direct absorption probe are evident in the comparison to data obtained with other techniques. The potential applications of the CRLAS technique include the study of predissociative states and molecular ions, where techniques such as R2PI are not well suited. Following the application of the ringdown concept to molecular spectroscopy by O'Keefe and Deacon and our own work with pulsed molecular beams, several other groups 34 recently have began to employ this powerful new spectroscopic tool, and applications to the detection of chemically generated optical gain were reported by Benard and Winker. as As a relatively new technique, the cavity ringdown method will very likely become more widely used in the years to come, as improvements in wavelength coverage and sensitivity continue to evolve. We hope that the present work is useful in the context of this rapidly evolving interest.

ACKNOWLEDGMENTS This research was supported by a the Experimental Physical Chemistry Program of the National Science Foundation (Grant no. CHE-9123335) and by a grant from the Petroleum Research Fund of the American Chemical Society (Grant no. 24049-AC6). J.J. Scherer thanks IBM for a predoctoral fellowship.

REFERENCES AND NOTES 1. Herbelin, J. M.; McKay, J. A.; KwoL M. A.; Ueunten, R. H.; Urevig, D. S.; Spencer, D. J.; Benard, D. J. Appl. Optics 1980, 19, 144. 2. Herbelin, J. M.; McKay, J. A. Appi. Optics 1980, 20, 3341. 3. Anderson, D. Z.; Frisch, J. C.; Masser, C. S. Appl. Optics 1984, 23, 1238. 4. O'Keefe, A.; Deacon, D. A. G. Rev. Sci. Instrum. 1988, 59, 2544. See also Ramponi, A. J.; Milanovich, E P.; Kan, T.; Deacon, D. Appl. Optics 1988, 27, 4606. 5. O'Keefe, A.; Scherer, J. J." Cooksy, A. L.; Sheeks, R.; Heath, J.; Saykally, R. J. Chem. Phys. Lett. 1990, 172, 214. 6. Heath, J. R.; Cooksy, A. L.; Gruebele, M. H. W.; Schmuttenmaer, C. A.; Saykally, R. J. Science 1989, 244, 564. 7. KogeiniL H. W.; Li, T. Appl. Optics 1966, 5, 1550. 8. Hecht, E.; Zajac, A. Optics, Addison Wesley, 2835. 9. The treatment is modeled after Siegmann, A. Lasers; University Science Books: Mill Valley, CA, 1986; Chapter 27. 10. Demtr'6der,W. Laser Spectroscopy; Springer Verlag, 1981, p 163. II. Anderson, A. B. J. Chem. Phys. 1978, 68, 1744. Miyoshi, E. J. Chem. Phys. 1983, 78, 815. Walch, S. E; Laskowski, B. C. J. Chem. Phys. 1987, 88, 1041. Bauschlicher, C. W. J. Chem. Phys. 1987, 88, 1041. 12. Kleman, B.; Lindkvist, S. Arkiv Fiir Fysik 1954, 8, 333. McCaffrey, J. G. J. Chem. Phys. 1989, 91, 92. Page, R. H.; Gudemann, C. S. J. Chem. Phys. 1991, 94, 39. 13. Bauschlicher, C. W.; Walch, S. P.; Siegbahn, P. E. M. J. Chem. Phys. 1982, 76, 6015. 14. Raghavachari, K.; Sunil, K. K.; Jordan, K. D. J. Chem. Phys. 1982, 83, 4633.

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15. 16. 17. 18. 19. 20.

Ziegler, T.; Snijders, J.; Baerends, E. J. Chem. Phys. 1981, 74, 1271. Spain, E. M.; Morse, M. D. J. Chem. Phys. 1992, 97, 4641. ,/kslund, N. Arkiv Fiir Fysik 1965, 30, 171. Pesic, D. S.; Weniger, S. C. R. Acad. Sci. Ser. B 1971, 273, 602. Page, R. H.; Gudemann, C. S. J. Chem. Phys. 1991, 94, 39. Powers, D. E.; Hansen, S. G.; Geusic, M. E.; Michalopoulos, D. L.; Srnalley, R. E. J. Phys. Chem. 1982, 86, 2556. Gole, J. L.; English, J. H.; Bondybey, V. E. J. Phys. Chem. 1982, 86, 2560. Moskovits, M.; Hulse, J. E. J. Chem. Phys. 1977, 67, 4271. Morse, M. D.; Hopkins, J. B.; Langridge-Smith, E R. R.; Smalley, R. E. J. Chem. Phys. 1983, 79, 5316. Rohlfing, E. A.; Valentini, J. J. Chem Phys. Lett. 1986, 126, 113. Anderson, A. B. J. Chem. Phys. 1978, 68, 1744. Bachmann, C.; Demuynek, J.; Veillard, A. Faraday Syrup. Chem. Soc. 1980, 14, 170. Walch, S. E; Laskowski, B. C. J. Chem. Phys. 1986, 84, 2734. Bauschlicher, C. W.; Langhoff, S. R.; Taylor, E R. J. Chem. Phys. 1987, 88, 1041. Morse, M. D. Chem. Rev. 1986, 86, 1049. Callendar, C. L. J. Chem. Phys. 1989, 90, 5252. Lessen, D.; Brucot, E J. Chem. Phys. Lett. 1988, 152, 473. Knickelbein, M. B.; Menezes, W. J. C. Chem. Phys. Lett. 1991, 184, 433. Gardner, J. M.; Lester, M. Chem. Phys. Lett. 1987, 137, 301. McQuaid, M. J.; Gole, J. L.; Heaven, M. C. J. Chem. Phys. 1990, 92, 2733. Unpublished CRLAS AIN spectra. Lester, M. University of Pennsylvania, private communication. Romanini, D.; Lehmann, K. K. J. Chem. Phys. 1993, 99, 6287; Meijer, G.; Boogaarts, M. G. H.; Jongrna, R. T.; Parker, O. H.; Wodke, A. M. Chem. Phys. Lett. 1994, 234, 269. Benard, D. J.; Winker, K. B. J. Appl. Phys. 1991, 69, 2805.

21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

35.

METAL-CARBON CLUSTERS" THE CONSTRUCTION OF CAGES AND CRYSTALS

J. S. Pilgrim and M. A. Duncan

Io II. III.

IV.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

182 185

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Metallo-Carbohedrenes: Mass S p e c t r o m e t r y . . . . . . . . . . . . . . . B. Metallo-Carbohedrenes: Photodissociation Experiments . . . . . . . . .

187 187 193

C. Metallo-Carbohedrenes: Possible Structures . . . . . . . . . . . . . . . . D. Nanocrystals: Mass Spectrometry . . . . . . . . . . . . . . . . . . . . . E. Nanocrystals: Photodissociation Experiments . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201 203 210 218 220 220

Advances in Metal and Semiconductor Clusters Volume 3, pages 181-221. Copyright 9 1995 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-788-2

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I. I N T R O D U C T I O N The discovery of C60, buckminsterfullerene, almost ten years ago by Smalley and co-workers 1-3 has had a profound impact on the field of cluster research. The notion that 60 carbon atoms would or could simply coalesce into a sphere resembling a soccer ball was regarded with much skepticism. However, those in the business of studying clusters knew that a "super magic" peak in a cluster mass spectrum indicates, in many cases, a structure of special stability (it could be closed geometrically, electronically, or both). The spherical geometry of C60 was confirmed later by both NMR 4 and X-ray diffraction. C60 represents only one of a class of similar clusters known as "fullerenes." This one molecule has spawned an enormous amount of research into the properties of clusters. The fact that a molecule that was stable enough to be isolated and studied macroscopically was discovered in a molecular beam has increased interest dramatically in this already well-established field. One major research direction has been the attempt to incorporate metal atoms into the fullerenes. So far this has resulted in the production of both endohedral and exohedral metallo-fullerenes. 5-17 However, to our knowledge there has been no substitution of metal for carbon in the fullerene cage network. Now it seems a second class of especially stable clusters has been discovered in a molecular beam. Coincidentally, they also contain carbon (though not exclusively). These are the "metallo-carbohedrenes" or "met-cars" clusters discovered by Castleman and co-workers 18--26in 1992. These species have been found to have the stoichiometry MsCI2, where M is a transition metal atom. They also display a super magic abundance in a mass spectrometer. The number of atoms and the superabundance led Castleman to propose a pentagonal dodecahedral structure for these clusters. This gives a closed-cage structure that is spherical like the fullerenes. Interestingly, the twelve pentagons that constitute the met-car is the same number found in C60. This is perhaps not so surprising, as C20 has been called the smallest member of the fullerene family. However, it has not been found experimentally. The first met-car discovered was the cation T~8C12. Castleman found this magic peak while investigating the dehydrogenation reactions of small hydrocarbons with transition metals. Isotopic labeling experiments using deuterated methane and methane-laC determined that there are no hydrogens in the structure but that there are 12 carbons. Shortly after this initial discovery Castleman and co-workers 19 found this superabundant stoichiometry for V, Zr, and Hf analogues. It was at this point that our research group became interested in these molecules. 27-30 We were able to reproduce quite nicely these magic peaks for Ti, V, and Zr using either acetylene or methane seeded in the carrier gas in our experiment. More importantly, however, we were able to produce these met-cars from Cr, Mo, and Fe. This was very interesting since there was and still is a question of how stable these clusters are as transition metals with more d electrons are incorporated into the cluster. It has yet to be determined whether all transition metals will form this stoichiometry, or if other structural types will begin to compete effectively with the 9

+

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met-car. We hope that the research results contained herein will begin to answer these questions. Additional work by Castleman and co-workers 26 included the adsorption of polar molecules onto the met-car. The adsorbate molecules investigated were water, ammonia, methanol, and benzene. The result of this work was that, at low partial pressures of reactant gas, the met-car coordinated anywhere from one to eight polar molecules and from one to four benzene molecules. At high partial pressures the met-car coordinated eight polar molecules and four benzene molecules. This uptake of molecules seems to corroborate the proposed structure and at the very least indicates that the metal atoms in the met-car are exposed and are in similar environments. Owing to the superabundance of these clusters in the mass spectra one must conclude that the cluster is exceptionally stable and that the bonding is quite strong. This motivated our group to investigate the photodissociation behavior of these molecules. A photodissociation event almost always proceeds by the lowest energy pathway. Thus, this experiment can determine which type of bonds in the met-car are the weakest. This is true in a relative sense even if the bond strength cannot be quantified. The photofragmentation patterns obtained from these experiments then can help to characterize the structure of the parent molecules as well as indicate any especially stable substructures. During the course of these experiments on the decomposition of the met-cars containing Ti we found other apparently super magic peaks in the mass spectra. These peaks extended out to over 3000 amu. These clusters, then, must be significantly larger than the met-car cluster (the Ti met-car mass is 528 amu). Using isotopic carbon labeling we were able to determine that the first of these peaks had the stoichiometry Til4Cl3. This stoichiometry had been found previously to be especially stable in several cluster systems. These systems include alkali-halide, titanium-nitride, and tantalum--carbide clusters. 31'24'2~In all of these cases the cluster was assigned to a face-centered-cubic, fcc, structure like that of the NaCI rock-salt lattice. The structural and growth patterns imposed on the clusters by this lattice turn out to explain our mass spectra quite well. Having established that the met-car was not the only special stoichiometry for the Ti system, other transition metals were investigated that were known to make the met-car. Vanadium formed the 14/13 crystallite as well, although no largerfcc clusters were found for this metal. Zirconium had been reported earlier by Castleman and co-workers 2~ to form larger structures than the met-car 8/12 cluster. In their experiment the mass spectra seemed to indicate a multiple cage-type building pattern. The proposed double-caged structure consists of face-sharing dodecahedra. Larger clusters involve the addition of cages to this two-cage structure. By joining the dodecahedra together in both one and two dimensions, the mass spectral abundances could be explained. However, some of the zirconium-carbon clusters observed had slightly nonstoichiometric structures as well as structures with dangling sub-units. The work on zirconium by our research group seemed to

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indicate a different structural pattern in our experiment. Again, we found that the

fcc crystal lattice pattern explained our mass spectra very well. Recently, work has been done on the niobium--carbon system. It is a logical choice for investigation considering its location in the transition-metal series relative to metals already known to form met-cars. Additionally, this metal might be expected to be an intermediate case in the formation of the met-car versus formation of thefcc crystallites. This is a result of separate work done by Castleman and co-workers 2~on tantalum in which it was found that only thefcc clusters were formed. Thus, vanadium formed both stoichiometries while tantalum formed only thefcc stoichiometries. The results of this work on niobium have indeed turned out to indicate intermediate behavior, as will be shown. The fcc crystallites are fascinating in that they are exceedingly small examples of the bulk structure of the transition-metal carbides. The bonding even in the bulk phase for these compounds is not understood completely. 32 There are contributions from metal-metal, metal--carbon, and carbon-carbon bonds. These crystallites or nanocrystals may turn out to have very interesting and useful properties and so may the met-cars. Thus, they may be very important from a materials science standpoint in the development of nanotechnology. For these reasons and to help examine the bonding in these compounds, our research group has also performed photodissociation experiments on thefcc crystallites. The photodissociation experiments have revealed some fascinating behavior from these unique molecules. There are at least two different dissociation pathways for the larger nanocrystals. The first is cleavage of the crystal along a crystal plane. This is we believe the first example of photochemical cleavage of a crystal in the gas phase. These results were quite unexpected and may have some usefulness in the development of a realistic nanotechnology in the future. This dissociation behavior has important implications for the bonding in these clusters. The second dissociation pathway, at least for most of thefcc systems studied, is the formation of the met-car 8/12 cluster from the nanocrystal. This seems a remarkable result at first. However, it is possible to devise a photodissociation mechanism that requires only a minor amount of rearrangement to get to the met-car from thefcc crystallite. This is especially true for the 14/13 cluster. Another remarkable result of these photodissociation experiments is that some of the metal systems form an 8/13 fragment preferentially. From the surface reconstruction mechanism proposed to form the met-car from nanocrystals, it is quite possible that the carbon in the center of the nanocrystal may not have time to vacate the collapsing crystal. When the carbon cannot escape it becomes trapped by the cage network. This cluster may have the most unique properties of anything discovered thus far. Our investigations to date have involved extending the range of metals that form the met-car structure. We have done this with Cr, Mo, Fe, and Nb. Photodissociation experiments on the met-cars have revealed interesting trends and periodicities depending on the metal in the cage. These two avenues of investigation have helped us to understand the bonding in the clusters. The formation of nanocrystals in the

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course of these investigations has also been very important and we have photodissociated these unique clusters as well. The surface reconstruction of these crystals has profound implications for their bonding. Photochemical cleavage is a competing mechanism in dissociating the nanocrystals and also helps explain the bonding.

