Advances in Physical Organic Chemistry, Volume 06

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 6

1968

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 1968 by Academic Press Inc. (London) Ltd.

All Rights Reserved

No part of this book may be reproduced in any form by photostat, microam, or any other means, without written permission from the publishers

Library of Congress Catalog Card Number :62-22125

PRINTED IN UREAT BRITAIN BY SPOTTISWOODE, B A L L A m Y N E AND COMPANY LIMITED LONDON AND COLCHESTER

CONTRIBUTORS TO VOLUME 6 E. K. FIELDS, Research an& Development Department, Amoco Chemicals Corporation, Whiting, Indiana, U.S.A. M. M. KREEVOY, School of Chemistry, University of Minnesota, Minneapolis, Minnesota, U.S.A.

S. MEYERSON,Research and Development Department, American Oil Company, Whiting, Indiana, U.S.A. S. I. MILLER, Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois, U.8.A.

H. A. SOHERAGA, Department of Chemistry, Cornell University, I t h a , New York 14850, U.S.A.

J. M. WILLIAMS, Jr.,School of chemistry, University of Minnesota, Minneapolis, ktinnesota, U.S.A.

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CONTENTS CONTRIBUTORS TO VOLUME 6

.

V

Mechanisms of Formation and Reactions of Arynes at High Temperatures E. K. FIELDS and S. MEYERSON I. Introduction . 11. Arynes from Aromatic Anhydrides . . A. Reactions of Benzyne with Benzene B. Reactions of Benzyne with Deuteriated Benzenes . C. Arynes from Aromatic Anhydrides Other Than Phthalic . D. Reactions with Chlorinated Benzenes . E. Reactions with Pyridine . F. Reactions with Thiophene and Benzothiophene . G. Reactions of Tetraphenylbenzyne from Tetraphenylphthalic Anhydride . 111. Benzyne from o-Sulfobenzoic Anhydride . IV. Benzyne from Acetylene . V. Conclusion . References .

16 21 26 32 46 50 64 67 58

Developments in the Study of A 4 2 Reactions in Aqueous Solution J . M. WILLIAMS, JR. and M. M. KREEVOY

.

I. Introduction 11. Gross Mechanism . A. Identification of Proton Transfer as the Rate-Determining Step . B. Pre Rate-Determining Steps C, Multiple Rate-Determining Processes .

63 64 64 79 83

viii

CONTENTS

111. Details of Mechanism . A. Structure of the Starting State . B. Direct versus Indirect Proton Transfer . C. Detailed Structure of Intermediates . D. Substituent Effects on Reactivity and the Electronic Structure of the Transition State . E. Non-Adiabatic Processes . IV. Conclusions, Apologies, and Acknowledgments . References .

a5

85 88 92 94 95 97 98

Calculations of Conformations of Polypeptides H. A. SCHERAGA I. Introduction . 11. Conventions . 111. Geometrical Data IV. Transformation of Coordinates . V. Terms Contributing to the Expression for the Total Energy . A. Torsional Energies . B. Nonbonded Interactions . C. Electrostatic Interactions . D. HydrogenBond . E. Distortion of Geometry . F. Role of Crystal Energy Calculations in Refinement of Energy Parameters . G. Free Energy of Hydration . H. Loop-Closing Potential . VI. Methods of Energy Calculation and Energy Minimization A. Hard-Sphere Potential . B. Complete Energy Expression VII. Results with Hard-Sphere Potential . VIII. Application of Complete Energy Expression to Results Obtained from the Hard-Sphere Potential . IX. Use of Complete Energy Expression for Conformational Energy Calculations, Including Energy Minimization . A. Hydrocarbons . B. Dipeptides . C. Random Coil; End-to-end Distance . D. Helical Structures . .

.

103 106 114 118 118 119 124 130 133 137 138 138 141 143 143 143 145 153 166 156 157 159 162

ix

CONTENTS

E. Gramicidin-S . F. Oxytocin and Vasopressin X. Conclusions . References .

. . .

173 175 178 179

I. Introduction . . 11. The Shape of Simple Species A. Some Valence Bond Results . B. Some Molecular Orbital Results . 111. Bonding Theory and Stereoselection , A. Electrocyclic Reactions . B. Cycloadditions . C. Sigmatropic Migrations . . D. Sigma-Sigma and Sigma-Pi Switch E. Substitution at Saturated Atoms . . F. Substitution at Unsaturated Atoms G. Addition and Elimination . H. Rearrangements . IV. Miscellaneous Factors and Stereoselection . A. Excited States and Molecular Vibrations . B. Magnetic Resonance Data . C. Collinearity and Coplanarity of Reacting Centers . D. Principles of Least Motion (PLM) E. Electrical Effects V. Stereoselection Deriving from Steric and Conformational Factors . A. Steric Effects . B. Conformational Analysis . VI. Conclusions . References .

185 188 188 191 201 202 217 235 243 246 265 272 287 293 293 295 296 301 303

.

.

Stereoselection in the Elementary Steps of Organic Reactions S. I. MILLER

AUTHORINDEX . CUMULATIVEINDEX OF AUTHORS. CUMULATIVEINDEX OF TITLES .

l**

. . .

308 308 313 321 323 333 345 347

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MECHANISMS OF FORMATION AND REACTIONS OF ARYNES AT HIGH TEMPERATURES ELLIS K. FIELDS Research and Development Department, Amoco Chemicals Corporation, Whiting, Indiana, U.S.A.

SEYMOUR MEYERSON Research and Development Department, American Oil Company, Whiting, Indiana, U.S.A. I. Introduction . . 1 11. A r y n e s from Aromatic Anhydrides . 5 A. Reactions of Benzyne with Benzene. . 5 B. Reactions of Benzyne with Deuteriated Benzenes . 8 C. Arynes from Aromatic Anhydrides Other Than Phthalic 15 D. Reactions with Chlorinated Benzenes 21 E. Reactions with Pyridine 26 F. Reactions with Thiophene and Benzothiophene 32 G. Reactions of Tetraphenylbenzyne from Tetraphenylphthalic Anhydride 46 111. Benzyne from o-SulphobenzoicAnhydride 50 IV. Benzyne from Acetylene 54 V. Conclusion 57 References . 5 8

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I. INTRODUCTION

THEfirst representation of an aromatic compound containing a formal carbon-carbon triple bond in the ring appeared sixty-five years ago, when Stoermer and Kahlert (1902) wrote the structure

~

?

(sic)as the probable intermediate in the reaction of bromocoumarin with alcoholic potassium hydroxide. However, it is only since 1940 that the

0 1

formation of benzyne (1) \

and other arynes and their reactions

(1) 1

l

2

E L L I S K . F I E L D S A N D SEYMOUR M E Y E R S O N

in solution have been adequately described. In the period since the pioneering experiments of Wittig et al. (1940, 1941, 1942, 1944a,b), Roberts et al. (1953, 1966), and Huisgen and Rist (1954, 1955), the formation of arynes has been substantiated by a large volume of work, and arynes are commonly invoked as intermediates for a whole host of reactions in solution. These are adequately described in reviews by Heaney (1962)and Wittig (1965). By contrast, the formation of arynes in the vapor phase has received scant attention. Wittig (1961) pyrolyzed bisiodophenylmercury (2) and phthaloyl peroxide (3)in argon at 600' and 5 torr and obtained 54% and 27% yields, respectively, of biphenylene (4) : 0

II

8

1

(3)

(4)

Fisher and Lossing (1963) decomposed o-diiodobenzene at 960' and 1 0-3 torr in a reactor coupled to a mass spectrometer and found a product

of mass 76, whose vertical ionization potential, 9.75 v., was appreciably higher than calculated for open-chain C6H4 isomers and strongly indicated formation of benzyne. This assignment was supported by the formation of biphenylene, mass 152.

Benzenediazonium-2-carboxylate(5), P\ O

Nz+ 2 -

was first prepared

(5)

by Hantzsch and Davidson (1896)and decomposed by Stiles and Miller (1960) t o benzyne in the liquid phase.

Berry et al. (1962,.1964)employed flash photolysis t o decompose solid benzenediazonium-2-carboxylateand showed by both ultraviolet and

FORMATION A N D R E A C T I O N S OF A R Y N E S

3

mass spectra of the products that benzyne formed in the vapor phase. Brown and Solly (1965)found that indanetrione at 500Ogave benzyne and isolated its reaction products with benzene and chlorobenzene. Our investigation of arynes in the gas phase was an outgrowth of examining over many years the behavior of organic molecules under electron impact in the mass spectrometer, and comparing it with their behavior in other energetic processes, particularly pyrolysis. We have found many compounds that exhibit parallel behavior in these two contexts (Fields and Meyerson, 1965,1966a; Meyerson andFields, 1966a)a rather surprising situation at first glance, considering the large energy difference involved. However, there is increasing evidence that in highenergy processes, such as electron impact (e.g. Meyerson et al., 1963), the reaction paths with the lowest energy requirements (those favored in pyrolysis) are likely to be favored even when enough energy is available to drive almost any conceivable reactions. Thus, for example (Fields and Meyerson, 1966a), dibenzothiophene 5,5-dioxide (6)gives a 70 v. mass spectrum with the relative intensities shown in Table 1. TABLE1 Mass Spectrum of Dibenzothiophene Dioxide

Mass

Belative intensity

216 200 188 187 184 168 160 162 151 160 140 139

100.0 0.24 11.46 36.1 3.95 40.8 32.6 5.10 11.69 14.33 4.38 27.3

The decomposition scheme shown can account for the major ionic products (solid arrows denote a supporting metastable peak). Clearly, the major primary decomposition processes are loss of SO and loss of CO, both of which require prior formation of a C-0 bond. This virtually demands isomerization to an internal sulphinate ester (7),

4

ELLIS K . BIELDS AND SEYMOUR MEYERSON 216+

200+

187+

188+

160+

168+

162+

140+

1s1+

139+

1so+

184+

paralleling the isomerization of alkyl aryl and diary1sulphones to sulphinate esters under electron impact (Meyersonet aZ., 1964; see also Meyerson and McCollum, 1959; Quayle, 1959); the sulphinate ester can then lose SO and give dibenzofuran (8). This spectrum, accompanied by the same interpretation, has also been reported recently by two other groups (Bowie et uZ., 1966; Porter, 1967).

Pyrolysis of dibenzothiophene 5,5-dioxideat 690' gave a 95% yield of two products, dibenzofuran and dibenzothiophene in the ratio 6 :1 (Fields and Meyerson, 1966a). The predominant reaction, therefore, involved overall loss of SO, presumably through an intermediate rearrangement

FORMATION AND REACTIONS O F ARYNES

5

to the sulphinate ester (7). Subsequently, the perfluoro derivative was found to behave in the identical fashion (Chambers and Cunningham, 1967) ; dibenzofuran also was obtained from dibenzothiophene dioxide by Wallace and Heimlich (1966), using strong bases at 300'. The strikingly parallel behavior of dibenzothiophene dioxide and other compounds upon electron impact and pyrolysis led us to examine the behavior in these contexts of aromatic polycarboxylic anhydrides, of which phthalic anhydride is the simplest member.

11. ARYNES FROM AROMATIC ANHYDRIDES A. Reactions of Benzyne with Benzene The partial mass spectrum (McLafferty and Gohlke, 1959 ; Meyerson, 1965) of phthalic anhydride and tentative structures of the ions in the main reaction sequence are: Mass 148

Relative intensity

Tentative structure

47

Parent ion

-GO*]

104

-co] 76

100

o C = O +

85

-CaHB

J.

60

40

The large amount of C6Htformed, most simply formulated as benzyne, although the structure is not established, prompted us to try to duplicate this reaction thermally. Accordingly, a 0.1 molar solution of phthalic anhydride in benzene (100ml.) was pyrolyzed at 690" under nitrogen at a steady rate of 30 ml/hr (Fields and Meyerson, 1965). The pyrolysis tube was Vycor, filled with Vycor beads; contact time was 11.5 sec, which gave a 58% conversion of the phthalic anhydride. Acetylene was steadily evolved, along with carbon dioxide and carbon monoxide in a 1 :1 ratio ; these were identified in the gas stream by mass-spectral analysis of samples taken at regular intervals. The benzene was distilled off and the products boiling over 180' (2 g) were analyzed by mass spectrometry on a Consolidated Model

6

ELLIS K . FIELDS AND SEYMOUR MEYERSON

21-103c instrument with the inlet system at 250’. The usual 7O-volt spectrum was supplemented by a low-voltage (7.5 ionizing volts, uncorrected) spectrum to help identify parent peaks. Final confirmation of the lighter and more abundant components was obtained by mass spectra of effluent from a gas-chromatographic column, measured “on the fly” (Gohlke, 1959; Lindeman and Annis, 1960; Watson and Biemann, 1964). I n particular, this technique permitted unequivocal identification of biphenylene ; both the spectrum and the retention time agreed precisely with those obtained by the same procedure on an authentic sample. The major portion of the pyrolysate, apart from 0.62 g of unconverted phthalic anhydride, was 1.05 g of a mixture of naphthalene (15%) and biphenyl (85%). Benzene (100 ml), pyrolyzed under identical conditions, gave no acetylene, and only 0.18 g of high-boiling product, which consisted of about 96% (0-17g) biphenyl and 4% (0-072g) terphenyl. Only a trace of naphthalene (about 0.2%, 0-0004g) was found. I n addition to naphthalene and biphenyl, about 1yoeach of biphenylene and triphenylene was found in the hydrocarbon portion of the phthalic anhydride pyrolysate. Neither was found in the benzene pyrolysis. These results indicated that phthalic anhydride gave benzyne on pyrolysis, and the benzyne subsequently reacted with benzene :

a+! H

H

FORMATION A N D R E A C TI ON S O F A R Y N E S

7

Biphenyl, benzocyclooctatetraene (9),and benzobicyclo[2,2,2]octatriene (10) resulted from the reaction of benzyne (by decomposition of benzenediazonium carboxylate) with benzene at 45" (Miller and Stiles, 1963). Both 9 and 10 have been found to go to naphthalene and acetylene; 9 on photolysis (Fonken, 1963), and 10 in a sealed tube a t 300" (Miller and Stiles, 1963). The high ratio of biphenyl to naphthalene may reflect a contribution from a second path, via the primary decomposition product in stepwise loss of carbon dioxide and carbon monoxide, paralleling the reaction sequence known to occur under electron impact. The intermediate species (11) could add to benzene to give biphenyl by subsequent loss of carbon monoxide or fluorenone by ring closure and loss of hydrogen :

0

@ \

0

o+o -

H

CIH.

/I

0

H

Evidence for fluorenone (12) as a minor product of the pyrolysis (a small peak at mass 180 that persisted at reduced ionizing voltage) was indeed found. Direct-coupled gas chromatography-mass spectrometry clearly identified a minor component as fluorenone ;and a precise mass-measurement on a high-resolution mass spectrometer established ClsH80+as the empirical formula of the major component of nominal mass 180. Following the discovery of benzyne and biphenylene formation by pyrolysis of phthalic anhydride (Fields and Meyerson, 1965), two separate groups announced isolation of substituted biphenylenes by pyrolysis of substituted phthalic anhydrides. Brown et al. (1966)obtained chloroand methyl-substituted biphenylenes by pyrolysis at 700-720' and 0.1 to 1.5 torr. The yields were (Brown et al., 1967): Phthalic Anhydride

Biphenylene

3-chloro 3,4-dichloro 3,6-dichloro tetrachloro 3,4:-dimethyl

2,6- or 2,"idichloro 2,3,6,i'-tetracMoro 1,4,6,8-tetrechloro octachloro 2,3,6,7-tetramethyl

Yield, 15 6.5 3.8 26 3

yo

8

ELLIS K . FIELDS AND SEYMOUR MEYERSON

Cava et al. (1966) passed the vapors of phthalic and tetrachlorophthalic anhydride over a glowing Nichrome coil at 800' at 50 torr, and trapped the pyrolysate on a cold finger kept at -78'. Phthalic anhydride gave 10-1 5% biphenylene, based on unrecovered anhydride ; tetrachlorophthalic anhydride gave 30% perchlorobiphenylene. I n view of the findings of Lindow and Friedman (1967),these products probably were accompanied by tetraphenylene and its derivatives.

B . Reactions of Benzpe with Deuteriated Benzenes To confirm reaction scheme (4)for the formation of naphthalene and biphenyl, phthalic anhydride was allowed to react with benzenedl (Fields and Meyerson, 1966c). Barring an appreciable isotope effect, two-thirds of the naphthalene should contain a deuterium atom and onethird only protium. Biphenyl arises in two ways: insertion of benzyne into a C - H bond of benzene and pyrolysis of benzene. Biphenyl from benzyne insertion should form with retention of the deuterium atom ; biphenyl from benzene pyrolysis should-again ignoring any isotope do, dl, and d2 on the statistical basis of losing two, one, or effect-be zero deuterium atoms from a total of twelve protiums and deuteriums in the over-all reaction of two benzene molecules. The amount of biphenylTDLE 2 Products from Pyrolysis of Phthalic Anhydride in Benzene-& Molecular weight

Number of D atoms

Relative abundance Calculated" Found

Naphthalene 37.0 63-0 0 0

128 129 130 131

38.6 49.9 10.0 1.5

Biphenyl 154 155 156 157 158 159

8.2 35.4 44.8 8.8 0.9 0.1

a On the basis of 94.5% benzene-dl and 5.5% benzene-& used as starting material.

FORMATION A N D R E A C T I O N S OF A R Y N E S

9

dl in excess of an appropriately calculated value would presumably be due to the benzyne insertion reaction. Actual results are shown in Table 2. The observed naphthalene results did not agree well with those calculated. Further, a considerable amount of both naphthalene and biphenyl contained more deuterium than could arise by the simple postulated reactions. To help clarify these results, benzene-d, was pyrolyzed alone at 690°, and both the benzene recovered and the biphenyl produced were analyzed for deuterium content. The results, shown in Table 3, reveal a TABLE 3 Products from Pyrolysis of Benzene-dl* Relative abundance Number of D atoms 0 1 2 3 4 5

4.2-aec contact

21-8013contact

Benzene

Biphenyl

Benzene

Biphenyl

10.6 84.6 4.9 0.1

7 31 53 9

27.4 52.6 17.3 2.6 0.2

13.7 35.0 33.8 13.8

-

-

-

3.2 0.5

considerable amount of scrambling of deuterium and protium in the recovered benzene and explain the discrepancies between calculated and observed results in Table 2. Oddly enough, although the pyrolysis of benzene to biphenyl and hydrogen was first recorded in 1866 by Berthelot (18660) and has been investigated innumerable times since then, labeled benzene had never been pyrolyzed to find if the recovered benzene had the same isotopic composition as the original. The biphenyl composition was calculated from benzene of the initial and h a 1 isotopic compositions, on the assumption of random combination of two benzene molecules with random loss of two out of twelve hydrogen atoms, and gave the figures in Table 4. Any isotope effect was ignored for these calculations: Shih et al. (1959) and Eliel et al. (1960) found that free-radical arylations in solution showed only small isotope effects. These comparisons strongly suggest that the biphenyl was formed preferentially from benzene that has undergone exchange. The agreement between calculated and observed isotopic distributions of the

10

E L L I S K . F I E L D S A N D SEYMOUR MEYERSON

biphenyl at a contact time of 21 sec is especially striking. The data may mean simply that the biphenyl undergoes exchange at the same rate as the benzene. However, the remarkably close agreement between calculated and observed distributions makes an explanation based on fortuitous considerations seem unlikely, and suggests instead a more fundamental cause. TABLE 4 Calculated and Observed Isotopic Composition of Biphenyl Relative abundance 4.2-sec contact

Number of D atoms 0 1 2 3 4 5

21-sec contact

Calculated from

Calculated from

Initial

Final

Observed

Initial

Final

Observed

3.4 35.6 61.0

5.2 37.1 52.9 4.6 0.2

7 31 53 9

3.4 35.6

12-9 36.1 33.8 13.7 3-1 0.4

13-7 35.0 33.8 13-8 3.2 0.5

-

-

-

-

61.0

-

-

-

The data suggest that hydrogen exchange among benzene molecules is much faster than biphenyl formation, and that the process by which benzene molecules undergo exchange leaves them in an activated state for the reaction to form biphenyl. The deuterium statistics do not uniquely defhe a single reaction mechanism. I n fact, the calculated distributions in Table 4 are nearly identical with distributions calculated on the assumption of random combination of two benzene molecules with random loss of one hydrogen atom from each of the reacting molecules. A four-center reaction for the formation of biphenyl from benzene

has been postulated and a second-orderrate constant has been calculated by Hou and Palmer (1965). Either this path or the free-radical reaction would, most simply, effect random loss of one atom from each of the

FORMATION A N D REACTIONS OF A R Y N E S

11

reacting benzene molecules. To be compatible with paths (6) and (7), the assumption of random loss of two atoms from the full hydrogen

complement of the two reacting molecules would require equilibration of the hydrogen atoms before the intermediate breaks down to yield biphenyl. This requirement could best be satisfied by formation of a complexperhaps of the donor-acceptor type-or an actual compound, a phenylcyclohexadiene (13), between two molecules of benzene or other aromatic compound, in which protium and deuterium atoms readily move and exchange.

Gordon and Burton (1952) vaguely hinted at such complex formation as an energy-transfer process in radiolysis studies on benzene. Burr and Scarborough (1960) irradiated deuteriated biphenyls with a cobalt-60 source, analyzed the hydrogen produced, and concluded that two processes were involved: a unimolecular decomposition and some sort of bimolecular process. The workers studying these systems analyzed only the hydrogen or acetylene produced, not the recovered aromatic compounds. Evidence for the production of cyclohexadiene and more highly hydrogenated derivatives has been found in the mercury-sensitized

12

E L L I S I(. F I E L D S A N D S E Y M O U R M E Y E R S O N

photolysis of benzene vapor and hydrogen (Forbes and Cline, 1941), in the glow discharge of benzene vapor (Mignonac and Saint-Aunay, 1930), and in the radiolysis of liquid benzene (Gordon et aZ., 1958), and of biphenyl (Hall and Elder, 1959). There might have been some contribution from reaction (9) followed

+ 2c6H5'

CoH5-GjH5

(9)

by (7), as Gaeumann and Rayraux (1962) demonstrated in the pyrolysis of biphenyl and biphenyl-dl, at 438-472" over 2-200 hours. Inradiolysis, such C-C bond rupture has been judged unlikely, because but little CBHQion results from electron impact on isolated biphenyl molecules in the mass spectrometer (Hall and Elder, 1959; see also Burr et aZ.,1960), and because species with even numbers of rings predominate among the polyphenyls formed in radiolysis of biphenyl (Hellman, 1957). That most of the exchange in our work likewise did not involve C-C bond rupture was shown by the pyrolysis of naphthalene and biphenyl separately in benzene-d, at 690" and 7.6 sec contact time. The results are given in Table 5. TABLE5 Pyrolysis of Naphthalene and Biphenyl in Benzene-&" Compound pyrolyzed Component recovered

Molecular weight

Benzene

c %I

Naphthalene

i2 128

f 154

Number of D atoms

Naphthalene Biphenyl Relative abundance

0 1 2

12 80 8

0

77.7

1

19.8 2.5

2 0 1 2 3

-

15

78 7

-

-

74.3 19.9 5.1 0.7

94.5% benzene-dl, 5.5% benzene-&; 1 mole of naphthalene or biphenyl:5 moles of benzene.

