Advances in
Physical Organic Chemistry
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Advances in
Physical Organic Chemistry Edited by
V. GOLD Department of Chemistry King’s College, University of London
VOLUME 3
1965
Academic Press, London and New York
ACADEMIC PRESS INC. (LONDON) LTD. Berkeley Square House Berkeley Square, London, W.l.
U.S. Edition published by ACADEMIC PRESS INC. 111 Fifth Avenue New York, New York 10003
Copyright 0 1965 by Academic Press Inc. (London) Ltd.
All rights reserved
No part of this book may be reproduced in any form by photostat, microfilm, or any other means, without written permission from the publisher.
Library of Congress Catalog Card Number: 62-22125
PRINTED I N GREAT BRITAIN BY SPOTTISWOODE, BALLANTYNE AND COMPANY LIMITED LONDON AND COLCEESTER
CONTRIBUTORS TO VOLUME 3 R. J. W. LE FEVRE, School of Chemistry, University of Sydney, New South Wales, Australia ALLANMACCOLL,William Ramsay and Ralph Forster Laboratories, University College, London, England
L. W. REEVES,Chemistry Department, University Vancouver 8 , B.C., Canada
of
British Columbia
DAVIDSAMUEL, Isotope Department, The Weizmann Institute of Science, Rehovoth , Israel BRIANL. SILVER,Isotope Department, The Weizmann. Institute of Science, Rehovoth, Israel
V
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CONTENTS CONTRIBUTORSTO VOLUME 3 .
.
v
. .
.
1 3 41 53 68 73 75 79
I . Introduction . . 11. Experimental Methods of Investigating the Rate of Reaction 111. Mechanism of Pyrolysis . . IV. The Experimental Results . . V. Regularities in the Experimental Data . . VI. Homogeneous Catalysis of Gas-Phase Eliminations . . VII. General Conclusions . References . .
91 92 96 100 103 117 119 120
MoI ecu Iar Refractivity and Polariza bi I ity R. J. W. LE F ~ V R E
I. Introduction . 11. Molecular Refraction . 111. Molecular Polarizability . IV. Molecular Anistropy and Stereochemistry . V. Hyperpolarizability . VI. Aspects of Polarizability Requiring Investigation VII. Miscellaneous Applications of Polarizability . References .
. .
.
.
.
.
Gas-P hase H e t e r o lysis ALLANMACCOLL
*
Oxygen Isotope Exchange Reactions of Organic Compounds
DAVIDSAMUEL and BRIAN L. SILVER I . Introduction . 11. Experimental Methods . 111. The Exchange of Hydroxylic Compounds with Water IV. The Exchange of Carbonyl Compounds with Water Vii
. . . .
123 125 128 147
viii
CONTENTS
. . 168 V. The Exchange of Carboxylic Acids with Water V I . The Exchange of Other Organic Compounds containing Oxygen with Water . 174 VII. The Exchange between Organic Compounds and Metal . 181 Oxides . VIII. Conclusion . 182 References . . 183 N.M.R. Measurements of Reaction Velocities and Equilibrium Constants as a Function of Temperature.
L. W. REEVES I. Introduction and Scope . . 11. The Bloch Equations with Incorporation of Chemical Exchange . . 111. Experimental Methods . . IV. Hindered Internal Motions of Molecules . V. Hydrogen Bonding, Tautomerism and Proton Exchange References . .
AUTHORINDEX. CUMULATIVEINDEX OF AUTHORS . CUMULATIVE INDEX OF TITLES .
.
187 193 228 233 259 265 271
. 281 . 281
MOLECULAR REFRACTIVITY AND POLARlZABlLlTY R. J. W. LE FBVRE
School of Chemistry, U n i v e r s ~of€ ~Sydney, N.S. W., Australia I. Introduction . . 11. Molecular Refraction . . A. “Additivity” of Molecular Refraction . . B. Refractions of Atoms and Ions . . C. Refractivity and Atomic or Molecular Dimensions . . D. Refractivity and Other Molecular Properties . . E. Dispersion of Refractivity . . F. Analytical and Miscellaneous Applications of Refractivity . . . 111. Molecular Polarizability . . A. Polarizability as a Directional Property . . B. Evaluation of Principal Molecular Polarizabilities . . C . Anisotropic Bond Polarizabilities . . D. Bond Polarizabilities and Other Bond Properties . . IV. Molecular Anisotropy and Stereochemistry . . A. Additivity of Bond Tensor Ellipsoids . . B. Applicability of Polarizability Anisotropy to Structural or Conforma. . tional Problems C. Directed Exaltations in Conjugated Systems . . D. Near-Isotropic Molecules . . V. Hyperpolarizability . VI. Aspects of Polarizability Requiring Investigation . . VII. Miscellaneous Applications of Polarizability . . References . .
.
I 3 4 20 25 32 34 38 41 42 44 48 51 53 54 55 64 65
68 73 75 I9
I. INTRODUCTION REFRACTIVEindices (n) of pure substances have been accurately measurable far longer than any other optical properties. The refractometers introduced by Abbe in 1874 and by Pulfrich in 1887 made easy and convenient the determination of n for a liquid to within five significant figures; interferometers, based on that described by Jamin in 1856, made possible higher precisions with liquids and have often been used to obtain the refractive indexes of gases and vapours. Details of these and other instruments in their modern forms, together with helpful operational instructions, and much information relevant generally to refraction, have been lately given by Bauer et al. (1960).
2
R . J.
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LE FEVRE
An unknown but certainly large number of refractive indices are scattered throughout the literature, particularly occurring in papers dealing with organic chemistry; their retrieval and collection into an up-to-date and complete list would today be an insuperable task. Fortunately, Beilstein’s Handbuch usually includes refractive indices among the physical constants quoted under each compound heading. Compilations of older refractive indices are in the 5th edn. of LandoltBornstein’s Physikalisch-chemische Tabellen (two vols. of which appeared in 1923, followed by six supplements during 1927-36) and in the 1st edn. of the International Critical Tables (issued in 1930); these two sources contain all the values available to Bruhl, Eisenlohr, von Auwers, and others who in the past have considered the relation of refraction to chemical composition. More recent data have been assembled by Egloff (1946) and the American Petroleum Institute (1953); Timmermans (1950)) after “systematic recourse to the whole of the chemical literature up to January lst, 1950” cites those physico-chemical constants which he judges to have been “established with a precision worthy of contemporary science ” ; Vogel, in papers to the J . Chem. Xoc. during the last thirty years, has provided new measurements of the refractive index of nearly 900 compounds. Many others, of varying accuracies, can be traced through the “Tables of Experimental Dipole Moments” lately prepared by McClellan (1963). The refractive index of a substance varies with the physical state of the latter, the temperature t, and the wave-length h of the light by which n is observed. The first two of these effects were early attributed to the density d. I n 1805 Laplace, arguing from Newton’s corpuscular theory of light, deduced that (n2- l)/d should be constant, but subsequent experiments by Arago and Petit showed this quotient for a liquid and its vapour to be not the same. Empirically, Gladstone and Dale (1858) found that (n- l)/d was adequately independent of temperature throughout a given state, and they and other workers proceeded to analyse (n- l)/d as an “additive-constitutive” property; Smiles (1910) gives a full account of this phase. However, the Gladstone-Dale expression imperfectly covered changes of state. More satisfactory in several respects was the equation ( l ) , published almost simultaneously by Lorenz (of Copenhagen) and Lorentz (of Leyden) during 1880: (n2- l ) / ( n + 2 2 )d
=
constant
=
r
(1)
Lorenz derived (1) by assuming that a material is made up of spherical molecules through which light travels slower than in the vacuum in which they are situated, while Lorentz proceeded logically from Maxwell’s electromagnetic theory and was thus able to explain, in addition, the
MOLECULAR R E F R A C T I V I T Y A N D P O L A R I Z A B I L I T Y
3
variations of n with X (dispersion). I n fact, however, exact compensation of n by d is not achieved by the left-hand side of ( I ) , which with liquids may increase numerically by about 0.01 % per degree of temperature rise; greatest invariance is represented by the expression of Eykman (1895): (n, - l ) / ( n+ 0.4) d = constant (2) Although empirical and lacking a theoretical basis, (2) is useful for interpolation purposes. Lorentz (1909) himself pointed out possible causes for the slight limitations of ( l ) ,and Bottcher (1952) has discussed an appropriate correction ; nevertheless, in practice the inconstancy of (1) with temperature is usually within the experimental error and the eqnation may safely be used as written above. 11. MOLECULARREBRACTION The specific refraction r of a substance multiplied by the molecular weight is the molecular refraction : M r = R ; with d in g/cm3, R is in om3 units. R, of course, is affected by the dispersion of n, so the wavelength should be specified (e.g. for carbon tetrachloride, R, = 26.31, R, = 26.45, RF = 26.86, R,. = 27.08 cm3; the four wavelengths indicated are those which have most frequently been used in the past: C = H, = 6563 8, D = Na = 5893 A, F = Hp = 4861 8, G’ = H, = 4341 8). With liquids, the requisite nA and d i measurements can obviously be made directly ;solids, in general, are examined in solution, and “mixture formulae” applied to the observations. If subscripts 1, 2, and 12 relate respectively to solvent, solute, and solution, and if concentrations are expressed as molar fractions f l and fi, or weight fractions w1 and w,, the apparent partial molar or specific refractions (R, or r,) can be extracted from equations (3) or (4),provided R1or r l is invariant with concentration :
(4’-1) ( n l l f l + M , f 2 ) / ( n ~ 2 + 2 ) d , , = R l f l + R 2 f i
+
(n&- l)/(n?z+ 2) d12 = w1 r1 w2r2
(3)
(4)
Weight fractions are arithmetically simpler in use than molar fractions. Since it is often found by experiment that (dl2-dl)/dlw2=P and (n&-n?)/w, = yn? are constant, r2 a t infinite dilution can be easily obtained from mean values of ,!I and yn? by (5): mr2= r 1 ( 1 - / 3 ) + C y n ~
where C = 3/dl(n! 1**
+ 2)’; cf. Le FBvre (1953).
4
R. J .
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LE F ~ V R E
Crystalline solids frequently exhibit anisotropy in their refractive indices, uniaxial crystals having two, n, and n,, and biaxial crystals having three, nor,ng, and nr, characteristic refractive indexes, in such cases the geometric mean is usually taken as 5 for insertion in (1): 5 = (n:n,)’’3 or ? = i (n,nfiny)1’3 (cf. Heigl and Wulff, 1931, for examples).
A. “Additivity” of Molecular Refraction The efforts of early workers, from Herschel in 1830, through Berthelot, Gladstone and Dale, Landolt, t o Conrady, Briihl and others in the 1890’s (cf. Smiles, 1910, for references) demonstrated the existence of connections between refraction and chemical composition. I n particular, Berthelot, using the product of (nz- l)/d and the equivalent weight, found equal differences for equal differences of CH, in analogous compounds, while Gladstone and Dale (1863), explicitly concluded that (n- l ) / d for a given liquid was made up from corresponding values for the component elements “modified by the manner of combination”. Bruhl (1880) adopted M(n2- l)/d (n2+ 2) and, surveying about 150 substances, carried through the first extensive analysis of R from the viewpoint of additivity, and compiled a list of “atom refractions”. These last were easily obtained once the constant difference for CH, was established by measurements of molecular refractions for a number of homologous series; then e.g. subtraction of xRCHa from the refraction of a hydrocarbon CxHZx+, gave 2Rhydrogen, of (XRcHa +Rhydrogen) from the refraction of C , H a X f lX, . gave Ratomx,of 2Rhydrogen from RCHagave Rcarbon,etc. Bruhl noted the “constitutivity ” of this property: the atom refractions of oxygens were not the same in aldehydes, acids, and varied dependently on the carbon being singly, doubly, or ethers ; Rcarbon triply bonded (and by comparing the R’s of related saturated and unsaturated molecules, knowing Rtrydrogen, he evaluated the increments in refractivity due to multiple linkages between carbon and carbon); later (1886a, b) he drew attention to the effects of conjugated unsaturation, and reported the range of atom refractions necessary for nitrogen in several classes of its compounds (1895, 1897, 1898). To illustrate these points some of Briihl’s refractivities are given in Table 1. By starting from such values, and reversing the arguments through which they were obtained, a way of solving problems of molecular constitution was opened. As the approach involved no destruction of materials or disturbance of equilibria, molecular refractions quickly became extensively applied to a variety of structural questions, particularly to those difficultly resolved by the ordinary chemical techniques of the time, e.g. the positions of double bonds in terpenes, the recognition of
MOLECULAR R E F R A C T I V I T Y A N D POLARIZABILITY
5
TABLE1 Some Refrectivitiesa Deduced by Bruhl
c
. .
H
.
Br
.
c1 1
N (in AlkylNHz) N (in AlkylzNH) N (in AlkylaN)
. . . . . .
. .
2.365 1.103 6.014 8.863 13.808 2.31 2.60 2.92 a
0 (in carbonyl group) 0 (inethers) . . 0 (inhydroxyl group) Ethylene bond . Acetylene bond . N (in ArylNHz) . N (in ArylzNH) . N (in ArylsN) .
2.328 1,655 1.506 1.836 2.22 3.01 3.40 4.10
For the H, line
geometrical isomers, the examination of keto-enol systems, etc. Briihl died in 1911. A Royal Institution “Friday Evening Discourse” (Briihl, 1906) made available to British chemists an account (in English) of his optical-chemical researches. (According to an anonymous writer (1911)’ Briihl gave this lecture in a “masterly manner” which obviously considerably impressed the audience.) A long obituary by von Auwers (1911) contains more details, both scientific and personal, and includes a complete list of references to Briihl’s publications. Briihl can justly be credited with having pioneered one of the first generally useful methods of physical-organic chemistry. His constants were revised and extended by von Auwers and Eisenlohr from 1910 onward; Table 2 is an extract from Eisenlohr’s 1923 data. Although the amendments to Briihl’s figures appear slight it is important to remember that the Rx’s shown are mean values. As measurements accumulated, the constitutive nature of this property became more and more obvious. Even the “constant ” for the methylene group depended somewhat upon the homologous series from which it was drawn. Concealed beneath the average R, of 4.59 cm3, quoted by Eisenlohr (1910), after recalculating Briihl’s values, were the facts that although 66 hydrocarbons, 92 aldehydes and ketones, 74 acids, 81 alcohols, and 190 esters, gave average R,’s of 4.60, 4.60, 4.59, 4-61, and 4.58 respectively, individual fluctuations within a series were sometimes between 4.11 and 4.86 cm3 (Vahrman’s 1960 estimate of 4-63 cm3 falls within this range). Increments appropriate to double and triple bonds seemed to vary with the number and length of the radicals attached, Eykman (1906) suggesting 1.51, 1-60, 1.75, 1-88, and cn. 2.00 om3 as CH2=CH2 by progressive substitution became CR2:CR2. Von Auwers (1935) proposed 2.325 om3 for C=C when terminally situated or 2-573 cm3 when within a chain, and Campbell and Eveslage
6
R. J.
w.
LE F ~ V R E
TABLE2 Some Itofrart ivitios Deduced by Eisonlolir ~~
C H GI Br I 0 (in cclrbonyl group) 0 (in ethers) 0 (in hydroxyl group) Ethylene bond Acetylene bond N (in AlkylNHz) N (in AlkylzNH) N (in AlkylsN)
Ra
R,
Ri3
R,
2.413 1.092 8.933 8.803 13.767 2.189 1.639 1.522 1.686 2.328 2.309 2.478 2.808
2.418 1.100 5-967 8.865 13.900 2.211 1.643 1.525 1.733 2-398 2.322 2.502 2.840
2.438 1.115 6.043 8.999 14.224 2.247 1.649 1.531 1.824 2.056 2.368 2.561 2.940
2.466 1.122 6-101 9.152 14.521 2.267 1.662 1.541 1.893 2-538 2.397 2.605 3.000
(1945) gave higher values still for internal bonds (2.267, 2.534, 2.696, 2.735, and 2.767 cm3, in order, for 1-, 2-, 3-, 4-, and 5-acetylenes). According to Huggins (1941) the molecular refractions of saturated
hydrocarbons are not strictly additive functions of atomic refractivities but are influenced by the types and amounts of chain-branching within their molecules. The variability of nitrogen and oxygen in their different combinations has already been mentioned. The analogous behaviour of sulphur (exhibiting atom refractions, for the H, line, from 3.34 in diethyl sulphate to 9.31 cm3 in diphenyl sulphide) and of other mult i valent elements, has long been known (cf. Smiles, 1910, p. 277). Inevitably, in view of the apparent imperfections, “additive ” treatments of molecular refraction have been criticized. Briihl has been accused of inconsistency in allotting increments for double or triple bonds between carbon and carbon but not for those between carbon and oxygen or carbon and nitrogen . . . “one might just as well use only one atomic constant for oxygen, add an increment for C=O, and use different atomic constants of hydrogen depending on whether it is bonded to carbon or oxygen. A corresponding remark applies to the distinction between the three atomic constants of nitrogen in primary, secondary, and tertiary amines. I n the first two, some of the hydrogen atoms are bonded to carbon and some to nitrogen, and it is arbitrary to ascribe the optical differences only to the nitrogen” (Fajans, 1949 a, b). Notwithstanding these and other objections the fact remains that tables such as Table 2 have an empirical usefulness for the testing of,
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
7
or deciding between, the various formulae often available for a given compound. Minor imperfections in additivity can be diminished ifas Eykman ( 1893) originally suggested-refractive values for groups are chosen from the measured molecular refractions of the nearest complete molecules (e.g. R for phenyl from R found for benzene minus RE); major departures from additivity can offer significant evidence on questions of structure or configuration. Two important illustrations are provided by poly-unsaturated and geometrically isomeric molecules. Briihl (1886a) had noted that the effect of unsaturation on molecular refraction could not always be represented by the increments previously deduced : two olefinic bonds when situated conjugatively increased the refraction abnormally, the difference between observed and calculated R’s being regarded as “optical anomaly”. I n 1907 he introduced the terms “optical exaltation ” and “optical depression ” to refer respectively to cases where the observed R exceeded or fell short of that calculated; numerically, depressions are commonly small but exaltations may be verylarge (see Smiles, 1910; von Auwers, 1924):
Benzene Diphenylmethane Styrene Phenylacetylene Bibenzyl Stilbene 1,4-Diphenylbutadiene Diphenyldiacetylene 1,6-Diphenylhexatriene Mesityl oxide Phorone Benzaldehyde Cinnamaldehyde Carvenone
R, observed
R, calc.
A R cm3
25.93 65.13 35.98 34.46 59-60 65.65 82.9 74.86 100.9 30.13 45.39 31.77 43.51 46.92
26.31 55.00 35.08 33.53 59.64 59.20 68.0 64.86 76.74 29.39 42.73 31.01 39.78 45.81
- 0.38 +0*13 0.90 0.93 - 0.04 6.45 14-9 10.0 24.2 + 0.74 2.66 0.76 3.73 1.11
+ +
+ + + +
+ + + +
The occurrence of positive exaltation has been frequently cited when fixing the relative positions of C=C and C=O units in structures containing two or more of these bonds; many examples are to be found in terpene chemistry (cf. Semmler, 1906 ; Gildemeister and Hoffman, 1928-31 ; or Simonsen, 1947-9). Briihl (1896) stated that, as a general rule, among geometrical isomerides the more stable, higher melting, and less soluble individual had the greater molecular refraction ; when the groups attached to the double
8
R . J.
w.
LE F ~ V R E
bond were unsaturated the disparity between Rtraans and Rcis was numerically more marked : R, cm3 Oleic acid Elaidic acid Ethyl maleate Ethyl fumarate Anisaldoxime (syn) Anisaldoxime (anti)
86.50 86.67 42.23 42.90 44.85 46.03
Such defective additivity has proved useful for structural assignments between isomers ; notably it has been invoked during the reconsideration of the natures of the aromatic diazo- and azo-compounds (see summary by Calderbank et al., 1948). Departures from additivity due to ring formation have also been utilized in structural investigations (e.g. Semmler (1906) used refraction to confirm the presence of %membered rings in sabinene and tanacetone) but here caution is necessary because exaltations are not uniformly associated with ring-size, seemingly being different in homo- and hetero-cyclic systems (cf. Hughes and Johnson, 1931). It is clear therefore that the empirical value of data such as Briihl and Eisenlohr attempted to provide depends very much on the range and details of the molecular environments from which the atomic and structural constants have been drawn. During the last three decades a most comprehensive overhaul and extension of previous sources has been undertaken by Vogel (refs. from 1934 onward; see also refs. to Vogel under Cowan, Cresswell, Grzeskowiak, Jeffery, and Kyte). By 1948the individual molecular refractions for the C, D, P, and G’ spectral lines had been recorded for 606 compounds whose purity criteria were also given; from this information Vogel deduced the values reproduced in Table 3. I n addition, throughout his work Vogel has regularly listed for each substance the magnitude of the product MnLO-the so-called “molecular refraction coefficient ” (Eisenlohr, 1925)-which, although devoid of foundation in theory, can in practice be split into additive-constitutive atomic and group coefficients. These last have been included in Table 3 since they make possible the prediction of nio for a liquid from its corresponding structural formula and molecular weight. Alternative analyses of refractometric data have been proposed, e.g. using G. N. Lewis’ (1923) ideas of valence and electronic bonding, Fajans and Knorr (1924) and independently Smyth (1925) deduced refractivities for octets and electron groups ; von Steiger (1921), Denbigh
9
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
TABLE 3 Atomic, Group, and Structural Refractivities given by Vogela
H (in CHZ) C (in CHz) 0 (in ethers) 0 (inacetals) CO (in ketones) CO (in methyl ketones) COO (in esters) OH (in alcohols) COzH F c1 Br I NH2 ( l a r y aliph. amines) NH (2aryaliph. amines) NH (aary arom. amines) N (3"y aliph. amines) N (3"y arom. amines) NO (nitroso) 0.NO (nitrite) NO2 (nitro) N . NO (nitrosamine) S (in sulphides) SH (in thiols) CS (in xanthates) SCN (in thiocyanates) NCS (in isothiocyanates) CN (in nitriles) C: C increment* C = C increment6 3-carbon ringc 4-carbon ringc 5-carbon ringc 6-carbon ringc CHz CH3 CzHs n-C3H7 iso-CaH7 n-C4Hs iso-C4H9 s-C~H~ n-CsH11 n-CsH13 n-C7H1~, n-CsH1-i C ~ H (allyl) S CsHs (phenyl) uJ.
1.026 2.572 1.753 1.603 4.579 4.730 6.173 2.536 7.191 0.81 5.821 8.681 13.825 4.414 3.572 4.548 2.698 4.085 5.130 7.187 6.662 7.748 7.852 8.691 12.84 13.313 15.445 5.431 1.545 1.959 0.592 0.303 -0.19 -0.15 4.624 5.636 10.260 14.895 14.905 19.500 19.530 19.330 24.140 28.725 33.395 37.960 14.425 25.136
chem. Soc. 1948, p. 1842.
1.028 2.591 1.764 1.607 4.601 4.758 6.200 2.546 7.226 0.81 5.844 8.741 13.954 4.438 3.610 4.678 2.744 4.243 5.200 7.237 6.713 7.850 7.921 8.757 13.07 13.400 15.615 5.459 1.575 1.977 0.614 0.317 - 0.19 -0.15 4.647 5.653 10.300 14.965 14.975 19.585 19.620 19.420 24.250 28.855 33.550 38.135 14.520 25.359 b
1.043 2.601 1.786 1.618 4.654 4.814 6.261 2.570 7.308 0.79 5.918 8.892 14.310 4.507 3.667 5.000 2.820 4.675 5.397 7.377 6.823 8.100 8.081 8.919 13.67 13.603 15.980 5.513 1.672 2.061 0.656 0.332 -0.19 -0.16 4.695 5.719 10.414 15.125 15.145 19.800 19.840 19.625 24.515 29.160 33.905 38.535 14.745 25.906
Terminal bonds.
1.040 2.655 1.805 1.627 4.702 4.874 6.315 2.588 7.368 0.78 5.973 9.011 14.620 4.570 3.732 5.273 2.914 5.155 5.577 7.507 6.928 8.358 8.233 9.057 14.22 13.808 16.300 5.561 1.720 2.084 0.646 0.322 - 0.22 -0.17 4.735 5.746 10.481 15.235 15.255 19.950 19,990 19.775 24.700 29.385 34.170 38.830 14.920 26.356 C
- 2.56 26.71 22.74 22.41 42.41 42.42 64.14 23.94 63.98 21.84 50.41 118.07 196.27 22.64 23.34 29.52 24.37 30.23 43.14 62.27 65.61 69.67 52.86 50.20 77.20 88.90 93.11 36.46 - 6.07 - 12.56 -4.72 -4.67 -4.56 - 3.53 20.59 18.13 38.72 59.25 58.95 79.81 79.54 80.21 100.46 121.10 141.75 162.43 57.60 122.03
Increments.
10
R. J . W . LE
FkVRE
(1940))and more recently Vogel (Cresswellet al., 1952) have developed a system of “bond refractions”. Smyth and von Steiger started from atomic refractions, such as are in Table 3, and argued that a quarter of the refractivity of carbon is contributed to a single bond, two quarters +Rhydrogen, = to a double bond, etc., so that Rc-H = 0~25RCarbOn
+
RC=C = Rcarbon -k Rduublebond) RC=C = 1*5Rcarbon Rtriplebond, = 0.5RCarbOnRhetonicoxygen, and so on. The imperfect additivity
0*5Rcarbon,
Re=
+
of the earlier atomic and structural refractivities is, of course, carried over to bond refractivities by such derivations. The bond refractions of Denbigh or Vogel depend directly upon molecular refractions determined by experiment : fundamentally the value found for the methylene group = R,-, + 2Rc-H and, in a homologous series can be written as RCHa correspondingly, the molecular refraction for any n-alkane is (n-
llRC-C
+ (2n+
RC-H
= RC,Ha,+a
the left-hand side of which, with a = R,-, + 6R,-, and b = Rcpc+ 2R,-,, becomes a + b ( n- 2). Denbigh and Vickery (1949) used the Na-D light refractions of eight n-alkanes, containing five or more carbon atoms, with which to compute (by the method of least squares) the “best fit” rectilinear and (n- 2). I n this way, the constants emerged relation between Ralkane a s a = 11.339 and b = 4.644, whence R,, = 1.674and RcPc = 1.296 em3. These results were then tested on 43 n-alkanes and 153 branched alkanes. Calculated and measured molecular refractions showed an average discrepancy over the whole range of 0.43%. The positive discrepancies, averaging 0.37 %, occurred predominantly among the higher n-alkanes, the negative discrepancies, averaging 0*46%, lay almost wholly among the branched alkanes. Statistically these divergencies were not attributable to random errors. Accordingly Denbigh and Vickery suggested small corrective “increments ’)for four types of branching : a methyl group in the 2-position carrying a n exaltation of 0.026 5 0.011 om3 in contrast to one within the chain causing a depression of 0.143 0.016 em3, and depressions of 0.244 f 0.026 and 0.307 f 0.030 om3 being required for ethyl and “larger substituents” respectively. As often noted with physical properties of first members of homologous series, the R1, of methane (6-588 cm3) may be slightly anomalous-it yields an estimate for RC-H (1.647 cm3)which is smaller than that deduced (1.674 cm3)from pentane and higher hydrocarbons. The “smoothing” procedure of Denbigh and Vickery diverts attention from a feature which occurs irregularly among different families of compounds: the refractivities of CH, groups (i.e. the values of b above) sometimes alternate as methylenes are inserted to extend the lengths of
11
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
n-alkyl substituents. I n molecules such as Si(SR),, CBH50R, and CH3.C O . CHR(C0 . OC,H,) the refractive contributions of CH2 are higher when R is being expanded to ethyl, butyl, hexyl, or octyl, while among the tetra-n-alkyl derivatives of carbon, silicon, germanium, and tin the alternation is reversed (Backer and Stienstra, 1932-5; Evans et al., 1935; Ceuterick, 1936; Korsching, 1946; Sauer, 1946; Vogel, 1948; Fajans, 1949a). Such alternations may often be discerned in data for compounds simpler than those just mentioned, as Table 4 illustrates. TABLE4 Some Refractivity Contributions Shown by Methylene Groups in n-Alkyl Chains
d R , from Me to E t Et to Pr Pr to Bu Bu to Am Am to Hex Hex to Hept Hept to Oct a
n-Alkanesa
RBr*
RI*
HgRzC
4.76 4.51 4.94 4.47 4.65 4.64 4.63
-
4.66 4.64 4.66 4.61 4.66 4.64
4.95 4.74 4.55 4.74 4.64 4.70 4.54
4.77 4.835 4.82 4.50 4.55
From Denbigh and Vickery (1949).
* From Vogel(l943, p. 636). c
-
d
e
SnR4c -
4.76 4.53 4.64 4.535 4.655 4.565
CaH5Rd CeHsORe 4.65 4.68 4.65 4.65 4.56 -
4.82 4.58 4.78 4.58 4.74
-
From Vogel (1948, p. 604). From Vogel(l948, p. 616).
From Evans et al. (1935).
With the n-alkanes quoted by Denbigh and Vickery alternation continues throughout up to C43H88, the last four differences being 4.56,4.86, 4.59, and 4.62. It is of interest that among the many physical properties of n-aliphatic hydrocarbons discussed by Mumford (1952) the molecular refractions were unique in not displaying a discontinuity at about Clo. Fajans (1949a) has attempted to correlate alternations of RCHawith the nature of the atoms to which the n-alkyl chains are attached ; when these atoms are “positive ”, alternations as with SnR, are t o be expected, when they are “negative”, the alternations should be as with CBH,OR. The examples given in Table 4, however, suggest that this generalization is difficult to apply. Nevertheless, that internal electric field effects, electronic deformations by near-by polar bonds, conformational factors, etc. are involved cannot be disputed. Unfortunately a priori quantitative treatments of such matters are not yet available and the “constancy” of RcPcand Rc-H must be justified by the close agreements so frequently seen between molecular refractions “calculated and observed”. Denbigh (1940) quoted fifty instances of varied types of molecules on which this additivity had been tested; he
12
R . J.
w.
LE FEVRE
concluded that “in point of accuracy the system of bond refractions appears to be about as satisfactory as the older system of atomic refractions, but in simplicity it is much the more preferable”. Vogel (1948, p. 607), independently of Denbigh and Vickery and a few months before them, also announced “best values ” for R ,, and Rc-c ; these were to form the basis of his subsequent extensive calculations of other bond refractions. Vogel used his own measurements exclusively and drew the mean refractivity of CH2 not only from nalkanes but also from n-alkyl halides and n-alkylbenzenes ; moreover he provided data for the C, F, and G’ lines as well as for the D line. The RD’sfor &H and C-C were respectively 1.676 and 1-296om3 (compared with 1.674 and 1.296 cm3 by Denbigh and Vickery). Table 5 TABLE 5 Bond Refrmtionsa and Bond Refraction Coefficients at 20”
(C--H) (C-C)
(C=C) (C=C) as terminal group (C-C) in cyclopropane (C-C) in cyclobutane (C-C) in cyclopentane (C-C) in cyclohexane (Car-Car) (C-CI) (C-Br) (C-1) (C-0) in ethers (C-0) in acetals (C=O) (C=O) in methyl ketones (C--S) (C=S) (C-N) (C=N) ( C N ) (0-H) in alcohols (0-H) in acids ( 8-H ) (S-S) (S-0)
(N-W 0-0) (N=O)
(N--N) (N-N)
1.669 1.286 4.12 5.82 1.48 1.36 1.25 1.26 2.66 6.48 9.32 14.47 1.53 1.45 3.30 3.46 4.57 11.70 1.55 3.69 4.80 1.65 1.80 4.77 8.02 4.88 1.76 2.42 3.96 1.95 4.09
1.676 1.296 4.17 5.87 1.49 1.37 1.26 1.27 2.688 6.51 0.39 14.61 1.54 1.46 3.32 3.49 4.61 11.91 1.57 3.76 4.82 1.66 1.80 4.80 8.11 4.94 1.76 2.43 4.00 1.99 4.12
1.693 1.301 4.28 5.97 1.52 1.38 1.26 1.28 2.76 6.58 9.54 14.96 1.55 1.47 3.36 3.53 4.70 12.52 1.59 3.82 4.87 1.67 1.83 4.87 8.28 5.03 1.79 2.49 4.07 2.02
-
1.704 1.328 4.38 6.07
1.54 1.41 1.28 1.30 2.822 6.64 9.68 15.28 1.57 1.48 3.39 3.57 4.78 13.05 1.63 3.95 4.91 1.68 1.83 4.94 8.45 5.1 1 1.80 2.51 4.17 2.08
~~
From Cresswell et al. (1952).
3.87 12.86 9.39 25.04 11.28 11.44 11.95 12.24 15.67 56.80 124.51 202.46 17.71 17.46 29.39 29.50 32.84 65.02 14.51 24.13 29.91 13.15 10.54 23.79 53.83 37.13 7.26 18.82 32.26 16.81 25.72 ..
~~
MOLECULAR REFRACTIVITY
A N D POLARIZABILITY
13
sets out the results of Vogel’s analyses as published in 1952; numbers relating to (‘Molecular Refraction Coefficients” are also included, since these, too, may be brought into a ((bond” system, and enable one to compute refractive indices a t 20” with an accuracy of 1yo or better. Both Denbigh and Vickery (1949) and Cresswell et al. (1952) consider bond refractions as superior to the older atom or group refractions. The advantages claimed for the former include (a) the assimilation into the bonds of the constitutive effects of the atoms concerned, which gives a neater scheme; (b) the number of parameters is less for compounds containing more than one multivalent element, e.g. for aliphatic amines the atomic system requires five parameters (the atom refractions of C and H together with three different values for N corresponding to primary, secondary, and tertiary amines) while the bond system needs only four-the bond refractions for C-H, C-C, H-N, and C-N; (c) the bond system leads logically to ideas that refraction within a bond may be anisotropic, so that in turn the anisotropic refractivities of whole TABLE6 Bond Constants for Groups
Group
(ED)
4.993 9.617 14.25 14.27 18.86 18.89 18.69 23.50 23.25 23.17 28.08 32.75 37.32 41.99 46.61 51.25 55.78 60.47 65.12 69.68 74.25 22.15 22.56
5.004 9,651 14.32 14.33 18.94 18.97 18.77 23.60 23.35 23.28 28.21 32.90 37.49 42.17 46.82 51.47 56.03 60.73 65.42 69.99 74.59 22.40 22.69
5.070 9.765 14.48 14.50 19.15 19.19 18.97 23.87 23.65 23.52 28.51 33.26 37.89 42.64 47.34 52.03 66.63 61.40 66.12 70.75 75.38 22.85 23.27
5.084 9.819 14.57 14.60 19.29 19.33 19.11 24.04 23.78 23.69 28-72 33.51 38.17 42.90 47.70 52.43 57.07 61.86 66.64 71.32 75.96 23.13 23.58
11.70 32.99 52.82 52.48 73.38 73.11 73.78 94.03 94.40 94.52 114.67 135.52 166.00 176.37 197.04 217.64 238.32 268.90 279.63 300.30 320.99 115.59 124.4
a Following Vogel’s convention, quantities in parentheses are for use in conjunction with bond refractions. Pyridyl group. Thienyl group. f
14
R. J.
w.
LE F ~ V R E
molecules may be understood-Silberstein (1917) f i s t noted the inadequacies of the older system in this respect; and (d) according to the dispersion theory, molecular refraction depends upon characteristic vibration frequencies, and these, in a molecule, are associated with bonds rather than atoms. However, although the scheme is neater it cannot, in fact, produce bond refractions which are invariant throughout all molecular environments. For this reason Vogel proposed (see Cresswell et al., 1952) overcoming the minor effects of branching in alkyl chains by using group refractions obtained by subtracting the refraction for one C--H bond from the value actually measured for the complete hydrocarbon. More recently a similar treatment has been given to the pyridyl group (Kyte et al., 1960) and the thienyl group (Jeffery et uZ., 1961). Table 6 quotes some of these data. Additivity is still not always satisfactory. For example, the observed R, for 2-methylpyridine is 29.06 cm3; from Tables 5 and 6 this should be (C-C) + (CH,) + (C5H4N),which is 28.70 0111,. Corresponding data for 2-methylthiophen are 29.29 om3 and 28-99 cm3. Such disagreements are beyond the limits of experimental errors. Slightly variable values of (C5H4N)and (C4H3S),appropriate for the positions substituted in the hetero-rings, are therefore needed. I n the last two papers cited the authors suggest the following (under the same headings as Table 6) : (C5H4N)in 2-Alkylpyridines 3-Alkylpyridines 4 -Alkylpyr idines (C4HsS)in 2-Alkylthiophens
22.67 22.56 22.55
22.84 22.74 22.72
23.41 23-29 23.27
23.85 23.70 23.68
115.23 115.68 115.72
22.86
23.00
23.56
24.01
124.5
A few modifications, likewise required for specific structural situations, had already been recognized by Vogel (cf. Table 5) : special refractivities were allotted to carbonyl in methyl ketones, to the C-0 links in ethers and acetals, or to the 0-H bonds in alcohols and acids. The refractions due to C=C depend on this group being terminal or not. Grzeskowiak et al. (1960) have lately reinvestigated the matter : from fifteen compounds of type CH-C(CHz),.COzR or CH=C(CH2)nCH3, five of type CH,.C=C.O.CO.R, and five of type R.CO.O.CH,.C= C. CHz.0 .CO .R , mean values of (R,,,)x are deduced respectively as : (R,)
(RLJ
(RF)
5.801 6.83 6.40
5.840 6.85 6.40
5.918 6.02 6.59
(Rci,) 6.050 6.07 6.68
(M4O) 24.888 25.43 27.45
M O L E C U L A R REPRACTIVITY
AND POLARIZABILITY
15
For terminal groupings the data are somewhat below the 1952 estimates. Other workers who have demonstrated the sensitivity of RcGc to the position of C=C in a carbon chain are von Auwers (1935), Campbell and Eveslage (1945), and Hennion and Banigan (1946). West and Rochow (1952) quote three refractions for C-Si respectively as the carbon atom is primary, secondary, or tertiary. Tolkmith (1959) has emphasized the structure-dependent nature of the refractivities of bonds between phosphorus and other elements. Bond refractions are least variable amongst elements of constant valency. This is to be expected since in their derivations any contributions of lone-pair electrons to the molecular refraction are distributed over the adjacent bonds. Thus the refraction of bonds to halogen are large because all outer-shell electrons of the halogen are concerned and not just the duplet by which the atoms are covalently united. Indeed, for such reasons, Smyth (1955, p. 410) and others have criticized the designation ‘(bond refractions for the quantities under discussion. The division of the molecular refraction between the bonds can remain constant only if the elements involved form with each other a constant number of bonds. Incorporation of refractivities due to unshared pairs leads to logical difficulties in certain cases, e.g. when determining the bond refractions of the linkages of sulphur to oxygen: R(,,, is not the same when computed from RRaSOzminus RaaS= 2RoO,or from RRaSO RRaSOa (Cresswell minus RRaS (Gillis and Price, 1953)) or from RRaSO4et al., 1952). Should the lone-pair refractivity contribution happen to exceed that of the bonding pair, subtractions of the kinds mentioned may even produce bond refractivities which are algebraically negative. Thus the average refraction of SO, estimated for the D-line from dialkyl sulphates and sulphites, is - 0.20. Other examples of negative refractions have been noted by Smyth (1955), Cresswell et al. (1952)) Sayre (1958), and Gillis (1960)) among bonds between oxygen and boron or phosphorus. Notwithstanding that negative refractions have no physical meaning, and that additivity is never perfect, the fact remains that bond refractions still have usefulness for the calculation of molecular refractions when structures are known; for such purposes the few negative values may be viewed as empirical (‘increments”. Vogel’s data, as summarized by Cresswell et al. (1952), covered thirty-five bonds between the atoms H, C, 0, S, N, P, F, C1, Br, and I. The information on the C-F linkage was annotated as preliminary, and details for many bonds of interest were omitted. Gillis (1960) has considerably extended the subject by critically surveying the measurements available in the literature for single ))
16
R . J. W . L E X h V R E
covalencies, particularly for those between H, C, and 0 on the one hand and the elements indicated in Table 7 on the other. Gillis utilizes only the physical properties recorded for liquid aliphatic compounds (he does not include aromatic derivatives) and usefully cross-checks with secondary sources (such as the Monograph by Rochow et al., 1957); his quoted bond refractions (Table 7 ) refer to the sodium D-line. TABLE7 quoted by Gillis (1960)
Bond Refractions for N+D-Line %C B-0 A1-C In-C Si-H Si-C Si-0 Ge-C Sn-C
1.88 1.74 3.2 5.9 3.22 2.47 1.87 2.9 4.11
Sn-0 Sn-Sn Pb-C
(2.0?) 9.6 5.25 3.63 3.18 4.52 4.0 5.4 6.9
P-c
P-0 As-C As-0
Sb-C Bi-C
0-0 Se-Se Se-H Se-C Te-C Zn-C Cd-C Hg-C Br-Br
2.27 11.6 6.5 6.0 7.9 5.4 7.2 7.2 18.7
Tolkmith (1959) had also prepared a list of bond refractions; those which are not included in, or differ notably from values shown in, Tables 5 and 7 , are here reproduced as Table 8. TABLE 8 Extract from Bond Refractions quoted by Tolkmith (1959) Si-H Si--F Si-Cl Si-Br Si-0 Si-S Si-N Si-C Si-Si Si-P -~
a
~
-
Warrick (1946).
* Cresswell et nZ. (1'354). c
1'-H P-F P-c1 I-Br P--0 I'=O
3.185a.b 1.6 ( k 0.l)a.b 7.1 ( k O.l)nJ' 10.15 ( + 0 4 6 ) a . * 1.77 (+0,03)a,* 6.2 ( & 0 . 0 5 ) a . b 2.16b 2.45 (+_0 . 0 5 ) a ~ b 5.75 ( & O . l ) a , * 5.29d ~~~~~
d e
E'-8 P=S P-N
P-c
~
~
~
2.26c, 4.27d, 4.01e 3.63" 8.8 ( 0.05)6peJ 12.05" 3.12 (kO.O5)c*d*"f.Q ( + 1.07 ( & 0.15)C.d ( - 1.24 (k0.02)e.g 7.45 ( +0.14)d.e 6.37 ( O.O7)dJ, 6.87e 3.466 1.29C, 3.6 ( 0.02)d*e.g
~~~
Feher a n d Rluincke (1967). Seyre (1958).
~~~
~
f
Tolkrnith (1958). Gillis c t crl. (1958).
Keeber and Post (1956).
Fluorine linked to carbon and other elements displays varying refractivities. Early measurements indicated that this halogen had a small atomic refraction, ca. 0.8 cms (Gladstone and Gladstone, 1891 ; Swarts, 1923). Vogel (1948, 1). 644) reported values for I? in the four
MOLECULAR REFR.ACTIVITY A N D POLARIZABILITY
17
n-alkyl fluorides from pentyl to octyl (e.g., for the D-line, ttherefractivities were respectively 0.74, 0.82, 0.72, and 0.93 om3); Henne et al., in many papers in the J . Am. Chem. SOC.from 1934 onward, have given examples falling between the limits 0.68 and 1.6 cm3; Cady and Rohrback (1949), using C,-containing molecules, deduced an atomic refraction of ca. 1.23 cm3 (D-line). By adding 0.25R,8,b,,, estimates for the bond refraction of C-F ranging from 1.3 to 2.3 (3111, are obtained. The molecular refractions (Na-D) recorded by the last-named authors for n-C,F12, iso-C5F12,and cyclo-C5F,, are respectively 26.87, 26.80, and 24.50 cm,; subtraction of the appropriate contributions for the C - C bonds and division by the number of G-F linkages produces 1.807, 1.802, and 1.802 cm3 for Rc-a. These consistent data exceed Vogel’s provisional quotations of 1.44-1.45 cm3 (Cresswell et al., 1952) ;they will satisfy some (e.g. for CF, . CH, . CC1,Me) but not all (e.g. for CH2Cl.CF2, CHClMe) of Henne’s numerous observations (cf. Henne and Hinkamp, 1945). Denbigh (1940), on the basis of information then available in the I.C.T. and Landolt-Bornstein’s Tables, proposed 1.72 om3 for Rc-a but noted that it could lead to errors in calculated molecular refractions of up to 4%. Bauer and Rutner (1960) give R, for C-F as 1.75 cm3 in perhalogenated environments, while Macey (1960) shows Rn to rise with the number of fluorines per molecule from 1.55 cm3 in 1-fluoralkanes to 1.88 om3 in the CF, group. It is an experimental fact, demonstrated clearly in the papers by Vogel, and Rohrback and Cady, that the refractive indices of fluorine compounds are less dependent on wavelength than is the case with most substances. Of relevance, therefore, are the magnitudes of Ramaswamy and Watson’s ( 1936) molecular refractions computed using refractive indices of gases extrapolated for light of infinite wavelength : Rm (RE-rr)m
BF3 6.09 2.03
NF3 7.08 2.36
CF4 7.29 1.82
SiF4 8.38 2,095
SFa 11.31 1.88
The bond refraction (RE-F), follows obviously ; (Rc-a)a again emerges as ea. 1.8 cm3. With this, Rm for HCF, should be about 1.6, (from Table 5) plus 3 x 1.8, i.e. 7.05, cm3; as directly determined by Ramaswamy (1935), R, was 6.98 (3111,. Ramaswamy and Watson (1936) also reported R,’s for a number of other simple molecules ; the bond refractions which may be inferred from these are inchded in TabIe 9, along with miscelIaneous data deducible from measurements cited by Buckley and Maryott (1953), incidentally while listing dielectric polarizations and dipole moments of gases. (Except where indicated, the bond values in Table 9 refer to the
18
R. J.
w.
LE F ~ V R E
TABLE9 Bond Refractions Deduced from Molecular Refractions of Gases
(P-F) ( Se-F) (Te-F) (Ge-C1) (Ti-Cl) (P-C1) (Sn-C1) ( Sn-Br) (Sn-I) (Hg-Cl) (Hg-W (Hg-1) Prom Rm’sof Ramaswainy and Watson (1936). From R, of WItt,soii ( 1 927) C From CH4. d From NH3. e From HzO. f From DzO. g From SiH4. h From PH3. 1 From PF5. From SeFe. k From TeFs. 1 From GeC14. nL From TiC14. a
From PC13 From SnC14. p From SnBr4. 4 From Sn14. r From HgC12. 5 From HgBrz. t From HgIz. 21 1.e. Rm for carbon monoxide. 1) From Rm of carbon dioxide. UJ 1.e. R , for nitric oxide. 2 From NOz. 3 From SOz. From SO3. A From 0 ~ 0 4 . 7’
0
Na-D line). There are some disagreements discernible between Tables 5, 7 , 8, and 9 (e.g. with the P-F bond in Tables 8 and 9, or with the Si-F bond in Table 8 and the 2.0g5 quoted from Ramaswamy and Watson). I n the main, however, disparities are not great, and may be due not always to errors of measurement (or extrapolation, in the cases where Rayshave been used) but rather to variations of bond orders and structural environmental features in the source-molecules. Table 8 shows discordant estimates for several phosphorus-containing bonds and includes a negative quantity for the linkage P=O. Tolkmith (1959) has discussed this problem by considering the refractivities of more than 600 organic compounds of phosphorus in conjunction with “known and well-established bond refraction data ” (from Vogel’s work as in Table 5) ; by using the latter to provide refractions of the “peripheral” portions of molecules, subtraction from the RD’s as measured gave the refractions appropriate to the central phosphorusholding groups. Tolkmith’s results are summarized in Table 10. Of
MOLECULAR REFRACTIVITY AND POLARIZABILITY
19
TABLE 10 Refractive Increments of Phosphorus Bonds Calculated by Tolkmith Bond
Refractive increments (D-light)cm3
P-Hydrogen P-Halogen P-Oxygen
2.2 (P-H) 1.5 (l’-F), 6.95 (P-Cl), 10.2 (P-Br) 4.15 (I’=O), 1.45 (P-OH), 1.35 (in P-OC, 1’-OSi), 1.45 (in P-OP) 11.90 (P=S), 6.25 (in €’-SH), 5.65 (in P-SC, 1’-SSi), 5.3 (in P--SP) 15.60 (P=Se), 7.3 (in P-SeP) 6.80 (P=N), 1.7 (in P-NHz), 1.5 (in P-NHC) 1.3 (in P-NCz), 1.9 (in P--N:C), 1.5 (in P-N-P) 1.85 (P-CaliphHtie),2.75 (P-Caromstic), 2.55 (in I’-C= N), 2.7 (in I’-CC13), 2.05 (in P-C: 0) 3.4 (P-Si) 3.5 (P-P) 5.40 (nnshared electron p i r )
P-Sulphur P-Selenium P-Nitrogen P-Carbon P-Silicon P-Phosphorus None
.-
~
~~
~
~~~~~~~~
~-
especial interest is the allocation of a refractivity to the unshared electron pair on a tricovalent phosphorus atom ; this refractivity is apparently not markedly influenced by the natures of groups attached to P through the 3p3 electrons of this atom. The difficulty of negative increments is thus avoided, the value for (P=O) being smaller (by 1-25 cm3)than that for the lone pair. Variations in the bond refractions (Tolkmith prefers to call them increments characteristic of the electron groups involved) of P-0, P-S, P-N, and P-C can be related to the other elements besides phosphorus which are held by the 0, S, N, or C atoms. Variations of P-X in a unit P-X-Y are moderate if X is strongly electronegative (e.g. when X = oxygen) and more pronounced if X is less electronegative (e.g. when X is carbon or sulphur). Tolkmith lists refractions for ca. 125 “central inorganic groups ” containing phosphorus with carbon, hydrogen, oxygen, nitrogen, silicon, sulphur, selenium, and halogen atoms; his scheme is justified by the success by which RD’s may be forecast even for complex structures, e.g. using Tables 5 and 10 we have : R, observed 24.96 41.99 45.79 41.01 42.84 26,21 25.05 53.10 66.86
20
R. J .
w.
LE FEVRE
Tolkmith (1959) also gives a preliminary estimate, equivalent t o about 2.8 cm3, for the refractive contribution of an unshared electron pair on a nitrogen atom. Development of a system for N analogous to that for P will obviously necessitate an overhaul of those bond refractions which, in Table 5, involve nitrogen (e.g. the RD’s for N-H, C-H, etc. minus must be reduced by 2.813; the observed difference, RMeaNO RMle3N, implies a refractivity for this nitrogen-oxygen bond of some 4.5 om3 in place of the 1.78 om3 previously quoted by Cresswell et al., 1952, for N+O; cf. Aroney et al., 1964d). B. Refractions of Atoms and Ions Atom refractions are known from direct measurement only for monatomic gases. Ramaswamy and Watson (1936), using data obtained by Damkohler (1934) and the Cuthbertsons (1932), deduced R,’s for the rare gases as He 0.52, Ne 1.03, A 4.14, Kr 6.27, and Xe 10-14 om3. Mercury vapour has been studied by Ladenburg and Wolfsohn (1930-2) and by Wusthoff (1936); the R value indicated (12.7-13.0 cm3) is close to that given by Evans et al. (1935) for combined mercury (12.84 cm3). Many authors have investigated the refractions of ions. By application of alligation formulae (e.g. as 3) to salt solutions, Wasastjerna (1922), Heydweiller (1925),and others evaluated the apparent molecular refractions of the solutes. At first it seemed that molar refractions of “strong ” electrolytes were independent of concentration, but accurate determinations by Kohner (1928) and Geffcken (1929) in the 1-5 molar range showed that this was not so, and that individual solute refractions differed from their magnitudes a t infinite dilution in ways having proportionality with concentration. The molecular refractions a t infinite dilution were, however, not always identical with those observed with gaseous salts (the halides of the alkali metals, thallium, mercury, tin, aluminium, and silver, have been examined in the vapour state by Wulff (1933), Bredig et al. (1934), Wulff and Schaller (1934), Koch and Kohner (1934), Goldschmidt and Holemann (1934), and Schroter (1931); cf. also Fajans, 1934). The refractive indices and densities of solid salts of the alkali halide series, studied by Spangenberg (1922), provided yet a third set of refractions. (More recent measurements by Kahn et al. (1953) have not seriously altered the situation; cf. also Roberts, 1949.) If ionic refractivities were additive the results, for a given salt, should be the same by each method ; Table 11 summarizes the situation for five cations and four anions. The data quoted are based upon the earlier estimates by Fajans and Joos (1924). Modifications suggested by subsequent work (e.g. Newman (1934), finding 9.05 cm3 for sodium chloride a t infinite dilution in water
MOLECULAR R E F R A C T I V I T Y A N D POLARIZABILITY
21
TABLE11 Molecular Refractionsa of t h e Alkali Halides for Na-D Light __ ___ Fluoride Chloride Bromide Iodide 2.70 2.34
9.20 8.58 7.59
12.87 12.25 10.56
19.44 18.82 15.98
3.00 3.00 3.02
9.50 9.20 8.52
13.17 12.87 11.56
19.74 19.44 17.07
4.73 5.03 5.16
11.23 11.23 10.85
14.90 14.80 13.98
21.47 21.47 19.75
6.08 0.38 0.74
12.58 12.68 12.55
16.25 16.25 15.78
22.82 22.82 21.71
8.74
15.24 15.24 15.25
18.81
25.48 25.48 24.27
Lithium
Sodium
Potassium
[2
Rubitl i um
Caesium 9.51 @
18.91 18.46
R,, R,, R, refer to refractions measured on gaseous, dissolved, or crystalline salts
respectively.
at 18") or Heigl and Wulff (1931), proposing small amendments in the cases of KCl, RbC1, CsC1, NaF, KF, RbF, and CsF), however, have been minor, and leave the orders of magnitude and directions of change very nearly as shown. A point of interest is the rough constancy of the differences between adjacent columns and corresponding rows (exemplified respectively by the R, refractions: K+ minus Na+ being 2.03 cms across the table, and Br- minus C1- being 3.67 em3 down the table). The additivity thus displayed is less perfect among the R, data but not sufficiently so to make unreasonable the idea that R, represents the sum of the refractions of the ions. Therefore, if R for one ion can be ascertained, the R's for others become accessible. Wasastjerna (1922) found the molecular refractions of hydrochloric, nitric, and sulphuric acids at infinite dilution in water to be 8.45, 10.43, and 13.42 cm3. He assumed that the refractivity of the proton-a nucleus without an electron-was zero, so that the R's just quoted were the refractions of the anions C1-, NO,, and SO; ; these, subtracted from the R, values observed for the corresponding salts, gave refractions attributable to the cations involved, e.g. RNac,
- R,,,
= 0.74
RNaNOs
-RHNos
= 0.76
RNasSO~
- R H ~ S O i = 1'42
REc,
-RHc,
= 2.85
-RHNO~
= 2'80
R K a B O 4 -%SOr
= 5.78
22
w.
R . J.
LE F ~ V R E
Heydweiller (1925) proceeded similarly. The mean estimates from many such operations are in Table 12 under W. and H. TABLE12
Refractions in em3 of Ions as Estimated by Various Authors ~
wc1Br-
I-
OHNO; SCNc10, BrO; 10, c10,
so;
NH: Li+ Na+ K+ Rb+ cs+ Mg++ Ca++ Sr++ Ba++ Al+++ Si+++
2.20 8.45 11.84 18.47 4.68 10.43
-
~
~
13.42 -
0.74 2.85 4.41 7.36 0.44 1.99 3.22 5.24
-
2.17 8.22 11.60 17-53 4.42 10.16 16.54 12.16 15-13 17.86 12.66 13.36 4.65 0.12 0.65 2.71 4.10 6.71 0.47 1.60 2.56 5.00 0.37 -
~-
F.J . c
B.d
B.H.e
M.M.f
2.44 9.07 12.66 19-21 4.76
2.12 7.59 10.42 15.62 5.1 9.54
2.50 7.69 10.52 15.84
2.27 7.44 10.24 15.14
-
-
-
-
-
-
-
-
_-
-
-
_-.
-
-
-
-
-
15.62 10.50 9.61 4.05 0 0.53 2.45 3.71 5.98
-
-
_-
__
-
4.31 0.20 0.48 2.26 3.79 6.54 0.26 1.40 2.57 4.28 0.17
-
-
2.13 4.12
-
-
-
-
0.19 0.53 2.19 4.57 7.04 0.30
0.08 0.46 2-13 3.58 6.18 0.25 1.36 2-52
-
3-58
-
0.16 0.11
-
0.13
-
~
By Wasastjerna (1922). By Heydweiller (1925). c By Fajans and Joos (1924), and Fajans (1934). d By Bottcher (1946). e Calculated from Born and Heisenberg (1924). fcalculated from Mayer and Mayer (1933). a b
Fajans and Joos (1924) and Fajans (1934) attempted to evaluate the refractions of “free gas’’ ions, using the data of the Cuthbertsons (1914) on the inert gases, of Heydweiller (1925) on solutions, and of Spangenberg (1922) on crystals. A refractive contribution of 0.48 cm3 was chosen for Na+ (gas) and one of 0-20 om3 for Na+ a t infinite dilution; thus the diminutions in R of ca. 0.3 cm3 from R, to R, for NaCI, NaBr, NaI, seen in Table 11, were attributed to the deformation of water sheaths by Na+ with consequential decreases in the refractive coiitributions of the solvent. This lowering effect is strong with Li+ and exceeds the raising caused by F-, leading to a net reduction (R, - R,) of 0.32 cm3
MOLECULAR R E F R A C T I V I T Y A N D POLARIZABILITY
23
with Lip. I n NaF the cationic and anionic influences about neutralize each other. Situations where F- predominates are illustrated by KF, RbF, and CsF. The Fajans and Joos refractions are in Table 12 under F.J. A more recent treatment of the subject is that of Bottcher (1946), who argued that while the proton undoubtedly has a negligible refractivity it can penetrate a water molecule to give an H30+ion having a smaller refractivity than HzO, so that apparently H+ carries a “negative” refractivity (compare Table 13). Bottcher therefore started with the TABLE13 Effects of‘ Proton Addition on Refractions of Molecules and IonsRrb
- AR O= S=
= 6.95 = 22.7
OH- = 4.76 SH- = 13.28 OH2 = 3.71 NH3 = 5.63 C1- = 9.07 Br- = 12.66 1= 19.21
OHSHOH2 SHz OH: NH: HC1
4.76 13.28 3.71 9.57 3.04 4.31 = 6.67 HBr = 9.14 HI = 13.74 = = = = = =
2.19 9.4 1.05 3.71 0.67 1.32 2.40 3.52 5.47
@Units= cm3. b Data from Fajans and Joos (1924) and Fajans (1934).
ions Li+ and Be++. These possess the helium configuration but, owing t o greater nuclear charges, both should be less deformable than He, the R for which is 0-52 cm3. As the charges of the nuclei of He, Li+, and Be++ run in the ratio of 2 :3 :4, and the radii roughly as 12 : 7 :3, approximate calculations of electron-nucleus attractive forces suggest an R for Li+ not above 0.07 cm3, and for Be++ a n R below that for Li+. Chemical reasons (hydrolysis of beryllium salts) led Bottcher to select lithium salts as replacements for the acids used in Wasastjerna’s method. Incidentally, Bottcher employs his own function (6) instead of the usual Lorentz-Lorenz expression, because it satisfies better all the types of concentration-dependence of R previously noted by Fajans and collaborators (cf. Bottcher, 1946, pp. 41-4) :
( n 2 - 1) (2n2+ 1) M / 9 n 2 d = 47rNa/3Q
(6)
where Q = 1 - c((2n2- 2)/a3(2n2+ l),a = radius of ion (or water molecule), a = 3R/4rN, n = refractive index, d = density, M = molecular (or ionic) weight, and N = Avogadro’s number. Bottcher’s results are in Table 12 under B. The remaining columns show two sets of examples of refractions which may be extracted from theoretical calculations, based on
24
1%.J . W . L E F k V R E
spectral data, by Born and Heisenberg (1924),Pauling (l927b), Schoppe (1934), etc.; on the whole these favour the measurements by Bottcher more than those by Wasastjerna or Fajans and 5 0 0 9 , but in the face of the divergences among the experimental observations listed it cannot be claimed that ionic refractivities are known with great accuracy. Nevertheless the following generalizations of interest can be drawn from Tables 11 to 13 and the associated references : (i)The refractions of anions are greater than those of cations (with the latter the positive charge restrains deformation of electrons by an externally applied field, but with the former there are more electrons present and each is therefore less strongly bound to the nucleus). (ii) The deforming action of cations on neighbouring ions or molecules varies inversely as the ionic radius and directly as the charge. (iii) The deformability of anions varies directly as radius and charge. (iv) The refractions of the inert gases Ne, Ar, Kr, and Xe run roughly as 1 :4 : 6 : 10, a sequence reflected by F,, Cl,, Br,, and I,, by F-, C1-, Br-, and I-, by Na+, K+, Rb+, and Cs+,and by HF, HCl, HBr, and HI (cf. Table 5 ;R H , is uniformly about 0.75RX-,consistently with H X having six non-bonding electrons and X- having eight). (v) The inert gases have refractions between those for the corresponding isoelectronic ions (compare R’s for F-, Ne, and Na+, of C1-, Ar, K+, etc. ; measurements by Bode (1930) indicate 4.84 and 7-36 om3 as the molecular refractions of NaH and K H respectively, whence R H - appears as 4-5 cm3, thus RH- > RHe> RLi+).(vi) Ions not of the inert gas type are more deforming than those that are (cf. Pauling, 1927a, b). (vii)Theresult of adding H+ to a neutral molecule or singly charged ion of refraction R can be forecast by empirical equations such as (cf. Fajans, 1934) :
AR/R
= 0*2859[1- exp ( - 0-2848R)I
(e.g. the quotients ARIR for NH3, H20, and C1- are 0.23, 0.19, 0-26 by calculation, against 0.23, 0.18, 0.26 by measurement, respectively). The mutual influences of ions on ions or ions on molecules are gross manifestations of the slighter effects of atom-atom or atom-group interactions within molecules. Such phenomena may be correlated by the propositions that the molecular refraction of a given electronic system is (a) decreased by the presence of adjacent positive charges, (b) increased by adjoining negative charges, and (c) increased whenever the field from a nuclear charge is split and distributed less symmetrically. Illustrations of these cases are (a) Ro-H in water is 1.84 om3, R 0 f - H in the hydroxonium cation is 1.01 cm3; R,, in ammonia 1.8 cm3, in the ammonium cation 1-1 cm3; (b) R,: in ketones is ca. 3.4 cm3, but in the carbonate anion it appears as ca. 4.1 cm3, RCENin neutral molecules is 4.8 cm3, while for CN- the refractivity is around 8 cm3; (c) the result
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
25
of dividing the 8+ charge of Ne is seen in the isoelectronic sequence Ne, HE’, HzO, NH,, and CH4, where the refractions rise from 1.0 cm3 through 2.0, 3-7, 5.5 to 6.4 cm3, or among isoelectronic ions with one negative charge, e.g. the R’s for F- (2.4), OH- (4.8), C1- (9.1), and SH(13.3 cm3). The reversals, noted previously, of the order of differences Rethylminus Rmcthylas alkyl chains attached to positive (C, Si, Ge, Sn, etc.) or to negative (0,S) atoms are extended provide further instances for inclusion under (a) or (b); the slight apparent increases in R, as halogens are progressively inserted into CH3X (Vogel, 1948, p. 1833) are in accord with (b). Proposition (c) covers systems for which a “multiplicity of equivalent dipolar structures, corresponding to conjugation in alternative directions” (Ingold, 1953, p. 127) is possible (e.g. acyl halides, in which Briihl and Eisenlohr thought the R, values to be exceptional since these were somewhat higher than the RX’s drawn from alkyl halides).
C. Refractivity and Atom,ic or Molecular Dimensions Division of ionic refractions (Table 12) by Avogadro’s number gives quotients which, in magnitudes, correspond to cubes of ordinary molecular measurements ;however, the evidence from experiment shows that the refractions of ions are proportional to the fourth, rather than to the third, power of the ionic radius r . Wasastjerna (1922) wrote : R,,,= (l/k)r4, where k was a constant, nearly unity and depending on the column of the periodic table to which the ion belonged. Kordes (1939-41) connected refractions with the “univalent ” radii listed by Pauling (1927). From his expressions the simple equation Rion= 0.606r4’6 can be obtained by rearrangement, which, although seemingly dimensionally incorrect, predicts (Table 14) refractions close to those listed in TABLE14 Refractions Calculated as 0.606~4.5cm3
A
R calc.
1.54a 1.36 1.81 1.95 2.16 0.82 1.18
4.2 2.42 8.75 12.23 19.4 0.25 1.28
r
HF-
c1Br-
I-
Mg++ Cat+
r He Ne Ar Kr Xe Sr++ Ba++
A
0.93 1.12 1.54 1.69 1.90 1.32 1.53
rA
R calc. 0.47 1.01 4.21 6.42 10.9 2.11 4.11
Li+ Na+
K+ Rb+
cs+
Al+++ Si+ttt
= I n CsH according to Hardor and Zintl (1931); Pnuling lists 2.08 R = 16.4 01113.
0.60 0.95 1.33 1.48 1.69 0.72 0.65
A,
R calc. 0.06 0.48 2.19 3.54 6.42 0.14 0.09
which gives
26
R. J .
w.
LE P I ~ V R E
Table 12 and-judged against experiment-superior to others which follow from the quantum or wave-mechanical calculations of Sternheimer (1954))Das and Wikner (1957))etc. Of side interest are applications now being made (Guy and Harrand, 1952; Pople and Schofield, 1957; Sundbom, 1958) of Kirkwood’s variation method to atoms and ions with partly filled d-shells (transition elements). For these theory predicts refractions considerably larger than those for closed shell atoms or ions. Indirect measurements are possible through the field emission microscope (Drechsler and Muller, 1952; Drechsler and Henkel, 1954; Drechsler and Liepack, 1956). The refractions of bonds show no immediate relationship with the inter-centre distances r between the atoms involved. According to Clark (1936a, b) and Goss (1936),simple diatomic molecules (e.g. H,, C12, etc.) have R’s which are proportional to r 3 , but such a rule has limited validity. In general, bonds of carbon with elements of a given group display a steady rise in refraction with increasing bond lengths (e.g. RcPcl,RCPBr,Rc-I) whilst among bonds of carbon with successive members of a period (e.g. C-C, C-N, C-0, C-F) the R’s tend to increase with diminutions of the r’s. Inspection of Tables 5 , 7, and 8 suggests that carbon-containing bonds C-E, if E is taken in turn from Group I1 through to Group VII, often have the smallest R when E belongs to Group IV. Gillis (1960) comments that the reduction of RCPE from Group I1 to Group IV may be related to the different hybridizations of the central atoms (sp,sp2 and sp3 respectively for central atoms of Groups 11,111,and IV) ;p orbitals are less deformable than s orbitals (Regnier and Regnier, 1954)) so that R values parallel diminutions in the s characters of the bonds concerned. The increases as E comes from Groups IV to V I I may not depend so much on hybridization as on the contributions to Rc-E from unshared pairs of electrons on E ; thus the bond refractions of Group V elements include the effects of one third of one lone pair, those of Group VI elements, one half of the effects of two pairs, and so on ; the consequences are particularly marked when E comes from periods other than the first (e.g. the rapid rises along the series C-Sn, C-Sb, C-Te, and C-I). Within a period the variations of R exhibited by the same bond in different environments can, qualitatively, be ascribed to hybridization: ROPE in water is ca. 1.84 cm3, in an alcohol ca. 1.66 cm3; in the former there are (naively expressed) two (1s- 2p) bonds, in the latter one (1s - 2p) and one (sp3- 293) bond; other examples of this type of analysis are set out by Karagounis (1962, p. 111) or may be inferred from the “octet” refractions tabulated by Smyth (1955, p. 409). Denbigh (1940) noted that the refractions of the C-C, Car-Car,
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
27
C=C, and C = C bonds plotted smoothly against bond orders ; indirectly therefore a connection between carbon-carbon separations and Rbonds became empirically available. Ten hydrocarbons containing conjugated double bonds were then considered and the refractions of the “single” bond intermediate between the two double bonds obtained assuming that all the other bonds had their normal^' refractions; these “single” bonds showed refractions falling between 1-67 cm3 in c@-trimethyl styrene and 2-92 cm3 in 2,4-hexadiene; the corresponding bond orders from the graph were 1-14 and 1.58 respectively. The average over the ten compounds was 1.29 “in fair agreement with Pauling’s generalization that this bond has about 20% double bond character, as a consequence of the conjugation” (Pauling, 1939). Vogel (in Cresswell et al., 1952) has used a similar approach to the question of the nature of bonds between aromatic rings and substituents therein. From his own data (Table 5) the ratios of the D-line refractions for single and double bonds were : Bond Carbon-carbon
Rsingle
Carbon-oxygen Carbon-netrogen Carbon-sulphur Nitrogen-oxygen Nitrogen-nitrogen
1.54 (ethers) {1‘2g6 1.46 (acetals) 1.57 4.61 2.43 1-99
Rdouble
]
Ratio
4.17 3.32 3.75 11.91 4.00 4-12
i
1 :3.2 1 :2.2 1 :2.3 1 :2.4 1 :2.6 1 : 1.65 1:2.1
The mean ratio 1:2.3 was taken for computing the refractions of double bonds which had not been-or could not be-investigated, e.g. C=Cl. Subtraction of (Rbenzene-RC-=)from the R observed for C6H5-X gave Robsfor the bond C,,-X; then the percentage double-bond character was obtained as
Pd
= 100(Robs
- Rsingle)/(Rdouble- Rsingle)
Table 15 gives a selection from the 64 results published; the authors themselves comment that the figures derived for the four C6H5-Hal molecules may be too low. Pauling (1960), from the shortening of the &C1 bond in C6H5C1(from that in CH,Cl), considers that C,,-C1 may have about 15% double-bond character, whilst Smyth (1941), from the dipole moments of monohalogeno-benzenes, had concluded that estimates around 4% were appropriate. The pa values of Table 15, whatever their errors, run roughly as expected for substituents having + M or - M effects in aromatic molecules. With + M groups the stabilities of dipolar structures,
R . J.
28
w.
LE FEVRE
TABLE15 Percentage Double-bond Character of Car--X
R, of bond
Bond
1.59 1.97 1.93 1.83 5.35 1.42 1.66 1.48 6.62 9.49 14.61 2.26 2.44 2.64 3.16
pd
10 23 22 I6 10 4 12 2 2 1 0.2 33 40 44 73
Bonds
Molecule containing bond PhMe PhCOMe PhCOzEt PhOMe PhSMe PhCHzOH PhCHzCl PhF PhCl PhBr PhI PhCN PhNOz PhNHz PhNMez
(@)X=G-C(@), determine the degree to which X in X-C=C tends to increase its covalency towards carbon; stability is greatest when X is N and least when X is halogen (Ingold, 1953). For - M substituents the stability criteria concern C=C-A=B and various possible excited @ ; the majority of well-known cases valency states, e.g. C-C=A-B of refractivity exaltations belong to this class, the molecules in which have conjugated chains terminated by groups AB such as CR=O, N=O, C-N, etc. The quantities listed under “RDof bond” in Table 15 should not be taken as implying that exaltations are concentrated in the C,,-X linkages; they are, of course, distributed over the whole conjugated system, and the proportions ascribable to the phenyl ring and to the (often polyatomic) substituent group cannot easily be foreseen. Ingold (1953, pp. 125-30)) noting that usually “the non-polar valency structure is an approximation to the normal mesomeric state”, analysed the situation by comparing aromatic with aliphatic compounds containing less the same single substituent. Subtraction of Rphenyl(i.e. Rbenzene R C P Hfrom ) Rphenyl--X. and of Ralkylfrom Ralkyl--9‘gave P and Q respectively; then P - Q = AR was regarded as a measure of the conjugation of X with phenyl. Table 16 shows results obtained by this process, using molecular refractions published by Vogel et al. and alkyl group refractivities as in Table 6. Comparisons in the upper part of the Table involve + M @
M O L E C U L A R REFRACTIVITY TABLE
A N D POLARIZABILITY
29
16
Exaltations due t o Coiljugtition of X with Phenyl in CoHsS
Ar-X
Alk-X
Ar-X
Alk-X
AR crns
Ph-NEtz Ph-NHEt Ph-NHZ Ph-SMe Ph-SH Ph-OBun Ph-OH
Et-NEtz Et-NHlSt I3un-NH Me-SMe Et-SH Me-OBun Me-OH
1.6 1.3 1.0 0.78 0.66 0.53 0.22
Ph-C1 I’h-Br I’h-I Ph-Me
Hexn--E’ Octn--F Bun-Cl Et-Br Pr-I Am”-Me
Ph-CN Ph-COzEt
MQ-CN Me-COzEt
0.98 0.81
I’ki-COMe I’h-NO2
Et--COMe Mo-NO2
n
2
Amn--F
Pll-F
AR cm3 0.08 0.00 -0.11 0.14 0.06 0.13 0.26
0.74 0.72
Indicates n iiorrnal nlkyl group.
substituents, in the lower, - M substituents. Among the former, the sequence N > 0 or S > Halogen, predicted by Ingold for AR, seems clear; among the four - M groups trends are less obvious although the exaltations quoted are typical in being fairly high. Toluene has been included since-whilst Me is not a + M group-“hyperconjugation” (CeH5CH3<+ C6H,CH,H+) can cause exaltation by redistribution of the negative charge in much the same way as, say, the lone-pair in CeH5NR,. Alternatively the fact that bonds seem to have higher refractivities in anions than in neutral molecules can be regarded as relevant (cf. R for the formate ion in water, 8-88 om3, but calculated as RCpH+ RC=, + Rc-o from Table 5 , 6.54 cm3; even with Ro-H added, the expected refraction is still ca. 1.5 om3 less than the R observed by Liihdemann, 1935). The earlier literature describes other attempts to generalize, in qualitative terms, the relations between exaltation and structure. Von Auwers and Eisenlohr (19 10, 1911)suggested using specific instead of molecular, exaltations : EZrefn. = 100 x (specificrefraction observed -specific refraction calculated), claiming that numerical values of EZ refn. displayed more plainly than did A R = Rohservc,t - Rcslcukted the sensitive dependence of refractivity on structural details (see Table 17) and the way in which disturbances in conjugated systems often tended to diminish exaltations. However, no successful additive scheme could be devised for the magnitudes of EZ refn. (although such measurements were usefully applicable to some structural problems, cf. Henrich, 1922, pp. 299-3 17, for examples). Failure is understandable since-as already stated-conjugation may not, always lead to exaltation : the
30
1%. J .
w.
LE FEVRE
1,3-diene chain, shown in Table 17 against EZrefn. = 1.9 cm3, produces no exaltation in furan, thiophen, pyrrole, cyclopentadiene, or benzeneactually the first four of these molecules display “depressions ” of refractivity, i.e. they are less deformable than would be expected if their component units behaved without conjugation and merely additively. TABLE17 Exaltation in Relation t o Structure ~
EZ refn. cin3a
Conjugated chain -CH-=CHCH=CII-CH=CH-CR=CH---CHdH--CH=O -CR=CH-CH=O - -CH=CH-CR=O -CH=CHCH=CH-CR=() -CH=CR-CH=CH-CB-() -CH=CH-C( OR)=O -CH=CR’-C( OR)=O -CH=CHCH=CH-C(OR)=O -CH=CR-CH=C H-C(OR)=O
1.9 1.1 1.8 1.25 0.90 3.3 2.7 0.80 0.50 2.4 2.0 ~
‘1
Values from von Anmers a n d Eisenlohr (1910, 1911).
Refractivity is markedly reduced whenever a system develops strong polarity. The effect is particularly noticeable in cases once formulated with “dative” or “semi-polar ” or “co-ordinate bonds”, such as those between N, 0, S, P etc. and B. The refractions of diethyl ether (22.5 cm3) and boron trifluoride (6.0 cm3) together exceed the measured value for the compound EtlO. BF, (26.6 cm3, Meerwein and Pannwitz, 1934) by 1.9 cm3. Sutton (in Hunter et al., 1945) indicated that refractivity contractions are ca. 3.4 cm3 in Me,N.BF3, and ca. 2 cm3 in Ph3P.BCl,, Et,S .BCl,, etc. ; in these and similar instances, of course, the dipole moments of the complexes greatly surpass those of the = 0-65D., p B F 3 = 0,pLNMrsBF3 = 5.8 D., cf. Wesson’s components (e.g. pMeaN Tables, 1948, for other data). Gillis (1960, p. 31) refers to attempts a t a priori calculations of these phenomena, starting from estimations of the charges QA and QBin A+ - B-, but so far no satisfactory approach has been achieved. Qualitatively an analogy is obvious with those salts (e.g. lithium halides) in which Rcationreduces Ranionmore than Ranion raises Rcation(cf. Rgasand Rcrystalvalues in Table 11) when cation and anion are brought into greater propinquity. I n general it appears that among isomeric molecules with similar shapes polarity and refractivity tend to run oppositely :
MOLECULAR HEFRACTIVITY A N D POLARlZABILITY
PD.
R, cm3
MeCN
MeNC
EtSCN
3.92 11.09
3.83 11.68
3.6 23.72
31
EtNCS 3.3 25-92
Among isomers with different shapes the “rule ” may not hold : PD.
R, cm3
n-PrC1
iso-PrC1
n-PrBr
iso-PrBr
2.10 20.85
2-15 20.99
2.13 23.69
2-19 23.96
(The R, for the isocyanide group has recently been reported by Gillis (1962);the moments of MeCN and MeNC are from Ghosh et al. (1953), and were determined via the Stark effect ; other data are from Smyth’s book (1955), Vogel (1943), and Hunter and Partington (1932).) Rough predictions of exaltations, in carbon chains a t least, should be possible through the observation, already noted, due to Denbigh (1940), that the refraction of a bond is smoothly related to the bond order. In Table 5 these are data for two sets of single, double, and triple bonds (those for carbon-carbon and carbon-nitrogen linkages) ; if the bond orders p be accepted as 1, 2, and 3 respectively then RD’sfor CC and CN are
‘ : R
=
4.6351, - 0*587p2- 2.752
REN = 3 . 8 8 5 ~ 0 . 5 6 5 ~ ~1.750 When inter-centre distances d are available the empirical equation ( 7 ) ‘OgP =
1.4085 (dsiugle -dobscrvcrl)
(7)
given by Pauling (1960, p. 239) permits the forecasting o f p ; maiiy values for d are today available (e.g. in the tables published by the Chemical Society, 1958). Refractivities thus obtained are approximate only. I n is 1.40 8;by (7), with dSiogle = 1.54 8, this correbenzene the dobserved sponds to p = 1-6, whence the refraction for Car-Car emerges as 3.15 cm3 (2-69 cm3in Table 5 ; the 1,2-, 2,3-, and 3-4-bonds in biitadiene have observed d’s of 1.35, 1.46, 1-35 d, so that bond orders of 1-86, 2.27, 1.86 respectively follow by ( 7 ) ; a molecular refraction of 20.00 cm3 is therefore expected, 0.31 cm3 higher than that deduced from Table 5 but well below the AR of 21.14 cm3 measured by Prevost (1928). I n the nitrile and isonitrile groups, the C...N separations are almost the same (1.16 and 1.17 A), hence refractivity differences must be mainly attributed to the Calkyl-C and Calkyl-N distances, which are 1.46 and 1.43 A ; if equation (7) wese applicable also to C...N linkages, the R of MeCN would exceed that of MeNC by 0.3 cm3, but, in fact, it is 0.6 om3less.