I!.

EXPERIMENTAL

The instrument used to form and study clusters in our group has been described previously. 33 A schematic of this instrument can be found in Figure 1. Cluster ions are formed in the gas phase by use of a Smalley-type laser vaporization source. The transition metal to be studied is loaded into the instrument as a pure rod. The rod is connected to a screw mechanism that continuously rotates and translates the rod. The rod is ablated using either the 308-nm line of a XeCI excimer laser or the second harmonic, 532 nm, of a pulsed Q-switched Nd:YAG laser. Both lasers are operated at 10 Hz. In either case the laser is focused down to a few millimeters diameter. A pulsed beam valve is used to sweep an inert carder gas (He in these experiments) over the rod during the laser pulse. This carrier gas is generally maintained at approximately 60-psig stagnation pressure. The interaction of the laser, metal rod, and carrier gas produces an intense plasma in the throat of our nozzle source where the temperature may be as high as 10,000 K.

Figure 1. The pulsed molecular beam machine with reflectron time-of-flight mass spectrometer (RTOF-MS) used to produce and analyze metal-carbon clusters.

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The source chamber on this instrument is maintained at a vacuum of 10-6 torr. As the plasma interacts with the nozzle source walls and cool parts of the carrier gas pulse it cools down to around room temperature. This mixture of ions, neutrals, and electrons then expands adiabatically into the main chamber where any clusters formed in the nozzle are cooled in all energetic degrees of freedom. In the case of the metal--carbon clusters, a hydrocarbon gas (usually acetylene or methane) is seeded into the carrier gas as described previously by Castleman and co-workers. 18 Evidently, these hydrocarbons become dehydrogenated in the intense conditions of the source and then react with the ablated metal atoms to form the mixed metalcarbon clusters. The resultant supersonic molecular beam from the expansion is skimmed approximately 10 cm downstream with a 2-mm diameter skimmer. The purpose of this skimmer is to remove clusters from the beam that have significant velocity orthogonal to the beam direction. It also serves as the entrance point into a differentially pumped mass spectrometer chamber. In the experiments described herein, only ionized clusters are studied. These cluster ions enter the extraction region of a Wiley-McLaren-type 34 time-of-flight mass spectrometer. Pulsed voltages on both primary (repeller) and secondary (draw-out-grid) extraction plates result in acceleration of these cluster ions into the field-free drift region of the mass spectrometer. Deflection plates are used to counteract the significant downstream velocity of the clusters (approximately 105 cm/sec). An electrostatic lens is used on the front end of the mass spectrometer to focus the ion packets. The ions enter a reflectron at the end of the first drift tube. They are then focused again by a second electrostatic lens and enter the final drift tube at the end of which is an electron multiplier tube. This experimental arrangement measures the nascent cationic cluster distribution. Photodissociation experiments in the reflectron instrument 33 have been described previously by our laboratory. In the photodissociation experiment the clus~r ion to be investigated is mass selected by use of a pair of pulsed deflection plates at the end of the first drift tube. These plates function as a mass shutter in which a static dc electric field is used to deflect all unwanted ions. The field is then pulsed to ground when the desired cluster is in the field zone. Thus, all clusters of lower or higher mass are deflected out of the trajectory that would allow them to reach the detector. After the cluster under investigation has been mass selected it can be dissociated. The dissociation event is accomplished at the turning point in the reflectron where the vertical component of the cluster motion is momentarily zero. 33 At that point the clusters are intersected with the photodissociation laser. The 308-nm XeCI excimer laser line, as well as both the second (532 nm) and third (355 nm) harmonics of a pulsed Q-switched Nd:YAG laser, have been used in these experiments. However, all photodissociation mass spectra included in this chapter were obtained using 532 nm. Those systems where other wavelengths were investigated did not show any substantial differences in either photofragmentation patterns or

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photodissociation cross sections. Not every system has been studied with all three wavelengths, but 532 nm has been used throughout. Photodissociation mass spectra are obtained from the average of an appropriate number of laser shots. The mass spectrum is also averaged with the laser off. A computer difference technique (laser on minus laser off) shows the photofragment ions as positive-going peaks and the depleted parent ions as a negative-going peak. As we have discussed elsewhere, absolute intensities of various fragment channels are difficult to measure. 33 Therefore, we focus our attention here on relative intensities.

i11. RESULTS AND DISCUSSION A.

Metallo-Carbohedrenes:

Mass Spectrometry

The first step in the investigation of metal--carbon clusters in our group was to try and reproduce the conditions of Castleman's experiment 18 in order to determine whether the met-car could be produced in our laboratory. Figure 2 shows the results of this attempt using a Ti sample rod with acetylene seeded at around 1% into the He carder gas. There is clearly a super magic peak in the spectrum with much +

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Figure 2. The mass spectrum of cationic clusters obtained by laser ablation of titanium with acetylene seeded approximately 1% in the helium expansion gas. The superabundant peak is the titanium metallo-carbohedrene at 528 amu.

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smaller evenly spaced masses on either side. A mass spectral analysis of this peak confirms its mass to be 528 amu. This mass is correct for a cluster containing eight titanium and twelve carbon atoms. The much smaller peaks on either side of the magic peak are found to be spaced by 12 amu. Since Castleman had already used deuterated methane to determine whether there were any hydrogens in this structure, ~8we did not try to repeat that experiment. The result of that analysis was that there are no hydrogens in the structure. However, methane-13C was used by both laboratories to determine that there are twelve carbons in the cluster. This experiment is critical owing to the mass coincidence of the major isotope of titanium (48Ti) and four carbons. Unfortunately, our instrument does not have enough resolution to determine the stoichiometry from the pattern of titanium isotopes alone. Incredibly, twelve methanes are completely dehydrogenated to form the metallo-carbohedrene. The spacing of adjacent peaks by 12 amu also indicates that only metal--carbon structures are growing in the cluster source and not metal-hydrocarbons. Having established the source conditions necessary to form the titanium metcars, it became a simple matter to do the analogous experiment with vanadium. This metal is known to form the met-car ~9and we are able to produce it in our experiment as well. Fortunately, there is no problem of mass coincidence in the vanadium system. Our laboratory is also able to reproduce the met-car stoichiometry for zirconium. 27 We have not, however, attempted to make the hafnium met-car. A major question that arises from the apparent superstability of the M8C12 structure concerns how pervasive this stoichiometry is in the transition-metal period. Do only Groups IVB and VB form the met-car? To answer this question, our first attempt at extending the met-car range was with chromium. Figure 3 shows the mass spectral abundances of clusters produced by use of a chromium sample rod with acetylene seeded in the He carrier gas. It is clear that the source conditions in this experiment also produce a superabundant cluster relative to other stoichiometries in the spectrum. The mass of this cluster corresponds to that of Cr8C~2. There is no mass coincidence of the major Cr isotope (52 amu) with any combination of C atoms. Thus, it seems that the met-cars extend at least into Group VIB. The lack of mass coincidence in the chromium-carbon cluster allows the exact stoichiometries to be determined even for the lower intensity peaks in the mass spectrum. The met-car is clearly a global maximum in the distribution, but closer inspection of the peak intensities reveals other local maxima. If it is assumed that the smaller masses represent intermediates in cluster growth, one can gain an understanding of the building-up process to get to the met-car for this system. Of course, the growth pattern may be specific for this transition metal and one may not infer that it is the same for titanium or vanadium. It is quite interesting that the first of these local maxima in the mass spectrum corresponds to CraC ~ . A possible explanation is that this cluster could simply be half of the met-car cage. It would, however, be difficult to rationalize such a structure since this would imply many

Metal-Carbon Cagesand Crystals

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dangling bonds. Nevertheless, the metal to carbon ratio of the met-car (M:C = 2:3) is maintained in this cluster. Castleman 21 has proposed a growth pattern consisting of MC 2 units for the met-car. It seems for Cr that if one looks at the local maxima between the first major peak, 4/6, and the met-car that the average increment is CrC 2, consistent with a MC 2 growth process. However, another interpretation of these spectra could be that the smaller masses observed are dead ends that are not able to continue the growth process. The second metal that was investigated in our laboratory for met-car formation was molybdenum. 28 This seemed a likely candidate since chromium had already been shown to work. In studying the behavior of formation of the met-cars within a group, it was noticed for Group IVB that the metals did not form the met-cars to the same extent. Even the growth patterns were different for Ti and Zr. From this trend it was not obvious whether molybdenum would form the met-car to the same extent as the chromium did. Figure 4 shows the mass spectrum obtained from a molybdenum sample rod under the same conditions that led to chromium met-car formation. The mass peaks in this spectrum are significantly broadened by the natural isotopic distribution of the molybdenum atom (it has seven isotopes spread over nine amu). The combination of these isotopes in a cluster with eight metal atoms leads to the broad peaks shown here. The Mo8C~2 ion is obviously the most abundant peak in the mass

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J.S. PILGRIM and M. A. DUNCAN

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processes that lead to production of bare metal and carbon atoms could cause the molecules to form preferentially according to one structural pattern or another. What is needed now is for either of the two groups to try and look at the other charge-state distribution under their experimental conditions. The major result of the work on chromium and molybdenum was that the formation of the met-car was shown to be more pervasive than previously thought. However, the ability of these metals to form the met-car seems to be more dependent on the source conditions. The Group IVB and VB metals seem to assume the met-car stoichiometry quite readily and under widely varied source conditions. Indeed, it is quite difficult experimentally to n o t form met--cars with these metals. Group VIB metals, on the other hand, required much finer adjustment of the plasma conditions to form a significant amount of metal--carbon clusters. Nevertheless, when the metal--carbon clusters are formed the met-car is the global maximum. The sensitivity of chromium and molybdenum towards forming the met-car seems to indicate, circumstantially perhaps, that this cluster is not as stable as it is for the earlier transition metals. These observations are consistent with the bonding theory proposed by Reddy and co-workers. 36 Figure 5 shows the distribution of metal-carbon clusters formed from an iron sample rod with acetylene seeded in the He carrier gas. From this figure it is clear

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J.S. PILGRIM and M. A. DUNCAN

that iron also forms a cluster with the stoichiometry Fe8C'~2. However, this cluster stoichiometry is by no means as superabundant as it is with the other metals investigated. In fact, Castleman and co-workers 22 were not able to produce ironcarbon clusters. There are several other stoichiometries that are equally abundant. These are FeTC~ and Fel2C~2. The met-car stoichiometry is not especially abundant even locally in the clump containing eight iron atoms. There is, significantly, a truncation in this clump after the 8/12 cluster. Truncations like this have also been used as a criterion for establishing a cluster as a magic peak. It seems from the iron experiment that, in Group VIII, other growth patterns can compete effectively with the formation of the met-car. In this group the met-car is only a slightly out-of-the ordinary stoichiometry in intensity. It will be shown in Section IIIB, by use of the photodissociation experiment, that Fe8C~2 is actually the met-car. Since in the iron system the met-car is already losing its superabundance, it is unlikely that transition metals further in the period would form the met-car. However, experiments will undoubtedly be attempted in the future to test the affinity of cobalt and other transition metals for formation of the met-car and metal--carbon clusters in general. One of the metals that seems to have been passed over initially is niobium. Given the fact that all of the Group IVB metals form the met-car and that vanadium does also, there is no logical reason to omit niobium from these investigations. Recently, however, both Castleman's group 37 and our laboratory 38 have investigated this species. Castleman found that, under different source conditions, different growth patterns could be induced in the niobium--carbon clusters, namely the formation of nanocrystals and met-cars. In addition, the other Group VB metal, tantalum, was shown by Castleman and co-workers 2~ to form only the fcc structures. Thus, the niobium system becomes even more interesting as an intermediate case for these competing structural growth patterns. Figure 6 shows the mass spectrum obtained using a niobium sample rod with methane seeded in the He carrier gas. The mass spectrum reveals many mixed niobium--carbon clusters. The spectrum can be characterized as a series of clumps with each individual clump containing the same number of niobium atoms. Clusters in the group containing eight niobium atoms seem to enjoy some special stability compared to groups containing more or less than eight atoms. In addition, within this group the cluster with twelve carbon atoms is followed by a significant truncation in intensity. From this behavior, the NbsC~2 cluster ion appears to be a slightly preferred stoichiometry and probably also has the met-car structure. Closer inspection of Figure 6 seems to reveal that the group with eight niobium atoms is indeed peculiar. If one ignores this group entirely, what is left is a steadily decreasing intensity for each group. This is perfectly normal behavior as the clusters with more atoms require more collisions for formation in the source. The locally significant stoichiometries in clusters with other than eight atoms fit a common structural motif that will be discussed later in this section. The point here is that the "met-car clump" is anomalous and may simply be superimposed on an underlying

Metal-Carbon Cages and Crystals

193 +

NbI,(i,,l

o!

.,.) . P,-I

9 ,,..)

I

III

.4

m,4

.,.)

C~

500

10'00

15'00

Mass (amu) Figure 6. The mass distribution of cationic clusters produced by laser vaporization of niobium with hydrocarbon seeded in the helium carrier gas.

growth pattern. These two growth patterns may in fact have no relation to each other. Thus, we do not attempt to use the growth pattern for clusters smaller than the 8/12 stoichiometry to infer any structural information about the met-car for this system.

B. Metallo-Carbohedrenes: Photodissociation Experiments There is much information to be gained by doing mass spectrometry experiments on the met-cars. The growth patterns in these spectra may point towards a particular structure for the more abundant stoichiometries. Super magic peaks in the mass spectra usually are the result of closed structures. These structures may be closed geometrically as in C60,~ electronically as in alkali metal clusters, or both. Conversely, these structures may not be closed in either sense but are the result of a compromise or maximization of both types of closure. Mass spectrometry then does not allow determination of the geometric structures with 100% assurance. Other experiments are needed to investigate the structures implied by the mass spectra. For this reason, we have undertaken photodissociation experiments to test the structure and investigate the bonding in the metallo-carbohedrenes. The logical choice for the initial photodissociation studies is the titanium met-car since this was the cluster that originally led to the proposed structure for the M8C~2 species. Figure 7 shows the photodissociation mass spectrum of TisC~2 from use of the 532-nm second harmonic of a pulsed Nd:YAG laser. As explained in Section

194

J.S. PILGRIM and M. A. DUNCAN

+

Ti8C 2 op,,q

1

!

t

I

250

500

750 +

0

V8C12 e"

J J:

U2.