The considerable amount of exchange that occurred between the naphthalene and the benzenedl furnished evidence of extensive C-H

FORMATION A N D R E A C TI ON S OF A R Y N E S

13

bond breaking. The almost identical amounts of naphthalenedl and biphenyl-d, produced may be significant if, as seems probable, the same process was involved. Our postulated bimolecular complex or phenylcyclohexadiene intermediate in the pyrolysis of benzene explained both hydrogen-deuterium exchange and ready intramolecular dehydrogenation to biphenyl without formation of highly energetic free hydrogen atoms. That intramolecular dehydrogenation was preferred was also shown by the formation of a small but measurable amount (0.2% of the yield of biphenyl) of naphthalene in benzene pyrolysis (Fields and Meyerson, 1966c), most likely arising by reaction (10).

@ H

__f_

o\l + H z

(10)

followed by the reactions already described. The similarity of the products obtained from benzene by pyrolysis and by exposure to ionizing radiation is noteworthy and suggests that TABLE 6 Products from Benzyne and Benzene-& ~~

Product

Relative concentrationa 0.6 4 4

49 45 24 8 4

0.4

0.5 1

3 3

6 15 12

7 19 100 Relative intensities in the low-voltage (7.6 volts, uncorrected)maas speatrum.

14

E L L I S K . F I E L D S A N D SEYMOUR M E Y E R S O N

the radiolysis results can be largely accounted for without involving ionized or electronically excited species as immediate precursors of the products. Thus, the same low-energy reaction paths may well predominate in both pyrolysis and radiolysis of benzene. Although the reaction of phthalic anhydride with benzene-d showed scrambling of protium and deuterium at 690°, especially a t 21 sec contact time, the scrambling at much shorter contact times is sufficiently low to permit ignoring it to simplify interpretation of results of labeling experiments. A solution of 0.002 mole of phthalic anhydride in 0.04 mole of benzene-d, was pyrolyzed a t 690Owith a contact time of 4.2sec. Starting benzene was 96.4% d6 and 3.6% d,; recovered benzene was 92.3% ds and 7.7% d 5 . The isotopic composition of the products is shown in Table 6. Of the deuterated naphthalenes, the d4 species is, as expected, the most abundant. However, naphthalene-d5 is almost as abundant, and there is a considerable amount of naphthalene-d,. I n recent vapor-phase free radical reactions, Fields and Meyerson (1967~) found phenylation of benzene-d, gave almdst as much biphenyl-&, as -d, and concluded that the reaction intermediate

could exchange protium and deuterium ; rearomatization apparently took place by loss of either protium or deuterium with almost equal ease. Evidently a similar mobility exists for protium and deuterium in the 1,4- and 1,2-adductsof benzyne with benzene-d :

where the movement of D and H is intramolecular and the transition states may not involve the relatively high energies that might otherwise be needed to break C-H and C-D bonds. The same is true for the biphenyl formed by insertion of benzyne into benzene-d,, whatever the intermediate for the insertion reaction may be. This seems especiallylikely if it has triplet free-radical character

FORMATION A N D R E A C TI ONS O F A R Y N E S

15

and thus resembles the Fields and Meyerson intermediate in vapor-phase arylation. Such biradical character of benzyne in solution, however transient, was shown by Kampmeier and Hoffmeister (1962) and Kampmeier and Rubin (1966),who generated benzyne by unimolecular radical elimination of iodine from 2-iodophenyl radicals : NO

C. Arynes f r o m Aromatic Anhydrides Other than Phthalic Other aromatic anhydrides also exhibit parallel behavior upon electrou impact and pyrolysis. The mass spectra of naphthalene-2,3-dicarboxylic anhydride and 1,8-naphthalic anhydride are qualitatively similar (Fields and Meyerson, 1967d): Naphthalene Anhydride Mess

2,3-

1,8-

Relative intensities

2,3-

1,8-

Suggested structures

‘ ‘ I

1 o=c,3,c=o

Pyrolysis of the anhydrides separately in benzene solution at 690’ gave the products shown in Table 7 (Fields and Meprson, 1967d).

16

ELLIS K . F I E L D S A N D SEYMOUR M E Y E R S O N

TABLE 7 Products from Naphthalene Dicarboxylic Anhydrides with Benzene Anhydride Product

Biphenyl Naphthalene Anthrmene, phenanthrene Phenylnaphthalene Binaphthylene, perylene (Molecularweight 252)

2,31,8Relative concentration'' 100 44 85 68 4

100 21 2 26

2

a From relative intensities in the low-voltage (7.5 volts, uncorrected) mass spectrum, normalized to biphenyl = 100.

The widely differing product distributions from the two anhydrides reflect the difference in structure and reactivity of the two naphthalynes. 2-3-Naphthalyne (14) behaves like benzyne, giving anthracene by 1,2and 1,4-addition,and phenylnaphthalene by insertion, as well as some binaphthylene (15) by dimerization :

0

(15) mass 252

FORMATION AND REACTIONS O F A R Y N E S

17

Perinaphthalyne (16) evidently prefers to react by hydrogen abstraction and insertion,giving naphthalene, biphenyl and phenylnaphthalene but relatively little anthracene (Reaction scheme 13):

The dimer of perinaphthalyne, perylene (17), is thermally more stable than binaphthylene (15) and a relatively larger amount is found in the naphthalyne-derived products. Lindow and Friedman (1967) showed that biphenylene breaks readily at the cyclobutadiene bond above 300' and gives tetraphenylene (tetrabenzocyclooctatetraene) and minor amounts of biphenyl. Presumably binaphthylene behaves similarly. A consequence of the tendency for perinaphthalyne to abstract hydrogen is the formation of a higher proportion of biphenyl than in the reactions of 2,3-naphthalyne. Fluoranthene (18) might be expected from reaction (14) of naphthalic anhydride and benzene (p. 18.), but it was not detected. As fluoranthene is thermally quite stable, its absence means it was probably not formed, suggesting that perinaphthalyne at elevated temperatures may react as a biradical, in a stepwise rather than concerted fashion. The ions of mass 126 from naphthalene-2,3- and -1,S-dicarboxylic anhydrides in the mass spectrometer may well be identical. At one atmosphere pressure in the vapor phase, however, the analogous neutral

18

E L L I S K * F I E L D S A N D SEYMOUR M E Y E R S O N

pyrolysis products evidently retain identity, as shown by the difference in product distribution.

Another pair of isomeric anhydrides that give similar mass spectra are pyromellitic (19) and melloph&ic (20) dianhydrides (Fields and Meyerson, 1967d). The major spectral features:

Pyromellitic

Mass 218

174 146

Mellophanio

Relative intensity 1.33 100

0.63 0.70

0.68 100 0.17

130 102

70.7

14.9 96.6

74

62.4

68.1

are accounted for by the reaction scheme (15). A minor process leads to an ion presumably having the structure of benzynedicarboxylic anhydride (21). The two formal structures shown on the opposite page are indistinguishable and may be equivalent. The ions of masses 174 and 130 are possibly benzocyclopropenones (formulas (22,23 opposite). The two spectra are generally similar except for the pronounced difference in intensity at mass 130, which suggests that the fragment ion derived from mellophanic dianhydride is the more stable species. If one assumes a minimum of bond breaking and no rearrange-

19

FORMATION A N D REACTIONS O F A R Y N E S

0

0

0

II

II

II

o=c )

"\

C

II

II

0

g

\

0-c

0

IIo 0

O\

102

J. 74

146 0

+

' 0

I/

- 0

174.

+ t b c q = 0 +

or

O - =c& f=], 4

130

130

(23)

20

ELLIS

I(. F I E L D S A N D SEYMOUR M E Y E R S O N

ment, the difference can be accounted for by the resonance-stabilized structure derivable from mellophanic, but not from pyromellitic, dian-

hydride. The ions of mass 130 decompose further to ions of mass 74, which may be pictured tentatively as benzadiynes 24:

Pyrolysis of 0.004 moles of each dianhydride together with 0.1 mole of benzene a t 690°, 15 sec contact time, gave 1.25 g and 1.1 g, respectively, of the following products (Fields and Meyerson, 1967d) :

Product

Pyromellitic Dianhydride

Mellophanic Dianhydride

Relative concentrationm Phenanthrene, anthracene Phenylnaphthalene Terphenyl Naphthylbiphenyl or diphenylnaphthalene

10 7 8

13 7 11

1

1

I, Relative intensities in the low-voltage mass spectra, normalized to biphenyl = 100.

The product of mass 178 from pyromellitic dianhydride is tentatively pictured as anthracene, and that from mellophanic dianhydride as phenanthrene, although we have not been able to distinguish between the two compounds by either mass spectrometry or gas chromatography. These products are formed by two 1,4-additions of the benzadiyne to benzene; phenylnaphthalene results from an addition and an

FORMATION A N D REACTIONS O F A R Y N E S

21

insertion; and terphenyl from two insertions, as shown for mellophanic &anhydride : 0

The small amount of naphthylbiphenyl probably forms from an addition to benzene and insertion in biphenyl.

D. Reactiolzs with Chlorinated Benzenes The reaction of benzyne from the pyrolysis of phthalic anhydride with chlorobenzene was expected to give chlorobiphenyls by insertion and naphthalene and chloronaphthalenes by 1,2- and 1,4-addition and rearomatization with respective loss of chloroacetylene and acetylene. To test this prediution, phthalic anhydridewas pyrolyzed in admixture with chlorobenzene at 690' (Fields and Meyerson, 196613). The major products and their relative parent-peak intensities in a low-voltage mass

22

E L L I S K . F I E L D S A N D SEYMOUR MEYERSON

spectrum were : naphthalene, 3.5 ; chloronaphthalenes, 30.0 ; chlorobiphenyls, 34.6 ; and dichlorobiphenyls, 100.0. The expected products from insertion and addition of benzyne were therefore indeed formed. I n addition, a small amount of biphenylene, 1.2 on the same scale, resulted.

However, pyrolysis of chlorobenzene alone under identical conditions, for comparison, gave somerather surprising results. Among the products, analyzed in the same way, were : naphthalene, 0.3 ; chloronaphthalenes, 0.1 ;chlorobiphenyls, 23.6 ;and dichlorobiphenyls, 100.0. Kramers (1877) and Cullis and Manton (1958) found diphenyl, 4-chlorobiphenyl, 4,4'dichlorobiphenyl, and some p-terphenyl as the products of pyrolysis of chlorobenzene. On the basis of a kinetic study at 770-850' and 12 torr, in which the main products were hydrogen, hydrogen chloride, and 4,4'-dichlorobiphenyl, Cullis and Manton (1958) proposed a chain mechanism in which chlorine atoms and chlorophenyl radicals were the chain carriers. The formation of naphthalene and chloronaphthalenes by pyrolysis of chlorobenzene had not hitherto been reported in the literature, and represents a reaction sequence unaccounted for by a simple chain reaction. These products are most readily explained by loss of hydrogen chloride from chlorobenzene to yield benzyne, which then reacts with chlorobenzene as shown in reaction scheme 17 (Fields and Meyerson, 1966b). The formation of benzyne from chlorobenzene at 690' is further substantiated by the presence of a small amount, 0-5 on the same scale, of biphenylene among the products. The high-temperature behavior of chlorobenzenethus parallels somewhat its behavior a t ordinary tempera-

FORMATION A N D REACTIONS OF A R Y N E S

23

tures in the presence of strong bases. Here, however, both o-halophenyl anion and benzyne are formed in a large excess of nucleophile, with which they undergo rapid reaction to yield products. Only in the vapor phase is benzyne able to react with excess chlorobenzenefrom which it formed. o-Chlorofluorobenzene on pyrolysis at 690' (Fields and Meyerson, 1967d)also gave products derived from benzyne by loss of HX, as well as those formed by loss of hydrogen, presumably from a phenylcyclohexadiene intermediate similar to that previously postulated. These were : Fluoronaphthalene 3 Chlorofluoronaphthalene 2 Chlorodifluoronaphthalene 2 Chlorodifluorobiphenyl 82 Dichlorofluorobiphenyl 14 Dichlorodifluorobiphenyl 100

A comparison was made of the relative amounts of similar products from o-dichlorobenzeneand o-chlorofluorobenzeneunder the same conditions : o-Dichlorobenzene Product Xz-biphenyl X3-biphenyl XI-biphenyl

o-Chlorofluorobenzene

Relative concentrations

4.5 64.8 100

2 96 100

The appreciably greater amount of XB-biphenyl from o-chlorofluorobenzene, together with the formation of naphthalene derivatives, suggests that an appreciable amount of the X,-biphenyl was formed by insertion of a halobenzyne. Benzyne in solution reacts as a dienophile : Wittig (1957)f i s t demonstrated this in the reaction of benzyne with furan. Corbett and Porter (1965) obtained further supporting evidence by isolating 1,4-addition products from benzyne with 1-vinylnaphthalene and 3-vinylbenzo[b]thiophene; Dilling (1966)did the same with styrene. Miller and Stiles (1963) generated benzyne by decomposition of benzenediazonium carboxylate and found that it adds to benzene at 45' to give the 1,4- and 1,2-adducts in the ratio 1:4, although evidence recently reported indicates that 1,2-addition under these conditions is minor except in the presence of Agf catalysts (Friedman, 1967). I n our

24

ELLIS K . FIELDS A N D SEYMOUR MEYERSON

study of the reactions of arynes and heteroarynes generated by pyrolysis of aromatic and heterocyclic anhydrides, we wished to determine the ratio of 1,4- and 1,2-addition, as a measure of dienophilic character of benzyne a t elevated temperatures. The competition is obscured in the reaction with benzene because both adducts decompose above 360" to give the same product, naphthalene, as shown in reaction scheme 4. To determine the preferred mode of addition at high temperatures, solutions of 1.48 g (0.01 mole) of phthalic anhydride in 14.7 g (0.1 mole) of each dichlorobenzene isomer were pyrolyzed at 690" under nitrogen in a Vycor tube filled with Vycor beads (Meyerson and Fields, 1966b). Contact time was 22 sec. The products remaining after removal of excess dichlorobenzene (1.15 g, 1.6 g, and 1.05 g, respectively, from the ortho, meta, and para isomers) were analyzed by mass spectrometry. Relative intensities of the parent peaks of the chlorinated naphthalenes, summed to include the species containing both chlorine isotopes, were taken as a first approximation to relative concentrations :

Dichlorobenzene Isomer

ortho

meta

para

Naphthalene Chloronaphthalene Dichloronaphthalene

2 15 100

5 97 100

2 100 15

The results indicate a preference for loss of acetylene over chloroacetylene, by a factor of about 7 :1, in the ortho isomer ; a preference for loss of chloroacetylene over acetylene by the same factor in the para isomer ; and about equal probabilities of losing acetylene and chloroacetylene in the meta isomer. The pronounced differences among the product distributions from the three dichlorobenzenesrule out any extensive scrambling of the chlorine atoms, such as was found for deuterium in deuteriated benzene a t high temperatures. That such scrambling of chlorine atoms does not occur is indicated further by our failure to detect mono- and trichlorobenzenes among the pyrolysis products of the dichlorobenzenes alone under the same conditions. The pyrolysis products most probably result from a strong preference of benzyne for 1,4- over 1,2-addition, coupled with a tendency to avoid adding to chlorine-bearing carbon atoms. I n the meta-isomer case, this reluctance is apparently balanced by the difficulty of adding at a carbon atom between two chlorine atoms, and so mono- and dichloronaphtha-

FORMATION A N D R E A C T I O N S O F A R Y N E S

25

lenes are formed in about equal amounts. The lesser products in the reactions with 0 - and p-dichlorobenzenes presumably arise chiefly via 1,2-addition. If the acetylene lost from the 1,2-adduct comes solely

from the 7- and 8-positions7then the 7 :1 preference for one product over the other is in fact a measure of the extent to which 1,4-is preferred over 1,2-addition. Originally, pyromellitic and mellophanic dianhydrides were thought to go to benzadiyne in possibly a concerted rather than stepwise fashion, because no products retaining an anhydride function could be found. I n the reactions with halogenated benzenes, however, such products do appear; evidently, at least in some environments, these dianhydrides first decompose to benzynedicarboxylic anhydride, followed by further loss of COz and CO. Thus, the reactions of pyromellitic dianhydride with the dichlorobenzenes give naphthalenedicarboxylic anhydride and chlorinated derivatives (Fields and Meyerson, 1967d):

ac)) - c?n,+Co

0

I1

c

0'C \

I1

0 0

I1

0

0

C

\C

11

1I

0

II

It

0 0

II

Distribution of products from reaction of 0-004mole of dianhydride with 0.02 mole of dichlorobenzene at 690' for 22 sec are shown in Table 8. The data indicate approximately the same relative tendencies to lose acetylene and chloroacetylene, in accord with %I preference for 1,4- over 1,a-addition, as was demonstrated by benzyne from phthalic anhydride in its reactions with the three dichlorobenzenes. 2

26

ELLIS K . F I E L D S A N D S E Y M O U R M E Y E R S O N TABLE 8 Products from Pyromellitic Dianhydride and Diohlorobenzene -__

Dichlorobenzeneisomer Product

Naphthalenedicarboxylicanhydride Chloronaphthalenedicarboxylicanhydride Dichloronaphthalenedicarboxylicanhydride

Ortho Mekz Para Relative intensity

0.3 1 7

0.1 3 4

0-4

11 2

Relative intensities in the low-voltage (7.5 volts, uncorrected) mass spectrum, normalized to unreaoted dichlorobenzene = 100.

Tetrachloroanthracene was formed in low yields ; the values for the m-, and p-dichlorobenzene isomers, respectively, on the same scale as in the Table were 2, 1, and 0, about in the expected proportions. The reaction of benzyne with hexachlorobenzene was tried (Fields and Meyerson, 1967d). This compound, in spite of steric crowding, is stable to heat (Krymtzky and Carhart, 1949)and to electron impact in the mass spectrometer (Meyerson and Fields, 1966~1,8s well as inert chemically. At 690' for 35 sec. it was recovered unchanged. With phthalic anhydride in a 2:l mole ratio, under the same conditions, it gave about a 6% conversion to hexachlorobiphenyl, the benzyne insertion product. Absence of any chlorinated naphthalene indicates the difficulty of forming a 1,4- or 1,2-adduct of benzyne with the completely shielded benzene ring. 0-,

E. Reactions with Pyridine With the discovery of benzyne formation by pyrolysis of phthalic anhydride, a new field was opened for the investigation of aryne reactions at lligh temperatures. A first concern was to determine the generality of aryne formation from aromatic acid anhydrides. Such syntheses could be of considerable significance because of the enormous quantities of aromatic mono- and polyanhydrides available from petroleum aromatics by oxidation. Accordingly, nine aromatic and two heterocyclic anhydrides were pyrolyzed in admixture with pyridine under standardized conditions, and the relative amounts of aryne or heteroaryne produced were determined by analysis of the reaction products (Fields and Meyerson,

F O R M A T I O N A N D R E A C T I O N S OF A R Y N E S

27

1966e). Although benzene as reactant gave far fewer products and isomers, it has the disadvantage of pyrolyzing to bi- and terphenyl, and there appeared no easy way to distinguish the products formed by benzene pyrolysis from those formed by aryne insertion. The products were identified in all cases by mass spectrometry, and in some by gas chromatography or by directly coupled gas chromatographymass spectrometry. In a typical experiment, a solution of 1.48 g (0.01 mole) of phthalic anhydride in 8-05ml(O.1 mole) of pyridine was pyrolyzed at 690" in dry, high-purity nitrogen flowing at the rate of 2.7 l/hr. Contact time was 20.2 sec. The products were distilled to recover 6.34 ml of pyridine. The distillation residue weighed 2.12 g, of which 0.06 g was removed for analysis by mass spectrometry. The remainder was dissolved in ether and separated into nitrogen bases (1.44 g) and hydrocarbons (0.62 g) by extraction with dilute hydrochloric acid. Analysis by gas chromatography, by comparison of retention times with authentic samples, gave the results shown in Table 9. TABLE 9 Gas Chromatographic Analysis Compounds Hydrocarbon8 Naphthalene High-boilinghydrocarbons

Nitrogen Bases Quinoline Isoquinoline 2-Phenylpyridine 3-Phenylpyridine' 4-Phenylpyridine Dipyridyl isomers unknowns

Area

yo

93 7 4.0 <0*1

23.9 13.4

3.3 42.4 12.9

Deduced from its retention time.

Analysis of the exit gases by mass spectrometry gave these results (nitrogen-free basis ; carbon monoxide confirmed in a similar run under helium) : carbon dioxide, 45.6 ; carbonmonoxide, 45.4; hydrogen cyanide, 1-8; acetylene, 0.4; hydrogen, 6.8; all values in mole per cent. Yields were calculated on the basis of aromatic anhydride. For example, 0.01 mole of phthalic anhydride with excess pyridine theoretically should give a total of 0.01 mole of the products of insertion and

TABLE10 Insertion and Addition Reaction Products of Arynes with Pyridine

Anhydride

Yielda

Insertion

Relative amountb

100

Phthalic

95

Phenylpyridine

Tetrachlorophthalic Tetraphenylphthalic

17.5 10

Tetrachlorophenylpyridine Tetraphen ylphenylpyridine

3 51

Trimellitic

52

Phenylpyridine Carboxyphenylpyr idine

18 37

Pyromellitic

88

Phenylpyridine Phenylenedipyridine Naphthylpyridine

22 14 6

Mellophanic

47

Phenylpyridine Phenylenedipyr idine Naphthylpyridine

29 14 28

Benzophenonetetracarboxylic dianhydride

82

Pyridylbenzophenone Dipyridylbenzophenone

36 13

1,s-Naphthalic Naphthalene-2,3-dicarboxylic

12 66

Naphthylpyridine Naphthylp yridine

7

Pyridylquinoline Bipyridyl Phenylpyridine Phenylpyrazine

Quinolinic

14d l.ld

(I

Percentage of anhydride converted into insertion and addition products.