32
B. J .
w.
LE F ~ V R E
Finally, the unlikelihood of successfully finding general relations between bond refractions and bond lengths or orders is underlined by the situation for nitrogeii-nitrogen linkages :
N-N N=N N=N
1.46 1.25 1.10
21 72 3
4.12 2.2
I
Table 5 Table 9
D. Refractivity and Other Molecular Properties
A number of relationships between refractive indices and other physical properties have, in the past, been discovered empirically (Partington, 1953, quotes 41 of these) ; examples are the connections between n and a (surface tension) recognized by Samygin (1937) or Joshi and Tuli (1951). The last-named authors introduced a quantity termed the “refrachor” [F],given by equation (8) [F]= -[P]log(n~-1) (8) in which [PIis the “Parachor” (Sugden, 1924) of the substance concerned; Samygin’s expression, the [PIof Joshi and Tuli, and Sugden’s [PI, all incorporate the fourth root of a; [I?], like [PI, can be analysed into atomic, group, and structural refrachors, and since slight variations in molecular structure result in marked differences of refrachors, Joshi and Tuli consider [Fl’s to be more useful than [PI’S in many circumstances (e.g. the refrachor values for the nitro and nitrite groups are 25.84 and 35.64 respectively, while the parachor values for the same are 73.8 and 75.3). It is obvious that any two temperature-invariant molecular “additive-constitutive ” properties, which both contain the molecular volume, can together yield an equation showing interdependence of apparently quite independent physical measurements. Lima (1948) generalized a situation revealed by Corry and Lagemann (1942)) Lagemann (1945), and Dunbar and Lagemann (1945), namely that molecular refractions, parachors, Souder’s viscosity constants, van der Waals b’s, critical volumes, and molecular magnetic rotations, were all linearly related to the molecular sound velocities (Rao, 1941). If one property can be written as G z D C H a ZG,,, and another as H = XHCH~+ZH,~ 1
+
where G,, and H,, are special “constitutive” corrections and x the number of methyleiie groups, then
MOLECULAR R E F R A C T I V I T Y A N D P O L A R I Z A B I L I T Y
33
G = (HGCHa/HCHe) - ( G C H ~zHsp/HCH~) + zG8p G = H(constant)- (other constants) or which represents a straight line. In certain instances molecular refractions can be correlated with spectral behaviour ; usually the subjects of such discussions have been mesomeric structures, formally capable of internal rotations about bonds, Thomson (1944) first drew attention to the refractivity diminutions found in passing from e.g. 6.56 om3 nitrobenzene t o benzene 6-22 cmy nitromesitylene t o mesitylene . 2,6-dichloronitrobenzene to m-dichlorobenzene . 6-16 om3 3,5-dichloronitrobenzeneto m-dichlorobenzene . 6.78 cm3 dimethylaniline to benzene . . 14.68cm3 dimethyl-p-toluidine to toluene . . 14.62 cm3 dimethyl-p-toluidine t o toluene . . 14.62cm3 dimethyl-m-toluidine to toluene . . 14.62cm3 dimethyl-o-toluidine to toluene . . 13.56cm3 dimethyl-o-chloroaniline to chlorobenzene . 13.57cm3 and attributed the smaller changes noted with ortho-substituents to steric inhibition of resonance. Curran and Palermiti (1951) recorded larger effects of the same kind when comparing p-disubstituted benzenes and durenes. Wepster (1957) then observed that the extinction coefficients of the 2500 A band in iso-octane for dimethylaniline and a number of 2- and 2,6-alkylated derivatives could be plotted rectilinearly against the remainders obtained by subtracting molecular refractions in the ways just illustrated. (Such remainders, of course, contain the exaltations AR plus some constant terms.) Since experiment shows that extinction coefficients have straight-line relationships with the basic strengths of p-nitroaniline and its derivatives, and that these basic strengths are likewise related to the rates of deacylation of the corresponding p-nitroacetanilides (Wepster, 1958), it is clear that further empirical expressions involving AR and these or similar phenomena can easily be foreseen. Bramley and Le FBvre (1960, 1962) noticed that with a number of uw-diphenylpolyenes and polyene ketones the exaltations of refractivity could be calculated as C ( h- D ) 3 where , h was the wavelength of maximum absorption recorded in the K-band, and C and D were constants. Bellamy (1955) has found correlations between AR and infra-red absorption spectra. The carbonyl stretching frequencies (as cm-l) of the following types of molecules plot linearly against the exaltations of refraction exhibited by the various compounds examined : R .COC1,
.
34
R. J .
w.
LE F ~ V R E
R . C02R, R . C02H, R . CO. NR2, and R . CO; (the cm-* range covered being from 1800 to 1560 cm-I). A close approach to a straight line is seen in Bellamy’s graph of AR versus the CH, out-of-plane deformation frequencies in the eight vinyl derivatives, CH, :CHF, CH,: CHC1, CH, :CHI, CH, :CHMe, CHZ :CH.OR, CH2 :CH. CO.R, CH2 :CH. COZR, and CH2:CH .CHO (the wave-numbers here increasing from about 840 to 970 cm-I). With infra-red spectra the comment made above again applies: since group frequency shifts have also been correlated with Hammett a values (Flett, 1948; Bellamy, 1955; etc.), pK, values of acids (Goulden, 1954), half-wave potentials of carbonyl-containing molecules (Fuson et al., 1954), chelate stabilities (Bellamy and Branch, 1954), bond strengths (Bellamy and Beecher, 1954), reactivities of alcohols (Taft, 1953), etc., it is obvious that many empirical equations are contrivable to link AR with electronic dist,ributions in molecules and their reactivities.
E. Dispersion of Refractivity From Tables 3, 5, and 6 it is seen that refractions change in some inverse manner with the wave-length h of the light by which they are measured ; the variations originate, of course, in the refractive indices entering the Lorentz-Lorenz function (1). Since 1827, a number of equations have been developed to describe dispersions of refractive indices nA (Wood, 1934, and Partington, 1953, give historical and other details); of these, those due to Cauchy (9) and Sellmeier (10) appear to be best known and most used
+ (C/h4)+ (D/Ao)+ .. . . .. . . . .. -A;) + . . . ni = (1 + c,+ C,) + c,Xq/(h2 - A?) + c, nA =
A + @/A2)
(9) (10)
I n (9), A , B, C, D , etc. are constants, as are C1,Cz, etc. in (10) for a given medium in a given physical state (see Edser, 1920); hl, A,, etc. are wavelengths of light which the refracting substance can electronically absorb. When the measuring light has an infinitely long wavelength, A in (9), and ( 1 + GI + C 2+ ...) in (lo), are seen to be n and n: respectively. When X is short compared with hl and A,, n2in (10) tends towards unity. When h is close to either hl or A&, n2exhibits large positive or negative values depending upon the magnitudes and algebraic signs of the denominators. To prevent n2 becoming + a or -03, Ketteler, Helmholtz, and others have inserted “frictional ” terms in (lo), thus improving its power to reproduce observed facts (see Wood, 1934, regarding sodium vapour, cyanine, p-nitrosodimethylaniline, etc.) which (9) cannot
M 0 L E C U L A R R E P R A C T I V I T Y A N D P 0 L A R 1 2 A B IL I T Y
35
cover. Strictly, therefore, the Sellmeier type of equation is to be preferred because it makes understandable the existence of spectral ranges where n increases with X (“anomalous dispersion ”) instead of diminishing (“normal dispersion”). However, anomalous dispersion, although a common phenomenon, only occurs at wavelengths near to points of maximum absorption; colourless media for which hl, A,, etc. are well removed from X show normal dispersion (which can be viewed as resulting when the characteristic A’S are all situated in the extreme ultraviolet region), and in such cases it seems that (a) in the approximate form nx = A + B/X2 is often sufficiently valid. Bruhl (1886b) tested available dispersion formulae on solutions of phosphorus in carbon disulphide and found Cauchy’s expression adequate. Bottcher (1952) reports an extensive examination of Cauchy and Sellmeier equations, using both two and three terms with the former: taking accurate data for the nx’s of n-hexane, toluene, cyclopentane, carbon tetrachloride, and pyridine a t seven wavelengths, he established the requisite constants with the refractive indices observed for h = 6562.9,5015.7, and 4471.5 d, and then proceeded to calculate the interpolated values for h = 5893.2 and 4861.4 d and the extrapolated values for h = 6678.1, 4340.5, and co 8. The results (or). cit., p. 257) show that the three-constant Cauchy and Sellmeier relations lead to practically identical estimates, agreeing with the figures from experiment to within 3 units in the fourth decimal place. Using the approximate form of (9) the third decimal place, at least, was reliable in all operations except the computation of n when the deviations between values from the simplified Cauchy and the Sellmeier or three-term Cauchy equations amounted to 0.0037 in the worst case (pyridine). The electronic polarization, EP,of a substance is given by M r , through equation (1)with n = n,. By (9), as approximated above, n = nh(B/X2)and is therefore accessible by measurements of refractive indices, nl and n2,a t two wavelengths, X1 and A,; then n ,= (A: n1-A;
nz)/(X:-hi)
(11)
As already noted, the data of Vogel and many other workers has usually included refractive indices a t four wavelengths ; accordingly when nl, n2, n3, and n4 are available a t X1, A,, As, and h4 respectively, n , follows by (12) : nz = (ng
- ni A:) (n; - n4) - (n?A! - nf hi) (n: - ng) (Xf -A:) (nz- ng) - ( X i -hi) (nf - n;)
(12)
The arithmetical tediousness of (12)) compared with (11) is seldom justified by the results. Another equation, convenient in use, is (13))
B . J.
36
w.
LE F ~ V R E
based on the observed fact that molecular refractions for a series of wavelengths, all distant from a characteristic wavelength, nearly always show a straight-line plot of Rx versus l / A 2 ; writing R1 = R a t R1AE/A:, where A. is the remote characteristic wavelength (which is not necessarily an absorption maximum wavelength), we have, for R1 and R , a t hl and A, (Smyth, 1923, 1924):
R = R,RZ(XE - AF)/(hgR1 -A? R,) (13) Equation (13) has been applied to many liquids (Smyth (1924), and Bottcher (1939) give good examples), R a, deduced from one pair of wavelengths generally emerging within 0.1% of that from two other wavelengths. A belief that R is 0.95RI, seems to have originated with Sugden (1934) ; in fact, however, the ratio R m/RDis somewhat variable, TABLE18 (Rm)hon,, Values Calculated from Table 5 Bond
(C-W (C-C) (C=C) (C=C) (C-C) (C-C) (C-C) (C-C)
Wavelength used
C,D,F,G’ C,D,G‘ C,D,F,C’ C,D,G‘ C,D,F,C’ C,D,G‘ D,C’ C,U,G’ C,D,F,G’ C,D,F,G’ C,D,F C,D,F C,D C,F,G‘ D,F,G‘ C,D,F,G’ C,D,F,G’ D,F C,D,G‘ C,D,F,G’ C,D,F,G’ C,P,G’ C,D,F C,D,F,G’ D,F,G‘ C,D,F,G‘ C,D,F,G’ C,D C,D
terminal cycloproparie cyclobutane cyclopentane cyclohexane
(Car-CY*r)
(C-CI) (C-Br) @--I) (C-0) ethers (C-0) acetals (C=O) (C=O) Me-ketones (C--8) (C=S) (C-X) (C=N) (CrN) (0-H) alcohols (8-H) (8-S) (8-0)
0--H) (N-0) (N=O) (N--N) (N-N)
c,n
~
._ ~~
__
(Rm)hond
cm3
1.644 1.254 3.937 5.670 1.437 1.323 1.237 1.229 2.546 6.361 9.064 13.92 1.490 1,429 3.242 3.383 4.419 10.79 1.490 3.509 4.718 1.628 4,654 7.72 4.75 1.76 2.35 3.80 1.80 3.97
MOLECULAR R E F R A C T I V I T Y A N D P O L A R I Z A B I L I T Y
37
and it is therefore always safer to calculate R by (13) in all cases for which dispersion measurements have been put on record. Unfortunately these data are often lacking. I n such instances Le FBvre and Steel (1961) recommend the use of bond R,’s as in Table 18. This was compiled from Table 5 , via equation (13)’ after discarding the Rx’s which did not plot rectilinearly against the remainder in pairs produced up to six estimates of ( R (when all the four wavelengths were utilized). The means of such extrapolations are tabulated in the right-hand column. Table 19 shows a few examples of R,’s calculated in three ways: (A) by fitting R,, RD, RF and R,. from the literature t o the equation R, = R + (constant)h-’, (B) as 0*95RD,and (C) by summation of bond polarizations from Table 18. !rhe R,’s under (C) are close to those under (A) and offer some justification for using Table 18 with molecules for which refraction-dispersion data are not known. TABLE19 Comparison of Em’s Calculated From Three Sources Molecule
(A) cm3
( R ) cm3
(C) cma
8.04 12.62 17.16 21.67 26.26 30.72 26.05 29.82 29.87 32.54
7.81 12.26 16.66 21.03 25.50 29.82 24.87 29.66 29.58 32.29
8.05 12.59 17.13 21.68 26.22 30.76 25.14 29.67 29.86 32.56
Dispersive power is more constitutive than refractivity-a fact first recognized by Gladstone (1886, 1SS7) when investigating the quotients (axl- nh,)/d and M(nhl -nx,)/d for additivity. Briihl (1891 ), using the Lorentz-Lorenz expression for the specific or molecular refractions, considerably extended the subject and prepared lists of “atomic” dispersions for the CI and y hydrogen lines; these were later revised by von Auwers and Eisenlohr. Tables such as those produced by the last-named author (1912, 1923) have always included values for Rg - R, and R, - R,. Predicted dispersions are sometimes satisfactory when absorption wavelengths are well away from the visible region (e.g. from Table 2 R,-R, for acetyl chloride and pentyl alcohol are 0.44 and 0*64cm3;the observed differences are 0.48 and 0.64 om3 2*
38
R. J .
w.
LE FEVRE
respectively). Refraction and dispersion are not correlative properties. Dispersive power seems very sensitive to conjugation (e.g. R, - R, for 2,4-hexadiene is, by calculation, 29-80- 28.77 = 1-03, by measurement, 31.95 - 30.38 = 1.57 em3) and in structures containing this feature “exaltations of dispersivity ” must be anticipated. I n line with the “specific exaltations of refractivity’’ already mentioned (p. 29), of von Auwers and Eisenlohr (1910, 1911), ‘(specificexaltations of dispersion” were also introduced. These are computed as 10011(RAl- RAa)observed - (RAl -RA,)calclIM
and recorded as percentages by dividing by the specific dispersions expected from the (‘atomic dispersions” (e.g. for the quoted example the specific exaltation of dispersion is 5411.03 = 52 % ; corresponding percentages for some other compounds are: benzene, 7 ; toluene, 1 1 ; m-xylene, 16; styrene, 45 ; isoprene, 38; cyclopentadiene, 4 ; diacetyl, 9; acetophenone, 35; etc.). Several useful empirical relationships which involve dispersion are in the literature. The “AbbB number”, given by (14)
A
(14)
= (nD-l)/(nF-nC)
is convenient since the difference in the denominator is directly measureable with an ordinary Abbe refractometer. Should the individual values of nF and nc be desired they can often be extracted from A by invoking Waldmann’s (1938) rule, expressed by (15) (nn- nc)/(nF- nc)
=
0.286
(15)
and said to hold within 10% for a wide range of liquids excepting those of high dispersive power, According to Bielenberg (1933), A may be regarded as a constitutive property ; it differs between homologous series yet within a series is fairly constant from one member to another. Polycyclic hydrocarbons have A’s around 20, benzene and its homologues, 30-35, aliphatic amines, 48-55, aliphatic hydrocarbons, 56-60, etc. (Bauer et al. (1960) show a chart on which chemical classes are located over their appropriate A ranges.)
F. Analytical and Miscellaneous Applications of Refractivity I n general the refractive indices of mixtures of non-interacting components plot smoothly against the proportions present ; the same is true of specific or molecular refractions. Equations (3) and (4)-when R1 and R,, or rl and r 2 , are known-obviously make possible the estimation of a concentration w,or f2 by measurement of n I 2 and d12 (since
MOLECULAR REFRACTIVITY AND YOLARIZABILITY
w1= 1- w2, andf, dilute solutions
= 1-f2).
3!)
Further, n12seems often to obey (16) with n12
= n,(l+y’w2)
(16)
so that observation of density is avoidable if y’ has been ascertained by previous work; then the weight fraction w2 of solute is (n12-n)ly’n,. Bauer et al. (1960) state that molarities more frequently give straight lines versus nI2 than do weight fractions, and illustrate this opinion by details for the system acetone-carbon tetrachloride. Arshid et al. (1955, 1956) have provided many examples of rectilinear relations between nf2and the molar fractions of constituents in binary mixtures, both aqueous and non-aqueous. Moreover, experiment showed that the square of the refractive index is truly additive when components do not interact (e.g. the graph of n2against concentration for azobenzene plus benzoquinone in toluene is calculable from those of azobenzene and benzoquinone separately in toluene) but that when interaction occurs (e.g. as with azobenzene and phenol) changes in slope of the straight lines take place at points corresponding t o the compositions of the inter-molecular complexes ; in this way hydrogen-bond and anioncation associations can be detected rapidly and simply on small quantities of materials. Specific refractivity increments, (n12-nl)/c, where c is in grams per cm3, are independent of c with aqueous solutions of proteins and many water-soluble macromolecules of natural or artificial origin (Oster, 1955) ; they-and dn/dc also-are best recorded by differential refractometers (such as that designed by Debye, 1946) and are necessary quantities in the determination of particle weights from light-scattering data. Another analytical application is due to Kurtz and Ward (1936), through the so-called “refractivity intercept ” b, which emerges when, for a given homologous series, n is written as ( d / 2 ) + b . As with the Abbe number A , b appears roughly to be characteristic of class; it varies from 1.029 for saturated polycyclic substances to 1.088 for conjugated diolefins (b’s for nine classes are tabulated by Bauer et al. (1960)) so that, given n and d for a pure unknown liquid, a reasonably correct guess can often be made concerning the class to which the compound belongs. Further, a sample containing two class members can be analysed from the apparent refractivity intercept by assuming that bapparent is additively made up of bl and b2 in the proportions x:(1 -z). Gooding et al. (1946) describe the application of this method to multi-component mixtures of “aromatics ”, naphthenes, and paraffins. Many other empirical correlations of refractive indices or specific
40
R . J. W . L E F E V R E
refractions with various physical properties, numbers of rings in mineral oil fractions, types of hydrocarbons, etc. are reported, discussed, and represented by graphs or nomograms in the Monograph by Waterman (1958); apart from its scientific interest, such information should have industrial uses. Finally, refractivity should not be neglected when investigating addition or condensation polymers. Le FAvre, C. G. et al. (1958), and Le Fkvre and Sundaram, K. M. S. (1962a, b, 1963a, b, 1964) have noted that frequently the specific refractions of these macro-molecular solutes a t infinite dilution in benzene or carbon tetrachloride are easily expressed in terms of L, the logarithm of the degree of polymerization as determined by the standard viscosimetric technique (for which therefore refractometry might sometimes be asimple alternative). Tolkmith (1959)hasproposed the employment of additive refraction constants for the estimation of polymer molecuIar weights. As an example he takes the polyphosphorus compound
1%
in which R
= NMe,.
The molecular weight is given by
M
=
286.25 + 1 0 7 . 0 5 ~
and the molecular refraction (using bond refractions as in Tables 5 and 10) by
R,
=
69*18+21*55~.
If RD thus expressed is equated to L(286.25 + 107*05~)/d where L = (n2- l ) / ( n 2 +2), then x: is obtainable from the observed n and d ; M follows as (17):
M
=
286.25 + 343.65(d - 4*138L)/(4*968L -d)
(17)
Tests showed that M’s secured v i a (17) were as accurate as others determined cryoscopically. The method is obviously generally applicable to all liquid polymers for which the structural pattern is known and is uniformly repeated throughout the macro-chain ; as x becomes larger the observable differences between the L’s and d’s of molecules with x and x+ 1 become smaller, and precision in M is thereby reduced. An analogous proposal by Farquharson (1936) to use Pascal’s constants
MOLECULAR R E F R A C T I V I T Y A N D P O L A R I Z A B I L I T Y
41
and diamagnetic susceptibilities was likewise most successful with low polymers.
POLARIZABILITY 111. MOLECULAR The polarizability of a particle is defined as the dipole moment induced by an electric field of unit intensity. If a field of intensity E is imposed upon a nucleus having an elastically attached electron held initially at the equilibrium distance r from the centre, a displacing force Ee will be balanced by a restoring force L.&, where e is the electronic charge and k is a force constant; the induced moment is moreover e.6r. Therefore, when E = 1 , 6 p = e 2 / L ;8,u is, by definition, the polarizability b. (Dimensionally, b is a volume since a charge has dimensions M1/2L3/2T-’, and k-being a force per length-has dimensions LVT-~. In the absence of an external field an electron so held would (neglecting damping) oscillate with a natural frequency v,, cycles per second given , is the mass of an electron; accordingly by (112,) ( k / w ~ ) ”if~m
b = e2/4n2v:m (18) In fact, of course, the electric vector in a light beam is not steady but varies sinusoidally with time, so that the intensity E must be amended to E o c o s 2 ~ v(where t v is the frequency of the light and t the time); the electron imagined above will therefore be executing forced vibrations. By arguments set out by Lorentz (1909) and explained in detail by Partington (1953), the general equation (19) is reached
+
c (&- v2)-l
(n2- 1) M / ( n 2 2) d = ( N e 3 / 3 r m )
k
(19)
This displays the facts that the field inside a dielectric is not simply that which is applied externally (but is modified by intervening polarized molecules), and that the medium may contain k kinds of oscillators each with its own proper frequency vo. I n the case of a single oscillator, the same in all the N molecules per gram-molecule, and when v 2 is negligible compared with V & we have (20), from ( 1 8 )and (19) :
R = 4rNb/3 (20) For light of infinite wavelength, v = 0 and R in (20) is the R,, previously mentioned, i.e. the electronic polarization, zP . Following Bhagavantam (1942), the molecular polarizability appears as ( 2 1 ): b
= e2/im(w$- UP
+ iwg)
(21)
(where w,, = 2nv0,w = 2nv and q is a “damping” term). Theoretically, therefore, polarizability should be a function of the frequency of the
R. J .
42
w.
LE FEVRE
incident light ; in practice, however--as just stated--v is usually much smaller than vo, so that, except when measuring n’s near absorption bands, the complications of (21) may be ignored and b regarded as a constant. The limiting value of (21) is given by (18). Numerically, with N = 6.023 x loz3molecules per gram molecule, the electronic molecular polarizability is, from (20), b = 0.3964 x R, cm3.
A. PoZarizabiZity as a Directional Property By elementary electrostatics a conductive sphere of radius a would, in a field of intensity E , acquire an electric dipole moment of a3E ; by the definition given above the polarizability of a molecule might therefore be identified with the cube of the molecular radius. Debye (1929) showed that with non-polar gases there is indeed a rough parallelism between the actual volumes of molecules inferred from the van der Waals equation and the molecular refractions obtained by direct measurement. He demonstrated that a Bohr hydrogen atom, with an electron describing an orbit of radius a, placed in a field E , would-if the orbital plane were perpendicular to the field direction-also develop a moment of a3E ;however, since this orientation of the orbital plane was a special assumption, he argued further thus: the potential energy of a hydrogen atom in a n electric field is, for the unexcited state, - 9a3E2/4 (Van Vleck, 1926), whilst the potential energy of a system of polarizability b in such a field is - bE2/2; accordingly b = 9a3/2, and polarizability again appeared as a cube of an atomic radius. Quantitatively, no expression based on r 3 fits all the known facts. Dalgarno (1962) has recently listed 83 experimental determinations of TABLE20 Polarizabilities and Radii Atom or ion 1024r3 cm3 Dalgarno’squoted polarizability x 1024 0.3964x R calc. in Table 14 Ne 1.4 0.40 0.40 Rb+ 3.2 CG. 1.7 1.4
1
F2.5
C1-
ca. 1.2
ca. 3
1.0
A 3.65 1.6
1.7
cs+
4.8 ca.2.5 2.5
Kr 4.8 2.5 2.5 Mg++ 0.55 0.07 0.10
5.9
3.5
xo
6.9 4.0 4-3
Ca++ 1.6 ca.0.6
0.51
Br7.4
I-
en.4.5
ca. 7
4485
Na+ 0.86 0.15 0.19 Sr++ 2.3 CU.l.1
0.84
10.1
7.7
K+ 2.35 ca.0.9 0.87 Ba++ 3.6 ca.1-7 1.6
MOLECULAR REFRACTIVITY A N D YOLARIZABILITY
43
atomic and ionic polarizabilities ; from his assessment of them he selected 16 values, as the most accurate available; these are reproduced here in Table 20 beneath the cubes of the radii already given in Table 14. Clearly polarizability and r 3 are not simply related; actually, as an empirical basis for prediction, the 4 5 t h power of r, used in Table 14, would be more satisfactory. It is generally believed that the polarizabilities of monatomic ions and molecules are independent of field direction. For undistorted quasi-spherical molecules (e.g. CH4, CCl,, etc.) the same is usually assumed. When two such atoms are held together, as in a diatomic molecule, the new system is not isotropically polarizable. The model discussed by Silberstein (1917) makes this understandable. If a unit field acts along the line of centres A-B it will induce primary moments parallel to itself in both A and B, and likewise if it acts a t 90" to A-B. Each primary moment will induce a secondary moment in its neighbour ; in the first case the secondary moments will add to the primary moments, but in the second they will subtract. Hence b along the line of centres exceeds that across it, and the polarizability of A-B is an anisotropic property. A similar situation is to be expected with the majority of polyatomic ions or molecules (see Table 21). The polarizability of a body can be mathematically described by an "ellipsoid of polarizability " possessing three orthogonal semi-axes bl, bz, and b,. By the equation (x2/bf) + ( y 2 / b 3+ (z2/bg) = 1, points represented by the co-ordinates x,y, z lie on a surface which in turn may be viewed as containing the imaginary end-points of moment vectors induced when a unit field is successively applied to the molecule in all possible orientations. With spherically symmetrical molecules the directions of action of the induced moments and the inducing field are always collinear ; with less symmetrical molecules the induced moments are usually at angles to the field which depend on the orientations of the molecules in the field, i.e. the field induces component moments parallel and perpendicular to itself. Onlywhen the fieldis parallel to one or another of the semi-axes, bl or b2 or b S , will such perpendicular components be zero; the moments induced in these special situations are known as the principal polarizabilities bl, bz, and 6, ofthe molecule. If, for example, a unit field acts at 8" to the bl direction and in the bl x b2 plane, two moment components blcosB and bZ will be induced, mutually a t go", and the resultant molecular moment will be a t tan-l[(b,/b,)tanB], not B", to the bl line. Reorientation of the molecule, to diminish potential energy by bringing bl,raxi,,l,,l,linto parallelism with the field, will tend to occur, but will be opposed by thermal agitation. The quantities bl, b2, and b, appear throughout the treatments
44
R. J.
w.
LE F ~ V R E
accorded by Langevin, Gans, Born, Debye, and others, to many optical and electrical phenomena, and in particular to refractivity, light scattering, dielectric polarization, and the Kerr effect ; they can be evaluated from quantitative measurements of the properties named. The degree to which a given molecule displays anisotropy of polarizability is sensitively connected with structure, conformation, and morphology. A method of stereochernical usefulness is therefore obvious-provided polarizability semi-axes can be computed a priori for comparison with those from experiment.
B. Evaluation of Principal Molecular Polarixabilities At least three observational equations are necessary (unless, from symmetry, a polarizability ellipsoid of revolution, with two equal semi-axes, can be safely foreseen, e.g. as with HX, CH3X, CHX,, etc.). The first of these is provided by (22), whereby the sum bl + b2 + b3 may be extracted from the electronic polarization EP of a molecule: gp
=
R,
=
( 4 ~ N / 9(bi+bZ+b,) )
(22)
A second equation, sometimes available, is (23), where d is the depolarization factor of light scattered transversely by the substance under examination : lOO/(6-7d) = [(bi-b’)‘+
(bz -b3)2+(b3-b1)2]/(bl+bz+b3)2
(23)
The third equation involves the so-called Kerr Constant B-the birefringence observed when polarized light of wavelength h traverses a I-cm path through an otherwise isotropic dielectric subjected to a unit electric field applied at 90” to the light beam and at 45” to the plane of polarization. By the Langevin-Born orientation theory, B can be written as (24),
B
+
=~v(n’
(e
+ 2)’ (6,+ 6,)/27nh
(24)
in which v, E , and n are, in order, the number of molecules per om3, the dielectric constant, and the refractive index; el is known as the “anisotropy” term, d 2 the “dipole” term. These terms are expanded as (25) and (26): 61 = (1/45kT) [ ( U I - U Z ) (bi-bz)+ (a2-a3) (b2-b3) + (a3-a1) (63-bl)1 (25) 62 =
( 1 / 4 5 k 2 T 2[(py-p;) ) (b,-bz]+ (&-&) (bz-b,) + W P i ) (4-bAl
(26)
Equation (25) contains “electrostatic ” polarizabilities (al, a2, and a3)
MOLECULAR R E PRACTIVI T Y A N D P 0LARI ZA B I L I T Y
45
as well as “electro-optical ” polarizabilities (bl, b,, and b 3 ) , but as these two polarizabilities roughly correspond respectively to the polarizations represented as EP+AP (1.e. the distortion polarization, DP)and EP in ordinary dipole moment work, Le FBvre and Le FBvre (1953) suggested that they could often be approximately converted by putting ai/bi= *P/ EP,whereupon (25) became (27)
81
=
(1/45kT)(,PIE,) [ ( b , - b , ) 2 + ( b e - b 3 ) 2 + ( b 3 - b 1 ) 3 - ]
(27)
Only a minority of distortion polarizations are available from experiment, a fairly extensive study of the dependence of the total dielectric polarization of a gas upon absolute temperature being required to provide a confident value for P. via the Debye equation
TP = ( E P+ AP)+ (constant/T) In some cases P , may be estimated as aP + R hy calculating A P ’ ~ from spectroscopic data in ways illustrated by Le FBvre and Narayana Rao (1954,1955). All else failing, it can be noted that .P/,P is commonly CQ. 1.1. Equation (27), as written, implies that O1 must always be algebraically positive and, so far, it happens that among non-polar molecules (for which 0, = 0) only positive O1’shave been reported. A negative value of B1 is not however theoretically impossible; it could arise were al/bl, a2/b,, and a3/b3not equal to one another (such a circumstance might occur in structures known-from the work of Coop and Sutton (1938)to exhibit anomalously large atomic polarizations, cf. Le FBvre and Sundaram (1963) on p-benzoquinone, and Chen and Le FBvre (1963) on 1,4-~yclohexanedione)or-in liquids-through non-equivalence of the effective internal fields acting in different directions upon ellipsoidally shaped molecules (Narayana Rao, 1958). Equation (26) contains, in addition to hi’s, moment components pl, p,, and p 3 ; these last are the resolutes of the molecular resultant dipole moment onto the axes I , 2, and 3 along which b l , b z , and b3 are the polarizabilities. Since, in D. units, permanent and induced moments have magnitudes relatively as lo-’* : lo-”, in an electric field a molecule will be overwhelmingly oriented by the former. Accordingly it is O2 which controls-through its Abi’s and Api’s-the algebraic sign of the Kerr constant B. Qualitative explanations of electric birefringence, including the significance of its algebraic sign, together with a digest of the formal derivations by Langevin and Born of equations (24) to (26), may be found in a Review article by Le FAvre and Le FBvre (1955e). From their modes of derivation, equations (22) to (27) are, strictly,
46
R. J.
w.
LE F ~ V R E
valid only for low-pressure gaseous media, experimental work with which is practically difficult or, with thermally unstable materials, impossible. Fortunately it has proved that-just as with molecular refractions and total dielectric polarizations-substances may be examined for electrical birefringence or light-scattering as solutes in carbon tetrachloride, benzene, dioxan, and other non-polar solvents. Details of the evaluation of the right-hand side of (23) a t infinite dilution in carbon tetrachloride have been given by Le F h r e and Purnachandra Rao (1957), and Le FBvre and Le FBvre, (1953, 1954, 1955, and later papers) have demonstrated that alligation formulae can be satisfactorily applied to “ specific Kerr constants” sK1, of mixtures, and the specific Kerr constant pK2of the solute a t infinite dilution m(sK2)extrapolated therefrom. Multiplication by M , then gives the molar Kerr constant ,(,K2) in this state. The molar Kerr constant of a species is defined by (28)
K ,
=
6BnXM/(~+2)~(n~+2)~d
(28)
and may be viewed as the difference per unit field of molecular refractions Rp and R, measured in directions parallel and perpendicular to the applied field direction. (Since B = (np- n,)/hE2, the dimensions of K , are M-l L4T2, corresponding to volume squared -G work.) Four measurements ( B I Zni2, , el, and 4,)are necessary for every solution containing a weight-fraction w2 of solute; then by arguments analogous t o those used by Le FBvre and Vine (1937) for dielectric polarizations, or in the derivation of equation (5): w(&z)
where /3
=
Mz[,K1(1 - p
+7’ + 6 -Hy‘
= ( d 1 2 - d l ) / d 1 ~ 2 y’ , is given H = 4n‘f/(n‘f 2) and
a q = (el, - e1)/w2,
+
-Jae1)]
by (16), 6
J
+
(29)
= (B,2-Bl)/Blw~,
= 2/(e1 2). Practical direc-
tions for making the observations involved are omitted-they are fully set out by Le FBvre and Le FBvre (1953)-except for saying that for routine determinations of BI2’sphotometric techniques, e.g. as outlined by Le FBvre and Ritchie (1963), are now recommended in place of the visual methods employed previously (cf. also, Badoz, 1956). By the end of 1963, m(mK2)’~ for about 440 substances had been published from the Sydney laboratories. So far as the sparse data extant for gases permit comparison, it seems that m(mK2)is usually With polar solutes Le FBvre and Le FBvre (1953) inferred close to ,K,,,. from experiment, and Buckingham (1956) from theory, that mKg,,/ oo(naI<2) should be approximately equal to p~as/p~o,utio,,-a ratio which may be forecast in various ways (cf. Buckingham and Le FBvre, 1952;
M 0 L E C U L A R R E F R A C T I V I T Y A N D P 0 L A R I ZAB I L I T Y
47
Le FBvre, 1953). Numerically, molar Kerr constants range from large negative values through to large positive ones (e.g. 2,2'-dinitrobiphenyl, - 962 x benzene, + 7.24 x 10-12, phenanthraquinone, +2570 x lo-''; Le FBvre and Le Fevre (1955e)list those known a t the date cited). From equations (24) and (28) it follows that
,%K = 2.rrN(d1+ d2)/9
(30)
and from (30) therefore, a t 25' and for Na-light
(8, + 8,)
=
a(mKz) x 0.2378 x
separation of from O2 is possible when BP and A-actually the righthand sides of equations (22) and (23)-are available ;then, if the resultant molecular moment p is taken as collinear with b,, we have bI+bz+b3 = A
2bl-b2-b3 (bl-bZ)'+
= 45E2T2d21p2=
(bZ-b3)'+
(b3-bI)'
=
B C
and bl = (A+B)/3
( A / 3 )- (B/6) (6C- 3B2)06/6 In the general case, when p acts a t known finite angles with the 1,2, and 3 directions, the components pl,p z , and p 3 must be inserted into (26))and extraction of the bi's from (22), (26)) and (27) becomes more tedious. Some typical polarizability ellipsoids, specified by their principal semiaxes, and drawn from a(mKz)values, are shown in Table 21. On p. 291 of Le FBvre and Le Fevre's Review (1955e)are listed all the bi's derivable from the seventy-odd electric birefringence measurements on gases (by Leiser, Kansen, Szivessy, Beams, and Stuart, with their collaborators, during the period 1911 to 1948; cf. Le FBvre and Le Fevre (1955e) for references). Comparison of results from the two sources led Le Fdvre and Le F&vre(1955e, pp. 289-91) t o claim "that-judged against the information a t present available-molecular polarizability ellipsoids can be determined from solution not less dependably than from the vapour phase )'; subsequent solvent-effect studies, notably those by Armstrong et al. (1958) and Le FBvre and Williams (1961, 1964))have however, indicated that this claim should be restricted to observations made in non-polar media, such as carbon tetrachloride; it does not convincingly cover data secured with chlorobenzene as solvent. bz (andb,)
=
R . J.
48
w.
LE F ~ V R E
TABLE21 Some Molecular Principal Polarizabilitiesa Molecule
Source 1.308 1-026 0.509 0.656 0.872 0.543 0.673 (t.911 1.590 1.057 1,120 2.263 2.562 1.478 1.683 1.971 1.616 1.015 1.072 0.890 0.7795
0.558 1.026 0.411 0.499 0.657 0.370 0.901 1-258 1.785 1.667 1.120 2.203 2.562 1.255 1.301 1.588 1,160 1.014 1.043 0.879 0.946
0.558 1.026 0.411 0.499 0.657 0.370 0.901 1-258 1.785 1.361 0.736 1.681 1.188 0.821
0.892 0.996 0.815
0.670 0.645 0.575 0.608
Armstrong et ul. (1958) Aimstrong et ol. (1958) Le FBvre and Le FBvre (1954) Le VBvre and Le FBvre (1954) Le FBvre and Le FBvre ( 1954) Le FBvre and Le FBvre (1954) Le FBvre and Rao (1957) Le FBvre and Ritcliie (1963) Le V'avre and Ritchie (1963) Le FBvre and Le FBvre (1964) Aroney and Le FBvre ( 1 960)b Le FBvre and Le FBvre ( 1 954) Le Fdvre and Le FBvre (1954) Le FPvre and Rao ( 1958) Le FBvre and Rao (1958) Le FBvre and Rao (1958) Le FBvre and Rao (1958) Le FBvre et nl. (1959)c Le FBvre et tsl. (1959)c Bramley et nl. (1959) Bramley et rtl. (1959)
Deduced from co(mKz)values obtained in carbon tetrachloride or benzene. P. 3600. c P. 1188.
a b
C . Anisotropic Bond Polarixabilities The principal polarizabilities of molecules can be analysed in terms of anisotropic bond polarizabilities. A suggestion that bonds may have different polarizabilities along their lengths and in the two perpendicular transverse directions was first made qualitatively by Meyer and Otterbein (1931) and pursued quantitatively by Sachsse (1935), Wang (1939), and Denbigh (1940). If a bond X-Y has principal polarizabilities b z Y , bgY, and bFY (L = longitudinal, T = transverse, V = vertical), then for a molecule XY,, with an angle YXY of 20", we have
bFYz = 2(bzY cos2O+ bFY sin20)
and
b z Y 2 = 2(bfY cos20 + bFY sin20) b$Yz = 2b"'v
Further, from the average polarizability of X-Y, via an equation a m logous t o (22),we have the sum (bzY + bgY + bFY).In fact, however, when
MOLECULAR REFRACTIVITY AND POLARIZABILITY
49
X = carbon, X must be linked by two single bonds or one double bond to other atoms, and, as set out a t some length by Le FBvre and Le Fkvre (1954, 1955a, c, e) the number of unknowns then exceeds the number of equations. This impasse can be overcome' by taking the C-H bond as isotropic-an assumption not likely to be seriously incorrect (cf. Le FBvre and Le FBvre, 1955e, p. 299). A selection of the bond polarizabilities obtained on such a basis by the Sydney group using ,(=K,) values is given, together with the structures from which they have been extracted, as Table 22. Attention is drawn to the following points: (a) Bracketed values are uncertain or preliminary. (b) The fact that with a given bond in different combinations the total (bEY + bgY + b $ y ) appears to vary may not be wholly due to imperfections in derivation since, as already mentioned (p. 5 ) and as Vogel's tables show, bond refractions sometimes display fluctuations of the same proportionate magnitudes. (c) The anisotropic polarizability of a bond is affected by the structural environment, notably is this the case when conjugation of X-Y with a double bond occurs (e.g. C-Halogen links in the arylhalides) as would be expected from the " non-classical " polarizability mechanisms long used in organic chemistry to formulate the temporary transmission of electrical effects from group to group or from substituent to reactive position (cf. Ingold, 1953). An environmental effect can also be foreseen, even when no change in formal bond order takes place, through the augmentations or diminutions of induced polarity in the bond under consideration by secondary fields from induced or permanent moments in nearby bonds. The signs and intensities of such fields must obviously depend upon bond orientations (i.e. upon molecular structure and conformation). (d) The ratio of longitudinal to transverse polarizabilities of the C-C bond is seen to be identical with that (3.67: 1) found by Bunn and Daubeny (1954) from the refractive indices and density of crystalline hexatriaWang-Denbigh estimates for contane, C36H74 ; the initial 1939-40 C C implied a ratio of roughly 90 : 1 (cf. however, Bolton (1954), Vuks (1957), and Mortensen and Smith (1960), regarding such a high and unique anisotropy). (e) When one of the atoms forming a bond carries an unshared pair of electrons (e.g. as in H-N, C-N, C-0, C-S, C-P, N=N, etc.) the polarizabilities of this duplet are, by the above method of calculation, incorporated into the polarizabilities of all the bonds to the said atom. Pending knowledge of the anisotropy of polarizability of 1 Chantry and Plane (1960) have recently suggested that measurements of absolute Raman intensities could supply the required additional information provided the treatment by Volkenstein (1941, 1960) be accepted as valid. From data on CH4 and cc14 b, and b, are deduced for the C-H bond as 0.0858 and 0.0546 and for C-C1 as 0.376 and 0.204 respectively in the units used in Table 22.
50
it. J .
w.
LE F ~ V R E
TABLE22 Bond Polarizabilities in 10-23 cin3 Units
-~
C-H
c-c c-c
C-F C-F c c 1 c-c1 c-c1 c c 1 c-Cl C-Br C B r U-Br C-Br U-I
c-I c-I c-I c=c
CrC
c-0 c=o c-s
N-H N-C C*r-C,r
c-P
c-4s C-Sb C-Bi 0-P 0-As N=N
0.064 0.099 0.098 (0.125) (0.07) 0.32 0.395 0.393 0.38 0.42 0.465 0.60 0.53 0.62 0.68 (0.88) 0.81 0.91 0.280 0.35 0.089 0.230 0.188 0.050 0.067 (0.224) (0.12) (0.13) (0.165) (0.19) 0.086 0.066 (0.285)
0.064 0.027 0.027 (0.04) (0.07) 0.22 0.16 0.lfJ5 0.lS5 0.195 0.31 0.26 0.27 0.24 0.47 (0.42) 0.42 0.53 0.073 0.13 0.046 0.140 0.169 0.083 0.069 (0.021) (0.15) (0.19) (0.22) (0.30) 0.145 0.198 (0.10)
0.064 0.027 0.027 (0.04) (0.03) 0.22 0.16 O.lg5 0.185 0.15 0.31 0.26 0.27 0.22 0.47 (0.42) 0.42 0.33 0.077 0.13 0.046 0.046 0.169 0.083 0.060 0.059 (0.15) (0.19) (0.22) (0.30) 0.145 0.198 (0.08)
a For refs. to underlying measurements of &$z), p, 9,etc., see Le PBvre and Le FBvre (1955, review) except where otherwise noted. b Brainley et al. (1959). c Bracketed because a recent unpublished redetcrmination has suggested 0.92, 0.37, and 0.37 as possibly more correct. d Le FBvre et al. (1963d). C Aroney et al. (196313, p. 1167). f Alternatively these four bonds may be nearly isotropic, cf. Aroney et al. (1963c, p. 1739). 0 Aroney et al. (1963d, p. 4938). h Armstrong and Le FBvre (1964).
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
51
lone-pair orbitals no other allocation seems justifiable. A safe viewpoint is that the data in Table 22 are empirical but appropriately usable in molecular situations analogous to those from which they have come.
D. Bond Polarizabilities and Other Bond Properties Reference has already been made (p. 31) to the limited success of attempts to connect bond refractivities with bond lengths. Denbigh, using data available prior to 1940, suggested that it was the longitudinal, rather than the mean, polarizability that seemed to be related to the intercentre distances TA-B in a link A-B. He proposed formulae of the type 102’bb;lB = Kr;B+c where K and C were constants depending on the type of bond involved and n was either 3 or 6. The four bonds, H-H, H-C1, H-Br, and H-I obeyed a cubic law, lOZ5bZX= 15*5r&,, but all others examined required n = 6 and-unless K were a reciprocal volume-led to dimensionally incorrect equations. For diatomic molecules formable from bL = m7rr3/4, hydrogen and the halogens, Brown (1961) has written in which m is a “bond factor ” (mH-H = 4,mHMX= 2 , mx--y = 1 ; both X and Y represent halogens); with m = 2 for H-X the expressions of Brown and Denbigh are numerically almost the same. Longitudinal polarizabilities, however, sometimes increase as r decreases ; Le FGvre (1958) therefore advanced (31)
which contained the third powers of lengths, a, b, and c being constants, and d (in A units) being taken as follows: when neither A nor B is a terminal atom, d = ?-observed) when B is a terminal atom, d = robserved +rB, and when A-B is a diatomic molecule, d = TAB + r , +rB. Equation (31) fitted bL’s from experiment reasonably well and had the advantage of covering also multiple bonds and bonds shortened by mesomerism. Certain empirical connections between polarizabilities and spectroscopic data have been noted. Torkington (1948) drew attention to the inverse sense in which the stretching force constants of the halogens and halogen hydrides varied with the mean polarizabilities of the molecules concerned, and further observed a linear dependence of force constants upon ionization potentials of the halogen X in the six compounds HX, CX4, Six,, BX,, PX,, and CH3X. In the light of Walsh’s (1946, 1947) demonstrations that changes of force constants, bond lengths, and bond energies are inter-related, Tolkmith’s conclusion (1959) that
52
n. J . w.
LE FEVRE
electron polarizabilities and bond energies are inversely proportional is not surprising. Bramley and Le F h r e (1960, 1962) started from the fact (Braude, 1955) that the wavelengths of maximum absorption for the K-bands of conjugated hydrocarbons showed a straight-line correlation with the “ chromophore lengths ” in the molecules concerned ; exaltations of polarizability A b were then predictable by expressions of the type: loz3A b = C(A,,, with C and A, as constants. The conclusion was reached that the exaltations in question were predominantly augmenting the major principal polarizability axes rather than either of the two minor ones. I n general, it appeared that the “longitudinal” polarizability of a conjugated system is a function of the cube of its lengtha prediction earlier made by Davies ( 1 952) from theoretical considerations. A quantity Q, evaluated by (32),
Q = ( l / r i ~(biB/M)l’S ) (32) (where r is the internuclear distance in the bond A-B, M is the reduced ern3)was shown by Le Fhvre mass for A-B, and bkB is in units of (1959) to be rectilinear with infra-red stretching frequencies v (as emp1) and that equations such as v = 9273Q-254
could often be usefully applied in the prediction of bL’s for bonds which are inaccessible to measurement via the Kerr effect (see also, Le FBvre, (1961a, b). Regularities, originally suspected by Denbigh (1940), in the bL/bT ratios of bonds, do not occur among the data of Table 22 ; no satisfactory way of forecasting such ratios appears yet to exist. Theoretical calculations have been published for a few bonds, many authors from Mrowka (1932) onward (Stuart, 1952, p. 367, and Bolton, 1954, give references) concerning themselves with the hydrogen molecule, for which Arai et al. (1952), using James-Coolidge type wave functions, deduced bF-= = 0.975 x and b:-= = 0.697 x Unfortunately owing to the variations in and smallness of the reported depolarization factors for hydrogen, and the failure by Bruce (1933) to detect a Kerr effect with hydrogen even at 82 atmospheres pressure under a field of 70,000 V per cm, this result cannot be checked against experiment. Bolton (1954) has computed longitudinal and transverse polarizabilities for singly, doubly, and triply bonded carbon atoms, and Mueller (1954) the longitudinal polarizability of the second of these ; agreement with experiment is fair for the b2C’s (but not the b:”/b$“ ratios):
53
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
I OZ4bgCfrom
Bond
c c c=c CEC
Experiment (Table 22)
Bolton
Mueller
(1954)
(1954)
0.99 2.80 3.5
0.70 2-86 4.06
2.9-3.1
-
Equation Equation (31) (32) 0.8 2.7, 3.6
1.2 2.9 3-6
IV. MOLECULARANISOTROPY AND STEREOCHEMISTRY As previously indicated (p. 43), the moment induced in a particle by ti unit incident electric vector is-except with spherically symmetrical (isotropically polarizable) bodies-a function of the orientation of the particle relatively to the polarizing field E. I n the general case, therefore, molecular polarizability must be regarded as a tensor of the second order. Adopting rectangular space-fixed co-ordinates, each component of the induced moment m is a linear vector function of the three components of E : m, = b, Ex b,, E,+ b,, E ,
+
+ b,, Ex + b,,
m, = b,, E,
E, + b,, E,
E, + b z , E, The nine coefficients characterize the transformation of the components of one vector (field) into those of the other (induced moment)+.g. b,, transforming E, into one of the three parts of m,. I n matrix symbolism the preceding three equations are incorporated in the tensor equation mz = b,
m =
+’E
where (4’) is the “polarizability tensor” or “operator” which turns E into m. The array of coefficients can be written
As the co-ordinates are rectangular, (4‘) is, for an optically inactive molecule) a symmetrical tensor, i.e. b, = bXv,b,, = b,,, and b,, = bvz, so that six independent elements only are required in its matrix. A geoby which it may be visualized, is as a metrical interpretation of “tensor ellipsoid” (cf. Gans, 1932, or Bottcher, 1952, for explanations) ; in the present relevance this is a polarizability ellipsoid. The symmetric (+I),
54
R . J.
w.
LE F ~ V R E
tensor can be transformed by appropriate rotation of its co-ordinate system into a quasi-scalar tensor (+), in the matrix of which the three pairs of non-diagonal elements (bgx,bxy,b,,, etc.) are all zero. The diagonal components b l , b2, and b3 are then the principal polarizabilities of the molecule and the directions along which they are measured are the principal axes of the molecular polarizability ellipsoid ; these b’s and directions are fundamentally connected with the structure of the molecule under consideration.
A. Additivity of Bond Tensor Ellipsoids The argument used on p. 48 assumed a tensor additivity of bond polarizability components. The data of Table 22 should therefore be usable, in reverse, for the calculation of molecular polarizability components for structures whose geometry is known, provided that the precaution mentioned a t the end of IIID is taken and that mutual interactions of polarizable units within a molecule (perhaps by Silberstein-like induction between uncombined atoms, cf. p. 43) can in general be disregarded (Bird et al., 1954). The second proviso has been questioned by Pitzer (1959), who says that it “seems most likely that there is some fortuitous cancellation of conflicting factors which allows the Denbigh-Le F h r e scheme to succeed over a limited range of substances . . .” and that the established adequacy of simple sum rules for the mean polarizability of a molecule in terms of mean bond polarizabilities is irrelevant since the said interactions “drop out of the first approximation to the mean polarizability of the entire molecule”. The matter has also been discussed by Mortensen and Smith (1960) who withhold judgment on the importance of “such interactions or of other factors in deviations from additivity . . . until a scheme assuming strict additivity has been given a fair trial”. Meanwhile accumulating measurements are increasingly indicating a not too imperfect additivity, demonstrated by comparing calculated and found molar Kerr constants. The prediction of ,,K for a given molecule requires an a priori estimation of the principal polarizabilities, b,, b2, and b3 and a knowledge of the components of the resultant dipole moment along the principal axial directions; these quantities are then united via equations (26)) (27))and (30) to yield the ,,K sought. Computational procedures are as outlined by Le FBvre and Le FBvre (1960) and described in detail by Eckert and Le Fkvre (1962a). Cartesian axes (X, Y, and Z) are arbitrarily set up within the frame-work of the three-dimensional structure to be examined, and the angles made by each bond with X, Y, and Z calculated (or measured by hand, in which case the models introduced by Barton.
(bxx-h)
bx,
b!CZ
b,X
(b,,-4
b,z
bX ,
bz,
(bzz - 4
=o
(34)
B. Applicability of Polarizability Anisotropy to Structural or Conformational Problems By following the procedures set out in the preceding section a fairly wide range of stereo-structural problems have been investigated in the Sydney laboratories; brief notes on many of these are given in Table 23.
R . J.
56
w.
LE FEVRE
TABLE23 Applications of Polarizability Anisotropy to Problems of Molecular Structure or Conformation Solutes
Conclusions drawn
References
Z-Methyl-but-2-ene, isoprene, ocimene, squalene, and squalane
Me& :CHMe and CH2 :CMe .CH :CH2 are planar; with isoprene the s-trans. form predominates; in ocimene the three C=C bonds are nearly parallel t o one another; squalene and squalane may have helically coiled structures
Le FBvre and Sundaram, 1963c
Dicyclopentadiene
The K , of the dimeride, m.p. 32”, formed at room temperatures corresponds with that calculated for the endo-form
Le FBvre and Snndaram, 1964
Cyclic olefins
The observed *,K of cyclohexene agrees best with that expected for a halfchair model; non-planar arrangements specified for 1,3- and 1,S-cyclooctadienes, for 1,5,9-cyclododecatriene, and for bicyclo(2,2,1) heptadiene, give predicted ,K’s in accord with experiment
Chen et al., 1966
d5-Cholestene
The measured ,,,K agrees with the value calculated assuming skeletal carbon-atom arrangements as described by Carlisle and Crowfoot (1945), for cholesteryl iodide
Eckert and Le FBvre, 1962a
Biphenyl derivatives
I n CT, biphenyl and its p-fluoro-, chloro-, bromo-, iodo-, and nitroderivatives are flat; 2,2‘- and 3,3’dinitrodiphenyls in benzene are roughly orthogonal
Chau et al.. 1959
Polyaryls
l n B, 0-,m-, and p-terphenyl, 1,3,5Le FBvre et nl., triphenylbenzene, 1,1’-binaphthyl, 1963h and 1,3,5-tri-ol-and-tri-fi-naphthylbenzene have “equivalent ” conformations in which the substituent phenyl-rings are rotated about the aryl-aryl junction lines by angles between 20’ and 56’; only 2,2’-binaphthyl appears to be planar
Tripheny lmethane
I n CT the phenyl groups are twisted by ca. 45’ out of the planes which intersect along the (Ph&)-H bond
Aronoy and Le FBvre. 19GOb
MOLECULAR R E F B A C T I V I T Y A N D POLARIZABILITY
57
TABLE23-continued Solutes
Conclusions drawn
References
cia- and transDeoalins
Both isomers have "two-chair" conformations
Le FBvre and Le FBvre, 1957
cis-2-Decalyl chloride
Steric course of replacement of OH by C1 involves retention of configuration with SOClz as reagent and inversion with PC15 and HC1 as reagents
Eckert and Le FBvre, 1964, b.
Cyclohexyl halides
Measurements are consistent with ratios of axial :equatorial conformations between 1:2 and 1:5 for cyclohexyl chloride, bromide, and iodide, in CT at 25"
Le FBvre et al., 1960
Cholesteryl halides and epicholesteryl chloride
The C-X bond is equatorially Eckert and attached at position 3 in the Le FBvre, 1962a cholesteryl halides; the C C 1 is axial in epicholesteryl chloride
Pentaerythrit yl tetrahalides
The four halogens are at the corners of a square plane containing the central carbon atom
Le FBvre et al., 1958b
cis-Dichloroethylene
The molecule is not planar
Bramley et al., 1959
a,w-Dihalogenoalkanes
Measurements indicate solutes present as mixtures of rotational isomers in CT at 25"; with ClCHzCHzCl results correspond to 73% trans and 27% gauche forms, with CrCHzCHzBr to 89% and 11yo respectively
Aroney et al., 1962a; Le FBvre and Orr, 1964
Aliphatic monohydric alcohols
Preferred conformation of ethyl alcohol is s-trans; evidence suggests that an s-trans-arrangementof the H-0-C-C unit is common throughout the series between methanol and octadecanol
Le FBvre et al. , 1960h; Le FBvre and Williams, 1960a
Phenol and p-substituted phenols
The H-0 link is out of the Ca plane in phenol and p-cresol; p-CICeH40H and p-BrCeH40H are effectively flat
Le FBvre and Williams, 1960b
a- and
Results reconcilable with flat molecules in CT a t 25"
Le FBvre and Sundaram, A. 196%
Anisotropy of G O bond deduced from paraldehyde and trioxan ; t,hen used to specify non-planar conformations of 1,4-dioxan and the other molecules named
Le FBvre and Le FBvre, 195Bb; Le FBvre et al., 1963d
,%Naphthols
Trioxan, dioxolan, ethylene carbonate, cineole, tetrahydrofuran, and methylal
58
R . J . W . LE F E V R E ~____ Solutes
-~
TABLE23-continued __
_-
~-
Conclusions drawn
References
2,3-Dichloro- and -diphenyl- 1,4dioxan
The so-called "cis" 2,3-dichloro-1,4dioxan, m.p. 52", is actually the trans-isomer ; the 2,3-diphenyl-1,4dioxans with m.ps. 46" and 132" should be designated cis and trans respectively; the dioxan ring has a chair conformation throughout
Chen and Le FBvre, 1965
Dimethylenepentaerythritol
The two spiro-1,3-dioxan rings each adopt a chair conformation
Le FBvre et uZ.,
Di-n-alkyl ethers
The effective conformation of diethyl ether (in CT, 25") has the terminal C M e bonds rotated ca. 24" from a flat zig-zag structure so that they are "trans" with respect to the C--0-C plane. A non-planar conformation for di-n-propyl ether, compatible with the observed m(,nKz), can be specified; with higher ethers the possibilities of internal rotations make this difficult
Aroney et al., 19620
Trialkyl orthoformates
Solutes appear as mixtures of rotational Aroney, et ul., l964f isomers having staggered arrangements of the R-0 bonds in the group HC(0C)a
Anisole and di-o. substituted anisoles
U,,-O--X.le triangle is ca. 22" out of tho Aroney el d., 1960b; Ce plane. The introduction of Me-, Aroney et al., 1964'0 C1-, or Br- substituents in both ortho-positions of anisole causes conformations in which the C,,-O-Me is approximately orthogonal to the Ce ring
a- and 15-lllethoxy-
Noii-planar conformations of C ~ O H ~ XLe FBvre and Le are indicated when X = a- or /3-MeO, FBvre, 1955b ; a-CHO, a-COMe, a-NOp, and a- or Le FBvre and Sundaram, A. /3-NH2 1962c
naphthalenes and other monosubstituted naphthalenes Dimethoxynaphthalenes and-anthracenes
195813
The 1,4- and 1,5-dii~iethosynal~hLo FBvre et al., 1963c thalenes, and 9-methoxyanthracene havo conformations in which the C-0--Me triangles are rotated about their C-0 bonds within & 30" of the Ar-plane; in 9,lO-dimethoxyanthracene the corresponding rotations are within about 30' from the cis- and trans-orthogonal positions
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
69
TABLE23-con.tinucd Conclusions drawn
Solutes
References
I n R measurements agree with each CS ring being twisted 37" about its 0-C1 . . C4 line from the flat configuration
Lc FBvre et 01.. 1962
Monocarboxylic acid esters
In the -CO .O R group it appears general that the C O - R triangle is rotated ca. 30" about the ( C 0 ) - 0 bond from a planar s-cisprecursor
Le FBvre and Sundaram, A. 1962a
Dicarboxylic arid e8tern
Dimetliyl oxalate (in dioxan) and Aroney et nl., 1962b, cf. Le FBvre and cliethyl oxalate in C T behave as mixtures of cis- and tmns-isomers, Sundaram, A., none of which is planar; measure1962a, and Le ments on diethyl malonate, succinate, FBvre et nl., 1957 adipate. etc. can be interpreted only if multicomponent mixtures of several (Bpecified)conformations are present
Diethyl, maleate, fumarate, and azodiformate
In diethyl inaleate the ethoxycarbonyl groups are twisted, one up and one down, by 90" from a planar model in which both carbonyl groups are disposed in the same clock-wise sense. In diethyl fumarate and azodiformate opposite twists of ca. 32' and 76", from that flat form in which the two C=O bonds are not antiparallel, give structures in arcord with observations
Armstrong et al., 1962
Cyclic dibasic acid anhydrides
Maleic, succinic, citraconic, itaconic, phthalic, and naphthalic anhydrides have flat structures, and glutaric, diphenic, camphoric, and cineolic anhydrides geometrically specifiable non-planar ones
Le FBvre and Sundaram, A., 196213
Di-n-alkylketones
Diethylketone has a n apparent conformation in which the two terminal C H Z - C H ~ bonds are rotated by 10" about the (C0)(CH2) axes out of planes at 90' -90' t o the (CHz)-(CO)-(CHz) triangle and in directions away from the 0-atom; results with higher homologues can be explained if mixtures of (specified) conformations are assumed for the solute species
Aroney et al., 1961b
Diphenyl et,her
.
+
60
R. J.
w.
LE FEVRE
TABLE23-continued Solutes
Conclusions drawn
References
cycloPentanone has a non-planar structure in harmony with that of cyclopentane ; cyclohexanone has a chair conformation ; cycloheptanone is an irregular non-planar molecule for which a single stereo-form cannot be specified. Measurements on camphor fit Bredt's formula. The negative ,K of 1,4-cyclohexanedione is explicable by this solute being either a flexible twisted boat structure, or a 1: 4 mixture of (specified) boat-chair forms
Le FBvre and Le FBvre, 1956b; Le FBvre et al., 1959b; Chen and Le FBvre, 1963
Biacetyl, benzil, and furil
Apparent conformations are nonplanar with the two R.CO halves twisted about the (C0)-(CO) axes by ca. 160", 97", and 119" from the flat cis-arrangements
Cureton et aZ.,l9Gl
Di-o-substituted benzaldehydes and acetophenones
The interplanar angles between the Ar-ring and the valencies of the extranuclear trigonal carbon atoms are ca. 0" in benzaldehyde, 2,4,6trimethylbenzaldehyde, and acetophenone, and ca. 90" in 2,4,6-trimethylacetophenoneand 2,3,5,6-tetramethylacetophenone
Aroney et nl., 1964a
Acrylic, crotonic, methacrylic, and tiglic aldehydes
Observations explicable if s-trans-s-ci8 mixtures present (in B a t 25") as follows: CH2 :CH .CHO, 4: 1, Me.CH:CH.CHO, 23:1, CH2 :CMe. CHO, 1: 1, and Me.CH:CMe.CHO, 18:l
Chen and Le FBvre, 1964
Phenylpolyenals and diphenylpolyenes
Bramley and Le Benzophenone (in B) has the phenyls FAvre, 1962 rotated ca. 40" from the flat structure. Measurements can be reconciled with the following conformations: cinnamaldehyde, s-trans, benzylideneacetophenone, s-cis, cinnamylideneacetophenone, mainly s-trans-s-cis, dibenzylideneacetone, mainly s-cis-s-cis, and dicinnamylideneacetone, mainly s-trans-s-cis-scis-s-trans; the phenyl groups may be twisted out-of-planearound their 1,ri-axes by 20-30'
cyclo-Pentanone, -hexanone, and -heptanone, camphor, and 1,4-cyclohexane dione
~
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
61
TABLE23-continued Solutes
Conclusions drawn
References
Arylamines and related molecules, piperidines, and piperazines
I n B, CsH5NH2 and CsHsNRz molecules Aroney and Le FBvre, 1956, 1960a, are pyramidal, with the H . . . H or Calk. . . C,,, lines parallel to the 1960b C 6-plane. Non-planar conformations are specified for phenyl hydrazine, hydrazobenzene, p-phenylenediamine, aud benzidine. I n Ph3N the phenyls are twisted 60-70" out of the planes which intersect along the fourth N-valency direction. N-phenylpiperidine is a chair structure with the CsHs-group athched equatorially. Both chairs and boats appear to occur with piperazine and its disubstituted derivatives
Acetanilide and it,s p-substituted derivatives
The angle between the Car-N-CCO and the N-CCO-0 plane is ca. 80" for acetanilide and its p-bromoderivative in B, and within the range 65-85" for these substances and for p-chloro- and p-methylacetanilides in dioxan
Aroney et nl., 1963f
Troger's Base
I n B, the Ar-rings are nearly perpendicular to one another and the CH2. N .CH2. N units are nonplanar in a way resembling the (CH2)4unit in trans-tetralin
Aroney et al., 1961a
2,2'-Bipyridyl
I n B or CT, the pyridyl rings are twisted about the 4,4'-axis by 10-17" from the flat trunw configuration
Cureton et ol., 1963
Morpholine
In B, morpholine has a chair structure with the N-H bonds almost, all disposed axially ; in CT and cyclohexane, the N-H links are distributed axially : equatorially roughly as 3 : 2
Aroney and Le FBvre 1958b; Aroney et al., 1964g
Tropiuone and 3 -halogenotropanes
Chair piperidine rings with equatorially attached N-methyl groups are contained in the solute conformations present in B
Eckert and Le FBvre, 1962b
4-Pelletierine
Results in B show the N-methylpiperidone ring to have a chair conformation and that in about half the solute molecules the N-methylpiperidine ring is constructed likewise
Eckert and Le FBvre, 1964a,
3
R . J.
62
w.
LE F ~ V R E
TABLE23-eon2int~ed ~-
Solutes
~
__
Conclusions drawn
References
Azoettiane
Observations reconcilable with CH3. C H Z.N : N . CHz .CH3 being "all-tmns "
Arinstrong and Le FBvre, 1964
Dialkyl sulphides, and diphenyl sulphide
Rotation of one C-Me bond 10" above and the other 10' below the C-S-C plane gives a n "equivalent " conformation for EtzS agreeing with experiment; a conformation for di-n-propyl sulphide can be analogously specified. In PhzS each CeH5 is rotated about its S-C bond hy cu. 42" from the flat form
Aroney et ul., 1963b
Diphenyl-sulphoxide and -sulphone
The Ce-rings in both solutes are approximately perpendicular to the C S - C plane.
Aroney et n l . , 1963a
Thianthren and its a-dioxide, and tetroxide
Equivalent conformations, folded about Aroney et nl., 1965a the S-.S line by 140f 10' in thianthren and about 138" in its a-dioxide or cu. 130' in the tetraoxide, are deduced for these flexible ("flapping") solutes in B
Triphenyl derivatives of P, As, Sb, and Bi
I n B the phenyl rings are twisted 4" out of the planes which intersect along the lines of action of the resultant moments; $ 5 4" is 59" in Ph3P, 53' in PhsAs, 41" in I'haSb, and (probably) 23' in PhsBi
Aroney et al., 1963c
Diphenyl mercury; acetylacetonates of Be and A1
I n CT, PhzHg is linear and probably planar. The acetylacetonates of Be and A1 are nearly isotropic, consistently with tetrahedral or octahedral arrangements of the two or three bidentate ligands respectively
Armstrong rf ol., 1957
Trialkyl borates
Results correspond with solute conformations in which the C-0 bonds make cu. 74' with a planar BOs unit
Aroney et nl., 1961c
Trialkyl phosphites and phosphates
The 0-C bonds are at 70" (or 47') to the symmetry axis in (RO)sP, and a t 83" in (R0)3PO, if phosphites and phosphates have polarizability ellipsoids of revolution
Aroney et al., 1964h
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
63
In all cases the conclusions reported refer to solutes a t infinite dilution, usually in carbon tetrachloride (CT) or benzene (B)-but sometimes in dioxan or cyclohexane (the solvent is indicated when it seems likely to affect seriously the dissolved species). The majority of the examples are flexible molecules in which the energy barriers to internal rotations about bonds are not too high; for this reason the interpretations in Table 23 are stated either in terms of mixtures, or of “effective” or “equivalent” conformation (meaning by these adjectives the specifiable models which etc.) which may permit a priori calculation of the observed ,K, presultant, often, of course, approximate t o the mean or predominant structures about which rotational oscillations are occurring with temperature dependent amplitudes. The information drawn from polarizability and polarization studies seems, in general, to compare reasonably with that from other physical methods, if the natures of these methods are borne in mind. The techniques of X-ray, neutron and electron diffraction and microwave spectroscopy provide metrical structural details of the highest precision relating to the crystalline or gaseous states ; flexible molecules in solution may be expected to adopt conformations between the extremes found in the states mentioned. Thus dimethyl oxalate, diethyl terephthalate, 1,2-dibromoethane, and 1,4-dimethoxybenzene all exhibit dipole moments as solutes, but nevertheless assume trans-and therefore nonpolar-forms in their solid phases (cf. Chemical Society Tables, 1958). Accordingly it is difficult to assess the correctness of the findings summarized in Table 23; when available, results secured in other ways have been quoted in the papers cited. Some relevant facts which have recently appeared are: the microwave spectrum of methyl formate corresponds to a planar skeleton for this molecule as a gas (Curl, 1959)in disagreement with conclusions from electron diffraction measurements on other esters as well as H .C0,Me (cf. Chemical Society Tables, 1958); the heterocyclic rings in the hydrochlorides of piperidine and piperazine are chairs (RBrat, 1960); in the crystal 2,2’-pyridil has a skew configuration analogous to b e n d , furil, etc. (Ashida and Hirokawa, 1961); 4,4’-dichlorodiphenylsulphonein the plane (Abrahams solid phase holds its c6 rings a t ca. 85” to the C-S-C and Sime, 1960; Bacon and Curry, 1960); by X-ray analysis the angles of fold in thianthren, its two dioxides, and its tetroxide, are 122”-128’ (Hosoya, 1963); the long-awaited examination of 1,4-~yclohexanedione (Hassel, 1953) is nearing conclusion, Groth and Hasssl(l963) describing the molecule, in a preliminary report, as a twisted boat in which the two C=O bonds are ca. 152” to one another; Trotter (1963a, b) has lately reported that the C6rings in tri-p-tolyl- and -p-xylyl-arsines are twisted
R . J.
64
w.
LE
FAVRE
36" and 37" from models having maximum interactions of the As lonepair with the Ar r electrons, while Aroney et al. (1963c, 1965a) estimated the corresponding angle in dissolved Ph,As as 37 3". The majority of the procedures currently being used in the conformational analysis of solutes (e.g. infra-red absorption differences between conformers, optical rotatory dispersions, NMR proton shifts, etc.) are qualitative and based upon empirical observations and analogies. It is therefore claimed that the present applications of anisotropic polarizabilities, built as they are on the theoretical arguments of Lorentz, Lorenz, Langevin, Born, Gans, Debye, and others, have-where solutes are concerned-advantages both in their foundations and in the quantitatively expressible natures of the conclusions they can provide.
C. Directed Exaltations in Conjugated Systems I n addition to their stereo-structural applications, molecular polarizability ellipsoids can provide information on the anisotropy of that cc extra " deformability which causes " exaltation " of mean refraction (cf. Section IIc). The method of approach was outlined by Ingold (1953, p. 136) and operated for monosubstituted benzenes by Le FBvre and Le FBvre (1954, 1955e), Le FBvre and Rao (1958), and Le FBvre (1956, 1961a): by subtracting from the experimental values of the principal polarizabilities for CBHSXand CH3X the corresponding polarizabilities of C6H, (i.e. those of benzene minus 0.064 x om3, from Table 22) and CH, (i.e. methane minus C-H), the apparent values of bg-X, bgPx, and b$-" for the C-X bond in the aromatic and aliphatic situations were obtained. The differences, (bF-"),,,, minus (bF-X)a,kyl where i = L, T, or V, were then as in Table 24. Thus the
F
c1 Br
I CN NOz CH3
- 0'045 +O.ll C0.165 0.24 0.22 0.23 - 0,075
+ + + a
In 10-23
+
0.04 -0.015 - 0.06
+ 0.07
- 0.07
-0.13 +0.13 cm3 units.
- 0.01 - 0.07 - 0.09 -0.14
-0 . 0 3 5 - 0.04 - 0.01
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
65
exaltations of polarizability associated with substituents in aromatic combination seemed to be concentrated along those directions in which electromeric or hyperconjugative electronic displacements were expected by qualitative organo-chemical theory to occur most readily. For the molecules of Table 24 these directions are those of the resultant dipole moments, i.e. the exaltations predominantly affect the molecular bl’s, often a t the expense of the bz’s and the 6,’s. Similar conclusions were reached by Le PBvre and Le FBvre (1955b) a propos the a- and p-monohalogenonaphthalenes. Anisotropic exaltations have also been described for pyridine, quinoline, isoquinoline, furan, thiophen, and pyrrole (Le FBvre and Le FBvre, 1955d; Le PBvre et al., 1959c)-the interest of the 5-ring heterocycles, as with C6H,F, being that the mean exaltations are negative (Ingold, 1953, p. 127). I n many other cases the markedly directional nature of exaltation has been revealed incidentally while selecting that K , calc. which best fits the ,K observed (cf. refs. in Table 23, also Hacket and Le FBvre (1961) on PCl, and POCI, ; Hearne and Le FBvre (1962) on mesoionic sydnones ; Le Fbvre et al. (1963a) on quinones ; Le FBvre and Sundaram, K. M. S. (1963d) on polynuclear hydrocarbons ; Le FBvre and Sundaram, K. M. S. (1964) on indene). The strongly anisotropic exaltations in conjugated polyenes have already been mentioned (p. 52). The fact that RD computed (from Tables 5 and 7 ) for the tryptych-boroxazolidine molecule, triisopropanolamine borate, exceeds that measured by ca. 2.7 cm3 (Aroney et al., 1964c) still awaits three-dimensional analysis, as does analogous behaviour of the other highly polar co-ordinated species indicated on p. 30; these, as a class, display some of the largest negative refractivity exaltations on record.
D. Near-Isotropic Molecules The unavoidable experimental errors associated with the determination of the molar Kerr constants of solutes become proportionately larger the smaller the ,(mKz)being measured (see Le FBvre and Le PBvre, 1954); in addition t o this, mK’s close to zero present problems of interpretation. A low m(mK2) need not necessarily mean that the structure under examination is isotropic, since sometimes tll and Oz in equation (30) can be of about the same magnitude but have opposite algebraic signs (2,2’-bipyridyl, as reported by Cureton et al. (1963), exemplifies such a situation). However, it is a fact that no K , has yet been convincingly established as exactly zero ; even the quasi-spherical molecules CH4and CC1, (the former as a compressed gas, Breazeale, 1936, Kuss and Stuart, 1941, the lat,ter as a solute or pure liquid, Armstrong et al.,
66
R. J .
w.