,

I

250

.

I

500

I

750

Mass (amu) Figure Y. The photodissociation mass spectra for TisC~2 and V8C~2metallo-carbohedrenes at 532 nm. The laser power in both cases was most likely high enough to result in muItiphoton absorption. Both species fragment by the loss of neutral metal atoms.

I, mass spectra with the laser on are subtracted from mass spectra with the laser off. With the laser off, there are no photofragments or depletion of the parent. Thus, the subtraction results in a negative peak for the parent, representing its loss in intensity by fragmentation, and positive peaks representing the photofragments themselves. From Figure 7 it is clear that the titanium met-car ions do in fact dissociate at 532 nm. The major cationic photofragments have metal/carbon stoichiometries of 7/12, 6/12, and 5/12 in decreasing order of intensity. These data suggest that the cluster dissociates by a sequence of neutral metal atom evaporations. There are several effects that combine to determine the intensity of a photofragment. The thermodynamics of the reaction, that is, the energy of the parent compared to the energy of

Metal-Carbon Cagesand Crystals

195

the fragments, is a very important one. Internal energy in the parent and the dissociation activation energy help to determine the unimolecular dissociation rate. Finally, all other things being equal, the amount of energy pumped into the cluster by the photodissociation laser is a determining factor in this dissociation rate. The result of all these parameters is that, usually, more stable clusters show up as more intense peaks in the photodissociation mass speCtrum. Interestingly, the major photofragment is the titanium atomic ion. The titanium atom has an ionization potential (IP) of 6.82 eV. There are two different processes that can lead to the atomic ion as a peak in the dissociation mass spectrum. The ion could be an actual photofragment, leaving the rest of the cluster neutral. Alternatively, the atom may leave the met-car as a neutral and then be ionized by the photodissociation laser. On the basis of experiments done on other metal--carbon clusters we believe that the metal atom fragments from the parent as the ion. The implication of this behavior is that the ionization potential of the titanium atom and Ti7C12 are close. Then, to the extent that the IPs of TiTCl2 and TiaCt2 are similar, we can infer that the met-car IP is close to that of the atom. The theoretical work of Jena and c o - w o r k e r s 36 places the IP of the titanium met-car at around 6 eV. Further experiments are required to determine the IP of the met-car directly. Figure 7 also shows the photodissociation mass spectrum of V8C'~2 obtained with use of the 532-nm second harmonic output of an Nd:YAG laser to fragment. Just as the growth patterns for these two metals are similar in the normal mass spectra, so are the photodissociation products. The vanadium met-car fragments according to an evaporation of neutral metal atoms. Atomic vanadium ion is prevalent as a photofragment in this system, which is analogous to the titanium met-car. We make the same inferences in both cases, that being the similarity in the IP of the met-car and the atom. Under the highest photodissociation laser pulse energies (approximately 100 mJ/cm2), we were not able to detect the loss of more than three metal atoms from either of these clusters. The extent of fragmentation in these experiments is determined by the binding energies of the fragments to the parent, the number of photons absorbed by the parent, and the unimolecular dissociation rate for the particular reaction mechanism involved. Thus, under higher laser powers the parent should fragment to a greater degree. Alternatively, an electronic resonance would greatly increase the probability of absorption and thereby the number of photons absorbed. Studies done to measure the power dependences of these photodissociation processes indicate that they are multiphoton in nature. Energy disposal into the modes of the cluster as well as theoretical values for the binding energy of atoms in the met-cars will be addressed in Section IIIC. Figure 8 shows the photodissociation mass spectra obtained for CraCk2 and FeaCl+2 at 532 nm. What is immediately obvious from these spectra is that these clusters undergo extensive fragmentation. The primary dissociation mechanism for these met-cars is again the loss of neutral metal atoms. However, both Cr and Fe met-car parents have lost up to six metal atoms. Interestingly, a fragment with a

196

J.S. PILGRIM and M. A. DUNCAN +

12 ~o ....q ,T.

.'1 "-'~ ~y'

z60

32 ."~

4bo +

1o

FesC12

~ >

~

,n

iI

".-I

-I

___J

c~ 260

4()0

660

Mass (amu) Figure 8. The photodissociation mass spectra for Cr8C~'2 and Fe8C]2 metallo-carbohedrenes at 532 nm. These species fragment extensively, losing up to six neutral metal atoms. The M3C2 fragment is a well-known stoichiometry for the bulk lattice of chromium carbide.

metal/carbon stoichiometry of 3/2 is found in the mass spectra for both of these metals. This fragment has not been seen in any of the other met-car clusters. The 3/2 stoichiometry is one of the well known bulk lattice structures for chromiumcarbide. 32 It is not, however, known for iron and we have no explanation for its appearance in the FesC~2 dissociation. The atomic ion is again a major fragment for both species. All of the first-row transition-metal met-cars studies have had atomic ion fragments. As discussed previously, the implication is that the met-car and the atom have similar ionization potentials. The extent of fragmentation of Cr and Fe may have significant implications for the strength of the metal--carbon bonds in these clusters. One possible explanation for the greater fragmentation in Cr and Fe relative to Ti and V is that Cr and Fe have

Metal-Carbon Cages and Crystals

197 +

o

ZF8Clz

, p..~

9 ;>

I

I

1

300

600

i

V I

900 +

7,10

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op.,i O0 CD

.p,i

J

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i

. . . .

t

750

I

1250

Mass (amu) Figure 9. The photodissociation mass spectra for ZrsC~2 and Mo8C~'2metallo-carbohedrenes at 532 nm. These species lose metal-carbon units rather than bare metal atoms. The loss of metal--carbon units seems to be limited to the second-row transition metals.

an electronic resonance at 532 nm. However, this is not believed to be the case, because the actual photofragments are less intense in these clusters than in the Ti and V systems at the same fragmentation laser power. The relative dissociation cross sections are smaller for the Cr and Fe met-cars. Therefore, the most likely explanation is that the binding energies in these clusters are less than those in the Ti and V analogues. This explanation has been supported by theory on the bonding as a function of metal d-orbital occupation, which will be discussed in Section IIIC. 39 Of the second-row transition-metal met-cars, ZrsC~+2 was the first to be dissociated. As mentioned previously, the zirconium met-car mass spectrum was reported by Castleman and co-workers 2~to be qualitatively different from their titanium and vanadium mass spectra. Evidence was presented for the formation of multiple-cage met-cars with the dodecahedra sharing a common face. Zirconium met-car clusters

198

J.S. PILGRIM and M. A. DUNCAN

containing up to four dodecahedra were reported. We have not been able to reproduce these data in our experiment, although we do have evidence for larger zirconium-carbon clusters. At any rate, the mass spectra of Castleman implies unique behavior for zirconium. We have therefore undertaken photodissociation experiments on the ZrsC~ met-car. Figure 9 shows the photodissociation mass spectrum of the zirconium met-car at 532 nm. It is immediately obvious that the photofragments are very different from those of any of the first-row metallo-carbohedrenes. The first photofragment does indeed correspond to loss of a neutral metal atom. However, other fragments correspond to loss of fragments differing by ZrC 2 units. This is highly interesting since Castleman 21 has proposed that the growth mechanism for the met-cars is through MC 2 units. Another interesting result of this supposed sequential mechanism is that the smallest major photofragment is ZraC ~ . Perhaps dissociation stops at this cluster owing to a special stability. Smaller photofragments are significantly reduced in intensity. The 4/6 stoichiometry could simply be half of the met-car cage. Equally interesting is the intensity of the atomic metal ion. It is less for this system than for any of the first-row systems. The implication is that the ionization potential for the zirconium met-car is considerably less than that for zirconium atom (IP[Zr] = 6.84 eV). Clearly, the behavior of the zirconium met-car is qualitatively different from the first-row met-cars. The loss of metal-carbon fragments points towards stronger metal-carbon bonds in this cluster. This bond strength variation needs to be addressed by theoretical calculations. The photodissociation of the zirconium met-cars still leaves open the question of whether the loss of metal-carbon fragments is unique to zirconium or is actually an indicator of specific differences between the first- and second-row metals. This exciting development in our study made the photodissociation behavior of the molybdenum met-car especially important. Figure 9 also shows the photodissociation mass spectrum for the Mo met-car at 532 nm. Several differences are immediately apparent from previous mass spectra. The main difference (as for zirconium) is that the peaks are very broad. This broadening is a result of the natural isotopic distribution for molybdenum (seven isotopes spread over nine amu). To assign mass spectra with this type of isotopic pattern we simply use the centroid of the peak and the weighted average atomic mass. Upon examination of the photofragments it is clear that the molybdenum met-car also fragments by the loss of metal-carbon units, although not precisely in the same manner as the zirconium met--car. For example, the first (largest) photofragment for molybdenum corresponds to loss of MoC 2 whereas the zirconium met-car simply lost an atom. What is even more interesting is that the smallest fragment is Mo4C ~ . This stoichiometry was also the smallest fragment for the zirconium system. Again, it is tempting to assign this fragment to being half of the met-car cage. However, the most interesting aspect of the molybdenum system presents itself upon examination of the photofragments in pairs. Let us assume, although there is no direct evidence to support this, that the photofragmentation is sequential and not

Metal-Carbon Cagesand Crystals

199

concerted. That is, the next smaller fragment comes from the fragment immediately larger than it. The first loss from the parent, then, is of MoC 2. The second fragment, Mo6C~, results from a loss of MoC from the first fragment. Combining these two losses gives a total loss of Mo2C 3. This is the precise stoichiometry of the five-membered ring in the proposed dodecahedron. Importantly, there is a significant truncation in intensity for the next smaller photofragment. This would imply a special stability of the 6/9 stoichiometry. The 6/9 stoichiometry should be locally more stable in this fragmentation series since it minimizes the dangling bonds at five (assuming that the parent is actually the dodecahedron), and any further decomposition would result in breaking a carbon--carbon bond (same assumption). To carry this argument further, the third fragment again results from loss of MoC2; and finally, the fourth fragment comes from a loss of MoC. The combination of these losses corresponds possibly to the loss of another five-membered ring. Unfortunately, we cannot determine the structure of the photofragments in our experiment. If the above mechanism is correct, then the 4/6 fragment would end up as a ring. As mentioned earlier, the structure could also be half of the met-car cage. It could just as well be some completely different structure, although the loss of Mo2C 3 is intriguing. Finally, the atomic ion is found to be very small in the molybdenum system. We interpret this again as a lowering of the IP for the met-car relative to the atom. It is interesting that the second-row met-cars have small atomic ion fragments whereas in the first row the atomic ion is the major fragment. The latest met-car to be studied by our laboratory in both mass distributions and photodissociation mass spectra is niobium. The mass spectrum has already been shown to be different from that of the other met-cars owing to its "clumpiness." Many significant local maxima are found that seem to represent an independent growth pattern from the met-car. It turns out that the photodissociation mass spectra are equally peculiar for the niobium system. Figure 10 shows the photodissociation mass spectrum for the niobium met-car at 532 nm. Owing to the significant intensity of niobium-carbon clusters immediately preceding the met-car 8/12 stoichiometry as well as the limited mass resolution of our experiment, our mass gate is not able to deflect these clusters enough out of the flight path to give a clean mass spectrum. However, we are able to correlate the fragments with the appropriate parent by adjusting the mass gate timing until the fragment intensity is maximized. The first photofragment in Figure 10 is NbTC~ . This fragment is the result of a loss ofMC 3 and has not been observed for any other met-car system. In the proposed dodecahedron the niobium (or any metal) atom would be bound to three carbons. However, to get an MC 3 fragment three carbon-carbon bonds have to be broken. We have presently no explanation for such behavior. The second fragment is 6/7, corresponding to a loss ofNbC 2 from the first fragment, again assuming a sequential mechanism. This has been observed as a common loss mechanism for the other second-row met-cars. Subsequent fragmentation events correspond to loss of NbC and NbC 2 in that order (perhaps indicating a five-membered ring fragment again). The result of all these losses produces the most abundant photofragrnent, Nb4C ~ .

200

I.S. PILGRIM and M. A. DUNCAN +

1,o

NbsCle 4,4 6,7 _

.

>

(1,)

e~)0

500 7~0 Mass (ainu)

10'00

Figure 10. The photodissociation mass spectrum of NbsC~2 metallo-carbohedrene at 532 nm. This cluster also loses metal--carbon units. The fragmentation pattern is different than for other second-row metallo-carbohedrenes with an initial loss of NbC3.

No other met-car system has displayed this stoichiometry as anything special in either growth or decomposition. The NbaC ~ cluster is very likely to be a fcc nanocrystal. It corresponds to the smallest crystal structure that is complete in three dimensions. The cluster would have the form of a 2 x 2 x 2 cube, that is, two atoms on a side in each of the three dimensions. Again, our experiment cannot determine structures directly; however, the face-centered-cubic packing pattern is well known for bulk niobium carbide. 32 As will be shown in Section lIID, this pattern is prominent in the mass spectrum. Finally, it appears that the atomic ion is a significant fragment for the niobium system, indicating similar IPS for the met-car and the atom. In the comparison of the photodissociation mass spectra of the second-row met-cars there seems to be a common loss mechanism to a certain degree. Only the zirconium system loses a single metal atom at any point in the decomposition. Otherwise, the loss mechanism is MC, MC 2, or both. Niobium is different in the initial loss of MC 3, which is likely to be the reason it ends up at the M4C4 stoichiometry rather than the M4C 6. At any rate, it is clear that the second-row metallo-carbohedrenes prefer to lose MC x units whereas the first-row met-cars almost exclusively lose metal atoms. This result was wholly unexpected and seems to imply some fundamental difference in the metal--carbon bonding in the two transition metal periods. Hopefully, careful theoretical calculations can explain the relative strengths of metal-carbon versus carbon--carbon bonds as one changes transition-metal period.