27 250 2

Addition

Relative amount’

Naphthalene Quinoline Tetrachloronaphthalene Tetraphenylnaphthalene Tetraphenylquinoline Naphthalene Quinoline Naphthoic acid Naphthalene Quinoline Anthracene Benzoquinoline Pyridylquinoline Naphthalene Quinoline Phenanthrene Benzoquinoline Pyridylquinoline Phenylnaphthyl ketone Dinaphthyl ketone Naphthylpyridylphenyl ketone

167 25 24 36 0.9 4 2

Anthracene Benzoquinoline Quinoline

155 5 12

Quinoline

see text.

Em w

1

I

5 29 3 23 5 1 20 2 12

4

a Relative intensities of parent peaksin the low voltage mass spectra. The intensities are all relative to a value of 100 assigned to bipyridyl. ‘With benzene.

tr

29 3 11

c

7 5

M

0

2

29

FORMATION AND REACTIONS O F ARYNES

addition : naphthalene, quinoline, isoquinoline, and phenylpyridjnes. The total weight of all products of the reaction, coupled with the approximate relative concentrations, as shown in Table 10, gave an estimated 0.0095 mole of products. The reactions of this study involved insertion of the aryne, as well as 1,2- and 1,4-addition followed by rearomatization (Scheme (18.

.

I1

-

~\l + c o 2 + c o

7

+ H2Cz

30

ELLIS K . FIELDS AND SEYMOUR MEYERSON

Table 10 shows the relative amounts of insertion and addition products formed from the various anhydrides. To ascertain that no substantial part of the products arose from pyridine itself, pyridine was pyrolyzed under the identical conditions. It gave a 2.2% yield of products, of which dipyridyl was 96.2%, terpyridyl, 2.7%, and unidentified, 1-1%. From the addition reactions of phthalic anhydride with pyridine, naphthalene was formed in much greater quantity than quinoline ; isoquinoline was either totally absent or present in only minute amounts. These facts indicated (a) if there were much 1,2-addition of benzyne, it occurred predominantly at the 1,2 and 3,4 atoms in pyridine; (b) 1,4addition took place at carbon atoms in preference to a nitrogen and a carbon atom. Studies with other systems indicate that arynes have a decided preference for 1,4- over 1,2-addition. Elimination of hydrogen cyanide was favored over that of acetylene in the rearomatization step. The ratio of hydrogen cyanide to acetylene in the exit gases was not identical with that predicted from the analysis of the less volatile products; this was probably due to secondary pyrolytic transformations of both gases under the reaction conditions. Such transformations were found in separate pyrolyses of hydrogen cyanide and acetylene alone. Tetrachlorophthalic anhydride gave a relatively low yield of products derived from tetrachlorobenzyne. The pyrolysis tube was badly carbonized ; evidently extensive decomposition of the anhydride, the aryne, or the chlorinated products had occurred. Tetrabromophthalic anhydride gave a still lower yield of products. These are not listed in the table because none of them retained all four bromine atoms and could be definitely ascribed to reactions of tetrabromobenzyne, although tribromo- and dibromonaphthalene were present in appreciable amounts. Tetraphenylphthalic anhydride also gave low yields of products of the reaction of tetraphenylbenzyne with pyridine. This was not because of the stability of the anhydride and its reluctance to form the aryne, but rather because the aryne preferred to stabilize itself intramolecularly. The behavior of tetraphenylphthalic anhydride is discussed in another Section. Trimellitic anhydride yielded products derived both from benzyne and carboxybenzyne. Decarboxylation at 690" should be extensive, and this compound then would react like phthalic anhydride. Under the circumstances, the survival of appreciable amounts of carboxybenzyne derivatives was surprising. The 4-methyl ester of trimellitic anhydride would probably be a stable source of carboxybenzyne methyl ester. Pyromellitic and mellophanic dianhydrides gave similar product distributions, derived from presumed benzadiynes. These arynes evi-

FORMATION A N D REACTIONS OF A R Y N E S

31

dently have a strong tendency to abstract hydrogen, as shown by formation of appreciable amounts of phenylpyridine, naphthalene, and quinoline. Products of both insertion and addition in the same molecule were also formed (naphthylpyridine, pyridylquinoline). This was also acid true of another dianhydride, benzophenone-3,3’,4,4’-tetracarboxylic dianhydride. The latter gave dinaphthyl ketone (the product of diaddition), dipyridylbenzophenone (the product of di-insertion), and naphthyl pyridylphenyl ketone (the product of addition plus insertion). An attempt was made to convert mellitic anhydride, the simplest aromatic trianhydride, to benzatriyne. It reacted with pyridine, but 0

j)$ 0

II

II

c-0 =O

c=o

C

I1

0

__f

0,

+scoa+3co

c-0 I1

0

apparently the products totally decomposed ; the only compounds isolated were those derived from pyridine itself. Because of its extremely low solubility, volatility, and decomposition temperature, mellitic anhydride is not amenable to handling in the same way as other anhydrides studied. The yield of products from 1,8-naphthalic anhydride was low, partly because of the thermal stability of the anhydride. At 690’ with 20-sec contact time, 50% was recovered unchanged. Its behavior contrasted anhydride, reflectmarkedly with that of naphthalene-2,3-dicarboxylic ing the greater difficulty of forming perinaphthalyne as against 2,3naphthalyne. Azafluoranthene should result from perinaphthalyne and pyridine by addition, but only the insertion product formed. This contrasted with the low temperature reaction of benzene with perinaphthalyne (from the oxidation of amino-l ,8-naphthatriazole with lead tetraacetate) to give fluoranthene (Rees and Storr, 1965). Quinolinic anhydride gave the products of pyridine addition and insertion, quinoline and pyridylquinoline. Naphthyridine may have been present at a concentration too low to detect. The major insertion product, dipyridyl, was also formed by pyrolysis of pyridine itself. To demonstrate clearly the insertion products of 2,3-pyridyne, quinolinic anhydride was also pyrolyzed in benzene to give the products shown in Table 10.

32

ELLIS K . F I E L D S AND SEYMOUR MEYERSON

Pyrazine-2,3-dicarboxylicanhydride gave no products of the reaction of the corresponding heteroaryne with pyridine; however, it gave a small but definite amount of phenylpyrazine with benzene, suggesting the formation of pyrazyne. This anhydride is readily converted by ring opening and rearrangement to succinonitrile (Brown et al., 1966).

F. Reactions with Thiophene and Benzothiophene The reactions of a series of arynes from aromatic anhydrides with thiophene and benzothiophene at 690' revealed some processes not as clearly evident with other reagents. I n a typical experiment, a solution of 2.96 g (0.02 mole) of phthalic anhydride in 31-46 ml (0.4 mole) of thiophene was pyrolyzed in dry, high-purity nitrogen flowing a t 2.7 l/hr. The contact time was 19 sec. The products were distilled to recover 27.4 ml of thiophene. The distillation residue, 2.5 g, was analyzed by gas chromatography, by comparison of retention times with authentic samples :

Product

Naphthalene Benzothiophene 2-Phenylthiophene 3-Phenylthiophene Bithienyl

Area,

%

47.5 6.1 20.9 6.8 19.4

Yields were calculated as in Section E on the basis of aromatic anhydride. The major products from the reaction of arynes with thiophene and benzothiophene by addition and insertion are shown in Table 11. Benzyne from phthalic anhydride reacted with thiophene at 690' to give naphthalene and benzothiophene by 1,4-addition and loss of sulfur, and by 172-additionand loss of acetylene, respectively, as well as phenylthiophene by insertion (Fields and Meyerson, 1966d, 1967e)(Scheme 19). The ratio of naphthalene to benzothiophene was about 9:1, nearly the same preferencefor 174-over172-additionas was inferred from thereaction of benzyne with dichlorobenzenesand pyridine at the same temperature, and again reflects the strong tendency of benzyne to act as a dienophile. Several products in minor amounts were formed in the reaction of phthalic anhydride with thiophene in addition to those listed. These

Naphthylthiophene

30 59

1,s-Naphthalic

Naphthalene-2,3-dicarboxylic

Phenylbenzothiophene

Pyridylthiophene

-

84

213

194

312

Anthracene, Phenanthrene Dibenzothiophene Naphtho[2,3-b]thiophene Tetrachloronaphthothiophene and tetrachlorodibenzothiophene

Naphthalene Benzothiophene Tetrachloronaphthdene Tetrachlorobenzothiophene Tetrachlorobenzothiophthene Anthracene Naphthothiophene Dithienobenzene Anthracene Naphthothiophene Dithienobenzene Naphthalene Naphthoic Acid Carboxybenzothiophene Anthracene Naphthothiophene Anthracene Naphthothiophene Tetraphenylnaphthalene Tetraphenylbenzothiophene Quinoline Pyridothiophene

Addition

57

100 250 81’

15 1.5 1.5 1 40 330 33 13 5 378 39 100 2 100 2

16

160 18 550 31 130 44

Relative amountb

or bibenzothienyl.

a Relative intensities of parent peaks in the low-voltagemass spectra. The intensities are all relative t o a value of 100assigned to bithienyl

Percentage of anhydride converted into insertion and addition products.

6

58

Benzothiophene Phthalic

Tetrachlorophthalic

23

Quinolinic

5

Phenylthiophene Carboxyphenylthiophene

72

Trimellitic

Tetraphenylphthalic

1

Dithienylbenzene

6

Mellophanic

Naphthylthiophene

10 31

Dithienylbenzene Naphthylthiophene

78

Pyromellitic

60 60

130

Tetrachlorophenylthiophene

24

Tetrachlorophthalic

Relative amountb 133

Insertion Phenylthiophene

%”

Yield,

68

Thiophene Phthalic

Anhydride

Relative intensity at mass 184measures the total contribution of dibenzothiopheneand nrtphthothiophene. The split between the two isomers was estimated by gas chromatography.

Y

Ta~m 11

Insertion and Addition Products of Arynee with Thiophene and Benzothiophene

34

ELLIS K . F I E L D S A N D SEYMOUR MEYERSON

0

include thiophthene, benzothiophthene, and naphthothiophene. These can all be accounted for by intermolecular transfer of hydrogeii from thiophene to benzyne and the formation of thiophyne (25) :

FORMATION A N D REACTIONS OF ARYNES

35

Thiophyne formation in this way requires that benzene be formed; benzene was found among the pyrolysis products from phthalic anhydride and thiophene, neither of which originally contained any benzene. The questions raised by these products led to a study of the pyrolysis products of thiophene itself. Thiophene, 0.4 mole, pyrolyzed alone under the identical conditions as with phthalic anhydride, gave 0.76 g of product (thiophene-free) that analyzed (relative intensities in the lowvoltage mass spectrum) : Benzothiophene Thiophene Phenylthiophene Bithienyl

7.2 1.8

5.4 100

Wynberg and Bantjes (1959) pyrolyzed thiophene at 800-850' for unspecified lengths of time and found these same products in different ratios. They explained the formation of benzothiophene and phenylthiophene by Diels-Alder addition of thiophene to itself:

Thiophthene was presumed to arise as a known product from thereaction of acetylene and sulfur (Hartough, 1952). We propose rather that thiophyne is formed by intramolecular dehydrogenation, and that the minor pyrolysis products of thiophene arise from the reaction of thiophyne with thiophene (Scheme 22). Phenylthiophene is a major product from benzyne and thiophene, and therefore suggests the intervention of benzyne in thiophene pyrolysis. A likely source of benzyne in this system is the 1,4-additionof thiophyne to thiophene followed by loss of acetylene and sulfur (Scheme 23). Such a scheme parallels the behavior of benzene, which a t 690' gives a small amount of naphthalene, arising presumably from intramolecular

36

ELLIS K . F I E L D S AND SEYMOUR MEYERSON

dehydrogenation to benzyne, as shown in Scheme (lo), and the known reaction of benzyne with benzene to give naphthalene.

The formation of bithienyIs can perhaps best be explained by invoking a thienyldihydrothiophene : H H 2a-J S

e

(IyYJ >f s

s

l=c@

L7J H

H H

H

(24)

~Jl--J+H2

Thienyldihydrothiophene is the thiophene analogue of the phenylcyclohexadiene intermediate deduced by Fields and Meyerson (1966~) from scrambling of protium and deuterium in pyrolysis of deuteriated benzene. Both intermediates account for the formation of dimerio species unaccompanied by highly energetic free hydrogen atoms.

FORMATION A N D REACTIONS O F A R Y N E S

37

Formation of naphthalene from phthalic anhydride and thiophene implies the extrusion of sulphur. Products arising from the reaction of this sulphur, possibly monatomic and hence highly reactive (Sidhu et al., 1966) with thiophene might be expected. Indeed, the mass spectrum revealed a product of molecular weight 116 and an isotopic distribution establishing the elemental composition as C4H4S2, doubtless thiophenethiol. The relative amounts of the products were : Product

Relative concentration'

Thiophenethiol Naphthalene Phenylthiophene Bithienyl

9.2 100.0 83.4 62-6

a From relative intensity in the low-voltage (7.5 volts, uncorrected) mass spectrum, normalized to naphthalene = 100.

The product mixture was extracted with potassium hydroxide and the recovered alkali-soluble products were analyzed by directly-coupled gas chromatography-mass spectrometry (Fields and Meyerson, 1967d). The separated product with the parent peak at mass 116, again accompanied by heavy-isotopic satellites with an intensity distribution indicating the formula C4H4S2,gave a spectrum qualitatively similar to that of thiophene-2-thiol in the API Catalog of Mass Spectral Data. The spectra contained the following as the most prominent peaks : Our product Mass

of molecular weight 116

2-Thiophenethiol

45 71 115 116

69-6 100.0 7,22 45.4

45.6 93.4 9.26 100.0

There are quantitative differences which, in the light of correlations described by Foster et al. (1963), suggest that our material consists chiefly of the 3-isomer. The substantially lower relative intensity at the parent mass parallels the known lower stability of this isomer (Houff and Schultz, 1953)to light, heat, and air. Thiophenethiol was also found in the products from a solution of

38

ELLIS K . F I E L D S AND SEYMOUR MEYERSON

sulphur in thiophene pyrolyzed (Fields and Meyerson, 1967d)under the identical conditions as for phthalic anhydride and thiophene, about 10% of the yield of bithienyl. I n addition, in both reactions, small amounts of a product of molecular weight of 198 withanisotopic profile indicating the composition C8H& was formed. As this was soluble in alkali, it is most probably bithienylthiol, from the insertion of a sulphur atom in bithienyl .

Tetrachloronaphthalene (26) and tetrachlorobenzothiophene (27) from tetrachlorophthalic anhydride formed by addition of tetrachlorobenzyne to thiophene and subsequent loss of sulphur and acetylene, respectively (Fields and Meyerson, 1967e):

CI 1,4-addition

1,2-addition

CI

Cl (27)

FORMATION A N D REACTIONS OF A R Y N E S

39

Tetrachlorophenylthiophene is the expected insertion product. Tetrachloronaphthothiophene (28) and tetrachlorobenzothiophthene (29) are most easily formulated as arising from the reaction of thiophyne with tetrachloronaphthalene and tetrachlorobenzothiophene, respectively:

Cl

(51

+ CzHz

c1

c1

The relatively large amount of (28) formed would demand the formation of a correspondingly large amount of tetrachlorobenzene by hydrogen transfer from thiophene to tetrachlorobenzyne. Tetrachlorobenzene was indeed found, though in amounts inadequate to account for

40

ELLIS K . FIELDS A N D SEYMOUR MEYERSON

28. The deficit is doubtless at least partly due to decomposition of tetrachlorobenzene a t 690'. Pyromellitic dianhydride pyrolyzes to formally a benzadiyne :

Anthracene results presumably from two 1,4-additions with elimination of sulphur :

Naphthothiophene results from both 1,4- and 1,2-addition :

Dithienobenzene,

, is formed by two 1,2-additions

and elimination of two molecules of acetylene ; naphthylthiophene,

FORMATION A N D REACTIONS O F ARYNES

-

by 1,4-addition and insertion ;and dithienylbenzene,%8'

41

8s1

by two insertions. The reaction of pyromellitic dianhydride with thiophene (Fields and Meyerson, 1967e)thus resembles the reactions of pyromellitic and other dianhydrides with pyridine, from which all combinations of insertion and addition products formed (Section E). In addition, there were small amounts of products probably resulting from hydrogen abstraction : naphthalene, benzothiophene, thiophthene, and phenylthiophene. These reactions possibly took place in a step-wise, rather than a concerted fashion, although the data tend to favor the formation of benzadiyne. Under the same conditions in which an appreciable amount of phthalic anhydride could be recovered, pyromellitic dianhydride gave no products that still retained an anhydride group.

.o-c=o Mellophanic dianhydride

0

= '& ' !o

with thiophene (Fields

II

0

and Meyerson, 1967e) gave almost the identical product distribution as pyromellitic dianhydride, although the yield was appreciably less. The lower yield probably resulted from using a dilute solution for the pyrolysis, instead of subliming the anhydride into the Vycor tube together with a nitrogen stream of thiophene, as with pyromellitic dianhydride. The mass spectra of the two anhydrides are quite similar, and leave little doubt that, both upon electron impact and pyrolysis, loss of the elements of the two anhydride groups leads to similar or identical species. The major products from trimellitic anhydride were those resulting from the reactions of carbuxybenzyne (Fields and Meyerson, 1967e): carboxyphenylthiophene, naphthoic acid, and carboxybenzothiophene. Only about 20% were those from decarboxylation :phenylthiophene and naphthalene. The yield of products from 1,8-naphthalic anhydride was low, partly because of the thermal stability of the anhydride (Fields and Meyerson, 1967e). At 690" with 20 sec contact time, 50% was recoveredunchanged.

42

ELLIS K . F I E L D S A N D S E Y M O U R M E Y E R S O N

Its behavior contrasted markedly with that of naphthalene-2,3dicarboxylic anhydride, reflecting again the greater difficulty of forming perinaphthalyne as against 2,3-naphthalyne. Both anhydrides gave appreciable amounts of naphthalene, formed by hydrogen abstraction from thiophene by the naphthalynes. Hydrogen abstraction by perinaphthalyne (from oxidation of amino-l ,8-naphthotriazole with lead tetraacetate) has been observed a t low temperatures (Rees and Storr, 1965). Tetraphenylphthalic anhydride gave a poor yield of products with thiophene. Similar results had been found in its reaction with pyridine (Fields and Meyerson, 1966e). This anhydride is discussed in Section G . Quinolinic anhydride decomposes at a lower temperature than do the aromatic anhydrides (Fields and Meyerson, 1967e). For this reason, it was allowed to react with thiophene at 600' and 40 sec contact time. The products, quinoline, pyridothiophene, and pyridylthiophene, are those expected from the 1,4- and 1 ,%additions and insertion of pyridyne with thiophene :

QI+(r-J-rn.-rn+s N '

N '

a 0 7 \"'. (30)

1.

+CaHz Whether the unusually high ratio of 1,4- to 1,2-addition product, 50 :1, is due to a markedly different reactivity of pyridyne as compared with

FORMATION A N D REACTIONS O F A R Y N E S

43

benzyne or whether the lower temperature favors greater discrimination remains to be determined. There were also small amounts of thieno-

presumably arose from the reaction of thiophyne with quinoline and thienopyridine, respectively. That hydrogen abstraction occurred was shown by the presence of pyridine in the pyrolysate. As benzothiophene was a product of both the reaction of benzyne with thiophene and the pyrolysis of thiophene alone (Fields and Meyerson, 1966d), we investigated the reaction of benzyne with benzothiophene. Pyrolysis of a mixture of phthalic anhydride and benzothiophene gave the products shown in Table 11. Anthracene and dibenzothiophene probably arose via l,2-, and phenanthrene via 1,4-addition to the thiophene ring :

Naphthothiophene is attributed chiefly to l14-additionof benzyne to the benzene ring of benzothiophene (Scheme 32). Our inability to distinguish between anthracene and phenanthrene, coupled with uncertainties arising from competition between addition

44

ELLIS K. F I E L D S AND SEYMOUR MEYERSON

reactions to the benzo and thieno rings, precludes any confident assessment of relative probabilities of 1,4- and 1,2-addition in this system.

Phenylbenzothiophene is the insertion product, and bibenzothienyl is formed primarily by dehydrogenation of benzothiophene, probably through an intermediate benzothienyl dihydrobenzothiophene. There were formed, additionally, small amounts of products of molecular weights 240 and 264 :

and, doubtless, isomeric species that can most easily be rationalized by hydrogen transfer from benzothiophene to benzyne and reaction of benzothiophyne with benzothiophene and with itself:

FORMATION A N D REACTIONS OF A R Y N E S

45

Both products, although in much smaller amounts, were also formed in the pyrolysis of benzothiophene alone (0.15 g of products from 0.05 mole of benzothiophene). As in the case of thiophene, they suggest intramolecular dehydrogenation to benzothiophyne. Two other minor products formed in the pyrolysis, not present in the starting benzothiophene, were phenylthiophene and bithienyl. According to our proposed scheme, these seem to demand the formation of thiophyne and/or thiophene from benzothiophene. Mass spectra of some aromatic dicarboxylic anhydrides give a clue to a possible mechanism. Both naphthalene-l,8- and -2,3-dicarboxylic anhydrides sequentially lose carbon dioxide and carbon monoxide upon electron impact to give an ion of mass 126, nominally naphthalyne, as was shown in Section C. In addition, both spectra show a peak of moderate intensity at mass 76, corresponding to an ion having at least the elemental composition of benzyne, suggesting the se( ence :

Such a reverse Diels-Alder reaction of benzothiophyne could generate thiophyne :

In addition to the two products mentioned, a thiophyne intermediate can also account for a small amount of thienylbenzothiophene found in the pyrolysis of benzothiophene. Phthalic anhydride reacted with dibenzothiophene at 690' to give a 10% yield of addition and insertion products. Naphthobenzothiophene isomers, the addition products, were formed in a 2 :1 ratio over phenyldibenzothiophene isomers, the insertion products-about the same ratio as was found in the reaction of benzyne with benzothiophene. The spectrum revealed no product of molecular weight 340, which would

46

ELLIS K . FIELDS AND SEYMOUR MEYERSON

have been evidence for formation of dibenzothiophyne. However, minor products could easily have gone undetected as a result of dilution by unreacted dibenzothiophene.