LE FEVRE
1958) show in this way a slight apparent anisotropy ; connected phenomena are that these supposedly isotropic substances give measurable depolarization factors for the Rayleigh light scattered by them (Cabannes, 1929; Bhagavantam, 1940; Stuart, 1952). Clearly, therefore, equations (23)-(27) have some minor inadequacies. Qualitative explanations advanced prior to 1952 were reviewed by Stuart in his book of that date. Le FBvre et al. (1956) attempted an a priori quantitative treatment of anomalous anisotropy in centrosymmetric non-polar structures along lines used previously for atomic polarizations (Le FBvre and Rao, 1954, 1955). The expression reached , of a CX4 molecule involved link moments pcx, b$-x and for the K b$-X, stretching and bending force constants, effective charges on atoms, and the rates of change of b f X and b$-X with elongation or contraction of the bond C - X for which the equilibrium internuclear distance is r. Unfortunately the derivatives dldr of bg-X and bgPx are unknowntheir differences (times 1013)need to be 4.2, 0.15, and 0.72 to give the ,K’s observed for CH4, CCl,, and CBr,-but the implication is that equation (30)should, for a general case, be amended to (37)
where O3 contains the factors mentioned above and differs from 0, and Be in being temperature-invariant. Accordingly with non-polar molecules, for which O2 will always be zero, estimates of O3 can be made by extrap, versus the reciprocal of absolute temperature to olating plots of K 1/T = 0 ; in this way Le F h r e and Le FBvre (1959a)concluded that for benzene, mesitylene, and tetrachloroethylene the 03’s were almost negligible, that for p-xylene O3 might cause ca. 15% of the observed molar Kerr constant, and that for carbon tetrachloride the whole of the apparent K , must be due t o 03. Whether or not the existence of O3 terms seriously limits the overall stereochemical usefulness of the Kerr effect became, therefore, an important question. Le Fkvre and Le FBvre (1955e),when introducing equation (37) thought it did not, believing that 03’s could only be possibly significant where near-isotropic molecules were concernedsince for these the mK’s would be small and the 03:01proportions perhaps high. In such cases molecular ellipsoids computed from ,R’s observed via equations (28)or (29) might represent the structures under examination as more anisotropic than they really are. Danger of errors from this cause were foreseen as greatest with quasi-spherical types, for which 8, = 0 and in which the groups attached symmetrically to a central atom are mutually separate or flexible, and as less for other
MOLECULAR REFRACTIVITY AND POLARIZABILITY
67
non-polar types having atomic skeletons which are more rigid or so constructed that distortions do not materially change preSultant. Subsequent work has been reassuring: even for those molecules in which polar bonds are flexibly and tetrahedrally or octahedrally arranged around a central atom (ie. structures markedly displaying “vibration polarizations” and “anomalous ” apparent dipole moments, cf. Coop and Sutton, 1938) the molecular anisotropies revealed by experiment have never been large. Some relevant molar Kerr constants are in Table 25; data for further substances might be added--e.g. for various polyvinyl chlorides and bromides, polymethyl acrylates and methacrylates, TABLZ25 Apparent Molar Kerr Constants of Some Quasi-spherical Molecules 102(,Kz)
Molecules
CCI4 (liquid) CBr4 C(N02)4 C(CHzC1)a C(CHzBr)4 Be(acac)gb Al(acac)$ (in dioxan) ~
1.14 7.3 3.0 1.3 0.85
1.0 6-0
References Le FBvre et al., 1956 Le FBvre et al., 1956 Le FBvre et al., 1958b Le FBvre et aZ., 1958b Le FBvre et al., 1958b Armatrong et al., 1957 Armstrong et al., 1957
~
Examined in carbon tetrachloride except for the two com. pounds indicated. b Acetylacetonates of Be end Al.
etc. (LeFBvre and Sundaram, K. M. S., 1962a,b, 1963a, b) pentaerythrityl tetracetate (Le F h r e et al., 1958b), or tetrabutoxytitanium ( h o n e y et al., 1963e)-but with them the position is complicated by O’, as well as O1 and O,, being most probably not zero. Dielectric loss experiments have established the non-polarity of the last five solutes in Table 25. If O3 is disregarded, the relative magnitudes of the right-hand sides of equation (23) for the molecules listed are given by mK+- (molecular refraction)‘. None of the quotients exceeds that of 0.0051 for CBr,. By contrast the corresponding figures for genuinely anisotropic non-polar structures are higher (e.g. 0.041 and 0.046 for triphenylene and coronene respectively, Le FBvre and Sundaram, K. M. S., 1963d);for liquid CS2the quotient is 0.053. The case of carbon bisulphide is mentioned because Buckingham , of this and Raab (1957)raised a suspicion that about a quarter of the K compound might be attributed to a temperature-independent component. The Le F‘8vres (1959a), however, think that disagreements among the recorded Kerr constant-temperature studies on CS2 make in such a conclusion uncertain. Armstrong et al. (1958) gave oo(mK2)CSs carbon tetrachloride as 27.8 x lop1’ at 25”, whence (with O2 = OS = 0)
68
R. J.
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LE F ~ V R E
10Z3bl= 1.31, and 10Z3(b2= b3) = 0.56. Such semi-axes are in harmony with the shape and dimensions of this molecule; they actually imply a slightly lower anisotropy than Stuart and Volkmann (1933) reported for CS2 as a gas at 56.7”-a change easily explicable as a “solvent effect,” if one takes as valid the views of Krishnan and Raman (1928), Krishnan (1929), Mueller (1936), Le Fevre and Rao (1955), Armstrong et al. (1958) concerning properties of a medium and the nature of the cavity occupied by a solute particle therein. Predictions that temperature-invariant factors contribute to the observed Kerr constant 3 (cf. Section 111,B) are not new. Voigt (1901) supposed that normally isotropic oscillators become anisotropic in an externally applied field and that, as a consequence, the polarizabilities of the dielectric in directions parallel and perpendicular to the field cease to be the same and double refraction results. Born and Jordan (1930) developed, via the quantum theory, a three-term expression to describe electric birefringence; two of these terms had dependence respectively on 1/T and 1/T2-as have Bland O2 in equations ( 2 5 ) and (26); the third was independent of T but, as Kronig (1930) pointed out, the information required for its a priori calculation was unfortunately not available. Both the Voigt effect and the Born-Jordan constant will-except near absorption lines-be small (Langevin, 1910 ; Neugebauer, 1933) ; their interest lies in the fact that they are predicted for isotropic molecules and should be found even with monatomic gases. More recently a novel approach to the problem has been made by Buckingham and Pople (1955), using the concept of hyperpolarizability.
V. HYPERPOLARIZABILITY In considering mechanisms by which a medium might display various polarizabilities (viz. deformations of electron distributions within atoms, displacements of atoms from their normal relative positions in molecules, and alterations of average orientations of molecules in bulk assemblages) induced polarities have usually been taken as having straight-line relationships with applied electric fields, and quantitative connections between polarizability and electrical and optical properties developed on this basis. Fundamentally such treatments involve an approximation that the energy of a molecule in a field can be represented as a function of no higher than the second degree in the field components (so that polarization, which is-a energy18 field, is proportional to the first power of the field, cf. Debye, 1929, p. 32). Where polarizability by orientation is concerned it has been established by experiment that dielectric constants E are changed, but only
MOLECULAR REFRACTIVITY AND POLARIZABILITY
69
slightly, by the imposition of fields considerably greater than those commonly used in such measurements (Debye, 1929, quotes results from Herweg, Kautzsch, and others up to 1928, cf. also Gundermann, 1930; Bottcher, 1952, p. 193; Smyth, 1955, p. 88; refs. to more recent work are cited by Kielich and Piekara, 1959, who have themselves contributed notably to this subject, both theoretically and practically). The alterations of E, although negligibly small from the viewpoint of ordinary dipole moment determination, nevertheless imply a nonrectilinear dependence of induced polarization upon field intensity. The possibility that electronic deformations in atoms and molecules might also have a curved relationship with field intensities has been on record for some time. The matter was raised qualitatively by Sutton (1946). Matossi and Mayer (1946, 1948), Gladisch and Senftleben (1947), and Sewell (1949))proceeding quantitatively, assumed in effect that b in equation (20) should for the general case be expanded to (b, + c‘E2+ . . .), i.e. that polarizability should correctly be shown as an increasing function (c‘ being a small positive constant) of the field intensity E . Calculations, using perturbation methods, by Coulson et al. (1952) suggested that with benzene the “low-field” polarizability bo is unlikely to be significantly augmented by fields below about los V/cm, so that direct observations of hyperpolarizability would require the application of voltages well above those known to cause dielectric breakdown. Buckingham and Pople (1955) have modified the Langevin-Born equations for electric birefringence to allow for a field-dependent polarizability such as (38) : pinducetl = b, E + (1/2)aE2+ ( l / 6 )cE3 (38) The final result, written as the molar Kerr constant (equation 28) of a gas a t low pressure, contains the “anisotropy” and “dipole” terms O1 and O2 (equations 25 and 26), already provided by the classical treatment, plus a third term which should be invariant with temperature. This third term has particular interest when the apparent molar Kerr constants of spherically symmetric molecules, for which a = 0, are being considered: if p = 0, and b, = b 2 = b,, then 8, and O2 both become zero, and the observed K , is simply
K , = 4nN~/81 (39) so that an experimental route to the hyperpolarizability constant c in equation (37) is opened. Values of c, obtained by multiplying the ,K’s of Table 25 by 10.7 x lopz4,range from 9.1 x to 78-1 x e.s.u.; for carbon tetrachloride c is 12.2 x The “low-field” polarizability of the lastnamed molecule should not-by (38)-be detectably altered by fields
*
70
R . J.
w.
LE FEVRE
less than about lo7V/cm; thus through a different argument one reaches much the same conclusion as did Coulson et al. (1952). Gradients exceeding 6 x l o 4 V/cm are seldom used in the observation of Kerr effects; to begin to see signs of saturation in commonly employed fields, therefore, quasi-sphericalmolecules with mK’sof more than 25,000 x would be required; although such may exist among randomly coiled polymer solutes none has yet been examined for voltage dependence. For small non-polar molecules and ordinarily attainable voltages the birefringences reported in the few cases studied have appeared to be proportional to the squares of the applied fields (Chaumont, 1916; Beams, 1931; Hootman, 1933; Le Pevre et al., 1956) as required by Kerr’s “law” (Kerr, 1880, 1882). By equation (39) even a monatomic gas might show an apparent molar Kerr constant, and indeed electric birefringences noted by Kuss (1940) with argon under 350 atmospheres pressure appeared to correat 25” and 1 atmosphere; if so, then c spond to an ,K of 0.07 x would be ca. 0.7, x I n order of magnitude such a Kerr effect is reconcilable with scattered light-depolarization data earlier found by Cabannes, Parthasarathy, and Ananthakrishnan (cf. Bhagavantam, 1942, p. 54); nevertheless Kuss himself (1940, p. 31) records his measurement with reservations due to a 0.007 yocontent of nitrogen in the argon used and possible errors in the pressure extrapolation calculations. Confirmation and extension of Kuss’ pioneer work is highly desirable : from equations (37) and (39) c should be 4.50,, yet, obviously, bond stretchings and deflections, thought to contribute to 9,, cannot be invoked for the inert gases; if, therefore, argon really displays double refraction in an electric field, equation (37) needs further amendment by the insertion of a c-containing fourth term; even so, however, the statement that the molecular distortions presumed to underly 0, ((could well be part of the mechanism operative in the phenqmenon of hyperpolarizability” (Le FBvre and Le FBvre, 1955e, p. 310) would not be thereby invalidated. Actually several mechanisms may simultaneously be active. As Coulson et al. (1952) remark, the idea of hyperpolarizability “is implicit in discussions of the inductive effect of polar groups attached to conjugated systems, and of the polarizing effect on such systems of polar reagents, such as have been given by Wheland and Pauling, following Lapworth, Robinson and Ingold; for in these it has been suggested that, superimposed on the classical polarization, is a non-classical one involving the electrons in r-type orbitals. ” Since fields in the neighbourhoods of ions or dipoles must enormously surpass those attainable by experiment (e.g. at points 3 A distant from a monovalent ion or a doublet of
MOLECULAR REFRACTIVITY
AND POLARIZABILITY
71
3 x lop1*e.s.u. the fields may be about 16 x l o 7 or 8 x l o 7 V/cm respectively), hyperpolarizabilities should not be ignored when applying electrostatic considerations to questions of reactivity and reaction kinetics ; hitherto, “low-field ” polarizabilities have usually been used in approaches of this kind (cf. Branch and Calvin, 1941; Waters, 1942; Moelwyn-Hughes, 1947; Remick, 1949; Ingold, 1953; Hine, 1956). With reactions in solution, solvation is sometimes more important than the dielectric constant of the medium. Solvation is essentially an electrostatic process. “When an ion or polar molecule is put into a solvent having polar molecules, it orients and attracts the molecules of the solvent, thereby doing electrostatic work; and work done, means energy lost, so that the system becomes more stable. The energy of solvation of an ion in a polar solvent can be very large, often of the order of the strength of a covalent bond” (Ingold, loc. cit., p. 345). Of thirty “basic principles” listed by Remick (1949, Appendix l ) , widely applicable throughout organic chemistry, a t least seven directly involved polarizability effects and in these the induced moments were apparently assumed to be proportional to the first power of the field. However, the relations between chemically inferred polarizabilities (electromeric and inductomeric processes) and those from physical measurement (refractivity data) have so far been qualitative only; more accurate connections may follow improved knowledge of the hyperpolarizability constants, shown as a and c in equation (38). Information on these is now beginning to accumulate. For non-polar molecules with centres of inversion a is zero, so that c for a structure of this symmetry should be accessible through the molar Kerr constant. A few estimates of a’s have been made from studies of the molecular refraction of imperfect gases, and from the depolarization of the (Rayleigh) light scattered by dense media. Credit for recognizing these sources is due to Buckingham (1956a, b, c) and Buckingham and Stephen (1957), although alternative approaches to the problem by Kielich, and Kielich and Piekara, described in papers from 1958 onward, have yielded numerically similar results. Buckingham ( 1 9 5 6 ~ )expanded the molecular refraction of a compressed gas in powers of the molar volume V : = A R + B R / V + C ~ / V Z ... + (40) and called A , , BIL,CR, . . . the first, second, third, . . . refractivity virial coefficient respectively. Thus
A,
=
lim
V+,R
=
4.rrNb0/3
where bo is the mean polarizability of an isolated molecule, and the
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subsequent coefficients describe deviations from ideal behaviour of the refractivity of the substance; BE accounts for the interactions of two molecules of an imperfect gas, CR for three, etc. The long expression deduced by Buckingham for B , contains b,, a, and c, together with terms relating to the permanent, low-field, dipole moment of the species concerned and to the (Stockmayer) intermolecular potential function assumed; therefore, when bo and c are known, a can be extracted from experimental values of B,. Buckingham and Stephen (1957) developed a general formula for the depolarization of light scattered by molecules which are small compared with the wavelength of the incident light and which range from non-polar spheres to polar ellipsoids; the argument incorporated the notion of hyperpolarizability, indicated here by (38). For polar liquids a substantial part of the depolarization appeared to depend upon the leading hyperpolarizability tensor describing the initial departure from a straight-line relationship between the dipole moment and the field strength. Buckingham and Stephen, from data in the literature, predicted that a for chloroform should be of the order + l O W 9 e.s.u., and for methane -0.21 x e.s.u. Blythe et al. (1960) have studied the variations with pressure of the refractive indexes of four polar gases and, by assuming c to be about 10 x arrive a t the following approximate values for i030 a :
CH3F
-2
CH3C1 - 8
NH3
so,
-7
-12
Everett and Munn (1963), using a similar experimental method, have e.s.u. ; they commore recently reported a for triethylamine as ment that, although high accuracy is not claimed and c is ignored, the interest of the estimate lies in its magnitude and positivity, in which respects it differs from the data of Blythe et al. Kielich (1962), from light e.s.u., i.e. as also scattering, deduced a for chloroform as 11.2 x positive; moreover, he has given the first statement regarding the directional character of hyperpolarizability by claiming that in CHCl3 the mean a just quoted corresponds to a , = 9-6 x and a2 = 12.1 x 10-29e.s.u., where a1 and a, are measured respectively along and perpendicular to the axis of rotational symmetry. The physical meaning of the algebraic sign of a is that in the context of equation (38) the induced dipole moment of a molecule is increased or diminished, as a is positive or negative, by the field due to neighbouring molecular dipoles -a process which obviously may be a function of molecular shape in relation to polarity.
MOLECULAR REFRACTIVITY AND POLARIZABILITY
73
That polarizability is not independent of density has been suspected for years: Kirkwood (1936), by expanding refractivity in powers of the molecular polarizability, showed that the leading term causing deviations from the value 4n-Nbo/3 is in ( l ~ ,for ) ~spherically symmetric molecules. Studies of the effects of collisions on the mean polarizabilities of molecules (cf. Cole et nl., 1960) have relevant theoretical interestpossibly also from the viewpoint of reaction mechanisms. At the near-contact distances which must occur between reagents and reactants, fields of extreme intensity may arise ; in these, as Coulson et al. (1952)say, the chance of a molecule becoming ionized “is so great that the whole concept of polarizabiIity loses it8ssignificance. ”
VI. ASPECTSOF POLARIZABILITY REQUIRING INVESTIGATION The fact that moleculas refractions depend on wave-length (seeSection 11, E) implies similar relationships among mean polarizabilities. The degrees to which anisotropies of polarizability are liable to dispersion is, however, not yet clear from experiment. Only in relatively few cases has the variation with X of the Kerr constant B (cf. p. 46) been examined (Havelock, 1909; McComb, 1909; Skinner, 1909; Lyon, 1915; Szivessy, 1920; Becker, 1925). Normally Havelock’s equation (40) appears satisfactorily to represent the observations recorded by a given worker,
B
=
h(n2- 1)2/nX
although there are divergences among the B’s quoted by different authors. The “constant” h is, in general, small; Szivessy (1920) found it to have a temperature coefficient (e.g. for nitrobenzene h was 141.3 x a t 6” and 111.1 x a t 24”). McComb (1909) reported Bx’s for twelve liquids over the wavelength range 440-66Omp; the magnitudes of the dispersions noted are illustrated by quotients such as 1-82,, 1.66, 1.60, 1.80, and 1.48 for B44o/B660 respectively with carbon disulphide, benzene, chloro- and nitro-benzenes, and chloroform. I n the molar Kerr constant, given by equation (as),the dispersion of B is partially compensated by that of n and the consequential changes in molecular anisotropy are less than might be expected a t first glance. The much investigated “standard” electric birefringent liquid, carbon disulphide, provides an example : the International Critical Tables (Vol. VII, p. 110) list B’s a t 20” for fifteen wavelengths between 440 and 660mp ; corresponding refractive indices, density and dielectric constant, are in the compilation of Timmermans (1950); R, is 20.39 em3
74
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LE F ~ V R E
(Armstrong et al., 1958); the following values therefore emerge for the two extreme A’s mentioned:
Amp
10%Kliqnid
440
26.73
1.164
0.630
660
23-44,
1.120
0.652
102,(b2 = b,)
The quantities 8, and 8, in equation (30) are commonly accepted as independent of A. While it can be argued that a bulk liquid is an unfair test of this assumption) the small apparent alteration of anisotropy with carbon disulphide warns us that similar phenomena may occur when m(mK2)’s are determined for solutes. No investigations into this particular problem are yet on record. Moreover, knowledge of the dispersion of B in the nltra-violet and infra-red spectral regions-once started but not pursued by Dierkesmann and Szivessy (1929) and Ingersoll(l931)could usefully again be sought, modern photometric techniques obviating many of the earier difficulties. Buckingham (1962) has recently drawn attention to the potential value of studies of electric birefringences of media in the vicinity of electronic absorption bands. (‘Anomalous’’ dispersion of double refraction in sodium vapour under high field intensities near the D-lines was recognized by Ladenburg about 1926 (cf. Wood, 1934, pp. 742-760), but apart from the experiments of Charney and Halford (1058)-on nitro-benzene a t infra-red frequencies associated with weak vibrational overtones-no organic liquid, solution, or gas seems to have been so examined. Buckingham (1962; see also Buckingham and DOWS,1963) has now developed a quantitative theory for the Kerr effect as the measuring light approaches and passes an absorption band. He predicts that the magnitude of B will be proportional to the square of the transition dipole moment and be determined by the moments and polarizabilities of the relevant electronic states. Close to an absorption line the rapidly changing Kerr effect may be a million times that in transparent regions of the spectrum. With polar species, qualitative features of the dispersion, e.g. whether B rises or falls as the frequency increases towards the resonance point, should be governed by the direction of the transition dipole moment with respect to molecular axes. When happliedis around A,, the temperature-independent contributornormally numerically unimportant, see equation (39)-can become dominant, since it has a (vapplied- vresonanJ3 dependence compared with the (vappued- v,,s,n,nt)-l dependence of the dipole orientation term. Buckingham and Dows suggest therefore that the dispersion of the Kerr effect offers better possibilities than the straightforward Stark effect for ((
M 0L E C U L A R R BFR A C T I V I T Y A N D P 0L A R I Z A B I L IT Y
75
measuring the dipole moment and the polarizability of an electronically excited molecule, and may also provide a means of obtaining accurate transition momenta, ’’ reliable figures for which have been hitherto unavailable. Further advantages of benefit to structural chemistry and spectroscopy are outlined in Buckingham’s 1962 paper, wherein apparatus required for the practical realization of his predictions is also suggested.
V l l . MISCELLANEOUS APPLICATIONS OF POLARIZABILITY Molecular or atomic polarizabilities, either as such, or as refractivities or refractive indices, enter very many of the quantitative expressions describing the physical and chemical behaviour of matter, e.g. equations for inter-molecular “dispersion ” energies (cf. Glasstone (1940), Stuart (1952), Rowlinson (1954), for reviews), for various phenomena involved in reaction kinetics (cf. Moelwyn-Hughes, 1947; Ingold, 1953), for reciprocal forces between anisotropic molecules (De Boer, 1936), etc. In particular, polarizabilities become directly concerned whenever electromagnetic radiation interacts with material media. Thus they are often cited in spectroscopic literature (cf. Bowen, 1943; Maccoll, 1947; Braude, 1955) and are currently being invoked in connection with solvent effects-frequency shifts and intensity changes-on infra-red spectra (cf. Williams, 1961; Hallam, 1963); intensities of Raman lines depend on derivatives of polarizabilities with respect to internuclear distances (cf. Long, 1953 ; Woodward, 1956; Krushinskii and Shorygin, 1961) while intensities of Rayleigh scatterings depend on &,-hence the interest in Raman-Rayleigh intensity ratios, which can give information on the rates of change of polarizability as atoms in molecules vibrate about their equilibrium positions (for examples, including CC14and CH4, and refs., see Rao (1940), Crawford et al. (1953); also Bhagavantam (1940), and Placzek (1934), regarding theory). Anisotropic molecular polarizabilities appear in expressions for the Cotton-Mouton (magnetic birefringence) and Faraday (magnetic rotation) effects (cf. Beams (1932), Cotton (1932), or Buckingham and Pople (1956), on the former, and de Mallemann (1926), on the latter). I n addition, they have been utilized in treatments of natural optical rotatory power (de Mallemann, 1930; Kirkwood, 1937; Brewster, 1959; cf. Kuhn, 1952; McKenna, 1959; Mason, 1963; for historical accounts and reviews of the subject). Brewster has combined earlier empirical and theoretical approaches by describing a centre of optical activity as an asymmetric screw pattern of polarizability, and draws therefrom correlations between screwhandedness (rationally assigned on the basis of experimental atomic
76
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polarizabilities) and observed optical rotations (or increments thereto for a particular centre). By inference, optical rotatory dispersion (cf. Djerassi, 1960) must also be a polarizability-based phenomenon. Tinoco’s work with helical macromolecules has emphasized that the rotatory power of a molecule is itself an anisotropic property (Hammerle and Tinoco, 1956; Tinoco, 1957, 1959; Tinoco and Woody, 1960) and accordingly should be alterable by applying external electric fields. Such effects, although not noticeable with small molecules (for which Eckert and Le Fkvre, 1961, found that electric birefringences could be observed normally, and without detectable changes in [ c c ] ~ ) have, in fact, been successfully demonstrated with the helical macromolecule poly-y-benzyl-L-glutamate dissolved in ethylene dichloride (Tinoco, 1959). The specific rotatory powers parallel and perpendicular to the helical axis prove to be notably different-so much so that Tinoco remarks that the anisotropy of optical activity “with its simple wavelength dependence should be a better characteristic of helical polypeptides than the dispersion of the average optical activity. ” Tinoco’s choice of solute was made in the light of investigations on the Kerr effects of macromolecules in media often having appreciable conductivities. The technique necessary was devised nearly simultaneously in Strasbourg by Benoit (1950) and in Berkeley by O’Konski and Zimm (1950), and has since been operated by two of these and other workers (cf. Tinoco, 1955; Applequist and O’Konski, 1956; Field and Norman, 1957; Tinoco and Yamoaka, 1959; O’Konski et al., 1959; Allais, 1962; Itzhaki, 1962; Ingram and Jerrard, 1962). I n principle a square-wave voltage pulse, of around lo-’ see duration, is applied to a solution in a Kerr cell and the short-lived birefringence detected photometrically, displayed on a cathode-ray oscilloscope, and recorded photographically. The theory involved in interpreting the traces obtained was originally set out by Beiioit (1950); subsequent extensions occur in some of the other papers quoted. Information on the polarizabilities, apparent polarizations, and shape-factors of the dissolved particles thus becomes available. I n particular, rotary diffusion constants, and hence estimates of axial ratios, can be derived from the rates at which Kerr effects decay after the voltage action has ceased. With anisotropic macromolecules the birefringence is often large, in harmony with the high apparent moments attributed to proteins, nucleic acids, and viruses in aqueous solutions (cf. Jungner and Jungner, 1952; Smyth, 1955, Chap. XIII). For actual dichroism to be observable with coloured solutes of these magnitudes and polarities under intense fields would not be unexpected (Platt, 1961; Bergmann and O’Konski, 1962). Other interesting reactions between anisotropically polarizable
MOLECULAR REFRACTIVITY AND POLARIZABILITY
77
molecules and external fields are involved in the direct measurement of the quadrupole moment of carbon dioxide (Buckingham and Disch, 1963) and in the determination of the absolute signs of spin-spin coupling constants in the nuclear magnetic resonance spectra of polyatomic molecules (Buckingham and McLauchlan, 1963) ; the second of these requires the imposition of a voltage gradient across the sample in an otherwise standard n.m.r. spectrometer, and under such circumstances the emergence of field-induced overtones would constitute a significant advance in n.m.r. methodology (Buckingham, 1963). Anisotropic shielding effects in n.m.r. spectra could be better explained were more information available on the anisotropies of diamagnetic susceptibility for the commoner bonds contained in organic molecules (cf. Jackman, 1959). Ziircher (1962) has lately shown that this can be deduced from knowledge of the corresponding electronic polarizabilities. Theoretical considerations led Kirkwood (1932) and Vinti (1932) to devise an equation connecting polarizability with susceptibility, and this, combined with calculations by Gans and Mrowka (1935), allows the correlation of the diagonal elements of the electron polarizability tensor (principal polarizabilities) with the diagonal elements of the magnetic susceptibility tensor (principal susceptibilities). Zurcher, using the bond polarizabilities shown, arrives a t numerical values for xL and xT (the longitudinal and transverse diamagnetic susceptibilities respectively) as foliows :
xf'c
= - 2-48 x
-&'" =
x:'"
- 4.54 x
= - 3.80 x
cm3/mole from be'"
=
1.12 x
cm3
cm3/molefrom bg'H
=
0.43 x
om3
cm3/mole from b:'"
=
0-83 x
om3
The b's quoted (from Mortensen and Smith, 1960) represent the two bonds as being more anisotropic than they appear in Table 22, but Ziircher comments that the Mortensen-Smith polarizabilities should be taken with caution. He stresses that his own calculations have an approximate character and involve quantities and equations of varying precision. Nevertheless their interest lies in the indication that the directions of greatest diamagnetic susceptibility in bonds should be perpendicular to those of greatest electronic polarizability and viceversa. Such an inverse relationship is in accord with empirical (BothnerBy and Naar-Colin, 1958) and theoretical (Pople, 1957) deductions to date; rough predictions of the shielding of a proton by a remote bond
78
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LE FEVRE
(i.e. a n electron group) can therefore be made via McConnell’s expression (McConnell, 1957). Polarizabilities are, of course, responsible for the birefringence which appears (or alters) whenever the orientations of anisotropic molecules in an assemblage are de-randomized (or changed) by any disturbing force. The strain-birefringence relations, stress-optical coefficients, etc., encountered among the phenomena of photo-elasticity are explicable on this basis (Griin and Kuhn, 1942; Treloar, 1956), as are the Maxwell effects exhibited by liquids and solutions flowing over stationary surfaces, i.e. when subjected to the shearing forces associated with velocity gradients (cf. Bhagavantam, 1940; Edsall, 1942 ; Jerrard, 1959; Scheraga and Signer, 1960). The ordered array of molecules in a crystal will usually-if their anisotropic polarizabilities and their dispositions relatively to the crystal axes are known-permit the calculation of the principal refractive indices of the crystal from a knowledge of its density (cf. Hartshorne and Stuart (1960), Bragg (1924); Bunn and Daubeny (1954), Le FBvre and Le FBvre (1955b), Aroney et al. (1964a), give examples in which, by the reversal of this procedure, molecular polarizabilities are deduced from observed refractive indices). The involvement of polarizability in light scattering by small molecules has already been mentioned; its role where large molecules are concerned is also important, although emphasis is usually rather more on depolarization factors in the former cases and on measurements of intensities in the latter (cf. determination of weight-average molecular weights of macromolecules by the photometric method introduced by Debye (1944, 1947)). The amplitudes of the electric vectors in the light beams commonly used in all scattering experiments are small, but Buckingham (1956a) has made the unexpected theoretical prediction that with very intense light (of energy densities of the order lo5 W cm-2) an isotropic medium composed of anisotropic molecules may become double refracting, through a tendency for the molecular axes of greatest polarizability to set themselves a t right-angles to the direction of propagation; the medium should thus appear to acquire an optic axis parallel to the light ray. As yet, the effect awaits experimental detection ; flash techniques are suggested by Buckingham. An equally surprising suggestion, which further underlines the widespread applicability of polarizability, is that the examination of scattering intensities and of Raman displacements from plasmas irradiated by intense laser beams in millisecond bursts may-by diagnosing the molecular and ionic species present-contribute to the solution of “re-entry ” problems facing plasma-sheathed hypersonic space vehicles (cf. Hughes, 1962; Fiocco and Thompson, 1963; Urtz, 1964).
MOLECULAR R E F R A C T I V I T Y A N D POLARIZABILITY
79
REFERENCES Abrahams, S. C., and Sime, J. G. (1960). Acta Cryst. 13, 1 . Allais, M. -L. (1962). J . Chim. phys. 59,873. American Petroleum Institute (1953). “Selected Values of Physical a n d Thermodynamic Properties of Hydrocarbons and Related Compounds ”, Carnegie Press, Pittsburgh. Anonymous (1911). Chem. News 103,84. Applequist, J. B., a n d O’Konski, C. T. (1956). Nature 178, 1464. Arai, T.,Ishiguro, E., Lotani, M., and Mizushima, M. (1952). Proc. Phys. SOC. (London)65,178. Armstrong, R. S., and Le FBvre, R. J. W. (1964). Australian J . Chem. 17,24. Armstrong, R.S., Le FBvre, C. G., a n d L e FBvre, R. J. W. (1957). J . Chem. SOC.371. Armstrong, R. S., Aroney, J. J., L e FBvre, C. G., L e FBvre, R. J. W., and Smith, M. R. (1958). J . Chem.Soc.1471. Armstrong, R. S., Aroney, M. J . , a n d L e FBvre, R. J. W. (1962). Ausfralicrn J . Chern. 15,703. Aroney, M. J., and Le FBvre, R. J. W. (1956). J . Chem. SOC.2775. Aroney, M. J., a n d Le FBvre, R. J. W. (1958a). Proc. Chem. SOC.82. Aroney, M. J., and L e FBvre, R. J. W. (1958b). J . Chem. SOC.3002. Aroney, M. J., a n d Le FBvre, R. J. W. (1960a). J . Chem. Soc. 2161. Aroney, M. J., and L e FBvre, R. J. W. (1960b). J . CIiem. SOC.3600. h o n e y , M. J., Le FBvre, R. J. W., and Parkins, G. M. (1960a). J . Chem. SOC.2890. Aroney, M. J., L e FBvre, R. J. W., and Shu-Sing Chang (1960b). J . Chem. SOC. 3173. Aroney, M. J., L e FBvre, R. J. W., a n d Sundaram, K. M. S. ( 1 9 6 0 ~ ) J. . Chem. SOC.1812. Aroney, M. J., Chia, L. H. L., and L e FBvre, R . J. W. (1961a). J . Cikern. SOC.4144. Aroney, M. J., Izsak, D., a n d L e FBvre, R.J. W. (1961b). J . Chem. SOC.4148. Aroney, M. J., Le FBvre, R. J. W., and Lenthen, P. M. ( 1 9 6 1 ~ ) J. . Chem. Soc. 4140. 1407. Aroney, M. J.,Izsak, D., and Le FBvre, R. J. W. (1962a). J . Chem. SOC. Aroney, M. J., Izsak, D., and L e FBvre, R. J. W. (1962b). J . Chem. SOC.3997. Aroney, M. J., L e FBvre, R. J. W., and Saxby, J. D. ( 1 9 6 2 ~ ) J. . Chem. SOC.2886. 4450. Aroney, M. J., Fisher, L. R., and L e FBvre, R. J. W. (1963a). J . Chem. SOC. Aroney, M. J., Le FBvre, R. J. W., and Saxby, J. D. (196313). J . Chem. SOC.1167. Aroney, M. J., L e FBvre, R. J. W., and Saxby, J. D. C. ( 1 9 6 3 ~ ) .J . Chem.Soc. 1739. Aroney, M. J.. L e FBvre, R . J. W., and Saxby, J. D. (1963d). J . Chem. SOC. 4938. Aroney, M. J., L e FBvre, R. J. W., a n d Saxby, J. D. (1963e). Australian J . Chem. 16,504. Aroney, M. J., L e FBvre, R. a. W., and Singh, A. N. (1963f). J . Chem.Soc. 5111. Aroney, M. J., Corfield, M. G., and Le FBvre, R. J. W. (1964a). J . Chem. SOC. 648. Aroney, M. J., Corfield, M. G., and L e FBvre, R. J. W. (1964b). J . Chem. SOC. 2954. Aroney, M. J.,Le FBvre, R. J. W., a n d Saxby, J. D. ( 1 9 6 4 ~ ) .Australian J . Chem. 17,289. Aroney, M. J., L e FGvre, R. J. W., a n d Saxby, J. D. (1964d). Can. J . Chem. 42, 1493. Aroney, M. J., Le FBvre, I<. J . W., and Rasby, J . D. (1964e). AustraZianJ. Chem. 18, No. 4.
80
R . J.
w.
LE F&VRE
Aroney, M. J., Le FBvre, R. J. W., and Singh, A. N. (1964f). J . Chem. SOC. 3523.
Aroney, M. J . , Chen, C. -Y., Le Fbvre, R. J. W., and Saxby, J. D. (1964g). J . Chem. SOC.4269. Aroney, M. J., Chia, L. H. L., Le FBvre, R. J . W., and Saxby, J. D. (196411). J . Chem. SOC.2948. Aroney, M. J., Le FBvre, R. J. W., and Saxby, J. D. (1965a). J . Chem. SOC. 571.
Aroney, M. J., Le FBvre, R. J. W., and Singh, A. N. (196513). J . Chem. SOC. 564.
Arshid, F. M., Giles, C. H., McLure, E. C., Ogilvie, A., and Rose, T. J. (1955). J . Chem. SOC. 67. Arshid, F. M., Giles, C. H., Jain, S. I<., and Hassan, A. S. A. (1956a). J . Chem. SOC.72. Arshid, F. M., Giles, C. H., and Jain, A. 8. A. (195613). J . Ghem. SOC. 659, 1272. Ashida, T., and Hirokawa, S. (1961). Acta Cr?yst.14, 774. Auwers, K. von (1911). Chem. Ber. 44, 3757. Auwers, K. von (1924). Ann. Chem. (Liebig’s)437, 63. Auwers, K. von (1935). Chem Ber. 68, 1635. Auwers, K. von, and Bonnecke (1914). “Tabellen zur Berechnung der Theoretischen Molrefraktionen Organischer Verbindungen ”, Berlin. Auwers, K. von, and Eisenlohr, F. (1910a). Chem. Ber. 43, 806, 827. Auwers, K. von, and Eisenlohr, F. (1910b). J . prakt. Chem. 82, 65. Auwers, K. von, and Eisenlohr, F. (1911). J.prakt. Chem. 8 4 , 3 7 . Auwers, K. von, and Eisenlohr, F. (1913). 2. phys. Chem. 83, 429. Backer, H. J., and Stienstra, F. (1932). Rec. traw. chim. 51, 1197. Backer, H. J., and Stienstra, F. (1933). Rec. traw. chim. 52, 912, 1033. Backer, H. J., and Stienstra, F. (1935). Rec. traw.chim. 54, 607. Bacon, G. E., and Curry, N. A. (1960). Acta Cryst. 13, 10. Badoz, J. (1956). J . Phys. Radium 17, 143. Barton, D. H. R. (1956). Chem. & I n d . (London), 1136. Bauer, S. H., and Rutner, E. (1960). J . Am. Chem. SOC. 82,298. Bauer, N., Fajans, K., and Lewin, S. Z. (1960). I n “Physical Methods of Organic Chemistry”, Ed. by A. Weissberger, 3rd edn., Interscience Publ., New York, Part 11, Chap. XVIII. Beams, J. W. (1931). Phys. Rev.37, 781. Beams, J. W. (1932). Rev. Mod. Phys. 4, 133. Becker, G. (1925). Ann. Physik 76, 849. Bellamy, L. J. (1955). J . Chem. SOC. 4221. Bellamy, L. J., and Beecher, L. (1954). J . Chem. SOC.4487. Bellamy, L. J., and Branch, R. F. (1954). J . Chem. SOC. 4491. Benoit, H. (1950). “Contribution B 1’6tude de l’effet Kerr present6 par les solutions &lubes de macromolecules rigides ”, Thesis, University of Strasbourg, Serie E, No. 93. Benoit, H. (1951). Alzn.phys. 6, 561. Benoit, H. (1952). J . Chim. Phys. 49, 517. Bergmann, K., and O’Konski, C. T. (1962). J . Chew&.Phys. 37, 1573. Bhagavantam, S. (1940). “Scattering of Light and the Raman Effect”, Andhra University, Waltair. Bhagavantam, S. (1942). “Scattering of Light and the Raman Effect”, Chemical Publg. Co., Brooklyn, New York.
MOLECULAR REXRACTIVITY
A N D POLARIZABILITY
81
Bielenberg, W. (1933). Phywik. 2 . 3 4 , 632. Bird, R. B., Curtiss, C . F., and Hirschfelder, J. 0 . (1954). “Molecular Theory of Gases and Liquids”, John Wiley, New York. Blythe, A. R., Lambert, J. D., Petter, P. J., and Spoel, H. (1960). Proc. Roy. SOC.A 255, 427. Bode, H. (1930). 2. physik. Chem. B 6 , 251. Bolton, H. C. (1954). Trans. Faraday SOC. 50, 1261, 1265. Born, M. and Heisenberg, W. (1924). 2.Physik 23, 388. Born, M., and Jordan, P. (1930). “Elementare Quantenmechanik”, J. Springer, Berlin. Bothner-By, A. A., and Naar-Colin, C. (1958). J . Am. Chem. SOC.80, 1728. Bottcher, C. J. F. (1939). Physica 6 , 59. Bottcher, C. J. F. (1946). Rec. trav. chim. 64, 14, 20, 39, 91. Bottcher, C. J. F. (1952). “Theory of Electric Polarisation”, Elsevier, Amsterdam. Bowen, E. J. (1943). Ann. Repts. Progr. Chem. 40, 12. Bragg, W. L. (1924). Proc. Roy. SOC. 105, 370. Bramley, R., and Le FBvre, R. J. W. (1960). J . Chem. SOC.1820. Bramley, R., and Le FBvre, R. J. W. (1962). J . Chem. SOC.56. Bramley, R., Le FBvre, C. G., Le FBvre, R. J. W., and Rao, B. P. (1959). J . Chem. Soc. 1183. Branch, 0. E. K., and Calvin, M. (1941). “The Theory of Organic Chemistry”, Prentice-Hall, New York. Braude, E. A. (1955). I n “Determination of Organic Structures by Physical Methods”, ed. E. A. Braude and F. C. Nachod, Academic Press, New York. Rev. 49, 625. Breazeale, W. M. (1936). P~HJS. Bredig, M. A., and Koch, F. K. V. (1934). 2.physik. Chem. B 24, 187. Bredig, M. A., Hirsch, T. v., and Wiist, J. (1934). 2. phys. Chem. B 24, 177. Brewster, J. H. (1959). J . Am. Cliem. SOC. 81, 5475. Brown, R. F. (1961). J . Am. Chem.Soc.83, 36. Bruce, C. W. (1933). Phys. Review 44, 682. B r a l , J. W. (1880). Ann. Chem. (Liebig’s)200, 139; 203, 1, 255. Briihl, J. W. (1886a). Ann. Chem. (Liebig’s)235, 1. Briihl, J. W. (188613). Ann. Chem. (Liebig’s)236, 233. Briihl, J. W. (1891). 2. physik. Chem. 7 , 140. Briihl, J. W. (1895). 2. physik. Chem. 16, 193,226. Briihl, J. W. (1896). 2.physik. Chem. 21, 385. Briihl, J. W. (1897). 2.physik. Chem. 22, 373. Briihl, J. W. (1898). 2. physik. Chem. 25, 576. Briihl, J. W. (1906). Proc. Roy. I n s t . cf. Brit. 18, 122. Briihl, J. W. (1907). Chem. Ber.40, 878, 1153. Briihl, J. W. (1908). Chem. Ber. 41, 3712. Buckingham, A. D. (1956a). Proc. Phys. SOC.69, 344. Buckingham, A. D. (1956b). Trans. Paraday SOC. 52, 611. Buckingham, A. D. ( 1 9 5 6 ~ ) Trans. . Faraday SOC.52, 747. Buckingham, A. D. (1962). Proc. Roy. SOC.A . 267, 271. Buckingham, A. D. (1963). Proc. Chem. SOC.p. 336. Buckingham, A. D., and Disch, R. L. (1963). Proc. Roy. SOC.A 273, 275. Buckingham, A, D., and Dows, D. A. (1963). Discussions E’araday SOC. 35,48. Buckingham, A. D., and Le FBvre, R. J. W. (1952). J. Chem. SOC.1932. Buckingham, A. D., and Lovering, E. G. (1962). Trans. Faraday SOC.58, 2077.
82
R. J .
w.
LE ~ E V R E
Buckingham, A. I)., and McLauchlan, K. A. (1963). Proc. Chews. SOC.144. Buckingham, A.D., and Pople, J. A. (1955). Proc. Phys. SOC. A 68,905. Buckingham, A. D.,and Pople, J. A. (1956). Proc. Phys. SOC.69,1133. Buckingham, A. D., and Raab, R. E . (1957). J . Chem. SOC.2341. Buckingham, A. D., and Stephen, M. J. (1957). Trans. Paraday Soc. 53, 884. Buckley, F., and Maryott, A. A. (1953). “Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State”, Nat. Bureau of Standards Circular 537, U. S. Govt. Printing Office, Washington. Bunn, C. W., and Daubeny, R. de P. (1954). Trans. Paraday SOC.50, 1173. Cabannes, J. (1929). “La Diffusion Mol6culaire de la LumiBre”, Les Presses Universitaires de France. Cady, G. H., and Rohrback, G. H., (1949). J . Am. Chem. SOC. 71, 1938. Calderbank, K.E.,Le FBvre, R. J. W., and Northcott, J. (1948). Chesrs. & Itad. (London) 158. Campbell, K. N., and Eveslage, S. L. (1945). J. Am. Chem. SOC. 67,1851. Carlisle, C. H., and Crowfoot, D. (1945).Proc. Roy. SOC.A 184, 64. Ceuterick, P.(1936). Bull. SOC. chim. Belg. 45, 545. Chantry, G. W., and Plane, R. A. (1960). J . Chem. Phys. 33, 634. Charney, E.,and Halford, R. S. (1958). J . Chem. Phys. 2 9 , 221. Chaumont, L. (1916). A n n . p h y s . 5, 17. Chau, J.Y. H., Le FBvre, C. G., and Lo FBvre, R. J. W. (1959).J . Chetn. SOC. 2G66. Chen, C. -Y., and Le FBvre, R. J. W. (1963). Australian J . Chetn. 16,917. Chen, C. -Y., and Le FBvre, R. J. W. (1964). J . Chem. Soc. 234. Chen, C. -Y., and Le FBvre, R. J. W. (1965).J . Chem. SOC.558. Chen,C. -Y.,LeFBvre,R. J.W.,andSundaram, K. M. S. (1965). J . Chem.Soc. 553. Clark, C. H.D. (1936a). Proc. Leeds Phil. Lit. SOC.Sci. Sect. 3, 208. Clark, C. H. D. (1936b). Nature 138, 126. Cole,R.H., Johnston, D.R., andoudemans, G. J. (1960).J.Chem.Phys.33,1310. Coop, I. E., and Sutton, L. E. (1938). J . Chem. SOC.1269. Corry, J. E.,and Lagemann, R. T.(1942). J . Chem. Phys. 10, 759. Cotton, A. (1932). Rapp. Cons. Phys. Solvny p. 418. Coulson, C. A.,Maccoll, A., and Sutton, L. E. (1952). Trans. Faraduy Soc. 48,106. Cowan, D.M., and Vogel, A. I. (1940). J . Chem. SOC.1528. Cowan, D.M.,and Vogel, A. I. (1943). J.Chem. SOC.16. Cowan, D. M., Jeffery, G. H., and Vogel, A.I. (1940).J . Chern. Soc. 171. Crawford, M.J., Stansbury, E. J., and Welsh, H. L. (1953).Can. J . Phys. 31, 954. Cresswell, W. T., Jeffery, G. H., Leicester, J., and Vogel, A. I. (1949). Reseurcls 2 , 46. Cresswell, W. T., Jeffery, G. H., Leicester, J . , and Vogel, A. I. (1951). Chem. & I n d . (London)376. Cresswell, W. T., Jeffery, G. H., Leicester, J., and Vogel, A. I. (1952). J . Chem. SOC.514. Cresswell, W. T., Leicester, J., and Vogel, A. 1. (1954).J . Phys. Chem. 58, 174. Cureton, P. H., Lc FBvre, C. G., and Le FBvre, R. J. W. (1961).J . Chem. SOC. 4447. Cureton, P.H., Le FBvre, C. G., and Le FBvre, R. J.W. (1963).J . Chem. SOC. 1736. Curl, R. F. (1959).J . Chem. Phys. 30, 1529. Curran, C., and Palermiti, F. M. (1951). J . Am. Chem. SOC. 73,3733. Cuthbertson, C., and Cuthbertson, J. (1932). Proc. Roy. Soc. 135, 40. Cuthbertson, C., and Cuthbertson, J. (1933). Proc. Roy. SOC.139, 517. Cuthbertson, C., and Cuthbertson, J. (1914). Phil. Trans. A 213,11.
MOLECULAR R E F R A C T I V I T Y A N D P O L A R I Z A B I L I T Y
83
Dalgarno, A. (1962). Advances in Phys. 11, 281. Damkohler, G. (1934). 8.physik. Chem. B 27, 130. Das, T. P., and Wikner, E. G. (1957). Phys. Rev. 107,497. Davies, P. L. (1952). T r a m . Faraday SOC. 47, 789. DeBoer, J. H. (1936). Trans. Faraday Soc. 32, 10. Debye, P. (1929). “Polar Molecules”, Chemical Catdog Co., New York. Debye, P. (1944). J. Ap p l . Phys. 15, 338. Debye, P. (1946). J . Ap p l . Phys. 17, 392. Debye, P. (1947). J. Ph ys . Ce: Colloid Chem. 51, 18. de Malleman, R. (1926). J. Phys. Radium 7,295. de Malleman, R. (1930). Trans. Faruday SOC. 26, 281. 36, 936. Denbigh, K. G. (1940). Trans. B’uraday SOC. Denbigh, K. G., and Vickery, B. C. (1949). Trans. Furaday SOC. 45, 61. Dierkesmann, A,, and Szivessy, G. (1929). Ann. Physik 3, 507. Djerassi, C. (1960). “Optical Rotatory Dispersion”, McGraw-Hill, New Yorli. Drechsler, M., and Henkel, E. (19.54). 8. angew. Phys. 6, 341. Drechsler, M., and Liepack, H. (1956). Naturwiss. 43, 52. Drechsler, M., and Miiller, E. W. (1952). 2. Phys. 132, 195. Dunbar, W. S., and Lagemann, R. T. (1945). J. Phys. Chem. 49,428. Eckert, J. M., and Le FBvre, R . J. W. (1961). J. Chem. SOC.2356. Eckert, J. M., and Le FAvre, R . J. W. (1962a). J. Chem. SOC.1081. Eckert, J. M., and Le FBvre, R . J. W. (1962b). J. Chem. SOC. 3991. Eckert, J. M., and Le FBvre, R.J. W. (1964a). J. Chem. SOC. 358. Eckert, J. M., and Le FBvre, R. J. W. (196413). J. Chem. SOC.3200. Edxall, J. T. (1942). Streaming Birefringence and I t s Relation to Particle Size and Shape, in “Advances in Colloid Science”, Volume 1, Interscience Publ., New York, p. 269. Edser, E. (1920). “Light for Students”, Macmillan, Chap. XV. EgloR, G. (1946). “Physical Constants of Hydrocarbons”, Reinhold, New York. Eisenlohr, F. (1910). 2 . p h ys . Chem. 75, 585. Eisenlohr, F. (1912a). 2.phys. Chem. 79, 129. Eisenlohr, F. (1912b). “ Spektrochemie organischer Verbindungen, Molekularrefraktion und Dispersion”, Enke, Stuttgart. Eisenlohr, F. (1923). I n Landolt-Bornstein’s “ Tabellen”, 5th edn. 2 , 968. Eisenlohr, F. (1925). Portschr. Chem. Physik ii physikal. Chem. 18B, Heft 9. Eisenlohr, F., and Roth, W. A. (1911). “Refraktometrisches Hilfsbuch”, Veit and Co., Leipzig. Evans, D. P., Gulwell, T., Griffiths, D. C., and Jones, W. J. (1935). J. Chem. S O C . 39. Everett, D. H., and Munn, R. J. (1963). Trans. Faraday Soc. 59, 2486. Eykman, J . K. (1893). Rec. trav. chim. 12, 160, 248. Eykman, J. K. (1895). Rec. trav. chim. 14, 185. Eykman, J. K. (1906). Chem. Weekblad 3, 706. Fajans, K. (1934). 8. phys. Chem. B24,103. Fajans, K. (1949a). In “Physical Methods of Organic Chemistry”, Ed. by A. Weissberger, 2nd edn., Interscience Publ., New York, Part 11, p. 1165. Fajans, K. (194910). Chem. Eng. News. 27, 900. Fajans, K., and Joos, G. (1924). 8.Physik 23, 1. Fajans, K., and Knorr, C. A. (1924). Chem. 2 . 4 8 , 403. Farquharson, J. (1936). Trans. Paraday SOC.32, 219. Feher, F., and Blnmcke, A. (1957). Chem. Ber. 90, 1934.
84
R . J.
w.
LE FEVRE
Field, J. A., and Norman, A. (1957). Arch. Biochem. Biophys. 70, 257; 71,170. Fiocco, G., and Thompson, E. (1963). Phys. Rev. Letters 10,89. Flett, M. St. C. (1948). Trans. Faraday Soc. 44,767. Fuson, N., Josien, M. L., and Shelton, E. M. (1954). J . Am. Chem. SOC.76,2526. Gans, R. (1932). “Vector Analysis”, Blackie and Son, London, Chap. IV. Gans, R., and Mrowka, B. (1935). Schriften konigsberg. gelehrten Ges. Naturw. K l . 12, 1. Geffcken, W. (1929). 2. physik. Chem. B 5, 81. Ghosh, S. N., Gordy, W., and Trambarulo, R. (1953). J . Chem. Phys. 21,308. Gildemeister, E.,and Hoffman, Fr. (1928-31). “Die iitherischen Ole”, 3rd edn., Vols. I, 11,and 111,Leipzig. Gillis, R. 0. (1960). Rev. Pure A p p l . Chem. 10,21. Gillis, R.G. (1962). J . Org. Chem. 27,4103. Gillis, R. G., and Price, C. C. (1953). J . Am. Chem. SOC.75,4750. Gillis, R.G., Horwood, J. E., and White, G. L. (1958). J . Am. Chem. SOC.80, 2999.
Gladisch, H., and Senftleben, H. (1947). Naturwiss. 34, 187. Gladstone, G.,and Gladstone, J. H. (1891). Phil. Mag. 31, 1. Gladstone, J. H. (1886). Trans. Chem. SOC.50,609. Gladstone, J. H. (1887). Proc. Roy. SOC.42,401. Gladstone, J. H., and Dale, T. P. (1858). Phil. Trans. 148,887. Gladstone, J. H., and Dale, T. P. (1863). Phil. Trans. 153,337. Glasstone, S. (1940). “Text Book of Physical Chemistry”, Macmillan, London, pp. 290-292. Goldschmidt, H., and Holemann, P. (1934). 2. physik. Chem. B 24, 210. Gooding, R. M., Adams, N. G., and Rale, H. T. (1946). I n d . Eng. Chem. (Anal.)
18,2.
Goss, F. R. (1936). Proc. Leeds Phil. Lit. Soc.. Sci. Sect. 3,231. Goulden, J. D. S. (1954). Spectrochim. Acta 6,129. Groth, P.,and Hassel, 0. (1963). Proc. Chem. SOC.218. Grun, F., and Kuhn, W. (1942). Kollid-2.101, 248. Grzeskowiak, R.,Jeffery, G. H., and Vogel, A. I. (1960). J . Chem. Soc. 4719, 4728.
Gundermann, H. (1930). Ann. Physik 6,545. Guy, J., and Harrand, M. (1952). Compt. rend. 234,616, 716. Hacket, N., and Le FBvre, R. J. W. (1961). J . Chem. SOC.2612. Hallam, H. E. (1963). I n “Infra-red Spectroscopy and Molecular Structure”, ed. M. Davies, Elsevier, Amsterdam. Hammerle, W. G., and Tinoco, I. (1956). J . Phys. Chem. 60,1619. Harder, A., and Zintl, E. (1931). 2.physik. Chem. B 14,265. Hartshorne, N. H., and Stuart, A. (1960). “Crystals and the Polarising Microscope”, Edward Arnold, London. Hassel, 0. (1953). Quart. Revs. (Lond.) 7,221. Havelock, T. H. (1907). Proc. Roy. SOC.80, 28. Havelock, T. H. (1909). Phys. Rev. 28, 136. Hearne, M. R., and Le FBvre, R. J. W. (1962). J . Chem. SOC.4735. Heigl, A., and Wulff, P. (1931). 2. Krist. 77,84. Henne, A. L., and Hinkamp, J. B. (1945). J . Am. Chem. SOC.67,1194, 1197. Hennion, G. F., and Banigan, T. F. (1946). J . Am. Chem. SOC.68,1381. Henrich, F. (1922). “Theories of Organic Chemistry”, trans. Johnson, T. B. and Hahn, D. A., John Wiley, New York.
MOLECULAR R E F R A C T I V I T Y A N D POLARIZA BI L I T Y
85
Heydweiller, A. (1925). Physikal. 2. 26, 526. Hine, J. (1956). “Physical Organic Chemistry”, McGraw-Hill, New York. Hootman, J. A. (1933). Plcys. Rev. 43, 749. Hosoya, S. (1963). Acta Cryst. 16, 310. Huggins, M. L. (1941). J . Am. Chem.Soc. 63, 116, 916. Hughes, E. C., and Johnson, J. R. (1931). J . Am. Chem. SOC. 53, 737. Hughes, T. P. (1962). Nature 194, 268. Hunter, E. C. E., and Partington, J. R . (1932). J . Chem. SOC.2812. Hunter, J. S., Phillips, G. M., and Sutton, L. E. (1945). J . Chem. SOC.146. Ingersoll, L. R. (1931). Phys. Rev.37, 1184. Ingold, C. K . (1953). “Structure and Mechanism in Organic Chemistry”, Cornell University Press, It,haca, N.Y. Ingram, P., and Jerrard, H. G. (1962). Nature 196, 57. International Critical Tables (1930). Ed.-in-Chief E. W. Washburn, 1st edn., Volume VII, McGraw-Hill, New York. Itzhaki, R . F. (1962). Nature 194, 1241. Jackman, L. M. (1959). “Applications of Nuclear Magnetic Resonance Spectroscopy in Organic Chemistry ”, Pergamon Press, London. Jeffery, G. H., and Vogel, A. I. (1948). J . Chem. SOC. 658, 674, 1804. Jeffery, G. H., Parker, R., andVogel, A. I. (1961). J . Chem.Soc. 570. Jerrard, H. G. (1959). Chem. Revs. 59, 345. Joshi, S. S., and Tuli, G. D. (1951). J . Chem. Soc. 837. Jungner, A., and Jungner, I. (1952). Acta Chem. Scand. 6, 1391. Kahn, A. H., Shockley, W., and Tessman, J. R. (1953). Phys. R e v . 92, 890. Karagounis, G. (1962). “Introductory Organic Quantum Chemistry ”, Academic Press, New York. Keeber, W. H., and Post, K. W. (1956). J . Org. Chem. 21, 509. Kerr, J. (1880). Phil. Mag. 9, 157. Kerr, J. (1882). Phil.Mag. 13, 153, 248. Kielich, S. (1958a). BUZZacad. polon. sci. 6, 215. Kielich, S. (195813). Acta Phys. Polon. 17, 259. Kielich, S. (1960). Ac taPhy s. Polon. 19, 149, 573. Kielich, S. (1962). Acta Phys. Polon. 22, 299, 477. Kielich, S. (1963a). Acta P l ~ y sPolon. . 23, 321, 819. Kielich, S. (1963b). Mol. Physics 6, 49. Kielich, S., and Piekara, A. (1958). J . Chem. Phys. 29, 1297. Kielich, S., and Piekara, A. (1959). Acta Phys. P O ~ O18, T L 439. . Kirkwood, J. G. (1932). Physik. 2 . 3 3 , 57. Kirkwood, J. G. (1936). J . Chem. Phys. 4, 592. Kirkwood, J. G. (1937). J . Chem. Phys. 5,479. Koch, F. K. V., and Kohner, H. (1934). Z . Physik. C‘hem. B 24, 194. Kohner, H. (1928). 2. physik. Chem. B 1, 427. Kordes, E. (1939). Naturwiss. 27, 30. Kordes, E. (1939a). 2 . p h y s i k . Chem. B43, 119, 173, 213. Kordes, E. (1939b). 2. physik. Chem. B 44, 249. Kordes, E. (1940). 2.physik. Chem. B48, 91. Kordes, E. (1941). 2. Elektrochem. 47, 152. Korsching, H. (1946). 2. Naturforsch. 1 , 219. Krishnan, K. S. (1929). Proc. Roy. SOC. A 126, 155. Krishnan, K . S., and Raman, C. V. (1928). Proc. Roy. Soc. A 117, 1, 589. Krishnan, K. S., and Raman, C. V. (1928). Phil. Mug. 5, 498.
86
R . J.
w.
LE F ~ V R E
Kronig, R . de L. (1930). “Band Spectra and Molecules”, Cambridge University Press, London. Krushinskii, L. L., and Shorygin, P. 0. (1961). Optics andSpectr. 11, 12, 80. Kuhn, W. (1952). 2. Elektrochem. 56, 506. Kurtz, S. S., and Ward, A. L. (1936). J . Franklin Inst. 222, 563. KUSS,E. (1940). “Elektrooptischer Kerreffekt bei hohen Drucken im Ubergangsgebiet gasformig-fliissig”, Dissertation, University of Berlin. Kuss, E., and Stuart, H. A. (1941). Physik. 2 . 4 2 , 95. Kyte, C. T., Jeffery, G. H., and Vogel, A. I. (1960). J . Chem. Soc. 4454. Ladenburg, R., and Wolfsohn, G . (1930). 2. Physik 63, 616, 634. Ladenburg, R., and Wolfsohn, G. (1931). 2. Physik 65, 207. Ladenburg, R., and Wolfsohn, G. (1932). 2. Physik 83,234. Lagemann, R. T. (1945). J . Am. Chem. SOC. 67, 498. Langevin, P. (1910). L e Radium 7 , 249. Le FBvre, C. G., and Le FBvre, R . J. W. (1953). J . Chem. SOC.4041. Le FBvre, C . G., and Le Fevre, R. J. W. (1954). J . Chem. Soc. 1577. Le FBvre, C. G., and Le FBvre, R. J. W. (1955a). Chem. & Ind. (London)506. Le FBvre, C. G., and Le FBvre, R. J. W. (1955b). J . Chem. SOC. 1641. Le Fevre, C . G., and Lo FBvre, R. J. W. (1955~).Chem. & Ind. (London) 1121. Le FBvre, C. G., and Le FBvre, R. J. W. (1955d). J . Chem. Soc. 2750. Le FBvre, C. G., and Le Fevre, R. J. W. (1955e). Revs. Pure and AppE. Chem. (Australia)5, 261. Le FBvre, C . G., and Le FBvre, R. J. W. (1956a). Chem. & I n d . (London)54. Le Fisvre, C. G., and Le FBvre, R . J. W. (1956b). J . Chem. Soc. 3549. Le FBvre, G. C., and Le FBvre, R. J. W. (1957). J . Chem. Soc. 3458. Le FBvre, C. G., and Le FBvre, R. J. W. (19594. J . Chem. Soc. 2670. Le FBvre, C. G., and Le FBvre, R. J. W. (1959b). Chem. CE? Ind. (Lolzdon) 1283. Le FBvre, C. G., and Le FBvre, R. J. W. (1960). Chap. XXXVI of “Physical Methods of Organic Chemistry ”, Ed. A. Weissberger, Interscience Publ., New York. Le FBvre, C. G., Le FBvro, R. J. W., and Rao, D. A. A. S. N. (19.56). J . Chem. Soc. 708. Le FBvre, C. G., Le FBvre, R. J. W., and Oh, W. T. (1957). Australian J . Chem. 10, 218. Le FBvre, C. G., Le FBvre, R. J. W., and Parkins, G. M. (19584. J . Chem. Soc. 1468. Le FBvre, C. G., Le FBvre, R. J. W., and Smith, M. R. (195813). J . Chem. Soc. 16. Le FBvre, C. G., Le FBvre, R. J. W., and Parkins, G. M. (1959a). J . Chem. SOC.1814. Le FBvre, C. G., Le FBvre, R. J. W., and Rao, B. I?. (1959b). J . Chem. SOC. 2340. Le FBvre, C. G., Le FBvre, R. J. W., Rao, B. P., and Smith, M. R. (1959~).J . Chem. SOC.1188. Le FBvre, C. G., Le FBvre, R. J. W., Pierens, R. K., and Roper, R. (1960a). Proc. Chem. SOC.117. Le Fbvre, C. G., Le FBvre, R. J. W., Rao, B. P., and Williams, A. J. (1960b). J . Chem. SOC. 123. Le FBvre, R. J. W. (1953). “Dipole Moments”, 3rd edition, Methusn, London. Le FBvre, R. J. W. (1956). Australian J . Science. 18,39, Le Fevre, R. J. W. (1958). Proc. Chem. SOC. 283. Le Fevre, R. J. W. (1959). Proc. Chem. Soc. 363. Le FBvre, R. J. W. (19614. J . Proc. Roy. SOC.N.S. WaEes 95, 1. Le Fevre, R. J. W. (1961b). Australian J . Chem. 14, 312.
MOLECULAR REFRACTIVITY A N D POLARIZABILITY
87
Le FBvre, R. J. W., and Orr, B. J. (1964). Australian J . Chem. 17, 1098. Le FBvre, R. J. W., and Rao, B. P. (1957). J . Chem. SOC. 3644. Le FBvre, R. J. W., and Rao, B. P. (1958). J . Chem. SOC.1465. Le FBvre, R. J. W., and Rao, B. P. (1960). J . Chem. SOC.119. Le FBvre, R. J. W., and Rao, D. A. A. S . N. (1954). Australian J . Chem. 7,135. Le Fhvre, R. J. W., and Rao, D. A. A. 8. N. (1958). Austratian J . Chem. 8, 329. Le FBvre, R. J. W., and Ritchie, G. L. D. (1963). J . Chem. SOC.4933. Le FBvre, R. J. W., and Steel, K. D. (1961). Chem. & I n d . (London) 670. Le FBvre, R. J. W., and Sundaram, A. (1962a). J . Chem. SOC. 3904. Le FBvre, R. J. W., and Sundaram, A. (196213). J . Chem. SOC.4009. Le FBvre, R. J. W., and Sundaram, A. ( 1 9 6 2 ~ ) J. . Ghem. SOC. 4756. Le FBvre, R. J. W., and Sundaram, A. (1963). J . Chem. SOC.974. Le FBvre, R. J. W., and Sundaram, K. M. S. (1962a). J . Chem. SOC.1494. Le FBvre, R. J. W., and Sundaram, K. M. S. (1962b). J . Chem. SOC.4003. Le FBvre, R. J. W., and Sundaram, K. M. S. (1963a). J . Chem. SOC.1880. Le FBvre, R. J. W., and Sundaram, K. M. S. (196310). J . Chem. SOC.3188. Le FBvre, R. J. W., and Sundaram, K. M. S. ( 1 9 6 3 ~ ) J. . Chem. SOC. 3547. Le FBvre, R. J. W., and Sundaram, K. M. S. (1963d). J . Chem. SOC.4442. Le FBvre, R. J. W., and Sundaram, K. M. S. (1964). J . Chem. SOC. 556. Le FBvre, R. J. W., and Vine, H. (1937). J . Chem. Sac. 1805. Le FBvre, R. J. W., and Williams, A. J. (1960a). J . Chem. SOC. 128. Le FBvre, R. J. W., and Williams, A. J. (1960b). J . Chem. SOC.1825. LeFBvre, R. J. W., and Williams, A. J., (1961). J . Chem. SOC.1671. Le FBvre, R. J. W., and Williams, A. J., (1964). J . Chem. SOC. 562. Le FBvre, R. J. W., Sundaram, A., and Sundaram, K. M. S. (1962). Bull. Chem. SOC. J a p a n 35, 690. Le FBvre, R. J. W., Sundaram, A., and Sunclaram, K. M. S. (1963a). J . Chem. SOC.
974.
Le FBvre, R. J. W., Sundaram, A., and Sundaram, K. M. S. (1963b). J . Chem. SOC. 3180.
Le FBvre, R. J. W., Sundaram, A., and Sundaram, K. M. S. ( 1 9 6 3 ~ ) .J . Chem. SOC. 4447.
Le FBvre, R. J. W., Pierens, R. K., and Sundaram, A. (1963d). J . Chem. SOC.479. Lewis, G. N. (1923). “Valence and the Structure of Atoms and Molecules”, Chemical Catalog. Co., New York. Lima, F. W. (1948). J . Am. Chem. SOC.70,3141. Long, D.A. (1953). Proc. Roy. SOC.A 217,203. Lorentz, H.A. (1880). Wid.Ann. Physik 9, 641. Lorentz, H. A. (1909). “ The Theory of Electrons”, Tenbner, Leipzig. Lorenz, L. (1880). Wied. Ann. Physik 11, 70. Luhdemann, R. (1935). 2. phys. Chem. B 2 9 , 1 3 3 , 1 5 0 . Lyon, N. (1915). Ann. Physik. 46, 749. Maccoll, A. (1947). Quart. Revs. (London)1, 16. McClellan, A. L. (1963). “ Tables of Experimental Dipole Moments”, Freeman. San Francisco and London. McComb, H. E. (1909). Phys. Rev. 29, 525. McConnell, H. M. (1957). J . Chem. Phys. 27, 226. McKenna, J. (1959). Ann. Repts. Progr. Chem. 56, 187. Macey, W. A. T. (1960). J . Phys. Chem. 64, 254. Mason, S. F. (1963). Quart. Revs. (London)17,20. Matossi, F.,and Mayer, R. (1946). Naturwiss. 33, 190.
88
R. J .
w.
LE FEVRE
Matossi, F., and Mayer, R. (1948). Phys. Rev. 74, 449. Mayer, J. E. and Mayer, M. G. (1933). Phys. Rev. 43, 605. Meerwein, H. and Pannwitz, W. (1934). J . prakt. Chcm. 141, 123. Meyer, E. H. and Otterbein, G. (1931). Physik. 2 . 3 2 , 290. Moelwyn-Hughes, E. A. (1947). “The Kinetics of Reactions in Solution”, 2nd edn., Oxford, Clarendon Press. Mortensen, E. M., and Smith, R. P. (1960). J . Chcm. PJL~s. 32, 502, 508. Mrowka, B. (1932). 2. Physik 76, 300. Mueller, C. R. (1954). J. Chcm. Phys. 22, 120. Mueller, H. (1936). Phys. Rev. 50, 547. Mumford, S. A. (1952). J. Chcm. Soc. 4897. Narayana Rao, D. A. A. S. (1958). Trans. Faraday SOC.54, 954. Neugebauer, T. (1933). 2.Physik 86, 392. Newman, F. H. (1934). Phil. Mag. 17, 1072. O’Konski, C. T., and Zimm, B. H. (1950). Science 11 1, 113. O’Konski, C. T., Yoshioka, K., and Orttiing, W. H. (1959). J. Phys. Ghcrn. 63, 1558. Oster, G. (1955). I n “ Physical Techniques in Biological Research ”, ed. G. Oster and A. W. Pollister, Vol. 1, Academic Press, New York. Chap. 2. Oster, G. (1960). 1 1 % “ Technique of Organic Chemistry ”, ed. A. Weissberger, Vol. 1, part 3, Interscience Publ., New York. Partington, J. R . (1953). “An Advanced Treatise on Physical Chemistry”, Vol. 4, Longmans Green, London, pp. 31-36. Pauling, L. (19274. J . Am. Chcrn.Soc. 49, 765. A 114, 181. Pauling, L. (1927b). Proc. Roy. SOC. Pauling, L. (1939). “The Nature of the Chemical Bond” 1st Edn. Pauling, L. (1960). “The Nature of the Chemical Bond”, 3rd edn., Cornell University Press. Pitzer, K. S. (1959). “Advances in Chemical Physics”, ed. I. Prigonine, Vol 11, Interscience Publ., New York, p. 59. Placzek, G. (1934). In Marx “Handbuch der Radiologie, VI”, Akademie Verlag, Leipzig. Platt, J. R. (1961). J. Chem. Phys. 34, 862. Pople, J. A. (1957). Proc. Roy. SOC. A 239, 541, 550. Pople, J. A., and Schofield, P. (1957). Phil. Mag. 2, 591. Prbvost, C. (1928). Annales chim. et phys 10, 410. Ramaswamy, K. L. (1935). Proc. I n d i a n Acad. Sci. A 2, 630. Ramaswamy, K. L., and Watson, H. E. (1936). Proc. Roy. SOC. A 156, 144. Rao, B. P. (1940). Proc. Indian Acad. Sci. 11, 1. Rao, M. R. (1941). J . Chcm. Phys. 9, 682. Regnier, J., and Regnier, S. (1954). J . chim. phys. 51, 181. Remick, A. E. (1949). “Electronic Interpretations of Organic Chemistry ”, 2nd edn. John Wiley, New York. RBrat, C. (1960). Acta Cryst. 13, 62, 459. Roberts, S. (1949). Phys. Rev. 76, 1215. Rochow, E. G., Hurd, D. T., and Lewis, It. N. (1957). “The Chemistry of Organometallic Compounds”, John Wiley, New York. Rowlinson, J. S. (1954). Quart. Revs. (London)8, 168. Sachsse, G. (1935). Physik. 2 . 3 6 , 357. Samygin, M. M. (1937). J.Phys. Chcm. U.S.S.R. 10, 455. Sauer, R. 0. (1946). J . Am. Chem. SOC.68, 954.
MOLECULAR REFRACTIVITY AND POLARIZABILITY
89
Sayre, R. (1958). J. Am. Cliem. SOC. 80,5438. Scheraga, H. A., and Signer, R. (1960). I n “Technique of Organic Chemistry”, ed. A. Weissberger, Vol. 1, part 3, Interscience Publ., New York. Schoppe, R. (1934). 2. phys. Chem. B 24, 259. Schroter, H.(1931). 2.Physik 67,24. Semmler, R.W. (1906). “Die Aetherische Oele”, Vol. 1, Berlin. Sewell, G. L. (1949). Proc. Cambridge Phil. SOC. 45,678. Silberstein, L. (1917). Phil. Mag. 33,92, 215, 521. Simonsen, J. L. (1947-9). “The Terpenes”, Vols. I and 11, Cambridge University Press, London. Skinner, C. A. (1909). Phys. Rev. 29,541. Smiles, S. (1910). “The Relations between Chemical Constitution and Some Physical Properties ”, Longmans, Green, London, Chap. VIII. Smyth, C. P. (1923). Phil. Mag. 45,849. Smyth, C. P. (1924). J. Am. Chem.Soc. 46,2151. Smyth, C. P. (1925). Phil. Mag. 50,361, 715. Smyth, C. P. (1941). J. Am. Chem. SOC. 63,57. Smyth, C.P. (1955). “Dielectric Behaviour and Structure”, McGraw-Hill, New York. Spangenberg, K. (1922). 2. Rrist. 57,494. Steiger, A. L. von (1921). Chem. Ber. 54, 1381. Sternheimer, R.M. (1954). Phys. Rev. 96,951. Stuart, H.A. (1952). “Die Struktur des Frcien Molekuls”, Springer-Verlag, Berlin. Stuart, H. A., and Volkmann, H. (1933). Ann. Physik 18, 121. Sugden, S. (1924). J. Chem. SOC. 125,1177. Sugden, S. (1934). Trans. Yaraday SOC. 30,734. Sundbom, M.(1958). Arkiw. B’ysik 13,539. Sutton, L. E. (1946). Trans. Paraday SOC. 42A,170. Swarts, F.(1923). J. chim. phyls. 20, 30. Szivessy, G.(1920). 2. Physik 2,30. Taft, R.W. (1953). J. Am. Chem. SOC. 75,4231. The Chemical Society (1958). “Tables of Interatomic Distances and Configurations in Molecules and Ions”, ed. Sutton, L. E., Special Publ. No. 11, The Chemical Society, London. Thomson, G. (1944). J . Chem. SOC.404, 408. Timmermans, J. (1950). “ Physico-chemical Constants of Puro Organic Compounds ”, Elsevier, Amsterdam. Tinoco, I. (1955). J. Am. Chem. SOC. 77,3476, 4486. Tinoco, I. (1957). J. Am. Chem. SOC. 79,4248, 4336. Tinoco, I. (1959). J. Am. Chem. SOC. 81,1540. Tinoco, I., and Woody, R. W. (1960). J . Am. Chem. SOC.32,461. Tinoco, I., and Yamoaka, K. (1959). J. Phys. Chem. 63,423. Tolkmith, H. (1958). J. Org. Chem. 23, 1690. Tolkmith, H.(1959). Ann. N.Y. Acad. Sci. 79, 187. Torkington, P.(1948). Nature 161,724. Treloar, L. R. G. (1956). I n “Die Physik der Hochpolymeren”, vol. 4, ed. H. A. Stuart, Springer-Verlag, Berlin, Chap. 5; also papers in Trans. Faraday SOC. from 1947 onward. Trotter, J. (1963a). Can. J . Chem. 41, 14. Trotter, J. (1963b). Acta Cryst. 16, 1187.
90
R . d . W . L E E’kVRE
Urtz, R. P. (1964). ‘‘Plasma Diagnostics using the Ranian Effect”, Tech. Doc Rep. No. R.A.D.C. TDR-64-5. Vahrman, M. (1960). J. Chem.Soc. 4135. Van Vleck, J. H. (1926). Proc. Nut. Acad. Sci. U.S. 12, 662. Vinti, J. P. (1932). Phys. Rev. 41, 813. Vogel, A. I. (1934). J. Chem. SOC.333, 1758. Vogel, A. I. (1939). J. Chem. SOC.1862. Vogel, A. I. (1943). J. Chem. SOC.636. Vogel, A. I. (1946). J. Chem. SOC.133. Vogel, A. I. (1948). J. Chem.80~.607, 610, 616, 624, 644, 654, 1809, 1814, 1820, 1825, 1833. Voigt, W. (1901). A n n . Physik 4, 197. Volkenstein, M. W. (1941). Compt. rend. wad. sci. U.R.S.S. 32,185. Volkenstein, M. W. (1960). “Struktur und Physikalische Eigenshaften der Molekule”, Teubner, Leipzig. Vuks, M. F. (1957). OptikaiSpektroskopiya2,494;Chem. Abs. 51, 134850. Waldmann, H. (1938). Helv. Chim. Acta 21, 1053. Walsh, A. D. (1946). Trans. Faraday Soc. 42, 56. Walsh, A. D. (1947). T r a m . Faraday Soc. 43, 60. Wang, S. N. (1939). J. Chem. Phys. 7, 1012. Warrick, E. L. (1946). J. Am. Chem. SOC.68, 2455. Wasastjerna, J. A. (1922). 2.phys. Chem. 101,193. Waterman, H. I. (1958). “Correlation Between Physical Constants and Molecular Structure”, Elsevier, Amsterdam. Waters, W. A. (1942). “Physical Aspects of Organic Chemistry”, 3rd edn., Routledge, London. Watson, H. E. (1927). Proc. Roy. SOC.A 117, 43. Wepster, B. M. (1957). Rec. trav. chim. 76, 335, 357. Wepster, B. M. (1958). I n “Progress in Stereochemistry”, ed. by W. Klyne and P. B. D. de la Mare, Butterworths, London, Chap. 4. Wesson, L. G. (1948). “Tables of Electric Dipole Moments”, Technology Press, Massachusetts Institute of Technology. West, R., and Rochow, E. G. (1952). J. Am. Chem. SOC. 74, 2490. Williams, R. L. (1961). Ann. Repts. P r o p . Chern. 58, 34. Wood, R. W. (1934). “Physical Optics”, 3rd edn., Macmillan, New York, Chap.
XV. Woodward, L. A. (1956). Quart. Revs. (London)10, 185. WdfT, P. (1933). 2. physik. Chem. B 21,353, 368. WuW, P., and Schaller, D. (1934). 2. Krisb. 87, 43. Wusthoff, P. (1936). Ann. Physik 27,312. Zurcher, R. F. (1962). Discussions Faraday SOC. No. 34, p. 66. Zurcher, R. F. (1962). J. Chem. Phys. 37, 2421.
GAS-PHASE HETEROLYSIS ALLAN MACCOLL William Ramsay and Ralph Forster Laboratories University College, London, W.C.1, England
.
I. Introduction 11. Experimental Methods of Investigating 1 tie 1Cittt: of Jtoactiun 111. Mechanism of Pyrolysis IV. The Experimental Results . V. Regularities in the Experimental Data . A. Halides . B. Esters . VI. Homogeneous Catalysis of Gas-Phase Eliminations . VII. General Conclusions References
.
.
. . . . .
91
92
96
100 103 103 . 112 . 117 . 119 . 120
.
I. INTRODUCTION INthe gas-phase it is possible to investigate the behaviour of a single molecule, uninfluenced by the presence of the remainder of the system. The effect of substitution in a parent molecule upon the rate of a given reaction can thus be studied without the complications arising from the co-operative effects of the solvent, as may occur in reactions in solution. For this reason, if for no other, the gas-phase would seem to offer overwhelming advantages for the investigation of substituent effects on the reactivity of organic molecules. The present chapter describes a number of investigations of homogeneous, molecular gas-phase elimination reactions of the type R’, RZ
,CH-CX,
/R4 R3
R’, + R2
,c
= (‘ ‘R3
where X = CI, Br, I, HC02, CH,CO,, C1C02, and the R’s are capable of a wide range of variation. It is, of course, essential to show that the reactions studied are in fact homogeneous and unimolecular for, if the reaction studied is heterogeneous or proceeds by a chain mechanism, then conclusions relating to substituent effects will be invalidated.