Metal-Carbon Cages and Crystals

201

C. Metallo-Carbohedrenes: Possible Structures The first structure proposed for the metallo-carbohedrene was the pentagonal dodecahedron of Castleman and co-workers. 18 However, neither the Castleman group nor our laboratory has been able to definitely determine the structure. We have, in trying to explain our data, attempted to show how they can be explained in the context of this structure. There are in fact several other proposed structures found in the literature that may be equally valid. Therefore, in the interest of fairness we present these structures here as well as the pentagonal dodecahedron. Figure 11 shows the well-known pentagonal dodecahedral (Th) structure proposed by Castleman and co-workers. Chemical intuition should immediately reveal that the M-C and C-C bonds are not likely to be the same length in this structure. The result is a distortion from a regular dodecahedron. Several theoretical groups 36'39-41 rapidly confirmed this structure for the M8C12 stoichiometry. It was found that the C--C bond is much shorter than the M-C bond and is near the length expected for a double bond. The picture presented by Lin and Hall 39 is one of localized rc bonds on the C 2 units with t~ bonds linking these units to the metal atoms. This situation can be visualized easier by looking at the metal atoms as being located at the vertices of a cube with the C 2 units capping the cube faces. It should not be inferred that M - M bonds contribute significantly to the bonding in this structure: the M - M separation is twice that of C-C. Jena and co-workers 36 calculated a binding energy of 6.1 eV/atom for the TisCl2 cluster within this bonding framework. Figure 12 presents an interesting structure, in Dza symmetry, first proposed by Chen and co-workers. 42 In this structure the eight metal atoms form a distorted

Figure 11. The pentagonal dodecahedral structure, Thsymmetry, originally proposed by Castleman for the metallo-carbohedrenes. The eight metal atoms are in equivalent environments.

202

J.S. PILGRIM and M. A. DUNCAN

0----@

I Figure 12. Another proposed structure, in D2d symmetry, for the metallo-carbohedrenes. The two structures shown are equivalent but have different atomic connectivities to emphasize the importance of metal-carbon and metal-metal bonding in this structure. The eight metal atoms are divided into two groups of four on the basis of their local environments.

cubic cage. Four of the six C 2 units are then added to point along the longest diagonal of each of the four parallelograms of the metal cage. Finally, the other two C 2 units are added to the top and bottom of the cluster. It is important to note that in this structure all of the metal or carbon atoms are not equivalent. The metal atoms are divided into two groups of four each; one group has four carbon nearest neighbors and one has five. In the description of the structure it is clear that the C 2 units at the top and bottom of the cluster are different from those on the parallelogram faces. Even though the metal atoms are not equivalent, they are all exposed, and therefore the uptake of polar molecules does not rule out this structure. It is interesting, though, that in this structure the M-C bonds are expected to be weaker than in the dodecahedron, yet we see MC fragments in the photodissociation experiments. Additionally, the M - M bonds are proposed to be stronger in this structure, whereas we see extensive evaporation of metal atoms (up to six) for the first-row met-cars. Of course, the photodissociation experiments do not rule out the D2d structure, and the two groups of metal atoms are intriguing if one recalls that only four benzene molecules were adsorbed by the met-car. 26 Another equally interesting structure, in Td symmetry, is presented in Figure 13. This structure was originally proposed by Dance 43 and later corroborated by others. 44'45 The structure can best be described as an inner set of four metal atoms arranged as a tetrahedron. Then, each of four other metal atoms cap the faces of the inner tetrahedron, forming an outer tetrahedron, a so-called tetracapped tetrahedron. Finally, the six C 2 units align themselves along the six edges that define the outer tetrahedron. This structure was found by several groups to be much lower in energy than the dodecahedral structure and the D ~ structure. The cluster described

Metal-Carbon Cages and Crystals

203

Figure 13. The structure proposed by Dance, 43 in Td symmetry, that has been found to be lowest in energy by theory so far. The structure consists of a tetracapped tetrahedron of metal atoms with six C2 units lying parallel to the edges of the tetrahedron. The metal atoms are also not equivalent in this structure with four six-coordinating metal atoms and four three-coordinating metal atoms.

here does not really expose all of the metal atoms equally 9 There are, as in the D ~ structure, two sets of metal atoms. Thus, this structure is interesting in regard to the uptake of the four benzene molecules but seems lacking in the uptake of the eight polar molecules. One possibility is that each of the four less coordinated (i.e., only three normal bonds) metal atoms is able to coordinate two polar molecules. The theory does not really address this assumption 9Further theoretical calculations would be very helpful in the resolution of this dilemma. There are, in addition, several other proposed structures. These range from an inner icosahedron of carbons surrounded by a cube of metal atoms 46 to a metal cube with the C 2 units actually in the faces. 47 The situation at this point has not been resolved. What is required to resolve structural questions is the isolation of the met-cars in macroscopic quantities. Some preliminary work in this area has been reported by Castleman. 25 With the isolation and purification of these clusters, powerful analytical techniques such as X-ray diffraction and NMR can be brought to bear. Presently, however, we should be very careful not to overinterpret our data.

D. Nanocrystals: Mass Spectrometry During the course of the experiments on the titanium met-car in our laboratory, it became immediately obvious that there are other special stoichiometries for the 9 + 29,30 titanium-carbon clusters other than T18C12. Figure 14 shows the mass spectra containing the larger titanium-carbon ionic clusters under different focusing con-

J. S. PILGRIM and M. A. DUNCAN

204

1413

T i n C m+

812

, p...d

> .,.,q

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I

1

250

I

I

1

1250

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828

+

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1044

o p,,,q

1404 /

25 i

1800

.~

I

1000

zz ^ ~

I

2244

I

I

2000

1

3000

Mass (ainu) Figure 14. The mass distribution of cationic clusters produced by laser vaporization of titanium with hydrocarbon seeded in the helium expansion gas. The upper trace shows mass peaks heavier than the metallo-carbohedrene under mild focusing conditions of the mass spectrometer. The lower trace shows the extent of formation of larger titanium-carbon clusters with the mass spectrometer focused on higher masses.

ditions in the mass spectrometer. These mass spectra are obtained by seeding about 1% methane in the He carrier gas. The first magic peak after the 8/12 cluster (528 amu) has a mass of 828 amu. Unfortunately, the mass coincidence of Ti (48 amu) and four carbons precludes direct assignment of the stoichiometry. We have therefore used methane-13C as the hydrocarbon precursor in the plasma. The 828-amu peak shifted by 13 amu when the isotopic methane was used. This cluster then must contain 13 carbon atoms. With the number of carbon atoms established it immediately follows that there are 14 titanium atoms in the cluster.

Metal-Carbon Cages and Crystals

3x3x3

205

3x3x4

Figure 15. The face-centered-cubic lattice for the 3 x 3 x 3 and the 3 x 3 x 4 nanocrystals. The dark balls represent carbon atoms and the open balls represent metal atoms.

The 14/13 stoichiometry has been found to be quite common in molecular beams. Castleman and co-workers 24 found this stoichiometry in titanium-nitrogen clusters. Alkali halide clusters also form this combination preferentially in supersonic expansions. 31 In addition, this stoichiometry was found by Castleman 2~ for the tantalum-carbon system. Therefore, the cluster has been found stable for metalcarbon systems and for the nitride of titanium. It should not be surprising, then, that the cluster is stable for the carbide of titanium. In all cases where this specific cluster was found the interpretation has been that the cluster represents a microscopic version of a face-centered-cubic crystal lattice. This bulk lattice type is exactly that found for titanium carbide. 32 We therefore believe the structure of this cluster to be a 3 x 3 x 3 fcc nanocrystal. Figure 15 shows the face-centered-cubic arrangement for the 3 x 3 x 3 and the 3 x 3 x 4 nanocrystals. The lower mass spectrum in Figure 14 shows larger titanium-carbon clusters with the mass spectrometer conditions set to detect higher masses. There are clearly many clusters larger than the met-car and the first 14/13 nanocrystal. We have attempted to interpret their stoichiometries using the fcc building pattern implied by the 828-amu cluster. At the masses shown in Figure 14 the resolution of the mass spectrometer is very poor. It was not possible to measure isotopic shifts with methane-laC Therefore, the masses shown in the Figure are only approximate and have progressively larger errors as one goes to higher masses. However, it is the general pattern of the peaks that determines the likely structural motif. The fcc scheme is able to explain all of the peaks in the mass spectrum (other than the met-car, of course). For example, the mass 1044 peak is likely to be a 3 x 3 x 4

206

J.S. PILGRIM and M. A. DUNCAN

nanocrystal with a slightly non-stoichiometric metal--carbon ratio of TilTC~-9 .. All of the peaks can be assigned in this manner, especially when slight nonstoichiometry is allowed. Interestingly, the nanocrystals described in this manner are all cuboidal with similar extent in all three dimensions. Table 1 shows our assignment for the titaniurrv-carbon clusters formed in our experiment. It is quite amazing that clusters as large a s T136C36, with apparently no hydrogens attached, can be formed in the molecular beam from use of a hydrocarbonprecursor. This observation is definitely true for the 14/13 nanocrystal, because we have determined its mass exactly, and it is presumed to be true for the larger nanocrystals. Shortly after the titanium experiment revealed this other growth pattern for metal-carbon clusters, the same fcc pattern was found for the vanadium--carbon system. Figure 16 shows the mass spectrum obtained with 1% methane seeded in 9

+

Table 1. MassesObserved in the Higher Molecular Weight Range Compared to the Predictions of Various Structural Schemes Predicted Masses for lixC Y Observed

Multiple Cages a

1044 -l- 12

1284 + 24

1212, 1320

1404 -1- 12

1476

1632 + 24

1716

1800+24

1884 + 24

2244 + 100

fcc b

Substituted C6oc

1080 (1044) 18,18 (17,19) 3x3• 1332 (1296) 22,23 (21,24) 3x3x5 . 1440 (1404) 24,24 (23,25) 3x4x4 1620 27,27 3x3x6 1800 30,30 3x4x5 1920 (1884) 32,32 (31,33) 4x4x4 2160 36,36 3x4x6

1044 9,51 1260 15,35 1404 19,31 1620 25,35 1800 30,30 1872 32,28 2232 42,18

Notes: IMultiple cages refers to face-shared dodecahedra. bfcc ideal lattices are given for X = Y with nonstoichiometric values in parentheses. CThe substituted C6o corresponds to replacing carbon atoms in the fullerene cage network with metal atoms. Stoichiometries corresponding to each mass and thefcc lattice patterns are given below it.

Metal-Carbon Ca~es and Crvstal.~

207

+

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V n t... In

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2 2 I

250

I

i

I

750

Mass (amu)

I

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1250

Figure 16. The mass spectrum of cationic clusters obtained by laser vaporization of vanadium with hydrocarbon seeded in the helium expansion gas. This system also contains a peak at higher mass than the metallo-carbohedrene, which we assign to the 3 x 3 x 3, fcc, nanocrystal.

the He carrier gas, a vanadium sample rod being used. It is clear from this Figure that the extent of larger metal--carbon cluster formation is less than for the titanium system. In fact, the only cluster larger than the met-car is the 3 x 3 x 3, V]4C1+3, nanocrystal. However, this particular fcc stoichiometry is definitely super magic for vanadium. The 1"1 metal--carbon ratio of the fcc lattice is well known to be a bulk form of vanadium carbide, 32 as it is for titanium carbide. Of course, this 1" 1 ratio cannot be maintained when all three indices of the nanocrystal are odd. Interestingly, the V14C13 stoichiometry results in a cluster with one excess positive atom (assuming the metal atoms are positively charged and the carbon atoms are negatively charged). Thus, this cluster is very stable as a cation, which is what we obtain in our mass spectrum. In fact, the neutral version of this stoichiometry for the alkali halide nanocrystal, Na]aF]3, was found to have the lowest IP of any cluster measured to date (1.89 eV). 31 As was mentioned previously, the iron system is different from the other metalcarbon systems in that the met-car stoichiometry is not excessively abundant compared to other combinations. The mass spectrum of iron--carbon clusters is shown in Figure 5. Another interesting difference in the iron--carbon system is that the clusters larger than the met-car do not appear to fit a fcc growth pattern. However, the most abundant larger cluster is Fe]2C~2, which maintains thefcc 1" 1

208

J.S. PILGRIM and M. A. DUNCAN

metal-carbon ratio. One might at first suppose that this cluster is a 2 x 3 x 4 fcc nanocrystal, but the 12/12 cluster has not been found to be superabundant in any other transition metal-carbon system that we have studied. Yamada and Castleman 48 have suggested that Cu12C12 may be an especially stable cluster having a face-centered tetragonal lattice similar to calcium carbide. That suggestion is based on the Cu2C 2 bulk structure of copper acetylide. However, iron carbide does not to our knowledge form this type of bulk structure. Another possibility has been suggested by Behrman and co-workers 49 based on their theoretical work with ZnO clusters. They have found that (ZnO)12 should be an especially stable spheroidal cluster similar to C60. This cluster, which contains six rhombuses, is the first of a series of ZnO spheroids that do not force the rhombuses to share an edge. The 12/12 cluster is also found to have the highest symmetry of any of the spheroids. A third possibility for the Fel2C~2 cluster is that it is simply the met-car with four bare iron atoms attached. This structure seems unlikely since the four attached iron atoms would have many dangling bonds. It would be extremely helpful to have a theoretical comparison of these three structures. In the meantime, the structure for Fel2Cl+2 remains a mystery. One of the most interesting transition metal--carbon systems studied to date has been the zirconium--carbon system. The metal has been shown to form the 8/12 met-car stoichiometry as have the other metals discussed. However, Castleman and co-workers 2~ have found that other larger zirconium-carbon clusters were formed in this experiment. The growth pattern in the experiment apparently was not consistent with thefcc stoichiometries that were found for TiN 24 and TaC. 2~These peculiar patterns for the zirconium system led to the proposal of multiple-caged dodecahedra. In this scheme the connected dodecahedra share a common face. For example the two-cage species stoichiometry can be arrived at by taking the initial dodecahedron, MsCI2, and adding another one directly to it. However, the second one will be missing a face since it will share one with the original dodecahedron. The second cage, then, will be MsCI2 minus M2C 3 (one five-membered ring), or M6C 9. Thus, the total stoichiometry for the two-cage species is M14C21. Castleman has found ZrnC22 to be stable in his investigation as well as Zq4C23, which ratios are close to the perfect stoichiometry predicted above. It is not clear why ZrlaC21 was not found. As one adds additional cages to the sides of the two-caged species special stoichiometries are predicted at M18C29 for three cages and at M22C35 for four cages. Castleman does see these stoichiometries as especially abundant in the zirconium--carbon mass spectrum. Curiously, the structure for the four-caged species does not build up from the three-caged system since the third (and fourth) cage(s) are attached differently to the two-cage subunit. Figure 17 shows the mass spectrum obtained for the zirconium--carbon system in our experiment. Clearly the met-car 8/12 peak is the most abundant cluster in the mass spectrum. There are also several other locally abundant peaks that are marked by significant truncations. The first of these other peaks has the stoichiometry Zrl4C13, indicating again the fcc motif in this system. The overall pattern can be

Metal-Carbon Cages and Crystals

209 +

812

ZrnCm

14 13 18,18 9

> . r--.4

I

I

I

I

1000

2000

3000

4000

I

5000

Figure 17. The mass distribution of cationic clusters obtained by laser vaporization of zirconium with hydrocarbon seeded in the helium carrier gas. There are many peaks at higher mass than the metal lo-carbohedrene. The pattern of these larger peaks indicates a face-centered-cubic structural motif with especially stable stoichiometries corresponding to completed crystal faces.

explained in terms of this type of structure with the most intense peaks representing essentially cuboidal dimensions; that is, the 14/13 is 3 x 3 x 3, the 18/18 is 3 x 3 x 4, the 24/24 is 3 x 4 x 4, and so on. These are in fact the most stable fcc clusters found for several other systems. It seems that the near cuboids are more stable than nanocrystals with dangling MC units, since all of the most abundant peaks correspond to completed crystal faces. The 1"1 stoichiometry found for zirconium-carbon clusters in our experiment is also found to be the bulk structure of zirconium carbide. 32 Owing to the limited mass resolution in our experiment and in Castleman's, it is impossible to determine the cluster masses exactly in these high-mass regions. However, we can determine the masses (hence, the stoichiometries) accurately enough to recognize certain growth patterns in the mass spectrum. In this context, then, the larger zirconium--carbon clusters in our experiment correspond to thefcc nanocrystals and not multiple-caged dodecahedra. In fact, the general appearance of our zirconium-carbon mass spectrum is very similar to the fcc structural motif found by Castleman for the growth of clusters in the tantalum-carbon system. It does not, however, look anything like Castleman's zirconium--carbon mass spectrum. We have no explanation for our inability to reproduce the Castleman mass spectrum.