G . Reaction8 of Tetraphenylbenzynefrom Tetraphnylphthlic Anhydride

As tetraphenylphthalic anhydride behaved quite differently from the other aromatic anhydrides, its mass spectrum and reactions at high temperatures (Fields and Meyerson, 1967f) are described separately. A partial mass spectrum is shown in Table 12. TABLE12 Partial Mass Spectrum of Tetraphenylphthalic Anhydride

Mass

Relative intensity

462 408 380 378 376 304 302 300

100.0 12.0 9.7 18.1 20.7 2.8 21.4 8.6

Suggested process by which formed

Parent (P) P -COa 408 CO 380-Ha 378-HZ 380 - CsH4 378- CeH4 or 380 - C& 376-c& or 378-C~He

-

Molecular hydrogen is lost in at least the two steps indicated. The spectrum suggests the reactions shown on page 47 as scheme (36). Benzyne seems to be lost in forming ions of masses 304, 302, and 300, although the spectrum shows no metastable peaks to establish these processes unequivocally. The high intensity of the ion of mass 302 relative to those of all ions of lower masses suggests a greater stabilization

47

FORMATION AND REACTIONS O F ARYNES

+

* - COI

380

CeHs L

380

380

378 376

.

in its structure, which is pictured as a biphenylene derivative of triphenylene :

+

-f

__f

L

378

+

-

302

L

0 1 \

TABLE13 Products from Pyrolysis of Tetraphenylphthalic Anhydride

w

z

Added reagent" Molecular weight

Pyridine

o-Xylene

Hexafluorobenzene

Quinoline

M F

Thiophene

N-Methylpyrrole

t, VJ

Benzonitrile

+

w

tr

Relative amountsb

v1

382 380 378 306 304 302

7 100 31 10 62 36

30 100 13 50 166 50

56 100 15 28 85 33

11 100 4 14 122 40

60 100 13 43 123 37

44 100 5 25 58 12

33 100 20 30 100 33

M

+-4

K

0

cl

w

z

M

+-4

" 0.01 mole anhydride in 0.1 mole reagent at 690"for 15-20

sec. Relative intensities in the low-voltagespectra, normalized to a value of 100 at mass 380 for intercomparison.

M

F O R M A T I O N A N D R E A C T I O N S OF A R Y N E S

49

The reaction products of tetraphenylphthalic anhydride with a variety of reagents are shown in Table 13. In all cases, compounds of molecular weights 382, 380, 378, 306, 304, and 302 were the major products. The variation in relative amounts was remarkably small, in view of the large differences among the chemical environments in which they formed. The yields of products involving added reagents were low in all cases. These results can best be rationalized by assuming the formation of tetraphenylbenzyne and its rapid stabilization intramolecularly to give triphenylbiphenylene :

380

304

The compound present in greatest concentration after that of molecular weight 380 is pictured as 2,4-diphenylbiphenylene ; elimination of the 3-phenyl group would lead to maximum relief of steric pressure. Compounds of molecular weights 382 and 306 are probably tetraphenyl- and triphenylbenzenes, respectively, formed by hydrogen abstraction; those of 378 and 302 are best pictured as formed by loss of hydrogen to give the triphenylene derivatives :

378

302

50

ELLIS K . FIELDS A N D SEYMOUR MEYERSON

I n the vapor phase at 690°, regardless of its environment, tetraphenylphthalic anhydride exhibits much of the same behavior reflected in its decomposition pattern under electron impact in the mass spectrometer.

111. BENZYNE FROM 0-SULPHOBENZOIC ANHYDRIDE o-Sulphobenzoic anhydride possesses potentially two good Ieaving groups, sulphur dioxide and carbon dioxide, and could yield benzyne upon pyrolysis : 0 @ $ O

C

-

~\~ + s o 2 + c o 2

II Wittig and Hoffmann (1961) obtained benzyne from a compound of somewhat similar structure, 1,2,3-benzothiadiazoIe 1,l-dioxide, at 0'. The mass spectrum of o-sulphobenzoic anhydride furnishes evidence for three competing decomposition paths (Scheme (38) on page 51). Relative contributions of the three paths can be estimated by summing the intensities of the ions arising by each of them in the 70 v spectrum : (I), 68.7%; (11),30.9% ; (111), 0.4%. However, voltage-dependence measurements show that the appearance potential of C7H40i is lower than that of C,H40+. At 9.5 ionizing volts (uncorrected),intensity of the C7H40$ion is about five times that of C7H40+,in sharp contrast to the situation at 70 volts, where intensity of C7H40+is twice that of C,H,O,+. Loss of SO2 is thus preferred at low energies, and might therefore be expected to be the preferred primary process also in pyrolysis (Grubb and Meyerson, 1963; see also Meyerson and McCollum, 1963; Meyerson, 1964; Turro et al., 1965). To test this prediction, a solution of o-sulphobenzoic anhydride (0.02 mole) in benzene (0.4mole) was pyrolyzed at 690°, with a contact time of 18 sec. The pyrolysate, after removal of benzene, weighed 2.2 g. The product mixture, determined by mass spectrometry, is shown in Table 14 together with the products from identical pyrolyses of benzene (35.5 ml) alone (0.3 g product) and of phthalic anhydride (2.96 g; 0.02 mole) in benzene (35.5 ml) (2.6 g product) for comparison. Relative concentrations (vol. %) of the three components for which we have the requisite calibration data (naphthalene :biphenyl :3,4-benzocoumarin = 71:100:21) match closely the relative intensities shown in Table 14,

FORMATION A N D R E A C T I O N S OF A R Y N E S

51

supporting the use of such mass-spectral data as a first approximation to relative concentrations. I n accord with our results Meyerson and Fields (1966a), Brown et al. (1967) have identified biphenylene and SO2 among the products of pyrolysis of o-sulphobenzoic anhydride at 730' and 0.05 torr.

path I

path 11

path I I I

140

The data strongly suggest the formation of benzyne from o-sulphobenzoic anhydride-from the products of its reaction with benzene by 1,2- and 1,4-addition (naphthalene, phenylnaphthalene) and insertion (biphenyl, about four times as much by weight as from benzene alone). The uncondensed gases from the reaction were a 1 :1 mixture of sulphur dioxide and carbon dioxide. This, in addition to the other products, indicates that the first step of Path 2, loss of sulphur dioxide, is the dominant primary process. However, the resulting zwitterion, unlike its cationic counterpart in the mass spectrometer, does not go on to lose carbon monoxide ;it stabilizes itself more easily by losing carbon dioxide

52

E L L I S K . F I E L D S A N D SEYMOUR M E Y E R S O N

TABLE14 Mass-SpectralIntensities of Pyrolysis Products Compound pyrolyzed Molecular weight

Identity

Benzene

Phthalic anhydride in benzene

o-Sulphobenzoic anhydride in benzene

Relative intensities‘, 128 152 154 180 196 204 230

Naphthalene Biphenylene Biphenyl Fluorenone 3,4-Benzocoumarin Phenylnaphthaleno Terphenyl

0.2 100

4

23.1

’ 67

2

-

100 0.9 9 2.5

100 3 20 10 10

’From spectra measured at 7.5 ionizing volts, uncorrected.

’Normalized to a value of 100 for biphenyl.

and going to benzyne. Anokher possible course for the zwitterion is to attack the benzene and give either biphenyl or the lactone of 2-hydroxybiphenyl-2’-carboxylic acid (30):

FORMATION A N D R E A C TI ON S O F A R Y N E S

53

The pyrolysate contained an appreciable amount of product of molecular weight 196, which could be either xanthone or the lactone 30. Directly coupled gas chromatography-mass spectrometry identified it as 30. The retention time and mass spectrum of this product agreed closely with those of an authentic sample of 30, synthesized by the method of Graebe and Schestakow (1 895), which was clearly distinguishable from xanthone on both counts. The formation of 30 parallels that of fluorenone from phthalic anhydride and benzene, observed by Fields and Meyerson (1965).

o-Sulphobenzoic anhydride (0.01 mole) with pyridine (0.4mole) at 690' and a contact time of 12 sec gave 2.2 g of products, which were analyzed by gas chromatography. These are shown in Table 15 along with the corresponding products from phthalic anhydride and pyridine, obtained under the same conditions for comparison. TABLE 16 Products from o-SulphobenzoicAnhydride and Phthalic Anhydride with Pyridine Compound pyrolyzed Product

o-Sulphobenzoic anhydride Area

Naphthalene Quinoline 2-Phenylpyridine 3-Phenylpyridine 4-Phenylpyridine Dipyridyl isomers

Phthalic anhydride

yo in gas chromatogram

19.8 4.3 19.3 13.2 8.1 32.6

28.8 2.7 17.2 9.6 2.4 30.4

Although there are appreciable differences in the product distributions from the two benzyne precursors, the general trend is about the same and leaveslittle doubt that both anhydridesreact at 690' by forming benzyne. I n Path I1 of the mass spectral scheme for the decomposition of o-sulphobenzoicanhydride, successive loss of SOzand CO from the parent ion gives an ion of mass 92, which may be represented as 31.

54

ELLIS K. F I E L D S AND SEYMOUR MEYERSON

Additional evidence that the thermal decomposition of o-sulphobenzoic anhydride parallels the mass spectral paths is furnished by the formation of phenol in its reactions with benzene and pyridine (at relative concentrations of 4 and 2 on the scales of Tables 14 and 15, respectively). Further, the reaction with benzene gives dibenzofuran and that with pyridine a compound of molecular weight 169, almost certainly a pyridine-derived analog of dibenzofuran, in relative concentrations of 12 and 2, respectively. These arise most likely from the zwitterion analog of 31 by hydrogen abstraction from, and by attack on, the other reagent present :

IV. BENZYNE FROM ACETYLENE Pyrolysis of acetylene to a mixture of aromatic hydrocarbons has been the subject of many studies, commencing with the work of Berthelot in 1866 (1866a, 1866b). The proposed mechanisms have ranged from formation of CH fragments by fission of acetylene (Bone and Coward, 1908) to free-radical chain reactions initiated by excitation of acetylene to its lowest-lying triplet state (Palmer and Dormisch, 1964; Palmer et al., 1966) and polymerization of monomeric or dimeric acetylene biradicals (Minkoff, 1959; see also Cullis et al., 1962). Photosensitized polymerization of acetylene and acetylene-d2and isotopic analysis of the benzene produced indicated involvement of both free-radical and excited state mechanisms (Tsukuda and Shida, 1966). In our study of the formation and reactions of arynes at high tempera-

55

FORMATION A N D REACTIONS O F A R Y N E S

tures, we pyrolyzed tenth-molar quantities of phthalic anhydride and acetylene, separately and in admixture, at 690' in a Vycor tube filled with Vycor beads in a stream of dry nitrogen for contact times of 4-5 sec (Fields and Meyerson, 1967s). The major products boiling above 150' are shown in Table 16. TABLE16 Pyrolysis of Acetylene and Phthalic Anhydride Compound(s)pyrolyzed

Acetylene Total weight of high-boiling products, g

0.36

Product Naphthalene Biphenylene Biphenyl Anthracene and phenanthrene Phenylnaphthalene Triphenylene Binaphthylene

Phthalic anhydride

Phthalic anhydride and acetylene

1.5

1.8

Relative intensity"

100 5

16 49 12 20 27

100 7 80 227 43 61 30

100 6 16 68 16 22 17

Relative intensities of parent peaks in the low-voltage (7.5 ionizing volts, uncorrected) mass spectra, normalized to naphthalene = 100.

The striking similarity in the nature and some of the relative concentrations of the products in the three reactions strongly suggests common mechanisms and intermediates for their formation. Phthalic anhydride gives benzyne upon pyrolysis ;the parallel behavior of acetylene suggests that it also forms benzyne at high temperatures. To test this hypothesis, phthalic anhydride, acetylene, and acetylene-d, were separately reacted with hexafluorobenzene at 690° under the same conditions as those used with acetylene alone. Phthalic anhydride gave tetrafluoronaphthalene, by 1,4-addition, and hexafluorobiphenyl, by insertion of benzyne, in a 1:5 ratio as estimated from the low-voltage mass spectrum and directly-coupled gas chromatography-mass spectrometry :

56

E L L I S K . F I E L D S A N D SEYMOUR M E Y E R S O N

F

F F

+CzFa

(41)

F

F F

Acetylene with hexafluorobenzene also gave tetrafluoronaphthalene and hexaffuorobiphenyl, though a 4 : l ratio, and also tetrafluoroanthracene. Acetylene-d2 under the same conditions gave tetrafluoronaphthalene-d, and hexafluorobiphenyl-d4 in a 9:l ratio, as well as tetrafluoroanthracene-d6. Benzyne probably forms from acetylene by cycloaddition reaction of acetylene and diacetylene, concerted or stepwise (Woodward and Katz, 1959; Woodward and Hoffmann, 1965a, b): H C

H

Diacetylene is a known pyrolysis product of acetylene; Linden and Reid (1959) and Aten and Greene (1961) from shock-wave pyrolysis studies postulated it as the fist product formed from acetylene. Thermochemical data (Greene et al., 1956; see also Gay et al., 1965)show that the reaction 2 C2H2--f C4H2+ H2 is exothermic to the extent of about 13 kcal/mole :

C2H

+ CzHz

D(C2H-H) = 114 kcal/mole (Knox and Palmer, 1981). -+ C4Hz + H; AH = -23 kcal/mole (Bradley and Kistiakowsky, 1961). D(Ha) = 104 kcal/mole (Cottrell, 1958).

F O R M A T I O N AND R E A C T I O N S O F A R Y N E S

57

Benzyne may react further with diacetylene to form naphthalyne, which in turn would be expected to react with hexafluorobenzene to give tetrafluoroanthracene : HC

F

F

Alternatively, tetrafluoroanthracene could form by the reaction of benzyne with tetrafluoronaphthalene. I n that case, however, some difluoroanthracene should also form by 1,4-addition of benzyne to the fluorinated ring. No difluoroanthracene or difluoroanthracene-d, was found in the products from the reactions of hexafluorobenzene with acetylene and acetylene-&, respectively. This evidence that benzyne is at least one of the intermediates in acetylene pyrolysis has many implications. However, as the ratios of products from acetylene and hexafluorobenzene differ appreciably from those obtained from phthalic anhydride, it might be best at this point to call acetylene a “ benzynoid” precursor. Additional data will be needed and are being accumulated to determine to what extent acetylene reactions proceed at high temperatures through a benzyne intermediate (Fields and Meyerson, 1967a).

V. CONCLUSION As our work on arynes a t high temperatures has progressed, it has become increasingly clear that at sufficiently high temperatures almost all aromatic compounds form benzyne, the “aromatic acetylene.’’ This parallels the behavior of most aliphatic compounds, which pyrolyze to some extent to acetylene. Certain good leaving groups facilitate benzyne formation-C02, CO, and SO2. However, even HX ( X = halogen) and Hz can function as leaving groups, as is shown by the formation of benzyne in the pyrolysis of chlorobenzene and benzene, respectively. 3

58

ELLIS K . F I E L D S A N D S E Y M O U R M E Y E R S O N

Some recent work on the formation and reactions of free radicals in the gas phase is pertinent a t this point. Fields and Meyerson (1967b, c ) discovered that aromatic nitro compounds at about 600' give free aryl radicals :

Ar-NOZ+ Ar. + NOz This process is accompanied by two competing reaction paths : (1) formation of aryloxy radicals by a nitro-nitrite rearrangement :

Ar-NO2 -+ ArONO + ArO. + NO and (2) formation of arynes, e.g. benzyne from nitrobenzene :

Both under electron impact in the mass spectrometer and thermally, the extent of loss of HNOz to give benzyne is small compared to the other processes; nevertheless, in the presence of reagents such as hexafluorobenzene this reaction becomes significant (E'ields and Meyerson, 1967d). Very likely, future work in our laboratories and elsewhere will uncover additional evidence for the ubiquitous role of benzyne in high temperature reactions, as well as exploiting reactions under electron impact in the mass spectrometer as a source of clues to new pyrolysis reactions.

REFERENCES Aten, C. F., and Greene, E. F. (1961). Combuetim an& Flame 5 , 5 5 . Berry, R. S., Spokes, G. N., and Stiles, M. (1962). J . Am. Chem. SOC.84, 3570. Berry, R. S., Clardy, J., and Schafer, M. E. (1964). J . Am. Chem. SOC. 86, 2738. Berthelot, A. (1866a). Jahreder. Fortschritte Chem. 516. Berthelot, A. (186613). Ann. chimphya. [4], 9,455. Berthelot, A. ( 1 8 6 6 ~ ) Jahreeber. . Fortschritte Chern. 540. Bone, N. A., and Coward, H. F. (1908). J . Chem. SOC. 93,1197. Bowie, J. H., Williams, D. H., Lawesson, S.-O., Madsen, 5. 0., Nolde, C., and Schroll, G. (1966). Tetrahedron 22, 3515. Bradley, J. N., and Kistiakowsky, G. B. (1961). J . Chem. Phye. 35,264. Brown, R. F. C., Crow, W. D., and Solly, R. K. (1966). C h m . I d . (London)343. Brown, R. F. C., Gardner, D. V., McOmie, J. F. W., and Solly, R. K. (1967). Awtral. J . Chem. 20, 139. Brown, R. F. C., and Solly, R. K. (1965). Chem. I d . (London) 181.

FORMATION A N D REACTIONS O F A R Y N E S

59

Burr, J. G., and Scarborough, J. M. (1960). J . Phys. Chem. 64,1367. Burr, J.G., Scarborough,J. M., and Shudde, R. H. (1960).J . Phys. Chem.64,1359. Cava, M. P., Mitchell, M. J., Ddongh, D. C.,and Van Fossen, R. Y. (1966). Tetrahedron Letter8 2947. Chambers, R. D., and Cunningham, J. A. (1967).Chem. Comm. 583. Corbett, T. G., and Porter, Q.N. (1965). Austral. J . Chem. 18, 781. Cottrell, T. L. (1958). “Strengths of Chemical Bonds.” Butterworths Scientific Publications, Ltd., London, 2nd ed. Cullis, C. F., and Manton, J. E. (1958). Trans. Faraday SOC.54, 381. Cullis, C.F., Minkoff, G. J., and Nettleton, M. A. (1962). Trans. Faraday SOC. 58,

1117. Dilling, W. L. (1966). TetrahedronLetters 939. Eliel, E. L., Meyerson, S., Welvart, Z., and Wilen, S.H. (1960).J . Am. Chem. SOC. 82,2936. Fields, E. K., and Meyerson, S. (1965). Chem. Cmm. 474. Fields, E.K., and Meyerson, S. (1966a).J . Am. Chern. SOC.88,2836. Fields, E. K., and Meyerson, S. (1966b). J . Am. Chern. Soc. 88, 3388. Fields, E.K., and Meyerson, S. (1966~). J . Am. Chem. SOC.88, 21. Fields, E. K., andMeyerson, S. (1966d). Chem. Comm. 708. Fields, E.K., andMeyerson, S.(19660). J . Org. Chem. 31, 3307. Fields, E.K., and Meyerson, S. (1967a). TetrahedronLetters, 571. Fields, E.K., andMeyerson, S. (1967b). J . Am. Chem. SOC. 89, 724. Fields, E.K., and Meyerson, S. (1967~). J . Am. Chem. SOC.89, 3224. Fields, E. K., and Meyerson, S. (1967d). Unpublished results. Fields, E. K., and Meyerson, S. (19670). I n “Oganosulfur Chemistry’’ (M. J. Janssen, ed.), p. 143. Wiley, New York. Petroleum Preprink, 12, Fields, E. K., and Meyerson, S. (1967f). Am. Chem. SOC. No.1, 57. Fisher, I.P.,and Lossing, F. P. (1963).J . Am. Chem. SOC.85, 1018. Fonken, G.J. (1963). Chem. I d . (London) 1625. Forbes, G.S.,andcline, J. E. (1941). J . Am. Chem. SOC.63, 1713. Foster, N. G., Hirsch, D. E., Kendall, R. F., and Eccleston, B. H. (1963). U.S. Bureau of Minea Report of Investigations 6433. Gaeumann, T., and Rayraux, J. M. (1962). Helv. Chim. Acta 45,1563. Gay, I.D.,Kistiakowsky, G. B., Michael, J. V., and Niki, H. J. (1965). J . Chem. Phys. 43, 1720. Gohlke, R. S. (1959). Anal. Chern. 31, 535. Gordon, S.,and Burton, M. (1952). Discussions Faraday SOC.12,88. Gordon, S.,Van Dyken, A. R., and Doumani, T. F. (1958).J . Phys. Chem. 62,20. Graebe, C., and Schestakow, P. (1895). Ann. Chem. 284,306. Greene, E. F., Taylor, R. L., and Patterson, W.L. (1958). J . Phys. Chem. 62,238. Grubb, H.M., and Meyerson, S. (1963).I n “Mass Spectrometry of Organic Ions” (F.W. McLafferty, ed.),p. 453. Academic Press, New York. Hall, K. L., andElder, F. A. (1959). J . Chem. Phys. 31,1420. Hmtzsch, A.,and Davidson, W. B. (1896). Chem. Ber. 29, 1535. Hartough, H. D.(1952). “Thiophene and Its Derivatives,” p. 49, Interscience, New York. Heaney, H. (1962). Chem. Rev. 62, 81. Hellman, M. (1957). National Bur. Standards Report 5765. U.S. Govt. Printing Office, Washington, D.C. Hou, K. C.,and Palmer, H. B. (1965).J . Chem. Phys. 69,863. H o d , W.H., and Schultz, R. D. (1953). J . Am. Chem. Soc. 75,631.