92
ALLAN MACCOLL
I n principle three types of homogeneous mechanisms need to be considered : radical non-chain, radical chain and unimolecular (Daniels and Veltman, 1939). The first two of these are multistep processes, having a common initial step R'RzCH-CR3R4S
+ RlRzCH-tR3R4
namely the homolytic splitting of the C-X followed by
2 + RlR2CH-CR3R4X RlR2C-CR3R4X
fRlRzCH-CR3R4
+2
(1)
bond. This may then be
+ HX + RlRzd-CR3R4X
+ RlRZCH-R3R4X
+ R'RZC=CR3R4
(2) (3)
For such a mechanism, the activation energy of the overall reaction must be a t least equal to the homolytic bond dissociation energy, D(R-X), of the R-X bond. While such a mechanism was first suggested by Daniels for ethyl bromide, it may now be ruled out since D(Et-Br) is considerably greater than 53 kcal mole-l, the activation energy of the ethyl bromide decomposition. It is possible, however, that such a mechanism may account for the pyrolysis of ally1 bromide (Maccoll, 19551, the activation energy being 45.5 kcal which is very close to the carbon-bromine dissociation energy (Szwarc et al., 1950), namely 47-50 kcal molep1. Steps ( 1 ) and (2) can lead to a chain mechanism if the radical R1R26-CR3R4X decomposes, RlRZdR3R4X + RlRZC=CRaR4+
k
(4)
steps (2) and (4)constituting the chain-propagating steps. A variety of chain-ending steps may then be postulated. The third type of mechanism that has been suggested is a one-step unimolecular decomposition, proceeding through a four-centred transition state
It will be seen later that the observed effects of substituents sequire a modification of this picture of the unimolecular mechanism. 11. EXPERIMENTAL METHODS OF INVESTIGATING THE RATE OP REACTION
For all the elimination reactions studied, with the exception of the iodides, the overall stoicheiometry conforms well to the equation R'R2CH-CR'R'X
+ R'RZC=CR3R4+ HX
93
GAS-PHASE HETEROLYSIS
In the case of the iodides, the stoicheiometry is 2 R'R9CH-CR3R41
+ RlRZCH---CHR3R4+ RlRzC=CR3R4+ 1 2 ;
the iodine is thought to be produced by a rapid reaction between hydrogen iodide and the alkyl iodide (Holmes and Maccoll, 1963). Since the reactions proceed with an increase in pressure, measurement of the total pressure as a function of time constitutes a simple means of following the reaction. If a reactant molecule gives r product molecules, then
Po-P =
?-Po- p
r--l
where P is the total pressure, p o - p is the pressure of the compound a t 100-
--
80 -
0
0 ._
Y
c
0 ._ c
-
W
-
0
20
40
60
80
100
yo Reaction (pressure) FIG.1. The verification of the st,oicheiometry of the pyrolysis of cyclohexyl bromide.
time t and p o is the initial pressure. As a verification of this procedure, the contents of the reaction vessel may be frozen out after a given time, and the mixture analysed for HX. Figure 1 shows, for the case of cyclohexyl bromide, that the percentage decomposition calculated from pressure measurements is in agreement with that determined by a direct analysis for HX. The variation of the rate constant with temperature can be expressed in terms of the Arrhenius equation k = A exp ( - E/ RT ), E being the energy of activation and A the frequency factor. 4
94
A L L A N MACCOLL
A more sophisticated technique is necessary in the case of those reactions which lead to more than one olefin. Thus s-butyl halides (Maccoll and Stone, 1961) pyrolyse to yield three isomeric butenes &-CH3--C‘H=CH--CHa
CHI. CH2. CHX .CH3
+ Iruns-CH3-CHdH-CH3 /
\
+H X
CH~~H-CHZ-CH~
Vapour phase chromatography may then be used in conjunction with kinetic studies to determine the proportion of the olefins produced. It is found that in clean reaction vessels, rates often tend to be both fast and irreproducible. This led to the technique of working in “seasoned” reaction vessels (Brearley et al., 1936; Ogg and Polanyi, 1935), that is, vessels that had had a large number of runs done in them, or where surfaces had been rendered inactive by a carbonaceous layer such as is deposited by decomposing ally1 bromide (Maccoll, 1955). When such vessels are used, it is found that the rate is usually much smaller than in clean vessels and also that the kinetic behaviour becomes reproducible. If packing the vessels with glass and re-seasoning them has no effect upon the rate, then it is reasonable to assume that the reaction is homogeneous if it is molecular, or, if it is of a radical chain character, that the chains are both initiated and terminated upon the walls. To distinguish between a molecular and an atom or radical chain mechanism, it is usual to add a substance, an inhibitor, which is capable of removing radicals from the system. Examples of such substances are nitric oxide (Staveley and Hinshelwood, 1936), propene (Rice and Polly, 1938), cyclohexene (Maccoll and Thomas, 1957) and toluene (Szwarc, 1948). The first of these, being an odd-electron molecule, can combine directly with free-radicals ; the others have readily removable hydrogen atoms to the double bond. Nitric oxidel R * + N O -+ RNO
R.+ C H ~ C H S H Z-+ RH + CH2-CH-CHz
has not yet been widely used in halide or ester pyrolyses; propene, cyclohexene and toluene have. The effect of such inhibitors is shown in Fig. 2 for the cases of n-propyl bromide (Maccoll and Thomas, 1957) and isopropyl bromide (Maccoll and Thomas, 1955) respectively. I n the former case addition of increasing amounts of cyclohexene causes a decrease in the rate coefficient to a limiting value, while in the latter the rate constant is unaltered by the addition of the inhibitor. The difference N. Capon (1964) has shown that, in the case of ethyl bromide, nitric oxide actually increases rather than inhibits the rate of pyrolysis.
95
GAS-PHASE HETEROLYSIS
in the effects of added inhibitor upon the order of the reaction and upon the Arrhenius parameters may a.lso be quite marked. Thus, under conditions of maximal inhibition, n-propyl bromide follows a first-order law (Blades and Murphy, 1952; Maccoll and Thomas, 1957), while in the absence of inhibitors the order is 1.5 (Agius and Maccoll, 1955; Semenov et al., 1955). The Arrhenius parameters for the decompositionof n-propyl 10
I
I
9 8: I
I
I
74 I I
I
i - P r B r (347°C)
6,;; I I
I
5- I I
4-
I I I
3-
I 1
I I
2-
:
-
I
1-
0
I
'-
0-0
I
100
I
200
n-PrEr (380iC)
-
I
300
400
Fro. 2. The effect of varying pressure of cyclohexene upon the first order rate coefficients for the pyrolyses of n-propyl and isopropyl bromide.
bromide and isopropyl bromide, together with those for ethyl formate and isopropyl formate, are shown in Table 1. The differencein behaviour in the two cases is quite striking. Where inhibition is observed, both the activation energy and the steric factor are increased. It is interesting to note that essentially the same Arrhenius parameters were obtained for isopropyl bromide over two very different temperature ranges, namely 310-350°C (Maccoll and Thomas, 1955) and 415-520°C (Blades and Murphy, 1952). It perhaps should be mentioned that, in the case of the halides, reactions which are subject to inhibition are much less reproducible than those which are not affected by the presence of inhibitor.
96
A L L A N MACCOLL
TABLE 1 The Effect of Inhibitors upon Arrhenius Parameters n-Propyl bromide Uninhibited
Isopropyl bromide Uninhibited Inhibited
Inhibited
-
E (kcal mole-') log A Reference
33.8 10.9 n
42.7 13.6 b
50.7 12.9
d
C
~-
47.7 13.60 d
~.
~
Ethyl formate
Isopropyl formate ~.
7 -
E (kcal mole-') log A Reference
47.8 13.62 e
50.7 13.0
1
7
Uninhibited
Inhibited
Uninhibited
Inhibited
40.01 9.40
44.14 11.33
f
B
44.23 12.39 h
44.0 12.58 9
Agius and Maccoll (1955). b Semenov et ol. (1955). c Maccoll and Thomas (1957). Blades and Murphy (1952). e Maccoll and Thomas (1955). f Makens and Eversole (1939). I Blades (1954). h Anderson and Rowley (1943). (1
111. MECHANISMOF PYROLYSIS
It has been seen (p. 92) that, on energetic grounds, a radical non-chain process may be excluded except in very special cases, and so no further consideration need be given t o this mechanism. This leaves the decision to be made between the radical chain and the unimolecular mechanisms. There is, a t the present time, no criterion which is both necessary and sufficient t o prove that a given reaction is proceeding by a unimolecular mechanism. Necessary conditions for a unimolecular mechanism are ( a ) first-order kinetics a t high pressures, ( b ) Lindemann fall-off a t low pressures, (c) absence of induction periods, ( d )lack of effect of inhibitors, and ( e ) an Arrhenius A factor of the order of lo1$ sec-l. An additional useful test, though neither a necessary nor a sufficient condition, is the absence of stimulation of the reaction in the presence of atoms or radicals. Finally, the effects of structural alterations on the rates of those related reactions that are claimed to be unimolecular should be capable of interpretation within the framework of current chemical theory. The pyrolyses to be discussed later in the chapter will now be briefly examined with respect to these criteria. They fall into three classes, I or 11,depending upon whether the reaction is incapable of being inhibited or not, and class 111, which consists of reactions studiedunder conditions of maximal inhibition. Too little work has been done to
97
GAS-PHASE HETEROLYSIS
identify unambiguously the chain mechanisms in class I1decompositions, and so these will not further be discussed. Class I and class I11 decompositions can reasonably be regarded as unimolecular, as will now be shown. All the reactions discussed subsequently show first-order kinetics, and for those systems which have been examined a t low pressures, the Lindemann fall-off. The latter are ethyl chloride, n-propyl chloride, isobutyl chloride (Howlett, 1952) and t-butyl chloride (Howlett, 1952 ; Roberts, 1961), cyclohexyl chloride (Swinbourne, 1958) and isopropyl bromide (Kale and Maccoll, 1964).
10.5 -
10.9-
-u
9.5-
Propene
x
Cyclopentadiene
0
Cyclohexene
A X
A
x-•
1
9.0-
0
0 0
x
00
A
0
VI
8.5 -
A
o 2,4-dimethyl pentene-2
-0 -
A
0
x x x
0 %
A I
100
!
200
300
400
It is worth while distinguishing between an induction period and autocatalysis. I n the former case, (dP/dt)o= 0, while in the latter (dP/dt), > 0. Examples are afforded by 1,2-dichloroethane (Barton and Howlett, 1949) and 1,2-dibromoethane (Good, 1956). None of the reactions under the conditions under which they are claimed to be unimolecular shows either of these effects. I n studies of inhibition it is necessary to show that the nature of the inhibitor is unimportant and also that the concentration of the inhibitor, after a certain limiting value, has no effect. I n the case of n-propyl bromide, propene, cyclohexene, 2,4-dimethylpentene-2, cyclopentadiene and toluene have all been shown to give the same maximally inhibited rate (Maccoll and Thomas, 1957). This independence of the
98
A L L A N MACCOLL
nature of the inhibitor is shown in Fig. 3, as is the lack of dependence upon the concentration of inhibitor. It has long been held that the A factor of unimolecular reactions should be of the order of magnitude of molecular vibration frequencies, sec-l. I n Fig. 4 is shown a distribution curve of log A values for a I
l
l
l
l
l
l
l
l
l
l
A A
Chlorides
A
Bromides 0 Iodides
A
x
0
A
A Esters
A
a
0
O
A
0
0
A
0
0
A
0
0
A
0
0
A
A
O
X
Number of reactions f o r which xclog A c x + O . 5
X
x I
10.5
A
A
X
X
A
o
o
r
x
A
o
o
x
x
x
o
A
x
o
x
x
x
x
Y l
A l
x l
o l
x l
Y l
x l
x l
o l
J
11.0 11.5 12.0 12.5 130 135 14.0 145 15.0 15.5 log A
FIG.4. The distribution of frequency factors in gas-phase unimolecular elimination.
number of halide and ester pyrolyses. The values are consistent with unimolecular reaction theory. Traces of bromine (Harden and Maccoll, 1955; Sergeev, 1956) or oxygen (Sergeev, 1956; Semenov et al., 1955; Agius and MaccoII, 1955) markedly increase the rate of pyrolysis of certain class I1 decompositions. On the other hand, little or no increase in rate is shown by certain class I decompositions in the presence of chlorine (Barton and
99
GAS-PHASE HETEROLYSIS
Onyon, 1949), bromine (Harden and Maccoll, 1955; Sergeev, 1956; Harden, 1957), oxygen (Barton and Onyon, 1949; Sergeev, 1956) or bromine atoms from decomposing ally1 bromide (Maccoll, 1955; Kale and Maccoll, 1957). On the basis of this evidence, it may be concluded that class I and class I11 decompositions are molecular in nature, and it remains to be TABLE 2 The Arrhenius Parameters and Temperature Ranges for Chloride Pyrolyses ____
~
Molecule
log A
E ( h a 1 mole-1)
Temp. range ("C)
- -
Ref.
-
14.60 13.63 n-Propyl chloride 13.45 n-Butyl chloride 14.00 14.50 Neopentyl chloride Isobutyl chloride 14.02 Isopropyl chloride 13.40 s-Butyl chloride 13.75 14.00 Cyclopentyl chloride 13.47 Cyclohexyl chloride 13.77 t-Butyl chloride 12.40 13.90 13.73 14.41 t-Pentyl chloride 13.82 2-Chloro-2,3-dimethylbutane 13.38 2-Chloro-2,3,3-trimethylbutane 13.80 ( - )-Menthy1 chloride 12.60 11.93 Neomenthyl chloride 11.04 Bornyl chloride 13.78 Isobornyl chloride 14.78 1,l-Dichloroethane 12.08 1,1,1-Trichloroethane 14.00 1,2-Dichloropropane 13.80 a-Phenylethyl chloride 10.78 a-Methoxyethyl chloride 11.46 Ethyl chloride
~
60.8 56.9 55.0 57.0 57.9 57 56.9 50.5 50.1 50.6 48.3 50.0 41.4 45.0 45.0 46.6 44.2 42.3 41.9 45.0 42.4 40.9 50.6 49.7 49.5 54.0 54.9 39.3 33.3
400-490 420-500 420-478 430-470 391-458 444-470 417-474 367-406 339-390 316-393 309-376 318-385 290-341 274-372 290-330 271-346 280-320 270-311 250-295 320-440 300-350 300-3'50 320-390 310-350 356-453 363-434 416-452 310-365 180-250
__
-
a b C C
d e
f
9 h
i
j k u 1 VrL VL
rn m
rn 0
P P ! l ?!
a r h S
t
___
=Barton and Howlett (1949). 6 Capon (1964). c Barton et al. (1951). d Heydtmann and Rinck (1961). e Maccoll and Swinbourne (1960). f Howlett (1952). Barton and Head (1950). h Maccoll and Stone (1961).6 Heydt,mann and Rinck (1961).f Swinbourne (1960). IC Swinbourne (1958). 1 Brearley et al. (1936). m Wong (1958). la Roberts (1961). Barton et al. (1952). Bamkole (1964) P Bicknell (1962);Bicknell and Maccoll (1961). Barton and Onyon (1950). 8 Stevenson (1957).t Thomas (1961). " Barton and Onyon (1949).
100
A L L A N MACCOLL
seen whether the effects of substituents can be correlated on the basis of current chemical theory.
IV. THEEXPERIMENTAL RESULTS The Arrhenius parameters for a series of unimolecular dehydrohalogenations are shown in Table 2 (chlorides), Table 3 (bromides), Table 4 (iodides) and for a series of dehydrocarboxylations in Tables 5 and 6.
TABLE3 The Arrhenius Parameters and Tempcrature Ranges for Bromide Pyrolyses
E: Molecule
log 9
(kcal mole-1)
Temp. range (“C)
Ref.
Ethyl bromide n-Propyl bromide n-Butyl bromide lsobutyl bromide n-Pentyl bromide n-Hexyl bromide Isopropyl bromide s-Butyl bromide Cyclopent’ylbromide Cyclohexyl bromide 4-Bromo-1-pentene a-Phenylethyl bromide t-Butyl bromide t-Pentyl bromide 2-Bromo-2,3-dimethylbutane 1,l-Dibromoethane
13.45 12.86 12.80 13.00 13.18 13.06 13.09 13.13 12.62 12.60 12.63 13.04 13.53 12.84 11.90 13.51 12.94 12.18 14.00 13.30 13.23 13.60 13.54 12.91
53.9 52.3 50.7 50.7 50.9 50.4 50.5 50.5 47.8 47.7 43.8 45.5 46.5 43.7 41.4 46.1 44.7 38.8 42.0 40.5 41.0 40.5 39.0 49.5
380-430 527-626 350-390 500-600 370-420 360-420 370-420 370-420 310-350 415-520 300-350 326-398 299-354 300-360 300-360 300-350 300-350 255-285 230-280 235-290 276-326 220-270 210-260 350-430
a b C
b c (I C
f f b
u
h
i j k 1 112 Tk 0
g 1L
A
P !l
a Thomas (1959). b Blades and Murphy (1952). c Maccoll and Thomas (1957). Harden and Maccoll (1959). e Green et al. (1960). f Maccoll and Thomas (1955a). Maccoll and Thomas (1955b). h Sergeev (1956). Kale et ul. (1958). f Kale and Maccoll (1957). Price et ul. (1956). E Green and Maccoll(l955). Thomas (1959). Stevenson (1957). 0 Harden and Maccoll(l955). p Harden (1957). 4 Good (1956).
101
GAS-PHASE HETEROLYSIS
TABLE4 The Arrhenius Parameters and Temperature Ranges for Iodide Pyrolyses
E Molecule Ethyl iodide Isopropyl iodide s-Butyl iodide a Lee (1959). Ogg (1937).
0
log A
(kcal mole-')
13.53 13.66 14.79 13-20 15.20
49.3 50.0 48.0 42.9 47.9
Benson and Bose (1962).
C
Temp. range ("C) 325-380 330-392 290-357 292-336 290-330
Holrnes and Maccoll (1963).
Ref. a b c
d c d
Jones and
TABLE5 The Arrhenius Parameters and Temperature Ranges in Unimolecular Ester Pyrolyses Molecule Ethyl formate Ethyl acetate Ethyl propionate Di-(2-ethylhexyl)sebacate Acetic anhydride Isopropyl formate Isopropyl acetate s-Butyl acetate y-Vinylisopropyl acetate* y-Acetoisopropyl acetate? Cholesteryl acetate Menthyl benzoate a-Phenylethyl acetate 1,2-Diphenylethylacetate t-Butyl formate t-Butyl acetate t-Butyl propionate t-Pentyl acetate t-Butyl chloroacetate t-Butyl dichloroacetate
log A 11.33 12.49 12.72 12.43 12.10 12.58 12.43 13.00 13.42 13.30 13.00 11-88 13.70 11.00 12-81 13.05 11.11 13.34 13.15 12.80 13.43 13.09 12.77
E (kcal mole-1)
Temp. range ("C)
44.1 47.8 48.5 47.1 34.5 44.0 44.2 45.0 46.3 46.6 44.4 37.4 44.1 38.1 43.7 43.3 34.6 40.5 40.0 39.2 40.3 38.1 36.1
540-650 510-610
Ref.
-
260-310 280-650 450-540 310-340 440-530 310-360 300-360 290-360 250-300 280-330 300-400 320-370 315-360 230-300 240-290 240-300 240-300 230-300 215-266 215-250
9 9 h i 2.
k
1
f
m n
f
0
0
* 1-Methylbut-3-enylacetate. t I-Methyl-3-oxobutyl acetate. 0 Blades (1954). b Blades, referred to in DePuy and King (1960). C Sommers and Crowell (1955). d Szwarc and Murawski (1951). e Anderson and Rowley (1943). f Emovon and Maccoll (1962). g Emovon and Maccoll (1964). h O'Connor and Nace (1953). 3 Barton et a2. (1953). 5 Taylor (1962). b Smith et a2. (1961). 1 Gordon et al. (1957). m Rudy and Fugassi (1948). n Warwick and Fugassi (1948). 0 Emovon (1963). 4*
102
A L L A N MACCOLL
In addition to the values given for esters in Table 5, a series of 28 esters have been studied by Scheer et al. (1963). However, these authors use the equation k = BT exp ( - E'/RT)
to express the temperature variation of their rate constants and so the values of the Arrhenius parameters are not strictly comparable with TABLE 6 Arrhenius Parameters (Scheer et aL, 1963)
10k (sec-1)
E' (kcal mole-1)
log B
4G.5 f0.8 46.2 f 0.5 42.2 f0.5 46.8f 1.1 44.5 f0.8 47.8 f 1.2 44.9 0.7 46.4 f 0.4 47.3 f0.5 42.6 f0.7 47.5 f 0.4 44.2 f 1.3 48.2 f0.5 46.3 f0.5 46.4 f 0-5
9.219 9.084 7.947 8.945 8.869 7.958 8.875 9.314 9.072 7.743 9.287 8.276 9.723 8.635 8.765
Secondary Act stes ( Isopropyl acetate 0.31 2-Butyl acetate 0.50 2-Pentyl acetate 0.61 3-Pentyl acetate 0.63 2-Heptyl acetate 0.7 1 3-Heptyl acetate 0.89 4-Heptyl acetate 0.99 3-Methyl-2-pentylacetate 0.62 2,4-Dimethyl-3-pentylacetate 0.38 1-Chloro-2-propjlacetate 0.082 1 -Dimethylamino-2-propyIacetate 0.46 1-Methoxy-2-propyl acetate 0.15
45.2 f0.7 47.0 42.3 & 0.6 43.3 f0.5 43.9 & 0.6 45.5 f 0.8 43.5 f0.6 41.8 f0.9 43.3 f0.5 42.4 f0.4 40.8 _+ 0.9 48.2 0.5
10.113 10.880 9.463 9.815 10.054 10.661 10.053 9.330 9.568 8.628 8.870 9.784
Tertiary Acetates (311OC) t-Butyl acetate 0.17 t-Pentyl acetate 0.42 2-Methyl-2-pentylacetate 0.47 3-Methyl-3-pentyl acetate 0.54 2,3-Dimethyl-2-butylacetate 0.57 1-Methylcyclohexyl acetate 0.29
42.4 f0.5 43.1 39.4 f 0.8 41.2f 1.0 40.1 f0.7 44.0 f 1.9
11.323 11.967 10,646 11.396 11.016 12.164
Compound
l'rimary Acetates (489°C)
Ethyl acetate n-Propyl acetate (1) (2) (3) n-Butyl acetate (1) (2) n-Pentylacetate 3-Methylbutyl acetate
0.57 0.52
2-Methylpropyl acetate 2-Methylbutyl acetate (1) (2) 2-Ethylbutyl acetate 2-Methoxyethyl acetate 2-Ethoxyethyl acetate
0.26 0.34
0.68 0.72 0.77
0.59 0.18 0.21
103
GAS-PHASE HETEROLYSIS
those in Table 5. Reference will be made to the conclusions arrived at by these authors when the mechanism of ester pyrolysis is discussed. It has been seen previously (Fig. 4) that the log A values are distributed fairly closely around a value of 13.25. This implies that the major factor influencing the rate is the activation energy. This, in turn, implies that the effects of substitution upon the rate of reaction of a parent molecule may be expressed either by the activation energy or by the ratio of the rate of decomposition of the substituted compound to that of the parent compound, i.e. the relative rate. Either of these methods will be used below, whichever is more convenient in a given case.
V. REGULARITIES IN THE EXPERIMENTAL DATA A. Halides The data presented in Tables 2 , 3 and 4 are best considered in the light of the effect of substitutions in a parent molecule, namely the ethyl halide, upon the rate of elimination or upon the Arrhenius parameters. Thus Green et al. (1953) concluded from the data for dehydrobromination that it was the nature of the carbon-halogen bond and not that of the carbon-hydrogen bond that was responsible for trends in the rate of elimination. This followed from the fact that a-methylation carried a very marked increase of the rate, whereas for /3-methylation the increase, though real, was small. The activation energies are shown in Table 7. TABLE7 Activation energies (kcal mole-1) for dehydrobromination
CH3. CHzBr
(CH3)zCHBr
53.9
47.8
CH3.CHz.CH2Br
CH3.CH2.CHBr.CH3
(CHd3CBr 42.2
(CH~)ZCB~.CHZ.CH~
50.7
466
40.5
(CH3)zCH.CHzBr
-
(CH3)zCBr.CH(CH&
50.4
-
39.0
This point can also be seen from the temperature ranges over which elimination can conveniently be studied in a static system, namely 350-430°C for a primary, 300-360°C for a secondary and 210-290°C for a tertiary bromide (Table 3). The next stage was the observation by Maccoll and Thomas (1955) that there existed an analogy between the effect of substitution upon the gas-phase elimination reaction (E,) and the effect of similar substitution upon the S,1 or E l reaction of the corresponding compounds
104
ALLAN MACCOLL
in polar solvents. Attention was drawn to the fact that, while there was little correlation between the activation energy for elimination of HX ( X = C1, Br), E(HX), and the homolytic bond dissociation energy, D(R-X), a clear correlation existed with the heterolytic bond dissociation energy D(R+X-). These latter two quantities are the heats of reaction of the processes RX + R+X,
D(R-X)
RX + R++X-,
D(R+X-)
the former leading to radicals and the latter to ions. Further evidence came from the rate relationships (CH3)sCBr % (CH3)zCHBr 9 CH3. CHzBr CH3. CHBrz > CH3. CHzBr > CHzBr .CHzBr
together with the fact that a-methoxyethyl chloride decomposes in the gas phase in a temperature range some 50" lower than does t-butyl bromide. These eliminations are in complete accord with the behaviour of the corresponding halides on solvolysis by the unimolecular mechanism. It was suggested that the transition state can be described as an elongation, with polarization (in the sense C6+---X6-) of the C-X bond, with some assistance from the polarized 8-C-H bond. Further it was suggested that the ,!3-C-H bond plays somewhat the same role in stabilizing the forming X- as does the solvent in the solvolytic reaction. Figure 5 shows the proposed energetics of the reaction. Curve (a) is the potential energy curve for the excited state leading to dissociation into ions. Curve (b) is the corresponding curve for the normal state. Curve (c) represents the hypothetical stabilization of the C+Br- system by the /%hydrogen atom, leading eventually to an olefin and hydrogen halide. Aa a result of the intersection of curves (b) and (c),a splitting will occur, leading to the curve (d) which represents the reaction path. The analogy between the gas-phase elimination reaction and the SN1 or E l reactions was more fully explained and documented in a paper presented a t the Kekule Symposium (Maccoll, 1959). It was, in fact, shown that for all the systems that had been examined the analogy was complete. A distinction was drawn between those reactions that show little effect of methyl substitution, e.g. CHz-CHz
1
1
CH2 -CH2
-
CHz=CHZ
CHz=CHz
and those for which the effect is large, e.g. alkyl halides and esters. The latter class of reactions was called quasi-heterolytic.
GAS-PHASE HETEROLYSIS
w
105
\\ \
\
2.
g
t
w
rC-Br
FIG.5. Diagrammatic representation of the energetics of dehydrohalogenation.
60 -
1
'T
-W
55-
E"
-0 2
Y
50-
Lu
45
-
D (R'X-1
(kcol.mole-')
FIG.6. The relation between the activation energy for gas-phase elimination E(H-X) and the heterolgtic bond dissociation energy D ( R + X - )for a series of organic halides.
106
ALLAN MACCOLL
The problem was again taken up in general terms at the Chemical Society Symposium on the Transition State (Maccoll, 1962). Here, the behaviour of carbonium ions in the mass spectrometer and in solvolytic reactions was examined in relation to the behaviour of the virtual carbonium ions postulated in the gas-phase elimination reaction. Such properties as the ease of formation of carbonium ions and their rearrangements were examined, and, where data were available, a linear relationship was found between the activation energy for elimination and the heterolytic bond dissociation energy. This relationship is shown in Fig. 6. The evidence that has been established is shown in Table 8. Prom an examination of the Table it will be seen that : ( a ) Electron releasing groups at the u-position and to a much lesser extent at the p-position increase the rate of elimination. ( b ) While u-halogen substitution increases the rate, /3-halogenation decreases it. TABLE8 Effects of Substitution on Rates of Elimination from Halides Variation of halogen R I > RBr > RC1 R = Et, i-Pr, s-Bu a-Methylation X = C1, Rr (CH3)3CX % (CH3)Z.CHX 9 CHs.CH2X (CH3)zCHI 9 CH3. CH2I ,!?-Methylation (CH3)zCH.CHzX > CH3.CHz.CHzX CH3.CHzX X = C1, Br (CH3)sC.C(CH3)zCl > (CH3)zCH.C(CH3)2C1> CH3. CHz .C(CH3)zCl> (CH3)3CC1 CHs. CH2. CHI. CH3 > CH3. CHI. CH3 a- and 8-Halogenation CH3. cCl3 > CH3. CHClz > CH3. CHzCl > CHzCl. CHzCl CH3. CHBr2 > CH3. CH2Br > CHzBr. CHzBr a- and 8-Phenylation PhCHX.CH3 N (CH3)sCX X = C1, Br PhCHZ.CHzX CH3.CHz.CHzX X = C1, Br p-Substituted a-phenylation p-FCaH4.CHCl. CH3 > PhCHX. CH3 > p-ClCeH4.CHCl .CH3 a-and 8-Vinylation CHz=CH. CHCl. CH3 CH3. CHCl. CH3 CHz=CH. CH2. CHBr CH3 CH3. CH2. CHBr .CH3 a-Methoxylation CH30. CHCl. CH3 9 CHI. CHzCl a-Acetylation CH3.CO .CHCl.CHs < CH3.CHz.CHzCl.CH3 X = C1, Br C,Hz,+l-,DzX 7 C,Hz,+lX Wagner-Meerwein rearrangements neo-CsH11, neo-C&, ,C02C1, bornyl chloride, isobornyl chloride Product olefins determined by the Saytzeff rule
-
N
.
-
107
GAS-PHASE HETEROLYSIS
(c) a- and /3-vinylation has little effect upon the rate. (d) Deuteriation retards the rate of elimination. (e) Rearrangements characteristic of carbonium ions in st polar solvent are also observed in gas-phase elimination. All these effects are analogous to those found for solvolytic reactions occurring in a polar solvent (Maccoll, 1959). It is proposed now to examine them in relation to a transition state represented by
on the understanding that the positive charge is distributed between the a-carbon atoms and the /3-hydrogen atoms. Such an intimate ion pair cannot be excluded on energetic grounds, as a rough order-of-magnitude calculation shows. I n fact, a large part of the energy for heterolysis is recovered as coulombic energy when the separated ions are allowed to form the ion pair. It will now be shown that the data in Table 8 are consistent with this formulation of the transition state. a- and /3-Methylation can be understood in terms of the hyperconjugative effect. Thus for the a-methylated series ethyl, isopropyl and t-butyl TABLE 9 Delocalization in the Carbonium Ion a-Methylated series _____
/I-Methylated seriew ~.
~~
C Ha-CHz+
Hf
CCHFCHZ
i
(3)
+ CH3-CH-ClLs
i
H+
‘ICH2=CH-CH3
‘I J (6)
+ CH-C(CH3)z
1 .I CHz=C(CH3)8 J (9)
r + (CH3)zCH-CHz
108
A L L A N MACCOLL
and for the ,$-methylated series ethyl, n-propyl, isobutyl, the carbonium ion can be represented as shown in Table 9. I n each case the number in brackets gives the number of resonance forms. It will be seen that two effects are in operation, which reinforce each other in the a-methylated series and oppose each other in the ,$methylated series. They are first the stability of the olefin, increasing in the order ethylene, propene, isobutene in both series, and the number of resonance forms increasing froni three to nine in the a-series and decreasing from three to one in the ,$-series. Evidence for delocalization of this sort may be found in the mass spectrum of ethane-l,l,l-d,. Peaks are found in the mass spectrum corresponding to CH,D and to CHD, (Schissler et al., 1951). These can be thought of as arising from the following processes :
(CH3CD3)f
C'H3f + CDz CHzDt + CDz
While this behaviour is highly suggestive, it must be remembered that in mass spectrometry excited states of the carbonium ion may be involved. I n the case of the a-phenylethyl cation, structures A-D need to be taken into account, while in the p-substituted species these have to be augmented by E. I n this way the effect of the phenyl group which
is equivalent to two methyl groups can be understood. At the P-position, the delocalization of the charge from the terminal atom to the phenyl group is effectively insulated by the intervening methylene group and
109
GAS-PHASE HETEROLYSIS
results in a relatively small amount of stabilization. I n the methoxy compound structures
+
+
CH~O-CH-CHB
H+ CH30CH=CH2
CH30=CH--CHs
F
(3)
H
G
contribute to the stability of the carbonium ion. I n the a-positions, a second halogen atom can stabilize the carbonium ion by resonance between the structures I-K + CH3-CHX
H+ CHz=CHX
CHs-CH=X+
I
J
(3)
K
whereas in the P-position it can exercise only its inductive electronwithdrawing effect. Thus a-halogeno substitution enhances the rate while 8-substitution decreases it. The results of a- and P-vinylation are of interest in the information they afford as to the nature of the transition state. For if the latter were t o be four-centred /
'/cI-c ,
I
H---X
- ,C'-c,
= \
I
/
I
H X
,c=c / >
\
H-X
it might be expected that the homolytic weakening of the P-carbonhydrogen bond in 2-bromopentene-4 would markedly increase the rate of elimination. Again for such a transition state, for both 2-bromopentene-4 and for a-methylallyl chloride, the extended conjugations implicit in the following resonance structures CHz=CH--CH=CH-CH3 H-X
CHZ=CH-CH=CH~ X-H
would be expected to enhance the rate. No such effect is observed; the two compounds decompose a t about the same rates as s-butyl bromide and isopropyl chloride respectively. Studies of the deuteriated halides have been carried out by Good (1956) and by Blades (1962a, b). Good found that isopropyl bromide-d, decomposed more slowly than isopropyl bromide, although it was difficult to say definitely whether the effect was upon the activation energy or upon the frequency factor of the Arrhenius equation. Blades (1962a) was able to show that for ethyl bromide-d, the effect lay mainly in the activation energy. For the elimination of protium and deuterium bromides from partially deuteriated ethyl bromides the difference in rate appeared to reside in the activation energy (Blades, 1962b). Blades
110
A L L A N MACCOLL
concluded from the results of these investigations that the carbonhydrogen bond is nearly broken in the transition state. This need not necessarily follow, since it is possible that the heterolytic bond dissociation energy, D(R+X-), is greater for the deuteriated molecule than for the hydrogen one. Also in the carbonium ion, (CzH,D5-,}+ the H+) and CzH,D4-,(D+) might make different structures C2Hz--1DS--z( contributions, thus explaining the greater rate of elimination of hydrogen bromide as compared with deuterium bromide. Thus the results of deuteriation studies are not necessarily inconsistent with the picture of the transition state presented here. Maccoll and Swinbourne (1960, 1964) observed elimination of hydrogen chloride in the pyrolysis of neopentyl chloride, even though this molecule does not possess a p-hydrogen atom. I n the reaction scheme (1)-(3), reaction (1) accounted for 75% of the total reaction. The products from ( 1 ) are those that would be expected from t-pentyl ( C H 3 ) z C d H .CHa (CH3)zCH.CHdHz CHz==C(CH3).CH2. CHI (CH&C=CH2 + CH3Cl (CH~)ZC=CHCI CHz=C(CHs) .CHzCI
chloride, and so the Wagner-Meerwein rearrangement is established. A similar conclusion was drawn by Lewis and Herndon (1961) in their study of the pyrolysis of neopentyl chloroformate. Bicknell (1962) found another Wagner-Meerwein rearrangement in the cases of bornyl and isobornyl chlorides. This was all the more surprising in that the major products from the former compound are tricyclene and camphene and from the latter camphene, despite the fact that there is in each compound a 6-hydrogen atom cis to the chlorine atom so that bornylene
f
R
BAS-PHASE HETEROLYSIS
111
might have been expected to be a major product. I n fact, it is formed to only about 20% and 25% in the two cases respectively. The reaction scheme is shown on p. 110. All the rearrangements in the gas-phase have their counterparts in solvolytic reactions in polar solvents. Similar rearrangements are also observed in the mass-spectrometer, one such example being the appearance of a fragment at mje = 28 in the mass spectrum of isobutane. To account for this, the migration of a methyl group in the carbonium ion must be postulated. Barton (1949)has emphasized the cis-nature of gas-phase elimination, a point further taken up by DePuy and King (1960). Barton et al. (1952) Pr‘
CH3 (’1 Menthyl cliloricle
c1 Neo-menthyl chloride
have shown that, in seasoned vessels, the pyrolysis of menthyl chloride is homogeneous and unimolecular and that the ratio of menthene-3 to menthene-2 is 3 :1. Bamkole ( 1964)has studied the pyrolysis of both menthy1 and neo-menthyl chlorides and in the former case has confirmed the product ratio observed by Barton et al. (1952). For neo-menthyl chloride the menthene-3 :menthene-2 ratio was 1:5-7. There is thus a reversal of the direction of elimination in going from menthyl to neomenthyl chloride. These experiments demonstrate the cis-nature of the elimination. There is also a departure from the analogy with solvolytic reactions, for in solution menthyl chloride yields predominantly menthene-3 by the E l mechanism (as it does in the gas-phase) but neo-menthyl chloride gives menthene-3 almost exclusively (as compared with the preponderance of menthene-2 in the gas-phase), Also the solvolytic elimination from neo-menthyl chloride is appreciably faster than that from menthyl chloride, whereas in the gas-phase menthyl chloride pyrolyses only slightly more rapidly than its isomer. Banthorpe (1963) has suggested that the enhanced rate of elimination from neo-menthyl chloride might “in part be an artefact caused by bimolecular attack of a solvent molecule on the favourable trans configuration”. For this reason, the breakdown of the analogy need not be too serious. It is of interest to note the enhancement of the rate of both the menthyl and neo-menthyl chloride pyrolyses over that of cyclohexyl chloride. A t 3OO0C, menthyl chloride pyrolyses some fifty times faster than does cyclohexyl chloride. Although the analogy between gas-phase elimination and the E l reaction is not maintained in this case, the observed
112
A L L A N MACCOLL
results are not inconsistent with the quasi-heterolytic character of the gas-phase elimination reaction.
B. Esters The effect of a-methyl substitution in ester pyrolysis may be calculated and is shown in Table 10. a-Methyl substitution thus increases the rate of elimination, a conclusion substantiated by other series reported by TABLE 10 a-Methyl Substitution in Ester Pyrolysis (Relative Rates) ~-
~~
~ _ _ _ _ _ _
Ethyl Isopropyl t-Butyl Formates (400")
1
20
Acetates (400")
1
26
7 2 0 } Maccoll, 1969 1660
Acetates (400')
1
24
2000
Scheer et aZ., 1963
Scheer et al. (1963). This is also shown by the fact that for primary, secondary and tertiary acetates the temperature ranges for which the conversion lay between 20 and 80% were respectively 452-537"C, 377-437°C and 287-337°C. On the other hand, /3-methyl substitution has only a relatively small effect. For a primary, secondary and tertiary series, the results are given in Table 1 1 . It is seen that the effect is small as compared with the effect of a-methyl substitution, but for the secondary and tertiary series the results suggest that /3-methylation causes a small but nevertheless significant increase in the rate of elimination. The effect of electron-withdrawing groups a t the /3-position is shown by a comparison of the ethyl acetate, 2-ethoxyethyl acetate and 2methoxyethyl acetate for which the relative rates (Scheer et al., 1963) are 1 : 0.37 :0.32. On the other hand, the substitution of an electronwithdrawing group a t the y-position enhances the rate of elimination (Emovon and Maccoll, 1964) the rate ratio for y-acetoisopropyl acetate to s-butyl acetate being 108:l a t 309°C. Smith and Wetzel (1951) have shown qualitatively that the strength of the acid and the rate of ester pyrolysis increased in the same direction. This conclusion is borne out by the work of Emovon (1963) who found for the series t-butyl acetate, t-butyl chloroacetate and t-butyl dichloroacetate that the rates a t 250°C were in the ratio 1 :4-4:18.6.
113
GAS-PHASE HETEROLYSIS
TABLE11
/3-Methyl Substitution in Acetate Ester Pyrolysis (Relative Rates) Primary series Temp. ("C)
Ethyl
489
1
---Isopropyl
41 1 308
n-Propyl 0.91
Isobutyl
Ref.
0.46
a
Secondary series s-Butyl
1 1
7
3-Methyl-2-pentyl
1.6 0.96
-
Tertiary series--
7 -
t-Butyl
a
t-Pentyl
a b
2.0
7
2,3-Dimethyl-2-butyl
311
1
2.5
3-4
n
237
1
1.5
-
b
Scheer et nl., 1963.
b
Emovon and Maccoll, 1962.
The effects of a- and /3-phenyl substitution can be calculated from the data of Table 5 . The reaction rates for ethyl acetate:a-phenyl ethylacetate :a , P-diphenylethylacetate are 1:45 :130. Thus a phenyl group in the cr-position, has a relatively large effect ; in the /3-position, a much smaller one. This behaviour is also observed with the halides, although in that case the enhancement of rate on a-phenylation is very much larger. Smith et ab. (1961) have measured the rate of gas-phase pyrolysis of esters of the type
With X in the 4-position, and Y = H, the rate sequence CHJO > CH3 > H > C1
was obtained. With Y in the 4-position and X = H, the order was reversed. Further, for both the a-aryl-P-phenylethyl acetates and the a-phenyl-P-arylethyl acetates, a correlation was observed with the Hammett u function. I n a subsequent publication Taylor et al. (1962) obtained an even better correlation with the CT+ function. I n that paper the effects of a wide range of substituents in the phenyl ring of a-phenyl-
114
A L L A N MACCOLL
ethyl acetate were also reported. Once again a linear plot was obtained when log k x / k , was plotted against o+ (Fig. 7 ) . Of particular interest is the order p - F > H > P-CI
which is just that recently observed by Bridge (1964) for the corresponding chlorides. 0.6
I
I
I
I
I
I
I
I
I
\
X 1
m
-0
0-
-0.1 -
-0.2
-
-0-3-0.4
-
-0.5
-
I
I
I
I
-0.8 -0.6 -0.4 -0.2
I
0
I
I
I
1
0.2 0.4 0.6 0 8
U+
FIG.7. A plot of log (k,/k,) against
U+
for the system X-
(after Taylor et al., 1962).
The effects of deuteriation upon the rate of ester pyrolysis have been determined by Blades and Gilderson (1960a, b) and by DePuy et al. (1959). The latter authors found a considerable isotope effect in 1-methylcyclophenyl-2,2,6,6-d4 acetate. Blades and Gilderson studied ethyl-l,1,2,2-d4acetate (1960a) and ethyl and ethyl-d, acetate (1960b). I n the latter paper, the rate of production of ethylene and ethylene-d4 was measured in a mixture of the two acetates. The effect observed was largely in the activation energy k H / k D= 0.8exp(1513/RT)
GAS-PHASE HETEROLYSIS
115
Thus the effect of denteriation is to reduce the rate of pyrolysis, as was found in the case of the halides. The direction of elimination from esters has been extensively studied (DePuy and King, 1960). I n general, where special structural features are absent, olefin with the smallest number of alkyl substituents is most abundant. Thus from s-butyl acetate 60% of butene-1 is produced, while from t-pentyl acetate, 2-methylbutene-1 occurs to the extent of 75%. I n distinction to the halides, which, as has been seen, give the Saytzeff product, the esters give predominately the Hofmann product. This may in part be due to the fact that the carboxylic acid which is found along with the olefin, is not capable of bringing about isomerization, as can the hydrogen halide in the case of the alkyl halides. The observed rate relationships in the case of the esters are summarized in Table 12. TABLE12 Effects of Substitution o n Rates of Elimination from Esters
(1) Effect of acid strength CHClz .COzBuY > CHzCl. COzBu’ > CH3. COzBuY (2) a-Methylation RCOzC(CH3)3 > RCOzCH(CH3)z > RCOzCHz .CH3 (3) j3-Methylation CH3.CH2. OAc > CHI. CHz. CHZ.OAc < (CH3)zCH.CHZ.OAC b u t (CH3)zCH.C(CH3)zOAc > CH3. CHz. C(CH3)zOAc > CH3. C(CH3)20Ac (4) j3-Alkoxylation CH3. CH(0Ac).CH3 > CzH50CHz. CH(OAC)CH~ > CH3. OCHz .CH(0Ac)CHs ( 5 ) a- an d j3-Phenylation PhCHz. CHPh. OAC > PhCHz .CHz .OAC > CH3. CHz .OAc (6) p-Substituted a-phenylation CH30 > Me > F > H > C1 (7) 8-Acetylation CHs. CO CHz .CH(0Ac). CH3 9 CH3. CHz. CH(0Ac).CH3
.
( 8 ) CnH!2,,+,-,DzOAc < C,H,,+,OAc (9) Product olefins determined b y the Hofmann rule
It will be seen from Table 12 that there is a good deal of similarity between the effect of substitution upon ester pyrolyses and upon halide pyrolyses (Table 8). No examples of gas-phase rearrangements of esters have so far been reported. However, Bunton and co-workers (1961) have examined bornyl and isobornyl methylxanthates and benzoates in the liquid phase
116
ALLAN MACCOLL
and have shown that bornylene, tricyclene and camphene are the products of decomposition. The results (Table 13) clearly indicate that TABLE13 Composition of Pyrolysis Products of Bornyl and Isobornyl Esters -...
Bornylene
Bornyl methyl-xanthate Isobornyl methyl-xanthate Bornyl benzoate Isobornyl benzoate
70 38.5 24.5 0
(yo) Tricyclene (yo) Camphene (%) 13.5 0 21.5 13
16.5 61.5 54 87
the expected product of &-elimination (bornylene)is the major product only in the case of the decomposition of bornyl methylxanthate. The justification for discussing these results in connection with gas-phase elimination is contained in Table 5. The values given there for di-(2ethylhexyl) sebacate and cholesteryl acetate, obtained from liquid phase studies, are in good accord with those for primary and secondary acetates, respectively, when studied in the gas-phase. Thus it may be concluded that, just as in the case of the halides, Wagner-Meerwein rearrangements in all probability occur in the gas-phase elimination from esters. Hurd and Blunck (1938) proposed a six-centred transition state in
gas-phase elimination. It became apparent to a number of authors that this formulation was not entirely satisfactory, since it is not capable of providing an explanation of the polar effects of substituent groups. Thus Maccoll (1958) suggested that the major factor influencing the rate of elimination from esters was the nucleophilic attack of the acyl group upon the /3-hydrogen atom, a view that was subsequently altered in favour of the prime importance of the heterolysis of the carbon-alkyl oxygen bond (Emovon and Maccoll, 1963). DePuy and King (1960) suggested the importance of a small degree of charge separation in the transition state, together with the strength of the forming olefinic bond; the latter has been challenged by Taylor et aE. (1962). These authora emphasized the importance of the stability of the carbonium ion. Scheer et al. (1963) have also stressed the importance of the heterolysis
GAS-PHASE HETEROLYSIS
117
of the carbon-alkyl oxygen bond and have suggested a two-stage mechanism, 1
R-C02R’
+ { RC02}-{
R’}+
2
3
{RCO,}-{R’}+
3
RCOaH+OI
where 01 is an olefin, with
In this fashion, the deuterium isotope effect could be explained without the necessity of postulating nearly complete carbon-P-hydrogen cleavage in the transition state. The representation of the transition state which is most in accord with the experimental facts is
I n terms of this model, the relationships of Table 12 can be understood. The major difference between the transition state in halide pyrolysis as compared with that for ester pyrolysis is thus the degree of hoterolysis.
VI. HOMOGENEOUS CATALYSIS o r GAS-PHASEELIMINATIONS No cxamples of catalysis of unimolecular elimination from halides 01’ esters have been reported. Failes and Stimson (1962) have shown that t-butyl chloride undergoes elimination in t,he gas-phase a t a rate independent of the partial pressure of added sulphur hexafluoride, a substance known to accelerate certain decompositions (Bose and Hinahelwood, 1959). However, the pyrolysis of alcohols, first studied by Kistiakowsky and Schultz (1934) is accelerated by the presence of hydrogen halides (Maccoll and Stimson, 1960). The former authors showed that t-butyl alcohol decomposed homogeneously t o yield isobutene and water, at a rate given by
kl =
4.8 x 1014exp ( - 65,500/RT)sec-I
For the same reaction, Barnard (1959) obtained the rate equation
k l = 3.24 x 10l1exp ( - 54,50O/RT)sec-l and further showed that nitric oxide had no effect on the rate. I n
118
A L L A N MACCOLL
contrast with these results, the reaction is homogeneous and bimolecular in the presence of hydrogen bromide, the rate equation being (Maccoll and Stimson, 1960)
a
- - [BUYOH] = k,[BurOH] [HBr] dt
Stimson and co-workers have made a detailed study of the homogeneous catalysis of olefin elimination from alcohols and the results are shown in Table 14. No induction periods were observed and cyclohexene and TABLE14 The Catalytic Dehydration of Alcohols
Molecule
Catalyst
10-12 A (cm3mole-1 sec-1)
E (kcal molo-1)
Temp. range ("C)
i-CaH70H S-CdHgOH t-CdHgOH t-CZH11OH t-C4HgOCH3 t-CrHgOH t-CrjHiiOH
HBr HBr HBr HBr HBr HCl HC1
1.0 5.8 9.2 1.0 0.67 2.0 6.7
33.2 34.9 30.4 27.1 25.6 32.7 34.0
369-520 387-510 315-422 308-415 258-371 328-454 370-503
d
Ref. a
b C
d e
f g
a Ross and Stimson (1960). b Failes and Stimson (1962). c Maccoll and Stimson (1960). Stimson and Watson (1960). e Stimson and Watson (1963). f Lewis and Stimson (1960). Watson and Stimson (1961).
propene had no effect upon the rates of the reactions, which were inferred to be molecular. This conclusion was in accord with the magnitude of the Arrhenius A-factors. Further, in the presence of mixtures of hydrogen chloride and hydrogen bromide, the catalytic effects were additive. Catalysis by hydrogen iodide was complicated by the formation of iodine. However, an estimate of the relative rate of catalysis by the hydrogen halide is shown in Table 15. (Stimson, private communication). TABLE15 Relative Rates of Catalysed Olefin Elimination Molecule
Temp. ("C)
HC1
HBr
HI
t-CSH11OH t-C4HgOH i-C3H70H t-CdHgOCH3
410 320 420 371
1
27 27 25 23
180 130
1 1 1
-
119
GAS-PHASE HETEROLYSIS
In Table 16, (Stimson, private communication) the effects of a- and /3-methyl substitution are shown. TABLE1G The Effects of a-and P-Methylationupon Catalysed Elimination a-Methylated series Temp. ("C)
CzH50H
i-CsHSOH
t-BuOH
440
1
25
1600
446
i-CaH.iOH 1 t-CaH90H 1
/3-Methylated series s-C~H~OH 2.0 t-C~H110H 1.7
361
(CH~)ZCH.CH(OH) .CHs 2.1 (CH~)ZCH.C(OH)(CH~)Z 1.7
Table 15 clearly shows that the catalytic effect is determined in part by the acid strength of the hydrogen halide (HI > HBr > HC1). Table 16 shows that while a-methylation has a relatively large effect upon the rate of elimination, the effect of /3-methylation is small. These observations are in accord with the representation of the transition state as
and the reaction can be regarded as essentially quasi-heterolytic.
VII. GENERAL CONCLUSIONS
It would appear from the foregoing that there is a class of gas-phase reactions for which the transition state is best represented as having an essentially carbonium-ion pair character. I n this way the effect of substitution at or near the centre of reaction can be interpreted, and the vast body of theory in the literature of physical organic chemistry used for the purpose of predicting rates of gas-phase reactions. In addition, the known properties of carbonium ions, as determined by the massspectrometer, can be invoked-as indeed they were in discussions of the SN1and E l reactions in polar solvents (Evans, 1946)-to correlate the effects of substituents in gas-phase eliminations. The advantage of studies in the gas-phase lies in the fact that the behaviour of a single molecule can be observed, without the added complication of the cooperative effect of the solvent. But gas-phase studies may, in turn,
120
ALLAN MACCOLL
throw further light upon the all-important problem of solvation. Table 17 shows the effect of solvation in reducing the energy of heterolysis. TABLE17
Energetics of Ionization of Bromides Primary D(R+X-)a E(HX)b E ( S , 1) C a
Maccoll, 1962.
Secondary 158 47.8 27
180
63.9 30 b
Table 3.
c
Tertiary 138 42.2
23
C. K. Ingold, 1953, p. 415.
Solvation energies are of the order of 100-150 kcal mole-] and decrease in the sequence C2H, > i-C3H, > t-C4H9. The role of the P-hydrogen atoms in stabilizing the transition state of gas-phase elimination has been suggested by Maccoll and Thomas (1955). This effect can be interpreted in either of two ways, namely the interaction of the developing chloride ion with a specific P-hydrogen atom, or the interaction with the smeared out totality of P-hydrogen atoms, due to internal rotation. The former alternative would be open to the same criticisms as was the fourcentred transition state. REFERENCES Agius, P. J., and Maccoll, A. (1955). J. Chem. SOC.973. Anderson, R. B., and Rowley, H. H. (1943). J. Phys. Chem. 47, 454. Bamkole, T. (1964) Ph.D. Thesis, University of London. Banthorpe, D. V. (1963). I n “Elimination Reactions”, Elsevier, London. Barnard, J. A. (1959). Trans. Faraday SOC.55, 947. Barton, D. H. R. (1949). J. Chem. SOC.2174. Barton, D. H. R., and Head, A. J. (1950). Trans. Faraday Soc. 46, 114. Barton, D. H. R., and Howlett, K. E. (1949a). J. Chem. SOC.155. Barton, D. H. R., and Howlett, K. E. (194913). J . Chem. SOC.165. Barton, D. H. R., and Onyon, P. F. (1949). Trans. Faraday Soc. 45, 725. Barton, D. H. R., and Onyon, P. F. (1950). J . Am. Chem. SOC. 72, 988. Barton, D. H. R., Head, A. J., and Williams, R. J. (1952). J . Chem. SOC.453. Barton, D. H. R., Head, A. J., and Williams, R. J. (1953). J. Chern. SOC.1715. Benson, S. W., and Bose, A. N. (1962). J. Chem. Phys. 37,2935. Bicknell, R. C. (1962). Ph.D. Thesis, University of London. Bicknell, R. C., and Maccoll, A. (1961). Chern. & Ind. (London) 1912. Blades, A. T. (1954). Can. J. Chem. 32, 366. Blades, A. T. (1960)Private communication referred to in DcPuy and King (ISGO). Blades, A. T. (1962a). Can. J. Chem. 40, 1527.
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Blades, A. T. (1962b). Can. J. Chem. 40, 1533. Blades, A. T., and Gilderson, P. W. (l960a). Can. J. Chem. 38, 1401. Blades, A. T., and Gilderson, P. W. (1960b). Can. J. Chem. 38, 1407. Blades, A. T., and Murphy, G. W. (1952). J. Am. Chem. Soc. 74, 6219. Bose, A. N., and Hinshelwood, C. N. (1959). Proc. Roy. Soc. 2594, 174. Bridge, M. R. (1964). Ph.D. Thesis, University of London. Brearley, D., Kistiakowsky, G. B., and Stauffer,C. H. (1936). J. Am. Chem. SOC. 58, 43. Bunton, C. A., Khaleeluddin, K., and Whittaker, D. (1961). Nature 190, 715. Capon, N. (1964). Ph.D. Thesis, University of London. Daniels, F., and Veltman, P. L. (1939). J. Chem. Phys. 7, 756. DePuy, C. H., and King, R. W. (1960). Chem. Revs. 60, 431. DePuy, C. H., King, R. W., and Froemsdorf, D. H. (1959). Tetrahedron 7, 123. Emovon, E. U. (1963). J. Chem. Soc. 1246. Emovon, E. U., and Maccoll, A. (1962). J. Chem. SOC.335. Emovon, E. U., and Maccoll, A. (1964). J. Chem. Soc. 227. Evans, A. G. (1946). “The Reactions of Organic Halides ”,Manchester University Press. Failes, R. L., and Stimson, V. R. (1962a). Australian J. Chem. 15, 437. Failes, R. L., and Stimson, V. R. (1962b). J . Chem. Soc. 653. Good, P. T. (1956). Ph.D. Thesis, University of London. Gordon, E., Price, S. J. W., and Trotman-Dickenson, A. F. (1957). J. Chem. SOC. 2813. Green, J. H. S., and Maccoll, A. (1955). J. Chem. Soc. 2449. Green, J. H. S., Maccoll, A., and Thomas, P. J. (1960). J. Chem. Soc. 184. Green, J. H. S., Harden, G. D., Maccoll, A., and Thomas, P. J. (1953). J . Chem. Phys. 21, 178. Harden, G. D. (1957). J. Chem. Soc. 5024. Harden, G. D., and Maccoll, A. (1955). J. Chem. SOC.2454. Harden, G. D., and Maccoll, A. (1959). J. Chem. Soc. 1197. Heydtmann, H., and Rinck, G. (1961a). 2. Physik. Chem. (Frankfurt)28, 85. Heydtmann, H., and Rinck, G. (1961b). 2. Physik. Chem. (Frankfurt)30, 250. Holmes, J. L., and Maccoll, A. (1963). J. Chem. Soc. 5919. Howlett, K. E. (1952). J. Chem. Soc. 3695, 4487. Howlett, K. E. (195213). J. Chem. Soc. 4487. Hurd, C. D., and Blunck, F. H. (1938). J . Am. Chem. Soc. 60, 2419. Ingold, C. K. (1953). “Structure and Mechanism in Organic Chemistry”, Bell, London. Jones, J. L., and Ogg, R. A. (1937). J. Am. Chem. Soc. 59, 1939. Kale, M. N., and Maccoll, A. (1957). J. Chem. Soc. 5020. Kale, M. N., and Maccoll, A. (1964). J. Chem. Soc. 1513. Kale, M. N., Maccoll, A., and Thomas, P. J. (1958). J. Chem. Soc. 3016. Kistiakowsky, G. B., and Schultz, R. F. (1934). J . A m . Chem. SOC.56, 395. Kistiakowsky, G. B., and Stauffer, C. H. (1937). J. Am. Chem. Soc. 59, 165. Leo, R. A. (1959). M.Sc. Thesis, Univcrsity of London. Lewis, E. S., and Herndon, W. C. (1961). J. Am. Chem. Soc. 83, 1961. Lewis, K. G., and Stimson, V. R. (1960). J. Chem. Soc. 3087. Maccoll, A. (1955). J. Chem. Soc. 965. Maccoll, A. (1958). J. Chem. Soc. 3398. Maccoll, A. (1959). I n “Theoretical Organic Chemistry ”, Butterworths, London, p. 230.
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Maccoll, A. (1962). Chem. SOC. Spec. Publ. No. 16, 158. Maccoll, A., and Stimson, V. R. (1960). J. Chem. SOC.2386. Maccoll, A., and Stone, R. H. (1961). J. Chem. SOC.2756. Maccoll, A., and Swinbourne, E. S. (1960). Proc. Chem. SOC.409. Maccoll, A., and Swinbourne, E. S. (1964). J. Chem. Soc. 149. Maccoll, A., and Thomas, P. J. (1955a). J. Chem. Soc. 979. Maccoll, A., and Thomas, P. J. (1955b). J. Chem. Soc. 2455. Maccoll, A., and Thomas, P. J. (1955~).J. Chem. SOC.5033. Maccoll, A., and Thomas, P. J. (1955d). Nature 176, 392. Maccoll, A., and Thomas, P. J. (1957). J. Chem. SOC.5033. Makens, R. F., and Eversole, W. G. (1939). J. A m . Chem. SOC.61,3203. O’Connor,G. L., and Nace, H. R. (1953). J. A m . Chem. Soc. 75, 2118. Ogg, R. A., and Polanyi, M. (1935). Trans. Faraday Soc. 31, 482. Price, S. J. W., Shaw, R., and Trotman-Dickenson, A. F. (1956). J. Chem. SOC. 3855. Rice, F. O., and Polly, 0. L. (1938). J. Chem. Phys. 6, 273. Roberts, B. (1961). Ph.D. Thesis, University of London. Ross, R . A., and Stimson, V. R. (1960). J. Chem. SOC.3090. Rudy, C. E., and Fugassi, P. (1948). J. Phya. Chem. 52, 357. Scheer, J. C., Kooyman, E. C., and Sixma, F. L. J. (1963). Rec. Trav. Chhn. des Pays-Bas 82, 1123. Schissler, D. O., Thompson, S. O., and Turkevich, J. (1951). Discussions Faraday SOC.10, 46. Semenov, M. N., Sergeev, G. B., and Kaprilova, G. A. (1955). Doklady Akad. Nauk SSSR 105,301. Sergeev, G. B. (1956). Doklady Akad. Nauk SSSR 106, 299. Smith, G. G., and Wetzel, W. H. (1951). J. A m . Chem. SOC.73, 975. Smith, G. G., Bagley, F. D., and Taylor, R. (1961). J. A m . Chem. Soc. 83, 3647. Sommers, E. E., and Crowell, T. I. (1955). J. A m . Chem. SOC. 77, 5443. Staveley, L. A. K., and Hinshelwood, C. N. (1936). Proc. Roy. SOC.154A, 335. Stevenson, B. (1957). Ph.D. Thesis, University of London. Stimson, V. R. Private communication. Stimson, V. R., and Watson, E. J. (1960). J. Chem. SOC.3920. Stimson, V. R., and Watson, E. J. (1963). J. Chem. SOC.524. Swinbourne, E. S. (1958). Australian J. Chem. 11, 314. Swinbourne, E . S. (1960). J. Chem. Soc. 4668. Szwarc, M. (1948). J . Chem. Phys. 16, 128. Szwarc, M., and Murawski, J. (1951). Trans. Faraday SOC.47, 269. Szwarc, M., Ghosh, B. N., and Sehon, A. H. (1950). J. Chem. Phys. 18, 1142. Taylor, R., Smith, G. G., and Wetzel, W. H. (1962). J. A m . Chem. SOC.84, 4817. Thomas, P. J. (1959). J. Chem.Soc. 1192. Thomas, P. J. (1961). J . Chem. SOC.136. Warwick, E., and Fugassi, P. (1948). J. Phys. Chem. 52, 1314. Watson, E. J., and Stimson, V. R. (1961). J. Chem. SOC.1392. Wong, S. C. (1958). Ph.D. Thesis, University of London.
OXYGEN ISOTOPE EXCHANGE REACTIONS OF ORGANIC COMPOUNDS DAVID SAMUEL and BRIAN L. SILVER Isotope Department, The Weizmann Institute of Science Rehovoth, Israel
.
.
I. Introduction . . I1 Experimental Methods 111. The Exchange of Hydroxylic Conipounds with Water A. Alcohols . B. Phenols . IV. The Exchange of Carbonyl Compounds with Water A. Ketones and Aldehydes . B. Quinones . . C. Esters, Amides and Acid Chlorides . V. The Exchange of Carboxylic Acids with Water VI. The Exchange of Other Organic Compounds containing Oxygen with Water A. Group IV-Silicon Compounds B. Group V-Nitrogen and Phosphorus Compounds C. Group VI-Sulphur Compounds . . D. Group VII-Iodine Compounds . VII. The Exchange between Organic Compounds arid Metal Oxides . . . VIII. Conclusion References . .
.
.
.
.
.
.
. . . . .
.
. .
.
.
.
123 126 128 128 144 147 147 166 167 168 174 176 176
179 181 181 182 183
I. INTRODUCTION ISOTOPE exchange reactions are reversible chemical processes in which two isotopes C and C* of the same element exchange places, and may be written simply as : AC+BC*
-+AC*+BC
It should be noted that no net chemical change takes place in these reactions,but only interchange of the isotopic label. Isotopic exchange reactions of oxygen have been studied ever since water enriched in the stable isotopes of oxygen (0lsand 0")became available in the 1930's (Lewis and Cornish, 1933; Urey et al., 1936).
124
D A V I D SAMUEL A N D B R I A N L. SILVER
Owing to the short half-life of the radioactive isotopes of oxygen ( 0 1 3 , OI4, 0 1 5 , OI9 and OZo)their use in such studies is not practical. Oxygen-16 with half-life of 2 min could, in fact, be used as a tracer for very rapid exchange reactions, but so far it has been employed only in a limited number of medical and physiological studies using flow systems (see Buckingham and Forse, 1963). Oxygen-17, with a nuclear spin quantum number of 512, gives a nuclear magnetic resonance spectrum a t frequencies which are sensitive to the detailed structural environment of the oxygen atom in the molecule. Under suitable experimental conditions the integrated signals are directly proportional to the concentration of each type of 017-containingatom in the sample. With the recent enrichment of 017in water on a large scale (Dostrovsky and Samuel, 1965) and the availability of commercial NMR spectrometers, the scope of oxygen exchange studies in situ has considerably widened. Applications of 0 1 7 are expected to multiply rapidly in the near future. Most of the investigations of the isotopic exchange of oxygen in organic compounds involve the use of 0l8.Enrichments of up to nearly 500 times the natural abundance (0.20470)of 0l8are now available, obtained by the fractional distillation of water. The large majority of exchange reactions studied are those between organic compounds and water. Although these studies have provided a great deal of information on the mechanisms of reaction of organic compounds, the use of water as one component of the system often causes complications due t o the concurrent hydrolysis of labile organic compounds. This may, however, often be turned to good use, as will be discussed in connection with exchange in derivatives of carboxylic acids (see Section IV,C). Apart from studies on the mechanism of exchange for its own sake, the isotopic exchange of 01’ with organic compounds is of importance as a control in tracer studies, particularly in systems of biological interest where water plays such a prominent role. Unfortunately, the value of many of the results published in the literature is severely limited by the fact that important experimental details such as acidity, temperature or concentration are often not stated with any accuracy. Some results are merely given as “exchange” or “no exchange” or in terms of percentage of exchange after a given reaction time. It should be noted that tracer studies, such as the determination of the position of bond fission in hydrolysis and oxygen transfer in various oxidation reactions, are not considered to be within the scope of this review. The use of 0l8for studying ion-pair intermediates in solvolytic 1 Throughout this chapter “exchange” will often be used as a short form of “isotopic exchange of oxygen ”.
OXYGEN ISOTOPE EXCHANGE REACTIONS
125
reactions and rearrangements by means of isotopic “scrambling )’is not included since these are not strictly exchange reactions. It is also not proposed to discuse enzyme-catalysed reactions. Most of the exchange reactions which will be dealt with in this review concern simple oxygen-containing organic molecules, such as alcohols, phenols, ketones, aldehydes and carboxylic acids and their derivatives. These will be discussed in detail in Sections 111, IV, and V. However, many organic derivatives of inorganic oxyacids, such as esters of phosphoric and sulphuric acids, have also been examined for oxygen exchange with water as part of studies on the mechanism of their reactions in aqueous solution. Since these esters and various related compounds, where oxygen is bound to an atom other than carbon have many features in common with one another, the mechanisms of such exchanges will be discussed as a group in Section VI. A few exchanges not involving water have been reported, such as the exchange of 0l8between organic compounds and alumina and other metal oxides, and are dealt with briefly in Section VII.
11. EXPERIMENTAL METHODS The rate of isotopic exchange of oxygen between an organic compound and water (or any other oxygen-containing medium) is determined by in measuring the rate of change of the concentration of 0l8 (or 0’’) either of the exchanging components of the system with time. I n order to simplify the kinetics of exchange, one component, usually the water, is taken in large excess so that its isotopic concentration can be considered to be constant. I n most cases the organic compound is dissolved in water, separated at given intervals of time, purified and analysed for its isotopic oxygen content. Either the water or the compound may be initially enriched in 018.
When the compounds are not very soluble in water, mixed solvents are used. Dioxan-water mixtures are the most common. Acetone undergoes exchange with water fairly rapidly and ethanol and other alcohols undergo exchange and other reactions under acid conditions (see Section 111). Problems due to the competing exchange between the components of a mixed solvent can be eliminated by using compounds enriched in 0ls and solvents (i.e. water-acetone) of natural isotopic abundance. Many isotopic exchange reactions are acid-catalysed and it is customary to use solutions of perchloric acid, since the perchlorate ion does not appear to undergo any isotopic exchange with water. Sulphuric acid has 5
126
DAVID SAMUEL AND BRIAN L. SILVER
also been used although it can undergo exchange at high acidities and high temperatures (Hoering and Kennedy, 1957). There appears to be no effect on changing the acid anion, at least in dilute solutions, on the exchange of 1-phenylethanol (Grunwald et al., 1957). However, some effect of the acid anion at high acidities on the rate of exchange of tertiary alcohols has been reported by Boyd et al. (1960) and was attributed to salt effects. The investigation of rapid exchange reactions of organic compounds is often limited by the time taken to separate the component. However, the exchange of water in the solvent shell of inorganic cations has been studied using line-width measurements on the NMR spectra of 017labelled water (Jackson et al., 1960; Connick and Fiat, 1963). Half-lives of the order of 10-4 sec have been measured and this technique might well be adapted to extremely rapid exchange of oxygen in organic compounds. Before the advent of commercial mass-spectrometers, analysis of OI8 in organic compounds was often carried out by converting the sample t o water and measuring the density of the water. This method is not very accurate, particularly at the low 0ls abundances available to early workers in the field. This fact, combined with the use of concentrated solutions in order to save OI8 and the poor control of reaction conditions, contribute to the difficulty of interpreting much of the work published prior to 1940. By far the most commonly used and accurate method of oxygen isotope analysis is mass-spectrometry. Since the isotopic analysis of oxygen in water is often easier and more accurate than that in an organic compound, one would prefer to analyse the water but, since water is usually present in large excess, the results obtained by this procedure are less accurate. Occasionally, the organic compound may be converted to water for analysis. Water vapour cannot be analysed directly in a mass spectrometer and so the oxygen of the labelled water is usually equilibrated with carbon dioxide which is then analysed. The equilibrium constant for this isotopic exchange reaction is known to a high degree of accuracy and may be accounted for in precise calculations. Usually, however, organic compounds are converted to a suitable gas (such as carbon dioxide, carbon monoxide or oxygen) which is then analysed for Ols. The most convenient gas is carbon dioxide which is obtained by various pyrolytic methods discussed elsewhere (see Samuel, 1962). Conversion to a gas is seldom quantitative and for very accurate work it would be necessary t o take into account isotope effects in the conversion process. Neither kinetic nor equilibrium isotope effects have been considered in most of the work described so far. The corrections involved are fairly small and may usually be ignored, since kinetic data are usually not more accurate than
OXYGEN ISOTOPE EXCHANGE REACTIONS
127
5 3%. The accuracy of the isotopic analysis of 0l8in organic compounds by mass spectrometry usually ranges from ~f:1 to 5% of the given enrichment. This figure may be improved, if necessary, by careful work and the use of accurately calibrated standards. Organic compounds with high enough vapour pressures can be introduced directly into the mass spectrometer for analysis. 018-labelled glycols (Long and Pritchard, 1956), acetone-Ols (Hamilton and Westheimer, 1959) and mixtures of cyclic ketones and water (Biemann, 1962) have been analysed in this way. Using a heated inlet system, Ols-labelled phenol, benzyl alcohol and benzyl phenyl ether have recently been analysed by direct mass spectrometry, with excellent reproducibility, provided the sample contains a t least 5 atom yo 0l8(Swain et a$., 1963). Direct mass spectrometry saves much preliminary work in preparing gaseous samples, but suffers from two disadvantages. The possibility of “memory” effectsin the mass spectrometer (i.e. the effect on the measurement of one sample by a previous one) and the danger that fragments of the organic molecule may be produced with mass to charge ratios coincidentally identical with that of the fragment containing oxygen used for calculating the Ols-abundance. But, as the techniques of mass spectrometry are improved and the cracking patterns of organic compounds elucidated, this method will obviously be more and more widely used. The hazards of separation and purification of organic compounds may be avoided if it is possible to analyse the reactants and products in solution by a spectroscopic-method. I n many molecules it has been found that there are detectable differences between the infra-red frequencies of bonds containing 0l8and those containing Ole (see Pinchas et al., 1963, and previous references cited therein). These differences can provide a basis for the quantitative spectroscopic analysis of 0l8, but so far relatively little use of this method has been reported owing to the difficulties of estimating the intensities of the relevant absorption bands accurately. One great advantage of “direct ” measurement is, however, the possibility of distinguishing between several non-equivalent oxygen atoms in the same molecule, such as the two oxygen atoms inp-hydroxybenzaldehyde. NMR spectroscopy of O1’-labelled compounds is a particularly useful technique for this purpose which is now being developed in a number of laboratories as an analytical tool. The chemical shift for oxygen ranges from 1-1000 p.p.m. relative to the water line as a reference. It will therefore be possible, for example, to follow the exchange of the hydroxy and carbonyl oxygen atoms in a compound without lengthy separation and degradation procedures.
128
DAVID SAMUEL AND BRIAN L. SILVER
111. THE EXCHANGE O F HYDROXYLIC COMPOUNDS
WITH WATER
A. Alcohols The exchange of 0l8between alcohols and water has received a great deal of attention, both on account of its intrinsic interest and also because of the insight that it gives into the mechanism of nucleophilic substitution at carbon. It is of historical interest that Polanyi and Szabo (1934)-in their classic proof that the alkaline hydrolysis of amyl acetate occurs with acyl-oxygen bond fission-noted that amyl alcohol had not undergone 018-exchange with the solvent water after 2 days a t 70°C. The first deliberate studies of isotopic exchange of oxygen as such were by Roberts (1938) who found no exchange between methanol and water in either 0 . 1 NaOH ~ or in 0 . 1 HC1 ~ a t 25°C. Senkus and Brown (1938) obtained essentially the same results using depleted water (i.e. containing less than the natural abundance of 0l8).No further work on alcohols was reported until the 1950's when the availability of comparatively large quantities of water enriched in 0lsmade accurate kinetic studies of exchange feasible. The mechanism of exchange of oxygen with alcohols can conveniently be discussed as a function of the structure of the carbon skeleton. I n the elucidation of the mechanism, studies of the absolute and comparative rates of exchange can be used as well as the rates of loss of optical activity and of various competing rearrangements in alcohols of suitable structure. Hence a large number of studies have centred on secondary and tertiary alcohols, where the stereochemistry can be studied by different means, and less attention has been paid to primary alcohols. Two mechanisms of isotopic exchange in alcohols can be considered, corresponding to the SN1and Sx2 mechanisms of nucleophilic substitution. Water is the nucleophile in this case, attacking a saturated carbon atom. I n all the studies reported so far, exchange occurs only in acid solution and it has always been assumed that the conjugate acid of the alcohol is the reacting species. ROH +[H30]+ + [ROH2]-'-+HzO [ROHzJ++HaO*
+ [RO*Hz]++HzO
At high acidities, there is always the possibility of reversible ether and olefin formation which can provide alternative paths for exchange and which must be taken into account in calculating accurate rate constants. However, the rates of dehydration and hydration of olefins are usually
* Throughout this review an asterisk will indicate an isotopically distinct oxygen atoinwhether it be 0 1 6 , 0 1 7 or 018.
O X Y G E N ISOTOPE EXCHANGE REACTIONS
129
slower than exchange (see Dostrovsky and Klein, 1955a; Grunwald et aE., 1957; Manassen and Klein, 1960). It is conceivable that a t very high temperatures the neutral form of the alcohol may also undergo observable exchange. This has not yet been verified experimentally. The two extreme mechanisms of exchange between a protonated alcohol and water are : (a) A two-stage process involving carbonium ion formation which may formally be depicted as
( b ) direct displacement of water on carbon
The stereochemical consequences of reaction ( a )are that if the carbonium ion becomes planar, and the leaving water molecule equilibrates with the solvent very rapidly, then each ionization of a C-0 bond results in exchange. When the alcohol is optically active due to asymmetry a t the cc-carbonatom, eachionizationwillalso causeracemization. It follows that honization
=
kracemization = &exchange
and kex,.,,/krac= 1where the k’s are the observed first-order rate constants. I n reaction ( b )each displacement results in inversion of configuration a t the central carbon atom as well as exchange. Here :
kexch
=
krac
or k e x c d k r a c = 0.5 In practice, the observed values of kexeh/lcr,,are rarely found to be either 0.5 or 1.0 but generally fall a t some intermediate value. Nevertheless, most interpretations have usually been in terms of the carbonium ion mechanism (a). I n the acid-catalysed exchange of optically active s-butyl alcohol (l), Bunton et al. (1955b) found that leerch/krac= 0.5 (see Table I), which is compatible with the direct displacement mechanism (b). However, other
TABLE1 The Kinetics of Exchange of Alcohols with Water Temp. ("C) n-Butyl alcohol s-Butyl alcohol
t-Butyl alcohol
105kla
Reference
0.007 0.056 6.7 26 2 47.8 80 125 74.9 38 2 9.5 4.4 14.3 35 12 27.3 1.33 15.4 19.7
Dostrovsky and Klein (1955a) Dostrovsky and Klein (1955b) Bunton et al. (1955b) Bunton et al. (1955b) Bunton et al. (1955b) Bunton et al. (1955b) Bunton et al. (1955b) Manassen and Klein (1960) Boyd et al. (1960) Boyd et al. (1960) Boyd et al. (1960) Boyd et al. (1960) Boyd et al. (1960) Boyd et al. (1960) Boyd et al. (1960) Boyd et al. (1960) Dostrovsky and Klein (1955a) Dostrovsky and Klein (1955a) Dostrovsky and Klein (1955a)
30.4"
0.0014 0.00561 3.62 0.00243 1.66 19.7 12.2 21000 0.0476 171 1.05 1.09
Dostrovsky and Klein (1955b) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Jeffrey (1961) Grunwald et aZ. (1957) Grunwald et al. (1957)
54.30
33-0
125" 125' 100.8" 100.8O 1oo.8° 100.8O 100.8" 101.4' 25" 25' 25O 25" 25O 25" 44.87O 50.01O 550 55O
'is0 1-Propanol, 2,Z-dimethyl (Neopentyl alcohol) Benzyl alcohol Benzyl alcohol, p-chloro
125" 25' 100" 25'
Benzyl alcohol, p-methoxy (Anisyl alcohol) Benzyl alcohol, p-methyl
100" 25O 100" 25'
loo0
LOO"
Benzyl alcohol, a-methyl
Condit'ions
30.4'
G-wald
et d.(1957)
Renzyl alcohol, a-vinyl
(a-phenylallylalcohol) Benzhydrol, p-methoxy (p-methoxydiphenylmethanol)
30"
0 - 0 5 HC104b ~
25' 25O 25' 25' 2T 25' 25O
0.101M HClO4b 0.265~ HC104b 0 . 3 9 4 ~HC1Odb 0.936~ HC104b 0 . 3 5 0 ~HC104" 0 . 6 3 0 ~HClO4' 0.101M HClO4 (90% dioxan) 0.105~ HClO4 (95.8% dioxan) 0.20M He104 (95.8% dioxan) 0 . 0 5 He104 ~ (98.01% dioxan)
25' 15' 25O Cyclopentane-1,2-diol trans-1,2-dimethyl
93.1
8 38 75 1040 120 670 15
72.5
Goering end Dilgren (1960)
Bunton et al. (1958d) Bunton et al. (1958d) Bunton et al. (1958d) Bunton et al. (1958d) Bunton et al. (1958d) Bunton et al. (1958d) Bunton and Henderson (1963) Bunton and Henderson (1963)
170
Bunton and Henderson (1963)
235
Bunton and Henderson (1963)
7.2 56
Bunton and Carr (1963b) Bunton and Carr (1963b)
59,7O 59.7O
1 . 0 1 He104 ~ 2.78~ Helo4
59.7O 59.7"
0 . 8 9 HClOs ~ 0 . 9 8 ~HClOi
0.3 0.38
Bunton and Carr (1963a) Bunton and Carr (1963a)
2-Cyclohexenol,cis-5-methyl
59.7O 59.7O 30.2'
1.23 7.6 6.4
Bunton and Carr (1963a) Bunton and Carr (1963a) Goering and Josephson (1962)
2-Cyclohexenol, trans-5-methyl
30.2"
Borneo1 Isoborneol 2-Norbornanol, 2,3,3-trimethyl (camphenilol, methyl) 2-Norcamphanol, 2,3,3-trimethyl (camphene hydrate)
22 25'
1.01M HClO4 2 . 7 8 He104 ~ 0.095~ He104 (35% aq. acetone) 0.095~ HClO4 (35% aq. acetone) 0.48H ~ C ~ O ~ ~ 0.48~ HC104
25O
0 . 4 8 HC104b ~
25'
0.48~ HC104b
1,2-Cyclohexanediol, &-1,2,-diniethyl 1,2-Cyclohexanediol, trans- 1,2-dimethyl
kl= First-order exchange rate constant (units: sec-l). 60% dioxan. c 40% dioxan. rate of heterolysis of C-0 bond. b
41.7
Goering and Josephson (1962)
0.2d 0.046d
Bunton et al. (1963) Bunton et al. (1963)
0.066d
Bunton et al. (1963)
79.4
Bunton et al. (1963)
132
DAVID SAMUEL A N D BRIAN L. SILVER
evidence indicates that the exchange is via a carbonium ion. I n particular, the exchange rate in strong acid is found to follow the H o acidity function. This is usually taken t o imply that the formation of the transition state does not involve the participation of a water molecule. Bunton et al. avoid the paradox by suggesting that whilst bond breaking and making in s-butyl alcohol are not synchronous, the leaving water molecule does not have time to move far away from the carbon atom before substitution occurs. I n other words, the leaving water molecule “shields” the developing carbonium ion on one side of the plane and water can attack the central carbon atom only from the opposite side, giving both exchange and inversion, and hence k,,,,,/krac = 0.5. I n later work, Bunton considers that the different values of li,,,,l/krac observed in different alcohols are due t o varying degrees of shielding by the leaving water molecule, resulting in varying proportions of racemization to inversion. Each dissociation of the carbon-oxygen bond results in the release of a water molecule which equilibrates with the bulk of the solvent. Random recombination of water with the carbonium ion results in exchange.