210

J.S. PILGRIM and M. A. DUNCAN

It was mentioned earlier that the niobium-carbon system was peculiar in that the met-car cluster seemed to be superimposed on a different underlying growth pattern. As for most of the other metals discussed, this growth pattern has turned out to be the face-centered-cubic crystalline arrangement. These niobium--carbon clusters are shown in Figure 6. Thefcc pattern is known to be the bulk structure of niobium carbide. 32 The first major peak is Nb4C] , which, as discussed in relation to the niobium met-car dissociation, is likely to be the 2 x 2 x 2 nanocrystal. This cluster is the smallest completefcc nanocrystal to have three-dimensional structure. The NbsC ~ cluster is also prominent and is probably a 2 x 2 x 2 crystal with one carbon replaced by niobium. Other locally prominent peaks smaller than the met-car are the 6/7 and 7/9 clusters. These are precisely the stoichiometries found for the fragments of the niobium met-car and interestingly do not have the characteristic 1" 1 metal--carbon ratio. Thus, the niobium met-car photodissociation and the niobium-carbon, mass spectra show the same stoichiometries to be locally stable. Clusters other than the met-car are the 9/9 and 14/13 nanocrystals, which correspond to 3 x 3 x 2 and 3 x 3 x 3 arrangements, respectively. The niobiumcarbon system starts with fcc structures earlier than the other transition metals studied (i.e., smaller than the met-car) while still making the met-car prominently and then promptly going back to the fcc pattern (Nb9C9). It appears that there are two different growth patterns competing here, although the photodissociation of the met-car seems to indicate some linkage between the two types of clusters. In short, most of the transition metals (Ti, V, Zr, Nb) that form the met-car are also found to adopt the fcc crystalline arrangement. A notable exception is iron, which is found to form an as-yet unexplained larger cluster. Also, Cr and Mo are not found to form any especially prominent clusters larger than the met-car. Perhaps this is not surprising because Cr and Mo are not known to have afcc bulk structure. The four metals described all employ this building pattern in the bulk solid state.

E. Nanocrystals: Photodissociation Experiments From the major peak stoichiometries in the metal-carbon mass spectra we are able to recognize the fcc growth pattern. Face-centered-cubic crystals are usually 31 indicative of a large degree of ionic bonding as in the alkali halide nanocrystals.The atoms in a perfect fcc crystal are in an octahedral environment. The angles involved in such an arrangement are not normal for covalently bonded carbon. The implications, then, are that either there is very little covalent bonding or the crystal is not perfect. Laser photodissociation experiments may provide some insight into this question. The smallestfcc nanocrystal in which any atom has all of the nearest neighbors it would have in the bulk structure is the M14C13,3 x 3 x 3, cluster. This cluster is the perfect starting point for investigation of decomposition pathways. Figure 18 shows the photodissociation mass spectrum for the Zrl4C] 3 cluster ion at 532 nm. The most abundant photofragment has the 8/12 stoichiometry of the met-car! It

Metal-Carbon Cages and Crystals

211

('

,

C3 ,

"~

i 9

!I

O'2 qO ("-- i! I ~~

^ I! 11,7 |

9 9 ~,--t

9

m i

I

I

5OO

1000

1500

Figure 18. l h e photodissociation mass spectrum of Zrl4C~3, the 3 x 3 x 3 nanocrystal, at 532 nm. The fragmentation event is likely to result from multiphoton absorption. The most abundant fragment from the nanocrystal is the metallo-carbohedrene, providing an unmistakable link between the two structural types.

would be too coincidental to assign this structure to anything other than the metallo-carbohedrene. To form this fragment the parent cluster loses six metal atoms and one carbon atom. Because the fcc stoichiometry is normally 1:1 (metal to carbon), it would be logical to suppose that ZrC units would be the major loss mechanism. Nevertheless, six neutral zirconium atoms are lost whereas only one carbon is. Other decomposition products (smaller than the 8/12) mimic, more or less, the fragments of the zirconium met-car dissociation. It is instructive to look at the structure of this nanocrystal in relation to the proposed dodecahedral structure of the met-car. The 3 x 3 x 3 crystallite has eight metal atoms at the vertices of a cube. There are six metal atoms in the faces of the cube and a carbon atom bisecting each edge of the cube. The last carbon atom can be found in the center of the crystal in an octahedral environment. Interestingly, the Zrl4Cl+3 structure lost six metal atoms and there are six unique metal atoms in the faces of the crystal. Furthermore, as one of the metal atoms vacates its position in the cube face, two carbons initially separated by the metal atom can become bonding. The result of the formation of this C-C bond is two edge-linked five-membered rings. These five-membered rings, not surprisingly, have an M2C 3 stoichiometry. If all of the metal atoms in the cube faces leave, and C-C bonds form in their place, the resulting structure is the identical pentagonal dodecahedron proposed for the met-car. The loss of carbon can be attributed to the central carbon

212

J.S. PILGRIM and M. A. DUNCAN

.~

z4

Figure 19. A pictorial representation of the relationship between the 3 x 3 x 3 nanocrystal and the metallo-carbohedrene. This rearrangement sequence is presented merely to show the minimum amount of reconstruction required to get from one structure to the other. In reality, the metal atoms would more likely leave sequentially. vacating during this surface reconstruction. This proposed rearrangement sequence can be seen graphically in Figure 19. The rearrangement sequence depicted in Figure 19 is presented primarily to show the minor amount of reconstruction required to form the pentagonal dodecahedron from the 3 x 3 x 3 nanocrystal. It is unlikely, however, that the metal atoms in the cube faces would leave the cube in the concerted manner shown in the Figure. The most likely scenario is a sequential process whereby one metal atom leaves,

Metal-Carbon Cages and Crystals

213 +

1,0 -~

ZF24C24 812

-,-.~

~

d

-~ 1 4 , 1 3

~

.,.)

C~ I

I

1000 2000 Mass ( a m u )

I

3000

Figure 20. The photodissociation mass spectrum of Zr24C~4,the 3 x 4 x 4 nanocrystal, at 532 nm. In addition to fragmenting into the metallo-carbohedrene, the 3 x 3 x 3 nanocrystal is also a prominent fragment. This is the first example of laser-induced cleavage of a crystal in the gas phase.

allowing the opposite carbon atoms to condense into the C 2 unit. The formation of the C 2 unit results in a release of energy that is then available to drive the next metal atom evaporation. We cannot be sure of the correct sequence of events that leads to the reconstruction that we know to take place. However, the sequential mechanism requires the lesser amount of energy to be provided externally. It is important to note the implications that this photochemistry has for the structure of the met-car. As shown, it is easy to rationalize the overall rearrangement process if the met-car has the pentagonal dodecahedral structure. Likewise, as shown in the recent theory work of Dance, TM a T d met-car can also be derived from 14113 decomposition. However, the structure proposed by Khan, 46 with a central carbon cage surrounded by external metal atoms, is totally inconsistent with this photochemical behavior. Production of the Khan structure from the 14/13 nanocrystal would require near-complete atomization and reassembly of the system, which is extremely unlikely energetically. Another surprising result was obtained when nanocrystals larger than the 3 x 3 x 3 were photodissociated. Figure 20 shows the photodissociation of Zr24C2+4 at 532 nm. The 24/24 stoichiometry corresponds to a 3 x 4 x 4 nanocrystal. The 8/12 is again the major photofragment. However, another photofragment with a significant local intensity is the 14/13. Undoubtedly, this is the 3 x 3 x 3 nanocrystal.

214

J.S. PILGRIM and M. A. DUNCAN

8,13

+

Ti14C1

i ..

9

J

il

9 o~',I

I

250

I

I

750

Mass (amu) Figure 21. The photodissociation mass spectrum of Ti14C~3 at 532 nm. Unlike the zirconium nanocrystal, the major photofragment is the metallo-carbohedrene with an extra carbon. We believe this carbon to be inside the met-car cage. This fragment is also found in the vanadium system. These clusters represent the first examples of an endohedral carbon atom. Therefore, the larger crystal fragments into a smaller one. The peak labeled 18/18 is also a smaller crystal than the 24/24, having a 3 x 3 x 4 structure. We believe these data represent the first example of"laser-induced cleavage" of a crystal in the gas phase. The closest analogy to this process is the collision-induced dissociation experiment of Whetten 31 on alkali halide nanocrystals whereby the nanocrystals were found to cleave along crystal planes upon collision with a surface. The term cleavage seems appropriate as these zirconium-carbon crystals fragment along crystal planes. It seems likely that the decomposition of these larger crystallites proceeds by a sequential mechanism owing to the presence of the met-car as a photofragment. The scenario would then be cleavage along one or more crystal planes to produce the 14/13, which then ejects the metal atoms in the faces to give the met-car. Evidence for this mechanism is, of course, circumstantial, and a concerted mechanism cannot be ruled out. 9 + Photodissociation experiments on the TilaCl3 nanocrystal yield some surprising results as well. Figure 21 shows the photodissociation of this cluster at 532 nm. As with the zirconium analogue, this crystallite loses six metal atoms. However, the cluster does not lose any carbon atoms! In the zirconium system we supposed that the central carbon of the crystallite escaped during the surface reconstruction.

Metal-Carbon Cages and Crystals

215

Apparently, the central carbon is not able to escape in the titanium rearrangement. The resulting titanium met-car from this photodissociation most likely contains an endohedral (inside the cage) carbon atom. There is recent theoretical evidence 45 that the titanium met-car is capable of supporting an endohedral carbon atom. The photodissociation of the V14C1+3 cluster at 532 nm also resulted in the production of the VaC~3 molecule as the most abundant photofragment. We believe these two systems represent the first cases of any cluster containing a caged carbon atom. Our laboratory has also photodissociated the larger titanium--carbon clusters. The next size up from TilaC] 3 is the slightly nonstoichiometric cluster, TilTC]9 . A perfect 3 x 3 x 4 fcc nanocrystal would have an 18/18 stoichiometry. It is still not clear why the titanium system forms these structures with carbon substituted for metal atoms. More importantly, however, this cluster does indeed undergo laser-induced cleavage to produce a large 14/13 photofragment. Nevertheless, the largest photofragment is still the met-car, but there does not appear to be an endohedral carbon atom (i.e., the fragment is TisC]2 ). The 8/12 photofragrnent actually does have a shoulder to higher mass that is likely the endohedral met-car, but it is greatly reduced in intensity. Perhaps the excessive rearrangement required to get from the 17/19 to the met-car allows the central carbon atom to escape. We have been unable, at this point, to carry the titanium system out to the crystal sizes studied for the zirconium system because of insufficient parent ion intensity. Further experiments on these larger titanium-carbon crystals would be very instructive. The two major results from the nanocrystal photodissociation experiments are the decomposition to the met-car and the photochemical cleavage of larger crystals to smaller ones. These results seem to be at odds in characterizing the bonding in these systems. The bonding in the metallo-carbohedrene, as discussed in Section IIIC, is believed to be mostly covalent with t~ bonds linking the C 2 units to the metal atoms, whereas the C 2 units themselves are a paradigm of covalent bonding. Conversely, the structure of the nanocrystals is easier to understand if the bonding is mostly ionic. If the bonding is purely electrostatic, then it is energetically favorable for a carbon anion to surround itself with an octahedral arrangement of metal cations. Neither of these two situations is likely to represent the actual bonding. The true bonding is likely to be a combination of both ionic and covalent contributions. The dual nature of the bonding can be rationalized in the following way. Consider the 3 x 3 x 3 crystal to be composed of 14 metal cations and 13 carbon anions in the fcc arrangement, that is, purely ionic bonding. The initial structure can be visualized as a perfect cube with equal metal-carbon bond distances and angles (as in the bulk solid). This crystal is placed in a vacuum and completely isolated from other clusters. The crystal immediately finds itself in an energetically unfavorable situation. It has too much surface area! Of its 27 constituent atoms, 26 are on the surface. The surface free energy of a cluster is always positive. 5~This is to say that every material has some surface tension. To remedy this situation, the cluster must lower its surface area. For a given volume, the geometric shape of lowest surface