60

E L L I S K. F I E L D S AND SEYMOUR MEYERSON

Huisgen, R., and Rist, H. (1954). Naturwiss. 41, 358. Huisgen, R., and Rist, H. (1955). Ann, Chem. 594, 137. Kampmeier, J. A., and Hoffmeister, E. (1962). J. A m . Chem. SOC.84, 3787. Kampmeier, J. A., and Rubin, A. B. (1966). Tetrahedron Letters 2853. Knox, B. E., and Palmer, H. B. (1961). Chem. Rev. 61, 247. Kramers, J. G. (1877). Ann. Chem. 189, 135. Krynitzky, J. A., and Carhart, N. W. (1949). J. A m . Chem. SOC. 71, 816. Lindeman, L. P., a n d h i s , J. L. (1960). Anal. Chem. 32,1742. Linden, H. R., and Reid, J. M. (1959). Chem. Eng. Progr. 55, No. 3, 71. Lindow, D. F., and Friedman, L. (1967). J. A m . Chem. SOC.89, 1271. McLafferty, F. W., and Gohlke, R. J. (1959). Anal. Chem. 31, 2076. Meyerson, S. (1964). J. Phys. Chem. 68, 968. Meyerson, S. (1965). Record Chem. Progr. 26, 257. Meyerson, S., Drews, H., and Fields, E. K. (1964). Anal. Chem. 36, 1294. Meyerson, S., and Fields, E. K. (1966a). Chem. Comm. 275. Meyerson, S., and Fields, E. K. (1966b). Chem. Ind. (London) 1230. Meyerson, S . , and Fields, E. K. (1966~).J. Chem. SOC.( B )1001. Meyerson, S., and McCollum, J. D. (1959). Abstr. A m . Chem. SOC., 136thMeeting, 295. Meyerson, S., and McCollum, J. D. (1963). Advan. Anal. Chem. Instrumentation, 2, 179. Meyerson, S., Nevitt, T. D., and Rylander, P. N. (1963). Advan. MassSpect. 2,313. Mignonac,M. G., andde Saint-Aunay,R. V. (1930). Bu11.Soc.chim.France, 47,623. Miller, R. G., and Stiles, M. (1963). J. A m . Chem. SOC.85, 1798. Minkoff, G. J. (1959). Can. J. Chem. 36,131. Palmer, H. B., and Dormisch, F. L. (1964). J. Phys. Chem. 68, 1553. Palmer, H. B., Hou, K. C., Sharma, R. K., andLabaye, J. (1966). A m . Chem.Soc. Petroleum Preprints, 11, No. 2, (2-71. Porter, Q. N. (1967). Austral. J . Chem. 20, 103. Quayle, A. (1959). Chimia (Aurau), Colloquium Spectroscopicurn Internationale VIII, 259. Rees, C. W., and Storr, R. C. (1965). Chem. Comm. 193. Roberts, J. D., Simmons, H. E., Carlsmith, L. A., and Vaughan, C. W. (1953). J . A m . Chem. SOC. 75,3290. Roberts, J. D., Semenow, D. A., Simmons, H. E., and Carlsmith, L. A. (1956). J . A m . Chem. SOC. 78, 253. Shih, C., Hey, D. H., and Williams, G. H. (1959). J . Chem.Soc. 1871. Sidhu, K. S., Lorn, E. M., Strausz, 0. P., and Gunning, H. E. (1966). J.A m . Chem. SOC. 88, 253. Stiles, M., and Miller, R. G. (1960). J. A m . Chem. SOC.82, 3802. Stoermer, R., and Kahlert, B. (1902). Chem. Ber. 35, 1633. Tsukuda, M., and Shida, S. (1966). J. Chem. Phys. 44, 3133. Turro, N. J., Neckers, D. C., Leermakers, P. A., Seldner, D., and D’Angolo, P. (1965). J. A m . Chem. SOC.87, 4097. Wallace, T. S., and Heimlich, B. M. (1966). Chem. Ind. (London) 1885. Watson, J. T., andBiemann, K. (1964). Anal. Chem. 36, 1135. Wittig, G. (1942). Natzcrwiss. 30, 696. Wittig, G. (1957). Angew. Chem. 69, 245. Wittig, G. (1961). Ann. Chem. 650, 20.

FORMATION AND REACTIONS O F A R Y N E S

Wittig, G., and Harborth, G. (1944a). Chem. Ber. 77,306. Wittig, G.,and Harborth, G. (194413). Chem. Ber. 77, 316. Wittig, G.,Pieper, G., and Fuhrmann, G. (1940). Ber. 73,1193. Wittig, G.,and Witt, H. (1941). Ber. 74, 1480. Woodward, R.B., andHoffmann, R. (1965a). J . Am. Chem. SOC. 87,395. Woodward, R.B.,and Hoffmann, R. (1965b).J . Am. Chem. SOC. 87,2046. Woodward, R.B., and Katz, T. J. (1959). Tetrahedron 5, 70. Wynberg, H., and Bantjos, A. (1959).J. Org. Chem. 24,1421.

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DEVELOPMENTS IN THE STUDY OF A-SE2 REACTIONS IN AQUEOUS SOLUTION JOEL M. WILLIAMS,

JR.

and MAURICE M. KREEVOY

School of Chemistry, University of Minnesota, Minneapolis, Minnesota, U.S.A.

. .

. . . . . . .

I. Introduction 11. Cross Mechanism A. Identification of Proton Transfer as the Rate-DeterminingStep . B. Pre Rate-DeterminingSteps C. Multiple Rate-DeterminingProcesses 111. Details of Mechanism A. Structure of the Starting State . B. Direct versus Indirect Proton Transfer C. Detailed Structure of Intermediates . D. Substituent Effects on Reactivity and the Electronic Structure of the Transition State E. Non-AdiabaticProcesses . IV. Conclusions, Apologies, and Acknowledgments References

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.

.

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. . . .

.

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.

63 64 64 79 83 85 85 88 92 94 96 97 98

I. INTRODUCTION

ELECTROPHILIC reactions, except for electrophilic aromatic substitution, had been very extensively neglected by organic kineticists up to about 1950. At that time there appears to have existed not one well-studied example of a reaction in which electrophilic attack by hydronium ion was known to be rate-determining. Since then, however, a wealth of information on such reactions has been forthcoming. The reactions studied have included, inter alia, aromatic hydrogen exchange (Batts and Gold, 1964a; Eaborn et al., 1966; Kresge and Chiang, 1967c; Longridge and Long, 1967; Ostman and Olsson, 1960), hydration of vinyl ethers (Kresge and Chiang, 1967a, b; Kiprianova and Rekasheva, 1962; Ledwith and Woods, 1966; Salomaa et al., 1966), hydration of simple olefins (Baliga and Whalley, 1965; Durand et al., 1966; Gold and Kessick, 1965; Schubert and Lamm, 1966), and the cleavage by acid of B number of different types of carbon metal bonds. I n part the new developments have sprung from the general resurgence of interest in organometallic compounds, but another important cause has been the 63

64

JOEL M.

WILLIAMS,J R .

A N D MAURICE M. KREEVOY

development of techniques by which it is possible to unambiguously identify such reactions. This work has been so successful that identification is almost routine in many cases. The present thrust in the field is to elucidate some of the finer details of A-SE2 mechanisms, including the manner in which the solvent participates, the possible importance of nonadiabatic processes, and the possible intervention of very short-lived intermediate states. This chapter is divided into two main sections. The first describes the well-established techniques for the identification of rate-determining proton transfers. The second describes the much more speculative work, much of which is still in progress, on the details of intermediary structures, including those of transition states. We will draw heavily on work done in this laboratory on the cleavage of mercurials for examples, but other work will also be used. Many further extensions will undoubtedly occur to the reader. Several conventions which will be used throughout this chapter may be worth noting. The solvated proton will be indicated by H+, bearing in mind that it is certainly much more complicated than this. Where one of the isotopes of hydrogen is intended, without specifying which, the symbol M is used. The adjective “hydrogenic” will be used to describe normal modes in which hydrogen atoms constitute the main moving masses, and also the frequencies to which these normal modes give rise. And the terminology of acid catalysis will be applied, even when the reaction consumes acid, as many of the carbon-metal cleavage reactions do. The temperature is always 25”, except where otherwise noted.

11. GROSSMECHANISM This section is devoted to the identification of the steps that lead from starting material to product.

A. Identijication of Proton Transfer as the Rate-Determining Xtep 1. General acid catalysis

The observation of general acid catalysis seems to be the oldest form of evidence favoring a rate-determining proton transfer. The form of the rate law, in general, is governed by the composition of the transition state and the starting state. Thus, if a reaction has an acid, AH, and a substrate, S, as starting state, and the proton is being transferred from the one to the other in the rate-determining step, both AH and S, at least, must be present in the transition state. Reactions are usually carried out in buffered solutions containing both AH and Hf. Since the latter

A-S,2 R E A C T I O N S

65

is also a proton source the rate law takes the form shown in equation (1).l

This is usually generalized as shown in equation (2) to take account of

the multiplicity of possible acids, AH. If the proton is transferred after the rate-determining step the reaction is not acid-catalyzed. If the proton is transferred in a fast step prior to the rate-determining step the rate law takes the simple form shown in equation (3) provided that the

anion, A- does not become attached to the substrate in some other way prior during the rate-determining step. If it does become so attached the rate law is again given by equation (1) or (2). Thus, in principle, one can distinguish the A-SE2 mechanism (rate-determining’ proton transfer) from the A-1 mechanism, but not from the A-2 mechanism by examining the rate law in buffer solutions. Sometimes the observation of general acid catalysis may be sufficient to identify the mechanism with considerable confidence. For example, in aromatic proton exchange catalyzed by ammonium salts, the only structurally attractive A-2 mechanism, shown in equations (4) and ( 5 ) , violates the principles of microscopic reversibility. Thus the elimination of the A-1 mechanism leaves only the A-SE2 mechanism. I n a more to or

fast

+ ArH’ [ArHH‘]+ + A[ArHH’]+ + A- 3 AH’ + ArH AH

(4) (5)

typical case, like the acid cleavage of allylmercuric iodide, a formally acceptable A-2 mechanism can be written (Kreevoy et al., 1966b), as shown in equations (6) through (8) so that the observation of general acid catalysis does not, in itself, establish an A-SE2 mechanism. (Such a mechanism is, however, firmly established by other evidence, discussed in Section IIA2.) Some reactions in which the observation of general 1 Parentheses signify concentrations of 2

R.D.

3*

the species concerned.

66

J O E L M . WILLIAMS, J R . A N D MAURICE M. K R E E V O Y +

fast

+ CHz=CH-CHzHgI A- + CH~CH-CHZH~I RD CH$H-CHZHgI + A-
AH

(6) (7)

acid terms in the rate law contributes to the evidence for a rate-determining proton transfer are shown in Table 1. TABLE1 Various A-SE2Reactions and Bransted a's -

Reaction

aa

2-Acetylcyclohexanoneanion protonation 2-Dichloromethylene-1,J-dioxolane hydrolysis Isotope exchange in azuleneb

0.4 0.60

Riley and Long, 1962 Gold and Waterman, 1968

0.61 0.67c 0.63 0.66 0.67 0.69

Thomas and Long, 1964

Cyanoketene dimethylacetal hydrolysis Ethyl vinyl ether hydrolysis Allylmercuric iodide cleavage Isobutenylmercuric bromide cleavage a 0 c

Reference

Gold and Waterman, 1967 Kreevoy and Elimon, unpublished Kreevoy et al., 1967 Kreevoy and Landholm, unpublished

The Brensted a's were determined by carboxylic acids unless otherwise noted.

The catalytic coefficientsfor this reaction are actually composite quantities. Anilinium ions were used.

a)

A-H + S

A- t H-S+

dl A-H

+S

A-

+ H-S'

FIG.1. Linear free energy relationships as predicted for simple three-body systems (Bell, 1959b). In (a) the energy of the starting state is assumed t o change with changes in AH. I n (a') the energy of the product state is assumed to change. I n either case ALE* is approximately proportional t o AAE".

A - S E ~R E A C T I O N S

67

If a proton-transfer reaction is visualized as a three-body process (Bell, 1959b), a linear free energy relationship is predicted between the acid dissociation constant, K H A , and the catalytic coefficient for the proton-transfer reaction, kHA. Figure 1 shows the relationships between ground-state energies and transition-state energies. This is a particular case of the Bransted Catalysis Law (Bransted and Pedersen, 1924)shown in equation (9). The quantities p and q are, respectively, the number of acidic sites in the acid and the number of equivalent basic sites in its conjugate base. After some earlier disagreement (for references see Gold, 1964; Bishop and Laidler, 1965)there seems to be a general trend back to the original, Bransted (1928) interpretation of these quantities. It is likely that the resultant q’s are oversimplified. For example, a higher q should, almost certainly, be assigned to H,O than to NHZ, but the Bransted rules assign them both unity. However, present structural information does not provide a general unambiguous alternative. There have now been a number of tests of equation (9) for A-SE2 reactions (see Table l),and some of the results are shown in Figs. 2a-c. It is accurately obeyed by catalytic coefficients for carboxylic acids, but other classes of acids give rise to systematic deviations. Phosphoric acid and bisulfate ion seem always to be above the line generated by carboxylic acids, and H+, if its conjugate base, HzO, is considered to be ~ is always below this line. Other homopresent in 5 5 concentration, geneous classes of acids, such as anilinium ions, may give rise to separate Brernsted lines (Thomas and Long, 1964). These deviations would seem to imply that the three-center model is at least oversimplified. It may ultimately develop that A-SE2 reactions can be distinguished from A-2 reactions by this pattern of deviations. At the moment, however, there do not appear to be enough examples, studied in sufficient detail, to reach a definitive conclusion. One advantageous consequence of these deviations is that they make general acid catalysis very easy t o observe, even with quite slow reactions. Bisulfate ion and H3P04generally seem to have catalytic coefficients similar to that of H+, and, in some cases, that of HSO; is larger than that of H+ (see Fig. 2a). General acid catalysis can, then, be easily established by studying H,POd-H2PO; buffers (Kreevoy et al., 1967), or HSOr-SOq- buffers (Kreevoy et al., 1967),or by comparing the rates in moderately concentrated H2S04with those in strong, monobasic, mineral acids (Bell et al., 1962; Kreevoy and Kretchmer, 1964; and Kresge et al., 1965a). I n dealing with the buffer systems it should be remembered that, for such strong acids, the degree of dissociation is not

68

J O E L M . WILLIAMS,

J R . AND MAURICE M . KREEVOY

Fra. 2. Brensted plots for some A-S,2 reactions. The acids are (1) CHs.COzH, ( 2 ) HCOzH, (3) ClCHZ.COzH, ( 4 ) FCHz.COzH, ( 5 ) NC.CH2.C0zH, (6) F2CH.C02H, (7) H3PO4, (8)HSO4-, and (9) H30+. The lines have been drawn through the carboxylio acids. (a) Isobutenylmercuric bromide cleavage (Kreevoy and Landholm, unpublished data). (b) Allylmercuric iodide cleavage (Kreevoy et al., 1967). (c) Ethyl vinyl ether hydrolysis (Kreevoy and Eliason, unpublished data; Kresge and Chiang, 1967a).

A-S,2

REACTIONS

69

constant under variations in buffer concentration, even at a constant buffer ratio, Appropriate corrections are easily made, however (Kreevoy et al., 1967). 2. Isotopic composition of the unreacted starting material In many cases it can be unambiguously demonstrated that the ratedetermining step does not occur after the proton transfer if the reaction is carried out in highly deuteriated water and the isotopic composition of either the product or the unreacted starting material is determined. The method is well illustrated by the acid cleavage of vinylmercuric iodide shown in equation (10) (Kreevoy and Kretchmer, 1964). When

+ M+ -+ C H z 4 H M f HgI+ (10) the reaction was carried out in 92 yodeuteriated solvent the only gaseous CHz=CHHgI

products were CzH4and CzH,D, with no mass-spectroscopically detectable C2HzDz. When the Mf is transferred to the substrate i t becomes equivalent with one or more of the original, carbon-bound protons. If the transfer of M+ is rapid and reversible, as it must be if some subsequent step i E rate-determining, there is a good chance that the Mf which comes off, in fact, wiIl be one of the original, carbon-bound protons. This would result in the accumulation of partially deuteriated starting material, which, in principle, could be isolated and determined. I n practice, however, in this case and in many others, it is easier to allow the reaction to run to completion, isolate and analyze the product. If deuteriated starting material was accumulating it would lead to dideuteriated product. Since it is not found (with a very sensitive analytical tool) proton transfer, or some step occurring before proton transfer, must be involved in the rate-determining step. I n the context of modern chemical-bondtheory it is very hard to visualize a rate-determining step for this reaction before proton transfer, and these results eliminate the possibility that carbon-mercury cleavage, occurring after proton transfer, is rate-determining. The only criteria for successful application of this method seem to be that the transferred proton becomes equivalent with one or more existing protons and that either the unreacted starting material or the product can be isolated without proton exchange in a form suitable for mass-spectroscopic or NMR analysis (Kresge and Chiang, 1967a). 3. Product composition from isotopically mixed solvents Until recently there seems to have been a misconception about the expected size and origin of the hydrogen isotope effect on the rate of reactions in which proton transfer to carbon is rate-determining (Long,

70

JOEL M. WILLIAMS, J R . A N D MAURICE M. K R E E V O Y

1960). Although this field is still not free of problems, considerable clarification has been achieved. The main source of confusion was the failure to recognize that far more than a primary isotope effect is produced when the solvent is changed from H20 to D,O. It is now well known that the M,O+ unit of the aquated proton imposes smaller restraining forces on its hydrogens (for small vibrations, in any event) than does liquid water (Kreevoy, 1964). One consequence of this is that, in an isotopically mixed solvent, the M,O+ units tend t o concentrate H. Another is, that when the positive charge is removed by proton transfer to a substrate, the untransferred protons of the M,O+ unit find their environment more restrictive. This leads (Kreevoy, 1964), on deuteriating all the exchangeable protons, to a secondary, solvent isotope effect, in the direction (kE/kD) < 1,superimposed on the primary isotope effect. The product of the primary and secondary effects in some cases is not much greater than unity (Purlee and Taft, 1956). Bunton and Shiner (1961b) first clearly pointed out the possible importance of this effect. The observed isotope effect is also reduced by the low zeropoint energy of the H,O+ hydrogen atoms in the starting state. Both effects were largely unrecognized. The first experimental demonstration of this dualism seems to have occurred in the case of vinylmercuric iodide cleavage (Kreevoy and Kretchmer, 1964). The quantity, KH/KD, defined as

(RH/RD),,,d. x (D/H)SOlV. measured in an isotopically mixed solvent, was 7.4 at 55". The ratio of rates in ordinary and deuteriated water, kH/kD, was less than 3. I n retrospect there are a number of factors in this study which make the values quantitatively less significant than they originally seemed (Kreevoy and Kretchmer, 1964),but there was and still is no doubt that KH/KD is substantially larger than kH/kD. The former is, in effect, the equilibrium constant for the reaction shown in equation (ll),where

*

(11) (D)*+ (HhOl". (H), + (Dholv. (H), and (D)+ represent the transition states for proton and deuteron

transfer, respectively. To an excellent approximation (Bigeleisen, 1955) KH/KD should be uninfluenced by secondary effects. It has a value very close to that suggested as a maximum by simple theory (Bell, 1959~). Table 2 shows some typical values of KH/KD. It can be seen that, in no case, is K H ~ K Dless than 3-5, even when cc is very close to unity. It is unfortunate that values of KH/KD for reactions with u < 0.5 are not yet available, but it may be tentatively concluded that values above 3 are required whenever the proton transfer step is essentially irreversible.

A-S&

71

REACTIONS

TABLE2 Values of Reaction

K

~

]

in K A-SE2 ~ Reactions

Reference

Acid

KH/Kn

Ethyl vinyl ether hydrolysis

HClO4

7.0

0.66

Allylmercuric iodide cleavage

HC104

7.8

0.67

Isobutenylmercuric bromide cleavage 2-Dichloromethylene-1,3dioxolane hydrolysis Isobutene hydration

HC104

6.8

0.69

HClO4

5.2

0.50

HC1O4

3-9

-0.9

Kreevoy and Eliason, unpublished Kreevoy and Straub, unpublished KreevoyandLandholm, unpublished Gold and Waterman, 1968 Gold and Kessick, 196513

On the other hand, values of K H / K D should approximate unity ( 5 50 yo) if the transferred proton equilibrates with the solvent protons, as in an A-1 or A-2 mechanism. In many cases this duplicates the information obtained from the isotopic composition of unreacted starting material, but KH/KD can be used even when there is no ,proton in the starting material with which the transferred proton becomes equivalent, and it can also be used with tritium at tracer levels. For this purpose KH/KT can, adequately, be related to KH/KD by means of equation (12) (Swain et al., 1958). 1-4410g( K H / K ~ )= log ( K ~ / K T ) (12) TABLE3 Values of

KHA/KDA

for gome A-SE2Reactions

Reaction Ethyl vinyl ether hydrolysis5 Allylmercuric iodide cleavages Isobutenylmercuric bromide cleavagec

5

7.0 7.0 7-8 7.8 6,8 6.8 6.8

ClCHzCOzH H3P04

FzCHCOzH HSO4FzCHCOzH &Po4

5.2 5.5 8.4 8-1 7.2 7.2 6.9

6.2 3.10 6-1 8.0 5-2 5.3 3.1

Kreevoy and Eliason, unpublished data.

b Kreevoy and Straub, unpublished data. c Kreevoy and Landholm, unpublished data.

Some values of KHA/KDA are shown in Table 3. These are obtained when general acid, MA, is used as the proton donor. Some of the product will always have M+ as the source of its hydrogen and equation (13) is useful in separating that contribution from KHA/KDA (Kreevoy et al., 1966b).

72

JOEL

M.

WILLIAMS,J R .

AND MAURICE

M. RREEVOY

It may be noted that

KHA/KDA values are only a little different from values, a t least when the acids are fairly strong. For monobasic acids values of catalytic coefficient ratios, k H A / k D A , are also similar t o KHA/KDA ; thus, for semi-quantitative mechanistic purposes these three quantities may be used interchangeably as a first approximation. An example of the utility of this generalization can be found in the protonation rates of 2-acetylcyclohexanone anion (Riley and Long, anion (Long and Watson, 1958). 1962) and 3-methyl-2,4-pentanedione It is by no means obvious from the k H / k , ratios, 1.7 and 1.1respectively, that proton transfer is rate-determining. Neither K H / K D nor any KHA/KDA is available. The transferred proton does not become equivalent with any existing proton in the substrate. However, the values of k H A / k D A , in the range 3.4 to 5.9 (Riley and Long, 1962), are decisive. Proton transfer must be essentially irreversible. KH/KD

4. Relations between isotope effects and Bransted cc

There is, at this time, no strong evidence requiring one to go beyond the simple picture of the A-SE2transition state shown in Fig. 3. Adopting 'I

FIG.3. The simplest possible A-S,2 transition state.

the simplest model, the primary kinetic isotope effect is defined by equation (14). This differs from K H / K D only by the factor 1, the equilibrium constant for the reaction shown in equation (15),which has a value (kdkD)1

(RH/RD)prod.(D/H)M,O+

+ (D)MaO

(14)

1

*

(15) of 0.69 0.02 (Pentz and Thornton, 1965; Heinzinger and Weston, 1964; Gold, 1963; and Kresge and Allred, 1963).' Values of ( k H / k D ) I are given (H)M30+

(D)MaO+ f (H)MaO

1 The experimental values range from 0.67-0.71. The present authors and Drs. Gold, Kresge and Long have agreed to use the value 0.69 until it is advisable to do otherwise in order to permit consistency in published data.