1
2
3
Thus Bunton and co-workers (1955, 1957)consider that the rate constant for the formation of the carbonium ion is equal to the rate constant for exchange, i*e*kionization = kexchangeA somewhat different mechanism for the exchange of secondary alcohols and water was put forward by Grunwald et al. (1957)on the basis of results for the exchange and racemization of optically active 1-phenylethanol (2). I n 0 . 0 1 ~ perchloric acid they found kexckl/krac= 0.82 0.04 a t two different temperatures. The result is interpreted in terms of the ion pair hypothesis of Winstein and co-workers (1956). It is assumed that the protonated alcohol ionizes to give a planar carbonium ion, but the leaving water molecule does not equilibrate immediately with the solvent. Instead it is held for some finite time in the solvent shell of the carbonium ion, and therefore has a greater chance of being recaptured by the carbonium ion than the water molecules in the bulk of the solution. The chances of return, as compared to escape from the solvent shell, depend
OXYGEN ISOTOPE EXCHANGE REACTIONS
133
on the relative lifetimes of the carbonium ion and of its solvent shell. If the lifetime of the ion is relatively long, then the dissociating water molecule has very little chance of remaining in the solvent shell long enough to be recaptured, and therefore every ionization results in exchange and in racemization, i.e. kionization - kexch= krac. On the basis of some plausible assumptions, Grunwald et al. suggest that the first solvent shell of the carbonium ion contains six water molecules, three on either side of the plane. An estimate was made of the ratio of the “lifetime ” of a water molecule in the solvent shell to the rate constant for the reaction of the carbonium ion with water. The “solvent shell” hypothesis is supported by the fact that the hydrolysis of optically active l-phenylethyl chloride gives 83% racemization and 17 yo inversion, almost the same percentage as that calculated from 0l8exchange in alcohol (2) a result which, inter atia, seems to indicate that C1- and H,O are equally effective at solvation. The influence of the structure of the carbon skeleton on the lifetime of the carbonium ion is demonstrated by the fact that whereas s-butyl alcohol (1)was inverted at each exchange of oxygen atoms, considerable racemization was found in 1-phenylethanol(2). The aromatic ring in (2) apparently increases the lifetime of the carbonium intermediate by resonance stabilization. I n p-methoxybenzhydrol (3), Bunton et al. (1958d) found that the rates of racemization and exchange are nearly equal, i.e. kexc,,= k,,, in both 60:40 and 40: 60 (v/v) dioxan-water at acidities ranging from 0.1 to nearly 1 . 0 perchloric ~ acid (see Table 1). Here the carbonium ion is stabilized by resonance with two aromatic rings and has sufficiently long life to enable the leaving water molecule to mix completely with the solvent water. The logarithms of the first order rate constants for both racemization and exchange were found to vary linearly with H o , with a slope of 1.3. The exact significance of linear dependence on the Hammett function in these systems is not entirely clear, since the H o function is defined in terms of the protonation of a neutral aromatic indicator. The deviation from strict linear dependence has led both Bunton et al. (1958d)and Grunwald et al. (1957)to consider using the J , (or Coor H E )function (Paul and Long, 1957;Long and Paul, 1957) which applies to the equilibrium formation of carbonium ions from neutral molecules. However, the final answer can only be determined at high acidities where the H o and J o functions diverge. Under these conditions, however, the reactions are often too fast to measure or tend to become more complicated owing to competing reactions, such as olefin formation or demethylation. I n another attempt at understanding the effect of acidity on the rate of exchange, Bunnett (1961)has re-analysed Bunton’s data for s-butyl alcohol in terms of his theory of w-values and 5*
134
D A V I D S A M U E L A N D B R I A N L. SILVER
claims that the reaction is SN2, but “possibly leaning considerably toward S,1”. Manassen and Klein (1960) returned to the fray by studying the concurrent acid-catalysed hydration, dehydration, isomerization and oxygen exchange of s-butyl alcohol (1) in water. By a similar kinetic analysis to that which Grunwald et al. (1957) had used for l-phenylethanol(2),it was estimated that here only two water molecules are in nearest-neighbour sites to the carbonium ion. A pentacovalent carbon intermediate is postulated, the bonds to the water molecules being partially covalent. This intermediate forms 2-butene by elimination, combines with solvent to form s-butyl alcohol, undergoes reversible elimination to form olefin and is solvolysed reversibly to bring about the oxygen exchange of the alcohol. It was suggested that the water molecules “help ” to remove a proton from the adjacent carbon atom in a secondary carbonium ion, thereby favouring elimination over substitution, i.e.
This cannot occur in a tertiary carbonium ion owing to steric hindrance and here, indeed, the ratio of elimination to substitution is less than for secondary alcohols. I n an attempt to elucidate the role of water in exchange, the effect of dilution of the solvent with a non-reactive component capable of solvating the carbonium ion was investigated by Bunton and Henderson (1963) in a study of the acid-catalysed exchange and racemization of pmethoxybenzhydrol(3) in moist dioxan. I n a highly aqueous solution, as mentioned before, the leaving water molecule equilibrated completely with the solvent and the planar carbonium ion is attacked impartially from either side so that kr,,/kexch= 1. I n a drier solvent, 95.8% dioxan, fewer water molecules are available for equilibration with the leaving water molecule, so that the latter will tend to be retained in the solvation shell of the carbonium ion and have a greater chance of recombination ; hence krac/kexch > 1. I n solvents containing a large proportion (98%) of dioxan the carbonium ion will be “solvated” predominantly by dioxan molecules and the expelled water molecules will again be free
135
OXYGEN ISOTOPE EXCHANGE REACTIONS
to equilibrate completely with the small number of water molecules in the solution before combining in a non-stereospecific way, and again k % C / L i l
'1.
In addition to the rates of exchange and racemization, Goering and Dilgren (1960) have used the rate of allylic rearrangement as an indication of the timing and stereochemistry of 0lsexchange. I n the acid-catalysed exchange, racemization and rearrangement of optically active a-phenylally1 alcohol (4) (a-vinyl, benzyl alcohol, see Table 1 ) in 60:40 (v/v) aqueoiis dioxan, 4% of the a-phenylallyl alcohol and 22 rt 8% of the racemic y-phenylallyl alcohol (cinnamyl alcohol) ( 5 ) derived from the active starting material are produced without oxygen exchange.
4
5
These results were discussed in terms of a carbonium ion intermediate common to exchange, rearrangement and racemization. The ratio of the rate constants for racemization and rearrangement to that for exchange is interpreted by basically the same general picture used by Grunwald et al. (1957). The leaving water molecule is considered to be held in the solvation shell of the carbonium ion, and consequently has a greater chance of being involved in the recombination step. The scheme proposed is as follows, using initially labelled alcohol (4) :
6
[
HzO)
2k1
> raccmic unlabellcd alcohol
Goering and Dilgren consider that there are only two water molecules in the solvation shell, one held on each side of the plane of the carbonium ion, which are eligible to react with the cation. The carbonium ion (6) is converted to the two optical isomers a t equal rates (kl).However, if the carbonium ion reacts with water before either of these two water molecules can mix with the bulk of the solvent molecules there is a 50%
136
D A V I D SAMUEL A N D B R I A N L. SILVER
chance that the original water molecule will be involved in the recombination step. I n this case half of the racemic material will not have exchanged oxygen atoms. I n more general terms, if k, k,, in the limiting situation k&/krao = 0.5 as was indeed found for s-butyl alcohol (1). At the other extreme, when k l < k2, kexch/krac= 1 as in p-methoxybenzhydro1 (3). With 1-phenylethanol(2) and a-phenylallyl alcohol (4) there is partial exchange of solvent molecules in the solvation shell prior to recombination to product and it is estimated that kllkz = &. Goering and Dilgren (1960) also make the point that Grunwald et al. (1957) failed to distinguish between reactions of differing charge types
( a ) RX - t R + + X ( b ) [RX]+ -+ R+ + X I n case (a), relatively stable ion pairs of the Winstein type are expected to be formed because of electrostatic attraction, so that the carbonium ion often retains its initial configuration. I n case ( b ) ,which applies to OI8 exchange between alcohols and water, there is no ion pair and, if the leaving group is the same as the solvent, the carbonium ion becomes symmetrical and planar. Nevertheless there is some evidence for ion pair return in this system since Goering and Dilgren found that the y-phenylallyl alcohol recovered from the rearrangement of O18-labelleda-phenylallyl alcohol in ordinary water, has a slightly higher 0" content than the water in the solvent. This indicates that the allylic rearrangement is partly intramolecular, involving the re-combination of the moieties formed in the ionization, a point that will be discussed again in connection with the exchange of cyclohexenols. The isotopic exchange reactions between a secondary alcohol and water were further investigated by Goering and Josephson (1962) in connection with the oxygen exchange accompanying the acid-catalysed allylic rearrangement of cis- (7) and trans-5-methyl-2-cyclohexenol(8) in aqueous acetone. OH I
7
8
It had previously been found that the rate of interconversion of enantiomers (krac)is several times greater than the rate of isomerization of the geometric isomers (kisom). I n the cis system (7)little exchange is
OXYGEN ISOTOPE E X C H A N G E REACTIONS
137
associated with the interconversion of enantiomers, indicating that racemization is largely intramolecular. On the other hand, in the racemization of the trans system (8)there is almost complete exchange. Goering and Josephson suggest that the cis-trans rearrangement and the isomerization involve a common carbonium ion, in which partial planarity is t o be expected because of the requirement of maximum p-orbital overlap. The formation of this ion probably proceeds most readily when the t
OH2
+
L t -
1 H
IT
‘I
10
bond of the leaving group is perpendicular to the plane of the double bond, since this gives a transition state with a lower activation energy as there is overlap of the p-orbital and the developing double bond. It is found, from a study of molecular models, that the favoured conformation of the molecule in the transition state will be close to the carbonium ions (9) and (10) with the leaving group on the “upper side” of the ion.
138
DAVID SAMUEL AND BRIAN L. SILVER
By the principle of microscopic reversibility the addition of water to the carbonium will have an identical transition state, and water will attack on the “upper surface”, i.e.
Attack on 10
Attarl; on 9
I n carbonium ion (9) the leaving water molecule is held in the solvation shell and there is only a 50% chance of this water molecule returning to its original site, since attack may occur a t the other site to give racemization and exchange. Thus kexck,[k ,,would in this case have a maximum value of 0.5. The observed value is 0 . 4 . For ion (lo), on the other hand, the methyl group may permit only one water molecule to “solvate” the upper part of the ion. If this molecule is the original leaving group, it may attack a t the other site (giving racemization and exchange) more quickly than it mixes with the solvent. If this were strictly true and the leaving water molecule always attacked the other site, the ratio kaxct,/kracwould be zero, i.e. there would be no exchange at all. Racemization will only occur if the water molecule does not always return to the same site from which it came. It was found that, in fact, kexc,,/krac= 0.03, i.e. that the reaction is almost entirely intramolecular. Bunton et al. (1963) have reported a preliminary study on the exchange of two bicyclic secondary alcohols. Isoborneol(l1) undergoes exchange ~ acid in 40 : 60 and racemization a t about equal rates in a 0 . 4 8 perchloric (v/v) aqueous dioxan.
0H 11
12
Borneo1 (12),on the other hand, undergoes exchange a t a much smaller rate (of the order of about lo6 times slower) (see Table 1) under identical experimental conditions but undergoes racemization and decomposition at the same time. The rate of heterolysis of borneol is about the same as that estimated for s-butyl alcohol under the same conditions. A detailed explanation of the differences in rate of exchange in bicyclic alcohols requires considerable further work.
OXYGEN ISOTOPE EXCHANGE REACTIONS
139
As might be expected, tertiary alcohols undergo a fairly rapid acidoatalysed exchange of oxygen with water. There are, however, several pathways by which this can be achieved. I n the case of t-butyl alcohol (13) these various reactions are : CH3
I
CH3-C-OH
I
k
+ H30
kz
CH3
[
I
C‘H3-C-OHz
+HzO
13
CH3
I CH3-C+ I
+HzO
CH3
CH2 k5
II
ks
I
-2 CH3--C
+&0+
CH3
Step k , accounts for exchange by the reaction of labelled solvent water with the carbonium ion. The reversible formation of an ether can be neglected in the case of tertiary alcohols on steric grounds but the facile reversible dehydration-hydration, steps k5 and Ic,, make the kinetics more complicated. However, by studying oxygen exchange in an equilibrium mixture of isobutene and alcohol, Dostrovsky and Klein (1955a) were able to simplify the rate expressions of the reactions shown in the above scheme and to show that k 4 / k 5varies from 20 to 30, depending on the temperature. I n other words, the rate constant for exchange is much greater than that for dehydration, which indicates that the mechanism of oxygen exchange does not involve elimination and rehydration of isobutene. The relative “partitioning ” of the carbonium ion between hydration (i.e. exchange) and elimination to olefin is obviously closelyrelated t o the proportion of olefin formed in the S,1 hydrolysis of related alkyl halides. The value of 2.8% olefin formation in water a t 25OC found on the basis of the exchange experiments agrees very satisfactorily with the value of 3% found in the solvolysis of t-butyl bromide in water (as calculated by extrapolation from aqueous ethanol solutions). Essentially similar results were obtained by Boyd et al. (1960) who found that the rates of 0ls exchange and of dehydration of tertiary
140
DAVID SAMUEL AND BRIAN L. SILVER
alcohols follow the Hammett acidity function (H,) with a slope of 1.2 (log k against - H o ) . This again indicates that water does not participate in the rate-determining step and rules out an exchange mechanism + involving the bimolecular attack of water on the oxonium ion ROHz which, in any case, is unlikely for steric reasons. Studies with optically active tertiary alcohols could help to clear up this point. Boyd et al. (1960) use the term “encumbered” carbonium ion to indicate some degree of interaction between the carbonium ion and the leaving or entering group. This concept is essentially the same as that finally reached by Bunton, by Klein, and by Goering on the basis of the stereochemical work described above. The rates of exchange in two tertiary bicyclic alcohols have recently been reported (Bunton et al., 1963). The rates of heterolysis of the C-0 bond at 25°C in dioxan-water (60:40 are given in Table 1. v/v) containing 0 . 4 8 HC104 ~
14
15
By extrapolating from the results of Dostrovsky and Klein (1955a) in water to (40 :60 v/v) aqueous dioxan and making a number of assumptions in order to compare the rates of exchange, Bunton et al. (1963)show that 2,3,3-trimethylnorcamphanol-2(camphene hydrate) (14) is very much more reactive than t-butanol, whereas 2,3,3-trimethyl norbornanol (methyl camphenilol) (15) is only slightly more reactive. A clear-cut analysis of the results has not yet been made but must await more detailed stereochemical and kinetic studies. The systems investigated are in any case somewhat complex owing to various competing reactions which occur, including decomposition and rearrangement. An interesting tertiary alcohol is pinacol(l6) in which both the rate of acid catalysed exchange and of rearrangement to pinacolone can be measured. Bunton et al. (195813) found that both reactions follow the Hammett acidity function Ho. The reaction is postulated to proceed through a carbonium ion as follows : (CH3)2C--C(CH3)2
I
I
OH O H
=’-[
,
(FW
1’
(CH~)ZC-C(CH~)~
OH I OH2 I
;--- (CH3)2C-;(CH3)2 I OH
+I
16 CH3.C.C(CH3)3
It
0
f
CH3-C-C(CH3)
I
OH
3
O X Y G E N ISOTOPE EXCHANGE R E A C T I O N S
141
The unrearranged pinacol, recovered after partial reaction in 018-enriched water, was found to contain 0l8from the solvent. This exchange presumably proceeds via hydration of the carbonium ion. Added pinacolone does not affect the rate of isotopic exchange, which rules out a mechanism involving exchange into the carbonyl group (see p. 147) and subsequent re-formation of pinacol as a reversal of the rearrangement. It was also shown that a mechanism for exchange via the formation and hydrolysis of the epoxide is unimportant. The ratio of exchange t o rearrangement kexch/krearrdrops with increasing acidity from 2.7 in 0 . 0 5 3 sulphuric ~ acid to 1.2 in 5 . 3 5 sulphuric ~ acid, which is interpreted as being due to the differing dependence of rearrangement and exchange on the activity of water. Rearrangement is presumed to proceed by a reaction of the carbonium ion that does not involve a water molecule, whilst exchange requires the addition of water to the carbonium ion ; the rate of this step is expected t o depend on the activity of water. A bimolecular attack of water on the conjugate acid of pinacol is not likely for both steric reasons and in view of the dependence on H,. An interesting point is that the rate of carbonium ion formation (i.e. rate of exchange plus rate of rearrangement) of pinacol is about one-fiftieth of that of t-butyl alcohol under comparable conditions. There is apparently no anchimeric assistance in the pinacol rearrangement and in this system a classical carbonium ion is formed which can then either rearrange or be trapped by the solvent. There are a t present insufficient data for a detailed discussion of the lower rate of exchange of pinacol relative to t-butyl alcohol. The 0l8exchanges accompanying the pinacol rearrangement in the cyclohexane- 1,2-dioI and cyclopentane- 1,2-diol systems have also been investigated. The pinacolic rearrangement of both cis- (17) and trans1,2-dimethylcyclohexane1,2-dioI (18) in aqueous acid gives l-acetylmethylcyclopentane and a small amount of 2,2-dimethylcyclohexanone
18
'CH3
142
DAVID SAMUEL AND BRIAN L. SILVER
(Bunton and Carr, 1963a). The rearrangement of each diol is also accomexchange panied by the conversion of one diol into the other and by 01* with the solvent. The proportionality of the rate of rearrangement to the acidity function ha, the deuterium solvent isotope effect, and the positive entropy of activation suggest an A-1 mechanism in which a carbonium ion is formed in the rate-determining step. This intermediate can then react with water to give either of the diols with isotopic labels or rearrange with ring contraction or methyl migration to the products shown. On the basis of the variation of products with acidity and temperature, the carbonium ion intermediate common to both diols is considered to have the less stable configuration formed by loss of an axial hydroxyl from the cis-diol (17) or of an equatorial hydroxyl from the trans-diol (18). The situation is more complicated in the case of the pinacolic rearrangement of the isomeric cyclopentane-1,2-diols (Bunton and Carr, 1963b). I n aqueous perchloric acid, cis-1, 2-dimethylcyclopentane-l,2-diol (19) is converted into a mixture of the trans-isomer, some 2,Z-dimethylcyclopentanone and a large amount of a tarry by-product (possibly a polymeric cyclopentadiene). No 0ls is found in the unrearranged cis(20)) on the other diol. The trans-1,2-dimethylcyclopentane-l,2-diol
OH
OH
J
I OH
H3C
/
I
OH
i'H3
20
hand, undergoes a rapid 0l8exchange and also forms a tarry product with some ketone, but no cis-diol. Again, on the basis of the proportionality of the rate to the ha acidity function, the solvent isotope effect and the Arrhenius parameters, it is suggested that in both diols the first step is a unimolecular (A-1) heterolysis of the conjugate acid. However, the very different products and rates of 018-exchangesuggest that a different carbonium ion is formed by each isomer.
OXYGEN ISOTOPE EXCHANGE REhCTIONS
143
The pinacol rearrangement of benzpinncol (21)to benzpinacoloiie was investigated in dioxan-water mixtures (1o:l v/v) a t 75°C: (Sparks and Fry, personal communication). (C~HS)~C-C(C~HS)~
I
I
OH
-
(C~~H~)~C.CO.C~HS
OH 21
After one half-life of the reaction, unreacted benzopinacol was isolated and found not to have undergone any exchange with the water of the solvent. This result is in contrast to the aliphatic pinacol rearrangement described earlier and indicates that the lifetime of the carbonium ion derived from benzopinacol is extremely short. I n fact, as in other instances of aryl migration, there is reason to believe that no classical unrearranged carbonium ion is formed but that rearrangement occurs via a bridged structure which cannot undergo exchange with solvent. The differences in rate of Ols-exchange and in the kinetics and products between the open-chain and cyclic diols indicate that, once a tertiary carbonium ion is formed, competition occurs between rearrangement and reaction with solvent (exchange and isomerization). The relative rates of each process appear to depend very largely on the stereochemistry of the system. As an example of a primary alcohol, Dostrovsky and Klein (1955b) studied the acid-catalysed exchange of n-butanol (22). I n contrast to t-butyl alcohol, it was considered unlikely that the exchange involves the formation of a carbonium ion. I n common with analogous reactions of derivatives of n-alkanes, it was suggested that the reaction involved a bimolecular attack of water on the conjugate acid of the alcohol. By the use of C14 as tracer it was shown that the dehydration of n-butanol is ' ' exchange was negligible under the experimental conditions in which 0 observed. Exchange between n-butyl alcohol and water goes via the scheme : C'H3.C'Hz.C'Hz.CHzO H kHsO+ r-' [CHs ( ' H z , ( ' H z ('Hz.OHs]+ 4 H z O 22
C'H3
I I
(!H3--C'--CH~-OH C'H3 23
144
D A V I D S A M U E L A N D B R I A N L. S I L V E R
In neopentyl alcohol (23),steric hindrance should discourage bimolecular attack on the a-carbon atom and indeed this alcohol undergoes exchange a t least 37 times more slowly than n-butanol. However, the partial participation of an SN1reaction cannot be ruled out, since the decrease in rate (see Table 1) appears to be much less than would be expected on purely steric grounds for a bimolecular reaction. The decrease in rate for the SN2reaction of ethoxide with the analogous halide has been shown to be of the order of 10° (Dostrovsky et al., 1946). Further work on the exchange of oxygen with primary alcohols, including the stereochemistry of exchange of optically active a-deuteriated primary alcohols, would be most desirable. Jeffrey (1961) has studied the effect of ring substitution in benzyl alcohol on the rate of 0l8exchange with water, in an attempt to cast some light on the borderline region between s N 1 and s N 2 displacements. His results are also included in Table 1. These results show that the overall rate of para-substituted benzyl alcohols is in the order CH309 CH, > H > C1> NOz which shows that since the electron donating groups accelerate the rate, the benzyl carbon atom is more positive in the transition state than in the reactant alcohol. I n addition, the rate of exchange is proportional to h, over the range of acidities studied, indicating that water does not participate in the formation of the transition state, on the assumption that the Zucker-Hammett hypothesis holds for this reaction. I n addition, as the electron-donating power of the substituent decreases, the entropy of activation was found to increase, which may indicate that a more “SN2-like” reaction occurs in the benzyl system. Some support for this interpretation is also given by the positive curvature of the Hammett sigma-rho plot. B. Phenols Little kinetic work on the exchange of OI8 between phenols and water has been reported. Under basic conditions phenol itself is resistant t o exchange even after 6 days a t 120°Cin 1~potassium hydroxide (Bunton and Frei, 1951), whilst /3-naphthol undergoes no measurable exchange after 20 h in 1~ potassium hydroxide a t 170°C. I n basic solution the mononitrophenols are also unaffected. However, 2,4-dinitrophenol is reported to undergo 10% exchange after 45 h a t 140°C in I N KOH (Fesenko and Gragerov, 1955)but this may be due to secondary reactions under the drastic conditions used. I n an attempt to prove the existence of a Meisenheimer-type addition complex of picric acid in 6~ NaOH at room temperature, Samuel and Petreanu (unpublished results) found no evidence of Ols-exchange.
145
OXYGEN ISOTOPE EXCHANGE REACTIONS
I n neutral solution, early work (Koizumi and Titani, 1938) indicated that no exchange took place between phenol and water during 48 h a t 100". I n acid solution, Oae and Kiritani (1964) have recently found that phenol undergoes slow isotopic exchange of oxygen with water a t 180°C in 1 0 hydrochloric ~ acid. a,fl-Naphthodiols undergo complete exchange in 24 h under the same drastic acidic conditions. The ease of 0ls exchange in acid solution in substituted phenols, according to Oae et al., falls in the order phenol > p-cresol > p-bromophenol > 2,4,6-tribromophenol 2,4,6-trimethylphenol. The mechanism of exchange is still not entirely clear but it appears that direct nucleophilic attack of water on the protonated phenol is involved. N
r
+
.OH
Electron-withdrawing groups in ortho or para positions will discourage the electrophilic addition of a proton to form the quinonoid dienone intermediate. Indeed, Fesenko and Gragerov (1955) found that o- and p-nitrophenols do not undergo exchange under fairly drastic conditions (130", 60 hh, 1~ sulphuric acid), although picric acid is half exchanged under the same conditions. It seems unlikely, but not impossible, that the alternative mechanism in which an aromatic carbonium ion is formed, occurs. Further support for nucleophilic displacement is obtained from the fact that phenols will react with other nucleophiles, such as ethanol and n-butyl mercaptan, under similar conditions to those used for exchange (Oae and Kiritani, 1964). A brief survey of the exchange between water and polyhydric phenols at various temperatures has been made (Fesenko and Gragerov, 1955). Great variations in the rate are found, as summarized in Table 2. Although insufficient data are available for a discussion of mechanism it would seem probable that the base-catalysed exchange of polyhydric phenols proceeds via quinonoid structures of the type, OH
HO
3.,,*
OH
- 0 h o -
O
0
0
H
\
0
-
t-------j
H
Ii
H
Evidence for this type of structure has recently been obtained from
etc.
TABLE2 The Kinetics of Exchange of Phenols with Water ~
Reference
140' 140' 140" 155' 155" 155' 170' 170'
H ydroquinone
H ydroxyhydroquinone ( 1,2,4-trihydroxybenzene) Phloroglucinol ( 1,3,5 -trihydroxybenzene )
50' 125" 140' 155"
Resorcinol (m-dihydroxybenzene)
~~
100" 115' 130" ~
a
kl = First-order exchange rate constant (units: sec-1).
Water 1N HzS04 1~ KOH Water 1N HzS04 1~ KOH Water 1N HzS04
1~ KOH
0.22 1.0 2.4 0.50 2.1 5.9 0.75 44
Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955)
50
Fesenko and Gragerov (1955)
5.0 11.0 21.0
Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955)
0.47 2.0 7.5
Fesenko and Gragerov (1955) Fesenko and Gragerov (1955) Fesenko and Gragerov (1955)
OXYGEN ISOTOPE EXCHANGE REACTIONS
147
proton N.M.R. studies of the dianion of phloroglucinol (Highet and Batterham, 1964). A detailed discussion of the mechanism of Oi8 ex-
change in phenols must await a more thorough kinetic study.
Iv. THEEXCHANGE O F CARBONYL COMPOUNDS WITH WATER A. Ketones and Aldehydes In view of the chemical importance of ketones and aldehydes it is surprising that so few quantitative studies of oxygen isotopic exchange with water have been made. Cohn and Urey (1938) found that both acetone and acetaldehyde exchange with water, the latter more rapidly. In the case of acetone, the exchange is catalysed by hydrogen and hydroxide ions and salicylic acid but not by the salicylate ion. I n other words, there is general acid but not general base catalysis. The rate of oxygen exchange was estimated t o be very much faster than the rate of enolization under comparable conditions. The simplest and most likely mechanism for exchange of carbonyl compounds in acid solution shown below was rejected by Cohn and Urey on the ground that “all known cases of apparent intramolecular proton shifts have always been found t o be prototropic changes”. It is not obvious why the two forms of the protonated ketone should not be rapidly interconvertible via proton transfers involving solvent water, or even by direct intramolecular transfer.
A kinetic study of this exchange must be done before a mechanism can be suggested, which should also include a study of the effect of deuterium in the medium on the rate of exchange. I n basic solution, simple addition of hydroxide ion to the carbonyl group seems to be the most probable mechanism for exchange. *
*
Enolization is unlikely as an essential step in the exchange since Senkus and Brown (1938) found that benzaldehyde (where enolization cannot occur) also undergoes 0l8exchange with water. This has been confirmed by many later workers. The only recent studies on the exchange of
148
D A V I D S A M U X L A N D B R I A N L. S I L V E R
oxygen between acetone and water are the control react,ionsin an enzymatic study of decarboxylation by Hamilton and Westheimer (1959). It was found that acetone undergoes about 15% exchange in 2.5 min and 65% exchange in 15 min at 20°C at pH 6.5 (phosphate buffer). The P-carbonyl group of acetoacetate undergoes 25% exchange after 2.5 min under the same conditions. The a-carbonyl group of pyruvic acid undergoes 50-70% exchange in 10-20 min at 15OC and 80-85% exchange in 25 min at 20-25°C (Brodskii et al., 1962). The 0lsanalyses in all these studies are not very accurate owing to the rapidity of the exchange, the difficulty in separating and drying the products and in specifically analysing the different oxygen atoms in the molecule. These difficulties could all be overcome by using NMR to observe O1'-exchange. Dahn (1964) showed that the y-carbonyl group in laevulinic acid undergoes exchange in basic solution whereas the carboxyl group does not. Menon (1964)has measured the rate of acid- and base-catalysed oxygen exchange between p-substituted benzophenones and water in 80% dioxan-water. The rate data for the acid-catalysed oxygen exchange are summarized in Table 3. TABLE3 Rate Constants and Activat,ion Parameters for the Acid Catalysed Exchange of p-Substituted Benzophenones, p-XCeH4.COle.CeH5, with Water in 20: 80 (v/v) ~ Aqueous Dioxan ( 0 . 0 1 HC104)
105k (sec-1) (40")
105k (sec-1) (50.3')
105k (sec-1) (75')
E,
AH*
AS*
(kcal)
(kcal)
(e.u.)
log PZ
1.86 1.71 1.58 1.33 1.17 1.03
5.59 5.32 5.03 4.00 2.94 2.66
35.75 33.16 31.73 18'85 18.23 16.03
18.9 19.0 19.3 17.3 17.2 17.1
18.3 18.4 18.7 16.7 16.6 16.5
-20.4 -20.2 -19.4 -26.2 -26.8 -27.3
8.4 8.4 8.6 7.1 7.0 6.9
The rate of exchange is found to be proportional to the stoicheiometric hydrogen ion concentration. It appears that the exchange proceeds predominantly by an acid-catalysed mechanism with only a small, if any, contribution from a neutral mechanism involving unprotonated benzophenones and water. The rate constants are in the order p-CH, > p-CH30 > H > p-Br > p-Cl> p-NO,. There is, however, a factor of only
149
OXYGEN ISOTOPE EXCHANGE REACTIONS
two in going from p-methyl- or p-methoxy- to p-nitro-benzophenone. Menon suggests the following mechanism :
It"
1'
6H I
+ HzO*
The lack of marked differences in the relative rates of exchange is attributed to the opposing effects on the two constants, K and L1 in the equation for the observed rate, kobs = k K , [ H + ] / 2where K is the protonation equilibrium constant and lc, the rate determining constant for the formation of the tetracovalent intermediate. The activation parameters for the acid-catalysed exchange (see Table 3) show that changes in rate constants are due to changes in both PZ and E,. I n fact, compounds of high activation energy, e.g. p-methylbenzophenone actually undergo exchange faster than those of low activation energy, e.g. p-nitrobenzophenone. The qualitative and quantitative effects of substitution on this acid-catalysed exchange, tend t o support the single mechanism shown above. The reversal in the usual order of p-methyl and p-methoxy groups has not yet been explained. The data for the base-catalysed exchange of p-substituted benzophenones and water are summarized in Table 4. The rate for thep-nitrocompound was too fast to measure under these conditions. The rate constants are in the order p-NO, B p-Br > p-Cl> p-H > p-CH, > p-CH,O. The trend in the rate constants in the base catalysed exchange is opposite to that found in the acid-catalysed exchange, with a factor of sixteen as one goes from p-methoxy to p-nitro. It was found that the base-catalysed exchange shows a second-order dependence on hydroxide ion concentration. A similar dependence of rate on the square of the hydroxide ion concentration has been found in a number of other base-catalysed organic reactions, including the exchange of 0l8in p-substituted acetanilides (Bender and Thomas, 1961a, see p. 164).
150
D A V I D S A M U E L A N D B R I A N L. S I L V E R
TABLE4 Rate Constants and Activation Parameters for the Base-Catalysed Exchange of p-Substituted Benzophenones, p-XCeH4. CO’8. CeHs with water in 20: 80 (v/v) Aqueous Dioxan ( 0 . 0 0 0 5 NaOH) ~
X
CH30
CH3 H c1 Br
104k (sec-1) (40’)
104k (sec-1) (50.3’)
104k (sec-1) (60’)
0.42 0.78 1.94 5.00 6.73
1.23 2.28 4.98 10.23 12.58
2.06 3.61 7.21
E,
AHt
AS*
(kcal)
(kcal)
(e.u.)
logP2
21.7 21.6 19.0 14.5 12.7
21.1 21.0 18.4 13.8 12.0
-9.8
10.7 10.9 9.5 6.7 5.6
-8.8
-15.3 -28.0 -33.4
This kinetic order has usually been interpreted in terms of a dianion intermediate. Menon ( 1964) therefore proposes the following mechanism for the catalysed exchange of p-substituted benzophenones : O*-
O*
II
R--C!-R‘
+ OH-
KL
I
R-(:-R’
I
OH
o*I
R-(I--R’
I
OH
O*Rz
I
+ O W +2 R-c‘-R’
+ HzO
I 0-
An alternative mechanism in which hydroxide ion displaces a hydroxyl group was rejected as unlikely. A rate equation kobs= K I K 2 k l [ 0 H - l 2 was derived using the constants shown in the above scheme. It was suggested that the effects of para-substitution on these three constants are in the same direction, hence the overall effect on the observed rate constant is more pronounced in the base-catalysed exchange than in the acid-catalysed one. The effect of planarity on the rate of exchange in ortho-linked benzophenones has been examined by Rotlevi and Samuel (unpublished
151
OXYGEN ISOTOPE EXCHANGE REACTIONS
results). The relative rates of exchange in 80% dioxan at 100°Care given below. 0
0
0
r)
I1
The rates appear to be determined by electronic effects and there seems to be rough correlation between the rates of exchange and the basicities of these compounds determined by Stewart et al. (1963). Dahn (1964) showed the effect of unsaturation and of steric hindrance on oxygen exchange in ketones in some qualitative studies. Cholestanone (24) underwent exchange lo3 times faster than cholestenone (25), a,p-unsaturated ketone. Whereas, aceto-(26 ; R = CH, ), propio- (26 ; R = CH,. CH2) and isobutyro-phenones (26; R = i-Pr) exchange 0 1 7 with solvent at a measurable rate, pivalophenone (26; R = t-Bu) with a
24
25
26
27
neighbouring t-butyl group did not exchange a t all. This indicates that steric hindrance t o bimolecular attack of water is an important factor. However, Fry (personal communication) finds that benzpinacolone (26; R = CPh,) undergoes fairly ready exchange in dioxan-water. Biemann (1962), using direct mass-spectrometry on mixtures of organic compounds and water found that cyclohexanone (27; R' = R" = H) underwent 90% exchange after 40 min a t room temperature, whereas 2-methylcyclohexanone (27; R' = H; R" = CH,) had undergone 30%
-
N
152
DAVID SAMUEL AND BRIAN L. SILVER
exchange and 2,2-dimethyl-cyclohexaiione (27; R' = R" = CH3) oiily 15% exchange under the same conditions (equal weights of ketone, water and isopropyl alcohol). The effect of polar neighbouring groups on Ols-exchange in ketones has been studied only qualitatively in keto-acids (discussed on p. 169). Roberts and Urey (1938) examined the rate of exchange between benzil (28) and water in connection with the benzilic acid rearrangement. At 70°C in neutral aqueous methanol the extent of exchange was measurable (162 7 % after 2.5 mins and 4 3 + 6% after 4 min). However, the exchange was virtually complete in the presence of 0.02N sodium hydroxide after 4 min, the shortest time in which the experiment could be performed. On the basis of these results the authors concluded that the first step in the benzilic rearrangement is a rapid reversible addition of hydroxide ion t o form an addition intermediate in which a proton shifts rapidly from one oxygen to another either intramolecularly or by a chain mechanism through the solvent. The rapidity of the exchange, as compared to the rate of base-catalysed rearrangement, shows that the rate-determining step in this reaction is the rearrangement of the tetrahedral ion. This supports one of the mechanisms for the benzilic rearrangement suggested by Westheimer (1936) on the basis of kinetics, and earlier by Ingold (1928). 0 0
It 1i
('6H5--C-('-C'sH5
28
H0 0
0- 0
*
+OH-
('6H5
I I1 I
-('-('
*OH
('6H5
I II I
C6H5-('--('-C(p,H5
*O-
I 1
There is very little kinetic evidence on the isotopic exchange of oxygen between aldehydes and water. Herbert and Lauder (1938a)) using a density method of isotopic analysis, made a rough study of the exchange between acetaldehyde and water, finding 60% exchange in about 2 h at room temperature. It was assumed that a reversible hydration-dehydration mechanism operated here. However, this rate of exchange is considerably slower than the rate of hydration of acetaldehyde (see Bell et al. (1956) and previous papers). It seems probable that Herbert and Lauder's early work is inaccurate and a more careful study would be most desirable.
OXYGEN ISOTOPE EXCHANGE REACTIONS
153
There have been some studies on the isotopic exchange of oxygen between sugars and water. It was established quite early (Goto, 1940, 1941) that glucose exchanges one sixth of its oxygen fairly readily with water and it was assumed that this was the oxygen on C1. Owing to poor methods of isotopic analysis and to lack of care in controlling the pH, many subsequent reports of exchange in sugars are of little interest. However, there is now a specific method of isotopic analysis of the oxygen in the carbonyl groups of sugars (Koshland and Stein, 1954). It was shown that maltose readily exchanges the oxygen atom of C1 with
I
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
9
PH
FIG.1. The effect of pH on the rate of exchange ( k e x )a t 61°C and on the rate of mutarotation (k,) a t 20°C.
solvent water a t pH 5 a t about 86"C, again probably by reversible hydration and dehydration. (Mayer and Larner, 1959; Halpern and Leibowitz, 1959). Rittenberg and Graff (1955)have made a detailed quantitative study of the effect of pH on the exchange of the C1oxygen of glucose with water. As seen from Fig. 1 there is a minimum in the rate of exchange a t p H 4. Exchange is estimated to be about 30 times slower than mutarotation and the activation energies for the two processes are quite different (23.4 kcal molep1 and 17.2 kcal molew1respectively). The pH-rate profiles for the two reactions have different shapes so that it appears that mutarotation is not the rate-determining step in exchange, which probably proceeds via the free aldehyde form of glucose. The lack of linearity with acid and base concentration may be due to the presence of several consecutive steps. Aleksankin and Grngerov (1961)made a semi-quantitative study of the acid-catalysed exchange of some ring-substituted benzaldehydes and
154
DAVID SAMUEL A N D BRIAN L. SILVER
found that aldehydes with electron-donating substituents undergo exchange more slowly than those with electron-accepting substituents. The exchange reactions were measured in fairly concentrated solutions of aldehydes in dioxan containing varying amounts (10-30%) of water. Percentages of exchange after given time intervals a t various temperatures were reported. Owing to the small amount of water used, exchange in neutral solution is fairly slow but is much faster in 0 . 1 ~ hydrochloric acid. TABLE 5 Exchange in Benzaldehyde Derivatives. (Aleksankin and Gragerov, 1961)
Neutral Dioxan-water
Acid (0.1~ HCl) dioxan-water >
, 7
ExTemp. Time change Temp. Time ("C) (h) % ("C) (h)
Substituent in Benzaldehyde
Exchange
%
CHO I
('HO 0x1
o-NO~
20"
24
70
20"
1
100
20"
24
80
20°
1
90
('HO I
p-NO2
155
OXYGEN ISOTOPE EXCHANGE REACTIONS
TABLE&continued Neutral Dioxan-water
Acid ( 0 . 1 HC1) ~ dioxan-water
r ,
EXTemp. Time change Temp. ( " C ) (h) % ("C)
Substituent in Benzaldehyde
ExTime (h)
change
3
65
%
CHO o-OH
70"
6
10
40'
CHO
o-OMe
60CH3 Q 70'
6
15
40'
3
40
70"
6
25
40"
3
45
70"
6
0
40'
3
30
50'
15
0
20'
24 (0.4~ HCl)
55
3
15
-
-
-
C;HO
p-OH
oy OH
3,4-0.CH2.O -
0-CH, CHO I
m-CHO
0
CHO
60"
156
DAVID SAMUEL A N D BRIAN L. SILVER
Preliminary results by Calhoun et al. (personal communication) on the exchange between para-substituted benzaldehydes and neutral dioxanwater (9 :I v/v) a t 75°C reveal that p-nitrobenzaldehyde undergoes exchange much more rapidly than p-dimethylaminobenzaldehyde in agreement with Aleksankin and Gragerov's results (1961). This is in the reverse order to that found for the acid-catalysed exchange of p-substituted benzophenones (see p. 148). The substituent effects on exchange are the results of opposing effects on protonation and nucleophilic attack of water. The variations in the order of rates of exchange indicate that these effects are of comparable order of magnitude. Samuel and Fiat (unpublished results), using 017N.M.R. for analysis, found that the rate of exchange of salicylaldehyde in dioxan-water mixtures is much less than that of either p-hydroxy-salicylaldehyde or of anisaldehyde (o-methoxybenzaldehyde). Similar qualitative results were reported by Aleksankin and Gragerov (1961) using 0 I 8 and conventional analytical techniques. It would appear that the hydrogen bonding between the ortho-hydroxyl group and the carbonyl oxygen retards the exchange of OI8 in salicylaldehyde by hindering the formation of two equivalent hydroxyl groups when water adds to the carbonyl group.
B. Quinones Little is known about the exchange of OI8between quinones and water. This is partly due to the difficulty of handling these compounds and to the ease with which they decompose. In connection with a tracer study on the periodate oxidation of phenol ethers, Adler et al. (1962) found that
p-benzoquinone undergoes 8% exchange with water in 1 min a t 65"C, which is much faster than originally reported by Fesenko and Gragerov
OXYGEN ISOTOPE EXCHANGE REACTIONS
157
(1955). The rate of exchange is even faster in o-benzoquinone (97; exchange in 10 sec at O'C) but is decreased by methyl substitution. Thus 3, 5-dimethyl o-benzoquinone undergoes 13.6% exchange a t 20°C in 2 mins. The effect of methyl groups is consistent with a mechanism involving the addition of water to the carbonylgroup. Rotlevi and Samuel (unpublished results) have examined the effect of methyl substitution and aromaticity in a series of p-quinones in 80% dioxan a t 100°C. The order of reactivity found was as shown in the formula on p. 156. Once again it is apparent that methyl groups and fused aromatic rings both tend to decrease the rate of exchange.
C. Esters, Amides and Acid Chlorides An important part of organic chemistry is concerned with compounds containing the grouping 0
II
R--C-X
where R is an alkyl or aryl group and X may be alkoxy, aryloxy, amino or halogen. The most common general reaction of the group may be written 0
I/
R-C-X
0
+ R'OH
/I
R-('-OR'
+ HX
Where X = alkoxy and R' = H this represents the hydrolysis of an alkyl ester. One of the earliest chemical applications of O18-enrichedwater was Polanyi and Szabo's demonstration in 1934 that the alkaline hydrolysis of n-pentyl acetate proceeds by acyl-oxygen bond fission.
The hydrolysis of carboxylic acid esters in acid solution was later also shown to proceed with acyl-oxygen bond fission (Datta et al., 1939). Day and Ingold (1941) suggested that the reaction might proceed either by the formation of a tetra-covalent intermediate or by direct bimolecular displacement via a "tetracovalent )'transition state. Urey and co-workers (Cohn and Urey, 1938; Roberts and Urey, 1938) in the course of investigations of esterification and of isotopic exchange of oxygen between organic compounds and water, found no exchange between either pentyl acetate or methyl benzoate and water at room temperature. I n view of the fact that these results were contradicted by later findings it is G
158
DAVID SAMUEL A N D BRIAN L. SILVER
only fair t o mention that, Urey worked with very slightly enriched 0lswater under neutral conditions, where hydrolysis is very slow, and used very insensitive analytical techniques. I n an attempt to find evidence for a reaction intermediate, Bender (1951) examined the hydrolysis of ethyl, isopropyl and t-butyl benzoates. These esters were synthesized with the carbonyl oxygen labelled with 01*and after partial hydrolysis in a mixture of isotopically normal water and dioxan (66 :34 v/v) the unhydrolysed substrate was recovered, purified and found to contain less OI8 in the carbonyl oxygen than at the start of the reaction. These results strongly supported the existence of a tetracovalent intermediate. The mechanism for exchange and for hydrolysis of an ester was given as : O*
The ratio of the rate constant of hydrolysis khydrol(measured by conventional titrimetric methods) to that of exchange keXchwas determined for ~ and base ethyl, isopropyl and t-butyl benzoates. I n 0.001 to 0 . 0 0 7 acid it was found to be in the range of 4 to 10 (see Table 6). It is of interest t o note that whilst the ratio khydrol/kexch was found to be the same for both acid and alkaline hydrolysis of ethyl benzoate, the absolute value of khydrol in acid differs by a factor of l o 4 from that in base. This was taken as evidence that a similar intermediate is formed in both acid and alkaline hydrolysis of esters. A later, more accurate determination O f khydrol/kexch showed that they differ in fact, by a factor of two, the ratio in basic solution being the larger (Bender et al., 1958). It was still, however, assumed that a common intermediate plays a central part in the hydrolysis of all derivatives of carboxylic acids (Bender, 1960). It will be seen that the extent to which exchange accompanies hydrolysis depends on the relative magnitudes of k,the rate of breakdown of the intermediate t o products (alcohol and acid), and of k', the rate of return to unhydrolysed ester, i.e. the relative partitioning of the intermediate. For instance, other things being equal, a better leaving group OR' will favour hydrolysis ovei exchange. The way in which steric and electronic factors affect the relative partitioning of the intermediate is an important and as yet only partially answered question, as will be seen in the course of this discussion.
TABLE6
0
I/
The Kinetics of Exchange of Carboxylic Acid Derivatives ( R - C X )
R
Temp. ("C)
x ~~
~~
CH30
0 CzH50 Cz&O CZH50 CzH50 CzH50 i-C-CaHjO i-C-C3H50 i-C-CZHjO t-C4-C4H90 t-C4-C4Hg0 p-C1 CsH4. CHzO p C 1 &H4. CHzO p-CH30 .CsH4.CHzO CsH50 CH30 CH30 CH30 CHBO CH30 NHz NH2 NHz NHz
Conditions and Solvent ~
25' 25.12' 25.12' 99" 9" 25' 40.2' 25' 62.5'' 62.5'
25' 62.5" 24.8' 24.8' 24.8' 0 ' 24.7' 24.7' 24.7" 24.7' 126' 40.7'
80" 109' 109'
10%"
with Water
khydro,lkexch
Reference
~~
33% dioxan 33% dioxan; 0 . 0 1 NaOH ~ Water; 0 . 1 NaOH ~ Water; 0 . 0 1 HC1 ~ 33% dioxan; 0 . 0 1 NaOH ~ 33% dioxan; 0 . 0 1 NaOH ~ 33% dioxan; 0 . 0 1 NaOH ~ 33% dioxan; 0 . 0 1 HCI ~ Water; 0 . 0 1 NaOH ~ 33% dioxan 33% dioxan 33% dioxan 0 . 0 1 NaOH ~ G6% dioxan 50% dioxan 66% dioxan 50% dioxan; 0.04 t o 0 . 0 9 ~ NaOH 33% dioxan; NaOH 33% dioxan; NaOH 33% dioxan; NaOH 33% dioxan; NaOH 60% dioxan; 0 . 0 5 NaOH ~ Water; 0 . 1 NaOH ~ Water; 0 . 1 NaOH ~ Water; 0 . 1 NaOH ~ Water; 0 . 1 HCl ~
-
1.8 7.4 2.5.5
-
-
-
-
-
5.8 10.6 4.8 5.2 14.7 11.3 10.1 5.4 2.7 3.7 11.4 7.6 7 150 > 60 7 192 Large
30+4 6.3 & 2 11+2 2.8 f 0.3 6.8 f 0.5 7.6[OH-] 0.53 187[0H-] 0.29 263[OH-J 0.21 7 374
Bender et al. (19611~) Bender (1931) Bender (1951) Bender (1951) Bender et al. (1938) Bender et cil. (1958) Bender et cil. (1958) Bender (1951) Bender (1951) Bender (1951) Bender (1951) Bender (19.51) Bender et a!. (1961b) Bender et al. (1961b) Bender et al. (1961b) Bunton and Spatcher (1956) Bender and Thomas (1961b) Bender and Thomas (1961b) Bender and Thomas (1961b) Bender and Thomas (1961b) Bender and Dewey (1956) Bender et al. (1958) Bender et aZ. (1958) Bender and Ginger (1955) Bender and Ginger (1955)
TABLE6 continued c Q,
X
Temp. ("C) 100" 100" 24,7" 24.7" 24.7' 24.7" 24.7' 24.7" 24.7' 24.7" 25" 25" 25'
p-CH3 .CaH5
c1
25'
p-CH3 .C6H5
c1
25'
2,4,(i-(CH3)3CsH3 C1
25'
2,4,6-(CH3)3CsHz
C1
25O
CSH5
CaHsCO. 0
62.6'
a
Phthalide
25a
y -Butyrolactone
25'
0
Conditions and Solvent
~ Water; 1 . 5 HC1 Water; 1~ Ba(0H)Z Water; 0.2401NaOH Water; 0 . 9 6 NaOH ~ Water; 0 . 2 4 NaOH ~ Water; 0.9601 NaOH Water; 0 . 2 4 NaOH ~ Water; 0 . 9 6 NaOH ~ Water; 0 . 2 4 NaOH ~ Water; 0 . 9 6 NaOH ~ 95% dioxan (initially neutral) 75% dioxan (initially neutral) 67% dioxan (initially neutral) neutral) 95% dioxan (initially neutral) 67 yo dioxan ; (initially neutral) 99% acetonitrile (initially neutral) 95% dioxan; (initially neutral) 75% dioxan; (initially neutral) 33% dioxan; (initially neutral) Water
k,=First-order exchange rate constant (units: sec-')
lojkl -
287 1.5 5.1 0.84 3.33 0.49 1.9 0.42 1.44 0
khydrol/kerch
-
0.46 0.135 0.208 0.216 0.284 0.332 0.452 0.467 0.697 Large
Reference Bunton et al. (1954) Bunton et al. (1954) Bender and Thomas (1961a) Bender and Thomas (196la) Bender and Thomas (1961a) Bender and Thomas (196la) Bender and Thomas (1961a) Bender and Thomas (1961a) Bender and Thomas (1961a) Bender and Thomas (1961a) Bunton el al. (1954)
3
25
Bunton e t nl. (1954)
8.2
18
Bunton et al. (1954)
Large
Bunton et crl. (1954)
51
Bunton et nl. (1954)
-
4.4 -
11 0.0652
Large
Bender and Chen (1963)
31
Bunton et al. (1954)
20
Bunton et al. (1954)
-
> 50
Bender et al. (1961h)
-
> 30
Bender et al. (1961b)
161
OXYGEN ISOTOPE EXCHANGE REACTIONS
Since Bender's original paper was published, increasing support for the idea of a tetracovalent intermediate in hydrolysis has accumulated from studies of exchange in various derivatives of carboxylic acids. It should be noted that although concurrent isotopic exchange of oxygen with hydrolysis is consistent with the formation of an intermediate, no physical evidence for such an intermediate has been obtained so far. I n fact there is no proof that the intermediate actually lies on the reaction path for hydrolysis although some evidence has been found to support this assumption (Johnson, 1964). On the other hand, it should be remembered that no exchange at all would be expected if the only mechanism were direct nucleophilic displacement on the carbonyl carbon. A list of the various carboxylic acid derivatives which have been used in these studies is given in Table 6, together with rate constants for exchange and hlydrollkexch ratios. It is seen from the table that the khydrol/kexch ratio varies from a factor of about 2 to nearly 200. The latter value is, in fact, only a practical limit caused by the difficulty of making accurate isotopic analyses at the concentrations of 0ls usually used. If the proportion of exchange falls below 1 or 2%, the resulting change in OI8 content of the ester is a t the limit of isotopic analysis. Bender suggests that all carboxylic acid derivatives hydrolyse by the same mechanism, even where no exchange of O'* at all is observed. I n the acid-catalysed exchange of benzamide (see Table 6), for instance, the apparent absence of Ols-exchange does not rule out the formation of a tetracovalent intermediate, since the observed result could be due to a very large khydrol/kexcl] ratio. A possible explanation for this high ratio in acid solution is the greater basicity of NH, than that of OH-, causing NH, to be lost in preference to H,O.
J
Independent support for this suggestion has been obtained by Swain (1961) who found a kinetic isotope effect k(N14)/k(N16) < 1 in the acid hydrolysis of benzamide. This is considered to be evidence that the C-N bond is shorter in the transition state than in the ground state and rules out a direct bimolecular displacement mechanism on carbonyl carbon.
162
D A V I D SAMUEL A N D B R I A N L . SILVER
The formation of the tetracovalent intermediate appears to be the ratedetermining step. On the other hand the hydroxide ion-catalysed hydrolysis of benzamide (Bender and Ginger, 1955) is accompanied by oxygen exchange with solvent (see Table 6). I n basic solution, the reaction proceeds via the symmetrical intermediate. QH C~H~-~--NH~
I
*OH
The khydrol/kexckl ratio is 0.21 in base, compared t o 4.8 for ethyl benzoate under the same conditions (Bender, 1951). Thus the ease of removal of a leaving group from the intermediate is OH- > NH;, again in accord with their relative anionic stability, whilst for the ester intermediate it is OR- > OH- which is the opposite order to their stabilities. It was suggested that the steric requirements of the -OR group might be the cause of this anomaly. Bender et al. (1958) determined the effect of temperature on the kilydrol/kexch ratio in the basic hydrolyses of both benzamide and of ethyl benzoate. I n each case an increase in temperature leads t o a decrease in khydrol/JC,,,k,.From the results, the activation energy for the formation of the tetrahedral intermediates may be estimated. However, the differences in the activation parameters for the two pathways by which the intermediate can break down are of greater interest. The energies of activation for each path are similar for amide and ester hydrolysis, but the values of the entropy of activation differ markedly, resulting in the differences in the k~,ydrol/kexchratio. This adds weight to the previous suggestion that steric factors are very important in the partitioning process. It might be thought that a two-step mechanism, i.e. formation and breakdown of a tetracovalent intermediate, would show a temperature dependence of the Arrhenius activation energy, such as has been found for acetic anhydride (Gold, 1948). No such dependence was found in hydrolysis and exchange, but a n analysis by Render showed that multistage reactions can lead to an ovrra11 activation energy that is not
29
x 30
163
OXYGEN ISOTOPE EXCHANGE REACTIONS
very sensitive to temperature, depending on the relative magnitude of the rate constants for individual steps. Bender and Thomas (196lb) examined substituent effects in the concurrent hydrolysis and exchange of a series of para-substituted methyl benzoates (29; R == CH,) where X i s amino, chloro and nitro. On general grounds the electronic demands of bond breaking for hydroxyl and methoxyl groups in the tetracovalent intermediate should be similar. However, significant variations (of the order of a factor of 10) in the IChydrol/kexch ratio on going from p-amino to p-nitro were observed (see Table 6). To explain this result more parameters are needed in the rate equation, and there is not much choice but t o consider the only steps which had previously been assumed not to affect the rate, i.e. proton transfers. Bender's original assumption that proton transfers involving the tetrahedral intermediate are not kinetically significant, was based on the fact that proton transfers between oxygen and nitrogen atoms are very fast and considered not t o affect the overall rate in most chemical reactions. The modified scheme for alkaline hydrolysis which includes proton transfer is as follows : O*
0*
O*-
I\
R-C-OCHStOH-
h
< kz
'
I R--C
I-
OCH,
lir
\I
R-C-0H+C1H3&
OH
,
k4/l O*H
I I
R--C-OCHJ OH
0 R-C-OCH3 II
+ O*H-
4
-
L
O*H R-C-OCH3 I
I
&
0
II
R--C-OH
+ CH10-
0-
Bender suggests that the rate constant k 2 for the breakdown of the intermediate is of the same order of magnitude as k4 the rate constant for proton transfer in the intermediate. The rates of proton transfer to oxy-anions and nitrogen bases are of the order of 108-109 1. mole-' sec-l (see Loewenstein and Connor, 1963). For k , to be of this magnitude requires an activation energy of about 6 kcal. molep1for the breakdown of the intermediate. Such an activation energy seems quite plausible.
164
DAVID SAMUEL A N D BRIAN L. SILVER
I n terms of this scheme, the value of the khydTol/kexchratio would decrease as the substituent changed from p-amino to p-nitro if k31k4 decreased. This change is in the expected direction since an electronegative substituent in the benzene ring would affect step k3 which concerns a bond nearer the reaction centre more than it would affect step k,. An interesting experiment which Bender suggested in this connection would be the determination of the deuterium solvent isotope effects associated with proton transfer in the reactions of the intermediate. I n contrast to alkyl benzoates the alkaline hydrolysis of benzyl esters ofp-chloro- andp-methoxy-benzoates (29; R = C6H,CH2)(Bender et al. 196lb), and of phenyl benzoate (29; R = CBH5)(Bunton and Spatcher, 1956) is not accompanied by detectable oxygen exchange. Attempts to explain this fact on either electronic or steric grounds are not entirely satisfactory. For instance, the methoxide ion and the benzyloxide ion have approximately the same basicity and, therefore, if the basicity of the leaving group were critical, one would expect a similar khydrol/kexcl, ratio. Experimentally, however, methyl benzoate undergoes 0lsexchange and benzyl p-chlorobenzoate does not. Moreover, the secondorder rate constants for the alkaline hydrolysis for simple alkyl benzoates and for benzyl benzoates are of the same order of magnitude, which indicates that it is the values of kexchwhich are so divergent. On steric grounds it might be argued that phenoxy and benzyloxy groups are so bulky that they are greatly favoured as leaving groups over the hydroxyl group. This would lead to the incorrect prediction that the hydrolysis of benzoic anhydride should be unaccompanied by oxygen exchange (see Table 6 ) . Moreover the t-butoxyl group is at least as bulky, if not more so, than the aryloxyl groups, yet exchange is observed with t-butyl benzoate (Bender, 1951). Thus the general question of partitioning of the intermediate is still not answered. It might be profitable to determine the khydrol/kexchratio for the saturated analogues of the cyclohexylmethyl benzoates (29 ; R = C6Hll.CH,) to see what part is played by the aromatic ring. An even more complicated situation is encountered in the alkaline hydrolysis ofp-substituted acetanilides (30)(Bender and Thomas, 1961a). The rate equation for the isotopic exchange of these compounds involves terms in [OH-] and [OH-]'. The original mechanism of hydrolysis proposed by Biechler and Taft (1957)in which there is a rapid pre-equilibrium addition and loss of hydroxide in the first step, is disproved by the fact that, although oxygen exchange is accompanied by hydrolysis, exchange is not as complete as it would be expected to be from that scheme. Bender considers the initial attack of hydroxide to be a rate process not an equilibrium. By use of low hydroxide ion concentrations
OXYGEN ISOTOPE EXCHANGE REACTIONS
165
it was possible to reduce the relative importance of the term [OH-J2 and to examine the part of the reaction that is first order in hydroxide. The scheme finally proposed is similar to that for esters and amide hydrolysis. From the comparative data for exchange and hydrolysis, values of k l and k,lk2 were derived for a series of p-substituted acetanilides.
1
CH3.C.NH.C6H4X
K H
0
II
k3
CHQ.C.OH+-NH.C:BH~X
0
II
CH3.(’O- + N H ~ . C G H ~ X
A Hammett sigma-rho relationship was found to apply to kl with a slope of + 1.0, indicating that electron-withdrawing groups facilitate addition to the carbonyl group, which is a reasonable result. The behaviour of k 3 / k 2is not, however, so simple. The sigma-rho plot of log k 3 / k 2has a slope of - 1.0. From the above scheme it would be expected that electronwithdrawing substituents might favour hydrolysis over exchange, by stabilizing the anionic leaving group. I n fact, exactly the opposite behaviour is observed. Two possible mechanisms are suggested to account for the experimental results. I n scheme (a) the exchange reaction proceeds through the symmetrical form (31)) having a negative charge on the nitrogen, which is stabilized by electron-withdrawing groups. I n scheme (b) hydrolysis proceeds through the dipolar ion (32). The equilibrium position in the formation of this ion will depend on the basicity of the nitrogen atom and this will be influenced by the nature of the substituent group X. Electron-withdrawing groups will decrease the basicity of nitrogen, thus reducing the proportion of dipolar ion and favouring exchange, as was found experimentally. If the breakdown of (32)is rapid, substituents will not have large effects on the rate of this step. Furthermore, in dioxan-water solutions the ratio khydrol/kexch for benzamide decreases with the decrease in the percentage of water, khydrol decreasing faster than kexch. This may be rationalized in terms of scheme (b) since the fraction of the tetrahedral 6*
166
DAVID SAMUEL AND BRIAN L. SILVER
intermediate in the dipolar form should decrease with solvent polarity. Additional support for a dipolar intermediate is provided by a number of other studies in which a second-order dependence on base has been found, including the alkaline hydrolysis of acetylacetone (Pearson and Mayerle, Scheme (a):
0-
0
I
I1
0
CH~.C;'.NH.CCH~X A CH3.v + N H . C C H ~ X I
I
OH
OH
li
products
*OH
OH
i)H
exchange
31
Scheme (1)):
0-
0-
I
CH~-C-NH.C'BH~X W
($
A
4H \H
I + I
CH3.C.NH2.Cc3H4X
C H ~ ~ C O Z-
+
NH2. CaHJ
0-
32
1951)the Cannizzaro reaction under certain conditions (Hammett, 1940), the alkaline hydrolysis of N-methylacetanilides (Biechlerand Taft, 1957) the alkaline cleavage of chloral hydrate (Gustafssonand Johanson, 1 9 4 8 ) and Menon's work on benzophenones (see p. 149). I n such hydrolyses no experimental distinction has yet been made between (i)the formation of a dianionic intermediate in an equilibrium process, and (ii) a kinetically equivalent situation in which the hydroxide ion removes a proton in a rate-determining step leading to the products. The latter mechanism is perhaps less likely in view of the very high rates of proton transfer between oxygen atoms in aqueous solution. The alkaline hydrolysis of methyl 2,4,6-trimethylbenzoate (33; R = R' = CH,) (Bender and Dewey, 1956)and of methyl 2,4,6-triphenylbenzoate (33;R = C,H,; R' = CH,) (Bunton et aZ., 1955a)arebothfound to proceed via acyl-oxygen fission, accompanied by some oxygen exchange indicating the formation of a tetrahedral intermediate. The acid hydrolysis of methyl 2,4,6-trimethylbenzoate (33; R = R' = CH,) has been studied at various temperatures over the range 3.1 to 1 1 . 5 H,S04 ~ (Bender et al., 1961b). The rate of hydrolysis was
O X Y G E N ISOTOPE E X C H A N G E R E A C T I O N S
167
found to be proportional to the h, acidity function and no exchange of 0" between solvent and the carbonyl group was observed. This fact and the positive values of the entropies of activation indicate that the mechanism of hydrolysis is a unimolecular heterolysis with carbonyl-oxygen bond fission to form an acyl cation. The basic hydrolysis of the t-butyl 2,4,6-triphenylbenzoate (33, R = C,H,; R' = t-butyl) is entirely with alkyl-oxygen bond fission (Bunton et al., 1955a). It would bc of interest to see whether any exchange occurs in the latter case.
It 33
The neutral and acid-catalysed hydrolysis of mesitoyl chloride in acetonitrile containing 1% Ol'-enriched water is not accompanied by 0l8 exchange (Bender and Chen, 1963). It is suggested that in both cases unimolecular heterolytic bond fission occurs with the formation of an acyl cation. I n alkaline solution a tetracovalent intermediate is postulated on the basis of a comparison of the effect of substituents on the rate of hydrolysis of the corresponding benzoate esters. The exchange of 0l8 in alkaline solution was not determined experimentally. The effect of solvent on the isotopic exchange between the carbonyl group and water in acyl chlorides was examined by Bunton et al., (1954). The rate of exchange increases with increasing water content in a dioxanwater mixture (see Table 6). The marked solvent dependence of the kllydro,/kCxch ratio may be an indication that proton transfer between oxygen and chlorine affects the partitioning of the tetracovalent intermediate. The ratio of hydrolysis to exchange is fairly large but measurable in benzoyl, p-toluyl and mesitoyl chlorides but no quantitative comparisons can be drawn because of differences in the experimental conditions. Further support for an addition-elimination mechanism (as opposed to the formation of an acyl cation) was obtained by Swain (1963) on the basis of the oxygen isotope effect in the methanolysis of benzoyl chloride in methanol. At 25"C, k(016)/k(01s) = 0.911 5 0.013, which is inconsistent with a carbonium ion mechanism. I n benzoic anhydride, O1'-exchange between the carbonyl group and water in initially neutral solution at 62~6°Cwas also found (Bunton et al., 1954).
168
DAVID SAMUEL AND BRIAN L . SILVER
O
II
Bunton et al. observed that the khydrol/kexch ratio in the series R-C-X decreases in the following order for changes in X
+
where X = NH3 > C1 > O.CO.CGH, > OR’ > NH,. This sequence is similar to the order of ease of ionization of X- from C-X (except that the positions of alkyl halides and ammonium compounds are reversed), indicating that the hydrolysis/exchange ratio gives a measure of the relative ease of breaking of the C-X and C-OH bonds. No exchange was observed between the carbonyl group and water in the alkaline hydrolysis of phthalide (34)or of y-butyrolactone (35) (Bender et al., 1961b). From the precision of the istopic analysis it was estimated that the khydrol/kexch ratio is greater than 50 for the former and greater than 30 for the latter, but no explanation of these results has been found.
34
35
36
The acid- and base-catalysed hydrolysis of the cyclic carbonate of 2,2diethylpropane-1,3-diol (36) is accompanied by oxygen exchange of the exocyclic (carbonyl) oxygen (Sarel et al., 1960). I n acid solution multiple ring opening and closing could perhaps account for the incorporation of oxygen. I n base, however, the results are still not clearly understood.
V. THE EXCHANGE OF CARBOXYLIC ACIDSWITH WATER
It is surprising that so few kinetic studies on the isotopic exchange with the carboxyl group were undertaken until very recently. Early work showed that the salts of carboxylic acids do not undergo exchange in neutral solution (Herbert and Lauder, 193813). However, under fairly drastic conditions (170°C for 3 h) Gragerov and Ponomarchuk (1959) found that potassium anthranilate (o-aminobenzoate) underwent 56% exchange. I n general, however, it appears that there is virtually no exchange in neutral solutions. I n alkaline solution it has always been assumed that exchange does not occur because of electrostatic repulsion between the hydroxide
OXYGEN ISOTOPE EXCHANGE REACTIONS
169
ion and the carboxylate group, although slight exchange was found for 2,4,6-triphenylbenzoic acid after 10 days a t 100°C (Buntonetal., 1955a). Greenzaid and Samuel (unpublished results) have found that benzoic acid does undergo a slow base-catalysed exchange a t 1OO"C, whereas mesitoic acid does not incorporate any 0ls after heating to 100°Cin 6 N sodium hydroxide in Ols-enriched water for 7 days. Roberts and Urey (1939a) established that the exchange between carboxylic acids and water is acid-catalysed. Free carboxylic acids are usually acidic enough for exchange without the addition of a mineral acid. Thus acetic acid has undergone 4.6% exchange after 16 h a t 25°C in 0l8-enriched water and 87.4% exchange after 3 h a t 100°C (Bentley, 1949). More recently Brodskii et al. (1962) reported that the exchange of acetic acid a t 42°C is first order, with a rate constant of 8.8 x lop6sec-' (i.e. a half-life of 20 h). They also found that the carboxyl group in pyruvic acid undergoes exchange with water with a rate constant of 8.3 x lop5 sec-l a t 15"C, suggesting that a neighbouring carbonyl group accelerates the rate of exchange of a carboxyl group by several orders of magnitude. This is not unexpected for the nucleophilic attack of water on carbon with a neighbouring carbonyl group. The situation is complicated by significant hydration of the carbonyl group in pyruvic acid. A more detailed study of exchange between acetic acid and water (Llewellyn and O'Connor, 1964a) showed that the rate varies with pH. It was found that exchange occurs with the conjugate acid and (at higher temperatures) in basic solution. It was not established with certainty whether the neutral molecule underwent exchange or not. On the basis of the deuterium solvent isotope effect on the rate of acid-catalysed exchange it was suggested that there is a fast proton pre-equilibrium followed by slow nucleophilic attack of water on the conjugate acid. The rate of exchange between pivalic acid and water was also measured (see Table 7). A kinetic analysis showed that the neutral species does not contribute significantly to the rate. There appears to be only a very slight decrease in rate in the sterically hindered acid. The exchange of oxalic acid was studied by Milburn and Taube (1959). It was found that the rate of exchange with water a t 25°C could be accounted for by a rate law involving a term proportional to the concentration of the neutral molecule and an acid-catalysed term. Bunton et al. (1960) compared the acid-catalysed exchange rates of benzoic and mesitoic acids. For benzoic acid, the exchange rate is proportional to the stoicheiometric acid concentration, suggesting that a water molecule participates in the transition state. This interpretation is consistent with the large negative entropy of activation, - 30 e.u. The energy of activation is 16 kcal. mole-l which is in the range typical of
w
4 0
TABLE7 The Kinetics of Exchange of Carboxylic Acids with Water Temp. ("C) Acetic acid Benzoic acid
42' 25-123' 73O 73" 73O 80" 101O 170'
Conditions
10514
Water Water (pH 1.5 to p H 11.35)
0.88
0 . 4 ~ 1.5501HzSO4 3 . 0 HzS04 ~ 0 . 0 7 HCIC ~ 0.05~ HzS04 Water
-
13.6 40 100 1.14 0.92 2.33
Reference
U P
U
Brodskii et al. (1962) Llewellyn and O'Connor (1964)
v)
Bunton et al. (1960) Bunton et al. (1960) Bunton et al. (1960) Bender et al. (1956) Bunton et al. (1960) Gragerov and Ponomarchuk (1959)
cl
+ z
M F
P
Z
U
W
Benzoic acid, rn-amino
150'
0 . 4 HC1 ~
Benzoic acid, m-chloro
liOo
170'
Water 0 . 0 6 4 ~HClC 0 . 4HCI ~
Benzoic acid, o-chloro
lloo
Water
4.4
Gragerov and Ponomarchuk (1959)
Benzoic acid, p-chloro
170" 80'
Water 0.064~ HClC
3.6 0.7
Gragerov and Ponomarchuk (1959) -4 M Bender el al. (1956)
Benzoic acid, o-hydroxy (salicylic acidb)
1loo
0 . 4 HCl ~
5
Gragerov and Ponomarchuk (1959)
Benzoic acid, rn-hydroxy
170° lloo
Water 0 4 HC1 ~
7.7 32
Gragerov and Ponomarchuk (1959) Gragerov and Ponomarchuk (1959)
Benzoic acid, p-hydroxy
110"
0 4 HC1 ~
15
Gragerov and Ponomarchuk (1959)
80"
3.0 5.3 1.13 13
Gragerov and Ponomarchuk (1959) Gragerov and Ponomarchuk (1959) P Bender et al. (1956) Gragerov and Ponomarchuk (1959) ? v) H
F
w
Benzoic acid, o-mercapto
170" 150"
Water 0 . 4 HCI ~
2.1 13
Gragerov and Ponomarchuk (1959) Gragerov and Ponomarchuk (1959)
Benzoic acid, p-methoxyb (anisic acid)
SO0
0.064~ HCIC
0.64
Bender et al. (1956)
Benzoic acid, p-methyl (p-toluic acid)
80'
0.069~ HCle
1.03
Bender et cl. (1956)
Benzoic acid, m-nitrob
17O9
Water
11
Benzoic acid, o-nitroh
170' 150"
Water 0.4~ HC1
5 11
cc Gragerov and Ponomarchuk (1959) Q Gragerov and Ponomarchuk (1959) M Z Gragerov and Ponomarchuk (1959) H
Benzoic acid, p-nitro*
170" 110'
Water 0 . 4 HC1 ~
21.6 9.0
Gragerov and Ponomarchuk (1959) 0 Gragerov and Ponomarchuk (1959) H
$3" 80' 100"
3.0%1HC1Odd 0 . 0 6 9 ~HC1" 0 . 4 3H ~ clog 2.09~ HC104d 3.78N HC104d
0.274 0.001 0.059 1.04 38
Buntoii et al. (1960) Bender et al. (1960) Bunton et al. (1960) Bunton et al. (1960) Bunton et al. (1960)
Benzoic acid, 2,4,6-trimethyl (mesitoic acid)
x
m
0
w
loo3 looo Oxalic acid
0
25"
M
M
x
d
X B
Z
Water ;varying acid concentration
Kinetics
Bunton et al. (1964)
0 M
Water (pH 1.5 to p H 10.9)
Kinetics
Llewellyn and O'Connor (19644
M
kd
Pivalic acid Pyruvic acidb
45-123'
15O
Water
8.3
Brodskii et al. (1962)
B 0 e H
kl=First-order exchange rate constant (units: sec-'). b Exchange in carboxylic group only. c 33% dioxan. 60% dioxan.
a
0
Z
m
172
D A V I D S A M U E L A N D B R I A N L. S I L V E R
ester hydrolysis by the A,,2 mechanism. It was suggested that the mechanism of exchange of benzoic acid is :
I n the second step, it is not possible to differentiate kinetically between (nucleophilic) addition of water to the carbonyl group or a synchronous displacement of a protonated hydroxyl group. I n mesitoic acid the rate of exchange (in aqueous dioxan) is proportional to ho. The positive entropy of activation ( + 9 e.u.) and the large energy of activation (33 kcal. molep1) are consistent with the formation of a transition state not involving water. It was suggested that exchange occurs by an A-1 mechanism, in which an acyl cation is formed.
It should be noted that the acid-catalysed hydrolysis of methyl mesitoate is also an A-1 reaction (Chmiel and Long, 1956). The effect of para-substituents on the rate of exchange of benzoic acid was examined by Bender et al. (1956). Small differences were found in the rates of exchange of m- and p-chlorobenzoic, p-anisic, p-toluic, mesitoic and benzoic acids in acid solution (see Table 7). No simple correlation between rates and electronic effects of the substituents could be found.
OXYGEN ISOTOPE EXCHANGE REACTIONS
173
As in ester hydrolysis, Bender suggested that exchange takes place by the addition of water to form a tetrahedral intermediate. The very slow exchange of mesitoic acid was attributed t o steric hindrance or an “orthoeffect” by the ortho-methyl groups. The rate constant kllydrolfor the hydrolysis of the ethyl esters of these acids is two to four times greater thank,,,,,, the rate constant for Ols-exchange of the free acid. The difference is presumed to be due to the fact that the acid is more resonancestabilized than the esters, although this is almost certainly not the only factor involved. The rate of oxygen exchange of a series of substituted benzoic acids was also studied by Gragerov and Ponomarchuk (1959) (see Table 7 ) who attempted to correlate the rate of exchange with the dissociation constants of the acids without much success. The rates of exchange (Gragerov and Ponomarchuk, 1959) fall in the following order :
This is the same order as the rates of acid hydrolysis of the corresponding methyl esters a t 50°C (NBSCircular 510,1951), except that the positions of p-nitro- and p-chloro-benzoates are reversed. A series of papers on the isotopic exchange with carboxylic acids has recently been published. The relative contribution and activation parameters of each of the pathways for exchange was determined from measurements on the rate of exchange as a function of pH. In contrast to acetic and pivalic acids (Llewellyn and O’Connor, 1964a), the strong inductive effect of the substituents in trifluoro- and trichloro-acetic acids increases the importance of the attack of hydroxide on the acid anion (O’Connor and Llewellyn, 1964b). The rates of exchange of water and oxalic acid in trisoxalato-complexes of chromiumI11 and cobalt-I11 were found by Bunton et al. (1964) to be very similar to those of the free acid, The exchange into the carbonyl (coordinated) and carboxyl groups are found to be kinetically equivalent, which together with the lack of labelled oxalate exchange supports the “oneended” dissociation mechanism for exchange and for racemisation of such complexes. The exchange in the carboxyl group of amino acids has hardly been investigated a t all. Two early studies (Mears, 1938; Mears and Sobotka,
174
DAVID SAMUEL A N D BRIAN L. SILVER
1939) showed that glycine underwent complete isotopic exchange at pH 1.9 after 24 h at 100°C.No exchange was found in neutral solution. This has been confirmed by recent measurements at 100°C (Samuel and Wassermann, unpublished results). As in most other substances, the exchange of amino-acids is acid-catalysed. Although Mears and Sobotka could not detect any exchange in the carbonyl group of the peptide linkage in pepsin at pH 4, they found an incorporation of about 3% 0ls in the whole enzyme. This roughly corresponds to the oxygen content of the free carboxyl groups of the constituent dicarboxylic acids. The rapidity of exchange into these free carboxyl groups was attributed t o the increasedreactivity in these acids in the protein due to the “structural properties”. It is a pity that this observation has not stimulated further work in view of the current interest in the effect of structure on the reactivity of proteins and particularly of enzymes. Samuel and Wassermann (unpublished results) have found that the relative rate of exchange is phenylalanine > glycine > serine in 0 . 5 ~ hydrochloric acid at 40°C. O’Connor and Llewellyn (personal communication) have determined the exchange parameters of glycine in the range 4M perchloric acid to pHl2.