216

J.S. PILGRIM and M. A. DUNCAN

area is the sphere. The nanocrystal can move towards a spherical shape by contracting metal atoms at the cube vertices and extending metal atoms in the cube faces. Of course, this could theoretically continue until all of the surface atoms actually do describe a sphere. However, in reality this process is also costing energy as the metal-carbon distances become larger and the optimum geometry is lost for maximization of the crystal lattice energy (the electrostatic energy). Equilibrium between reduction of the surface free energy and maximization of the bond energy is reached somewhere between a cube and a sphere. In this new geometry, the bond angle constraints on the carbon atoms are not so severe as in the perfect cube. The result is more favorable overlap for covalent bonding. Thus, the nanocrystal is likely to have both ionic and covalent bonding character regardless of the bonding in the bulk crystal. This picture of a distorted nanocrystal for the 14/13 cluster is also supported by the calculations of Dance. TM The niobium-carbon cluster system is particularly interesting. The mass spectrum, as discussed in Section IliA and shown in Figure 6, has several locally abundant peaks. These peaks correspond, for the most part, to near-stoichiometric fcc nanocrystals. Each of the clumps corresponds to a fixed number of Nb atoms with various amounts of carbon attached. This system, then, provides an opportunity to photodissociate metal--carbon crystals with every number of metal atoms represented (up to 14). Table 2 shows the results of this comprehensive photodissociation study of niobium-carbon clusters containing from 4 to 14 niobium atoms. The fragments listed in the Table were produced by use of the 532-nm dissociation

Table 2. The Major Photofragments of Nb.C g Parent Ions at 532 nm Fragments Formed (Columns) Vs. Parent Ion (Rows)a 1/0

2/'2

3/3

4/4

X

X

X

5/6 6n 7/9 8/12 9/9 10/10 11/13 12/12 13/13 14/13

X X X X X x X X x X

X X x X X X X X X X

X X x X X x x X x X

Note:

4/4

5/6

6/7

X X x X X X x X x X

X x X X x x X x X

x X X X X X x X

7/9

8/9

9/9

X X X X

X X X

X 0

X X 7/8

X X 8/10

0 X X

10/10 11/13 12/12 13/13

O O 10/12 10/12

O O O

0 0

0

q'he parent ion is given in the row label. Major photofragments are indicated by an X in the stoichiometry given by the column label. An 0 indicates the stoichiometry given by the column label is correct for the number of Nb atoms in the photofragment but that the number of carbons is not known. A number gives the stoichiometry of the photofragment that is closest to that given by the column label.

Metal-Carbon Cagesand Crystals

217

laser. Using the 355-nm third harmonic of the Nd:YAG laser, we obtained the same fragmentation patterns. It is therefore likely, under these circumstances, that the photodissociation event is a result of nonresonant absorption. The main result of this study is, hopefully, immediately apparent in Table 2. The row labels correspond to the parent ion that was photodissociated whereas the column labels are the photofragments. These labels are the same. Take the Nbl2Cl~ parent for example. Photodissociation of this cluster produced the fragments, 8/9, 7/9, 6/7, etc. These photofragments are also locally abundant parent ions in the mass spectrum. Thus, the cluster stoichiometries that were found to be especially stable in the growth of the niobium--carbon clusters (i.e., 4/4, 6/7, and 9/9) are also found to be the major decomposition products. As we pump large amounts of energy into these clusters during the photodissociation event, the parent ions attempt to stabilize by throwing off fragments. As this process continues, an especially stable cluster may be formed that then resists further decomposition. Consequently, intense peaks in the fragmentation pattern generally correspond to the most stable stoichiometries. The fact that we form the same stoichiometries in the growth process seems to indicate that our experiment allows the clusters to explore various configurations until thermodynamically stable ones are found (the so-called exploration of phase space). However, the implication is also that our clusters have considerable energy in internal modes. The clusters are "hot." This condition is, in fact, necessary for us to see any fragmentation at all. The nanocrystals and met-cars simply have so many internal degrees of freedom that even many-photon absorption at 532 nm (2.33 eV) is likely to be redistributed within the cluster and not result in dissociation. Even if the entire photon energy could be channeled into liberating one atom from the cluster, one photon would most likely not be enough. Theoretical estimates for the bond energies in these metal--carbon clusters place them well above 5 e.V/atom. 36'39'40However, if the cluster is already near the dissociation point because of internal energy incurred in the formation process, the photodissociation laser can provide the extra energy required for the cluster to dissociate. Put another way, the photodissociation laser provides the energy required to increase the unimolecular dissociation rate so that the fragmentation occurs on the microsecond time scale of our experiment. The internal energy of indium-phosphide semiconductor clusters and its role in photodissociation has been studied by Mandich and co-workers. 5l Finally, we discussed previously the implications for the extent of met-car formation using the results from the iron--carbon system. It was noted that the 8/12 was not superabundant compared to several other stoichiometries in the mass spectrum. The notable higher mass stoichiometry was the Fel2C~2 cluster. Figure 22 shows the photodissociation mass spectrum of this cluster as 532 nm. Clearly, this figure shows the major photofragment to be the FesC~2. We believe this to be evidence that the iron system does indeed form the met-car, though not to the extent of the earlier transition metals. It seems that iron is near the cut-off for the special stability of the 8/12 stoichiometry as other growth processes begin to compete more

218

J.S. PILGRIM and M. A. DUNCAN

+

819

(' .12

~ p,,,~

o~,,I

.,.)

C~ !

I

5O0

1000

Mass (amu)

Figure 22. The photodissociation mass spectrum of Fe12C~2 at 532 nm. Although the iron metallo-carbohedrene was not especially abundant in the nascent mass distribution, it is the major photofragment of this parent. Thus, the iron met-car does enjoy a special stability.

effectively. It is interesting in this system that the nascent cations produced in cluster growth do not correspond to those produced in photodissociation. Apparently, growth kinetics lead to a variety of structures, but the stable met-car is the result of decomposition.

IV. CONCLUSIONS Metallo-carbohedrenes are a stable class of metal-carbon clusters. The met-car stoichiometry, MsCI2, is found to be prevalent in more transition metals than previously thought. These structures are formed from Cr, Mo, Fe, and Nb in addition to their well-established formation from Ti, V, Zr, and Hf. The preference for this stoichiometry seems to decrease for the later transition metals. Theoretical predictions agree with this observed trend. One explanation is that the overall binding energy for this cluster is lowered as more metal d-electrons are added. These extra d-electrons may go into C 2 antibonding molecular orbitals, thus weakening the complex. Metallo-carbohedrenes fragment according to very specific patterns. In the first-row transition metals, met-cars generally dissociate by loss of neutral metal atoms. Within this row, met-cars containing the later transition metals fragment

Metal-Carbon Cages and Crystals

219

more extensively at a given laser wavelength and power. The chromium and iron analogues lose up to six metal atoms. This behavior seems to indicate that the M-C bonds are weaker for the later transition metals. In the second-row transition metals, met-cars dissociate by the loss of MC x (x = 1,2). Apparently, the M--C bonding in these complexes is quite different than in the first-row structures. Curiously, there is not a noticeable trend in the extent of fragmentation for the later transition metals in the second row. The molybdenum and zirconium analogues both fragment down to MaC ~ . In the first-row met-car photodissociations, the atomic ion is also found as a fragment, indicating a similar ionization potential for the cluster and the atom. Nanocrystals are also a stable class of metal--carbon clusters. Most of the metals that form the met-car also form the face-centered-cubic crystallites. These structures have been found for Ti, V, Zr, and Nb. Only Cr and Mo were not found to assemble in this fashion. Interestingly, the metals that do form the nanocrystals have thefcc lattice type in the condensed phase, whereas Cr and Mo do not. In the firstand second-row transition metals, formation of the fcc nanocrystals seems to decrease for the later transition metals. That is, larger crystallites are formed from earlier transition metals. Iron has been found to form a larger cluster that may not befcc. The structure of this cluster remains a mystery. Nanocrystals also fragment according to very specific patterns. The first-row nanocrystals produce the met-car as the major photofragment. The met-car, however, most likely contains a carbon atom inside the cage. The second-row crystals are different. Zirconium--carbon fcc clusters fragment into the met-car without a trapped carbon. The niobium system does not produce the met-car as a fragment at all. The nanocrystals of Ti and Zr that are larger than the 3 x 3 x 3 system also fragment to give smallerfcc crystals. This laser-induced-cleavage appears to be a new phenomenon. Vanadium does not undergo this process. Niobium--carbon clusters cleave to form smaller crystals exclusively, even though the parent ions are almost all smaller than the 3 x 3 x 3 crystal. The larger iron cluster fragments to produce the met-car. Metallo-carbohedrenes and nanocrystals are extremely interesting combinations of matter. Both are likely to have unique electronic and magnetic properties. Bulk metal--carbides are known to be good conductors. However, many strange quantum effects may come into play with clusters as small as these. These materials are equally interesting from a geometric standpoint. Two fundamental shapes are suggested by both theory and experiment for these systems, the sphere and the cube. Perhaps these structures are the equivalent of a molecular erector set. Of course, these clusters may also find applications in catalysis. After all, they have very high surface areas and contain transition metals. The formation of the clusters themselves involves extensive dehydrogenation reactions. At this point, there is no way to predict the impact of such molecules on our technology. Most importantly, the future direction of research should be the production and isolation of these structures in the condensed phase. Only then can their true value be determined.

220

J.S. PILGRIM and M. A. DUNCAN

ACKNOWLEDGMENTS We gratefully acknowledge support for this work from the U.S. Department of Energy (contract nos. DE-FG09-90ER 14156 and DE-FG05-93ER 14402). We appreciate the help of Prof. Gary Newton and Donald Wagner in the preparation of artwork. We would especially like to thank Lori Brock for her many contributions in all aspects of the work on the niobium--carbon system.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. I 1. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

Kroto, H. W.; Heath, J. R.; O'Brien, S. C.; Curl, R. E; Smalley, R. E. Nature 1985, 318, 162. Kroto, H. Science 1988, 242, I 139. Curl, R. E; Smalley, R. E. Science 1988,242, 1017. Kr~itschmer,W.; Lamb, L. D.; Fostirpoulos, K.; Huffman, D. R. Nature 1990, 347, 354. Diederich, E; Whetten, R. L. Acc. Chem. Res. 1992, 25, 119. Curl, R. E; Smalley, R. E. Sci. Am. 1991, 265, 54. Chai, Y.; Guo, T.; Jin, C.; Haufler, R. E.; Chibante, L. E E; Fure, J.; Wang, L.; Alford, J. M.; Smalley, R. E. J. Phys. Chem. 1991, 91, 7564. Shinohara, H.; Sato, H.; Saito, Y.; Ohkochi, M.; Ando, Y. J. Phys. Chem. 1992, 96, 3571. McElvany, S. W. J. Phys. Chem. 1992, 96, 4935. Gillan, E. G.; Yeretzian, C.; Min, K. S.; Alvarez, M. M.; Whetten, R. L.; Kaner, R. B. J. Phys. Chem. 1992, 96, 6869. Tanigaki, K.; Ebbesen, T. W.; Saito, S.; Mizuki, J.; Tsai,' J. S.; Kubo, Y.; Kuroshima, S. Nature 1991, 352, 222. Fischer, J. E.; Heiney, E A.; Smith, A. B. Acc. Chem. Res. 1992, 25, 112. Ruoff, R. S.; Lorents, D. C.; Chan, B.; Malhotra, R.; Subramoney, S. Science 1993, 259, 346. Martin, T. E; Bergman, T.; G6hlich, H.; Lange, T. J. Phys. Chem. 1991, 95, 6421. Beck, R. D.; St. John, P.; Homer, M. L.; Whetten, R. L. Science 1993, 253, 879. a. Ijima, S. Nature 1991, 354, 56. b. Ijima, S.; Ichihasi, T. Nature 1992, 356, 776. Ebbesen, T. W.; Ajayan, P. M. Nature 1992, 358, 220. Guo, B. C.; Kearns, K. E; Castleman, A. W., Jr. Science 1992, 255, 1411. Guo, B. C.; Wei, S.; Purnell, J.; Buzza, S.; Castleman, A. W., Jr. Science 1992, 256, 515. Wei, S.; Guo, B. C.; Purnell, J.; Buzza, S.; Castleman, A. W., Jr. Science 1992, 256, 818. Wei, S.; Guo, B. C.; Purnell, J.; Buzza, S.; Castleman, A. W., Jr. J. Phys. Chem. 1992, 96, 4166. Guo, B. C.; Wei, S.; Chen, Z.; Kerns, K. E; Purnell, J.; Buzza, S.; Castleman, A.W., Jr. J. Chem. Phys. 1992, 97, 5243. Chert, Z. Y.; Guo, B. C.; May, B. D.; Cartier, S. E; Castleman, A. W., Jr. Chem. Phys. Lett. 1992, 198, 118. Chen, Z. Y.; Castleman, A. W., Jr. J. Chem. Phys. 1993, 98, 231. Cartier, S. E; Chen, Z. Y.; Walder, G. J.; Sleppy, C. R.; Castleman, A. W., Jr. Science 1993, 260, 195. Guo, B. C.; Kerns, K. P.; Castleman, A. W., Jr. J. Am. Chem. Soc. 1993, 115, 7415. Pilgrim, J. S.; Duncan, M. A.J. Am. Chem. Soc. 1993, 115, 4395. Pilgrim, J. S.; Duncan, M. A. J. Am. Chem. Soc. 1993, 115, 6958. Pilgrim, J. S.; Duncan, M. A. J. Am. Chem. Soc. 1993, 115, 9724. Pilgrim, J. S.; Duncan, M. A. Intl. J. Mass Spectrom. and Ion Processes 1994, 138, 283. Whetten, R. L. Acc. Chem. Res. 1993, 26, 49. Toth, L. E. Transition Metal Carbides and Nitrides; Academic: New York, 1971. Cornett, D. S.; Peschke, M.; LaiHing, K.; Cheng, P. Y.; Willey, K. E; Duncan, M. A. Rev. Sci. Instrum. 1992, 63, 2177.