A-S,2

73

REACTIONS

in Table 4. Simple theory (Bell, 1959c) predicts (kH/kD)I= 4.2, if one of the antisymmetric stretching frequencies of the M,O+ unit (2060 cm-l for H,O+) is lost in the transition state, The frequency cited was obtained with solid H,O,+Br- at low temperature (Rudolph and Zimmermann, 1964). A frequency of 2330 cm-l would be necessary to produce a calculated rate ratio of 5.0. The secondary isotope effects, (kH/kD)II, can be defined as all the kinetic isotope effects other than that associated with the transferring proton and is mathematically given by equation (16). They are also kH/kD = (kH/kD)I (kH/kD)II (16) listed in Table 4. Since l2 is the expected value of (kH/kD)II if proton transfer were complete in the transition state (Swain and Thornton, 1961), equation (17) can be written by analogy with the Brarnsted

(17) log (kH/kD)II = ‘%log(z2) Catalysis Law (equation (9)). The quantity mi is, clearly, the isotopic analogue of the Brmsted a,and Table 4 shows that they are numerically similar where data are available for comparison. TABLE 4 Primary and Secondary Isotope Effects and a.

Isotope exchange in 1,3dimethoxybenzene Isotope exchange in azulene Isotope exchange in 1,3,5trimethoxybenzene Ethyl vinyl ether hydrolysis Allylmercuric iodide cleavage Isobutenylmercuric bromide cleavage 2-Dichloromethylene-1, 3-dioxolane hydrolysis Isobutene hydration

0.60 2 0.02 0.69

Kresge and Onwood, 1964 Gruen and Long, 1967

6.4%0

0.68

0.52

6 . 2c~ ~

0.58

4.9

0.66

5.0

0.65

0.73 0.6d Kresge and Chiang, 1967c 0.56 0.66 Kreevoy and Eliason, unpublished 0.58 0.67 Kreevoy, et al., 1964

4.7

0.54

3.6

0.72

2.7

0.54

0.61

0.83 0.69 Kreevoy and Landholm, unpublished 0.51 0.50 Gold and Watennan, 1968 Gold and Kessick, 1965 0.84

This value is derived making the assumption that the Wheland intermediate is equilibrated with the solvent which equates the isotope effect on proton removal, kF/kg, with KH/K=. * A much lower value was reported earlier (Challis and Long, 1965). C A lower value was previously reported (Kresge end Chiang, 1962). This datum is based on the three carboxyIic acids reported (Kresge and Chiang, 1961). Q

74

J O E L M.

WILLIAMS,

JR. AND MAURICE M. KREEVOY

Gold (1960) and Kresge (1964) have derived equation (18) for relating kx, the rate constant in a D,O-H,O mixture containing X atom fraction

5 --(1- X kH

-IX11-K4)2 (1- Xll+zsrk D /kH)

(1-X+XZ)3

(18)

of deuterium, to kD/kH, ui,X, and 1. I n several cases these quantities are all independently available. Figures 4a-c show that the concordance between the calculated and experimental values of kx/kH is excellent. This agreement does not, in itself, constitute good evidence in favor of an A-SE2 mechanism, because, particularly for values of ui near unity, similar predictions are made for other mechanisms (Gold, 1960; and Kresge, 1964). However, by trial and error, values of kx/kH can be used to estimate ai when kH/kDis available but KH/KD is lacking (Kresge and Chiang, 1967b). Alternately, the Brransted a may be used in the place of a( when it is available. It is then possible t o work backwards to (kE/kD)I and KH/KD. As already shown (Section IIA3) has direct utility for the identification of an A-S,2 mechanism. I n this section a transition-state model has been explicitly assumed and it has been implicitly assumed that for equal solute concentrations the activity of a solute is the same in H,O, D,O, and isotopic mixtures. It was shown that these assumptions are consistent with the results. However, the results do not establish the model, which will be discussed a t greater length in Section IIIB, and the assumption is only a fair approximation (Goodall and Long, 1968). 5 . Rates in moderately concentrated mineral acid

Some time ago it was suggested by Zucker and Hammett (1939) that the behavior of the rates of acid-catalyzed reactions in moderately concentrated mineral acid (1-10~)could be used as a criterion for the degree of hydration of transition states. More recently this suggestion has been elaborated by Bunnett (1961). An acidity function, Ho, analogous to pH, was defined (Hammett, 1940) by equations (19) and (20) where HI+ and I are the protonated and unprotonated forms of an

indicator, respectively, and the other symbolism is conventional. It was originally thought that yI/yHI+would depend on the indicator charge type and the degree of hydration of the protonated and unprotonated forms, but not, otherwise, on the indicator structure, so that in a given solution, H , could be uniquely defined for neutral indicators protonating

A-S,2

I

0

I

0.2

I

0.4

75

REACTIONS

I

0.6

I

0.8

I

FIG.4. Rate constants as a function of the solvent isotopic composition. The solid lines have been generated from b,k,, and adonly. (a) Allylmercuric iodide cleavage at 35": k,/kD=3.12 and q=0.67 (Kreevoy et al., 1966b); (b)Isobutenylmercuric bromide cleavage a t 25' : k H / b=2.55 and at= 0.83 (Kreevoy and Landholm,unpublished data) ; and (c) Isobutene hydration a t 25': kH/kD= 1-45and ad=0*84(Gold and Kessick, 1906). The experimental points represent 5 % errors in the rate constants and 1 in the isotopic composition.

76

JOEL M. WILLIAMS, J R . AND MAURICE M . K R E E V O Y

FIG.5. Reaction rates in concentrated perchloric acid as a function of Ho. The circles are the experimentally obtained rate data. The dashed lines represent unit correlations with the hydronium ion concentration, while the solid lines represent unit correlations with Ho. (a) Methylmercuric iodide cleavage at 100" (Kreevoy, 1957). (b) Cyclopropylmercuric iodide cleavage a t 25" (Kreevoy and Thoreen, unpublished results). (c) Vinylmercuric iodide cleavage at 25' (Kreevoy and Kretchmer, 1964).

A - 8 ~ 2R E A C T I O N S

77

without a change in hydration. For an A-1 reaction carried out in similar solutions the rate would be given by equations (21) and (22), in which

lOgkaPp== logk:-Ho

(22)

kappis the apparent, first-order, rate constant and k$ is the infinite dilution second-order rate constant. For an A-2 reaction an equation of the same form as 22 would apply, but an acidity function H, appropriate to the more hydrated transition state would be necessary. It was suggested that H should be, approximately, -log(H+). The latter declines much less rapidly than H o with increasing (H+)because the activity of water in such solutions is declining. Early attempts were made to identify A-S,2 reactions by such a criterion, but they have encountered a variety of difficulties, some general to the method and some specific to this type of reaction. Among the former is the problem of indicator specificity in determining H o (Kresge and Chiang, 1961) and the possibility of varying the degree of hydration of the transition state by varying the acid concentration (and, thereby, the water activity). Among the latter is the high catalytic activity of the bisulfate ion (Section IIA1) putting a cloud over any sulfuric acid data. Three plots of log kaPpvs. - H o for A-S,2 reactions are shown in Figs. 5a-c. It is quite evident that such plots yield no straightforward criterion of mechanism. A more sophisticated attempt to use the acidity function is described below (Section IIIE2). 6. Entropy and volume of activation

Entropies of activation, AS*, for a wide variety of A-SE2 reactions appear, without exception, to be negative; usually < -10 cal mole-1 deg-l (Matesich, 1967). A selection of fairly typical values is shown in Table 5. This observation can be used t o distinguish A-S,2 reactions from A-1 reactions, which usually give positive values of AS* (Schaleger and Long, 1963). There are a number of factors, some of which are avoidable, which can operate to make a measured value of AS* less useful than it might otherwise be. As already pointed out in Section IIA1, HSOg and H,PO, are comparable to H+in catalytic activity at room temperature. Further, the degrees of dissociation of HSO, and H3P04decline sharply with rising temperature. Thus the temperature derivative of an apparent rate constant obtained in 1 - 1 0 ~H2S04 or H,P04 is a very complicated

78

J O E L M . W I L L I A M S , J R . A N D M A U R I C E M. K R E E V O Y

TABLE5

Entropies of Activation in Aqueous Solution near 25'

Reaction Ethynyl ethyl ether hydrolysis Ethyl vinyl ether hydrolysis

AS*, cal mole-1 deg-1

-5 -8

-11

Ethynyl methyl ether hydrolysis Allylmercuric iodide cleavage Isotope exchange in 1,3,5trimethoxybenzene Vinylmercuric iodide cleavage

Acid

Reference

H3Of (buffer) Stamhuis and Drenth, 1961 HC1 Salomaa et al., 1966 HCIO4

-12

Kresge and Chiang, 1967b H30+ (buffer) Stamhuis and Drenth, 1961 HCIO4 Kreevoy et al., 1966b

-16

HClO4

Kresge el al., 1967

-17

HC104

Kreevoy and Kretchmer, 1964

-10

quantity and any value of AS* derived from it is almost impossible to interpret. The inclusion of fairly small quantities of organic cosolvents can have a substantial effect on AS*, particularly if the cosolvent has a substantial hydrocarbon portion, as does t-butyl alcohol (Winstein and Fainberg, 1957). The assumption that AH* is constant over long temperature ranges may not be reliable (Hulett, 1964). This means that AS* should only be compared with other values based on rate constants covering approximately the same temperature range. Long extrapolations from media of high acidity are also risky (Amett and Mach, 1966). Finally, the interpretation of AS* in solution is much simpler if it can be confined to the solvent contribution to AS* (Kreevoy, 1963a). This means that substrates should be small enough or rigid enough so that changes in the internal entropy can be neglected. The values in Table 5 are thought to be relatively free of disturbing influences. Some of those tabulated by Matesich (1967) seem quite badly perturbed. The volume of activation, A Y * , which is -RTa(lnk)/ap, has been suggested as a criterion of mechanism (Whalley, 1964). Known volumes of activation for A-SE2reactions, measured near 25', seem to be limited to o l e h hydration ( - 12 cm3 mole-1 for isobutene at 35", Baliga and Whalley, 1965) and allylmercuric iodide cleavage ( - 11 om3 mole-l at 25", Halpern and Tinker, 1965). It is impossible to generalize from so few examples, but, in principle, it seems possible that AT"" is less dependent on structural ramification than AS*, and therefore easier to interpret. Against this must be weighed the experimental difficulties in

~ 4 - 8 ~R E2A C T I O N S

79

getting dV*. I n any event, like AS*, dV* can only be useful in distinguishing A-SE2 reactions from A-1 reactions, which generally give AV* values in the range - 2 to + 6 cm3 mole-l (Whalley, 1964). For A-2 reactions the range seems to be about - 5 to - 15 cm3 mole-', which apparently will not be distinguishable from that for A-Sx2 reactions. Taken all together it does not appear likely that the thermodynamic quantities of activation will be as useful as isotope effects in identifying A-SE2mechanisms. B. Pre Rate-Determining Steps In a number of the reactions discussed in the foregoing sections one or more rapid equilibria preceding the rate-determining step have been demonstrated or can be visualized. Where these occur they have characteristic effects on the form of the rate-law, and their detection usually presents no special difficulties, but sometimes such equilibria can give rise to interesting peculiarities, and sometimes they give added insight into the structure of a transition state. 1. Complexing

The ability of Hg(I1) to form tri- and tetra-coordinated ions with suitable ligands is well known. With alkylmercuric halides the formation constants are usually too small for such ions to be conventionally demonstrated (Brown et al., 1965a). It is likely, however, that such complexes would cleave more readily than the uncomplexed materials. These expectations have been strongly supported in a study of the cleavage of allylmercuric iodide by acid and iodide ion (Kreevoy et al., 1966a; equations (6) to (8)). The rate was of the form shown in equation (23), in which S is the substrate. The terms which are linear in iodide ion

concentration are thought to represent the reaction of C8H6HgI, and those proportional to the square of the iodide ion concentration, the reaction of C8H,HgI,". Formic acid was the general acid studied. Table 6 shows the values of the various rate constants and their maximum contributions to the overall conversion rate. The general similarity of the iodide ion-catalyzed reactions to those

80

JOEL M . WILLIAMS, J R . A N D MAURICE M. KREEVOY

TABLE6 Rate Constants for Equation (23) (Kreevoy et al., 1966a) Rate constant,

k

Value 1.41 x 10-2 0.4 (1.8& 0.2) x 102 a p-z+ 1-1) x 10-3 (2.5& 0.7)x 10-1 (1.09 0.05)x 10-4 4 x 10-2 2 5.6

a

Units, sec-1

Maximum yo contribution to kl

M-1 M-2 M-3

100 65

M-2

35 29 40 80 40

M-3

30

M-1 M-2

M-1

This value was previously reported incorrectly.

without this catalyst was illustrated by showing that the isotope effect on k H , kHI, and kHIawas virtually the same. The only mechanism consistent with this, and also reasonable within the general framework of bond theory, is complexing followed by cleavage. The terms in equation (23) which are independent of the acid concentration show little or no solvent isotope effect. This and considerations following from the Brarnsted Catalysis Law make it unlikely that these terms represent cleavage of the complexed substrate by water. A ratedetermining, unimolecular rearrangement from the u- to the r-allylic mercurial was suggested. Oxidative cleavage of some sort is another possibility. I n equations (24) through (as), kHI/kH is shown to be the iodide ioncomplexing constant of the cleavage transition state, H. Similarly kHIz/kHIis the iodide ion-complexing constant of SHI.Since the iodide

+

kx = ( k T / h ) K g

(28)

K

(29)

= ~ H I / ~ H

ion-complexing constant is a sensitive probe of the covalency of an Hg(I1) compound, as shown in Table 7, the values of these ratios can be used to give an indication of the situation prevailing in these transition states. The values of kHI/kHand kHIq/kHIare 400 and OM-' respectively

A-S,2

81

REACTIONS

(Kreevoy et al.,1966a). A comparison with the values in Table 7 suggests some progress away from covalent carbon-mercury bonds in the transition states, but certainly does not permit any formulation which requires TABLE7 Iodide Ion Complexing Constants Complexing constant, ~ -

Reaction

+ + + +

Hgz+ I- + HgI+ IHgIz HgI' HgIz I- + HgI, I- + HgIiHgI, CHSHg+ I- + CH3HgI I- + CzH5HgIF CzHsHgI

7x 9x 5x 2x 5x -1

+

+

+

Reference

1

10'2

Bjerrum et al., 1958 Bjerrum et al., 1958 Bjerrum el aE.,1958 Bjerrum et al., 1958 Simpson, 1961 Barbieri and Bjerrum, 1965

1010

103 102

10s

them to be substantially broken. Entirely similar conclusions are and kHFormIn/kHFormI, reached by considering the ratios, kHFormI/kHForm which have the values 400 and 5 0 respectively ~ ~ (Kreevoy ~ et al.,1966a). In addition, the change in the charge type of the acid seems to have strikingly little effect on these ratios. Table 8 lists some A-SE2 reactions which have been shown to be facilitated by complexing. TABLE 8 Reactions Facilitated by Complexing ______-__ __

Reaction

Complexing agent(s)

Allylmercuric iodide cleavage Protiodeiodination of iodo-2,4,6trimethoxybenzene Triethylboron cleavage Heterocyclic mercuric chloride cleavages Isobutenylmercuric iodide cleavage

I-

Reference

C1-, Br-, I-

Kreevoy et al., 1966s Batts and Gold, 1964b

RCOzH c1-

Toporcer et al., 1966 Brown et al., 1965b

I-

Kreevoy and Melquist, unpublished

2. Disproportionation A possible path for A-S,2 type reactions, only recently recognized (Kreevoy et al., 1966a), is shown in equations (30) and (31), using an fast

2RHgI RzHg

+ H+ + I-

RzHg RH

+ HgIz

+ RHgI

(30) (31)

82

JOEL M. WILLIAMS, JR. A N D MAURICE M. EREEVOY

organomercuric iodide as an example. Such a path will, clearly, become more important if a complexing agent for HgIz is present, and can be suppressed by the initial addition of Hg12. If it is assumed that no significant buildup of RzHg takes place, disproportionation contributes a term of the form shown in equation (32) to the overall rate. Here k2 is

the rate constant for cleavage of RzHg and K1 is the equilibrium constant for the disproportionation. It is noteworthy that reaction via disproportionation cannot be detected from the dependence of the initial rate on the substrate concentration ;that is identical with the behavior expected for straightforward cleavage. Significant disproportionation contributions to the overall rates have been demonstrated for allylmercuric iodide (Kreevoy et al., 1966a) and isobutenylmercuric iodide cleavages (Kreevoy and Melquist, unpublished data). They may have perturbed rate constants reported for vinylmercuric iodide cleavage (Kreevoy and Kretchmer, 1964). Fortunately, most qualitative indications of mechanism are applicable to k2K1/(Hg12)in about the same way as kH. As yet there seems to have been no use of the disproportionation as a tool for unraveling mechanisms. It has rather been a complication which must be identified and then eliminated. Possibly, it might provide an indirect route for the study of the dialkylmercurials which are very unpleasant compounds to isolate. 3 . Prototropic equilibria The form of the rate law for an A-SE2reaction may also be changed by acid dissociation preceding the rate-determining step. This occurs most often when an amine nitrogen is present in the molecule. An example is enamine hydrolysis, the path of which, for strong acid only, is shown in equations (33) through (35) (Maas et al., 1967). The result is that the reaction does not appear to be acid-catalyzed a t pH values below the pK, of the substrate. This complication can usually be revealed by carrying the study to pH values above the pK, of the substrate, but at least one example is known (the hydrolysis of 1-piperidyl-2-methyl-1propene) in which the decline in the H+-induced rate above the pK, is almost exactly compensated by the growth of an H+-independent rate of the neutral substrate, presumably involving the solvent (water) as a general acid (Maas et al., 1967). Such a situation leads to conventional general acid catalysis at pH > pKa of the substrate. I n an acidic buffer

A-SE2 R E A C T I O N S

83

.H HzO+

CH3

>C-CH=N

0

I_/

series of

-----f --f

+

fast steps

solution of pH c pK, the rate will be of the form shown in equation (36), which is equivalent to equation (37). Thus, the reaction may appear to

be catalyzed by general bases but not by hydroxide ion. I n this situation KH/K= still has the significance discussed above (Section IIA3), as does the isotopic composition of the unreacted starting material, but all kinetically derived quantities will contain contributions from the equilibrium parameters of the dissociating substrate. C . Multiple Rate-Determining Processes If steps following the rate-determining step are several orders of magnitude faster than the rate-determining step (in terms of actual conversion of material, not rate-constants) then the rate of production of the ultimate product, the rate of consumption of the starting material, and the rate of passage of material through the rate-determining step are all identical and conventional rate laws apply. Two examples are shown in equations (38) through (40) and (41) through (43). The significance + n

CHz=CHOCzHs

+ H+ R.D.\ CH&H-.OCzHs

(38)

+

*

+ HzO

CH3CH==OCzHs

series of --+ --+

+ CH&H=O

fant etepa

+ CzHtjOH + H+

(39)

84

J O E L M. W I L L I A M S , J R . A N D M A U R I C E M . 3 R E E V O Y

d(CH3CHO) d(CHZ=CHOCzH5) = = kH(H+)(CHz=CHOCzH5) dt dt (CH3)zC=CHHgBr i

+ Br-

(CH3)2C.CH2HgBr d(HgBr2) dt

-=-

+ H+ % (CH3)2;.CHzHgBr

(40) (41)

series of --f

--f

-+ (CH~)ZC=CHZ + HgBr2

fast steps

d[(CHa)zC=CHHgBr] = k,(Ht)[(CH3)2C=CHHgBr] dt

(42)

(43)

of the kH's is unaffected by the steps shown in equations (39) and (42). Very slow reactions following a proton transfer also are not troublesome ; they can simply be ignored. I n a number of cases, however, the picture is complicated by severaI steps of fairly comparable rate. An example is aromatic protiodetritiation as shown in equations (44) and (45). The second step is essentially ArT

+ H+

kA

k-i

kT \H

(44)

irreversible because the concentration of (originally labeled) aromatic compound is low compared to that of the (originally inactive) solvent. Since the second step and the reverse of the first differ only isotopically, they cannot be vastly different in rate. Since the intermediate, ArTH+, does not accumulate, its rate of formation via the first step must be equal to its rate of decomposition via the second and the reverse of the fist. Thus there can be no single, clear-cut, rate-determining step. The steady-state approximation gives equation (46) for the overall rate. To

evaluate kn, the isotope effect, k-l/k,, must be separately evaluated with the aid of additional approximations (Batts and Gold, 1964a; Kresge and Chiang, 1967c; and Longridge and Long, 1967). Another sort of difficulty occurs in the cleavages of organomercuric halides. Unrelated secondary reactions occur at rates which may be comparable with the rates of proton transfer. A n example (Kreevoy and Kretchmer, 1964) is given in equations (47) through (51). The CHz=CHHgI

+ H+

c2R4xgI'

CzH4HgI+ faat

+C2R4 + Bgx'

(47) (48)

85 (49)

HzO

+ CzH3Hgf Hg'

CH&H=O

+ H g " + H+

slow + HgIz + HgzIz(s)

(60) (51)

reaction shown in equation (51) is slower than the proton transfer, but fast enough to prevent the experimental determination of an infinitetime concentration of HgI, corresponding to equations (47)through (49). I n some cases the difficulty has been circumvented by including small concentrations of halide ion in the reaction mixture (Kreevoy et al., 1966b) but this must be done with caution, as higher concentrations of halide ion are appreciably catalytic (Kreevoy et al., 1966a). As in any kinetic study, there are in A-SE2 reactions a wide variety of side reactions that may be encountered. To get interpretable results these must be effectively eliminated or their contributions and effects carefully scrutinized.

111. DETAILSOF MECHANISM The object of this section is to consider work associated with the detailed description of the proton transfer process in A-SE2 processes. Included are the nuclear arrangement and electronic structure in the starting state, the transition state, and important intermediate states, as well as the dynamics of the process. This work seems hardly more than begun, and many problems remain. Nevertheless some results have been achieved and the relative promise of various possible approaches can be assessed. Needless to say, much of the contents of this section is speculative.