VI. THE EXCHANGE OF OTHERORGANICCOMPOUNDSCONTAINING OXYGENWITH WATER Research into the isotopic exchanges of oxygen of organic compounds has naturally been mainly concerned with oxygen bonded to carbon. There is, however, growing interest in the exchange reactions of organic compounds where oxygen is bonded to other elements, such as nitrogen, phosphorus, sulphur, silicon and iodine. Much of this work has been a search for addition intermediates of the “Bender” type (see p. 158), in the hydrolysis of esters of oxyacids. The isotopic exchange of oxygen between water and organophosphorus compounds has also been studied quite thoroughly in view of its biological implications. An additional reason for a discussion of exchange in inorganic acid esters and related compounds lies in the fact that the rates of exchange between oxyanions and water are often profoundly affected by organic substituents. Thus, the orthophosphate ion at pH 1 and 100°C has a half-life for oxygen exchange of about 130 h, whereas cyclic ethylene phosphate at pH 1 at 30°C has a half-life for exchange of 6 min. The discussion that follows will be grouped according to the position in the periodic table of the atom bonded to oxygen. No reports of isotopic exchange of oxygen with oxygen-containing organic compounds of elements in the first three groups have been published. N
OXYGEN ISOTOPE EXCHANGE REACTIONS
175
A. Group I V : Silicon Compounds The exchange of oxygen between organo-silicon compounds and water has received no systematic attention. Khaskin (1952) stated that Et,SiOH (37;R = C2H5)underwent complete exchange with 0I8-water after 5 h a t 100°C andPh,SiOH (37;R = CGH5)underwent 40% exchange in 1 h a t 100°C. Both reactions were presumed to proceed by addition of water to give a pentacovalent intermediate with two hydroxyl groups on silicon. Isotopic analyses were performed by density measurements of the residual water. Silicon as a second-row element has d-orbitals available for bonding and is known to form complexes with co-ordination numbers of five and even six. Pentacovalent compounds with sp3d hybridization are known to exist. However, during the course of an investigation of the reactions of triarylsilicon halides, Allen and Modena (1957) found that exchange between Ols-enriched water and triphenylsilanol (37;R = CGHB) was very slow in neutral (9O:lO v/v) aqueous dioxan and was acid-catalysed, although no quantitative data were given. They consider their results to be evidence against a mechanism in which a pentacovalent intermediate is formed in nucleophilic substitution reactions of these compounds. They suggest that the hydrolysis of organo-silicon halides as well as the isotopic exchange of oxygen in trisubstituted silicon proceeds by bimolecular displacement on silicon. There is a t present little evidence that pentacovalent intermediates are involved in displacement reactions a t silicon in organo-silicon compounds (Eaborn, 1960). Further work on exchange in silicon compounds is desirable before a decision for or against such an intermediate can be made. (See Sommer et al. (1964) and previous papers.) r
1
B. Group V : Nitrogen and Phosphorus Compounds 1. Nitrogen compounds
Hydroxylamine (38; R' = R"= H) does not undergo exchange (Bothner-By and Friedman, 1952) and presumably the mono N- and NN-disubstituted hydroxylamines do not undergo exchange either, but this has not yet been investigated experimentally.
38
176
D A V I D S A M U E L AND B R I A N L. S I L V E R
In a recent study on the hydrolysis of di-isopropylphosphofluoridate (DFP), Samuel and Silver (1963) found that benzohydroxamic acid (38; R' = H ;R" = C6H5.GO) had not undergone exchange after 10 min a t pH 7.6 a t room temperature. In fact, it appears that under all the conditions studied the )N-OH group does not undergo isotopic exchange. Similar results were obtained with the -N=Q group. Nitrosobenzene does not undergo exchange after a few minutes a t 180°C in neutral aqueous dioxan (Gragerov and Levit, 1960). This is somewhat surprising as one could envisage a mechanism in which water added to the -N=O group t o form a gem-diol. No exchange has been found even under more drastic conditions ;i.e. 1h a t 100°C or 25 min in 0.2N hydrochloric acid or 5 min in 0 . 2 ~sodium hydroxide. No exchange was found in p-NNdimethylamino-, p-nitro- and o-methoxy-nitrosobenzene. Hydroxynitroso compounds, on the other hand, do undergo fairly extensive exchange on being heated in alkaline or acid solution. For example p-hydroxynitrosobenzene (39)undergoes 41yoexchange in 0.2N alcoholic hydrogen chloride after 5 min a t lOO"C, and 1-nitroso-%naphthol (40) undergoes 42% exchange after 5 min a t 80°C in the same solvent and 417, exchange in 0 . 2 alcoholic ~ sodium hydroxide after 5 min a t 100°C. It was suggested that here the carbonyl group of the tautomeric ketoform undergoes exchange. It has not yet been shown experimentally that this is indeed so.
40
The exchange of amine oxides has not yet been examined. Nitromethane (Gragerov and Levit, 1960) and nitrobenzene (Roberts, 1938 ; Gragerov and Levit, 1960) do not undergo exchange even under very drastic conditions. It should be recalled that exchange with the nitrate ion only occurs in strong acid solution by the reversible formation of a nitronium cation [NO,]+ (Bunton et al., 1052). This mechanism cannot occur in
OXYGEN ISOTOPE EXCHANGE REACTIONS
177
organic nitrocompounds. No reports of exchange with esters of either nitrous or nitric acid have yet been published. 2. Phosphorus compounds The nature of the phosphorus-oxygen bond in the phosphoryl group >P=O is still not entirely clear. One important difference between the phosphoryl and carbonyl groups is the presence of comparatively lowlying d-orbitals in the phosphorus atom and, although the phosphoryl and carbonyl groups have some resemblance to one another, the former shows the effects of greater polarity and polarizability (Paddock, 1964). The existence of stable pentacovalent phosphorus compounds suggests that a pentacovalent intermediate may be formed in the hydrolysis of esters and acyl halides of phosphoric acid
Considerable effort has been expended in attempts to demonstrate the existence of this type of intermediate. With this object in mind, Halmann made a careful study of the hydrolysis of diethylphosphorochloridate (41; R’= R”= CzH50; X = C1) (Dostrovsky and Halmann, 1956) ; dimethylphosphinic fluoride (41; R‘ = = R”= CH3; X = F); diethylphosphinic chloride (41 ; R’ = R”= C2H6; X = Cl), di-isopropyl phosphorofluoridate (41; R’ = R”= i-Pro ; X = F), (Halmann, 1959) and phosphorus oxychloride (41; R’ = R”= = X = C1) (Halmann and Kugel, 1964) in Ols-enriched water and found that there is no accompanying exchange of oxygen with solvent water. After partial reaction no 0l8was found in the unreacted compound and only one atom of 0l8per molecule was found in the organo-phosphorus product. Kinetic evidence had previously shown that these reactions are almost certainly bimolecular (Dostrovsky and Halmann, 1956) and so it was concluded that the addition of water to the phosphoryl group does not occur in a preliminary fast and reversible step. This conclusion may be correct, but there are two reservations. First, lack of detectable exchange is not conclusive evidence against formation of an intermediate, as may be seen in the case of the acid hydrolysis of benzamide (p. 161). Secondly, the possible stereo-chemistry of a pentacovalent phosphorus intermediate must be taken into account. The tetracovalent intermediate in carbonyl compounds probably has four approximately sterically equivalent sp3 carbon orbitals, whereas the pentacovalent intermediate with phosphorus as a central atom is expected to show sp3d hybridization. The five bonds are directed to the apices of a trigonal
178
DAVID SAMUEL AND BRIAN L. SILVER
bipyramid and appear to fall into two groups, at least as far as reactivity is concerned. Phosphorus pentachloride in CCI4 solution, for instance, exchanges three of its chlorine atoms with labelled chloride rapidly and the remaining two chlorine atoms more slowly (Downs and Johnson, 1954). Presumably the two “axial” chlorines are the least reactive. One conceivable explanation for the non-exchange of oxygen above could be that an intermediate i s formed but the incoming water molecule occupies a relatively “reactive ”position compared to the hydroxyl group originating from the phosphoryl oxygen. I n this case breakdown of the complex would proceed either via loss of halogen or loss of the original attacking water and no exchange would be observed. The acid- and base-catalysed hydrolysis of di-n-propyl phosphonate (40; R’ = R” = C,H,O; X = H) proceeds with P-0 fission and is also not accompanied by any exchange of oxygen with solvent (Samuel and Silver, unpublished results). However, these compounds also undergo an acid- and base-catalysed hydrogen exchange of the phosphorusbonded hydrogen (Luz and Silver, 1961). Since oxygen exchange does not accompany hydrogen exchange, it was concluded that the latter reaction does not proceed via addition and subsequent loss of water. This also applies to phenylphosphonous acid (41; R’ = C6H, ; R” = OH ; X = H) where no oxygen exchange was detected, although hydrogen exchange is fairly rapid (Reuben et al., 1963). Oxygen exchange does accompany the hydrolysis of mono-methyl phosphate in concentrated acid solution (Bunton et al., 195% ; Haake and Westheimer, 1961). By using a careful purification technique to remove product inorganic phosphate (which contains 0ls)Samuel and Silver (unpublished results) have shown that this exchange is acid-catalysed but it is a t present impossible to distinguish between bimolecular displacement of water by water and the formation of a pentacovalent intermediate. The reversible formation of mono-methyl or symmetrical dimethyl pyrophosphate was shown to be unlikely from the effect of the concentration of the ester on the rate of exchange. Haake and Westheimer (1961) found that no exchange accompanies the hydrolysis of dimethyl phosphate (41; R’ = R” = CH,O; X = OH) or of cyclic ethylene phosphate (42). The ratio khy&ol/ke.& was measured and found to ~ acid compared with 20 for dimethylphosphate. be 5 in 0 . 1perchloric Since khydrol is lo7times greater for ethylene phosphate then for dimethyl phosphate it is seen that both khydroland kexeh are greatly accelerated in the cyclic compound. Acceleration of hydrolysis might be expected on the basis of ring-strain, but this cannot account for acceleration of exchange, since exchange is not accompanied by ring opening. Haake and Westheimer have attempted to rationalize the results on the basis ofthe stereoN
N
179
OXYGEN ISOTOPE EXCHANGE REACTIONS
chemistry of various alternative transition states and intermediates.
43
42
The situation in phosphine oxides is not entirely clear. Triphenylphosphine oxide (41; R’ = R” = X = C6H5)does n o t undergo exchange in water or 6 N perchloric acid (Samuel, unpublished results). However, some exchange does occur in dioxan-water containing HC1 (Denney et al., 1964). Trialkylphosphine oxides (41; R’ = Rrr= X = n-octyl) appear to undergo some exchange, which is considerably increased in a strained bicyclic system (43)(Green, 1963; Lapidot and Samuel, unpublished results), in which the phosphorus atom is incorporated in a four-membered ring. It appears that ring strain is associated with an increase in the rate of isotopic exchange in the phosphoryl group.
C. Group V I : Sulphur C o m p o u n d s No exchange was found in the acid- or base-catalysed hydrolysis of ethylene (44) and trimethylene sulphite (45) (Bunton et al., 1958a). The result in acid solution indicates that no tetracovalent intermediate is formed and also that reversible ring opening does not occur.
I
CHz- 0, /s=O CH2-0
&”*,
CH2-OH
I
CH2-0.(
,6H S \O
-I
CH2-OH CH2-OH
* + HzSOzO
/CHz-O\ ,S=O
CH2
\CHz-0
44 45
The kinetics of hydrolysis in alkaline solution show that no appreciable reversible ring opening occurs. However, when a solvent containing 0.94 atom yo excess 0lswas used, it was found that the recovered ethylene sulphite contained 0.016 atom yo excess OI8. Bunton et al. interpreted this result as indicating no significant exchange but Davis (1962) considers that these same results prove the formation of a tetracovalent intermediate. Further work is needed to settle this point.
180
DAVID SAMUEL AND B R I A N L . SILVER
There has been some doubt about hobh the point of bond cleavage and the exchange of oxygen between water and dialkyl sulphates. Isotopic oxygen exchange between dimethyl sulphate and water was originally suggested by Kursanov and Kudryavtsev (1956) from their results obtained in heterogeneous conditions. Considerable doubt was cast on these results by Lauder et al. (1961). Samuel and Weiss-Broday (unpublished results) found that in concentrated solutions, 0lscould be incorporated into diethyl sulphate (46) by trans-esterification with the Ols-labelled ethanol formed during the hydrolysis, the 0lsnow being in the alkoxy oxygen. More recently Gragerov and Tarasenko (1961) have confused the issue by again suggesting on the basis of isotopic bookkeeping that the exchange of the sulphuryl oxygens in dialkyl sulphates with water does occur. Gragerov and Tarasenko isolated the alcohol at various stages in the acid and alkaline hydrolysis of dialkyl sulphates and found aprogressive decrease in 0l8content with time. This was explained as due to the fact that the first alkyl group comes off with alkyl-oxygen fission, the second with acyl-oxygen fission and that the balance can be accounted for by exchange between sulphuryl oxygen and water. The latter assumption was not verified by direct experiment.
46
No exchange accompanies the alkaline (Christman and Oae, 1959) and acid (Oae et al., 1963) hydrolysis of phenyl benzenesulphonate (47). The absence of exchange is consistent with an S,2 displacement involving attack of water on sulphur but (as discussed in connection with benzamide, p. 161) this in itself does not rule out the formation of an intermediate.
0
0\s,0C6H5
\o
47
R\ ,s=o R
\ s.”o C6H5’
48
49
No exchange was detected between water and dimethylsulphoxide (48 ; R = CH,) (Leonard and Johnston, 1962) or diphenylsulphoxide (48; R = C6H5)in either 1 . 0 hydrochloric ~ acid or 1 . 0 sodium ~ hydroxide at 100°C (Samuel and Weiss-Broday, unpublished results). Oae et al. (1961) found no exchange on pouring diphenyl sulphoxide in concentrated sulphuric acid into 018-enrichedwater indicating that ionization to a doubly charged cation R2Sff, did not occur. Diphenyl sulphone (49) does not undergo isotopic exchange with water even under fairly drastic acid or
OXYGEN ISOTOPE EXCHANGE REACTIONS
181
alkaline conditions (Christman and Oae, 1959). Oae et al. (1961) did, however, report that various sulphoxides underwent isotopic exchange of oxygen with Ols-labelled sulphuric acid. The mechanism of this reaction is not clear.
D. Group V I I : Iodine Compounds The iodine-bonded oxygen atoms of iodosobenzene (50; R = H) and p-iodosobenzoic acid (50; R = COZH) exchange with water a t room temperature. Aromatic iodoxy-compounds (51) undergo isotopic exchange readily a t higher temperatures ( 100°C) (Gragerov and Levit, 1963). The ease of exchange in iodine-oxygen compounds as compared
R 50
51
to its absence in the groups >SO, )SOz, -NO, and -NOz may be due to the ready tendency of iodine to increase its covalency. It seems probable that the polarizability of the large iodine atom is also important in lowering the activation energy for attack by water.
VII. THEEXCHANGE BETWEEN ORGANICCOMPOUNDSAND METAL OXIDES I n the course of a study of oxide catalysts, Karpacheva and Rozen (1951a) observed that liquid ethanol and acetic acid underwent exchange with labelled oxides. The details of these experiments are not clear. The mechanism of exchange with ethanol at high temperatures ( > 2OOOC) was considered t o be the reversible formation of “ethyl aluminates ” though this would not provide a means of isotopic exchange unless bond making and bond breaking occurred in different positions. High-temperature exchange was also observed on kaolin, alumina, chromium oxide and zinc oxide (Karpacheva and Rozen, 1951b). Alumina, in particular, has been known to cause various chemical reactions in organic compounds even at comparatively low temperatures (Lederer and Lederer, 1962). There have been a few reports of exchange of 0l8between alumina and organic compounds such as benzoyloxycholestenone (Dahn et al., 1959) and dihydropyran (Gender et al., 1963). The mechanism of these reactions is still not understood but it appears
182
D A V I D S A M U E L A N D B R I A N L. S I L V E R
that carbon-oxygen bond fission is facilitated when compounds are adsorbed on the solid surface. It has recently been shown that the extent of exchange depends on the type of alumina used (Samuel and Wassermann, 1964a) and that alcohols, ketones and acids dissolved in inert solvents (such as benzene or hexane) can undergo exchange a t temperatures from 25 to 100°C. It is interesting to note that the stereochemistry of u- and P-cholestanolsis preserved when 0l8is incorporated, indicating that the organic molecule is probably rigidly held on the alumina surface. Neopentyl alcohol also undergoes exchange without rearrangement. Further work on this type of exchange is most desirable. Apart from its preparative value it is of interest for studying organic reactions on surfaces and also as a means of obtaining information on the mechanism of chromatographic adsorption. It should be noted that this exchange has so far been reported only for alumina and has been found not to occur with silica under analogous conditions (Samuel and Wasserman, 1964b). Its occurrence seems possible with other oxides, particularly those with an amphoteric character such as zinc oxide. VIII. CONCLUSION
It has been seen that a great deal of information on the mechanism of isotopic exchange of oxygen in organic compounds has been obtained during the last 10 years. I n secondary and tertiary alcohols, carboxylic acids and esters, the mechanisms of exchange are fairly clear through the use of stereochemistry and kinetic competition experiments. A great deal more remains to be done in order to understand the mechanism of exchange in primary alcohols, phenols, aliphatic ketones and quinones. The reasons for the presence or absence of exchange of oxygen bonded to atoms other than carbon in organic compounds is still not a t all clear and a detailed kinetic study of this problem would be most desirable. With the introduction of spectroscopic methods of isotopic analysis (including infra-red and particularly 01' N.M.R.) many of these problems can be elucidated. It is to be hoped that this will soon be done and that the use of isotopic oxygen exchange will be extended to studies of the structure and reactions of macromolecules of biological interest and to surface chemistry in order to further the understanding of these important systems. ACKNOWLEDGEMENT We wish to thank Professors M. L. Bender, A. Fry and our colleagues in the Isotope Department of the Weizmann Institute for reading and
O X Y G E N ISOTOPE EXCHANGE REACTIONS
183
commenting on the manuscript. We are particularly grateful to Prof. A. Fry for communicating the results obtained by his students prior to publication and to Prof. D. R. Llewellyn and Dr. C. O’Connor for the manuscripts of their papers still in press. REFERENCES Adler, E., Balkehag, I., and Smith, B. (1962). Acta Chem. Scand. 16, 529. Aleksankin, M. M., and Gragerov, I. P. (1961). Zhur. Obshchei Khim. 31, 3167. Allen, A. D., and Modena, 0. (1957). J . Chem. SOC.3671. Bell, R. P., Rand, M. H., and Wynne-Jones, I<. M. A. (1956). Trans. Paraday Soc. 52, 1093. Bender, M. L. (1951). J . Am. Chem. SOC.73, 1626. Bender, M. L. (1960). Chem. Revs. 60, 53. Bender, M. L., and Chen, M. C. (1963). J . Am. Chem. SOC. 85,30. Bender, M. L., and Dewey, R. S. (1956). J . Am. Chem. SOC.78, 317. Bender, M. L., and Ginger, R. D. (1955). J . Am. Chem. SOC.77,348. Bender, M. L., and Thomas, R. J. (1961a). J . Am. Chem. SOC. 83, 4183. Bender, M. L., and Thomas, R. J. (1961b). J . Am. Chem. SOC.83,4189. Bender, M. L., Stone, R. R., and Dewey, R. S. (1956). J . Am. Chem. SOC. 78,319. Bender, M. L., Ginger, R. D., and Unik, J. P. (1958). J . Am. Chem. SOC. 80, 1044. Bender, M. L., Ladenheim, H., and Chen, M. C. (1961a). J . Am. Chem.SOC.83,123. Bender, M. L., Matsui, H., Thomas, R. J., and Tobey, S. W. (1961b). J . Am. Chem. SOC.83, 4193. Bentley, R. (1949). J . Am. Chem. SOC. 71, 2765. Biechler, S. S., and Taft, R.W. (1957). J . Am. Chem. SOC. 79, 4927. Biemann, K. (unpublished results), p. 238 i n “Mass Spectrometry”, McGraw-Hill, 1962. Bothner-By, A., and Friedman, L. (1952). J . Chem. Phys. 20, 459. Boyd, R.H., Taft, R. W. jr., Wolf,A.P.,andChristman,D.R. (1960). J . Am. Chem. SOC. 82, 4729. Brodskii, A. I., Aleksankin, M. M., and Gragerov, I.P. (1962). Zhur. ObshcheiKhim. 32, 829. Buckingham, P. D., and Forse, G. R. (1963). Intern. J . Appl. Radiation and Isotopes 14, 439. Bunnett, J. F. (1961). J . Am. Chem. SOC. 83, 4978. Bunton, C. A., and Carr, M. D. (1963a). J . Chem. SOC.5854. Bunton, C. A., arid Carr, M. D. (1963b). J . Chem. SOC.5861. Bunton, C . A., and Frei, Y. F. (1961). J . Chem. SOC.1872. Bunton, C. A., and Henderson, R. B. (1963). Tetrahedron Letters, 1829. Bunton, C. A., and Llewellyn, D. R. (1957). J . Chem. SOC.3402. Bunton, C. A., and Spatcher, D. N. (1956). J . Chem. SOC.1079. Bunton, C. A., Halevi, E. A., and Llewellyn, D. R. (1952). J . Chem. SOC. 4913. Bunton, C. A., Lewis, T. A., and Llewellyn, D. R. (1954). Chem. d2 Ind. (London) 1154. Bunton, C. A., Comyns, A. E., Graham, J., and Quayle, J. R. (1955a). J. Chem. SOC. 3817. Bunton, C. A., Konasiewicz, A., and Llewellyn, D. R. (1955b). J . Chem. SOC. 604. Bunton, C. A., de la Mare, P. B. D., Lennard, A., Llewellyn, D. R., Pearson, R. B., Pritchard, J. G., and Tillett, J. G. (1958a). J . Chem. SOC. 4761 and previous papers.
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Bunton, C. A., Hadwick, T., Llewellyn, D. R., and Pocker, Y.(1958b). J . Chem. SOC.403. Bunton, C. A., Llewellyn, D. R., Oldham, K. G., and Vernon, C. A. ( 1 9 5 8 ~ )J. . Chem. SOC. 3574. Bunton, C. A., Llewellyn, D. R., and Wilson, I. (1958d). J . Chem. SOC.4747. Bunton, C. A., James, D. H., and Senior, J. B. (1960). J . Chem. SOC. 3364. Bunton, C. A., Khaleelnddin, K., and Whittaker, D. (1963). Tetrahedron Letters 1825. Bunton, C. A., Carter, J. H., Llewellyn, D. R.. O’Connor, C., Odell, A. L., and Yih, S. Y. (1964). J . Chem. Soc. 4615. Calhoun, A., Bufalini, M., Sparks, B., and Fry, A., personal communication. Chmiel, C. T., and Long, F. A. (1956). J . Am. Chem. SOC.78, 3326. Christman, D. R., and Oae, S., (1959). Chem. & Ind. (London)1251. Cohn, M., and Urey, H. C. (1938). J . Am. Chem. Soc. 60, 679. Connick, R. E., and Fiat, D. N. (1963). J . Chem. Phys. 39, 1349. Dahn, H. (1964). “Proceedings of Conference on Preparing and Storing Marked Molecules”, (Brussels, Nov. 1963), Euratom, 1964, p. 1303. Dahn, H., Menasse, R., and Tanim, C. (1959). Helv. Chim. Acta 42, 2189. Datta, S. P., Day, J. N. E., and Ingold, C. K. (1939). J . Chem. SOC.838. Davis, R. E. (1962). J . Am. Chem. SOC. 84, 599. Day, J. N. E., and Ingold, C. K. (1941). Trans. Paraday Soc. 37, 686. Denney, D. B., Tsolis, A. K., and Mislow, K. (1964). J . Am. Chem. SOC.86, 4486. Dostrovsky, I., and Halmann, M. (1956). J . Chem. SOC.1004. Dostrovsky, I., and Klein, F. S. (1955a). J . Chem. SOC. 791. Dostrovsky, I., and Klein, F. S. (1955b). J . Chem. SOC.4401. Dostrovsky, I., and Samuel, D. (1965). “The Isotopes of Oxygen” (in press). Dostrovsky, I., Hughes, E. D., and Ingold, C. K. (1946). J . Chem. Soc. 173. Downs, J., and Johnson, R. E. (1954). J . Chem. Phys. 22, 143. Eaborn, C. (1960). “Organosilicon Compounds”, p. 110, Academic Press, New York. See also Baker, R., Bott, R. W., Eaborn, C., and Jones, P. W. (1963). J . Organometal. Chem. 1, 37. Fesenko,V. V., and Gragerov, I. P. (1955). Doklarly Akad. Nau1cS.S.S.R. 101, 696. Fry, A., personal communication. Gender, W. J., McLead, G. L., Stouffer, J. E., Manos, P. T., and McGines, R. G. (1963). Chem. & Ind. (London)1658. Goering, H. L., and Dilgren, R. E. (1960). J . Am. Chem. Soc. 82, 5744. Goering, H. L., and Josephson, R. R. (1962). J . Am. Chem. Soc. 84, 2779. Gold, V. (1948). Trans. Paraday SOC. 44, 506. Goto, K. (1940). J . Chem. SOC. Japan 61, 1283. Goto, K. (1941). J . Chem. SOC.Japan 62, 408. Gragerov, I. P., and Levit, A. F. (1960). Zhur. Obshchei Khim. 30, 3726. Gragerov, I. P., and Levit, A. F. (1963). Zhur. Obshchei KAim. 33, 544. Gragerov, I. P., and Ponomarchuk, M. P. (1959). Zhur. Obshchei Khim. 29,3895. Gragerov, I. P., and Tarasenko, A . M. (1961). Zhur. Obshchei Khim. 31. 3878. Green, M. (1963). Proc. Chem.Soc. 177. Greenzaid, P., and Samuel, D., unpublished results. Grunwald, E., Heller, A., and Klein, F. S. (1957). J . Chem. SOC.2604. Gustafsson, C., and Johanson, M. (1948). Acta Chem. Scand. 2, 42. Haake, P. C., and Westheimer, F. H. (1961). J . Am. Chem. SOC.83, 1102. Halmann, M. (1959). J . Chem. SOC. 305. Halmann, M., and Kugel, L. (1964). J . Chem. SOC. 3733.
OXYGEN ISOTOPE EXCHANGE REACTIONS
185
Halpern, M., and Leibowitz, J. (1959). Biochem. et Biophys. Acta 36, 29. Hamilton, G. A., and Westheimer, F. H. (1959). J . A m . Chem. SOC. 81, 6332. Hammett, L. P. (1940). “Physical Organic Chemistry”, p. 350, McGraw-Hill. Herbert, J. B. M., and Lauder, I. (1938a). Trans. Faraday SOC. 34, 432. Herbert, J. B. M., and Lauder, I. (193813). Trans. Paraday Soc. 34, 1219. Highet, R. J., and Batterham, T. J. (1964). J . Org. Chem. 29, 475. Hoering, T. C., and Kennedy, J. W. (1957). J . A m . Chem. SOC.79, 56. Ingold, C. K. (1928). Ann. Rep. Chem. SOC.25, 124. Jackson, J. A., Lemons, J. F., and Taube, H., (1960). J . Chem. Phys. 33,553. Jeffrey, D. A. (1961). Ph.D. Thesis, University of Arkansas. Johnson, S. L. (1964). Tetrahedron Letters, 1481. Karpacheva, S . M., and Rozen, A. M. (1951a). Doklady Akad. Nauk S.S.S.R. 75, 239. Karpachcva, S. M., and Rozen, A. M. (1951b). Doklady Akad. Naukt7.S.S.R. 81, 425. Khaskin, I. G. (1952). Doklady Akad. NaukS.S.S.R. 85, 129. Koizumi, M., and Titani, T. (1938). Bull. Chem. SOC. Japan 13, 463, 607. Koshland, D. E., Jr., and Stein, S. S. (1954). J . Biol. Chem. 208, 139. Kursanov, D. N., and Kudryavtsev, R. V. (1956). Zhur. Obshchei Khim 26, 1040. Lapidot, A., and Samuel, D., unpublished results. Lauder, I., Wilson, I. R., and Zerner, B. (1961). Aust. J . CILem. 14, 41. Lederer, E., and Lederer, M. (1962). “Chromatography”, VoI. 4, “Comprehensive Biochemistry”, (ed. M. Florkin and E. H. Stotz,) Elsevier, Amsterdam. 84, 3701. Leonard, N. J., and Johnston, C. R. (1962). J . A m . Chem. SOC. Lewis, G. N., and Cornish, R. E. (1933). J . A m . Chem. SOC.55, 2616. Llewellyn, D. R., and O’Connor, C. (1964a). J . Chem. SOC. 545. Llewellyn, D. R., and O’Connor, C. (1964b).J . Chem. SOC. 4400. Loewenstein, A., and Connor, T. M. (1963). Rev. Bunsen Phys. Chem. 67, 280. Long, F. A., and Paul, M. A. (1957). Chem. Revs. 57, 935. Long, F. A., arid Pritchard, J. G. (1956). J . Am. Chem. SOC.78, 2663. Luz, Z., and Silver, B. (1961). J . Am. Chem. SOC.83, 4518. Manassen, J., and Klein, F. S. (1960). J . Chem. SOC. 4203. Mayer, F. C. Jr., and Lamer, J. (1959). J . A m . Chem. SOC. 81, 188. Mears, W. H. (1938). J . Chern. Phys. 6, 295. Mears, W. H., and Sobotka, H. (1939). J . A m . Chem. SOC.61, 880. Menon, B. C. (1964). Ph.D. Thesis, University of Arkansas. Milburn, R. M., and Taube, H. (1959). J . Am. Chem. SOC.81, 3515. Oae, S., and Kiritani, R. (1964). Bull. Chem. s’oc. Japan, 37, 772. Oae, S., Kitao, T., and Kitaoka, Y. (1961). Chem. d3 Ind. (London)291. Oae, S., Fukumoto, T., and Kiritani, R. (1963). Bull. Chem. SOC. Japan, 36, 346. Paddock, N. L. (1964). Quart. Revs. (London)18, 168. Paul, M. A., and Long, F. A. (1957). Chem. Revs. 57, 1. Pearson, R. G., and Mayerlc, E. A. (1951). J . A m . Chem. SOC.73, 926. Pinchas, S., Samuel, D., and Silver, B. L. (1963). Spectrochimica Acta 20, 179. See also Laulicht, I., and Pinchas, S. (1964). Anul. Chem. 36, 1980. Polanyi, M., and Szabo, A. L. (1934). Trans. Faraday SOC. 30, 508. Reuben, J., Samuel, D., and Silver, B. L. (1963). J . Am. Chem. SOC. 85, 3093. Rittenberg, D., and Graff, C. (1958). J . A m . Chem. SOC.80, 3370. Roberts, I. (1938). J . Chenz. Phys. 6, 294. Roberts, I., and Urey, H. C. (1938). J . Am. Chem. SOC. 60, 880. Roberts, I., and Urey, H. C. (1938). J . AWL. Chern. SOC. 60, 2391.
186
D A V I D S A M U E L A N D B R I A N L. S I L V E R
Roberts, I., and Urey, H. C. (1939). J . Am. Chem. Soc. 61, 2580. Roberts, I., and Urey, H. C. (1939). J . Am. Chem. SOC.61, 2584. Rotlevi, E., and Samuel, D., unpublished results. Samuel, D. (1962). Methodology of Oxygen Isotopes, in, “Oxygenases”, cd. 0. Hayaishi, Academic Press, Now York. Samuel, D., and Fiat, D. N., unpublished resiilts. Samuel, D., and Petreanu, E., unpublished results. Samuel, D., and Silver, B. L. (1963). J . Am. Chenr. S o c . 85, 1197. Samuel, D., and Wassermann, I. (19G4a). Chem. & I d . (London) 891. Samuel, D., and Wassermann, I. (1964b). Anal. Biocliem. 9, 246. Samuel, D., and Weiss-Broday, M., unpublishcd results. Sarel, S., Levin, I., and Pohorlyes, L. A. (1960). J . Chem. SOC. 3079. Senkus, M., and Brown, W. G. (1938). J . Org. Chem. 2, 569. Sommer, L. H., Stark, F. O., and Michael, I<. W. (1964). J . Am. Chem. SOC. 86, 5683. Sparks, B., and Fry, A., personal communication. Stewart, R., Granger, M. R., Moodie, R. B., and Muenstcr, L. J. (1963). Can. J . Chem. 41, 1065. Swain, C. G. (1961). M. I. T. Progress Report. Laboratory for Nuclear Scienco (NYO 2668). Swain, C . G. (1963). M.I.T. Progress Report. Laboratory for Nuclear Scionco (NYO 10065). Swain, C. G., Tsuchihashi, G. I., and Taylor, L. J., (1963). Anal. Chem. 35, 1415. Urey, H. C., Ptgram, G. B., and Huffman, J. R. (1936). J . Chem. Phys. 4, 623. Westheimer, F. H. (1936). J . Am. Chem. SOC.58, 2209. Winstein, S., Clippinger, E., Fainberg, A. H., Heck, R., and Robinson, G. C. (1966). J . Am. Chem. SOC. 78, 328.
N.M.R. MEASUREMENTS OF REACTION VELOCITIES AND EQUILIBRIUM CONSTANTS AS A FUNCTION OF TEMPERATURE’ L. W. REEVES Chemistry Department, University of British Columbia Vancouver 8 , B.G., Canada
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I. Introduction and Scope . A. Definitions of Chemical Shift and Coupling Constants . B. Resonance Condition and Relaxation Times . . 11. The Bloch Equations with Incorporation of Chemical Exchange . A. The Modification of Gutowsky, McCall and Slichter . B. McConnell Equations . C. The Piette and Anderson Equation . D. Relationship of Mean Lifetime T t o Chemical Kinetics . . E. Quantum Mechanical Treatments . I?. Spin-Echo Methods . G. Double Resonance Methods . H. Measurement of Lifetimes using “Rapid Passage” Solutions of the Bloch Equations . . I. Electron Exchange Reactions J. Nuclear Electric Quadrupole Effects . . 111. Experimental Methods. . A. Measurements of Tz . B. Variable-Temperature-Apparatus IV. Hindered Internal Motions of Molecules . A. Alicyclic Ring Systems. . B. Substituted Ethanes . . C. Other Intramolecular Rearrangements . V. Hydrogen Bonding, Tautomerism and Proton Exchange A. HydrogenBonding . B. Tautomerism . . C. Proton Exchange Reactions References . . .
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187 188 190 193 196 209 211 213 214 218 224 226 226 227 238 228 230 233 233 245 252 259 259 261 263 268
I. INTRODUCTION AND SCOPE THEpurpose of this chapter is to indicate and review the information which may be obtained about organic molecules from the temperature dependence of their N.M.R. (nuclear magnetic resonance) spectra. The 1 Article written while on Leave-of-Absence at Physical Chemistry Laboratory, South Parks Road, Oxford, England. The hospitality of Professor R . E. Richards is gratefully acknowledged. 187
188
L. W . R E E V E S
parameters normally obtained from a study of t,he N.M.R. spectra are the chemical shifts (Proctor and Yu, 1950), nuclear spin-spin coupIing constants via electrons (Gutowsky and McCall, 1951) and nuclear relaxation times (Andrew, 1955). The organic chemist should a t this stage be familiar with chemical shifts and coupling constants so that apart from a definition of these quantities the material here will contain only a discussion of their temperature dependence. Reference to nuclear spin relaxation times will be made in somewhat more detail. Since temperature effects on N.M.R. spectra arise largely from the influence of temperature on rate processes it will be essential to devote a considerable part of this chapter to the connection between reaction velocities and N.M.R. spectra. Although not all useful nuclei contained in organic compounds have been fully explored from the chemical point of view it is as well t o point out that nuclear magnetic resonance methods can be applied to study all atoms which make up organic molecules. The resonances of the following nuclei can be observed: H1, H2 and H3 (Tiers, 1964); Fig; N14 and N16; O1'. C13. P31.S33.BIO and Bl1; and SiZg(Pople et al., 1959). Many of these nuclei are present in low natural abundance (Varian Associates, 1964) and some have, in addition to a nuclear magnetic moment, a nuclear electric quadrupole moment (Pople et al., 1959). Some interesting temperature-dependent effects on spectra can arise in organic molecules containing these latter nuclei (Pople, 1958b). The nuclei of chlorine, bromine, and iodine occur in good natural abundance with a favourable nuclear magnetic moment but they have received little attention because the signals are broad owing to the effects of nuclear electric quadrupole moments. The electric field gradients near a halogen nucleus are invariably large in organic molecules since they occur at the periphery of the molecule in a univalent state, and this leads t o short relaxation times and consequent broad signals (Masuda and Kanda, 1954). The principles set out here apply to all the nuclei above and, with due care exercised in interpreting the origin of the temperature dependence in a given case, a bounty of detailed information about a molecule is available. It will not be the purpose of this survey to include a summary of N.M.R. studies of the molecular crystals of organic compounds (Andrew, 1955). The information available from these studies relates to molecular motion and crystal structures. Y
,
I
1
A. Definitions of Chemical 8hift and Coupling Constants If the bulk diamagnetic effects of a n organic liquid are ignored (Bothner-By and Naar-Colin, 1958) and the magnetic field Hi a t a
TEMPERATURE EFFECTS O N N . M . R . SPECTRA
189
nucleus i is considered when a large external field H o is applied we have R simple relation ; Hi == Ho(1- ~ i ) (7) The shielding constant uivaries with nucleus i in a molecule because of varying electronic environment. I n general, uiis a tensor quantity since it is also a function of the orientation of the molecule in the external magnetic field. The very rapid isotropic reorientation of an organic molecule in a liquid or gas renders oia scalar quantity experimentally. The chemical shift is most conveniently expressed by choosing a reference signal with resonant field H,, and expressing all other signals as a fractional change in field necessary for resonance at a fixed frequency of detection. The resonance condition is given by the Larmor precession frequency w i , ~i = ~ i H i (2) where yi is the magnetogyric ratio of the i t h nucleus (Pople, et al., 1959). Thus the chemical shift becomes :
Temperature-dependent chemical shifts arise when an atom in a molecule is involved in an unsymmetrical intra-molecular re-orientation, e.g. the population of the methyl groups in methyl nitrite in cis and trans forms varies with temperature (Phillips, 1958), or when there is an intermolecular exchange process between distinct sites on two molecules, e.g. the -OH signal in a mixture of hydrogen-bonding molecules, such as methanol and water. A consideration of the time scales involved in observation of temperature-dependent chemical shifts will be delayed anti1 later. Hyperfine field-independent splittings arise in N.M.R. spectra from an indirect coupling of the nuclear moments p in a molecule via the electronic system. The interaction energy between two nuclear moments piand pi is of the form
E u. . = -K..p..p. 23 2 3
(4)
Kij is a constant which usually increases in numerical value as the two nuclei i and j are separated by fewer chemical bonds. This scalar coupling is usually expressed in terms of the co-linear angular momentum vectors of the nuclei and the constant is given in cycles per second.
7
I,. W. R E E V E S
190
J , is the coupling constant in cycles per second. If the two nuclei i and j are separated by three or more bonds, the value of Jij will depend on molecular conformation since J , is dependent on intervening bond angles (Karplus, 1963). Clearly, therefore, in any molecule which has more than one stable conformation the values of coupling constants can be temperature-dependent if the relative population of the conformations 1962). varies with temperature (Gutowsky et d.,
B. The Resonance Condition and Relaxation Times If an isolated nucleus is considered, the Larmor precession formula may be written in terms of wo:
w o is the angular frequency in radians per second. The magnetogyric ratio y of the nucleus under study is the ratio of the maximum observable value of the magnetic moment to the maximum observable angular momentum Ifi = (Ih/27r) (Andrew, 1955). To simplify early discussion, the observed nucleus will be assumed to have a spin quantum number, I , of +. Equation (2) describes the nuclear Zeeman energy gap of LIE= (fiwi/2m-)which separates the two levels. Absorption of radiation a t a radiofrequency w o causes transitions of nuclei to the higher energy level but, in order to maintain a population of the lower level and energy absorption, the nuclei must have means of dissipating the absorbed energy other than by radiating it. This implies interactions of a nucleus with the surrounding medium in the form of electrons and other nuclei. This dissipation of nuclear spin energy represents a relaxation process. The thermal distribution of the nuclear spin energies in a magnetic field Ho is described by the Boltzmann factor exp(2pHo/kT,). For a nucleus of spin the energy difference of the nuclear Zeeman levels in a magnetic field H , is given by (pH,/I) = 2pH0. Here k is the Boltzmann constant, and T, is the equilibrium temperature of the system. For protons in a field of 5,000 gauss the excess fraction of nuclei in the lower level at 25°C is about 4 x 10V. The observation of magnetic resonance in a bulk sample therefore depends on a very small proportion of the total number of spins and, if the absorption of radio-frequency w, is excessive a saturation effect occurs, even in the presence of a relaxation process. Consider a set of Cartesian co-ordinate axes, as in Fig. 1, which are fixed in space; these are often called the “laboratory frame” (Bloch, 1946). The z direction is taken to be that of a large polarizing field H o about which the angular momentum vector and associated magnetic
+
TEMPERATURE EFFECTS ON N.M.R. SPECTRA
191
moment of nuclei will precess in the manner of a gyroscope subjected to a torque (Hay, 1953). Quantum restrictions prevent exact alignment of field and angular momentum vectors (Andrew, 1955) and the only observables are the projection of these angular momentum along the field direction. The precession of a single angular momentum vector OA about the field direction is illustrated in Fig. 1, the direction of precession being appropriate for a nucleus having a positive y . Figure 1 serves t o illustrate the distinction between two relaxation times associated with the nuclear spins in a resonance experiment. The bulk sample will consist of an assembly of nuclei-say lO”--which will be polarized in the “ z ” direction and the equilibrium polarization M,, which is equal to the nuclear magnetic moment per unit volume, will
FIG.1.
arise because of a slight excess of moments aligned with, rather than against the field at room temperature. The initial creation of the field H, or any change in the value of H, immediately produces a non-equilibrium distribution of alignments in the magnetic moments, and the ratio of the number of nuclear spins in the upper level to that in the lower level must change to reach a new equilibrium value according t o the new Boltzmann factor which contains H, as an exponent. This implies an interchange of energy between the nuclear spins in question and the rest of the sample. The rest of the sample is considered t o be all the electrons and other nuclei and is referred to as the “lattice”. The nuclei, being isolated from the lattice, interchange energy with it, in general quite slowly, and some easily accessible time elapses before a new equilibrium magnetization is attained. I n the Bloch (1946) formulation of the N.M.R. experiment, which is most useful in a modified form t o describe temperaturedependent chemical exchange effects, the simple assumption of a first
192
I>. W. R E E V E S
order growth or decay law is incorporated. The relaxation time characteristic of this first order law for magnetization in the z direction is called T1, the spin-lattice relaxation time. It is described by the equation:
Mo is the equilibrium nuclear magnetization in the z direction; M, is the instantaneous value of this magnetization. For the purposes of studying temperature-dependent effects in diamagnetic liquids it is usual (and convenient for observation) that T, is of the order 10-1 to 10 sec for protons in organic liquids contaminated perhaps with a little dissolved paramagnetic oxygen. Nuclei such as C13 and Si29are isotopically dilute and better insulated from the lattice and so do not relax as easily as protons and relaxation times may be several minutes or even longer (Pople et al., 1959). The contributions to T,arise from rapid fluctuations of the magnetic field a t the nucleus due to the motion of the molecule in which the nucleus is embedded and to other molecules a t closest approach (Bloembergen, et nl., 1948,1961). A reasonable value of the T 1for protons in water can be estimated on the basis of random motions of one proton with respect to the other (Bloembergen, 1961). The rapidly fluctuating magnetic fields in liquid water a t one proton due to the magnetic moment of the other in sec and the same molecule involve correlation times T~ of the order this is well removed from the “Larmor” period, typically of the order lo-’ to lo-* sec, so that energy interchange involving these motions is relatively ineffective. A refined calculation for liquid water including motions of neighbouring molecules at room temperature gives a value 3.4 sec, comparing well with the measured value 3.6 sec in degassed water (Bloembergen et aZ., 1948). The second relaxation time T, called the spin-spin or spin-phase memory time can be understood from a consideration of the net magnetization in the xy plane of Fig. 1. A large field H o along the z direction causes polarization of the nuclear magnetism, each individual spin precessing about the z direction above or below the plane xy. The projection on the xy plane of the angular momentum vectors can be imagined as if all nuclei in the sample were placed at the origin without affecting their interactions as they exist in the normal liquid. The phase of the rotating vectors in the xy plane will be random in the absence of a rotating magnetic field at the Larmor frequency, and thus the resultant xy magnetization is zero (Hahn, 1950). The radio-frequency which is applied perpendicularly to Ho in circularly polarized form can a t the Larmor frequency coo of the assembly align the individual vectors in the
TEMPERATURE EFFECTS ON
N.M.R.
SPECTRA
193
xy plane to give a resultant. The nuclear resonance signal induced in a detection coil arises from the co-operative effects of the vectors in the xy plane. Randomly phased nuclei would cause the net signal induced to be zero. The interruption of phase coherence of the xy magnetization by whatever means is associated with a characteristic exponent ( l / T , ) where T,is the spin-spin relaxation time. Thus
The processes governing T zinvolve a much smaller proportion of the energy of the spin system corresponding to w1 = yH, where HI is the vector of the rotating magnetic field of the radiofrequency ; i.e. H, < Ho. An inhomogeneous magnetic field is a non-intrinsic contribution to in conventional N.M.R. spectrometers and adds dephasing of spins (T,) to the intrinsic processes of mutual interchange of energy between two spins, thus interrupting their phase coherence, and local field variations in the sample due to the other nuclear magnetic dipoles nearby (Andrew, 1955). Chemical processes involving sudden changes in Larmor precession frequency will also interrupt the phase coherence of a set of nuclei of given Larmor frequency and in a certain critical region of lifetimes will affect the value of T , measured but will not affect T I . Normally in a liquid T I N T , but when T,< T Ian exchange process might be suspected. 11. THEBLOCHEQUATIONS WITH INCORPORATION OF CHEMICAL
EXCHANGE I n a system of weakly interacting nuclear spins, the nuclear magnetizaation vector M per unit volume obeys the simple vectorial equation (Bloch, 1946) dM dt ~
=
~[MxH]
(9)
The relaxation forces are added to this equation as an afterthought to describe phenomenologically the behaviour of an isolated assembly of nuclear spins in an N.M.R. experiment. Further modification allows the description of chemical exchange. If the above vectorial equation is resolved first along the fixed
194
L. W. R E E V E S
Cartesian axes of Fig. 1 with the usual magnetic fields acting upon the system, then Ho = H, H, = HI cos w t
Hu
=
-H,sinwt
(10)
The fields H , and H g are the result of decomposing the linearly polarized field 2H1coswt = H , of radiofrequency produced along the axis of a coil into two contrarotating circularly polarized fields one of which is effective at the Larmor frequency in causing resonance (Andrew, 1955). The resulting Bloch Equations become
il!lz = y ( M y H ,+ M,H, sin w t ) - H,/T2
By= y(M,Hl cos wt - M,Ho)
- MYIT,
AFz = ---l/(M,H, sin wt + M,H, cos wt) +
(MKMj
(11)
These simultaneous differential equations, which have the relaxation forces added, are simplified by transforming to a set of Cartesian axes rotating a t an angular frequency w about the z axis. This transformation is achieved by the substitution
M,
=
u cos wt - v sin wt
Mu
=
- (usin wt + v cos w t )
(12)
The Bloch Equations become U z;+-++dwv
=
0
T2
where
AW = (yHo-w)
= (00-W)
The solution of equations (13) is simplified under the ideal experimental conditions of “slow passage ”. The frequency of the radiation w , equal in this treatment to the angular velocityof the rotatingframe ofreference, is changed very slowly so that the u,v and z magnetizations come to equilibrium a t each frequency as the resonant condition w = w ois passed. I n view of the direct proportionality between frequency and field, the
T E M P E R A T U R E E F F E C T S O N N . M . R . SPECTRA
195
experiments where frequency is fixed and magnetic field changed and the converse amount to the same thing. I n order to take advantage of crystal oscillators the frequency is kept constant in the normal experiment and the magnetic field ('swept". I n the treatment of the Bloch equations the frequency w is swept. Since the equilibrium magnetizations u, v, and z remain constant in the rotating frame their time derivatives are equated to zero. ? i = @ = J $ z -- 0 (14) The solution of the three simultaneous equations in u, v and M , is now simplified and the results are
If the radiofrequency field H , is very small, i.e. y H , = w1 4 y H o , then it is easy to achieve the experimental condition for protons in which w;LT1T2< 1 , so that the last term may be neglected in the denominator. The resonance line shape then takes a Lorentzian form, which can be written as u=
v =
1 +x'2 -wlTzMox
(a)
- w11 +x2 T2M!?
(b)
1
i
J
Mo = M, (c) where the function x = ( w o- w)T2varies from - 03 to + m in passing t,hroughresonance at x = 0. The nature of the transformationrepresented by equations (12) for the rotating frame determines that the u direction in the rotating frame is that of the rotating field H 1 of the radio-frequency and v is 90" out of phase with this. Equation (13b) shows that the v magnetization change is effective in changing M , and is responsible for the absorption of energy. The detection of the v signal in a suitable coil corresponds to the absorption mode. This absorption of energy can be detected as a drop in voltage across a single coil perpendicular to a magnetic field or the loss of a balance in a bridge circuit or by detecting the emission of signal in a coil orthogonal to the transmitter coil (Andrew, 1955). I n the bridge method and crossed-coil spectrometer adjustments
196
L. W. R E E V E S
are possible to detect the absorption mode v and the dispersion mode u. Equation (16b) may be used to show that the width of the resonance a t ) the absence of saturation (i.e. when half maximum height is ( 2 / T 2 in w:T,T2 < 1). Most lines in liquids arise from systems where there is interaction between nuclear spins, and are not Lorentzian in shape. Natural line shapes are closer to a Gaussian shape in the tails of the intensity distribution in liquids. The relationship between peak width at half height and T 2 is still retained and gives values in agreement with more rigorous transient methods (Hahn, 1950).
A. The Modijication qf Gutowsky, McCall and Slichter (“G.M.S”) Treatment The simplest modification of the Bloch equations for chemical exchange is the consideration of two sites A and B of different Larmor frequency between which a nucleus X of spin 4 can exchange. The Larmor frequency change will be considered as arising from a difference in chemical shift between site A and site B. The first description of chemical exchange was incorporated into the Bloch equations by Gutowsky et ab. (1953) but this involved interruption of spin-spin coupling which we shall discuss later. The consideration of chemical exchange between chemically shifted sites with no spin-spin coupling was considered later by Gutowsky and Saika (1953) and this does not involve the statistical factors necessary in a treatment for interruption of spin coupling (Kaplan, 1958) or the complications of second order spectra (Kaplan, 1958). I n chemical terms a typical exchange process of the type considered is the hindered internal rotation problem in NN-dimethylformamide (Gutowsky and Holm, 1956).
Restricted rotation about the C-N bond causes exchange-modified proton spectra to occur in the methyl group a t readily accessible temperatures. I n this case the exact solution of the modified Bloch equations is further simplified because we have the restriction that the A and B sites are equally populated. I n cases where the population of A and B sites is lopsided the exact solutions are complicated. I n the case of symmetrical population one has also the subtle difference that the exchange A -+B is accompanied by a simultaneous mirror image
T E M P E R A T U R E E F F E C T S O N N . M . R . SPECTRA
197
exchange of B --f A. I n unsymmetrical populations, e.g. hindered inversions of substituted cyclohexanes (Reeves and Strermme, 1960),this is not the case. No extra complications are introduced into the treatment by this last difference, however. The method of solving the Bloch equations by Gutowsky and co-workers (1953; Gutowsky and Holm, 1956) has been simplified by McConnell (1958) but it is instructive to pursue the original analysis first since the statistical basis is rather more obvious (Loewenstein and Connor, 1963). Rearranging the Bloch equations (13a) and (13b) for the two Larmor precession frequencies in site A and site B, respectively ( w o+ Sw/2) and (wo- Sw/2), we obtain four equations for magnetizations, uA,uB, v, and vB (Gutowsky et al., 1953). These can conveniently be reduced to two equations by considering just the zy plane (Fig. 1)magnetization in each site, i.e. G, =
UA fiv,
GB =
u,+~v,
(17)
The complex numbers G, and GB give a resultant rotating magnetization, the imaginary components being proportional to the absorption mode signal. These two equations, one for each site, are written d2+[&-i(dw+S,j2)
1 1
G, = - i w l M o
GL( = - i w l M o
(a) (b)
1,
(18)
It is usual to consider T , A = T 2 B = T 2 ,although the later method due to McConnell(l958)is easier to apply when these are not equal. I n this case the equilibrium magnetizations in the x direction are the same for equally populated sites if the very small chemical shift effect Sw is ignored. The symbol 01 is introduced to describe the constant multiplying G in the two equations, which thus become
The exchange process envisaged imposes the following useful conditions : (a)A nucleus in site A or B may change site in a very short time and spend a vanishingly small time during the interchange compared to the 7*
198
L. W. R E E V E S
lifetime in A or B. The condition is equivalent to all intermediate stages having a very short lifetime. ( b ) T Iand T 2for nuclei in sites A and B are independent of the lifetime in each site rAand rB. (c) rAand rBare pseudo first-order lifetimes for nuclei in sites A and B since the spectra are sensitive to the decay of magnetization in one site. These lifetimes are the reciprocals of the first-order rate constants for transfer out of the respective sites. The exchange process causes a nucleus obeying equation (19a) instantaneously to change over to obeying (19b)or vice versa. Equations (19a) and (19b) are two first-order differential equations and are integrated to :
G; is the value of GA a t t = 0, providing an integration constant for (19a). If we consider an individual nucleus, then equation (20) represents the magnetization G ( t ) with a particular value G; at t = 0. A similar equation holds for G,(t). When exchange is occurring, it is necessary to take account of the depopulation with time of those nuclei from each site which have initial magnetizations G I and G i and further to average over all possible initial magnetizations G r and God which differ for groups of nuclei in the sample. The depopulation of each site is first order, so that the probability dp that nucleus X will leave site A during the interval dt between times t and ( t + d t ) is given by
This result can be used in equation (20) to compute (GA), an average value of G A ( t )for all those nuclei X which have an initial magnetization G , = G; at t = 0. Thus m
This average for the group of nuclei X with initial magnetizations G; is further averaged over all initial values GF. The exchange and
TEMPERATURE EFFECTS O N N.M.R.
199
SPECTRA
(aA).
The initial initial states are then taken into the averaging to give magnetizations G f are equal to the magnetizations a t the point of exchange G B ; thus this average may simply be performed :
(G9
=
(8,)
(24)
Substituting into (23) gives
The total magnetization in the xy plane is given by the weighted average
(a> = P =z
A
m
+PB(G3)
- h M o [ ( T.a + T~U ) + ~ T A d -W ) (1+ “ A T * ) (1 o1,TB)
+
~ A
+ %~P d _
-1
_
_
(26)
wherep, andp, are the populations of sites Aand B. I n order to describe the absorption mode signal it is necessary to extract the imaginary part and gBcontain imaginary terms. I n general of (G>, remembering that aA4 a complicated expression results (Gutowsky and Holm, 1956). If it is supposed that T,, = T,, = T,,then
where
and
_
_
200
L. W. R E E V E S
Detailed balancing for a simple two-site exchange leads t o
The amplitude of the v mode signal may be plotted by changing A w , the difference in frequency between the applied radio field and the mean of wA and wB,and if pA= pB= 0.5 the signals take on the appearance in Fig. 2 as a function of the exchange rate parameter (76). At fast rates of exchange, (76) < 1, the spectrum consists of a sharp peak centred on the
0.0 r =
2.0
0.1
r=IO
I
2
1
0
-1
_
-2
FIG.2. Calculated lineshapes for an N.M.R. doublet at different rates of exchange. The notation is as follows r = 78,t = 2 / T z 8 and s = A w / 8 (Connor and Loewenstein, 1963).
population-weighted mean of the two contributing resonant frequencies wA and wB. The line width of this resonance will in practice be limited by the homogeneity of the magnet but the true line width approaches the natural line width 2/Tzin angular units. As the exchange rate becomes comparable with the frequency difference between sites A and B the single resonance is broadened. I n this region with a single broadened resonance the lifetime may be conveniently obtained by using a simpler formula of Piette and Anderson (1959) which we shall discuss later. These formulae are, of course, applicable only when there is no saturation of the resonance due t o a high R.P. field, i.e. y2H:T1T24 1. At the point when (76) = 1 the single resonance has maximum half width and this has been called the “coalescence lifetime ” and if the rate of exchange is varied solely by a temperature adjustment we can also speak of a
TEMPERATURE EFFECTS O N N . M . R . SPECTRA
201
coalescence temperature.” As the rate of exchange decreases below this value, i.e. the lifetime on sites A and B increases, separation into two separate resonance peaks occurs. When the tails of the separated resonances overlap appreciably (Gutowsky and Holm, 1956) there is an apparent change in the chemical shift defined as the frequency difference between the two maxima of absorption. At longer lifetimes two separated broadened resonances occur, centred on w A and wB, and finally, a t very long lifetimes, (76) > 100, the line width of each resonance approaches ( 2 / T 2 )the , natural line width. Considering the steady state method of N.M.R. detection, it is fair t o say that the region of lifetimes where detectable line width effects occur is 100 > ~6 > 0.01 but that actual measurement of lifetimes is quite inaccurate a t the extremes of this range. I n terms of actual first-order rate constants, if 6 is of the order to 1 sec. This is a 100 radians than T may be measured in the region region not normally available t o other techniques and, furthermore, rate measurements are made on a system in chemical equilibrium. The features described above may be seen in the proton resonance spectrum of NN-dimethylformamide for the methyl protons. In this particular case the chemical shift difference is only 6 C.P.S.a t 30 Mc/s and this illustrates the limitations of studying line widths of the separated resonances because overlap and coalescence of the two signals occurs over a very limited region of lifetimes. The techniques applied in such a case to obtain lifetimes from a steady state spectrum are the following: ‘l
1. Slow exchange limit
At low temperatures the variation in line width of separated resonances can be studied. This is called the “slow exchange” limit. The imaginary part of ( G ) in equation (26) near resonance frequency w A = (wo+6w/2), where wo is the weighted mean frequency of the two resonances, becomes
The imaginary part is
The expression in brackets is formally identical with the ordinary v mode solution of the unmodified Bloch equation (15b) where
wYT1T2< 1 and (35)
202
L. W. R E E V E S
T,, is the spin-spin relaxation time in site A, and rA is the lifetime in site A. The line is thus “Lorentzian” in shape with a width ( A O ) ~=, (2/ThA). ~ The value of T2A may be obtained a t lower temperatures or in many cases, since the actual line width is limited by magnet inhomogeneities, a sharp signal from an included standard peak as in tetramethylsilane may be used. The method of measuring small line widths by “fast passage ’’ techniques has been adequately dealt with before (Pople et al., 1959). 2 . Intermediate exchange rates This includes the region of r values where the peaks overlap and coalesce. There are essentially three methods of treating spectral data in this region to obtain the life-times. The line shape function may be generated using equation (27) and compared with experiment (Gutowsky and Holm, 1956). It is usual to standardize the chemical shift Sw in an arbitrary scale unit and construct a set of curves with variable T. Comparison of experimental spectra with these standard curves provides quite a reliable method for evaluating 7. The advent of fast computers has provided another method of comparing theoretical and experimental spectra. The comparison of line shapes does not have the elegance of using a closed form solution of the exchange equations for r. Many chemical systems lend themselves well in the slow and fast exchange regions to a simple evaluation of r and, providing the kinetics outside the intermediate rate region are in agreement on each side with a single activation process, this is the simplest way to deal with exchange broadened spectra. A second method, first introduced by Gutowsky and Holm (1956), is to measure the change in apparent chemical shift in the region where the two peaks collapse to one. I n the case where A and B are equally populated T A = T B = 27 andp, = pB. Equation (27) for the v-mode gives two minima of signal a t - a and + a , two maxima for the absorption peaks and a minimum between these. Above the coalescencetemperature the two maxima coincide. Differentiation of equation (27) with respect to d w allows a location of these maxima (Gutowsky and Holm, 1956). The result is
where
(37)
T E M P E R A T U R E EFFECTS O N N . M . R . S P E C T R A
203
The value Aw = 0 is associated with a maximum or a minimnm, depending on whether r is long or short. The location of the maxima is simplified if l/T2 in each site is small compared t o So e 6, the chemical shift in radians sec-l. The collapse of the two peaks depends on r the lifetime parameter and no correction for overlapping tails of the peaks is necessary. The observed separation 6w, is then given by
if raw > d2. It also follows that if Sw, = 0, then (raw) 6 d2. The critical lifetime for exact collapse is therefore given by
where ( v A - vB) is the frequency difference (in cycles) between the A and B sites. I n NN-dimethylformamide the small chemical shift difference between sites A and B compels the retention of terms in (1/T2),and the non-zero solution of equation (36) for d w is
Gutowsky and Holm (1956) have made numerical solutions of equation (40)and shown that, for T, = (1/3Sw), awe does not equal (wA- wB) = 80 even with slow exchange, if there is appreciable overlap of the components. A correction is therefore necessary to give the true Sw and this is obtained from equation (40). A third method of dealing with the intermediate exchange region is particularly sensitive to non-ideal spectrometer conditions and consists of measuring the exact intensity ratio between two maxima and the intermediate minimum before collapse. This has been used by Rogers and Woodbury (1962) in a survey of energy barriers for rotation in substituted amides. I n the absence of appreciable overlap (i.e. 6 $ 1/T2) the following equation may be verified by taking the ratio of the v mode intensity at the maxima to that a t the intermediate minimum value obtained by differentiating the v mode expression (27), as in equation (36).
for where
(76) = & d ( 2 r + {+?+}1’2) (r6/2) > 1 maximum v mode intensity r = minimum v mode intensity
(41)
204
L. W. R E E V E S
The most accurate method in the intermediate exchange region and the one applicable over the largest range of lifetimes is the generation of the line shape and direct comparison with experiment. 3 . Fast-exchange limit When 78 and T~ are small the single averaged resonance, broadened by exchange, decreases in half width until the value (2 / T z )is achieved in the limit of very fast exchange, (76) < 1. The imaginary part of G in equation (26) may then be written as m
This represents a signal centred on Winean =
P A WA -I-PB W B
(43)
The line width limit with very fast exchange is (2 / T 2 )where T2A = TZB = T , . Equation ( 4 2 )merely gives the v mode signal in the absence of exchange, as in equation (15b) when o ? T 1 T 2< 1. Equation (43)is a very useful relation since, in the limit of very fast exchange, chemical shift changes can be determined by changes in p Aand p B ,the concentrations of species present in equilibrium. I n the region where significant lifetime broadening occurs the line width can be used to measure the rates of exchange by using a modified treatment of the problem by Meiboom et al. (1957).
I n the simple case :p A = ps
=
0.5; TZA=
T,,;
rA =
T~ =
27,
The line broadening due to exchange is merely (#) since the line width measured is (2/T2').It is understood that line broadening due to magnet inhomogeneity is included in the term ( l / T z ) .If 6 is large and T z is long (e.g. 2 sec.) then the first term on the right-hand side of equation ( 4 5 ) can be neglected. This preliminary discussion of chemical exchange, although it is limited mostly to exchange between two equally populated sites, includes the principles by which N.M.R. spectra can be interpreted in terms of lifetimes of nuclei on these sites. The collapse of spin multiplets due to interruption of spin-spin coupling between two nuclei by a n exchange process can be accommodated with only a few extra considerations,
TEMPERATURE EFFECTS O N N.M.R. SPECTRA
205
provided the N.M.R. spectrum is first order, that is JAB < SAB. It is sometimes necessary to distinguish between a bond-breaking exchange process and a hindered internal rearrangement of the molecule. The interruption of spin coupling implies a bond-breaking mechanism. Simplest of these cases is a proton exchange process in ethyl alcohol
+
+
CH3. CH2. OH CH3. CHz.OH* + CH3. CHz.OH* CH3. CHz .OH
This process is slow in absolute alcohol but becomes very rapid in the presence of a small amount of acid or base (Arnold, 1956). The chemical shift between methylene protons and hydroxyl protons can be made large compared to the nuclear spin-spin coupling between them. I n the case where no acid is added the lifetime of hydroxyl protons on a given molecule is long in relation to J , the coupling to the methylene protons. The hydroxyl proton shows a regular triplet of intensity ratios 1: 2 : 1. As acid is added the triplet collapses to a single line owing to the above exchange process. The intermediate and fast exchange regions have been treated by Meiboom and co-workers (1957; Meiboom, 1961) and the influence of the parameter t = ( 1/T26)[where 6= J in this case] is included. The lifetime T is obtained in the intermediate exchange region either by fitting the observed spectrum with a spectrum calculated for various values of T in the form of the parameter (76) or by the ratio of maximum to minimum intensity in this region (Gutowsky and Holm, 1956; Rogers and Woodbury, 1962). Careful tests must be made to ensure that this ratio r is not a function of H,, the radio-frequency field strength. Some care must be taken in the evaluation of the true chemical lifetime when spin coupling is interrupted, since the exchanging spins and those spins which remain on the molecule see the exchange process €rom a different point of view (Meiboom, 1961). This is well illustrated in the case of proton exchange in water,
+
HzO H*OH
+ H*OH + H2O
I n a slow-exchange approximation the proton spectrum of water should consist of a very strong line for the species H2016with a weak line, perhaps with a small isotopic shift, for H2018. There are six-resonances in the proton spectrum of H2017since this oxygen isotope has a spin of 512. The proton exchange process, catalysed by acid and base, averages these eight Larmor frequencies to a single line. The main contributions t o line broadening in the fast exchange limit are the Larmor frequencies in HzO1'; the species H20I8and DOH can be ignored. It is important to note whether, in the exchange process, both protons exchange a t once or one at a time (Grunwald et al. 1957) since in the 017magnetic resonance
206
L. W. R E E V E S
spectrum the molecules containing this isotope are selectively observed. The vast majority of exchanging protons do not affect the line widths of the 0 1 7 resonance a t all but the resonance is sensitive only to those spin transfers involving H2017.The 0 1 7 resonance is ideally a triplet by spinspin coupling to two equivalent protons and the appearance of this triplet on collapse is sensitive to whether both protons leave the H 2 0 simultaneously or not. Even when they exchange separately account must still be taken of the fact that an incoming proton has a probability 0.5 of having the same z component of spin magnetization as the outgoing one, so that no change in Larmor frequency of the 0 1 7 resonance occurs
I 1
2
3
6
4
810
1 0.6 0.0 1.5 2
0.3 0.4
1
r
FIG.4 (For leguncl seo under Fig. 0, page 307.)
and no line broadening is contributed. The important property of the system for kinetic data is the average chemical lifetime and, in internal rotations, which produce chemical shift averaging, every exchange is
TEMPERATURE EFFECTS O N N.M.R. SPECTRA
207
effective in magnetic averaging but this is not the case when spin multiplet collapse is due to transfer of magnetic nuclei. I n Pigs. 3, 5 and 7, a plot of the exchange rate parameter r = (h), where 6 EJ in radians sec-l, is made against ratio of maximum to minimum intensity. This ratio is influenced by the natural line widths. must therefore be In order to obtain lifetimes, the parameter t = ( 1/T26) varied t o match a particular experimental spectrum. Figures 3a, 5 and 7 correspond to an exchange-averaged signal due to a doublet, triplet and quadruplet of a non-exchanging magnetic spin which is coupled to one, two or three nuclei of magnetic spin 4,respectively, which exchange
, K ‘ t
= 0.00
r
FIG.5
J
t = 0.10-
I
01
I
_
_
uz
-
I--L-L-L.-
0 3
04
0 6
d 0 8 1
r
FIG.D FIQS.3-6. Theoretical curves used in obtaining the exchange rate from observed line shapes (Loewenstein and Meiboom, 1957). (Fig. 3 for broadened spin-spin doublet; Fig. 4 for spin-spin doublet collapsed into asimple broadened line; Figs. 5 and 6 are corresponding curves for triplets. u = A / 6 w , where A is the width of the line a t half-amplitude, w is half the spin-spin splitting; r = 2 S h , where r is the mean lifetime between exchanges and 26w the angular frequency of the spin-spin splitting; t = 1/T26o, where Tz is the transverse relaxation time in the absence of exchange. The ordinate in Figs. 3 and 5 is the ratio of maximum to minimum in a broadened multiplet.)
208
1,. W. R E E V E S
from the molecule one a t a time, as in (CH3)3NHt,(CH,)2NH,t and CH3.NH3+. Figures 4, 6 and 8 show the line width at half height dvl,i divided by 6 = J , as a function of r = (76) with various values oft defined
r
FIG.7. Methylammonium ion (Grunwald et al., 1957). Ratio of maximum to central minimum of the CH3 quadruplet as function of the exchange rate. The quantity t is a measure of the line width in the absence of exchange. The other symbols are defked in the caption of Fig. 3-6, which shows samples of the curves from which the figure was obtained. I
I
I
4-
U
-
I
1 8
I
I
-41
1
2
1
r FIG.8. Methylammonium ion (Grunwald et al., 1967). Half-width of the CH3 reeonance as function of the exchange rate. The ordinate is the quantity u = A / & where d is the width of the line at half-amplitude. The other symbols are defined in the caption of Fig. 3-6 which shows samples of the curves from which the figure was obtained.
TEMPERATURE XFFECTS O N N .M.R. SPECTRA
209
above. An actual experimental spectrum taken a t various stages of collapse for the methyl group in CN, . NH,+ is shown in Fig. 9 from the work of Meiboom and co-workers.
c-----l
10 sec
1sec
FIG.9. Collapse of quadruplet in spectrum of trimethylammonium ion (Grunwald et al., 1957). (The exchange rate increases from top to bottom. At the left the CH3 resonance on slow passage, a t right the water resonance of the same solutions on fast passage. Note the shortening of the wiggles” with increasing exchange rate, which is a measure for the broadening of the water line.)
B. McConnell Equations I n a simple transfer process of nucleus X between Larmor frequencies of two sites Aand B the Bloch equations have been modified by McConnell
(1958) to include exchange directly. If symbols have their previously defined significance the magnetizations in the rotating frames for two sites A and B are written
u = u,+us v = v,+vn M , M$+MI,3 =;
The modification introduced by McConnell (1958) is the addition of terms such as - uA/rZg, which measures rate of decrease of magnetization u in site A due to exchange to the site B, while the capture of magnetization into the A site is described by the positive term ( + U B / r B ) . The same conditions for the G.M.S. equations (Gutowsky et al., 1953) are operative and in the “slow passage’’ approximation the time derivatives of magnetizations become zero, as in the Bloch treatment. When this slow-passage condition is added, the absorption spectrum may be described by solving the six simultaneous algebraic equations for G = (u+iv). Strong scalar coupling of spins in A and B sites invalidates the basis of the simple Bloch equation for an exchange process. The G.M.S. equation for exchange between two sites of equal populations is = T2, = T,, rA= rB= 7 ; 1/r2 = obtained by using the conditions TZa4 1/T2+117; and M,A = M,B = Mo/2. The treatment of exchange amongst more than two sites is possible by means of the McConnell equations and it can be seen that for the slow-passage solutions 3n algebraic equations result, where n is the number of distinct Larmor frequencies or magnetic sites available. The McConnell equations have been used by Meiboom (1961) in the problem of proton transfer in water amongst seven possible Larmor frequencies. I n this case, the population of one Larmor frequency in H2016greatly exceeds the other six in H2017. The result obtained by Meiboom by setting up matrices of the exchange probabilities between various sites is, in the fast exchange limit,
TEMPERATURE EFFECTS O N N.M.R.
211
SPECTRA
I n this expression T is the average lifetime between exchanges of protons bonded to a specific oxygen nucleus; Pi is the relative intensity of the ith line, is the frequency difference (in radians sec-l) between the ith and TZmeas. is the exchange-influenced line and the dominant line (HZOle), relaxation time and T 2 the natural relaxation time. The McConnell equations are also suitable for describing transient N.M.R. experiments when the rate of change of magnetization cannot be set equal to zero (McConnell and Thompson, 1959) and differential equations must be solved. The case of transfer between two sites of very different T I and T z values can be accommodated easily and McConnell has shown that under slow passage conditions if
< TIATZA T I B , TBB < 713 m!T1, T 3< 1 Tin, Tzn
and
(i.e. no saturation in the ‘B’ resonance) and TA
2
the absorption mode signal is given by
C. The Piette and Anderson Equation The exchange problem for many sites has been solved by using the method of Gutowsky et al. (1953). The total xy plane magnetization is then given by the following expression
G = -yH,Mo
i.
2 j
pj
[1
+ T/T2j+id WjT]
Pj [ ~ / ( T z+)idmj j T ] [1+ T / ( T z ) j-I-idmjTI-’
j
(51)
The equation is valid for sites j of chemical shifts Sj and populations p j ; is the mean time between reorientations or site changes. The other symbols have their previously defined significance. This equation reduces to that of Arnold (1956) when (T& is independent of j . The equation can further be simplified to that of Gutowsky and Saika (1953) if there are only two sites, A and B, and by denoting T - ~ = ( T A + T B I). The above equation is simplified by introducing a modified relaxation time Tj where T[i= T - ~ +(T2)y1. I n the slow-exchange limit the line-broadening due to exchange may T
212
L. W. R E E V E S
be obtained by expanding equation ( 5 1 )and neglecting small terms. The line width of the resonances is described by an equation identical in form to the Bloch slow-passage solutions but with a relaxation time T ; describing the line width :
I n the case of a simple two-site exchange, T = ( k / 2 )where k is the mean first-order rate constant, (ki+ ki)= 2k. The assumption of an Arrhenius law for the temperature dependence
k
=
A exp ( - E,/RT)
(53)
where A is a frequency factor, yields on substitution into ( 5 2 ) , log (rdv-Tzj')
=
log 2A(1 -Pj)- Ea/2.303RT
(54)
Thus a plot of log [rdv- (T&I] versus 1/T should give a straight line of slope ( - Ea/2.303R). I n the fast-exchange limit a single broad line is observed, and the apparent relaxation time T"observed is given by
The additional assumption that T 2 is independent of site is required, j T , for all sites. The symbol V is representative of the second i.e. T Z = moment of the separate lines
v = c Pj(wj- ( w ) ) 2
=
((w2)
j
where
(w) =
xPjwjand j
(w')
=
-(w),)
(56)
x Pjw3. j
Now if 7 < T 2in equation ( 5 5 ) and a normal activated exchange process is assumed, i.e. log ( ~ d v T z - ' )= log (VTZIBA)+ Ea/2.303RT, the simplified expression derived from equation ( 5 5 )with
This reduces to equation (45) if exchange process.
V
T
(57)
< T 2is
is equated to ( P / 2 ) in a two-site
TEMPERATURE EFFECTS O N N . M . R . SPECTRA
213
D. Relationship of Mean Lifetime T to Chemical Kinetics Let us consider the case of exchange between n magnetically distinct sites, which produce in the slow-exchange limit n lines, and exchange is possible between all environments. If the fractional population of site j is p j then detailed kinetic balancing at chemical equilibrium between sites j and i leads to
~ implies a probability (117-J per unit time When j = i, 1 / =~0. ~This of a jump to a site i from a site j. The general analysis for n sites shows that in the slow-exchange limit the line width for the j t h resonance line is given by 1
-
T;
=
1 -+-
T2j
1 7-j
ri is the mean lifetime in site j and is due to the exchange of magnetization by all routes to all other sites. This is related to the mean lifetime T in equation (52) by the equation,
Thus equations (52) and (59) are equivalent. The measurements of temperature dependence of T~ will give the temperature variation of the sum of all rate constants involving transfers from sitej. I n the fast-exchange limit the line width is sensitive only to the mean lifetime T for all sites, i.e. the mean rate of exchange is measured. The ideal method of dealing with a complex exchange process is to make measurements of the line widths in the slow-exchange limit thus obtaining rate constants out of each site as a function of concentration (population) of other sites in order to derive the reaction mechanism. Then, if required, the temperature dependence of rate constants can be investigated. Certain simplifying assumptions may have to be made about relative rates of certain processes. This is essentially the method used by Meiboom and co-workers in solving fairly complex protolysis problems of the substituted ammonium ion. We shall discuss only the temperaturedependence aspects of this work. Additional statistical factors mentioned earlier occur in these bondbreaking proton transfer reactions. A simple illustration is given by Loewenstein and Connor (1963). Proton transfer between NH4+ ions can be measured by line broadening of the 1 : 1 : 1 triplet ofthe NH4+ion.