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34. Wiley, W. C.; McLaren, I. H. Rev. Sci. Instr. 1955, 26, 1150. 35. Jin, C.; Haufler, R. E.; Hettich, R. L.; Barshick, C. M.; Compton, R. N.; Puretzky, A. A.; Dem'yanenko, A. V.; Tuinman, A. A. Science 1994, 263, 68. 36. Reddy, B. V.; Khanna, S. N.; Jena, P. Science 1992, 258, 1640. 37. Wei, S.; Guo, B. C.; Deng, H. T.; Kerns, K.; Purnell, J.; Buzza, S. A.; Castleman, A. W., Jr. J. Am. Chem. Soc. 1994, 116, 4475. 38. Pilgrim, J. S.; Brock, L. R.; Duncan, M. A. J. Phys. Chem. 1995, 99, 544. 39. Lin, Z.; Hall, M. B. J. Am. Chem. Soc. 1992, 114, 10054. 40. Reddy, B. V.; Khanna, S. N. Chem. Phys. Len. 1993, 209, 104. 41. Lou, L.; Guo, T.; Nordlander, P.; Smalley, R. E. J. Chem. Phys. 1993, 99, 5301. 42. Chen, H.; Feyereisen, M.; Long, X. P.; Fitzgerald, G. Phys. Rev. Lett. 1993, 71, 1732. 43. a. Dance, I. G. J. Chem. Soc., Chem. Comm. 1992, 1779. b. Dance, I. G. J. Chem. Soc., Chem. Comm. 1993, 1306. c. Dance, I. G.J. Am. Chem. Soc. 1993, 115, 11052. d. Dance, l.J. Am. Chem. Soc., submitted. 44. Lin, Z.; Hall, M. B. J. Am. Chem. Soc. 1992, 115, 11165. 45. Lou, L.; Nordlander, P. Chem. Phys. Len., in press. 46. Khan, A. J. Phys. Chem. 1993, 97, 10937. 47. Pauling, L. Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 8175. 48. Yamada, Y.; Castleman, A. W., Jr. Chem. Phys. Len. 1993, 204, 133. 49. Behrman, E. C." Foehrweiser, R. K.; Myers, J. R.; French, B. R.; Zandler, M. E. Phys. Rev.A 1994, 49, R1543. 50. Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; Wiley: New York, 1994. 51. Rinnen, K. D.; Kolenbrander, K. D.; DeSantolo, A. M.; Mandich, M. L. J. Chem. Phys. 1992, 96, 4088.

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INDEX Birge-Sponer plots nonlinear, 33-35 of HgAr, 33-34 of Rydberg states, 33 Birge-Sponer-extrapolation, 27 Bond dissociation values, of AI complexes, 32 Bond lengths (Re), of metal.rare gas diatomic molecules, 2-9 Buckminsterfullerene (C60), 182

tOe (see Fundamental frequency) Ab initio calculations, on cationic complexes, 20 Ag.Ar molecule, 19 bond length of, 19 bond strength of, 19 comparison with copper complexes, 19 orbital hybridization, 19 A1Ar, CRLAS studies of, 176 Ar repulsion, 20 Ar2, 56 Atom-atom potential function and non-additive potentials, 65 and polarization correction, 65 possible failures of, 64 Atomic clusters electronic spectra of, 149 study of, 114 Avoided crossings, 22 Axial mode buildup, 168

Ca, collision process, 49 CaAr, 22 Cages, of metal--carbon clusters, 181'221 Campargue-type expansion, 157 CAPS (see Cavity-attenuated phase shift) Carbon clusters analysis by cold source, 126 and Franck-Condon factors, 119 and laser polarization, 119, 121 autodetachment features, 129 comparison with Au clusters, 130 electron affinities of, 122 electronic structure of, 123 Franck--Condon approximation of, 129 negative ion photodetachment studies of, 119-130 photoelectron spectra of, 120, 121 photoelectron spectroscopy of anions, 119 polarizability, 129

BaArn clusters, 68-70 atom-atom potentials of, 69 molecular dynamics simulations of, 68, 70 Back-polarization, 20, 25, 28, 33 BAr, potential well, 28 BeAr cation, 25 and bond length, 26 back-polarization, 26 potential curve, 26 Be Kr cation, 25 223

224

spectral studies of, 114, 115 study of using negative ion photodetachment techniques, 113-148 threshold photodetachment spectra of, 124-130 total photodetachment cross section spectra of, 127-130 trends in electronic structure, 124 Carbon trimer, 89-98 CASSCF potential energy surface, 97 diode laser spectroscopy of, 93 dispersed fluorescence studies, 91, 92 generation of, 90 internal dynamics of, 92 laser-induced grating spectroscopy of, 106 LIF studies of, 90 prior studies, 89 rotationally resolved SEP spectra of, 93, 94 semirigid bender studies of, 95, 96 SEP study, 92-94 spectral studies, 89 CASSCF-CI calculations, 27, 28 Cavity ringdown laser absorption spectroscopy (see CRLAS) Cavity ringdown time, 151 Cavity-attenuated phase shift (CAPS) method, 151 phase shift, 153 schematic of, 151,152 sensitivity of, 153 theoretical sensitivity limits of, 154 theory of, 152-153 Cd complexes predissociation of, 47 spin-forbidden collisional deactivation of, 46 Cd predissociation action spectrum of complexes, 46 predissociation product, 49 rare gas complexes of, 46 spin--orbit splitting of, 49 CdAr, 24, 38

INDEX

CdAr double-resonance studies of, 35 potential energy curves of, 39 CdXe, 49 CdXe isotopomers, 46 CdXe, LIF spectra of, 46 Cluster science, 149-180 Copper dimer (Dicopper) and CRLAS analysis of, 171-173 CRLAS spectra of, 172, 173 description of, 171 Hund's case (a), 171 Copper trimer and CRLAS analysis of, 173-176 and Jahn-Teller effect, 86 calculation of vertical excitation energies, 174 CRLAS comparison of with R2PI studies, 175,176 CRLAS vibronic spectra of, 175 electronic structure of, 174 Jahn-Teller distortions, 174 R2PI experiment of, 174 Coupling, of E-I-I states, 36 CRLAS advancement of, 154 and analog-to-digital conversion resolution, 162 and axial mode buildup, 168 and axial resonances, 169 and cavity geometry, 165 and cavity length, 168 and cavity resonances, 163 and copper dimer, 171-173 and decay digization, 162 and detector noise, 162-163 and laser noise, 162-163 and laser performance, 156 and laser quality, 169 and LIF techniques, 158 and long coherence lengths, 166 and mirror characteristics, 169, 170 and photon lifetime, 160 and pulse times, 161 and supersonic molecular beam of clusters, 157

Index and TEM 00 beam waist of the cavity, 165 and TEM mode quality, 163, 164 and time-of-flight mass spectrometer, 160 and waveform recording instrumentation, 162 applications of, 170-178 as a technique for cluster science, 149-180 Berkeley versions, 157, 159 description of, 150--151 Fourier transform of data, 167, 168 history of, 151-160 improvement in sensitivity, 155, 156 input pulse characteristics, 167 mirrors with multiple-layer dielectric coatings, 169 pulsed laser approach, 166, 167 schematic of early version, 155 sensitivity of, 160-170 Crystals, of metal--carbon clusters, 181-221 d-Hole, 19 d-Shell shielding effect, 22 De (see Dissociation energies) DF (see Dispersed fluorescence) Dicopper (see Copper dimer) Dipole polarizability, 16 Dispersed fluorescence (DF) spectra, 87 Dispersed-fluorescence measurements, 27 Dispersion, 9 Dissociation energies (De), of metal-rare gas diatomic molecules, 2-9 Double-minimum potential curves, 23 Double-resonance study, of HgNe, 25 Double-well potential curve, 24, 25 Dunham-type expansion, 91 Effective charge (Z), 12 calculation of, 13-14 definition of, 12 Electric dipole transitions, forbidden, 31 Electron core, of Be, 25 Electronic mixing, 44

225 Etalon, 151 Excited-state configuration, mixing of, 33 Fabry Perot theory, 166 Fast dynode photomultiplier detector, 158 Fixed frequency photoelectron spectroscopy, 115 description of, 116-119 Fluorescence dip technique, 108 Four-wave mixing processes, 105, 108 Franck--Condon-accessed region, 46 Fundamental frequency, 12 comparison of, 15 Half-collision experiments, 49 Hamiltonian, 88 Hard-sphere radius, 18 Hg atoms in rare gas matrices, 66--68 and Jahn-Teller distortion, 66 as opposed to clusters, 68 spectral studies of, 66, 67 symmetry of, 66 Hg, in Ar matrices, 55 HgAr, 24 bound-free absorption measurements of, 75 coherent excitation of, 77 direct dissociation of, 75-76 double-resonance spectra of, 72-73 ground state, 56 potential energy curves, 37-38 potential energy diagram, 71 pump--probe observations of, 76, 77 short-pulse excitation of, 71 states of, 55 vibration recurrences, 74, 76-78 HgAr2 cluster, 56-58 laser-induced fluorescence studies of, 56 LIF spectra, 58 mass-resolved multiphoton ionization studies of, 56, 57 potential surfaces, 58 predissociation of, 57 HgAr3 cluster, excitation spectrum of, 60

226

HgAr4 cluster, 61-62 HgAr5 cluster, isomers of, 62 HgArn clusters, 56 atom-atom additive potentials, 64 binding energies of, 60 binding energies of, 60-63 calculated vs. experimental spectral shifts, 61 ground state structures, 62 ground state surfaces, 63 ground-state geometries, 60-63 increasing complexity, 62-63 large, 65 molecular dynamics simulations of, 60 MPI assignments of, 63-64 MPI spectra of, 59, 60, 63 observation of, 56 pair potential, 60 solvated structures, 62 trends, 60 two-photon ionization spectrum of, 58 HgN2, observations of resonances of, 78-80 HgXe adiabatic states of, 50, 51 and collisional quenching, 51 and molecular states, 50 laser-induced fluorescence studies, 50 p-Hole contributions, 44 Hund's case (a), 43 and copper dimer, 171 Hund's case (b), 43 Hund's case (c) behavior, 56 Hund's case, 35, 38 Hybridization, of Na, 42 Induced-dipole moments, 20 Ion-induced-dipole expression, 16 Ion-induced-dipole forces, 32 Ion--quadrupole term, 32 Ionic state, 15 Jahn-Teller effect, 86 Lambda doubling, 45 and Kr, 43

INDEX

Large-amplitude motion, in small clusters, 85-111 Laser-induced fluorescence (see LIF) Laser-induced grating spectroscopy, 105-109 description of, 105, 106 energy level scheme of, 106 two color, 107 Lennard--Jones potential function, 17 Lennard-Jones-type repulsive term, 12 LIF (laser-induced fluorescence), 86 of molecular clusters, 150 LIF spectroscopy, 24 Lille, 26 dispersive attraction, 26 LiNe, 26 Longitudinal resonances, 166 Lorentzian linewidth, 47 Lorentzian shape, of vibrational bands, 46 M.RG (see also Metal.rare gas) M-RG cations, 23 partial charge, 23 Magnetic circular dichroism (MCR), 43 and spin-orbit coupling constants, 43 MCR (see Magnetic circular dichroism) MCSCF ab initio calculations Mg.Ar, 21 Na.Ar, 21 MCSCF calculations, of diatomic molecules, 20-21 Met-cars (see Metallo-carbohedrenes) Metal atom-rare gas van der Waals complexes, 1--80 polarizability, 2 Metal atoms excited states, 2 ground states, 2 Metal--carbon clusters construction of cages, 181-221 construction of crystals, 181-221 Metal-rare gas dynamical processes, 70--80 experimental observation of, 70 measurements of, 70--80

Index Metal.rare gas diatomic molecules, 2-54 Ag.Ar, 19 AI complexes, 29-30 and attractive dispersion forces, 53 and charge distribution, 11 and effective temperatures, 51 anomalies, 17 attractive forces, 11 Birge--Sponer behavior, 52 bond lengths, 2-9 bonding trends, 53 calculation of effective charge, 13-14 CEPA calculations, 18 comparisons of groups, 19-20 CRLAS studies of, 176 CRLAS vibronic spectra of, 177, 178 dissociation energies, 2-9 effective charge, 11 ground state complexes, 51-54 ground states, 8 group 1 and 11 metal atoms, 16-19 group 14 atoms, 32-33 group 2 and 12 metal atoms, 19-22 lambda doubling, 53 Li.He, 18 lithium complexes, 16 mixed states, 36 molecular states of, 3--6 Na.He, 18 polarizability, 9, 11 potential maxima of, 52 problems with data collection, 51 properties of ground state, 51 quadrupole polarizability, 16 radii values, 54 repulsive forces, 11 Rydberg states, 23-35 sodium complexes, 16 spin--orbit coupling, 35 spin-orbit mixing, 9 strongly bound excited cations, 3--6 synthesis of, 51 trends in dissociation energies, 9 trends in group 12 elements, 22 trends in lithium complexes, 17 trends in sodium complexes, 17

227

weakly bound excited states, 7 weakly bound states, 54 Metal.rare gas polyatomic molecules, 55-70 and solvation processes, 55 HgArn clusters, 55-66 Metallo-carbohedrenes (met-cars), 182 abundance in mass spectrometer, 183 analogues of buckminsterfullene?, 193 analysis by reflectron instrument, 186 analysis of using pulsed molecular beams, 185-187 and crystal formation, 184 anionic clusters, 190 containing various metals, 182, 184 Cr containing, 188, 191 Fe containing, 191 + 195 fragmentation of V 8C12, geometry of, 183 incorporation of polar molecules, 183 mass spectral analysis of Cu containing, 208 mass spectral analysis of F containing, 207 mass spectral analysis of nanocrystals, 203-210 mass spectral analysis of Ta containing, 208,209 mass spectral analysis of Ti containing, 208,209 mass spectral analysis of V containing, 207 mass spectral analysis of Zn containing, 208,209 mass spectral analysis of Zr containing, 208,209 mass spectroscopy of, 187-193 mass spectroscopy of cationic clusters, 187, 193 mass spectroscopy of Mo containing, 190 mass spectroscopy of Ti containing, 193, 194, 203,204 Mo containing, 189, 191 Nb containing, 192, 193, 199 NbC system, 184