A. Structure of the Starting Xtate Originally the proton was written H+, and thought to be not too different from other small cations, such as Lii. Then, in recognition of the unique strength of the bond between the proton and its fist molecule of water of hydration, it was, for quite a time, written as H,O+ (Bell, 1941). Later the first hydration shell of the H,O+ unit was also found to be quite strongly bound, giving HgO4+(Bascombe and Bell, 1957; Eigen and DeMaeyer, 1959). Recent work has suggested that further hydration can also be significant (Hoegfeldt, 1966; Robertson and Dunford, 1964). I n view of this the present authors have, for most

86

J O E L M . WILLIAMS, J R . A N D MAURICE M. K R E E V O Y

purposes, reverted to the original formulation for the aquated proton without, however, reverting to the original naivete about its structure. The structure of liquid water is also in doubt. There is a good deal of evidence that the short-range structure below or immediately above 25" resembles that of ice, but beyond that, difference of opinion is evident (Kavanau, 1964a; Falk and Ford, 1966; Scatchard, 1966). The vibrational spectrum of liquid water shows very broad bands, in both infrared and Raman spectra. Table 9 shows frequencies which have been assigned to the various vibrational modes, but it should be remembered that these represent, in general, band centers and an individual water molecule may have frequencies differing by as much as several hundred wave numbers from those cited. The values cited may not even be those most often occurring. The intensity of an 0-H stretching vibration commonly increases sharply with hydrogen bond formation (Pimentel and McClellan, 1960) so that strongly hydrogen bonded 0-H groups would contribute more than their numbers would suggest to the overall distribution of absorption and weakly hydrogen bonded 0-H groups less. TABLE 9 Vibrational Frequencies of Ha0 and DzO Frequency, cm-1 W

Mode

-

HzO

~~

l

DzO

Reference

~~

Va, Vs

3395

2500

6

1646

1220

75

705

75

500

525 357

Fox and Martin, 1940 Plyler and Williams, 1936 Fox and Martin, 1940 Plyler and Williams, 1936 Wahfen, 1964 Cartwright, 1936

a A third libration probably has a value between 600 and 700 cm-1. We have chosen the average, 600 om-1, for our calculations.

The vibrational spectrum of H+ is even harder to interpret. Absorption increases at all frequencies in the infrared and the already broad water bands get broader, but not symmetrically. The additions to the water bands have been interpreted as the new bands of the H80+unit in H+ (Falk and Gigudre, 1957). The suggested frequencies are shown in Table 9. On the other hand it has been suggested that the rapid proton shifts from one oxygen to another precludes a band spectrum for that unit in water (Ackermann, 1961) and its absorption has been

A-S,2

a7

REACTIONS

assigned to the generalized increase in absorptivities. I n this view the additions to the discrete water bands presumably are to be assigned to outer hydration water molecules. An interpretable, though still broad, spectrum can be obtained at -170' for the crystalline compound HgOtBr- (Rudolph and Zimmermann, 1964). The frequencies assigned to the H,O+ unit of this structure are also shown in Table 10. They may or may not be appropriate to that unit in liquid water. The frequencies of the outer three water molecules in solid HgO$Br- are very unlikely to be applicable to liquid water since the two environments seem quite different. TABLE10 Suggested Frequencies of H&+

Frequency, cm-1 Mode

(Fak and CiguBre, 1967)

(RudoIph and Zimmermann, 1964)

2900 2900 1205 1750

2630 2060 1313 1846 738 902

Evidence from NMR spectra (Kresge and Allred, 1963; Gold, 1963) supports the intuitively attractive idea that only the M,O+ unit of M+, in an isotopically mixed solvent, has an isotopic composition significantly different from the water. The isotopic equilibrium constant, 1 (0.69, Section IIA4), then pertains to the distribution of isotopes between M,O+ and M20. It could be calculated if the frequency distributions (including librations and restricted translations) were known for liquid H20,D20,and Hf and D+ in those solvents. Since only uncertain approximations of typical frequencies are available, an unsophisticated estimate, made by means of equation (52) (Bunton and Shiner, 1961a) log1 =

4 z v+H,o-+ r, VHaO 3600

seems to be all that is justified. The summations in equation (52) were taken over all the isotopically sensitive frequencies. Using the fiequencies for H20 given in Table 9 and those of Falk and GiguGre (1957) for H,O+ the value of 1.0 was obtained. With the fiequencies of Rudolph and Zimmermann (1964) a value of 0.77 was obtained. When using the

88

J O E L M . WILLIAMS,

J R . AND MAURICE M . K R E E V O Y

Falk and GiguBre frequencies the librational frequencies of H,O+ were assumed to be the same as those in water. When using the Rudolph and Zimmermann frequencies the cited values were used for the librations. I n both cases the restricted translations were assumed to be isotopically insensitive. The even more simplified approximations of Bunton and Shiner (1961a)give a value of 0.73 for 1. Water structure in the neighborhood of typical, hydrophobic substrates is probably somewhat different from that in the bulk of the solvent. Such substances dissolve in water with large, negative standard entropies and enthalpies and are thought to increase the number and/or strength of water-water hydrogen bonds (Kavanau, 196413). The details of this structuring are uncertain.

B. Direct versus Indirect Proton Transfer I n water an acid, AH, can transfer a proton, cooperatively, through one or several water molecules, as shown in Fig. 6. For proton transfer from trimethylammonium ion to trimethylamine, .n is known to be

FIG.6. A generalized mechanism for proton transfer from an acid, AM, to a substrate, S. n can be zero or some small integer.

predominantly one, but it is predominantly zero for proton transfer from methylammonium ion to methyl amine (Luz and Meiboom, 1963). These results were obtained by examining the effect of the reaction on the NMR spectrum of the water. No such determination seems possible in the case of A-SE2reactions and no general alternative has yet been devised. Several particular transition-state models can be discarded on the basis of the results in Section IIA3. Thus, the one in which both MI and M, (Fig. 6) occupy double-minimum potential functions in the transition state, and both are moving, predicts substantially smaller values of KH/KD than those found. A simplified version of the linear, hydrogenic motions in such a system is shown in Fig. 7. The hydrogen isotope effect attending the exchange of protium at MI with a deuterium of the water is given, in reasonable approximation, by equation (53) (Melander, 1960). (This

A-S,2

REACTIONS

89

approximation considers only stretching vibrations.) If, for convenience, the reasonable values, vHaO= 3400 cm-l and vDaO= 2500 cm-l are chosen, a value of 3.0 is obtained, which is well below the observed values (Table 2). Also excluded is a model in which only M2 is moving in the transition state. On this basis it is not possible, however, to exclude a model in which A and 0 have been pushed together in .the activation process so that M2 occupies a single-minimum potential function in the transition state and only Ml is in translational motion.

vs:-3000 om-1 whenMz=MI=H; -2550 cm-1 when Mz=H, M1=D

FIQ.7. The linear vibrations of one particular simplified transition state model; n= 1 (Fig. 6). The arrows indicate the direction and approximate relative motion in the two normal modes: v+ (the reaction coordinate) and vg.

One method has been proposed for testing the n = 0 model for monobasic acids (Kreevoy, 1965b). That involves the relation between KHA/KDA (defined in Section IIA3) and k H A / k D A . If the n = 0 mechanism is correct, and if there are no isotope effects other than the primary isotope effect, KHA/KDA is given by equation (54). To test this equation

(KHAIKDA) = ( ~ H A / ~ D Ax )(HA)/(DA) (kHA/hDA)

(54)

in an isotopically mixed solvent is replaced by the ratio of

k2p to k22, the ratio of catalytic coefficients in the two pure solvents.

In principle (HA)/(DA)could be measured (spectroscopically) in the mixed solvent. I n practice it has been replaced by (K92/Z3K,Hf'). These replacements imply that AGO is zero for the transfer of a nonexchanging substance from H20 to D20. The resulting prediction is shown in equation ( 5 5 )and tested in Table 11. The agreement must be considered KHA/KDA

=

Ha0 kDaO DaO 1 3 K H z 0 HA / DA )(KDA I HA )

(55)

satisfactory. The assumption about the AGO of transfer implies an equilibrium constant of unity for the transfer. This is thought, possibly, t o be in error by as much as a factor of 1-2 or 1.3 (Goodall and Long, 1968). I n addition the accumulated experimental error in the four quantities involved is not trivial. This agreement does not establish that n (Pig. 6) must be zero but it is consistent with that conclusion. It 4

(D

0

0

u

F

z

4

TABLE11 Test of Equation (55)

H

F

E! Reaction

Acid

kp:/k”,p,”

HSOT FaCHCOzH HSO; FzCHCOzH ClCHzCOzH

8.0

(CH3)zS+OH

K~:/lsK~ ( K S~A / K = A ) ~ “

( K=A/KDA)O~’

Reference

Lim Q

Allylmercuric iodide cleavage Isobutenylmercuric bromide cleavage Ethyl vinyl ether hydrolysis

5.1 5-2 5.3 6.2

1.38 1.32 1.38 1.32 1.05

11.0 6.7 7.2 7.0 6.5

2.2

2.520

5.5

8.1

8.4 7.2 7.2 5.2 7.8

N Kreevoy and Straub, unpublished data lp Eireevoy and Lmdholm, u unpublished data F4 Kreevoy and Eliason, b unpublished data C l Williams and Kreevoy, 0 unpublished data M

z

2 K

a

The value of I is assumed to be identical to the value in water.

A-SE2 R E A C T I O N S

91

requires that, if n # 0 , the force constants operating on M2 in the transition state are very similar to those in the starting state. Similar conclusions have been reached by Albery (1967) who has examined this problem in great detail. Another approach to the problem of the value of n is to determine the degree of hydration of the transition state in an aprotic, nearly anhydrous, solvent. This has been done (Williams and Kreevoy, unpublished data) for ethyl vinyl ether hydrolysis in dimethylsulfoxide (DMSO). I n nearly anhydrous DMSO containing very low concentrations of hydro-

F I ~8. . A reasonable structure for H+in DMSO. A very strong hydrogen bond seems required.

chloric acid, the equilibrium constant for the reaction shown in equation (56) is 0.45 (Kolthoff and Reddy, 1962). No acids other than H+ and H+ + Ha0

+ H30+

(66)

H,Of are present. (Both, of course, must interact very strongly with the DMSO solvent.) I n such solutions, at 25", the hydrolysis rate can be described by equation (57) in solutions containing up to five volume per

cent of HzO. The H+ term, involving an anhydrous transition state, accounts for most of the reaction, which is why kHs0 is somewhat uncertain. The value of n for the H90+reaction is not known, but the H+ reaction must involve a transition state in which n is zero, since DMSO is incapable of a cooperative transfer. The transfer of this information to aqueous solutions is somewhat risky, but other observations help to connect data from the aqueous and DMSO solutions. The isotope effect on the equilibrium constant of equation (56), KHaO/KDao, is only about 1.2. The infrared absorption due t o H+in DMSO is very broad, featureless, and seems to center around 1200 cm-l. Both of these observations (Williams and Kreevoy, 1967) seem to require a very strong hydrogen bond between the primarily protonated DMSO molecule and its neighbor, as shown in Fig. 8. If that

92

J O E L M. WILLIAMS, J R . A N D M A U R I C E M . K R E E V O Y

DMSO molecule can be replaced by a substrate, it seems likely that a water can be similarly replaced in the solvent shell of H,O+. Also, the value of KH/KT in 95 per cent DMSO (18.6; WilIiams and Kreevoy, unpublished data) is similar to that in water (16.7 ;Kreevoy and Eliason, unpublished data) again suggesting similar transition states. C. Detailed Structure of Intermediates I n any reaction mechanism study, the question of the existence and structure of intermediates always arises. Intermediates and virtual intermediates (Melander, 1961) are quite likely in A-S,2 reactions because hydrogenic and heavy atom motions are not usually well coupled. Thus, if heavy atom changes as well as a proton transfer are required to convert starting material to product they will generally take place in separate steps. If these steps are separated by potential energy minima the atomic arrangements corresponding to these minima are, of course, called intermediates. If no minima intervene the steps are usually separated by inflections on the potential energy surface and the atomic arrangements corresponding to such inflections have been called virtual intermediates (Melander, 1961). K ~ signal the presence of intermediates. For Values of K ~ I often example, in allylmercuric iodide cleavage, the value of 7-8 for K=/KD at 25" (Kreevoy et al., 1966b; and Kreevoy and Landholm, unpublished data) requires that the reaction coordinate consist, almost solely, of hydrogenic translation. Since carbon-mercury bond cleavage must occur to give the products, an intermediate (or virtual intermediate) must either precede or follow the rate-determining step. Since the values of the iodide ion catalytic coefficients seem to preclude extensive carbonmercury cleavage before the rate-determining step (Section IIB 1) the latter step must lead to the intermediate. The carbonium ion,

+

CH, .CH .CH2HgI,might serve as that intermediate but that would be difficult to reconcile with relative reactivities. The rate-determining step for allylmercuric iodide cleavage could be written as shown in equation (58) if the carbonium ion were the intermediate. This is analogous to the rate-determining step for propene hydration (equation +

H+ + CHZ=CHCHzHgI -+ CH3.CH.CHzHgI H+

+ CHt=CH*CH3

(58)

+ --i'

CH3.CH.CH3

(59)

(59)) but it is about six powers of ten faster (Kreevoy et al., 1966b; Baliga and Whalley, 1964) and it is unlikely that the inductive effect of

A-S&?R E A C T I O N S

93

the halomercurial group alone could account for such a large difference in rate. An attractive alternative intermediate is an olefin-mercuric iodide r-complex, which is also an intermediate in deoxymercuration (Kreevoy and Kowitt, 1960). This structure for the intermediate is

further supported by the observation that the halomercuric group seems to interact with the double bond in the starting state (Kreevoy et at., 1966c)so that the geometry of the starting state may not be too different from that of the r-complex. A high value of a, considered in the light of the Hammond Postulate (Lumry and Eyring, 1954; Hammond, 1955), may suggest an intermediate. For this purpose either the Brernsted a or ai will serve. For example, ai for isobutene hydration is close to unity (Gold and Kessick, 1965a, b). This implies that the transition state resembles the product of the rate-determining step. That, in turn, suggests that the product of the rate-determining step resembles the transition state in energy. The overall reaction product, t-butyl alcohol, does not, so there must be an intermediate which is probably the carbonium ion. I n this case the value of K H / K D , 3.5, might not, in itself, have precluded heavy atom involvement in the reaction coordinate. Fragmentary evidence of this type on acid-catalyzed borohydride hydrolysis suggests an interesting intermediate. The Brransted a has not been evaluated with high, quantitative reliability, but it seems to be close to unity (Davis et al., 1962). The first obvious product is BHBOHor BH,OH,, neither of which would, likely, be of energy comparable with the transition state. An intermediate of composition BH, has been suggested, but isotopic evidence indicates that the incoming proton does not become equivalent with those already present (Jolly and Mesmer, 1961). An intermediate having a three-center structure

would seem to meet all the requirements. It can be seen from these examples that a wide variety of results can be used to supplement the information originally obtained from a or KEIKD.

94

J O E L M. W I L L I A M S , J R . A N D M A U R I C E M . K R E E V O Y

D. Substituent Effects on Reactivity and the Electronic Structure of the Transition State I n A-S,2 reactions, as in others, a good deal of semiquantitative information about the electron distribution in the transition state can be obtained from relative reactivities. While no rigorous proof is available it seems likely that the Brransted a,when derived from carboxylic acids, measures the fractional negative charge on the A fragment of HA. Similar considerations suggest that ui measures 1-2, where x is the residual positive charge on that portion of the solvated H+ not being transferred. These intuitions are supported by the near identity of u and q,as shown in Table 4. The Hammett p and the Taft-Hammett p* can be used to evaluate the partial charge at various positions in the substrate fragment of the transition state. Sometimes deviations from the Taft-Hammett correlations can be used for the same purpose (Kreevoy, 1963b; Barlin and Perrin, 1966). The positive charge developed at a particular carbon is thought to be approximately -p*/4.5 or -p/3.6 or Apk,/5, where dpk,,, is the deviation of a phenyl or vinyl compound from a TaftHammett plot. Not many A-S,2 reactions have been studied in sufficient detail t o test these relationships. The hydration of four olefhs, RC(CHs)==CH2 (R =CHs, CH,CH,Cl, CH,OCH,, and CH,Cl), by 29.5 % HC104 at 38' gave a p* of - 3.5, suggesting 0.8 as the fractional positive charge on the central carbon of the transition state (Taft, 1960). This is in reasonable agreement with the indication of 0.16 fractional positive charge on the untransferred residue of H+, obtained from the value of ui,0.84 (Section I I A 4 ) . A p of - 4.0f 0.3 is available for the A-SE2 hydration of styrenes (Durand et al., 1966)but no values of 01 seem to be available, Further quantitative testing of the proposed relationships will require more experimental results. Certain qualitative indications of electronic structure can be obtained from available results. The reactivity of alkylmercuric iodides toward aqueous acid declines with increasing ramification of the alkyl fragment (Kreevoy and Hansen, 1961). This is inconsistent with the development of any significant carbonium ion character at the carbon attached t o mercury. The acid cleavage rate for (CH&C=CHHgI is lo3 faster than that of vinylmercuric iodide (Kreevoy et al., unpublished data). This suggests -0.4 carbonium ion character at the carbon bearing the methyl groups in the transition state. The total influence of two methyl if reasonable values are groups on a carbonium ion should be assumed for p* and h, the Baker-Nathan parameter (Kreevoy, 1963b)

-

-

N

N

A-Sa2

REACTIONS

95

are assumed. The values of a and ai (Section IIA4) on the other hand, suggest 0.8 positive charge on the substrate in the transition state. The difference is probably associated with the iodomercurial group. This view is also supported by the ease with which the iodomercurials can be cleaved, compared with the difficulty of hydrating the corresponding non-mercurial olefins. The f i s t steps of the two reactions would be analogous if simple carbonium ions were formed from the iodomercurials. N

E. Non-Adiabatic Processes Investigators studying proton transfer reactions have been perennially interested in the possibility of proton tunneling (Bell, 1959d). Recently there has also been interest in the possibility that the transition state for such reactions may not have a fully equilibrated environment (Bell, 1965). Both possibilities arise because of the small mass of the proton. This opens the possibility of non-classical behavior, i.e., tunneling. It also may allow the proton to move so fast, both by classical and nonclassical paths, that heavy atom rearrangements cannot keep pace. The tunneling possibility, a t least, seems to rest on a firm theoretical foundation (Bell, 1959d). 1. Tunneling Among the criteria that have been suggested for tunneling are : (1) Anomalously large isotope effect ; (2) Curved Arrhenius plots ; (3) Significantly positive standard isotopic entropies ; and (4) Significant deviations from the Swain-Schaad relationship (Swain et al., 1958) in the direction (kE/kD)> (kE/kT)0.5D3. The anomalously large isotope effects observed in the proton abstraction from nitroalkanes by certain pyridine bases (Funderburk and Lewis, 1964; Bell and Goodall, 1966)have been attributed to tunneling. There seems to be no other reasonable attribution. No unambiguous effect of this type has yet been identified in an A-SE2reaction. Since the expected value in the absence of tunneling is not certain (Section IIA3) the anomaly would have to be quite large to be interpreted confidently. Curved Arrhenius plots and negative standard isotopic entropies h a w been observed for proton abstraction from a hydrocarbon acid (Bell et al., 1956) and for proton transfer to hydrocarbon anions (Caldin and Kasparian, 1965). A negative AS" value has also been associated with u=/K= for proton transfer to allylmercuric iodide (Kreevoy et at., 1966b).

96

J O E L M . WILLIAMS,

JR.

AND MAURICE M . KREEVOY

Tunneling has been suggested as the cause of these effects, and “parabolic barrier widths” of 1.3 A assigned (Caldin and Kasparian, 1965; Kreevoy, 1965a). Again the attribution seems reasonable, and no alternative is apparent. Small deviations from the Swain-Schaad relationship have been attributed to tunneling in a base-catalyzed elimination (Shiner and Martin, 1964). I n view of the approximate nature of the relationship small deviations must be viewed skeptically. For A-S,2 reactions measurement of AS” associated with tcH/icD seems to be the tool most likely to identify tunneling. High precision can be obtained (Kreevoy et al., 1966b), and the method is easily adaptable to long temperature ranges, and (if alcoholic solvents are used) t o low temperatures. I n view of the presently available results it seems that proton tunneling is confined to the top 20 yoof the barrier, at most, and that the effects to be attributed to it will be small. The more profound effects to be expected from deep tunneling seem absent in A-SE2and related reactions. 2. Non-equilibrated environment A number of types of experimental observations have led to the suggestion of a non-equilibrated environment. The values of AS* reported in Section IIA6 are unexpected. The localization entropy of a proton on a particular oxygen site in liquid water is - 8 cal. mole-I deg-l; AX”= - Rln55. The entropy associated with bimolecularity cannot be more negative than this. At the same time the relaxation of the solvent cage of the H,O+ unit, caused by the proton transfer to the substrate, should lead to a substantially positive entropy contribution. The entropy of protonation of trimethylamine is 15 cal mole-I deg-I (Bell, 1959a). Thus, one would have, generally, predicted values of AS* near zero for A-Sz2 reactions and in no event more negative than - 8 cal mole-I deg-l. I n fact, almost all the reported values are more negative than - 8 cal mole-l deg-l (Table 5). One can rationalize this situation if the solvation of the H,O+ unit is almost intact in the transition state. Since solvent must be mobilized around the substrate fragment to solvate the developing positive charge, a substantially negative solvation entropy is predicted if the solvent formerly solvating the H30+unit has not had time to populate the many new states made available to it. When this is added to the negative entropy due to the bimolecularity the observed AS’ values become reasonable. The anomalous catalytic coefficient of HSO, becomes reasonable if the solvation of the acid fragment of the transition state is characteristic of the acid itself (Kreevoy et aZ., 1967). The solvation of the SO4fragment

A-SE2 R E A C T I O N S

97

in the transition state is probably very little different from the SO4 fragment of HSO,. Thus this transition state, compared especially to that for H+ as an acid, would be reasonably well solvated, even though solvent rearrangement could not keep pace with proton transfer. Kresge et al. (1967)have recently chosen to emphasize those features of A S and AH* for aromatic proton exchange which behave as would be predicted from equilibrium theory. However these systems show the quantitative anomalies referred to in a fairly typical way. The AS+ values for H+ are more negative by 5-10 cal mole-’ deg-l than can be readily accommodated and the catalytic coefficient for HSO, is as large or larger than that for H+ (Kresge et al., 1965a). The postulate that only the “free ” water should be counted as possible sites for the surplus proton, introduced to help rationalize the position of H+on Brcansted plots (Bell, 1943; Kresge et al., 1967)makes the values of AX* for this acid even harder to understand because it reduces the localization entropy to about - 6 cal mole-l deg-l. A promising tool in the investigation of the non-equilibrium environment hypothesis is the aHrecently defined by Kresge et al. (1965b). This is a quantity, analogous to the Bronsted a, but based on a comparison of the sensitivity of the rate to the acid concentration in the 1 - 5 ~acid region with the sensitivity of a closely related equilibrium. Environmental effects should govern aH almost completely, so that, if the environmental reorganization lags behind the electronic reorganization aH should be systematically smaller than the Bronsted CL or ai. The larger discrepancies should be associated with the reactions having the most negative values of AX*. The only reliable values of a= available seem to be 0.44 and 0.55, for isotope exchange in trimethoxybenzene (Kresge et al., 1965b) and azulene (Challis and Long, 1965). These reactions show Brsnsted a’s of 0.6 and 0.61, respectively, and their AS* values are - 16 and - 7 cal mole-l deg-l, respectively (Matesich, 1967).