214
L. W. R E E V E S
The line width is sensitive to rNH4+ but this is one-quarter the inverse rate constant because each transfer involves only one proton. Further, each proton has one chance in three of attaching itself to a nitrogen in the same spin state. The chemical rate constant is therefore given by
E. Quantum Mechanical Treatments The problem of exchange narrowing involving a correlation time spectrum was first tackled by Bloembergen et al. (1948) in the original theory for the narrow N.M.R. lines observed in liquids. The theory has
8
dl6
FIG.10. Calculatod nuclear magnetic resonance spectrum of two interacting spin 4 nuclei with a relative chemical shift 26 and a coupling strength J , plotted as a function of the deviation d of the frequcncy of the driving field from the averago frequency of the two nuclei. The spectrum is symmetric around d = 0 and only the positive half is shown. The spectra are for R = J / 6 = 1 and for several values of the exchange rate T = l i d (Alexander, 1962).
been greatly generalized using quantum mechanical methods by Anderson (1954),Kubo (1954), Kubo and Tomita (1954) and Sack (1958). The problem of chemical exchange is a special case of these theories which deal with random fluctuations of frequency over a model distribution and are appropriate to estimations of nuclear relaxation times. The chemical exchange problem is one of a low frequency contribution to the correlation time spectrum between well defined distinct Larmor frequencies. The specialized application to chemical exchange problems has been achieved by Kaplan (1958) and extended by Alexander (1962,1963). I n the limits of weak coupling (J/S < 0.10) for all sites the quantummechanical and classical results already discussed are identical. The power of the quantum mechanical methods is shown in solutions where
TEMPERATURE EFFECTS O N N.M.R. SPECTRA
215
coupliiig in strong (S/J < 10). The illustrations of these methods iiivolve knowledge of density matrices (Fano, 1957) which a t present are almost entirely the domain of theoretical chemists and physicists. Figure 10, taken from the work of Alexander (1962)) shows the collapse of the “A” part of an AB spectrum with ( J / S )= 1 as the exchange lifetime decreases. I n some experimental work the presence of strong coupling is ignored and the error in exchange lifetimes must be considerable. No attempt has been made as yet to treat the exchange problem experimentally by matching the theoretical spectrum for a given lifetime in a complex case with second-order effects due to similar values of J and 6. The problem is best avoided in accurate work by appropriate deuteriation of complicating sites in a proton resonance spectrum. It may also be necessary to decouple the deuterium coupling by a strong R.F. field a t the deuterium Larmor frequency.
F. Spin-EchoMethods Only a brief mention of this technique will be possible. The “Spin Echo” method, as such, was first developed by Hahn (1950). The essential features are the application of a short intense radio-frequency pulse which matches the condition a t the Larmor frequency yH,t
= wlt =
61
The effect, considered in a rotating frame a t the Larmor frequency, is to rotate the magnetization into the x‘y’plane of Fig. 1. This pulse is immediately followed by a signal which decays with a characteristic time T,*and is influenced by the sum of all relaxation processes, both intrinsic and extrinsic (field inhomogeneity). I n so far as the value of w1 = y H , covers the total N.M.R. spectrum of one nucleus, the signal (((freeinduction decay”) is modulated by all frequency differences in the spectrum due to constructive and destructive interference of the freely precessing nuclear moments a t a series of specific Larmor frequencies. The free induction decay signal contains all the information in the absorption spectrum with the advantage that no signal saturation occurs in the absence of an H , field and the disadvantage that a Fourier transformation must be made to obtain simple aspects evident in a steady state spectrum (Abragam, 1961). The relaxation forces present in the system reduce the resultant moment in the x‘y’plane as nuclei precess faster or slower than the mean Larmor frequency. This gives rise to the free induction decay. The process of dephasing of nuclear spin moments in the x’y’plane can be
21 6
L.
w.
REEVES
reversed by applying after a time interval satisfying the condition
(yH,)t,
=
?T
T
a second intense pulse
= W1tU
This second pulse inverts the vectors in the x‘y’ plane and they immediately begin to reverse the dephasing process and refocus at a time 27. The conditions t, < T < T,,T, must be met. The refocusing of the vectors is accompanied by an “echo” signal of the original free induction decay. The amplitude of this spin echo is reduced from that of the initial amplitude of the free induction decay. The qualitative reason for this is that intrinsic relaxation forces and diffusion of molecules from one part of a n inhomogeneous field to another cause nuclear spin moments to get out of step in the dephasing and phasing process which produces the echo. These intrinsic relaxation forces involve correlation times that are very short on the time scale of the pulse intervals and, depending on the homogeneity of the magnetic field, the spin diffusion is a t least comparable in time scale to the pulse intervals, Nuclei which get out of step do not refocus and contribute to the echo amplitude. The extrinsic relaxation mechanism of an inhomogeneous magnetic field does not in the absence of diffusion reduce the echo amplitude, and therefore homogeneous fields are not required for most applications of the spin-echo method. I n this simple two-pulse experiment the echo amplitude can be expressed as a function of pulse interval A A0
=
[
exp - - Tz 2r
- ~ .
kwl 3
where k = ( y 2 G 2 D / 4 )(Hahn, 1950; Carr and Purcell, 1952, 1954). A / A ois the amplitude ratio of echo to free induction decay for pulses spaced at intervals T with a nuclear system of natural relaxation time Tz. The damping of echo amplitude by diffusion is contained in the second term. As usual, y is the magnetogyric ratio, G is the average linear field gradient over the sample (dH/dl),, and D is the diffusion constant. The echo amplitudes do not follow a simple exponential decay with time unless ( 12/y2G 2D ) $ T 2 . Figure 11 shows diagrammatically (Muller and Bloom, 1960) the arrangement of echoes and pulses which occur in a general type of three-pulse spin-echo experiment. I n this diagram a pulse of duration 0 to t orotates the magnetization by the angle ~ / 2 This . pulse is followed by the free induction decay with time constant T t determined by both extrinsic and intrinsic relaxation forces. At a time T~ ( T $ ~ t l , to)a pulse
T E M P E R A T U R E E F F E C T S ON N . M . R . SPECTRA
217
of length tl = 2t0 rotates the magnetization by an angle rr. No free induction decay arises after this pulse if the condition w l t l = rr is satisfied. I n general, a small induction tail may occur, and it is indicated in the figure. A spin echo occurs a t time 2r1, and this is a primary echo. The Carr-Purcell experiment is simply a repetition of this primary echo. If a third pulse is applied a t time r2,it is followed by an induction decay and three more echoes in the general case. The stimulated echo can be used to measure T 1in the absence of diffusion and it is the one which occurs at time ( r Z+ r l ) . The dependence on diffusion may be used either as an absolute or relative method, for measuring diffusion constants. When G is small the diffusion effect is small but in the experiments of Carr and Purcell (1952, 1954) it can be eliminated. The first echo at time 27 may be
FIG.11. Arrangement of echos and pulses in three-pulse spin-ocho experiment (Muller and Bloom, 1960).
rephased again in the x’y’ plane by a second echo a t time 47. This , echo, rr, echo, rr, sequence of pulses may be repeated to give ~ 1 2 rr, echo .... etc., a t times 0, 7 , 27, 37,. . . etc. This experiment has often been referred to as a “Carr-Purcell” train. I n actual experiments the number of pulses may be as high as l o 5 and one experimenter has boasted privately of a train of a million pulses with intervening echoes. The amplitude envelope of this echo train is in general exponential. The pulses may be spaced as close as lop5sec apart and the random dephasing due to molecular diffusion in this period is negligible. The slower diffusion effect is overtaken by the pulse repetition rate. This important new variable in the spin-echo experiment is one that the steady-state spectrometer does not have. The simple expression for relative amplitudes becomes A = exp[- 1- - + -1G Z y y 2 D r 2 ] t A, TZ 3
218
L.
W. R E E V E S
The time 7 is half the interval between pulses and can be made so small as to render the second term in the exponent negligible. The pulse repetition rate cannot be made fast enough, however, to affect the very rapid fluctuations of local magnetic fields which give rise to the natural relaxation time T 2 . Let us examine the diffusion effect more closely. A small element of solution in which there is a field gradient will be associated with a mean Larmor frequency for the group of nuclei in it. Diffusion during a period 27 will cause a Gaussian distribution of frequencies about the mean to develop as a model system. Chemical exchange also causes random dephasing as well as diffusion so that it is also amenable to study in a Carr-Purcell experiment. Whereas diffusion effects in the absence of chemical exchange can be eliminated by a high rate of pulse repetition in an inhomogeneous field, chemical exchange in the presence of diffusion is best studied by variation of the pulse repetition rate in a fairly homogeneous field. The homogeneous field ensures that the second term in the exponent in equation (63) is small because the field gradient G is small. Chemical exchange, unlike diffusion, represents the random dephasing due to jumps between discrete Larmor frequencies and the distribution, as it evolves in time, must be treated rat,lier differently from the “Gaussian” diffusion effect. There has been surprisingly little attempt to describe the spin-echo effects which arise with chemical exchange. Woessner (1961) discusses chemical exchange in pulse experiments using the Bloch equations. The free induction decay signal for a two-site exchange process of lop-sided populations has been calculated for various values of the reduced The first order rate constants kA and k, exchange lifetime (kBTSB). refer to exchange of magnetizations of sites A and B respectively (kg = 1/7B, k A = 1/78). The behaviour predicted corresponds to a long free-induction decay in the slow-exchange limit which is modulated by the chemical shift difference (wA- wB). This is otherwise exponential with a decay constant a mean relaxation time for the two sites which includes governed by T,*, the effect of field inhomogeneity. As the exchange rate increases the exponential decay is damped by exchange, and near a critically large damping the modulations become longer corresponding to the collapse of the chemical shift (Gutowsky and Holm, 1956). Near critical damping the decay becomes non-exponential in character and a t critical damping kB = kA 2: IwA-wBI/n for two equally populated sites. The situation corresponds to the critical lifetime a t the coalescence temperature of the steady-state spectrum. As exchange rates increase further the induction decay becomes longer but is not modulated and finally it becomes
TEMPER-\TURE EFFECTS ON N.M.R.
SPECTRA
219
exponential again. These featurcs are illustrated in Fig. 12 from the work of Woessner (1961) and they have been experimentally confirmed by Reeves and Wells (1962) in a study of free induction decays of methyl nitrite as a function of temperature (Fig. 13). Woessner (1961) goes further and calculates the amplitude of echoes following a second pulse if diffusion effects are neglected. I n the absence
f h b
FIG.12. Theoretical relative free decay signal amplitude versus reduced time after a 90" pulse for several values of reduced transfer rate when P, = P,, C, = C',, T2, = Tzb, and w,- wb = 20/Tzb(Woessner, 1961). Coefficients "C" are rate constants.
of exchange and any spin-spin coupling the echo amplitude is a pure exponential (equation 62) but exchange introduces modulations as is shown in Fig. 14. No simple formula is developed, however, which might be used to extract lifetimes from the experiments. Luz and Meiboom (1963) use the equations of McConnell (1958) to solve the Carr-Purcell sequence in the presence of exchange. Certain serious approximations are required in the solution but a simple expression in closed form is derived for the fast-exchange limit. This
L. W. R E E V E S
220
limit is particularly useful because it is one where the experimental difficulties of the steady state method are extreme, the line width approaching the naturaI line width.
Here T is the mean lifetime on a site for a nucleus under study and ( 1/Tzg) is the experimentally observed decay constant with a pulse repetition
-370
u I -43.5"
0
20
40
60 80
100
I
20
40
60 80
100
msec
FIQ.13. Free induction tail signals for pure methyl nitrite at various temperatures (Reeves and Wells, 1962).
rate of g pulses sec-l in the presence of exchange. The true natural relaxation time in the absence of exchange, To,is observed at the fastest pulse repetition rates. Chemical shifts Si (in radians per sec) of site i are measured from the centre of gravity of the steady-state spectrum ( x p i S i = 0, where piis the population of site i). i
The equation can be seen to be correct at the limit of very fast pulsing rates when the right-hand side becomes zero, while with very slow pulse repetition rates (g --f 0) the equation becomes that of Piette and Anderson (1959), given before as equations (45) and (58). The equation has been applied to the protolysis reactions of the trimethylammonium ion in
TEMPER-4TURE EFFECTS O N N.M.R.
SPECTRI
d
-> 1
-I
aqueous solution, when the line width of water is close to natural line width . Allerhaiicl and Gutowsky (1964) have investigated the wider apIdicability of the Meiboom equation and, by numerical methods nsing a computer, have investigatcd the accuracy with which the echo amplitudes follow a true exponential decay. They conclude that the
FIG.14. Theoretical spiri-echo ainplitudes at time t = 27 versuq reduced 7 r 111 90 -1SO" pulse 5equenres for several values of reduccd transfer ratc whcm l',z= P,,, (',, = (',,, Tj,, = TL,,. arid w,, - w,, = 20/T2,, (Worssner, 1082).
decays are exponential over a wide range of experimental conditions. Blooin rt 01. (1964) have shown, using simple probability theory without assuming the Bloch equations, that the Carr-Purcell sequence produces echo amplitudes which, for two sites in the absence of spin coupling, are always expressible as a sum of two exponentials. The differential equations obtained from the solutions are those of McConnell (1958). The echo envelope in the Carr-Purcell experiment is shown to be a superposition of two exponentials in the case of two Larmor frequencies wdi and w , ( . M(4nT) = ,4,er;~'(-r,.4nT)+A,exp( - r 2 . 4 n T )
(65)
222
L. W. R E E V E S
I n this expression n is the number of pulses, r is half the pulse interval, rl and r 2 are decay constants, A l and A , are constants which depend on the initial conditions of the experiment. The nuclear magnetization at time (4nr) is M ( 4 n r ) . (lt is unfortunate that the literature of spin-echo work uses the symbol r for pulse intervals and chemical exchange literature the same symbol for exchange lifetime.) I n the symmetrical population case the decay constants become : (a)Short r limit (k = k-i = k,, r k 4 1, w r 4 1 where w = ( w A - w B ) / 2 and valid for w 2 k and w < k, i.e. fast and slow exchange) : ri = k
k
+kwnr2
(66)
The two roots of ri being r l and r 2 ( b ) Long r limit, slow pulse rates : w2
ri = k ~ k k (67) 2k in the very fast exchange limit. One of the roots of (67), r = ( w 2 / 2 k )is identical with equations (45) and (58) since w 2 = 8 ’ , k r (1,’~).Natural relaxation times have been
FIG.15. Echo modulation pattern in 1,l-dichloroethane at 22’C. Total sweep is 1.5 sec (Powles and Strange, 1962).
TEMPERATURE EFFECTS ON N.M.R.
SPECTR-4
223
omitted and can be added as an afterthought. The convergence on the steady-state spectrum result is necessary in the limit of very slow pulsing rates. The use of this general theory depends on whether the spectrometer is phase-sensitively detected a t the radio-frequency, in which case any component of the magnetization in the x’y’ plane can be selected, or diode-detected, in which case only the magnitude of the magnetization can be observed. Pulse techniques have been used by Powles et a1 (1960, 1962) to measure temperature dependence of nuclear spin-spin coupling in molecules such as methanol and acetaldehyde, which have steady-state spectra approximatingtoanAX,case (Popleetal. 1959). Hahn andMaxwell (1951, 1952)showed that modulations of echo amplitudes could be explained on the basis of scalar couplings. I n the limit of weak coupling the formulae are simplified and the chemical shift modulation disappears. I n a CarrPurcell experiment the amplitude of the nth echo E,(t) in an AX3 case can be shown to be E,(t) = &I 15 cos 7 ~ J+t cos 3nJtI (68) where J is the nuclear spin-spin coupling constant in the AX, case. The experimental result is shown in Figs. 15 and 16 for 1,l-dichloroethane
FIG.1G. Echo modulation pattern in methyl formate a t 22OC. Total sweep is 4 sec (Powles and Strange, 1962).
224
I.. \V. R E E V E S
and methyl formate a t 120.8 Rlc (Powles, 1962). This method has the advantage of high precision in the measurement of ?J which is approached only by the “Wiggle Beat” method (Reilly, 19%) and thus a small temperature dependence can be accurately determined. Proton exchange effects can also be studied since these lead to a collapse of coupling in cases siieli as methanol (Powles and Strange, 1962, 1964).
G. Double Resonance Methods Forskn and Hoffman (1!)63) have introduced a nuclear-nuclear double resonance method for studying chemical lifetimes in the region of the slow exchange limit. This new method can be adapted to extend the range of rate processes measured to a region not accessible by the single resonance method (Gutowsky arid Saika, 1953). The theory of homonuclear clecoupling was developed by Freeman and Anderson (1962) and apparatus for such studies is now generally available (Kaiser, 1960: Turner, 1962; Freeman, 1960). One method used by ForsGn and Hoffman (1963) is to study tlic slow7 cxchange limit for two sites A arid B with strong irradiation and consequent saturation of the B resoiiance while the A resonance is observed with a weak R.F. field H I . The McConnell equations (1958) may be coiitracted and terms describing the magnetization in the B site omitted. For the z-magnetization in the ,4 site we have, in hLcConnell’s notation,
The slow-passage line width (Piette and Anderson, 1959) is given by equation (59). Experimental conditions to be maintained are : r2-+ < T . ~or rA49 T2.+.It is then possible t o obtain several slow-passage signals of site A during the time T~I. The value of T,, can be shortened in a stead)--state experiment by using a more inhomogeneous field. The signal A may be recorded in a time long compared to r2-+but short compared to T , +. The absorption mode signal is then given by vL4when t i , = dA = 0. The equations for time-dependence ofu, and v 4 magnetizations are also simplified by omission of terms . E C , / T ~and vn/ru (see equation (47)), since signal B is saturated, i.e. ii, - A w u i
= - U.~/T~.,
d++Aw,~,= - V ~ ~ / T , ~ ~ - W ~ M ~
(70)
The simplest experiment is to examine resonance of site A and tthen carry out an instantaneous saturation of B a t t = 0. The magnetization
225
TEMPERATURE EFFECTS O N N . M . R . SPECTRA
+:
I I I I ! ! I
:
I
: I
I I I ! ! I I I I I I
:
I ! I I ! I !
+:
I ! !
: :I
1
FIG. 17. Salicylaldehyde-2-hydroxyacetophenone. The decay and recovery of the N.M.R. signal intensities (Cases I and 11). The arrows pointing downward ( & ) indicate the moment when the saturating R.F. field is turned on and the arrows pointing upward ( f ) indicate the moment when the saturating R.F. field is turned off. The markers in the lower part of the figures are second intervals. (a)The decay to a new equilibrium value of the hydroxyl signal A upon the sudden saturation of the hydroxyl signal B and its progressive recovery upon the instantaneous removal of the saturating R.F. field a t B, (b) the analogous decay and recovery of the hydroxyl signal H (ForsBn and Hoffman, 1963).
M t will attain a new eqnilibrium value with an exponential decay constant T ~ ~ . The new equilibrium value
is given by
226
L. W. R E E V E S
The intensity ratios at, t = 0 and t = give tlic. ratio T , ~ ~ / while T , the exponential decay coiistant gives 71a separately. The converse experi~ TIB. The chemical lifement may be performed to determine 7 1 and times T~ and 7B are thus easily determined from these results. The corresponding experiments on the hydroxyl resonance in a 5.65: 1 mixture of salicylaldehyde (A) and 2-hydroxyacetophenone (B) are illustrated in Fig. 17 (ForsBn and Hoffman, 1963) together with recovery of magnetization on removal of the saturating field for both sites A and B. This second case requires the inclusion of the B magnetizations when considering site A since the saturating field a t B has been removed. The additional condition that p , pBis required before the recovery can be described by a single time constant. The further experiments of recovery of A signal after prolonged saturation of B site and recovery of A signal after saturation of both A and B resonances have been considered. This method of double resonance promises t o be a very useful one particularly with exchange lifetimes in the range 1-10 see. rl)
H. Measurement of Lifetimes using ‘‘Rapid Passage ” Xolutions of the Bloch Equations There has not been much space in this article to discuss the complex behaviour of nuclear magnetizations during “transient rapid passage ” experiments when time derivatives in the Bloch equations (1946) must be retained. McConnell and Thompson (1957, 1959) have devised a method whereby the rate of sweep through two resonances which are undergoing exchange-averaging in the slow limit is fast. The time spent in passing through one resonance is short compared to the time of sweeping the field between the two resonances. The intensity ratios of the resonances may be used to obtain the lifetime on each site if sweep rates are carefully controlled. The exchange rate of protons between ammonium ions via a small concentration of ammonia has been determined by this method (McConnell and Thompson, 1959).
I. Electron Exchange Reactions Bruce et al. (1956) have examined the electron transfer rates between NN,N’N’-tetramethyl-p-phenylenediamine (TPMD) and “Wurster’s Blue ” (WB)which is the one-electron oxidation product of this molecule. I n acid solutions of pH 3.2 containing acetic acid and TPDM the proton resonance of all signals is sharp, but on adding a small amount of W.B. the ring and methyl protons of TPDM selectively broaden. The rate constant for electron transfer between radical and molecule is given by
TEMPERATURE EFFECTS ON N.M.R. SPECTRA
227
where A is the concentration of free radical and ( A v , ) is the half width of the signal. McConnell and Weaver (1956) and Giuliano and McConnell (1959),as well as Myers and Sheppard (1961),have used nuclear magnetic resonance techniques to study electron transfer reactions.
J. Nuclear Electric Quadrupole Effects Two different situations arise from the effect of the nuclear electric quadrupole. The examination of the resonance of a nucleus with a quadrupole moment shows a usually small value of T, which is determined by the relaxation process associated with the nuclear quadrupole energy levels in the electric field gradient at the nucleus. The larger this field gradient and the larger the quadrupole moment, the more efficient is the relaxation process. Moniz and Gutowsky (1963) have measured, as an example, the T ivalues for N14in typical organic compounds. The contribution of the quadrupolar relaxation mechanism to Tclcan be roughly estimated as 1 - 3 _ _-
Ti
21+3 4012(21+ 1)
(73)
The quantity ( e 2qQ) is the known quadrupole coupling constant and is made up of the electronic charge e, electric field gradient q and nuclear quadrupole moment Q. r, is a correlation time for molecular motion, q is an asymmetry parameter and I is the nuclear spin quantum number. In organic nitrogen compounds T iranges from 1-50 msec. The product (e2qQ)is quite small for nitrogen because the quadrupole moment is small. The nucleus of chlorine has a quadrupole moment some three and a half times larger than nitrogen so that in chlorinecontaining molecules with roughly the same correlation time spectrum and electric field gradient the relaxation time T 1is twelve times shorter. The N.M.R. signals from chlorine, bromine and iodine are very broad for this reason, as was noted in the Introduction. The temperature dependence of T,for a nucleus such as nitrogen is a reflection of the temperature dependence of the correlation time r 4 for reorientation of the molecule. Moniz and Gutowsky (1963) find that these activation energies vary in the range 1.4 to 3.2 kcal for nitrogen-containing organic liquids and do reflect the overall size of the molecule. The value of T zis also small for quadrupolar nuclei. The second situation of interest which arises from the electric quadrupole moment is the problem of a nucleus of spin & with scalar coupling to a nucleus of spin greater than $. The lifetime of the spin states of the quadrupolar nucleus is short and the scalar coupling is interrupted by
228
L. W. R E E V E S
the rapid transitions between these spin states. Theoretically the problem is analogous to an exchange process. T Ifor the nucleus spin Q with I = Q is still long but T zis shortened. Pople (1958b) has tackled this problem for coupling between nitrogen, with small quadrupole moment and spin 1, and a proton. The slow-exchange approximation applies in some organic nitrogen compounds and the line shape function for each component of the 1 :1 : 1 triplet is
where r j is the lifetime of the state of nucleus N14in the state with I, =j . The 1 :1: 1 proton resonance triplet is not equally broadened in each member of the multiplet since the lifetimes of the nitrogen spin states are not all the same. The broadening of the two outer lines is greater than that of the central line by a factor of +. Pople (1958) derived the equations for intermediate rates of transfer between the spin states of nitrogen and predicts the observed collapse to a single broad line. The halogen nuclei, which have larger quadrupole moments, do not contribute to the N.M.R. spectrum. Very rapid transitions amongst the spin states of the halogen nuclei cause all trace of coupling to halogen nuclei to be removed. I n organic nitrogen compounds with anN-H bond the absence of catalysed proton exchange must be assured even before the true quadrupolar effect is seen, since proton transfer is also a n exchange process and the two effects are additive. Further work (Bacon et al., 1963) has extended the model to spin 2. Raising the temperature results in a longer correlation time and the spectrum tends toward one characteristic of a slower exchange process. This is in direct contrast to a true chemical exchange process. A broad N-H triplet will become sharper on raising the temperature if proton exchange is absent. The solution for an even higher spin quantum number, 9/2, has been achieved by Muetterties and Packer (1963) in the long correlation-time limit.
111. EXPERIMENTAL METHODS
A. Measurements of T z When exchange broadening is appreciable in either slow or fast exchange limits the amount of exchange broadening is obtained by the difference between natural line width and total line width. I n many cases of extreme exchange broadening the line width can be taken as entirely due t o exchange. Care must be taken to ensure that there is no saturation
TEMPERATURE E F F E P T S ON N.M.R.
SPECTRA
229
and t,hat “slow passage’’ conditions are achieved. Lack of saturation can be checked by changing R.F. power over a factor of five or so and ensuring that signal intensity is proportional to power. Good symmetry of signal is indicative of slow passage conditions. I n a region where exchange broadening is smaller or where natural line width is required a transient “wiggle beat” method is best. I n this context “natura1”line width is interpreted to mean the line width due to all relaxation forces, including magnet inhomogeneity (Jacobssohn and Wangsness, 1948). If the sweep rate of the magnetic field IyI (dH,/dt) < T: then wiggles will appear after the signal due to a microscopic nuclear magnetization which is induced a t resonance, persists €or a time T:, and beats against the R.F. field. The v mode signal takes the form v = B exp ( - t/Tz)cos 4 at2
(75)
where a = Iyl(dH,/dt), Tg is the relaxation time in the magnet concerned and B is a constant. The form of the signal is an oscillation with exponentially decaying amplitude. The time constant of the decay is TZ and beats get more and more rapid as the frequency of the H I field differs from (yH,). The exponential decay can be used to determine T,*. A precaution must be taken in using this method (Szoke and Meiboom, 1959) since the wiggle beat decay may be artificially damped also by the receiver coil. This radiation damping is most serious when high packing factors for receiver coils are obtained in commercial spectrometers, as is shown by the formula 7R = ( 2 r ? ? M 0 QY1-l
(76)
where rR is a damping factor additional to Tz,71 is the filling factor of the coil, N othe nuclear magnetization, Q is the quality factor of the receiver coil, and y the magnetogyric ratio. The effect of radiation damping is shown in Fig. 18. I n one case the receiver coil is tuned off resonance slightly so that no radiation damping occurs. The effective Tz values measured are 1-7 sec and 0.3 sec respectively. Meiboom (1961) has used a method for measuring 27, developed earlier by Solomon (1959) which is also suitable for narrow lines but is somewhat more troublesome. It has the advantage that in the limit that homogeneity over the sample volume is small compared to HI, the measured value of T2 is not affected by magnet in homogeneity. The signal is swept by changing the magnetic field to the centre of the line so that magnetization is flipped adiabatically through 90’. The sweep is then stopped and the decay constant T(H,) observed from a.
230
L. W. R E E V E S
continuously measurillg rt-:corder. If extrapolated to zero 11, field this time constant becomes the relaxation time T,. The measurement of TZ from the free induction decay following a 5r12 pulse has not generally been exploited for measurement of exchange since it has no advantage over readily available steady-state methods.
t
1 sec
I
FIG.18. Measurement of effective T2 from the decay of tho “wiggles” after fast passage. The top record was made in the absence of appreciable radiation damping. I n the bottom record radiation damping is present (Szoke and Meiboom, 1959).
The use of the Carr-Purcell pulse sequence for T 2has only recently been studied but it does have the advantage of the new variable, pulse separation.
B. Variable-Temperature Apparatzcs Variable temperature accessories are now available with commercial spectrometers. The nature of restricted space in a magnet gap and the necessity of constant temperature at the pole faces renders temperature measurement and control a much more difficult problem than in most other kinetic and equilibrium measurements. The space requirement necessitates a flow system for heat transfer with good Dewar vessels for leads and N.M.R. probe attachments. The heat-transfer medium has
T E M P E R A T U R E E F F E ( TS O N N . M . R . S P E C T R A
231
almost certainly to be a gas and this suffers from low heat capacity, with consequent sensitivity to external conditions. For optimum spectrometer performance in a steady-state method of detection the sample must be spun, and this is an additional complication. The demand for higher magnetic fields has inevitably led to smaller gaps in which to work and permanent magnet systems have smaller gaps a t lower magnetic fields. It is something of a triumph that N.M.R. spectra of liquids have been taken over the temperature range - 110” to 500°K with only marginal loss of field homogeneity. Temperature control is very important and, as more systems are re-investigated, it is becoming evident that this was not satisfactory in many early measurements. The introduction of field shim coils activated by very small currents has helped considerably to recover the homogeneity lost a t low temperaturcs (Golay, 1958; Anderson, 1956). Tcmperature measurement is best made by inlet and outlet thermocouples placed as near the sample coil as possible. I n the crossed-coil spectrometer the orthogonality of receiver and transmitter coils is critical (Varian Associates, 1960) and both the 2: mode leakage and the balance change as the N.M.R. probe is cooled. It is as well not to cool the receiver coil unless there is a base-line stabilizer operating off an audio side-band frequency and an R.F. source with phase-sensitive detection at the radio-frequency. Modern commercial spectrometers often include these features. The radio-frequency bridge method of detection suffers similar faults of variable phase and voltage balance with changing temperature. Single coil spectrometers, which have been developed for analytical use for organic chemistry, do not have these problems. Shoolery and Roberts (1957) developed a design in which the receiver coil is cooled but sample spinning is possible. An additional advantage, that samples may readily be interchanged at low or high temperature, is incorporated. The design is explained by the diagram taken from thcir work (Fig. 19). This design has been improved by using a controlledtemperature gas stream. Nitrogen gas flows through a heat exchanger placed a t the bottom of the Dewar vessel with liquid nitrogen. The pressureof the gas is carefullyregulated and kept constant. It is necessary to use high-grade nitrogen, free of hydrocarbons, so as to prevent blockage. The nitrogen stream is then led via thermally insulated leads (Dewar-jacketed or enclosed in “Styrofoam”) into a chamber with an electrical heater. The electrical Keater is connected via a relay t o a temperature-sensing device near the inlet to the probe. Constant-temperature regulation of the gas stream may be achieved to within +0.2”C, with deterioration of control a t the extremes of temperature.
232
L. W. R E E V E S Collect chuck
Turbine Ground gloss joint Heated air
Teflon cup Coaxial connector
FIG.19. Vacuum-jacketedreceiver coil insert (Shoolory and Roberts, 1957).
Inlet
1:'
D
FIG.20. Dewar-jacketedN.M.R. insert (Franconi and Fraenkel, 1960).
TEMPERATURE EFFECTS O N N . M . R . SPECTRA
233
Franconi and Fraenkel(1060a) have added the feature of interchangeable inserts for different radio-frequencies (Fig. 20). Thermostatted nitrogen or air is blown over the sample via the inlet and goes out via C. A copper-constantan thermocouple is inserted at H and allowed to come within 1 cm of the receiver coil. The Dewar jacket A has a standard taper to accommodate different inserts for receiver coils. The R.F. plugs are cemented to the bottom of the Dewar container at P and G. A brass ring a t the top enables rotation of the insert coil for balancing. A teflon cup E is used as the bearing for spinning the sample tube. Pople et al. (1958) have a rather different design in which the receiver coil remains outside the Dewar jacket and use a 15-mm. standard probe insert. This method did have advantages before base-line stabilization of spectrometers became common since negligible cooling of the receiver coil occurs. It is possible to improve this design further to allow interchange of samples (Reeves and Jansen, 1964) a t any temperature. Piette and Anderson (1959) used a modification of the design of Shoolery and Roberts (1957) and have an excellent diagram of their apparatus in the paper. The temperature may also be measured by the separation between C-H and hydroxyl peaks in liquid methanol or ethylene glycol.
IV. HINDERED INTERNAL MOTIONSOF MOLECULES A. Alicyclic Ring Xystems The frequency factor and enthalpy of activation for the inversion of the chair of cyclohexane, as below, are important quantities and as a result several laboratories have pursued this problem to arrive, after some controversies, a t a solution. Cyclohexane exists in two identical chair forms which interconvert.
1(4
If we number hydrogen atoms 1 and 2 a t any carbon, their designations axial and equatorial are opposite in the two identical molecules. The inversion process can be labelled by the Larmor frequencies between which hydrogen 1 and 2 oscillate (Lemieux et al., 1958). The rate of inversion of these chair forms comes in the range accessible to N . M . R . exchange broadening studies. Jensen and Berlin (1960) first reported that line broadening occurred when a solution of cyclohexane in carbon 8*
234
L. W. R E E V E S
disulphide was cooled t o - 100°C. Few details were giveii a i d an energy barrier AG+ = 9.7 kcal/mole-l was quoted with zero entropy assumed for the activation. Jensen et al. (1962) repeated the work and based the analysis on a line separation near coalescence (Gutowsky and Holm, 1956)together with the temperature of signal coalescence (106-5°K). In this work a AG+ = 10.0 kcal mole-1 and a chemical shift of 27.3 0.p.s. a t 60 Mc/s between axial and equatorialprotons a t - 100°Cwas obtained. Examination of the symmetry of cyclohexane in the chair form shows that there are two possible chemical shifts 6, and 6, and four types of coupling constant J,,,,, J,,,,, J,,,, andJ,,,, with a 12-spin system (Corio, 1960). If the rate of interconversion between the two chairs is slow a very complicated A,$, spectrum results (Bernstein et al., 1957). The extraction of the chemical shift parameter is a very complex process in this spectrum and Jensen and coworkers (1960, 1962) merely measured the collapse of two distinguishable peaks in the low-temperature spectrum. The fact that they came out with a quoted chemical shift which agrees with later values is a coincidence. Harris and Sheppard (1961) measured the line width in the fastexchange limit, which has been shown to be a satisfactory procedure by Alexander (1962, 1963) provided second-order spectra a t lowtemperature collapse to a single sharp line at high temperature. The equation of Piette and Anderson (1959) was used and values A H + = 9.0 0.2 kcal mole-1 and ASS. = - 7.9 _+ 1 e.u. were obtained with the assumption (S,-S,) = 18.2 C.P.S. a t 40 Mc/s from the earlier study. Agreement with the first study was satisfactory and a negative entropy of activation suggested. I n order to avoid the complicated spectra with 12 spins, two sets of workers studied CGDllH, a substance which is available commercially (Anet et aZ., 1964; Bovey et aZ., 1964b). I n this molecule only one proton remains and is axial in one chair form and equatorial in the other. A simple two-site exchange process of the most elementary kind results (Gutowsky and Saika, 1953). The coupling constants J,,,,, J,,,,, J,,,, and J,,,, are now all H-D coupling and first order. These cause unresolvable splittings to occur which were removed by a strong irradiation at the deuterium resonance frequency (Bloom and Shoolery, 1955). Both of these studies of deuteriated cyclohexane are in agreement and suggest a virtually temperature-independent AG* value of 10.3-10.6 kcal mole-', AH* = 10.9 5 0.6 kcal mole-l and AX+ = 2.9 -+ 2.3 e.u. A transmission coefficient of 0-5is assumed in the inversion process. The results obtained by Harris and Sheppard (1961) have been recalculated and the values of A H + and ASS: now agree with the results on deuteriated cyclohexane. A spin-echo study by Meiboom (1962),using the Carr-Purcell method
T E M P E R A T U R E E F F E C T S ON N.11.R.
SPECTRA
235
with the approximate equation of Luz and Meiboom (1963), gives fair agreement for AGS. = 10.7 kcal molew1, A H + = 11.5 kcal mole-l and entropy of activation of + 4.0 e.u. The pulse method and steady state results show (S,-6,) = 28.7 C.P.S. at 60 Mc/s. Theoretical estimates of the height of the barrier to inversion have been made by Shoppee (1946), 9-10 kcal mole-I, and Beckett et a2. (1947), 14 kcal mole-l. A more recent theoretical estimate is that by Hendrickson (1961), 12.7 kcal mole-l. The symmetry of the intermediate boat form assumed in these calculations suggests an entropy of activation of 4.9 e.u. The diagram of Jensen et al. (1962), given as Fig. 21, is undoubtedly quite
FIG.21. Energy relationships in cyclohexaue (Jensen et al., 1962).
close to the best experimental values for the energy relationships in cyclohexane conformations. Tiers (1961) has studied the temperature-dependent fluorine N.M.R. spectra of perfluorocyclohexane in CFC1, down to - 66°C. The spectra of the separate chair forms are much simpler than in cyclohexane since for fluorine the coupling constant between geminal positions, Jgcmis large (284 & 1 c.P.s.) and I(S, - S,)l is 728 & 2 C.P.S.at 40 Mc/s. All other F-F couplings are quite small (1-5 c.P.s.). The pattern of the ABBG system a t low temperature approximates to a simple AB pattern (Bernstein eb aE., 1957). The coalescence temperature for the AB collapse is higher ( - 30" to - 40°C) and even a t room temperature there is substantial exchange broadening ( 23.9 c.P.s.). From line-width studies between 155" and 263°K Tiers has estimated dG4 = 9.9 kcal mole-I at 207°K increasing to 10.9 kcal mole-l at 298.5"K (a transmission factor 0.5 being assumed). This barrier is ident,ical at the low temperature with the value in cyclohexane. A H 4 is given as 7-5 & 0.3 kcal mole-l and ASS. = - 10.7 e.u. The last figure for the negative entropy is a firm one and surprising since it implies more ordered activat'ed state which is presumably different from the boat intermediate in cyclohexane itself.
-
-
236
L. W. R E E V E S
Inversion in cyclo-octane has been investigated by Harris and Sheppard (1961) down to - 160°K. At this temperature thereis considerable exchange broadening ( 5.8 c.P.s.). A low enthalpy of activation of 2.6 & 0.9 kcal molep1 was suggested with an abnormally large negative - 30 e.u. The conformational inversion process under study entropy is not easy to define. The conformations set out below would indicate that each separate form should contain four non-equivalent protons, which are designated by numbers. N
-
pseudo-boat
pseudo-chair
Anet and Hartman (1963) have taken proton resonance spectra of pentadecadeuteriocyclo-octanea t low temperatures (as low as 138°K) with strong irradiation a t the deuterium frequency. Only two nonequivalent protons are revealed as sharp lines chemically shifted by 18.8 C.P.S.a t 60 Mc/s. The activation parameters associated with the coalescence and subsequent exchange-narrowing at increasing temperatures are A H + = 7.7 kcal mole-l, AX+ = 4 e.u. and a coalescence temperature (T,) for the two lines of 161.7"K. Meiboom (1962) obtains a different result from spin-echo measurements on cyclo-octane itself, i.e. two activation processes are important in different temperature ranges. The results of Anet and Hartman (1963) must be regarded as definitive that only one conformational averaging process is involved in the nuclear magnetic resonance studies. The activation parameters of Anet and co-workers (Anet and Hartman, 1963; Anet et al., 1964) have been obtained from five separate considerations of the spectra, slow exchange limit,, chemical shift collapse, ratios of maximum t o minimum intensity in the intermediate region, coalescence temperature and line narrowing in the fast-exchange limit. I n both the case of deuteriated cyclohexane and cyclo-octane all rates fit an accurately linear plot of log k against the reciprocal of the absolute temperature. The existence of only two types of protons in cyclo-octane has been interpreted by Anet and Hartman (1963) as evidence for the skewed crown conformation (Dewey and Van Tamelen, 1961). The simplest modification of the six-membered alicyclic ring t o achieve two identical chair forms is the inclusion of a hetero-atom, such as 0 or S. Several of these systems have now been studied a t low temperature. Claeson et al. (1961) and Liittringhaus et aZ. (1961) observed the spectra of individual
TEMPERATURE EFFECTS O N N.M.R.
SPECTRA
237
and identical chais forms of 1,2-dithiane-4,4,5,5-d4below - 30°C. The spectrum a t low temperature ( < 238'K) is a simple AB system and the German workers who made a more thorough study from the kinetic viewpoint obtain AG* = 11.7 kcal molew1 at 225°K and estimate AX* = 0. The spectra were not decoupled from the first order H-D couplings. 1,3-Dioxan in acetone has a free energy of activation of 9.7 5 0.2 kcal mole-l (Friebolin et al., 1962). The -CH, group at the 2-position is chemically shifted to low field and gives a simple AB spectrum a t low temperature. Attempts to obtain the spectra of individual conformers of 1,4-dioxan a t low temperature have failed. It appears that this ring is more flexible and the barrier to inversion is smaller. 1,3-Dithian has been studied in carbon disulphide and the same workers report a value 9.4 5 0.3 kcal mole-l for AG+ . The present writer is aware that spectral changes do occur in pyran on cooling but the spectrum is too complicated to interpret in terms of any barrier height. NN-Dimethylpiperazine was studied by Reeves and S t r ~ m m (1961b) e and an activation energy of 13.3 kcal mole-l was reported. I n this molecule the methyl groups remain equivalent a t all temperatures so that inversion a t the 1- and 4-carbon atoms between axial and equatorial methyl groups is rapid a t all temperatures. This process involves only the interchange of methyl groups and a lone pair of electrons on the nitrogen. The ring protons have a n A,B2 spectrum a t low temperature and collapse to a single sharp line above room temperature ( +45%). Since some of the earlier measurements were made without electric shim coils, Reeves and Inglefield (1964) have repeated the work and obtained more accurate data. From a study of the fast exchange limit, using the equation of Piette and Anderson (1959), they find an activation energy 13.05 5 0.35 kcal mole-l and a n entropy activation - 9.7 e.u. The value of the activation energy, obtained by least squares, fits a plot of log ( r A v T z - 1 ) versus 1/T t o a 99-80/, correlation. At low temperatures evidence of some coupling between ring protons and the N14 spin is obtained. This is very small but sufficient to prevent accurate analysis of the ring spectrum. Perfluoropiperidine has been studied by Reeves and Wells (1962) and gives some very spectacular spectral changes on cooling. The two equivalent chair forms are shown below :
238
L. W. R E E V E S
Fluorine chemical shifts are much larger than those of protons so that the a-,/3- and y-fluorine atoms have large chemical shifts compared to piper-
idine protons. As in perfluorocyclohexane (Tiers, 1961) the geminal coupling is large and all other coupling constants small so that a t low tem-
-93°C I
-79°C -66°C I
-I
1
-46°C
I
; 1 1
t 56OC
-500
0
+500
+I000
+I500
c/sec
FIa. 22. Fluorine magnetir resonance spectra of porfluoropiperidine in CClnF soliition at a series of toniperatiires (Rrrves and Wells, 1962).
perature three separate A13 spectra for a-,/3- and y-fluorine resonances are resolved. These collapse at high temperature into three fairly narrow lines which always contain small splittings due to 1,2- and 1,3-fluorine coupling. The spectra a t various temperatures in CFCl, are illustrated in Fig. 22. The very large exchange broadening which occurs as the AB spectra collapse to a single line can be used to compute a value of dC;+ of 8.9 kcal mole-'& 207"Kand A H + = 5.7 & 1.5kcal mole-I with a large negat'ive entropy of activation, AS# = - 15.5e.u. This negative entropy
TEMPERATURE EBFECTS O N N.M.R. SPECTRA
239
is to be compared with a similar negative entropy for perfluorocyclohexane (Tiers, 1961). Large negative entropies of activation are also obtained by Brownstein (1962)in the conformational averaging of cis-, muco- and alloinositol hexa-acetates. The methyl protons in the acetate groups, which are chemically non-equivalent, have small chemical shifts (Lemieux et al., 1957). If we label the acetate groups in sequence as being axial or equatorial (la2e3a4e5a6e being contracted to ‘‘aeaeae ”) the conformational averaging in these three isomers can be designated a8
aeaeae
+ eaeaea
allo: aeaaee
+ eaeeaa
cis:
muco :aaceea + eeaaae
Tho acetate groups in the cis form a t room temperature give a single sharp resonance, while a t low temperatures two resonances occur for two types of methyl groups. The muco- and allo-methyl groups are more complex. Brownstein (1962)used several methods to obtain the rates of interconversion leading to energy barriers and entropies of activation :
cis
allo P~~UCO
AGS. (kcal mole-l) 15.4 (292°K) 12-6(240°K) 10.5 (197°K)
AX* (e.u.) - 30.1 -29.6 - 29.2
AH+ (kcal mole-l) 6.6 5-48 4.7
A second energy barrier of A H + = 20.2 & 2 kcal mole-I was suggested for the muco isomer in a different temperature region. The possible boat forms intermediates of the muco isomer were considered. The enthalpies of activation should decrease as the number of acetate groups which are required to eclipse on inverting chair to chair decreases. To obtain this number we have to ask the question, (‘How many acetate groups which are adjacent in the ring have opposite orientation, i.e. ae?” All six qualify in the cis isomer, four in the allo and only two in the muco-form. The enthalpies decrease in this order. The study of simple monosubstituted cyclohexanes is hampered by the low symmetry of the remaining 11-spin system. Reeves and Strermme (1960)and Jensen and Berlin (1960)simultaneously published results on the cyclohexyl halides. The conformational averaging at room
TABLE1 Inversion Rates and ConformationalPreferences for Six- and Eight-memberedRings. Rate quantities (kcal/mole)for chair-to-chair path unless otherwiseindicated (Bovey et al., 1964a)
Fraction equatorial form; Compound
AG:, ("K)
AH*
AS*
10.w lO.1+ 0.1 (206.3') 10.6 (206.5') 10.7 (206.5') 9.9 (206.5") 9.76 (217'-269')
-
11.5+ 2.0 9.0+ 0.2 11.5 7.5+ 0.3 9.57* 0.10
%O (4.9b; chair-to-boat) --7.9+ 1.0 4.0; chair-to-boat - 9.7, - 10.7 -0.83-t 0.50
Solvent
Cyolohexane
Perfluorocyclohexane Cyclohexyl fluoride
-
Cyclohexyl chloride
%
10.5C
-
-
-
-
%
10.85C
z 11.7C -
Cyclohexyl iodide
trans- 1,2-Dichlorocyclohexane trans- 1,2-Dibromocyclohexane trans-1,2-Chloro-iodocyolohesane trans- 1,3-Dichlorocyolohexane trans- 1,3-Dibromocyclohexane 1,l-Difluorooyclohexane cis-Inositol hexaaoetate allo-Inositol hexaacetate muco-Inositol hexaacetate
11.85" z 11.95c
%
-
9.8 (% 194') 9.9 ( % 194') 11.6 15.4 (292") 12.6 (240') 10.5 (% 197')
6.60 5.48 4.7
;
O H
-30.1 -29.6 - 29.2
Ref.
3 4
+
z 11.7c Cyclohexyl bromide
A Go (G",,-G",,)
@ M
5
0,635; 242 cal; 218" 0.667; 250 cal; 180" 0.772; 416 cal; 167°-1870 0,785; 518 cal; % 200" 0.60; 0.72; 240,610 cal; 298" 0.820; 580 cal; 169"-187" 0.769; 482 cal; z 200" 0.75; 420 cal; 192" 0.69; 458 cal; % 200° w 200 cal; 169"-195' 0.35,,-,,; % -300 cal; 149°-1880 0.29,,-,,; 0.32,,-,,; 280 cal; 180"
6
7
8 9 10
8 9
7 9 11 11 12 13 13 14 15 15 15
M
:
m
7.81 (21OO)d
Cyclo-octane
7.8 (165O)e
Perfluorooyclo-octane 1,2-Dithian-4,4,5,5-d~ 3,3,6,6-Tetramethyl-1,2-dithiane 3,3,6,6-Tetramethyl-1,2-dioxane eis-4,5-Diacetoxy-l,2-dithiane 1,3-Dioxane 5,5-Dimethyl-1,3-dioxane 2,2-Dimethyl-1,3-dioxane 1,3-Dithian 5,5-Dimethyl-1,3-dithian 2,2-Dimethyl-1,3-dithian cis-l,2-Diacetoxycyclohexane N,N'-Dimethylpiperazine Perfluoropiperidine
vinyl chloride CF3CI CS2
cs 2 cs2
CS2
acetone acetone CS2
cs2
CSa methanol CFC13
8.1
(%
162")
10.9 (% 206") 11.6 (230') 11.7 (% 225') 13.8 (271") 14.6 (285") 13.9 (x265') 9.7f 0.2 11.2f0.25 ( % 220") < 8.0 9.4+ 0.3 10.3f 0.15 9.8+ 0.2 (% - 193") 10.5 % 13.3 (% 235') 8.90 (207")
%
5.4f 0.3 %
7.0 -
11.5 15.6 17.9 12.0
-
1 2 4 + 2.0
+ 0.3d (ground-state to
14 17 18 19 19 18 20 20 20 20 20 20 20 12 21
6.7 14.6f Z -7.2 -
7.3
-
-
-
16
ZO
-
5.7+ 1.5 (207')
4
-
-
ll.2+ 2.0
4
activated complex) - 5.7e (ground-state to activated complex) - 4.4 (ground-state to ground-state) - 19
7.3 -
- 15.5
0
+ 0.5 kcal, following Harris and Sheppard (3). b Theoretical estimate, baaed on symmetry considerations; corresponds t o AH* = 11.1 kcal. c Rough estimate, subject to large error, probably a t least + 1.0 kcal. a Reported value is 9.7 kcal, and is corrected by
20Oo-25O0 K. temperature range. e 160"-170"K temperature range. f Transmission coefficient taken as
Z
d
+.
References: (1)Jensen et al., 1960; (2) Jensen et al., 1962; (3) Harris and Sheppard, 1961; (4) Meiboom, 1962; (5) Tiers, 1960; (6)Bovey et al., 1964; (7) Berlin and Jensen, 1960; (8) Reeves and Stremme, 1960; (9) Neikam and Dailey, 1963; (10) Eliel, 1959; (11)Reeves and Strffmme, 1961a; (12) Reeves and Strc~mme, m 1961h; (13) van Dort and Sekuur, 1963; (14) L. F. Thomas, unpublished; (15) Brownstein, 1962; (16)Anet and Hartman, 1963; (17) Claesonetal., 1960; w (18) Luteringhaus et aZ., 1961; (19) Claeson et a!., 1961; (20) Friebolin et al., 1962; (21) Reeves and Wells, 1962. w d Y
* 0
242
L. W. R E E V E S
temperature is weighted in favour of an equatorial halogen because of the 3,5 diaxial repulsions present when the halogen is axial.
At low temperatures ( < 218°K) separation of two complex peaks is observed for the C-1 proton. The high-field resonance is assigned to the axial proton, as in locked rings, and this is also suggested by the fact that it is broader because a larger coupling Jg,,z,contributes to the basic splittings which make up the peak. The two studies agree very well in figures for conformational preference of the halogens. These C-1 resonances are very complex and although they do appear to have a centre of gravity from the intensity point of view it is unrealistic to assign an accurate chemical shift to these peaks. One can say that (8, - 8,) 2 0.59 and 0-68 p.p.m. for chloro- and bromo-cyclohexane, respectively. The conformational preference for the halogens is best obtained from the intensity of separate H-1 peaks at low temperature and not from assumptions regarding the chemical shifts at low temperature and the time-weighted average a t room temperature. These results, together with most other work on alicyclic ring systems up to December 1963, have been summarized by Bovey et al. (1964a) whose excellent compilation is included as Table 1. I n 1,2-trans-disubstituted compounds Reeves and Strramme (1961a) have shown from low-temperature intensity measurements of the separated adjacent proton resonances that conformational preferences ee or aa are a function of the polarity of the solvent. Deuteriation of both sets of adjacent CH2 protons a t the 2- and 6-positions simplifies the appearance of the -CHX proton in cyclohexyl compounds. First-order deuterium couplings contribute to a considerable apparent line width of 3-6 C.P.S. (Allan et al., 1963; Premuzic and Reeves, 1962). At low temperature the position of the adjacent proton resonance is a reliable measurement and it has been shown, using the time-weighted average method, that the acetate, formate, trifluoroacetate and nitrate esters have the following equatorial preferences: 76%, Sly0,76% and 73% with probable errors of 5 1yo. Cyclohexyl fluoride has been carefully studied by Bovey et al. (1964a). The F19 magnetic resonance, although very complicated by the low symmetry of the coupled protons, exhibits a very large conformational
TEMPERATURE EFFECTS O N N.M.R. SPECTRA
243
chemical shift (6,-6,) = 20.5 p.p.m. as compared to the adjacent proton shift of 0.46 p.p.m. A convincing study of the line widths of the PIQ resonance with and without proton-decoupling as a function of temperature leads to dG+ = 9.76 kcal mole-I (217"-269"K), d H + 9-57kO.1 kcal mole-1 and ASS. = - 0.83 2 0.5 e.u. The equatorial preference of 63.5% compares with a figure 66.7% obtained by Jensen and Berlin (1960) for a different solvent. Arguments are presented regarding the pathways available to an inverting mono-substituted cyclohexane. An elegant study of cyclohexanol by Anet (1962) a t low temperature was made possible by remote deuteriation of the 3,3-, 4,4- and 5,5protons. The remaining protons constitute a n (AB)2Xsystem (Pople et al., 1957) which can be solved explicitly for chemical shifts and coupling constants. Sharp resonances are observed for the "X" proton adjacent to the alcohol grouping on C-1. The simple triplet, each component of which is further split into a triplet of smaller separation, can be interpreted in terms of two time-averaged coupling constants a t room temperature. The extreme values of the coupling constants can be obtained by locking the -OH group in axial or equatorial positions with 4-t-butyl groupings cis or trans. Variation of conformational preference with solvent was also investigated. At low temperature the acetate has values J,,,, = 11.43 c.P.s., J,,,, = 4.24 C.P.S. for the equatorial conformer and J e l e , zJ,,,, = 2.71 C.P.S. in the axial acetate conformer. The gauche couplings are surprisingly different and point to the danger of assumptions about their magnitude in estimating conformational preference in a time-averaged spectrum. These coupling constants are certainly sensitive to the substituent a t C-1. I n some methyl derivatives of cyclohexane very complicated spectra which change with temperature have been reported but no reliable data on either rates of inversion or conformational preference (Muller and Tosch, 1962) can be obtained. Studies of cyclohexane, cis- and transdecalin, cis- and trans-hydrindane and cis-bicyclo (3.3.0) octane over a range of temperatures have been performed by Moniz and Dixon (1961). No parameters are quoted for cyclohexane but the authors show a spectrum at 172°K (40 Mc/s) which is given as Pig. 23. cis-Hydrindane with cis-fused 5- and 6-membered alicyclic rings gives two broad resonances a t room temperature which broaden further and at 146°K merge into a single peak with unresolved fine structure. A very tentative value of dGS: = 6.4 kcal mole-I is estimated from coalescence of an assumed chemical shift of 0.55 p.p.m. cis-Decalin is also a mobile ring system and shows spectral changes with temperature. The ring junctions in trans-decalin have a strong locking effect and only -CH2groups remote from the ring fusion points will have appreciable motion. The
244
L. W. R E E V E S
spectral changes a t low temperature are marginal. It is clear that these bycyclic systems are worth study only after considerable specific deuteriation of ring protons.
1
-70
,
I
,I
I
O t
-59 -51 -42
Ho
CIS
FTC-. 23. N . M . R . apertrum of r y ~ l o h e x a n e-OO?/, in CRe at 1 7 2 O K (t,ntramethylsilann
internal reference = 0) (Moniz and Dixon, 1961).
Anet (1964) has investigated ring inversion in cycloheptatriene. The inversion process may be represented as
I
11
H6
Below 130°K the methylene protons give two non-averaged resonances separated at 123°K by 1.27 p.p.m. but still with a temperature dependence of the chemical shift, which shows that there is still interconversion of forms I and 11. By studying line widths of the methylene resonance in the fast-exchange limit, the activation energy for the inversion was found to be 6.3-t.0.5 kcal mole-I. Earlier published spectra for the resolution of distinct 7,7-methyl groups in 2-t-butyl3,7,7-trimethyltropilideneat 173°K (Conrow et al., 1963) have been used by Anet (1964) to compute dG+ = 9.2 kcal mole-I a t - 87" for a similar inversion process in this molecule.
TEMPERATURE EPBECTS O N N.M.R. SPECTRA
245
B. Substituted Ethnes The hindered rotation about the C-C bond in ethane derivatives is a periodic function of the “vicinal ” angle specified to describe the rotation. The symmetry of the periodic potential function is dependent upon the symmetry of the substitution in the ethane derivative. In most ethane derivatives the potential energy barriers to rotation are low (2-6 kcal mole-l) and rates of inter conversion between rotational isomers are too TABLE2 Proton Resonance Spectra, for Substituted Ethanes Form of spectrum Compound
Slow rotation CHs-CHz’S CH3-CH‘Xz CH3-CH’XY CHzX-CHzX CHzX-CHz’ Y CH3-CX3 CHs-CXz Y CH3-CXYZ CHzX-CHYz CHzX-CHYZ CHZU-CX~ CHzU-CXZ Y CH2U-CX Y Z CHXz-CHXz CHX2-CH Yz CHXz-CHYZ C H X Y-CHX Y (meso) CHXY-CHXY (dl) CHUV-CHX Y
ABzCz ABCz ABCD A4 (trutis) and AzBz ( p u c h e ) AzBz (tru,is) ancl ABCD ( ~ U U C / L E ) A3 ABz ABC ABz ancl AHC Three ABC Az A2 and A B Three A B TWOA2 Two A B Three A B Az and A B Three Az Six A B
Rapid rotcttion AzB3 (allJ H H equal) , AB3 (all J H H equal) , AB3 (all J H H equal) , A4 AzBz (all JEIH, not equal) AS A3 A3 ABz ABC AZ Az AB -4.21
AB AB Az Az Two A B (mixture of two isomers)
fast even a t the lowest accessible temperatures to obtain N.M.R. spectra of the distinct forms which symmetry will allow. Two methods have been used to study such compounds. It is possible to load the ethane structure with bulky groups and to restrict rotation rates by increasing the steric hindrance to rotation, thus permitting resolution of individual rotational isomers a t low temperature. Other methods depend on the fact that in an unsymmetrical ethane derivative the temperaturedependence of populations of individual rotor levels modulates both the chemical shift and the coupling constants between vicinal atoms. An
246
L. W. R E E V E S
accurate study of thc temperature dependence of chemical shifts and coupling constants should, in the absence of other effects which cause a temperature dependence, yield information on the rotational barriers. Pople (1 958a) has classified the symmetry of the nuclear spin systems of substituted ethanes which are either locked or rapidly rotating in terms of the usual rotation (Pople et al., 1957) for N.M.R. spectra, as shown in Table 2. Use of this table can be illustrated by the specific example of the molecule CHBX.CH2X. This has tlirce rotational isomers
x
X 1 gariche
H&: X
H& H X
I1 trans
Two of these rotamers are identical gauche forms 1and 111. I n the trans form the four hydrogen atoms are related by inversion through a centre of symmetry and are therefore equivalent. They give an A, spectrum. I n I and I11hydrogen atoms are either gauche of trans to an X atom. The gauche hydrogen atoms are equivalent and the trans hydrogen atoms are equivalent. The spectrum of I1 is an A2B, case. The time-averaged spectrum of all three forms is the same since each hydrogen is subject t o an identical potential function with an appropriate phase shift in the vicinal angle. An A, spectrum therefore occurs but is chemically shifted from the A, spectrum in the pure trans form. The population of gauche and trans forms is a function of temperature, the gauche form becoming more populated as the temperature increases. The time-weighted average chemical shift of the A, spectrum is therefore dependent on temperature. Table 2 is not complete if the atoms X, Y and Z have nuclear spins suitable for study for magnetic resonance methods. Considerable use of a fluorine resonance in a substituted ethane has been made in the literature, and the type of N.M.R. spectrum involved in these cases has been more adequately described by Lee and Suttcliffc (1958). If each rotational isomer is a separate species, the time-weighted average chemical shift is given by (Pople, 1958a)
, exp ( - E , / k T )+ 6, V , exp ( - E , / k T ) + a3 V 3exp ( - E 3 / k T ) a = 6, - VvI exp ( - E J W ) + v2exp-( - E , / L T )+ v3exp ( - E , / ~ T )
TEMPERATURE EFFECTS ON N.M.R. SPECTRA
247
In this expression Vl, V 2and V 3 arc partition functions for torsional vibration which can be temperature-dependent, S1, 6, and S3 are chemical E z and E , shifts of the given proton in the three separate rotamers, El, are the energies of the potential maxima from the zero point torsional levels in each separate rotamer. Coupling constants are averaged in a similar way by replacing S in equation (77) by J in order to obtain J averaging. It is possible to obtain partial averaging where two rotamers interconvert rapidly with each other but slowly with a third. In a sense partial averaging always occurs in any N.M.R. spectrum since variations in shielding due to vibrations, although small, are always averaged. Sederholm and Petrakis (1961) have claimed the measurement of a small temperature-dependent effect vibrational origin in gases. Buckingham (1962) has pointed out other factors which may contribute to this temperature dependence in gases. Pople et al. (1957) have demonstrated that the spectrum of 1-chloro-2-bromoethaneis of the AzBz type and therefore either the rotation is very rapid in this substance or the molecules exist entirely in the trans form. A gauche form gives an ABCD spectrum. Variable-temperature studies of heavily loaded ethanes CBrFz. CHBrPh, CF,Br .CHBrC1, CFzCI.CHClPh and CFzBr.CFBrC1 were completed by Drysdale and Phillips (1957). Between 0 and 200°C the gem fluorine atoms were found to be non-equivalent and not to change in chemical shift appreciably except for CFzCl.CHClPh where the chemical shift between the gem fluorine atoms decreased slightly at che highest temperatures. This was wrongly interpreted in terms of only one rotamer being stable but, as Nair and Roberts (1957) pointed out, even if there is free rotation the gem difluoro atoms will not be equivalent because of the asymmetric carbon-2. Phillips (1958) noted that on cooling CFzBr.CBr(CN)CHsto temperatures between 213°K and 173°K the resolution of spectra of separate rotamers occurred with exchange-broadening in the critical rate region. Assignment to specific rotamers was doubtful at this stage but an 700 cal was tentatively suggested for two enthalpy difference of undefined forms. CP,Br. CBr,CN in chloroform also showed exchange effects in the N.M.R. spectra at low temperature. Broadening below 248°K was finally resolved as two spectra in the region 175"K, one an AB spectrum from the two identical forms with Br atoms in trans positions and the other a single line of lower intensity for the Br-Br gauche form. Populationratios of 0.39, 0.39 and 0.22 were obtained. A careful study of CFC1Br.CFClBr between 177" and 300°K by
-
248
L. W. R E E V E S
Thompson et al. (1962) shows that the Pl0 spectra at room temperature axe consistent with superposition of the time-averaged spectra of three rotamers of two stereoisomers. These are shown below.
Br cl+;;F
Br Br&l
J3r F&: Br
Ia.
Ib
T$:; F
Jc
Br
Hr c+ll:
F& C1
Hr TIa
c1
Br
Ilk)
IIC
The isomers I and I1 are meso and dl forms which, even though rotation about the C-C bond on the N.M.R. time scale is fast, give distinct single peaks separated by 48.4& 0.2 C.P.S.at 56.4 Mc/s. At the lowest temperatures one would expect the following spectra of the six distinct molecules. I a represents case A,. I b and Ic are AX cases; IIa, I I b and IIc are distinct A, cases and should in the absence of accidental overlap give three singlets. These are all reliably assigned and the rotationally averaged spectrum a t room temperature is accounted for in terms of populations and chemical shifts of individual rotamers. The energies in the potential minima and maxima are summarized in Table 3 taken from TABLE3 Potential Energies as a Function of Rotation in CFCIBr-CFClBr (Thompson et al., 1962)
Configuration Ia Iab Ib Ibc Ic Ica
Energy (kcal/mole) 0.000
> 10.2a
0.438
> 10.2a 0.438 > 10.2a
Configuration
IIa IIab IIb IIbc IIC
IIca
Energy (kcal/mole) 0.119 9.7 0.000 > 10.2* 0.450 > 10.2b
a The energies of configurations Iab and Iac are equal. The energy of either Ieb or Ibc is equal t o 10.2 kcal/mole. b The energy of IIbc or IIac is equal to 10.2 kcal/mole.
TEM PER A TU R E EF F EC T S ON N . M . R . SPECTRA
249
this work. Gutowsky (1962) has discussed in detail the necessary conditions for magnetic non-equivalence due to molecular assymmetry and conformational preference. The conformational preference effect in averaged spectra for rotamers may be eliminated at high temperature with low barriers but in molecules with one asymmetric carbon, e.g. CF,P,Br. CFBrCl the difference between “a” and “ b ” chemical shifts persists because of an intrinsic asymmetry effect. Brey and Ramey (1963) recorded spectra of CF,Br .CFBrCl for the F19 resonance at low temperature and saw signals representative of individual rotamers. Newmark and Sederholm (1963) attacked the general problem of comparing computed coupling constants and chemical shifts from low-temperature spectra of individual rotamers with known temperature-dependent populations with those measured experimentally at high temperature in the fast-exchange limit. The agreement was only within 10% for computed and experimental coupling constants. The chemical shifts a t high temperature were also in error. This study alone casts grave doubts on the procedure widely adopted of measuring temperature-dependent chemical shifts and coupling constants in the fast-exchange limit and assigning these variations entirely t o temperature-dependent weighting of the individual rotomers. Newmark and Sederholm (1963) have shown from the low temperature spectra of CF’,Br .CFBrCl that its rotamers have energies E l = 0, E2 = 313 cal mole-I, E 3 = 746 cal molep1, and assignments are made. There is a considerable literature of temperature-dependent coupling constants in substituted ethanes. Experimentally it is just possible to record coupling constants t o within 0.01 C.P.S. and thus smallvariations over a large temperature range of even 1 C.P.S. or less are accurately amenable. The wiggle beat method, the spin-echo method and the evaluation of a many-line second-order spectrum in a region where it is very sensitive t o changes in coupling constant, all qualify as very precise measurements. It is not surprising therefore that experimental prowess has been followed sometimes by rather too enthusiastic interpretations of the origin of these small temperature effects. I n some cases, even if only 10% of the measured variation does not originate from variations in conformational averaging, then serious errors result in either the individual rotamer coupling constants and chemical shifts or the assigned energy barriers to rotation. Assumptions about the coupling constants in individual rotamers when experimental values are not known for the particular molecule under study can lead to serious discrepancies of ambiguous origin (Brey and Ramey, 1963; Karplus, 1963).
250
L. W. R E E V E S
Graham and Waugh (1957),Fessenden and Waugh (1962)and Shoolery and Crawford (1957)have all measured temperature-dependent coupling constants or chemical shifts. I n particular, the second pair of workers over found the variation of a vicinal coupling constant H1-G--C-Flg a range 233" to 373°K in CHC12.CFzClto be 0.2 C.P.S. in a total of 5.4 C.P.S. This extremely small variation was used to estimate the potential energy differences between the two forms. It is possible to invoke the use of data for rotamer populations from other techniques, such as measurement of the intensities of infrared
T (OK)
FIG.24. Tho tenqmruturc dependonce of J,, and vH in liquid CHClzCHClz (Gutowsky ct al., 1962). The chemical shift vH is upfield with respect t o the internal reference, CHC13, and was observed a t 60 Mc/s. The best-fit lines drawn through the experimental points were calculated with equation (77). The values derived from the calculations are J F H = ( + )2.01+0.08 c.P.s., J F H = ( + )16.35+0.80 c.P.s., A E = E , - E # = + 1 0 8 5 + 3 0 cal, and v," = 75.0 rf: 0.2 c.P.s., v F = 114.0+ 1.6 c.P.s., A E = + 1100+ 35 cal, from J,, and v, respectively.
bands (Sheppard and Turner, 1959; Gl~towsliyet al., 1062). This does help to test the consistency of assumptions regarding temperaturedependent values of J and 6. The additional variable of polarity of solvent a t one temperature can, with the aid of intensity measurements in infrared bands, be used to estimate values of J or 6 associated with particular rotamers in simple cases where gauche forms are identical. A typical result of these studies is taken from the work of Gutowsky et al. (1962) who measured the temperature dependence of JHccnand 6, for the molecule CHC1,. CHCI,. I n Fig. 24 the values of JHCCH and 6, a t different temperatures are compared with a theoretically calculated curve using the parameters in the figure caption. Experimental errors are shown as vertical lines. A summary of the energies for the hindered rotors obtained by these
SPECTRA
TEMPERATURE EFFECTS O N N.M.R.
251
\vorliers is given in Table 4 and compared with other values obtained by independent methods. The agreement seems to be satisfactory but, in view of the experiments of Newmark and Sederholm (1963), it is clear that N.M.R. used in this way needs the corroboration of other techniques. The temperature dependence of fluorine coupling constants in molecules of the type CP,=CPY is quite large and must have its origin in processes not connected with conformational averaging (Ramey and Brey, 1964). TABLE4 Summary of AE's Obtained in Several Ways for Some Liquid Haloethanes which have Two Equivalent gauche Forms (From Gutowsky, Belford and McMahon, 1962) Compound
AE"
Source
+
CHClz .CHClz 1050 30 cal (JHH> 1100+35
1080f40 IR. Ramd
Compound
AE"
CFCl2. CHCl2
400 f4 cal 420 & 130
CFzCl. CFClz CHClz .CHFz
495 40 350+50
(JHH> IR
Source
(JHF>' IRc
<JE> 2760 + 120 2300 300 ( k )350+ 150 (gas) IR, Ram"
* AE is defined as E,-E, where gauc7ie designates the two equivalent forms.
* From Abraham and Bernstein (1961), data re-analysed by Gutowsky et nl. (1962). ' Kagarise (1968).
'' J'angseth and Bernstein (1940); Tiagarisc and Rank (1952). Klaboc and Nielsen (19G1).
Sheppard and Turner (1959) have obtained proton-proton coupling constants between chemically equivalent protons by observing C13 side band proton resonances. Molecules such as CH,Cl. C13H2C1 have magnetically non-equivalent protons, and coupling constants JnccHcan be measured. By varying the dielectric constant of the solvent these workers were able, with the aid of additional information from the infrared spectra, to estimate coupling constants in individual rotamer forms. Abraham and Pople (19GO) measured the temperature dependence of the spin coupling constant in acetaldehyde and propionaldehyde. They were able to show that in the most stable forms the carbonyl group eclipses the methyl group in propionaldehyde and a hydrogen atom in acetaldehyde. Powles and Strange (1962)made more extensive measurements of J,, by the spin-echo method and assumed an earlier value of 1-16kcal mole-l for the energy barrier to internal rotation. Harris and Sheppard (1963) extended the use of magnetic nonequivalence introduced by the natural C13 abundance (1.1%) to
252
L. W. R E E V E S
perfluorohaloethanes. The value of d E = (Egauche - E',,,,,) was obtained from previous infrared measurements, and from averaged values of J, the extreme values Jt,,, andJgauche were computed. Some exchangebroadening was observed in CF2C1.CFzI and CF,Br.CF,Br at low temperature but resolution of individual rotamers was never complete. C. Other Intramolecular Rearrangements After the initial studies of Gutowsky and Holm (1956) on the rotation barrier in amides about the C-N bond, Phillips (1958) completed a survey of several types of molecules amenable to the N.M.R. technique. The methyl groups in NN-dimethylformamide show distinct signals at room temperature and collapse to one line on raising the temperature. This is due to the internal rotation
This type of internal rotation has now been observed in many related compounds. Nitrosamines such as the NN-dimethyl-compound have distinct signals at room temperature which show motional averaging a t high temperature
Alkyl nitrites have an inversion rate suitable for study by proton resonance R\O--N//O cis
R '0-NNo trans
I n this case the two forms of the molecule in equilibrium are not equally populated. Aldoximes have also been studied.
anti
syn
Since this early survey by Phillips (1958) many other hindered internal motions have been investigated and more precise studies made
253
T E M P E R A T U R E EEFFECTS O N N . M . R . S P E C T R A
on those mentioned already. Gutowsky and Holm (1956) estimated the barrier in NN-dimethylformamide and NN-dimethylacetamide to be 7 2 3 and 12 k 2 kcal respectively. Phillips (1958) finds the barrier in NN-dimethylnitrosamine to be 23 kcal mole-I with a frequency factor of More recent studies of NN-bis (trifluoromethyl) nitrosamine suggest that corresponding fluoro-compounds have much lower barriers to rotation (Andreades, 1962). TABLE5 Values of E,, logA, ACfas98.a and Tofor Hindered Internal Rotation about the Central C-N Bond of Some Substituted N,N-Dimethylamides as Determined by Proton Magnetic Resonance Spectroscopy ( y o = 60.000 Mc/s) (From Rogers and Woodbury, 1962)
Amide N,N-Dimethylformamide N,N-Dimethylacetamide N,N-Dimethylpropionamide N,N-Dimethyltrifluoroacetamide
Ea kcal mole-’
18.3k0.7 1 0 . 6 k .4 9.2+ .7 9.3k .6 N,N-Dimethyltrichloroacetamide 9 . 9 + . 3 N,N-Dimethylacrylamide 6 . 8 k .7 N,N-Dimethylbenzamide 7.7+ .5 N,N-Dimethylcarbamylchloride 7 . 3 k .5
log A 10.8k0.4 7.8k .2 7 . 3 + .5 6 . 8 + .4 9.1+ *2 6.0+ .5 7.2+ . 4 6 . 1 k .3
[email protected], kcal mole-l
21.0 17.4 16.7 17.6 14.9 16.1 15.3 16.5
Tc, OK 421.6 360.3 334.4 367.9 287.1 284.9 326.0
Sunners et al. (1960), Franconi and Fraenkel (196Ob), Rogers and Woodbury (1962) and Allerhand and Gutowsky (1964)have allre-studied amides. Sunners et al. (1960) have demonstrated the non-equivalence of the two NH protons in formamide by using a sample containing N15 (which has a nucleus of spin of 3). At elevated temperatures both hindered rotation about the C-N bond and proton exchange can be distinguished in different temperature ranges. I n an acetone solution containing 10 mole % of solute the barrier to rotation was determined as 18 k 3 kcal mole-l and the activation energy for proton transfer in pure liquid formamide as 10 k 3 kcal mole-l. The effect of amide structure on the rotation barrier was the object of more precise work in the study of Rogers and Woodbury (1962). Several methods for analysing the rate processes from steady-state spectra were combined. The energy barriers and frequency factors are summarized in Table 5. There is some variation in the coalescence temperature T,and the energy barriers E,. Agreement with Gutowsky and Holm (1956) for the molecule NN-dimethylacetamide is good, but
254
L. W. R E E V E S
the barrier obtained for NN-dimethylformamide is much higher than two earlier values (7 +_ 3 kcal mole-l, Gutowsky and Holm, 1956; and 9.6 2 1.5 kcal mole-l, Franconi and Fraenkel, 1960). No simple explanation can be offered for the discrepancy. Leaving aside the large value obtained for NN-dimethylformamide, the variation of E, is not greatly sensitive to electron withdrawing power of the substituent. I n perfluoroNN-dimethylacetamide, (CF3)2N.CO .CF,, non-equivalence of the fluorine resonances of the N-CF3 groups was not detected even a t the lowest temperature studied. The barrier to rotation must be considerably lower in this compound. Allerhand and Gutowsky (1964) have re-examined NN-dimethylt,richloroacetamide by the independent spin-echo method. They obtain activation parameters which are not in good agreement with previous studies or with steady-state spectral studies repeated in this work for the same molecule. The spin-echo method yields parameters E,= 14.6 2 0.6 kcal-l and log A = 12.5 2 0.4 compared with E, = 9.9 0.3 kcal mole-l and log A = 9.1 k 0.2 obtained by-Rogers and Woodbury (1962).
The origin of systematic errors between these results is at present not clear. The experiments arc not easy and any lack of care can mean errors in T 2or a saturation effect in the broad signal in the steady state method. The spin-echo method is more difficult to apply in practice. Common problems are the maintenance of a stable Carr-Purcell train of pulses at the resonant frequency in a homogeneous magnet. Unless the , on pulse lengths are first pulse has an R.F. phase shift of ~ 1 2 errors cumulative. Diffusion effects must be completely eliminated as there is danger that part of the dependence of apparent T 2on pulse interval originates from this factor. It is presumed a t this stage that different laboratories have mastered the art of temperature measurement and control a t the sample. I n any event a small difference in absolute temperature would not be serious if relative temperature measurement is good. The lack of agreement, among workers is a disturbing factor of temperature-dependent N.M.R. work a t this time and it can only be hoped that more systems will be studied carefully by both spin-echo and steady-state methods to locate the origins of the discrepancies. Allerhand and Gutowsky (1964) also report E, = 14.0 0.9 kcal molc-l and log A = 10.9 k 0-6 for the barrier in NN-dimethylcarbamyl chloride from spin-echo measurements. Observation of exchange-broadcning at, low temperature in alkyl nitrites was first reported by Pictte et nl. (1057) and by Phillips et al. (1957). A comprehensive study of nitrites by Piette and Anderson (1959)
TEMPERATURE E F F E C T S ON N.M.R.