228

INDEX

photodissociation analysis of Zr containing, 210, 211, 213 photodissociation experiments of, 184, 193-200 photodissociation of Cr8C[2, 195, 196 + 195, 196 photodissociation of F e8C12, photodissociation of M o8C12, + 197, 198 photodissociation of NbsC~2, 199, 200 + photodissociation of Z r 8C12, 197, 198, 200 photofragments of, 194 possible structures, 201-203 predicted properties of, 219 stoichiometry of, 183 theoretical structures, 201,202,203 TisCI2, 182 Ti containing, 187, 188 V containing, 188 Metallo-fullerenes, 182 Mg atomic state, 24 MgAr, 21, 22, 24 MgAr effective charge of, 22 potential energy curves, 36 MgKr, 20 MgNe, 22 MgXe, 22 ab initio calculations of, 50 Franck-Condon accessible energies of, 49 laser-induced fluorescence studies of, 49 RKR experimental calculation, 50 spin--orbit coupling of, 50 Mixed states, 36--41 Molecular beam/mass spectrometer, 185-187

schematic of, 185 Molecular clusters electronic spectra of, 149 study of, 114 Molecular-beam sources, 85 Multiplet splittings, 41 Na.Ar, 21 and spin-orbit coupling, 42

dipole moment, 16 potential curves, 16 Nanocrystals, 203-210 as a class of stable meta--carbon clusters, 219 comparison with metallocarbohedrene structure, 212 Fe containing, 207 mass spectral analysis, 203-210 observed mass spectroscopically, 206 photodissociation experiments, 210-218 photodissociation experiments of Fe containing, 217, 218 photodissociation experiments of Nb containing, 216, 217 photodissociation experiments of Ti containing, 213,214, 215 photodissociation experiments of V containing, 213, 215 photodissociation experiments of Zn containing, 213 predicted properties of, 219 proposed structures of, 205 V containing, 207 NaXe, dispersed fluorescence measurements of, 46 Negative ion photodetachment spectra, 130-146

Negative ion photodetachment techniques, 113-148 limitations, 114 schematic of, 116 Neutral electron affinity, 116 Nondegenerate molecular states, 40 One-electron mixing, 44 Orbital character of rare gases, 41-46 Penetration model, of B, 27 Penetration, of Rydberg orbital, 24, 33 PES (see Potential energy surface) Phase angle uncertainty, 154 Photodissociation experiments, of metallo-carbohedrenes, 184 Pockels cell, 155

Index Polarizability, 20 Potential energy curves CdAr, 39 HgAr, 37-38 MgAr, 36 of A1 complexes, 30 ZnAr, 39 Potential energy surface (PES) determination of, 87 of small clusters, 86 Predissociation lifetime, of Cd complexes, 46 Predissociation, of Cd complexes, 47 Pump-probe and beat period, 78 and inner turning point of, 77 and recurrences, 77 and wave-packet motion, 77, 78 Pure FI states, 9-22 and bond length, 9-22 and dissociation energy, 9-22 Pure-A states, 23 A1Ar, 23 A1Kr, 23 Quadrupole, effective charge model, 41 Quadrupole moment, 22 ab initio calculations, 11 Quadrupole polarizability, 16 Quantum defect theory, 29, 32 Quantum mechanical calculations, 45 Radial electron density plot, 24, 25 Radial-type coupling, 49 Rare gas atoms, 2 Rare gas matrices, 43 and Hg atoms, 66-68 Rare gas polarizability, 9 Rare gas, Rydberg orbitals of, 44 Rare gases, orbital character, 41--46 Re (see Bond lengths) Reflectron instrument, 186 REMPI, (see Resonance-enhanced multiphoton ionization) Resonance-enhanced multiphoton ionization (REMPI), 150

229 Ringdown decay and detection schemes, 165 and longitudinal resonances, 166 and transient digitizers, 165 model of, 161 Rovibrational states, of floppy triatomics, 86 Rydberg atomic states, 31 Rydberg constant, 29 Rydberg orbitals, 29 diffuse, 31 Rydberg state, 13-14, 15, 23-35 AIAr, 27 and potential barrier, 27 and rare gas size, 24 BAr, 27 binding energy, 28 comparison of A1 and Mg, 28 group 1 atoms, 26 groups 2 and 12 atoms, 23-26 groups 3 and 13 atoms, 27 of Al, 27 of AI complexes, 29, 31 of In, 27 of rare gases, 41 of symmetry, 31 Rydberg type states, (n + 1), 24 SCF (see Self-consistent field calculations, 18) Self-consistent field (SCF) calculations, 18 of Lille, 18 of NaHe, 18 Semirigid bender (SRB) model, 95 SEP (see stimulated emission pumping) Si, FI alignment, 33 SiAr, 32 SiAr cation, ab initio calculation, 33 SiAr, ground state, 53 Silicon clusters negative ion photodetachment studies of, 115 negative ion photodetachment studies of, 130-146 study of using negative ion photodetachment techniques, 113-148

230

UV photoelectron spectral studies of, 115 Silicon dicarbide, 98-105 comparison to carbon trimer, 98 dispersed fluorescence studies of, 100, 101,102, 104 energy plot, 103 further spectroscopic studies, 103 Laser-induced grating spectroscopy of, 107 LIF study of, 99 PES determination, 99 rotationally resolved SEP spectra of, 104 structure of, 98 Silicon dimer, 130--135 comparison of techniques, 131-133 electronic structure of, 130, 13 l, 133,134 photodetachment studies of, 13 l, 132 photoelectron studies of, 131,132 spectroscopic constants of, 134 spectroscopic studies of, 130 threshold photodetachment spectrum of singlet band, 135 Silicon tetramer, 140-146 ab initio calculations of, 142 ab initio geometries of, 144 excitation energies, 146 Franck-Condon analysis of spectra, 142, 143, 145 photoelectron spectra of, 140, 14 l, 142 structure of, 142 threshold photodetachment spectra of, 142, 145 Silicon trimer, 135-140 ab initio studies, 135 and Jahn-Teller distortions, 135, 137 and Jahn-Teller interactions, 135 assignment of photoelectron spectrum, 137 bond angles, 138 excitation energies of, 137 photodetachment spectrum of, 138, 139 photoelectron studies of, 136

INDEX

sequence band structure, 140 spectral simulation of, 140 Small clusters large-amplitude motion in, 85-111 spectroscopic studies of, 85-111 Smalley-type cluster source, 117 Spectroscopic constants, of Na complexes, 42 Spin-orbit coupling, 35, 41 matrix elements, 40 Spin-orbit matrices, 40 Spin-orbit operator, 35 of Cd complexes, 47 Spin-orbit-induced predissociation, 46-51 SRB (see Semirigid bender) Stimulated emission pumping (SEP), 87 Strong mixing, 22 Swarm bands, 158 Tang-Tonnies model, 17 TEM 00, 164 Threshold photodetachment spectroscopy (see also Zero kinetic energy electron (ZEKE) spectroscopy) schematic of, 118 description of, 116-119

/-Uncoupling operator, 45 van der Waals complexes, metal atom-rare gas, 1-80 Van Vleck "pure precession" hypothesis, 45 Wigner threshold law, 124, 133, 138 Xe complexes, relatives strengths, 50

Z (see Effective charge) ZEKE (see Zero kinetic energy electron spectroscopy) Zero kinetic energy electron spectroscopy (ZEKE), 115

Index

Zn, action spectrum of, 49 Zn complexes of, collisional deactivation of, 47 Zn-Xe van der Waals complex, 10 and repulsive forces, 10 polarizability, 10 ZnAr, 24, 38 LIF spectra of, 47

2 31

potential energy curves of, 39 ZnKr, LIF spectra of, 47 ZnXe doublet or triplet states, 40 predissociation action spectrum of, 48 radial relative nuclear velocity during dissociation, 49 spin--orbit-induced coupling, 47

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CONTENTS: Introduction, Lanny Liebeskind. Orthomanganated Aryl Ketones and Related Compounds in Organic Synthesis, Lindsay Main and Brian K. Nicholson. Cyclopropylcarbene-Chromium Complexes: Versatile Reagents for the Synthesis of Five-Membered Rings, James W. Hemdon. Organic Synthesis via Vinylpalladium Compounds, Richard C. Larock. Ruthenium Catalyzed Oxidative Transformation of Alcohols, Shun-lchi Murahashi and T. Naota. Palladium-Catalyzed Carbonyl Allylation via Allylpalladium Complexes, Yoshiro Masuyama. Index. Volume 4, In preparation, Winter 1996 ISBN 1-55938-709-2

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CONTENTS: Preface, Lanny Liebeskind. Recent Progress in Higher Order Cyanocuprate Chemistry, Bruce H. Lipshutz. The Evolution of a Commercially Feasible Prostaglandin Synthesis, James R. Beh/ing, John S. Ng and Paul IN. Collins. Transition Metal Promoted Higher Order Cycloaddition Reactions, James H. Ridgy. Acyclic Diene Tricarbonyiron Complexes in Organic Synthesis, Rene Gree and J.P. Lellouche. Novel Carbonylation Reactions Catalyzed by Transitions Metal Complexes, Masanobu Hidai and Youichi Ishii. Volume 5, In preparation, Winter 1996

ISBN 1-55938-789-0

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CONTENTS: Preface, Lanny S. Liebeskind. Recent Advances in the Stille Reaction, Vittorio Farina and Gregory P. Roth. Seven-Membered Ring Synthesis via Iron-Mediated Carbonylative Ring Expansion and G-Alkyl-~-Allyl Complexes, Peter Eilbracht. New Catalytic Asymmetric Carbon-Carbon BondForming Reactions, Masakatsu Shibasaki. Recent Improvements and Developments in Heck-Type Reactions and Their Potential in Organic Synthesis, Tuy~t Jeffery. Index.

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Advances in Molecular Structure Research Edited by Magdolna Hargittai, Structural Chemistry

Research Group, Hungarian Academy of Sciences, Budapest, Hungary and Istvdn Hargittai, Institute of General and Analytical Chemistry, Budapest Technical University, Budapest, Hungary "Progress in molecular structure research reflects progress in chemistry in many ways. Much of it is thus blended inseparably with the rest of chemistry. It appears to be prudent, however, to review the frontiers of this field from time to time. This may help the structural chemist to delineate the main thrusts of advances in this area of research. What is even more important though, these efforts may assist the rest of the chemists to learn about new possibilities in structural research. This series will be reporting progress in structural studies, both methodological and interpretational. We are aiming at making it a "user-oriented" series. Structural chemists of excellence will be critically evaluating a field or direction, including their own achievements, and charting expected developments."

- - From the Preface Volume 1, 1995, 352 pp. ISBN 1-55938-799-8

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CONTENTS: Introduction to the Series: An Editor's Foreword, Albert Padwa. Preface, Magdolna Hargittai and Istv~n HargittaL Measuring Symmetry in Structural Chemistry, Hagit Zabrodsky and David Anvir. Some Perspectives in Molecular Structure Research: An Introduction, Istv~n Hargattai and Magdolna HargattaL Accurate Molecular Structure from Microwave Rotational Spectroscopy, Hans Dieter Rudolph. GasPhase NMR Studies of Conformational Processes, Nancy S. True and Cristina Suarez. Fourier Transform Spectroscopy of Radicals, Henry W. Rohrs, Gregory J. Frost, G. Bamey Ellison, Erik C. Richard, and Veronica Vaida. The Interplay between X-Ray Crystallography and AB Initio Calculations, Roland Boese, Thomas Haumann and Peter Stellberg. Computational and Spectroscopic Studies on Hydrated Molecules, Alfred H. Lowrey and Robert W. Williams. Experimental Electron Densities of Molecular Crystals and Calculation of Electrostatic Properties from High Resolution X-Ray Diffraction, Claude Lecomte. Order in Space: Packing of Atoms and Molecules, Laura E. Depero.

Volume 2, In preparation, Winter 1996

ISBN 0-7623-0025-6

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CONTENTS: Preface, Magdolna Hargittai and Istvdn HargittaL Conformational Principles of Congested Organic Molecules: Trans is Not Always More Stable Than Gauche, Eiji Osawa. Transition Metal Clusters: Molecular versus Crystal Structure, Dario Braga and Fabrizia GrepionL A Novel Approach to Hydrogen Bonding Theory, Paola Gilli, Valeria Ferretti, Valerio Bertolasi and Gastone Gilli. Partially Bonded Molecules and Their Transition to the Crystalline State, Kenneth R. Leopold. Valence Bond Concepts, Molecular Mechanics Computations, and Molecular Shapes, Clark R. Landis. Empirical Correlations in Structural Chemistry, Vladimir S. Mastryukov and Stanley H. Simonsen. Structure Determination Using the NMR "Inadequate" Technique, Du Li and Noel L. Owen. Enumeration of Isomers and Conformers: A Complete Mathematical Solution for Conjugated Polyene Hydrocarbons, Sven J. Cyvin, Jon Brunvoll, Bjorg Cyvin, and Egil Brendsdal.

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Advances in Molecular Electronic Structure Theory Edited by T h o m H. Dunning, Jr., Molecular Science Research Center, Pacific Northwest Laboratory, Richland, Washington This series presents an outstanding collection of articles written by some of the top theorists in the field and will be of special note to chemists interested in fundamental molecular processes. REVIEW: "This is the opening volume of a new annual series in theoretical chemistry. The editor is a former group leader at Argonne National Laboratory and most of the authors are present and former collaborators of the Argonne group . . . . this is an excellent volume, that is highly recommended to both theoreticians and experimentalists."

Journal of the American Chemical Society Volume 1, Calculation and Characterization of Molecular Potential Energy Surfaces 1990, 275 pp. $97.50 ISBN 0-89232-956-4 CONTENTS: Introduction to the Series: An Editor's Foreword, Albert Padwa. Introduction, Thom H. Dunning, Jr. Analytical Representation and Vibrational-Rotational Analysis of Ab Initio Potential Energy and Property Surfaces, Walter C. Ermler and Hsiu Chinhsieh. Calculation of Potential Energy Surfaces, Lawrence B. Harding. The Analytical Representation of Potential Surfaces for Chemical Reactions, G.C. Schatz. Characterization of Molecular Potential Energy Surfaces: Critical Points, Reaction Paths, and Reaction Valleys, Elfi Kraka and Thom H. Dunning, Jr.. Long-Range and Weak Interaction Surfaces, Clifford E. Dykstra. The Von Neumann-Wigner and Jahn-Teller Theorems and Their Consequences, Regina F. Frey and Emest R. Davidson. Volume 2, 1994, 209 pp. ISBN 0-89232-957

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CONTENTS: Introduction, Thom H. Dunning, Jr. Electronic Structure Theory and Atomistic Computer Simulations of Materials, Richard P. Messmer. Calculation of the Electronic Structure of Transition Metals in Ionic Crystals, Nicholas W. Winter, David K. Temple, Victor Luana and Russell M. Pitzer. Ab Initio Studies of Molecular Models of Zeolitic Catalysts, Joachim Sauer. Ab Inito Methods in Geochemistry and Mineralogy, Anthony C. Hess and Paul F. McMillan.