SPECTRA
255
was followed by studies on metliyl nitrite hy Gray and Reeves (1960). At low temperature the intensities of lines due to distinct forms give the isomer ratios while the high-temperature chemical shift, regarded as a time-weighted average of these forms, extends the range of temperature over which these ratios can be measured. The results of these studies are summarized in Table 6. It is now generally agreed that the origin of these barriers is partial double-bond character in the N-0 bond about which hindered rotation occurs. TABLE 6 Results for Alkyl Nitrites (Piette and Anderson, 1959)
Compound Energy barrier to rotation E , (kcal) Transition temperature in "K Ratio cisltl-am Separationin C.P.S. between a carbon protons a t 198°K for the two isomers Shift in C.P.S. of carbon protons at 198°K Shift inc.p.s. of acarbonprotons from phenyl pealrin toluene std. at 298'K
Methyl nitrite
Ethyl nitrite
+
n-Propyl nitrite
+
Isopropyl nitrite
9.0 f2 23013 0.303
9.0 2 22713 2
9.0 2 227k3 2
6.0+ 2 233+3 16
43 1 2
43+2
43+2
3015
105 12
69+2
7.3+ 1 130 1 2
96 1 2
Grant et al. (1960) suggest that all assignments of resonance peaks t o isomers, except in methyl nitrite a t low temperature, should be reversed. These workers have measured the dielectric constants of alkyl nitrites over a range of temperatures. If this is correct, the reciprocals of the figures in Table 6 should be taken for the corresponding isomer ratios. N-Methylethyleneimines (Roberts and Bottini, 1958; Loewenstein et al., 1960) show exchange-broadening at low temperature. The exchange process may be represented aa :
The N-methyl group and the lone pair on the nitrogen interchange a t measurable rates. At low temperatures in the compound designated above this leads t o a non-equivalence of the C methyl groups and C protons. I n this compound, N-methyl-2,2-dimethylaziridine,the
256
L. W . R E E V E S
activation energy measured in the pure compound is 10 kcal mole-' and the frequency factor A = 5 x l o 7sec-l. The measurements were repeated in methanol and CCl, solution giving E, = 6.8 kcal mole-l, A = 2 x lo5 see-l and E , = 7-8kcal mole-l A = 1 x lo9 sec-l respectively. I n N-methyl-2-methyleneaziridine ;
the activation energy in the pure liquid is reported as E, = 6.4 kcal mole-l and A = 1 x log sec-l. The question of planarity of cyclobutane systems has been studied by Lambert and Roberts (1963). If two puckered conformations of cyclobutane exist then a substituent R has two possible environments, pseudo-axial and equatorial to the ring : R
k7 pseudo-axial
R
A
pseudo-equatorial
A temperature-dependent chemical shift of the PI9resonance in group R has been found in several of these related derivatives. Assuming that a simple two-site exchange process modulates the chemical shift in a very fast-exchange limit, Lambert and Roberts (1963) have estimated free energy differences between two puckered forms of 400 to 1100 cal mole-l, depending on the choice of ring substituents. Anet (1962) made careful measurements of the C13-H satellites in cyclo-octatetraene at a series of temperatures between 218'K and room temperature. The temperature-dependent charge observed is the bondjumping process indicated below :
la
11)
If C-1 is a C13 nucleus, the C13-H side band of the proton a t C-1 introduces magnetic non-equivalence and the coupling between equivalent chemical protons in the ring appears as sub-structure on these G I 3
TEMPERATURE EFFECTS ON N.M.R.
SPECTRA
257
side bands. If the double bonds are fixed, coupling to proton on C-2 gives a splitting equal approximately to the cis coupling constant in ethylene. No splitting is expected to arise from the presence of a proton on C-8 because of the expected vicinal angle (Karplus, 1959). Rapid interconversion between identical I a and I b forms causes a mean coupling of 6 C.P.S. to be seen. There are also some other long-range couplings which complicate the CI3 side bands a little. The collapse of the doublet from 11.8 C.P.S. to a more complex structure has been observed by Anet (1962). If AS* = 0 then AH* has been estimated as 13.7 kcal molep1 for this bond-jumping process. Singly-bridged biphenyl compounds (Kurland et al., 1964) show considerable changes in proton resonance spectra between 178" and 335°K. The compounds studied are described by the structure below where X is either oxygen or sulphur :
The methylene protons at position A become non-equivalent in two identical twisted conformations of the aromatic rings. The inversion between the two twisted conformations renders the methylene protons equivalent in the fast-exchange limit. Collapse of the AB spectrum a t low temperature to a single line a t high temperature yields the following parameters for the activated inversion process,
I. X = 0: E , = 9.2 k 1 kcal mole-'; AS* = 25 e.u. (189°K) 11. X = S: E , = 16-1 0.3 kcal mole-I; AS* < 2 e.u. (315°K) The configiirational stability of primary Grignard reagents can be studied by an interpretation of exchange effects in the proton resonance spectra as a function of temperature (Whitesides et al., 1963). These changes in spectra are related to the high energy barrier in heavily substituted ethanes. The molecule studied is shown below in three rotamer forms of which only two are non-equivalent.)
MgC'o: H80:Haoy ChIes
CMe3
H
H
MgCl
I
CMe3
H
Ha I1
H"
111
At room temperature, protons (a) are magnetically equivalent and give a simple triplet with 1 : 2 : 1 intensity ratios. Below 261°K the spectra of individual rotamer forms begin to resolve. It is possible to 9
258
L. W. R E E V E S
distinguish two spectra at low temperature; one a simple triplet corresponding to rotamer I and the second a complex spectrum due to identical forms I1 and 111. The dialkylmagnesium compound Mg(CH,. CH2.CMe,), undergoes a similar rotational averaging in the temperature range 300" to 383°K. At the highest temperature the CH2-group is a simple triplet. yy-Dimethylallyl magnesium bromide appears to be exceptional among allylic Grignard reagents in giving a temperature-dependent proton resonance spectrum in the range 193" to 298°K. (Whitesides et al., 1962). At room temperature the intramolecular rearrangement below is fast on the time scale of N.M.R. measurements and at 233°K spectra of the individual molecules are separately resolved in ether solution : CH3;c4 CH3
--
CH3, /CH=CH* CH3°C'MgBr
The enthalpy of activation is 7 f 3 kcal mole-l and log A = 3 to 4. An interesting example of an intramolecular rate process which has been recently studied (Lansbury, 1964)is the inversion at the methylene group of 7,12-dihydropleiadineand a similar inversion in the trans-7,12diacetate. Ha(OAc) I
7.
The inversion process interchanges pseudo-axial and pseudo-equatorial protons in the dihydrocompound. The -CH2group gives a single line at room temperature and an AB spectrum a t 238°K. The experimental results give AG* = 13.6 kcal mole-l, T, = 280°K and AS+ = - 5.7 e.u. for the dihydro-compound and AGS. = 14.5 kcal mole-', T, = 280°K and AS* = - 13.2 e.u. for the diacetate. The kinetics of oxygen migration in two compounds have been directly measured from N.M.R. measurements. The exchange process
p
TEMPERATURE EFFECTS O N
N.M.R.
SPECTRA
259
has an activation energy E, = 17.2 & 1.5 kcal mole-l (Diehl et al., 1962). Both 017and H' resonances were used in the study of this exchange reaction. Englert (1961) found an enthalpy of activation AH+ = 6 f 2 kcal mole-l in the related dibromo compound substituted at the 1-and 4-positions.
V. HYDROGEN BONDING, TAUTOMERISM AND PROTON EXCHANGE A. Hydrogen Bonding A temperature-dependent chemical shift of the -OH proton in ethanol (Packard and Arnold, 1951)was interpreted by Liddel and Ramsey (1951) as arising from a change in the average number of hydrogen bonds. The rupture of hydrogen bonds leads to a large shielding effect and the proton resonance moves to high field. The lifetime of individual hydrogen bonds is far too short in most cases to resolve separate resonance peaks for each type of hydrogen bond in a solution. A study of temperature dependence of peak positions in the fast-exchange limit has the same uncertainties associated earlier with fast-exchange limit approximations. It is possible to corroborate the N.M.R. measurements with infrared data and arrive ar either the energies of hydrogen bonds or chemical shifts associated with them. I n rarer cases of strong intramolecular hydrogen bonds the resolution of peaks for separate hydrogen-bonded species are seen. Early exploratory studies of concentration-dependent -OH chemical shifts in inert solvents (Huggins et al., 1956; Reeves and Schneider, 1957) indicated the great sensitivity of the chemical shift to hydrogen bonding. For the first time self-association in chloroform could be experimentally demonstrated and very weak associations of chloroform with rr-donors, such as olefins and aromatic compounds, produced accurately measurable chemical shift changes. Temperature-dependent chemical shifts in acetic acid (Reeves and Schneider, 195813) were found to be as high as 0.49 C.P.S.per degree in liquid acetic acid and 0.74 C.P.S.per degree in the vapour at 40 Mc/s. Total shifts of over 5 p.p.m. were recorded between liquid acetic acid a t room temperature and gaseous acetic at 573°K. Considerable shifts were reported by Schneider et al. (1958) for simple binary hydrides of the first two periods between the liquid state at low temperature and the gaseous state. As might be expected, methane and ethane showed a zero chemical shift after appropriate diamagnetic corrections (Schneider et al., 1958), but very sizeable chemical shift changes were recorded for ethylene and even
260
L. W. R E E V E S
larger ones for acetylene. At least in ethylene the shift can be dissociated from very large diamagnetic anisotropies of the molecule and indicates very considerable hydrogen-bonded self-association in the liquid state. There is now a large literature on this general subject even if the review is restricted to temperature dependence . Aselection will therefore be made of a few papers which illustrate the principles rather than give a comprehensive presentation. The origin of these large chemical shift changes is associated with the very strong electric field present along the direction of the hydrogen bond formation (Pople and Marshall, 1968). The work of Allan and Reeves (1962, 1963) illustrates the use of chemical shift measurements to obtain enthalpies of formation for both intra- and inter-molecular hydrogen bonds involving the same molecules. The measurements do not rely on infrared studies of the same systems but the thermodynamic results from the two techniques are in agreement. I n ortho-halogenophenols the equilibrium at finite concentrations in an inert solvent can be represented as two chemical equations
trans
&-trans dimer
The intramolecular process (a) amounts to hindered rotation about the C-0 bond of the phenol. It may be exclusively studied therefore by obtaining accurate chemical shifts at infhite dilution in an inert solvent at a series of temperatures. The equilibrium constant can be written
where So and 8, are chemical shifts of the -OH proton in the cis and trans forms respectively, is the measured chemical shift at infinite dilution.
TEMPERATURE EFFECTS ON N . M . R . SPECTRA
26 1
If AS for the cis -+transconveraion is reasonably assumed to be zero then the temperature-dependence of K1 is given by;
If temperature studies are made two useful equations exist between the three unknown K,, 8, and St. The value of the third unknown, a,, is obtained by extrapolating aMWto low temperature, when the equilibrium exclusively favours the cis form. Values of A H = 2356, 2141 and 1651 cal mole-l are obtained for o-chloro-, -bromo- and -iodo-phenol respectively with an error of ? 50 cal molep1. These enthalpies agree very well with those obtained by Baker (1958) from infrared band intensities. The chemical shift of the -OH proton is linearly dependent on concentration of the phenol in the range 1-4 mole yoat all temperatures studied. The variation of this linear slope with temperature can be ascribed to Kz = (where
K1
S M , is the measured chemical shift of - OH a t a finite concentration c, 8,, the chemical shift in the trans form with 6, = 0, a,, the chemical shift in the trans OH proton of the dimer, u the stoichiometric number of moles of phenol, and M , the number of moles of solvent) can be derived solely on the assumption that the chemical shift of the cis OH-pSoton in the dimer is the same as in the monomer and that (atu- 8,) = 8 p.p.m. The latter value is based on an earlier correlation of hydrogen-bonding strengths with chemical shift changes for OH-0 hydrogen bonds (Reeves et ul., 1960). The enthalpy of formation of the intermolecular hydrogen bond in the cis-truns dimer is computed as 5.6 f.0.4 kcal mole-, for all the o-halogenophenols studied. This result is of the correct magnitude and is satisfactorily independent of the phenol studied. Later studies of sterically hindered o-substituted phenols by Somers and Gutowsky (1963) a t varied concentration and temperature are consistent with this work. B. Tuutomerism Tautomerism is a combination of hydrogen-bonding and slow interor intra-molecular proton transfer. Jarrett et al. (1953) reported proton resonance spectra of acetylacetone (2,4-pentanedione) and 3-methyl2,4-pentanedione. The spectra were found to be a superposition of
262
L. W. R E E V E S
spectra of two molecules, one keto and one enol form. The rate of interconversion is too slow to average out the signals of individual forms. Intensities of peaks associated with each form can be used as a very precise measure of the keto-enol equilibrium (Grimley, 1963) and the method has great advantages over the destructive chemical methods. Reeves (1957) investigated the effects of solvents on the equilibrium in acetylacetone. The spectrum of acetylacetone is a superposition of the spectra of the two molecules below with 18.6k 0.6% of keto form at 298°K. IS 11s IS I 1v I
keto
en01
Distinct signals are seen in the N.M.R. spectrum for all groups with separate Roman numerals above. I n the enol form proton transfer between the oxygen atoms is fast on the N.M.R. time scale and the methyl groups of the enol form are equivalent. I n pure acetylacetone the temperature dependence of the intensity ratios for enol and keto - Henol = A H ) of 2705 k 100 forms gave an enthalpy change (Hketo cal mole-l. Reeves and Schneider (1958) studied solutions of acetylacetone in di- and tri-ethylamine which cause the equilibrium to shift entirely in favour of enol form. Triethylamine is a catalyst for an exchange process involving interchange of hydroxylic and olefinic protons in the enol form. The simple exchange process between two equally populated sites has an activation energy E, = 8 kcal mole-' over the temperature range 298"-374"K. I n diethylamine the hydrogenbonded complex with acetylacetone indicates fast exchange between N-H and OH protons in CC1, solution a t room temperature but a slower exchange with the olefinic proton. At 347°K a single broadened line signifies proton exchange amongst all three sites. Several other studies of tautomerism by N.M.R. methods have been made since these early studies, but no attention has been paid to temperature dependence. Forsen and Hoffman (1964) have studied the base-catalysed exchange process between enolic and olefinic protons in acetylacetone by a multiple resonance method developed from their earlier studies (Forsen and Hoffman, 1963). They have been able to show that the proton transfer occurs through a small amount of keto form. The exchange process involves three sites, keto-methylene group, the enol-hydroxyl group and the enol CH- group. The methods used show great promise for the future study of multi-site exchange processes.
TEMPERATURE EFFECTS ON N.M.R. SPECTRA
263
C. Proton Exchange Reactions The main emphasis of studies of proton transfer by means of proton resonance has been on their mechanism. Concentration- and pHdependence of rates to determine the individual order of reactions do not come within the scope of this review. I n some cases proton resonance methods have been able to solve the dual problem of mechanism and temperature dependence of individual rate. Qualitative studies of the proton exchange in pure ethanol were reported by Sohneider and Reeves (1958). The simultaneous shift t o high field and collapse of the -OH triplet was demonstrated as the temperature is raised. Connor and Loewenstein (1961) measured the activation energies for proton transfer reactions in ammonium and methyl ammonium ion solutions. Proton transfer reactions of the type R3NH++ R3N
+ RaNH++ R3N
and R3NH++HzO + NR3
+ R3N + HzO + HNR3+
(R = H or CH3 - )
have activation energies near zero. The value of AGS: is always near 5100 cal mole-l, with a large negative entropy of activation near - 20 e.u. The activation energy for the reaction NH4++ HzO -+ H3Ot
+ NH8
islarge, E, = 12.2 kcalmole-l; AGS: = 15-74kcalmole-l and AS+ - = 14 e.u. Loewenstein and Szoke (1962)measured activation energies for proton transfer reactions in water over the range 293"-353°K. The Arrhenius activation energies are 2.6 -t 0-3kcal mole-I in the acidic range and 4-8 0.5 kcal mole-l in the basic range. I n these two ranges the intermediate must be the hydronium and hydroxide ion respectively. Precise investigations of rate constants, activation parameters, and salt effects for the acid dissociation of (CH3)3NH+in aqueous solution, have been made by Grunwald (1963). The activation parameters associated with the reactions
+
+
BH+ HzO .+ B H30+
(where B is in the base) are AH+ = 11.29 kcal mole-l ASS: = 17.9 e.u. and dCS; = 80 cal moleu1 deg-l. I n two important cases where the site of protonation was in doubt N.M.R. spectra at low temperature have provided an unequivocal answer. By cooling solutions of acetamide, NN-dimethylacetamide, formamide and NN-dimethylformamide in fluorosulphuric acid to
264
L. W. R E E V E S
203"K, Gillespie and Birchall (1963) obtained proton resonance spectra of the protonated forms. The spectra can only be interpreted in terms of 0 protonation to give a >C=,-H
group. Some novel schemes for protonation of aromatic systems with protons floating in rr-electron clouds have been finally put to rest by the elegant work of MacLean and Mackor (1961). The proton exchange between the conjugate acid of the aromatic system and the acid used in the protonation can be slowed sufficiently a t -70°C if the acidic medium is an HF/BF, mixture. Proton resonance spectra can be unequivocally assigned to a non-aromatic conjugate acid of the type
HoH I.
'..,,' ,
I n this medium a t low temperature even alcohols have a Iong-lived
+
species which can be identified as containing the - OH2 group. Proton exchange among the three possible protonation sites in sites) appeared to occur without intervention mesitylene (the -&H of an acid molecule to carry the proton. The activation energy of this process has been measured ils 10 kcal mole-l. I n hexamethylbenzene the C-methyl positions are protonated and the proton jump process has the same activation energy. I n pentamethylbenzene the proton is always located on the -G-H site. Later results of MacLean and Mackor (1962) are more comprehensive. Intermolecular proton transfer via a solvent molecule has been established for mesitylene, anisole and m-xylene, but in hexamethylbenzene the transfer is always intramolecular. High activation energies of a t least 8 kcal mole-l were measured for proton transfers from the carbonium ion and this was associated with a weak interaction between )dH2
and H -ly
'CH3
groups with the solvent. The classical cyclohexenyl carbonium is asymmetric and has been eliminated by observing that the N.M.R. spectrum consists of only two types of protons even a t 213°K (Olah and Tolgyesi, 1961). It is evident
T E M P E R A T U R E E F F E C T S ON N . M . R . SPECTRA
265
that in strongly protonating media like HF/BF, and fluorosulphuric acid, which remain liquid at low temperatures, the study of individual carbonium ions and other protonated weak bases by N.M.R. offers the best method of determining structure and studying the exchange reactions. Saika (1960) determined the activation energy for exchange among -NH protons in N-methylformamide and N-methylacetamide by proton resonance methods. ( E , = 14 & 2 kcal mole-1 in each case). The rates of acid hydrolysis were also measured in a novel way to give activation energies 13 k 3 and 15 & 3 kcal mole-l respectively. The rates of exchange of BF3 among ether and alcohol complexes has been studied as a function of temperature by proton and fluorine magnetic resonance (Rutenberg et al., 1963 ; Diehl, 1958). REFERENCES Abragam, A. (1961). “Principles of Nuclear Magnetism”, Oxford University Press, London. Abraham, R. J., and Bernstein, H. J. (1961). Can. J . Chem. 39, 39. Abraham, R. J., and Pople, J. A. (1960). Mol. Phys. 3, 610. Alexander, S. (1962). J . Chem. Phys. 37, 967, 974. Alexander, S. (1963). J . Chem. Phys. 38, 1787. Allan, E. A., and Reeves, L. W. (1962). J . Phys. Chem. 66, 613. Allan, E. A., and Reeves, L. W. (1963). J . Phys. Chem. 67, 591. Allan, E. A., Premuzic, E., and Reeves, L. W. (1963). Can. J . Chem. 41, 204. Allerhand, A., and Gutowsky, H. S. (1964). J . Chem. Phys. 41, 2115. Anderson, P. W. (1954). J . Phys. SOC.Japan, 9, 316. Anderson, W. A. (1956). Phys. Rev. 102, 151. Andreades, S. (1962). J . Org. Chem. 27, 4163. Andrew, E. R. (1955). “Nuclear Magnetic Resonance”, Chapter 2, Cambridge University Press, London. Anet, F. A. L. (1962a). J . Am. Chem. SOC.84, 671. An&, F. A. L. (196213). J . Am. Chem. SOC.84, 1053. Anet, F. A. L. (1964). J . Am. Chem. SOC.86,458. Anet, F. A. L., and Hartman, J. S. (1963). J . Am. Chem. SOC.85, 1204. Anet, F. A. L., Ahmad, M., and Hall, L. D. (1964). Proc. Chem. Soc., 145. Arnold, J. T. (1956). Phys. Rev. 102, 136. Bacon, J., Gillespie, R. J., and Quail, J. W. (1963). Can. J . Chem. 41, 3063. Baker, A. W. (1958). J . Phys. Chem. 62, 744. Beckett, C. W., Pitzer, K. S., and Spitzer, R. (1947). J . Am. Chem. SOC.69, 2488. Bernstein, H. J., Pople, J. A., and Schneider, W. G. (1957). Can. J . Chem. 35,65. Bloch, F. (1946). Phys. Rev. 70, 460. Bloembergen, N. ( 1 961). Ph.D. Thesis, “Niiclear Magnetic Relaxation ”, Benjamin, New York. Bloembergen, N., Purcell, E. M., and Pound, R. V. (1948). Phys. Rev. 73, 679. Bloom, A. L., and Shoolery, J. N. (1955). Phys. Rev. 97, 1261. Bloom, M., Reeves, L. W., arid Wells, E. J. (1964). J . Chem. Phya. In press. 9*
266
L. W. R E E V E S
Bothner-By, A. A., andNaar-Colin, C. (1958). Ann. N.Y. Acad. Sci. 70, 833. Bovey, F. A., Anderson, E. W., Hood, F. P., and Kornegay, R. L. (19644. J. Chem. Phys. 40, 3099. Bovey, F. A., Hood, F. P., Anderson, E. W., and Kornegay, R. L. (1964b). Proc. Chem. SOC.146. Brey, W. S., and Ramey, K. C. (1963). J. Chem. Phys. 39,844. Brownstein, S. (1962). Can. J . Chem. 40, 870. Bruce, C. R., Norberg, R. F., and Weissman, S. I. (1956). J. Chem. Phys. 24,473. Buckingham, A. D. (1962). J. CAem. Phys.36, 3096. Carr, H. Y., and Purcell, E. M. (1952). Phys. Rev. 88, 415. Cam, H. Y., and Purcell, E. M. (1954). Phys. Rev. 94, 630. Claeson, G., Androes, G. M., and Calvin, M. (1961). J. Am. Chem. Soc. 82, 4428. 83, 560. Connor, T. M., and Loewenstein, A. (1961). J. Am. Chem. SOC. Conrow, K., Howden, M. E. H., and Davis, D. (1963). J. Am. Chem. SOC.85,1929. Corio, P. L. (1960). Chem. Revs. 363. Dewey, R. S., and Van Tamelen (1961). J. Am. Chem. SOC.83, 3729. Diehl, P. (1958). Helv. Phys. Acta 31, 685. Diehl, P., Christ, H. A., and Mallory, F. A. (1962). Helv. Chim. Acta. 45, 504. Drysdale, J. J., andPhillips, W. D. (1957). J. Am. Chem. SOC.79, 319. Eliel, E. L. (1959), Chem. & Ind. 568. Englert, G. (1961). 2. Elektrochem. 65, 854. Fano, U. (1957). Rev. Mod. Phys., 29, 74. Fessenden, R. W., and Waugh, J. S. (1962). J. Chem. Phy6.37, 1466. ForsBn, S., and Hoffman, R. A. (1963). J . Chem. Phys. 39,2892. ForsBn, S., and Hoffman, R. A. (1964). J. Chem. Phys. 40, 1189. Franconi, C., and Fraenkel, G. (1960a). Rev. Sci. Instr. 31, 657. Franconi, C., and Fraenkel, G. (1960b). J. A m . Chem. Xoc. 82,4478. Freeman, R. (1960). Mod. Phys. 3,435. Freeman, R., and Anderson, W. A. (1962). J. Chem. Phys. 37, 8 5 ; I b d , 2053. Friebolin, H., Kabuss, S., Maier, W., and Luttringhaus, A. (1962). Tetrahedron Letters, 683. Gillespie, R. J., and Birchall, T. (1963). Can. J . Chem. 41, 148. Giuliano, C. R., and McConnell, H. M. (1959). J. Inorg. & Nuclear Chtm. 9, 171. Golay, M. J. E. (1958). Rev. Sci. Inst. 29, 313. Graham, D. M., and Waugh, J. 8. (1957). J. Chem. Phys. 27, 468. Grant, R. F., Davidson, D. W., and Gray, P. (1960). J. Chem. Phys. 33, 1712. Gray, P., and Reeves, L. W. (1960). J. Chem. Phys. 32, 1878. Grimley, T. B. (1963). MoZ. Phys. 6 , 329. Grunwald, E. (1963). J. Phys. Chem. 67, 2208; Ibid. 2211. Grunwald, E., Loewenstein, A., and Meiboom, S. (1957). J. Chem. Phys. 27, 630. Gutowsky, H. S. (1962). J. Chem. Phys. 37,2196. Gutowsky, H. S., and Holm, C. H. (1956). J. Chem. Phys. 25, 1228. Gutowsky, H. S., and McCall D. W. (1951) . Phys. Rev. 82, 748. Gutowsky, H. S., and Saika, A. (1953). J. Chem. Phys. 21, 1688. Gutowsky, H. S., McCall, D. W., and Slichter, C. P. (1953). J . Chem. Phys. 21,279. Gutowsky, H. S., Belford, G. G., and McMahon, P. F. (1962). J. Chem. Phys. 36, 3353. Hahn, E. L. (1950). Phys. Rev. 80, 580. Hahn, E. L., andMaxwell, D. E. (1951). Phys. Rev. 84, 1245. Hahn, E. L., and Maxwell, D. E. (1952). Phys. Rev. 88, 1070. Harris, R. K., and Sheppard, N. (1961). Proc. Chem. SOC.418. Harris, R. K., and Sheppard, N. (1963). Trans. Faraduy SOC.59, 606. Hay, G. F. (1953). “Vector and Tensor Analysis”, Dover, New York, 86.
T E M P E R A T U R E E F F E C T S ON N.M.R.
SPECTRA
2 67
Hendrickson, J. B. (1961). J . Am. Chem. SOC.83,4537. Huggins, C. M., Pimentel, J. C.,andShoolery, J. N. (1956). J . Phys. Chem.60,1311. Inglefield, P. G., and Reeves, L. W. (1964). Unpublished work. Jacobssohn, B. A., and Wangsness, R. K. (1948). Phys. Rev. 97, 630. Jarrett, H. S., Sadler, M. S., and Shoolery, J. N. (1953). J . Chem. Phys. 21, 2092. Jensen, F. R., and Berlin, A. J. (1960). Chem. & I n d . 998. Jensen, F. R., Noyce, D. S., Sederholm,C. M., and Berlin, A. J. (1962). J . Am. Chem ; Chem. SOC.84, 386. Kagarise, R. E. (1958). J . Chem. Phys. 29,680. Kagarise, R. E., and Rank, D. H. (1952). Trans. Faraday Soc. 48, 394. Kaiser, R. (1960). Rev. Sci. Instr. 31, 963. Kaplan, J. I. (1958). J . Chem. Phys. 28, 278; Ibid. 29, 462. Karplus, M. (1959). J . Chem. Phgs. 30, 11. Karplus, M. (1963). J . Am. Chem. SOC.85, 2870. Klaboe, P., and Nielsen, J. R. (1961). J . MoZ. Specfroscopy,6,379. Kubo, R. (1954). J . Phys. SOC.Japan, 9,935. Kubo, R., and Tomita, K. (1964). J . Phys. SOC.Japan, 9, 888. Kurland, R. J., Rubin, M. B., and Wise, W. B. (1964). J. Chem. Phys. 40,2426. Lambart, J. B., and Roberts, J. D. (1963). J . Am. Chem. Soc. 85, 3710. Langseth, A., and Bernstein, H. J. (1940). J . Chem. Phys. 8, 410. Lansbury, P. T. (1964). J . Am. Chem. Soc. 86, 2524. Lee, J., and Sutcliffe, L. H. (1968). Trans. Paraday Soc. 54,308. Lemieux, R. U., Kullnig, R. K., Bernstein, H. J., and Schneider, W. G. (1957). J . Am. Chem. SOC.79, 1005. Lemieux, R. U., Kullnig, R. K., Bernstein, H. J., and Schneider, W. G. (1958). J . Am. Chem. SOC. 80, 6008. Liddel, U., and Ramsey, N. F. (1951). J. Chem. Phys. 19, 1608. Loewenstein, A., and Connor, T. M. (1963). Ber. Bunsenges. fur Phys. Chem. 67, 280. Loewenstein, A., and Meiboom, S. (1957). J. Chem. Phys. 27, 1067. Loewenstein, A., and Szoke, A. (1962). J . Am. Chem. SOC.84, 1151. Loewenstein, A., Neumer, J. F., and Roberts, J. D. (1960). J . Am. Chem. SOC. 82, 3599. Luttringhaus, A., Kabuss, S., Maier, W., and Friebolin, H. (1961). 2.Naturforsch. 16B. 761. Luz, Z . , and Meiboom, S. (1963). J . Chem. Phys. 39, 366. McConnell, H. M. (1958). J. Chem. Phys. 28,430. McConnell, H . M., and Thompson, D. D. (1957). J. Chem. Phys. 26, 958. McConnell, H. M., and Thompson, D. D. (1959). J . Chem. Phys. 31, 85. McConnell, H. M., and Weaver, H. E. (1956). J . Chem. Phys. 25, 307. MacLean, C., and Mackor, E. L. (1961). J . Chem. Phys. 34, 2207; Ibid. 2308. MacLean, C., and Mackor, E. L. (1962). Discussions Faraday Soc. 34,165. Masuda, Y., and Kanda, T. (1954). J . Phys. SOC.Japan, 9, 82. Meiboom, S. (1961). J . Chem. Phys. 34,375. Meiboom, S . (1962). “A.C.S. Symposium on High Resolution N. M. R.”, Boulder, Colo. Meiboom, S., Luz, Z., and Gill, D. (1957). J . Chem. Phys. 27, 1411. Moniz, W. B., and Dixon, J. A. (1961). J . Am. Chem. SOC.83, 1671. Moniz, W. B., and Gutowsky, H. S. (1963). J . Chem. Phys. 38, 1165. Muetterties, E. L., and Packer, K. J. (1963). J . Am. Chem. SOC.85, 3035. Muller, B., and Bloom, M. (1960). Can. J . Phys. 38, 318.
268
L. W. R E E V E S
Muller, N., and Tosch, W. C. (1962). J. Chem. Phys. 37, 1167. Myers, 0. E., and Sheppard, J. C. (1961). J. A m . Chem. SOC.83,4739. Nair, P. M., and Roberts, J. D. (1957). J. Am. Chem. SOC.79, 4565. Neikam, W. C., and Dailey, B. P. (1963). J. Chem. Phys. 38,445. Newmark, R. A., and Sederholm, C. M. (1963). J. Chem. Phys. 39, 3131. Olah, G. A., and Tolgyesi, W. S. (1961). J. A m . Chem. SOC.83, 5031. Packard, M. E., and Arnold, J. T. (1951). Phys. Rev. 83, 210. Phillips, W. D. (1955). J. Chem. Phys. 23, 1363. Phillips, W. D. (1958). Ann. N.Y. Acad. Sci. 70, 817. Phillips, W. D., Looney, C. E., and Spaeth, C. P. (1957). J. MoZ. Spect. 1, 35. Piette, L., and Anderson, W. A. (1959). J. Chem. Phys. 30, 899. Piette, L., Ray, J. D., and Ogg, R. A. (1957). J. Chem. Phys. 26, 1341. Pople, J. A. (195th). MoZ. Phys. 1, 1. Pople, J. A. (1958b). MoZ. Phys. 1, 168. Pople, J. A., and Marshall, T. W. (1958). MoZ. Phys. 1, 199. Pople, J. A., Schneider, W. G., and Bernstein, H. J. (1957). Can. J. Chem. 35,1060. Pople, J. A., Schneider, W. G., andBernstein, H. J. (1958). J. Chem. Phys. 28,601. Pople, J. A., Schneider, W. G., and Bernstein, H. J. (1959). “High Resolution Nuclear Magnetic Resonance ”, McGraw Hill, New York. Powles J. G., and Hartland, A. (1960). BUZZ.Amp. 9,474. Powles, J. G., and Strange, J. H. (1962). Discussions Faraduy SOC.34, 30; MoZ. Phys. 5, 329. Powles, J. G., and Strange, J. H. (1964). MoE. P l ~ y s8, . 169. Premuzic, E., and Reeves, L. W. (1962). Can. J. Chem. 40,1870. Proctor, W. G., andYu, F. C. (1950). Phys. Rev. 77, 717. Ramey, K. C., and Brey, W. S. (1964). J. Chem. Phys. 40, 2349. Reeves, L. W. (1957). Can. J. Chem. 35, 1351. Reeves, L. W., and Jansen, W. (1964). Unpublished results. Reeves, L. W., and Schneider, W. G. (1957). Can. J. Chem. 35, 251. Reeves, L. W., and Schneider, W. G. (1958a). Can. J. Chem. 36, 793. Reeves, L. W., and Schneider, W. G. (1958b). Trans. Faraday SOC.54, 314. Reeves, L. W., and Strermme, K. 0. (1960). C m . J. Chem. 38,1241. Reeves, L. W., and Strsmme, K. 0. (1961a). Trans. Faraduy SOC.57,390. Reeves, L. W., and Strsmme, K. 0. (1961b). J. Chem. Phys. 34, 1711. Reeves, L. W., and Wells, E. J. (1962). Discussions Faraday SOC.34. Reeves, L. W., Allan, E. A., and Stremme, K. 0. (1960). Can. J. Chem. 38, 1249. Reilly, C . A. (1956). J. Chem. Phys. 25, 604. Roberts, J. D., and Bottini, A. T. (1958). J. Am. Chem. SOC.80, 5203. Rogers, M. T., and Woodbury, J. C. (1962). J. Phys. Chem. 66, 540. Rutenberg,A. C., Palko, A. A., andDrury, J. S. (1963). J.Am. Chem. SOC. 85,2702. Sack, R. A. (1958). Mol. Phys. 1, 163. Saika, A. (1960). J. A m . Chem. SOC.82, 3540. Schneider, W. G., Bernstein, H. J.,and Pople, J.A. (1958). J. Chem.Phys.28,605. Schneider, W. G., and Reeves, L. W. (1958). Ann. N. Y. Acad. Sci. 70, 858. Sederholm, C. M., and Petrakis, L. (1961). J. Chem. Phys. 35, 1174. Sheppard, N., and Turner, J. J., (1959). Proc. Roy. SOC.A252, 506. Shoolery, J. N., and Crawford, B. L. (1957). J. MoZ. Spec. 1,270. Shoolery, J. N., and Roberts, J. D., (1957). Rev. Sci. Inet. 28, 61. Shoppee, C. W. (1946). J. Chem. Soc. 1138. Solomon, I. (1959). Comptes Rendus 248, 92; Ibid. 249, 1631. Somers, B. G., and Gutowsky, H. S. (1963). J. Am. Chem. SOC.85,3065.
Tl3MPEBATURE EBYNCTS ON N.M.R.
SPECTRA
2 ti!)
Sunners, B., Piette, L. H., and Schneider, W. G. (1960). Can. J . Chem. 38, 681. Szoke, A., and Meiboom, S. (1959). Phys. Rev. 113, 585. Thompson, D. S., Newmark, R. A., and Sederholm, C. M. (1962). J . Chem. Pbys. 37,411. Tiers, G. V. D. (1961). Proc. Chern. SOC. 389. Tiers, G. V. D. (1964). Private Communication. 847. Turner, 0. W. (1962). J . Chern. SOC. van Dort H. M., and Sekuur, T. J. (1963). Tetrahedron Letters, 683. Varian Associates (1946). “N. M. R. Table”, 4th Edn. Available from Varim Associates, Palo Alto, California. Varian Associates (1960). “N. M. R. and E. P. R. Spectroscopy”. Porgamon Press, Oxford. Weizmann Institute of Science, Rehovoth, Israel. (1960). “Tables of ExchangeBroadened N. M. R. Multiplets.” Whitesides, G. M., Nordlander, J. F., and Roberts, J. D. (1962). Discussions Paraday SOC.34, 189. Whitesides, G. M., Kaplan, F., and Roberts, J. D. (1963). J . Am. C?kern. SOC.85, 2167. Woessner, D. E. (1961). J . Chem. Phys. 35, 41.
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AUTHOR INDEX Numbers i n itulics refer to the pages
01%
which references ure listed at the end of each articlc.
A Abragam, A., 215, 265 Abraham, R. J., 251, 265 Abrahams, S. C., 63, 79 Adams, N. G., 39, 84 Adler, E., 156, 183 Agius, P. J., 95, 96, 98, 120 Ahmad, M., 234,236, 265 Aleksankin,M. M., 148, 153, 154, 156, 169, 170, 171, 183 Alexander, S., 214, 215, 234, 265 Allais, M. L., 76, 79 Allan, E. A., 242, 260, 261, 265, 268 Allen, A. D., 175, 183 Allerhand, A,, 221, 253, 254, 265 Anderson, E. W., 234, 241, 242, 266 Anderson, P. W., 214, 265 Anderson, R. B., 96, 101, 120 Anderson, W. A., 200, 220, 224, 231, 233, 237, 254,265, 266, 268 Andreades, S., 253, 265 Andrew, E. R., 188, 190, 191, 193, 194, 195,265 Androes, G. M., 236, 241, 266 Anet, F. A. L., 234,236,241,243,244, 256, 257, 265 Applequist, J. B., 76, 79 Arai, T., 52, 79 Armstrong, R. S., 47, 48, 50, 59, 62, 65, 66, 67, 68, 74, 79 Arnold, J. T., 205, 211, 259, 265, 268 Aroney, J. J., 48, 65, 66, 67, 68, 74, 79 Aroney, M. J., 20, 47, 50, 56, 57, 58, 59, 60, 61, 62, 65, 67, 78, 79, 80 Arshid, F. M., 39, 80 Ashida, T., 63, 80 Auwers, K. von, 2, 5, 7, 15, 29, 30, 38, 80
B Backer, H. J., 11, 80 Bacon, G. E., 63, 80 Bacon, J., 228, 265 Badoz, J., 46, 80 Bagley, F. D., 101, 113, 122 Baker, A. W., 261, 265
Bamkole, T., 99, 120 Banigan, T. F., 15, 84 Banthorpe, D. V., 111, 120 Barnard, J. A., 117, 120 Barton, D. H. R., 54, 55, 80, 97, 98, 99, 101,111,120 Batterham, T. J., 147, 185 Bauer, S. H., 17, 80 Bauer, N., 1, 38, 39, 80 Beams, J. W., 70, 75, 80 Becker, G., 73, 80 Beckett, C. W., 235, 265 Beecher, L., 34, 80 Belford, G. G., 190, 250, 251, 266 Bell, R. P., 152, 183 Bellamy, L. J., 33, 34, 80 Bender, M. L., 149, 158, 159, 160, 162, 163, 164, 166, 167, 168, 170, 171, 172, 183 Benoit, H., 76, 80 Benson, S. W., 101, 120 Bentley, R., 169, 183 Bergmann, K., 76, 80 Berlin, A. J., 233, 234, 235, 239, 241, 243, 267 Bernstein, H. J., 188, 189, 192, 202, 223, 233, 234, 235, 239, 243, 246, 247, 251, 253, 259, 265, 267, 268, Bhagavantam, S., 41, 66, 70, 75, 78,80 Bicknell, R. C., 99, 110, 120 Biechler, S. S., 164, 166, 183 Bielenberg, W., 38, 81 Biemann, K., 127,151,183 Birchall, T., 264, 266 Bird, R. B., 54, 81 Blades, A. T., 95, 96, 100, 101, 109, 114, 120,121 Bloch, F., 190, 191, 193, 226, 265 Bloembergen, N., 194,214,265 Bloom, A. L., 234, 265 Bloom, M., 216,217,221, 234,265,267 Blumcke, A., 16, 83 Blunck, F. H., 116, 121 Blythe, A. R., 72, 81 Bode, H., 24, 81 Bolton, H. C., 49, 52, 53, 81 Bonnecke, 2, 80 Born, M., 22, 24, 68, 81
272
AUTHOR 1 N D P X
Bose, A. N., 101, 117, 120, 121 Bothner-By, A. A., 77, 81, 175, 183, 188, 266 Bottcher, C. J. F., 3, 22, 23, 35, 36, 53, 69, 81 Bottini, A. T., 255, 268 Bovey, F. A., 234,241, 242, 266 Bowen, E. J., 75, 81 Boyd, R. H., 126, 130, 139, 140, 183 Bragg, W. L., 78, 81 Bramley, R., 33, 48, 50, 52, 57, 60, 81 Branch, G. E. K., 71, 81 Branch, R. F., 34, 80 Braude, E. A., 52, 75, 81 Brearley, D., 94, 99, 121 Breazeale, W. M., 65, 81 Bredig, M. A., 20, 81 Brewster, J. H., 75, 81 Brey, W. S., 249, 251, 266, 268 Bridge, M. R., 114, 121 Brodskii, A. I., 148, 169, 170, 171, 183 Brown, R. F., 51, 81 Brown, W. G., 128, 147, 18G Brownstein, S., 239, 241, 266 Bruce, C. R., 226, 266 Bruce, C. W., 52, 81 Briihl, J. W., 2,4, 5, 7, 35, 37, 81 Buckingham, A. D., 46, 67, 68, 69, 71, 72, 74, 75, 77, 78, 81, 82, 247, 266 Buckingham, P. D., 124,183 Buckley, F., 17, 82 Bufalini, M., 156, 184 Bunn, C. W., 49, 78, 82 Bunnett, J. F., 133, 185 Bunton, C. A., 115,121, 129, 130, 131, 132, 133, 134, 138, 140, 142, 144, 159, 160, 164, 166, 167, 169, 171, 173, 176, 178, 179,121,183,184
C Cabannes, J., 66, 82 Cady, G. H., 17, 82 Calderbank, K. E., 8, 82 Calhoun, A., 166,184 Calvin, M., 71, 81, 236, 241, 266 Campbell, K. N., 5, 6, 16, 82 Capon, N., 94,99,121 Carlisle, C. H., 56, 82 Carr, H. Y., 216, 217, 266 Carr, M. D., 131, 142,183 Carter, J. H., 171, 173, 184 Ceuterick, P., 11, 82 Chang, Shu-Sing, 57, 58, 79 Chantry, 0. W., 49, 82 Charney, E., 82
Chau, J. Y. H., 66, 82 Chaumont, L., 70, 82 Chen, C.-Y., 45, 56, 58, 60, 61, 80, 82 Chen, M. C., 160, 166, 167,183 Chia, L. H. L., 61, 62, 79, 80 Chmiel, C. T., 172, 184 Christ, H. A., 259, 266 Christman, D. R., 126, 130, 139, 140, 180, 181,184 Claeson, G., 236, 241, 266 Clark, C. H. D., 26, 82 Clippinger, E., 132, 186 Cohn, M., 147, 157,184 Cole, R. H., 73, 82 Comyns,A. E., 132,166, 167,169,183 Connick, R.E., 184 Connor,T. M., 163,185,197,200,213.263, 266, 267 Conrow, K., 244, 266 Coop, I. E., 45, 67, 82 Corfield, M. G., 58, 60, 78, 79 Corio, P. L., 234, 266 Cornish, R. E., 123, 185 Corry, J. E., 32, 82 Cotton, A., 75, 82 Coulson, C. A., 69, 70, 73, 82 Cowan, D. M., 8,82 Crawford, B. L., 250, 268 Crawford, M. J., 75, 82 Cresswell, W. T., 8,10,12, 13,14, 15,17,20, 27, 82, 83 Crowell, T. I., 101, 122 Crowfoot, D., 56, 82 Cureton, P. H., 60, 61, 65. 82 Curl, R. F., 63, 82 Curran, C., 33, 82 Curry, N. A., 63, 80 Curtiss, C. F., 54, 81 Cuthbertson, C., 20, 22, 82 Cuthbertson, J., 20, 22, 82
D L)ahri, H., 148, 151, 181, 181 Dailey, €3. P., 241, 268 Dale, T. P., 2, 4, 84 Dalgarno, A., 42, 83 Damkohler, G., 20, 83 Daniels, F., 92, 121 Das, T. P., 26, 83 Datta, S. C., 157, 184 Daubeney, R. de P., 49, 78,82 Davidson, D. W., 255,266 Davies, P. L., 52,83 Davis, D., 244,266 Davis, R. E., 179, 184
AUTHOR INDEX Day, J. N. E., 157,184 De Boer, J. H., 75, 83 Debye, P., 39, 41, 68, 69, 78, 83 de la Mare, P. B. D., 179, 183 De Malleman, R., 75, 83 Denbigh, K. G., 8, 10, 11, 13, 17, 26, 31, 48, 52, 83 Denney, D. B., 179,184 Depuy,C. H., 101, 111, 114, 115, 116,121 Dewey, R. S., 159, 166, 170, 171, 172, 183, 236, 266 Diehl, P., 259, 265, 266 Dierkesmann, A., 74, 83 Dilgren, R. E., 135, 136, 184 Disch, R. L., 77, 81 Dixon, J. A., 243, 244, 267 Djerassi, C., 76, 83 Dostrovsky, I., 124, 129, 130, 139. 140, 143, 144, 177,184 Downs, J., 178, 184 Dows, D. A., 74,81 Drechsler, M., 26, 83 Drury, J. S., 265, 268 Drysdale, J. J., 247, 266 Dunbar, W. S., 32, 83
E Eaborn, C., 175, 184 Eckert, J. M., 54, 55, 56, 57, 61, 76, 8.1 Edsall, J. T., 78, 83 Edser, E., 34, 83 Egloff, G. 2, 83 Eisenlohr, F., 5, 8, 29, 30, 37, 38, 80, 83 Eliel, E. L., 241, 266 Emovon, E.U., 101, 112, 113, 116,121 Englert, G., 259, 266 Evans, A. G., 119,121 Evans, D. P., 11, 20, 83 Everett, D. H., 72, 83 Eversole, W. G., 96, 122 Eveslage, S. L., 5, 6, 15, 82 Eykman, J. K., 3, 5, 7, 83
F Failes, R. L., 117, 118, 121 Fainberg, A. H., 132, 186 Fajsns, K., 1, 6, 8, 11, 20, 22, 23, 24, 38, 39, 80, 83 Falkehag, I., 156, 183 Fano, U., 215, 266 Farquharson, J., 40, 83 Feher, F., 16, 83 Fesenko, V. V., 144, 145, 146, 156, 184
273
Fessenden, R. W., 250, 266 Fiat, D. N., 156, 184, 186 Field, J. A., 76, 84 Fiocco, G., 78, 84 Fisher, L. R., 50, 62, 79 Flett, M. St. C., 34, 84 Forse, G. R., 124, 183 F o r s h , S., 224, 225, 226,262, 266 Fraenkel, G., 232, 233, 253, 254, 266 Franconi, C., 232, 233, 253, 254, 266 Freeman, R., 224,266 Frei, Y. F., 144, 183 Friebolin, H., 236, 237, 241, 266, 267 Friedman, L., 175, 183 Froemsdorf, D. H., 114,121 Fry,A., 143, 151, 156,184, 18C Fugassi, P., 101, 122 Fukumoto, T., 180, 185 Fuson, N., 34, 84
G Gans, R., 53, 55, 77, 84 Geffcken, W., 20, 84 Gensler, W. J., 181,184 Ghosh, B. N., 92, 122 Ghosh, S. N., 31, 84 Gildemeister, E., 7, 84 Gilderson, P. W., 114,121 Giles, C. H., 39, 80 Gill, D., 204, 205, 267 Gillespie, R. J., 228, 264, 265, 266 Gillis, R. G., 15, 16, 26, 30, 31, 84 Ginger, R. D., 158, 159, 161, 183 Giuliano, C. R., 227,266 Gladisch, H., 69, 84 Gladstone, G., 16, 84 Gladstone, J. H., 2, 4, l G , 37, 84 Glasstone, S., 75, 84 Goering, H. L., 131, 135, 136, 184 Golay, M. J. E., 231, 266 Gold, V., 162, 184 Goldschmidt, H., 20, 84 Good, P. T., 97, 100, 109,121 Gooding, R. M., 39,84 Gordon, E., 101,121 Gordy, W., 31, 84 Goss, F. R., 26, 84 Goto, K., 153, 184 Goulden, J. D. S., 34, 84 Graff, C., 153,185 Gragerov, I. P., 144, 145, 146, 148, 153, 154, 168, 169, 170, 171, 173, 176, 180, 181,183,184 Graham, D. M., 250, 266
274
AUTHOR I N D E X
Graham, J., 132, 166, 167, 169, I83 Granger, M. R., 151, 186 Grant, R. F., 255, 266 Gray, P., 255,266 Green, J. H. S., 100, 103, 121 Green, M., 179, 184 Greenzaid, P., 169, 184 Griffiths, D. C., 11, 20, 83 Grimley, T. B., 262, 266 Groth, P., 63, 84 Griin, F., 78, 84 Grunwald, E., 126, 129, 130, 132, 133, 134, 135, 136, 184, 205, 206, 207, 208, 209, 263, 266 Grzeskowiak, R., 8, 14, 84 Gulwell, T., 11, 20, 83 Gundermann, H., 69, 84 Gustafsson, C., 166, 184 Gutowsky, H. S., 188, 190, 196, 197, 199, 201, 202, 203, 205, 210, 211, 218, 221, 224, 227, 234, 249, 250, 251, 252, 253, 254,261,265,266, 26r,269 Guy, J., 26, 84
H Haake, P. C., 178, 184 Hacket, N., 65, 84 Hadwick, T., 140,184 Hahn, E. L., 192, 196, 215, 216, 223, 266 Halevi, E. A., 176, 183 Halford, R. S., 82 Hall, L. D., 234, 236, 265 Hallam, H. E., 75, 84 Halmann, M., 176,184 Halpern, M., 153, 185 Hamilton, G. A., 127, 148, 185 Hammerle, W. G., 76, 84 Hammett, L. P., 166, 185 Harden, G. D., 98,99, 100, 103,121 Harder, A., 25, 84 Harrand, M., 26, 84 Harris, R. K., 234, 236, 241, 251, 266 Hartland, A., 223, 268 Hartman, J. A. S., 236, 241, 265 Hartshorne, N. H., 78, 84 Hassan, A. S. A., 39, 80 Hassel, O., 63, 84 Havelock, T. H., 73, 84 Hay, G. F., 191, 266 Head, A. J., 99, 101, 111, 120 Hearne, M. R., 65, 84 Heck, R., 132,186
Heigl, A., 4, 21, 84 Heisenberg, W., 22, 24, 81 Heller, A., 126, 129, 130, 132, 133, 134, 135, 136,184 Henderson, R. B., 131, 134, 183 Hendrickson, J. B., 235, 267 Henkel, E., 26, 83 Henne, A. L., 17, 84 Hennion, G. F., 15, 84 Henrich, F., 29, 84 Herbert, J. B. M., 152, 168, 185 Herndon, W. C., 110, 121 Heydtmann, H., 99,121 Heydweiller, A., 20, 22, 85 Highet, R. J., 147, 185 Hine, J., 71, 85 Hinkamp, J. B., 17, 84 Hinshelwood, C. N., 94, 117, 121, 122 Hirokawa, S., 63, 80 Hirsch, T. V., 20, 81 Hirschfelder, J. O., 54, 81 Hoering, T. C., 126, 185 Hoffman, F. R., 7, 84 Hoffman, R. A., 224, 225, 226, 262, 266 Holemann, P., 20, 84 Holm, C. H., 196, 197, 199, 201, 202, 203, 205, 218, 234, 252, 253, 254, 266 Holmes, J. L., 93, 101, 121 Hood, F. P., 234, 241, 242, 266 Hootman, J. A., 70, 85 Horwood, J. E., 16, 84 Hosoya, S., 63,85 Howden, M. E. H., 244, 266 Howlett, K. E., 97, 99, 120, 121 Huffman, J. R., 123, 186 Huggins, C. M., 259, 267 Huggins, M. L., 6, 85 Hughes, E. C., 8, 85 Hughes, E. D., 144, 184 Hughes, T. P., 78, 85 Hunter, E. C. E., 31, 85 Hunter, J. S., 30, 85 Hurd, C. D., 116, 121 Hurd, D. T., 16, 88
I Ingersoll, L. R., 74, 85 Inglefield, P. G., 237, 267 Ingold, C. K., 25, 28, 49, 64, 65, 71, 75, 85, 121, 144, 152, 157, 184, 185 Ingram, P., 76, 85 Ishiguro, E., 52, 79 Itzhaki, R. F., 761, 85 Izsak, D., 57, 59, 79
275
AUTHOR I N D E X
J Jackman, L. M., 77, 85 Jackson, J. A., 126, 185 Jacobssohn, B. A., 229,267 Jain, S. K., 39, 80 James, D. H., 169, 170, 171, 184 Jansen, W., 233, 268 Jarrett, H. S., 261. 267 Jeffery, G. H., 8, 10, 13, 14, 15, 17, 20, 27, 82, 84, 85, 86 Jeffrey, D. A., 130, 144, 185 Jensen, F. R., 233, 234, 235, 239, 241, 243, 267 Jerrard, H. G., 76, 78, 85 Johanson, M., 166, 184 Johnson, J. R., 8, 85 Johnson, R. E., 178,184 Johnson, S. L., 161, 185 Johnston, C. R., 180, 185 Johnston, D. R., 73, 82 Jones, J. L., 101, 121 Jones, W. J., 11, 20, 83 Joos, G., 20, 22, 23, 83 Jordan, P., 68, 81 Josephson, R. R., 131, 136, 184 Joshi, S. S . , 32, 85 Josien, M. L., 34, 84 Jungner, A., 76, 85 Jungner, I., 76, 85
K Kabuss, S., 236, 237, 241, 266, 267 Kagarise, R. E., 251, 267 Kahn, A. H., 20, 85 Kaiser, R., 224, 267 Kale, M. N., 97, 99, 100, 121 Kanda, T., 188, 267 Kaplan, F., 196, 214, 257, 269 Kaplen, J. I., 267 Kaprilova, G. A., 96, 98, 122 Karagounis, G., 26, 85 Karpacheva, S. M., 181, 185 Karplus, M., 190, 249,257, 267 Keeber, W. H., 16, 85 Kennedy, J. W., 126, 185 Kerr, J., 70, 85 Khaleeluddin, K., 115, 121, 131, 138, 140, 184 Khaskin, I. G., 175, 185 Kielich, S., 69, 72, 85 King, R. W., 101, 111, 114, 115, 116, 121 Kiritani, R., 145, 180, 185 Kirkwood, J. G., 73, 75, 77, 85 Kistiakowsky, G. B., 94, 99, 121
Kitao, T., 180, 181, 185 Kitaoka, Y., 180, 181, 185 Klaboe, P., 251, 267 Klein, F. S., 126, 129, 130, 132, 133, 134, 135, 136, 139, 140, 143,184, 185 Knorr, C . A., 8, 83 Koch, F. K. V., 20, 81, 85 Kohner, H., 20, 85 Koizumi, M., 145, 185 Konasiewicz, Z . , 129, 130, 132, 169, 183 Konnegay, R. L., 241,242, 266 Kooyman, E. C., 102, 112, 113, 116, 122 Kordes, E., 25, 85 Kornegay, R. L., 234, 241, 242, 266 Korsching, H., 11, 85 Koshland, D. E., Jr.,153, 185 Krishnan, K. S . , 68, 85 Kronig, R. de L., 68, 86 Krushinskii, L. L., 75, 86 Kubo, R., 214, 267 Kudryavstev, R. V., 180, 185 Kugel, L., 177, 184 Kuhn, W., 75, 78, 84, 86 Kullnig, R. K., 233, 239, 267 Kurland, R. J., 257, 267 Kursanov, D. N., 180, 155 Kurtz, S. S . , 39, 86 Knss, E., 65, 70, 86 Kyte, C. T., 8, 14, 86
L Ladenburg, R., 2 0 , 8 6 Ladenheim, H., 166,183 Lagemann, R. T., 32, 82, 83, 86 Lambert, J. B., 256, 267 Lambert, J. D., 72, 81 Langevin, P., 68, 86 Langseth, A., 251, 267 Lensbury, P. T., 258, 267 Lapidot, A., 179, 185 Lamer, J., 153, 185 Lauder, I., 152, 168, 180, 185 Lederer, E., 181, 185 Lederer, M., 181, 185 Lee, J., 246, 267 Lee, R. A., 101,121 Le FBvre, C. G., 40, 43, 46, 47, 48, 49, 50, 54, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 74, 78, 79, 80, 82, 86 Le FBvre, R. J. W., 3, 8, 20, 33, 37, 40, 43, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 71, 62, 64, 65, 66, 67, 68, 70, 74, 76, 78, 79, 80, 81, 82, 83, 84, 86, 87 Leibowitz, J., 153, 185
276
AUTHOR INDEX
Leicester, J., 10, 13, 14, 15, 16, 17, 20, 27, 82, 83 Lemieux, R. U., 233,239,267 Lemons, J. F., 126, 185 Lennard, A., 179,183 Lenthen, P. M., 62, 79 Leonard, N. J., 180, 185 Levin, I., 168, 186 Levit, A. F., 176, 181, 184 Lewin, S. Z., 1, 38, 39, 80 Lewis, E. S., 110,121 Lewis, G. N., 8, 87, 123, 185 Lewis, K. G., 118,121 Lewis, R. N., 16, 88 Lewis, T. A., 160, 167, 185 Liepack, H., 26, 83 Liddel, U., 259, 267 Lima, F. W., 32, 87 Llewellyn, D. R., 129, 130, 131, 132, 133, 140, 160, 167, 169, 170, 171, 173, 176, 178, 179,183,185 Loewenstein, A., 163, 185, 197, 200, 205, 206,208, 209, 213, 255, 263, 266, 267 Long, D. A., 75, 87 Long, F. A., 127, 133, 172,184,185 Looney, C. E., 254, 268 Lorentz, H. A., 3, 41, 87 Lorenz, L. Z., 87 Lotani, M., 52, 79 Lovering, E. G., 81 Liihdemann, R., 28, 87 Luttringhaus, A., 236, 237, 241, 266, 267 Luz, Z., 152, 178, 185, 204, 205, 219, 235, 267 Lyon, N., 73, 87
M McCall, D. W., 188, 196, 197, 210, 211, 266 McClellan, 2, 87 Maccoll, A., 69, 70,73, 75,82,87,92,93,94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 106, 107, 110, 112, 133, 116, 117, 118, 120,120,121,122 McComb, H. E., 73, 87 McConnell, H. M., 78, 87, 197, 209, 210, 211, 219, 221, 224, 226, 227, 266, 267 Macey, W. A. T., 17, 87 McGines, R. G., 181,184 McKenns, J., 75, 87 Mackor, E. L., 264, 267 McLauchlan, K. A., 77, 82 McLead, G. L., 181,184 MacLean, C., 264, 267 McLure, E. C., 39, 80 McMahon, P. F., 190, 250, 251, 266
Maier, W., 236, 237, 241, 266, 267 Makens, R. F., 96,122 Mallory, F. A., 259, 266 Manassen, J., 129, 130, 134, 185 Manos, P. T., 181, 184 Marshall, T. W., 260, 268 Maryott, A. A., 17, 82 Mason, S. F., 75, 87 Masuda, Y., 188, 267 Matossi, F., 69, 87, 88 Matsui, H., 159, 160, 164, 166, 168, 183 Maxwell, D. E., 223, 266 Mayer, F. C., Jr., 153,185 Mayer, J. E., 22, 88 Mayer, M. G., 22, 88 Mayer, R., 69, 87, 88 Mayerle, E. A., 166, 185 Mears, W. H., 173, 185 Meerwein, H., 30, 88 Meiboom, S., 204, 208, 206, 208, 209, 210, 219, 229, 230, 234, 235, 236, 241, 266, 267, 269 Menasse, R., 181, 184 Menon, B. C., 148, 150, 185 Meyer, E. H., 48, 88 Michael, K. W., 175, 186 Milburn, R. M., 169, 185 Mislow, K., 179, 184 Mizushima, M., 52, 79 Modena, G., 175, 183 Moelwyn-Hughes, E. A,, 71, 76, 88 Moniz, W. B., 227, 243, 244, 267 Moodie, R. B., 151, 186 Mortensen, E. M., 49, 54, 77, 88 Mrowka, B., 52, 77, 88, 84 Mueller, C. R., 52, 53, 68, 88 Mueller, H., 68, 88 Muenster, L. J., 151, 186 Muetterties, E. L., 228, 267 Muller, B., 216, 267 Miiller, E. W., 26, 8 3 Muller, N., 243, 268 Mumford, S. A., 11, 88 Munn, R. J., 72, 83 Murawski, J., 101, 122 Murphy, G. W., 95, 96, 100, 121 Myers, 0. E., 227, 268
N Naar-Colin, C., 77, 81, 188, 266 Nace, H. R., 101,122 Nair, P. M., 247, 268 Neikam, W. C., 241, 268 Neugebauer, T., 68, 88 Neumer, J. I?., 255, 267
277
AUTHOR INDEX
Newman, F. H., 20, 88 Newmark, R. A., 249, 251, 268, 269 Nielsen, J. R., 251, 267 Norberg, R. F., 226, 266 Nordlander, J. F., 258, 269 Norman, A., 76, 84 Northcott, J., 8, 82 Noyce, D. S., 234, 235, 241, 267
0 Oae, S., 145, 180, 181, 184, 185 O’Connor, C., 169, 170, 171, 185 O’Connor, G. L., 101, 122 Odell, A. L., 171, 173, 184 Ogg, R. A., 94, 101,121,122, 254, 268 Ogilvie, A., 39, 80 Oh, W. T., 59, 86 O’Konski, C. T., 76, 79, 80, 88 Olah, G. A., 264, 268 Oldham, K. G., 178, 184 Onyon, P. F., 99,120 Orr, B. J., 57, 87 Orttung, W. H., 76, 88 Oster, G., 39, 88 Otterbein, G., 48, 88 Oudemans, G. J., 73, 82
P Packard, M. E., 259, 268 Packer, K. J., 228, 267 Paddock, N. L., 177, 185 Palermiti, F. M., 33, 82 Palko, A. A., 265, 268 Pannwitz, W., 30, 88 Parker, R., 14, 85 Parkins, G. M., 40, 48, 79, 86 Partington, J. R., 31, 32, 34, 41, 85, 88 Paul, M. A., 133, 185 Pauling, L., 24, 25, 27, 31, 88 Pearson, R. B., 179, 183 Pearson, R. G., 166, 185 Pegram, G. B., 123, 186 Petrakis, L., 247, 268 Petreanu, E., 144, 186 Petter, P. J., 72, 81 Phillips, G. M., 30, 85 Phillips, W. D., 189, 247, 252, 253, 264, 266, 268 Piekara, A., 69, 85 Pierens, R. K., 50, 57, 86, 87 Piette, L., 200, 220, 224, 233, 234, 237, 253, 254, 265, 269 Pimentel, J. C., 259, 2/37 Pinchas, S., 127, 185
Pitzer, K. S., 54, 88, 235, 265 Placzek, G., 75, 88 Plane, R. A., 49, 82 Platt, J. R., 76, 88 Pocker, Y., 140, 184 Pohorlyes, L. A., 168, 186 Polanyi, M., 94, 122, 128, 185 Polly, 0. L., 94, 122 Ponomarchuk, M. P., 188, 170, 171, 173, 184 Pople, J. A., 26, 68, 69, 75, 77, 82, 88, 188, 189, 192, 202, 223, 228, 233, 234, 235, 243, 246, 247, 251, 259, 260, 265, 268 Post, K. W., 16, 85 Pound, R . V., 192,214, 265 Powles, J. G., 222, 223, 224, 251, 268 Premuzic, E., 242, 265, 268 PrBvost, C., 31, 88 Price, C. C., 15, 84 Price, S. 5.W., 100, 101, 121, 122 Pritchard, J. G., 127, 179, 183, 185 Proctor, W. G., 188, 268 Purcell, E. M., 192, 214, 216, 217, 265, 266
Q Quail, J. W., 228, 265 Quayle, 5.R., 132, 166, 167, 169, 183
R Raab, R. F., F7, 82 Rale, H. T., 39, 84 Raman, C. V., 68, 85 Ramaswamy, K. L., 17, 18, 20, 88 Ramey, K. C., 249, 251, 266, 268 Ramsey, N. F., 259, 267 Rand, M. H., 152,183 Rank, D. H., 251,267 Rao, B. P., 46, 48, 50, 57, 60, 64, 65, 75, 86, 87, 88, 81 Rao, D. A. A. S. N., 66,67,68, 70,86,87,88 Rao, M. R., 32, 88 Ray, J. D., 254, 268 Reeves, L. W., 197, 219, 220, 221, 233, 237, 238, 239, 241, 242, 255, 259, 260, 261, 262, 263, 265, 266,267, 268 Regnier, J., 26, 88 Regnier, S., 26, 88 Reilly, C. 4.. 224, 268 Remick, A. E., 71, 88 RBrat, C., 63, 88 Reuben, J., 178, 185 Rice, F. O., 94, 122 Rinck, G., 99, 121 Ritchie, (2. L. D., 46, 48, 87
278
AUTHOR INDEX
Rittenberg, D., 153, 185 Roberts, B., 97, 99, 122 Roberts, I., 128, 152,157,169,176,185,186 Roberts, J. D., 231, 232, 233, 247, 255, 256,257, 258, 267, 268, 269 Roberts, S., 20, 88 Robinson, G. C., 132, 186 Rochow, E. G., 15, 16, 88, 90 Rogers, M. T., 203, 205, 253, 254, 268 Rohrback, G. H., 17, 82 Roper, R., 57, 86 Rose, T. J., 39, 80 Ross, R. A., 118, 122 Roth, W. A., 83 Rotlevi, E., 150, 157, 186 Rowley, H. H., 96, 101, 120 Rowlinson, J. S., 75, 88 Rozen, A. M., 181, 185 Rubin, M. B., 257, 267 Rudy, C. E., 101,122 Rutenberg, A. C., 265, 268 Rutner, E., 17, 80
s Sachsse, G., 48, 88 Sack, R. A., 214, 268 Sadler, M. S., 261, 267 Saika, A., 196, 211, 224, 234, 265, 266, 268 Samuel, D., 124, 126, 127, 144, 150, 152, 156, 157, 169, 173, 174, 176, 178, 179, 180, 182, 184, 185, 186 Samygin, M. M., 32, 88 Sarel, S., 168, 186 Sauer, R. O., 11, 88 Saxby, J. D., 20, 50, 58, 61, 62, 64, 65, 67, 78, 79, 80 Sayre, R., 15, 16, 89 Schaller, D., 20, 90 Scheer, J. C., 102, 112, 113, 116, 122 Scheraga, H. A., 78, 89 Schissler, D. O., 108, 122 Schneider, W. G., 188, 189, 192, 202, 223, 233, 234, 235, 239, 243, 246, 247, 253, 259, 262, 263, 265, 267, 268,269 Schofield, P., 26, 88 Schoppe, R., 24, 89 Schroter, H., 20, 89 Schultz, R. F., 117, 121 Sederholm, C. M., 234, 235, 241, 247, 248, 249,251, 267,268, 269 Sehon, A. H., 92, 122 Sekuur, T. J., 241, 269 Semenov, M. N., 95, 96, 98,122 Semmler, R. W. 7, 8, 89
Senftleben, H., 69, 84 Senior, J. B., 169, 170, 171, 184 Senkus, M., 128, 147,186 Sergeev, G. B., 96, 98, 99, 100, 722 Sewell, G. L., 69, 89 Shaw, R., 100,122 Shelton, E. M., 34, 84 Sheppard, J. C., 227, 268 Sheppard, N., 234,236, 241, 250, 251, 266, 268 Shockley, W., 20, 85 Shoolery, J. N., 231, 232, 233, 234, 250, 259,261, 265, 267, 268 Shoppee, C. W., 235, 268 Shorygin, P. O., 75, 86 Signer, R., 78, 89 Silberstein, L., 14, 43, 89 Silver, B. L., 127, 176, 178, 185, 186 Sime, J. G., 63, 79 Simonsen, J. L., 7, 89 Singh, A. N., 50, 58, 61, 79, 80 Sixma, F. L. J., 102, 112, 113, 116, 122 Skinner, C. A., 73, 89 Slichter, C. P., 196, 197, 210, 211, 266 Smiles, S., 2, 4, 6, 7, 89 Smith, B., 156, 183 Smith, C. P., 8, 15, 26, 27, 31, 36, 69, 76, 89 Smith, G. G., 101, 112, 113, 114, 116,122 Smith, M. R., 40, 47, 48, 57, 58, 65, 66, 67, 68, 74, 86 Smith, R. P., 49, 54, 77, 88 Sobotka, H., 173,185 Solomon, I., 229, 268 Somers, B. G., 261, 268 Sommer, L. H., 175,186 Sommers, E. E., 101, 122 Spaeth, C. P., 254, 268 Spangenberg, K., 20, 22, 89 Sparks, B., 143, 156, 184,186 Spatcher, D. N., 159, 164, 183 Spitzer, R., 235, 265 Spoel, H., 72, 81 Stansbnry, E. J., 75, 82 Stark, F. O., 175, 186 Stauffer, C. H., 94, 99, 121 Staveley, L. A. K., 94,122 Steel, K. D., 37, 87 Steiger, A. L. von, 8, 89 Stein, S., 153, 185 Stephen, M. J., 71, 72, 82 Sternheimer, R. M., 26, 89 Stevenson, B., 99, 100, 122 Stewart, R., 151, 186 Stienstra, F., 11, 80 Stimson,V. R., 117, 118, 121,122 Stone, R. H., 94,99,122
279
AUTHOR I N D E X
Stone, R. R., 170, 171, 172,183 Stouffer, J. E., 181, 183, 184, Strange, J. H., 222, 223, 224, 251, 268 Strcamme, K. O., 197, 237, 239, 242, 261, 268 Stuart, A., 78, 84 Stuart, H. A., 52, 65, 66, 68, 75, 86, 89 Sugden, S., 32,36, 80 Sundaram, A., 50, 56, 57, 58, 59, 67, 87 Sundaram, K. M. S., 40, 45, 56, 58, 59, 65, 67, 87, 79, 82 Sundbom, M., 26, 89 Sunners, B., 253, 269 Sutcliffe, J. H., 246, 267 Sutton, L. E., 30, 45, 66, 69, 70, 82, 85 Swain, C. G., 127, 161, 167,186 Swarts, F., 16, 89 Swinbourne, E. S., 97, 99,110,122 Szabo, A. L., 128,185 Szivessy, G., 73, 74, 83, 89 Szoke, A., 229, 230, 263, 267, 269 Szwarc, M., 92, 94, 101, 122
T Taft, R. W., Jr., 34, 89, 126, 130, 139, 140, 164, 166,183 Tamm, C., 181, 184 Tarasenko, A. M., 180, 184 Taube, H., 126, 169, 285 Taylor, L. J., 127, 186 Taylor, R., 101, 113, 114, 116, 122 Tessman, J. R., 20, 85 Thomas, P. J., 94, 95, 96, 97, 99, 100, 103, 120,121,122 Thomas, R. J., 149, 159, 160, 163, 164, 166, 168, 183 Thompson, D. D., 211,226,267 Thompson, D. S., 248, 269 Thompson, E., 78, 84 Thompson, S. O., 108,122 Thomson, G., 33, 89 Tiers, G. V. D., 188, 235, 238, 239, 241, 269 Tillett, J. G., 179, 183 Timmermans, J., 2, 73, 89 Tinoco, I., 76, 84, 89 Titani, T., 145, 185 Tobey, S. W., 159, 160, 164, 166, 168,183 Tolgyesi, W. S., 264, 268 Tolkmith, H., 15, 16, 18, 20, 40, 51, 89 Tomita, K., 214, 267 Torkington, P., 51, 89 Tosch, W. C., 243, 268 Trambarulo, R., 31, 84 Treloar, L. R. G., 78, 89
Trotman-Dickenson, A. F., 100, 101, 121, 122 Trotter, J., 63, 89 Tsolis, A. K., 179, 184 Tsuchihashi, G. I., 127, 186 Tuli, G. D., 32, 85 Turkevich, J., 108, 122 Turner, J. J., 250, 251, 268 Turner, 0. W., 224, 260
U Unik, J. P., 158, 159, 161, 183 Urey, H. C., 123, 147, 152, 157, 169, 184, 185, 286 Urtz, R. P., 78, 90
v Vahrman, M., 5,90 Van Dort, H. M., 241,260 Van Tamelen, 236, 266 Van Vleck, J. H., 42, 90 Varian Associates, 188, 231, 269 Veltman, P. L., 92, 121 Vernon, C. A., 178, 184 Vickery, B. C., 10, 11, 13, 83 Vine, H., 46, 87 Vinti, J. P., 77, 90 Vogel, A. I., 10, 11, 12, 13, 14, 15, 16, 17, 20, 25, 27, 31, 82, 83, 84, 85, 86, 90 Voigt, W., 68, 90 Volkenstein, M. W., 49, 90 Volkmann, H., 47, 68, 89 Vuks, M. F., 49, 90
w Waldmann, H., 38, 90 Walsh, A. D., 51, 90 Wang, S. N., 48, 90 Wangsness, R. K., 229, 267 Ward, A. L., 39, 86 Warrick, E. L., 16, 90 Warwick, E., 101, 122 Wasastjerna, J. A,, 20, 21, 22, 25, 90 Wassermann, I., 173, 174, 182,186 Waterman, H. I., 40, 90 Waters, W. A., 71, 90 Watson, E. J., 118, 122 Watson, H. E., 17, 18, 20, 88, 98 Waugh, J. S., 250, 266 Weaver, H. E., 227, 267 Weiss-Broday, M., 180, 186 Weissman, S. I., 226, 266
280
AUTHOR INDEX
Wells, E. J., 219, 220, 221, 237, 238, 341, 265,268 Welsh, H. L., 75, 82 Wepster, B. M., 33, 90 Wesson, L. G., 30, 90 West, R., 15, 90 Westheimer, F. H., 127, 148, 16’2, 178, 185, 186 Wetzel, W. H., 101, 112, 113, 114, 116,122 White, G. L., 16, 84 Whitesides, G. M., 257, 258, 265 Whittaker, D., 115, 121, 131, 138, 140, 184 Wikner, E. G., 26, 83 Williams, A. J., 47, 57, 86, 87 Williams, R. J., 99, 101, 111, 120 Williams. R. L.. 75. 90 Wilson, I. 131,’133, , 180, 184, 185 Winstein, S., 132, 186 Wise, W. B., 257, 267 Woessner,D. E., 218, 219, 221,269 Wolf, A. P., 126, 130, 139, 140, 183 Wolfsohn, G., 20, 86 Wong, S. C., 99, 122
Wood, R. W., 34, 74, 90 Woodbury, J. C., 203,205,253, 254,268 Woodward, L. A., 75, 90 Woody, R. W., 76, 89 wulff, P., 4, 20, 21, 84, 90 Wiist, J., 20, 81 Wiisthoff, P., 20, 90 Wynne-Jones, K. M. A., 152,183
Y Yamoaka, K., 76,89 Yoshioka, K., 76, 88 Yih, S. Y., 171, 173, 184 Yu, F. C., 188, 268
Z Zerner, B., 180,185 Zimm, B. H., 76, 88 Zintl, E., 25, 84 Ziircher, R. F., 77, 90
CUMULATIVE INDEX OF AUTHORS Brand, J. C. D., 1, 365 Brown, H. C., 1, 35 Collins, C. J., 2, 1 Ferguson, G., 1, 203 Le FBvre, R. J. W., 3, 1 Long, F. A., 1, 1 Meccoll, A., 3, 91 Reeves, L. W., 3, 187 Robertson, J. M., 1, 203 Samuel, D., 3, 123 Schaleger, L. L., 1, 1 Shatenshtein, A. I., 1, 1513 Silver, B. L., 3, 123 Stock, L. M., 1, 35 Symons, M. C. R., 1,284 Whalley, E., 2, 93 Williamson, D. G., 1, 365 Wolf, A. P., 2, 201 Zollinger, H., 2, 163
CUMULATIVE INDEX OF TITLES Activation, entropies of, and mechanisms of reactions in solution, 1, 1 Activation, volumes of, use for determining reaction mechanisms, 2, 93 Ammonia, liquid, isotope exchange reactions of organic compounds in, 1, 156 Aromatic substitution, a quantitative treatment of directive effects in, 1, 35 Aromatic substitution reactions, hydrogen isotope effects in, 2, 163 Aromatic systems, planar and non-planar, 1, 203 Directive effects in aromatic substitution, a quantitative treatment of, 1, 35 Carbon atoms, energetic, reactions with organic compounds, 2, 201 Electron spin resonance, identification of organic free radicals by, 1, 254 Electronically excited molecules, structure of, 1, 365 Energetic tritium and carbon atoms, reactions of, with organic compounds, 2, 201 Entropies of activation and mechanisms of reactions in solution, 1, 1 Equilibrium constants, N.M.R. measurements of, as a function of temperature, 3, 157 Exchange reactions, hydrogen isotope, of organic compounds in liquid ammonia, 1, 156 Exchange reactions, oxygen isotope, of organic compounds, 3, 123 Excited molecules, structure of electronically, 1, 365 Free radicals, organic, identification by electron spin resonance, 1, 284 Gas-phase heterolysis, 3, 91 Heterolysis, gas-phase, 3, 91 Hydrogen isotope effects in aromatic substitution reactions, 2, 163
282
CUMULATIVE I N D E X O F TITLES
Hydrogen isotope exchange reactions of organic compounds in liquid ammonia, 1, 156 Isotope effects, hydrogen, in aromatic substitution reactions, 2, 163 Isotope exchange reactions, hydrogen, of organic compounds in liquid ammonia, 1, 166 Isotope exchange reactions, oxygen, of organic compounds, 3, 123 Isotopes and organic reaction mechanisms, 2, 1 Mechanisms, organic reaction, isotopes and, 2, 1 Mechanisms, reaction, use of volumes of activation for determining, 2, 93 Mechanisms of reactions in solution, entropies of act,ivation and, 1, 1 N.M.R. measurements of react,ion velocities and equilibrium constants as a function of temperature, 3, 187 Non-planar and planar aromatic systems, 1 , 203 Nuclear magnetic resonance, see N.M.R. Oxygen isotope exchange reactions of organic compounds, 3, 123 Planar and non-planar aromatic systems, 1, 203 Polarizability, molecular refractivity and, 3, 1 Radicals, organic free, identification by electron spin resonance, 1, 284 Reaction mechanisms, use of volumes of activation for det,ermining, 2, 93 Reaction mechanisms in solution, entropies of activation and, 1, 1 Reaction velocities and equilibrium constants, N.M.R. measurements of, as a funct,ion of temperature, 3, 187 Refractivit,y, molecular, and polarizability, 3, 1 Resonance, electron spin, identification of organic free radicals by, 1, 284
Solutjon, reachnsjn, enbropiesofactivation and mechanisms, I , 1 Structure of electronically excited molecules, 1, 365 Substitution, aromatic, a quantitative treatment of directive effects in, 1, 35 Substitution reactions, aromatic, hydrogen isotope effects in, 2, 163 Temperature, N.M.R. measurements of reaction velocities and equilibrium constants as a function of, 3, 187 Tritium atoms, energetic, reactions with organic compounds, 2, 201 Volumes of activation, use of, for determining reaction mechanisms, 2, 93