IV. CONCLUSIONS,APOLOGIES, AND ACKNOWLEDGMENTS

It is clear that much remains to be done in this field, but we believe that this review also summarizes a considerable level of understanding. We want to emphasize that the foregoing review was not meant to be exhaustive, and is almost entirely limited to results in dilute, aqueous solution. We apologize in advance to those authors whose important work has been overlooked. We know of no practical, systematic way to search the literature for the sort of results we have summarized. We thank Professors Gold and Jencks for their thoughtful comments 4*

98

J O E L M. W I L L I A M S , J R . A N D M A U R I C E M . K R E E V O Y

on this manuscript. Finally, we want to thank the U.S. National Science Foundation for support through grant GP 5088 and through a Postdoctoral Fellowship to J. M.W. We also thank other agencies which have provided funds to make the research summarized here possible. REFERENCES Ackermann, T. (1961). 2.Physik. Chem. 27,34. Albery, W. J. (1967).I n “Progress in Reaction Kinetics” (G. Porter, ed.). Pergamon Press, Oxford and New York. Arnett, E. M., andMach, G. W. (1966).J . Am. Chem. SOC.88, 1177. Baliga, B. T., and Whalley, E. (1964). Can. J . Chem. 42, 1019. Baliga, B. T.,and Whalley, E. (1965). Can. J . Chem. 43, 2453. Barbieri, R.,and Bjerrum, J. (1965). Acta Chem. Scand. 19,469. Barlin, G.B., and Perrin, D. D. (1966). Quart. Revs. 20, 75. Bascombe, K. N., and Bell, R. P. (1957). Disc. Faraday SOC.24, 1. Batts, B. D., and Gold, V. (1964a). J . Chem. SOC. 4284. Batts, B. D.,and Gold, V. (1964b). J . Chem. SOC.Suppl. 1, 5753. Bell, R.P. (1941). “Acid-BaseCatalysis ”,p. 40.Oxford University Press, London. Bell, R.P. (1943). T r a m . Faraday SOC.39, 253. Bell, R. P. (1969a). “The Proton in Chemistry”, p. 65. Cornell University Press, Ithaca, New York; (1959b). ibid, p. 166; (19590). ibid. p. 184; (1959d). ibid. p. 205. Bell, R. P. (1965). Disc. F a r d a y SOC.39, 16. Bell, R. P., and Goodall, D. M. (1966). Proc. Roy. SOC. A294, 273. Bell, R.P., Fendley, T. A., and Hulett, J. R. (1956). Proc. Roy. SOC.A235, 453. Bell, R.P., Preston, J., and Whitney, R. B. (1962).J . Chem.Soc. 1166. Bigeleisen, J. (1955). J . Chem. Phy8. 23, 2264. Bishop, B. M., and Laidler, K. J. (1965). J . Phys. Chem. 42, 1688. Bjerrum, J., Schwarzenbach, G., and SWn, L. G. (1958). “Stability Constants” Part 11,“Inorganic Ligande”, p. 121. The Chemical Society, London. Brensted, J. N. (1928). Chem. Revs. 5, 322. Br0nsted, J. N.,and Pedersen, K. (1924). 2. Physik. Chem. A108, 185. Brown, R. D., Buchanan, A. S., and H d r a y , A. A. (1965a). Aust. J . Chem. 18, 1507. Brown, R. D., Buchanan, A. S., and Humffray, A. A. (1965b). At&. J . Chem. 18, 1513. Bunnett, J. F. (1961).J.Am. Chenz. SOC. 83,4978. Bunton, C. A., and Shiner, V. J., Jr. (1961a). J . Am. Chem. Xoc. 83,42. Bunton, C. A.,and Shiner, V. J., Jr. (1961b).J . Am. Chem.Soc. 83,3214. Caldin, E.F., and Kasparian, M. (1965). Dkc. Faraday SOC.39,25. Cartwright, C. H.(1936). Phye. Rev. 49,470. Challis, B. C.,and Long, F. A. (1965). J . Am. Chem. SOC.87, 1196. Davis, R.E., Bromels, E., and Kibby, C. L. (1962). J . Am. Chem. SOC.84, 885. Durand, J. P., Davidson, M., Hellin, M., and Coussemant, F. (1966). Bull. SOC. chim. France 52. Eaborn, C., Jackson, P. M., andTaylor, R. (1966). J . Chern. SOC.B, 613. Eigen, M.,and DeMaeyer,L. (1959).In “The Structure of Electrolytic Solutions” p. 64 (W. J. Hamer, ed.). Wiley, New York. Falk, M., and Ford, T. A. (1966). Can. J . Chem. 44,1699.

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Falk, M., and Giguhre, P. A. (1957). Can. J. Chem. 35, 1195. Fox, J. J., and Martin, A. E. (1940). PTOC. Roy.SOC.A174, 234. Funderburk, L., and Lewis, E. S. (1964). J. Am. Chem. SOC. 86, 2531. Gold, V. (1960). Trans. Faraday SOC.56, 255. Chem.Soc. 141. Gold, V. (1963). PTOC. Gold, V . (1964). Trans. Faraday Soc. 60, 738. Gold, V., and Kessick, M. A. (1965a). Disc. Farad. SOC.39, 84. Gold, V., and Kessick, M. A. (1965b). J. Chem. SOC.6718. Gold, V . , and Waterman, D. C. A. (1907). Chem. C m m . 40. Gold, V . ,and Waterman, D. C. A. (1968) J. Chem. SOC.,in press. Goodall, D. M., and Long, F. A. (1968). J. Am. Chem. SOC.90, 238. Gruen, L. C., and Long, F. A. (1967). J. Am. Chem. SOC. 89,1287. Halpern, J., and Tinker, H. B. (1965). Private Communication, University of Chicago. Hammett, L. P. (1940). “Physical Organic Chemistry”, p. 267. McGraw-Hill, New York. Hammond, G. S. (1955). J. Am. Chem. SOC. 77,334. Heinzinger, K., and Weston, R. E., Jr. (1964). J.Phys. Chem. 68, 744. Hoegfeldt, E. (1966). Acta Cienntq. Veenezolana 17, 13. Hulett, J. R. (1964). Quart. Revs. 18, 227. Jolly, W. L., and Mesmer, R. E. (1961). J. Am. Chem. SOC. 83,4470. Kavanau, J. L. (1964a). “Water and Solute-Water Interactions”, p. 8. HoldenDay, San Francisco and London; (1964b). ibid. p. 22. Kiprianova, L. A., and Rekaaheva, A. F. (1962). Doklady A M . Nauk S.S.S.R. 142, 689. Kolthoff, I. M., and Reddy, T. B. (1962). Inorg. and Nuclear Chem. 1, 189. 79, 5927. Kreevoy, M. M. (1957). J. Am. Chem. SOC. Kreevoy, M. M. (1963a). I n “Technique of Organic Chemistry”, Volume VIIIPart I1 (S. L. Friess, E. S. Lewis, and A. Weissberger, eds.). Why-Interscience, New York and London. Kreevoy, M. M. (1963b). Bull. SOC. chirn. France, 2431. Kreevoy, M. M. (1964).J. Chem. Ed. 41, 636. Kreevoy, M. M. (1965a). Disc. Faraday Soc. 39,57. Kreevoy, M. M. (1965b). Disc.Paraday Soc. 39, 101. Kreevoy, M. M., and Eliason, R. W. (unpublisheddata). University of Minnesota. 83, 626. Kreevoy, M. M., and Hansen, R. L. (1961). J. Am. Chem. SOC. Kreevoy, M. M., and Kowitt, F.R. (1960). J. Am. C h m . SOC. 82,739. Kreevoy, M. M., and Kretchmer, R. A. (1964). J. Am. Chem. SOC.86, 2435. Kreevoy, M. M., and Landholm, R. A. (unpublished data). University of Minnesota. Kreevoy, M. M., and Melquist, J. L. (unpublished data). University of Minnesota. Kreevoy, M. M., and Straub, T. S. (unpublished data). University of Minnesota. Kreevoy, M. M., and Thoreen, J. W. (unpublished results). University of Minnesota. Kreevoy, M. M., Goon, D. J. W., and Kayser, R. A. (1966a). J. Am. Chem.SOC. 88, 5529. Kreevoy, M. M., Landholm, R. A., and Melquist, J. L. (unpublished data). University of Minnesota. Kreevoy, M. M., Straub, T. S., Kayser, W. V., and Melquist, J. L. (1967). J. Am. Chem. SOC.89, 1201.

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Kreevoy, M. M., Steinwand, P. J., and Kayser, W. V. (1964). J . Am. Chem. SOC. 86, 5013. Kreevoy, M. M., Steinwand, P. J., and Kayser, W. V. (196613). J . Am. Chem. SOC. 88, 124. Kreevoy, M. M., Steinwand, P. J., and Straub, T. S. ( 1 9 6 6 ~ ) J. . Org. Chem. 31, 429 1. Kresge, A. J. (1964). Pure AppZ. Chem. 8, 243. Kresge, A. J., and Allred, A. L. (1963). J . Am. Chem. SOC.85, 1541. Kresge, A. J., and Chiang, Y. (1961). Proc. Chem. SOC. 18. Kresge, A. J., and Chiang, Y. (1962). J . A m . Chem. Soc. 84, 3976. Kresge, A. J., and Chiang, Y. (1967a). J . Chem. SOC. B, 53. Kresge, A. J., and Chiang, Y. (1967b). J . Chem. SOC. B, 58. Kresge, A. J., and Chiang, Y. ( 1 9 6 7 ~ ) J. . Am. Chem. SOC. 89, 4411. Kresge, A. J., and Onwood, D. P. (1964). J . Am. Chem. SUC.86, 5014. Kresge, A. J., Chiang, Y., and Sato, Y. (1967). J . A m . Chem.Soc. 89, 4418. Kresge, A. J., Hakka, L. E., Mylonakis, S., and Sato, Y. (19654. Discuss.Faraday SOC. 39, 75. Kresge, A. J., More O’Ferrall, R. A., Hakka, L. E., and Vitullo, V. P. (1965b). Chem. Comm. 46. Ledwith, A., and Woods, H. J. (1966). J . Chem. SOC.B, 753. Long, F. A. (1960). Annals New York Acad. Science 84, 596. Long, F. A., and Watson, D. (1958). J . Chem. SOC.2019. Longridge, J. L., and Long, F. A. (1967). J . Am. Chem. SOC. 89, 1292. Lumry, R., and Eyring, H. (1954). I n “Mechanisms of Enzyme Action”, p. 123 (W. D. McElroy and B. Glass, eds.). Johns Hopkins, Baltimore. Luz, Z . , andMeiboom, S. (1963). J . Chem. Phys. 39, 366. Maas, W., Janssen, M. J., Stamhuis, E. J., and Wynberg, H. (1967). J . Org. Chem. 32, 1111. Matesich, M. A. (1967). J . Org. Chem. 32, 1258. Melander, L. (1960). “Isotope Effects on Reaction Rates”, p. 20. Ronald Press, New York. Melander, L. (1961). Arkiv Kemi 17,291. Ostman, B., and Olsson, S. (1960). Arkiv Kemi 15, 275. Pentz, L., and Thornton, E. R. (1965). U.S. At. Energy Comm. Report No. NYO-3041-1. Pimentel, G. C., and McClellan, A. L. (1960). “The Hydrogen Bond”, p. 196. Freeman, San Francisco and London. Plyler, E. K., and Williams, D. (1936). J. Chem. Phys. 4, 157. Purlee, E. L., and Taft, R. W., Jr. (1956). J . A m . Chem. SOC.78, 5807. Riley, T., and Long, F. A. (1962). J . A m . Chem. SOC.84, 522. Robertson, E. B., and Dunford, H. B. (1964). J . Am. Chem. SOC. 86, 5080. Rudolph, J., and Zimmermann, H. (1964). 2.Physik. Chem. 43, 311. Salomaa, P., Kankaanpera, A., and Lajunen, M. (1966). Acta Chem. Scand. 20, 1790. Scattchard,G. (1966). .FederationProceedings 25, 954. Schaleger, L. L., and Long, F. A. (1963). Adv. Phys. Org. Chem. 1, 1. Schubert, W. M., and Lamm, B. (1966). J . Am. Chem. SOC.88, 120. Shiner, V. J., Jr., and Martin, B. (1964). Pure Appl. Chem. 8, 371. Simpson, R. B. (1961). J . A m . Chem.Soc. 83, 4711. Stamhuis, E. J., and Drenth, W. (1961). Rec. Trav. Chim. 80, 797. Swain, C. G., and Thornton, E. R. (1961). J . Am. Chem. SOC.83, 3884.

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Swain, C. G., Stivers, E. C., Reuwer, J. F., Jr., and Schatitd, L. J. (1958). J . Am. Chem. SOC. 80, 5885. Taft, R. W., J r . (1960). U.S. Naval Research Project NR055-295, Final Report. Thomas, R. J., and Long, F. A. (1964). J . Am. Chem.Soc. 86,4770. Toporcer, L. H., Dessy, R . E., and Green, S. I. E. (1965). J . Am. Chem. SOC.87, 1236. Walrafen, G. E. (1964). J . Chem. Phys. 40, 3249. Whalley, E. (1964). Adv. Phys. Org. Chem. 2, 93. Williams, J. M., Jr., and Kreevoy, M. M. (19G7). J . A m . Chem. SOC. 89,5499. Williams, J. M., Jr., and Kreevoy, M. M. (unpublished data). University of Minnesota. Winstein, S., and Fainberg, A. H. (1957). J . A m . Chem. SOC. 79, 5937. Zucker, L., and Hammett, L. P. (1939). J . A m . Chem. SOC.61, 2791.

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CALCULATIONS OF CONFORMATIONS OF POLYPE PTlDES HAROLD A. SCHERAGA Department of Chemistry, Cornell University, Ithaca, New York 14850, U.S.A.

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I. Introduction 11. Conventions 111. Geometrical Data IV. Transformation of Coordinates V. Terms Contributing to the Expression for the Total Energy A. Torsional Energies B. Nonbonded Interactions C. Electrostatic Interactions D. Hydrogen Bond . . E. Distortion of Geometry F. Role of Crystal Energy Calculations in Refinement of Energy Parameters G. Free Energy of Hydration . H. Loop-ClosingPotential VI. Methods of Energy Calculation and Energy Minimization A. Hard-Sphere Potential B. Complete Energy Expression VII. Results with Hard-Sphere Potential VIII. Application of Complete Energy Expression to Results Obtained from the Hard-Sphere Potential IX. Use of Complete Energy Expression for ConformationalEnergy Calculations, Including Energy Minimization A. Hydrocarbons B. Dipeptides C. Random Coil; End-to-end Distance D. Helical Structures E. Gramicidin-S F. Oxytocin and Vasopressin X. Conclusions , References

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103 106 114 118 118 119 124 130 133 137 138 138 141 143 143 143 145 163 166 156 167 169 102 173 176 178 179

I. INTRODUCTION A polypeptide chain can assume an extremely large number of conformations because of the possibility of rotations about the single bonds of the backbone and side chains. The totality of these conformations, in random sequence along a chain, constitutes the so-called “random coil ”,a 103

104

HAROLD A . SCHERAGA

concept that is vcry familiar to the chemist who deals with synthetic polymers. I n the random-coil form, the polypeptide chain has a considerable amount of conformational entropy. However, under appropriate conditions of temperature, pH, solvent, etc., the various intramolecular interactions may cause the chain to adopt a rather limited number of conformations, despite the considerable reduction of conformational entropy. Presumably, the native form of most proteins is a member of this small class of relatively ordered conformations. It is now possible to compute the internal energy for any arbitrary conformation. I n principle, in a computation, one can group conformations of equal energy, and thereby obtain information about the entropy, and hence free energy, of the system. Computations are currently being carried out under the assumption that the native protein has a narrow distribution of conformations about an equilibrium one, and that this distribution has the highest statistical weight (Scheraga, 1965a, b, 1966, 1967b). I t must be emphasized that this is still an assumption, which must be proven for each protein separately only by computing the conformation and then comparing it with the experimentally determined conformation. Presumably, this assumption will gain wide acceptance if its validity can be demonstrated in a few cases. The assumption is a plausible one since many proteins are known to denature reversibly; also, in many cases, the native conformation of a protein can be re-attained after re-oxidation ofreductively-cleaved disulfide bonds (Anfinsen, 1964). The results of these experiments do not constitute a proof of the validity of this assumption, since the protein could conceivably exist in a state of metastable equilibrium, which is highly favored kinetically. Nevertheless, this approach provides a reasonable working hypothesis, which is enabling progress to be made. I n speaking of the protein as being in a state of highest statistical weight, it must be emphasized that the statement is made about the total system, protein plus solvent. At one temperature (or solvent, pH, etc.), the statistical weight of the system may be maximized if the protein is in its native state, while, at another temperature (or solvent, pH, etc.), the statistical weight may be maximized if the protein is in a denatured state. The computations reported here pertain to conditions under which, hopefully, the protein will be in its native state. Another aspect of the question as to whether the native state of a protein is an equilibrium one concerns its conditions of synthesis in contrast to the conditions under which it is studied by the protein chemist. As a protein is synthesized, we may envisage it peeling off the ribosomes. Even if it is synthesized under equilibrium conditions, the conformation of the growing chain (which could change as each amino acid is added t o it)

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

105

would be such as to maximize the statistical weight of the whole system (involving the ribosomes, messenger RNA, transfer RNA’s, etc.) ; and protein synthesis is probably not taking place under equilibrium conditions. I n contrast, the isolated protein is placed in a different environment when its conformational properties are studied. We do not know whether the conformation adopted, after addition of the C-terminal amino acid during synthesis, is the one that exists in the solution (or crystal) under study by the chemist. The general feeling is that the conformation probably is essentially the same under these various conditions; this feeling is supported by the fact that, for example, active enzymes are detectable under these various conditions. This fact, plus the reversibility of denaturation and disulfide bond regeneration, is the basis of the assumption that native proteins exist in an equilibrium state. Accepting this assumption as a basis for calculations, we seek the protein conformation of lowest energy. After the energy minimum is obtained, it is then necessary to explore the nature of the energy surface to obtain the statistical weight. For example, a native conformation of highest statistical weight may not be the one of lowest energy, if there are many more ways (i.e. a large entropy factor) to obtain conformations of a given energy higher than that of minimum energy. With these introductory remarks we can state the approach of current efforts to compute the conformations of polypeptides of known amino acid sequence. First of all, it is necessary to obtain an expression for the energy of the system (protein plus solvent) as a function of the coordinates of the atoms of the system. Secondly, with the aid of a computer, the energy must be minimized. Finally, the nature of the energy surface in the neighborhood of the minimum must be explored to obtain the statistical weight. Since the problem of calculating polypeptide conformation is so complex, it has been approached by making many simplifying assumptions and then removing these assumptions in stages until a computer program could ultimately be developed to yield the structure of a protein. Thus, initial calculations (Sasisekharan, 1961, 1962; Ramachandran et al., 1963a, b; Schellman and Schellman, 1964; Scheraga, 19658, b, 1966; Nemethy and Scheraga, 1965; Scheraga et al., 1965a, b; Leach et al., 1966a, b ; Nemethy et al., 1966a, b) made use of a hard-sphere potential, which was subsequently replaced by more complete energy expressions. We will trace the development of energy expressions and computational procedures. Rather than cover the whole field of conformational calculations, we will confine our considerations to polypeptides ;low-molecularweight model compounds will be discussed only insofar as they provide information about the various components of the energy of a polypeptide.

106

HAROLD A . S C H E R A B A

11. CONVENTIONS

It is worthwhile to begin the discussion by first stating the conventions adopted for the description of polypeptide conformation. These conventions (Edsall et ab., 1966) were discussed at the 1965 Gordon Conference on Proteins ; some additional nomenclature was suggested at a workshop on protein conformation in Madras in January 1967. The whole subject is, at present, under consideration by the IUPAC-IUB Commission on Biochemical Nomenclature. The orientations of the groups on the a-carbon may be specified in terms of Fig. 1 for alanine. Looking from the hydrogen atom on the a-carbon toward the a-carbon, one proceeds from the amino to the carboxyl to the side-chain methyl group by a clockwise rotation for L-amino acids, and by a counter-clockwise rotation for D-amino acids

L-Alanine

D-Alanine

FIG.1. Illustration of absolute spatial configurations of Wyman, 1958).

L-

and D-alanine (Edsall and

(Edsall and Wyman, 1958). These absolute configurations have been established by the work of Bijvoet et al. (1951) andTromme1 and Bijvoet (1954). Unless otherwise noted, all amino acids are considered to be in the L-configuration. A portion of the backbone of a polypeptide chain, in terms of which the backbone conventions may be stated, is shown in Fig. 2. The direction of progress along the chain is taken from the amino to the carboxyl terminus, in agreement with that generally used in reporting protein sequences. Since the group

usually behaves as a rigid unit during conformational changes [with the peptide bond (C'-N) remaining in the trans (or occasionally cis) conformation], this rigidly connected sequence of atoms is designated as a

CALCULATIONS OF CONFORMATIONS O B P O L Y P E P T I D E S

107

"peptide unit". The term "residue" is reserved for the amino acid residue in the chemical sense, i.e. for the group of atoms -NH-CaHR4'OBond angles are denoted by the symbol T, a subscript i referring to the residue, with the symbols of the atoms defining the bond angle placed in brackets following the symbol T. For example, ri[NC"C'] denotes the angle formed by the C"N and c"C' bonds of the ith residue. Rotation around the N-C" bond is denoted by +,rotation around the C"--C' bond by $I, and (if allowed for in the computations) rotation around the peptide (C'-N) bond by w . The sequential numbering of

FIU.2. Perspective drawing of a section of apolypeptide chain representing two peptide units. The limits of a ~ e e i d v eare indicated by dashed lines. The recommended notation for the backbone atoms and for bond rotations is shown (Edaall et al., 1966).

atoms or bonds is denoted by subscripts, i.e. +i, $I$, wi, Ci, Ni, etc., all belonging to the ith residue. With this choice, bonds +i and $Ii are located within the ith residue, while bond wi connects residues i and i + 1. The conformation of the ithpeptide unit is defined with respect to the preceding peptide unit by the dihedral angles +i, &, and wi, where the angles $Ii and w,.are contained in the peptide unit,while precedes the C" atom at the beginning of the peptide unit. Although the @ atom is part of the side chain, its position is also completely determined by the backbone rotational angles, since it is rigidly connected to the C" atom. With these designations, the c",C', and 0 atoms and the side chain of residue i are contained in peptide unit i, while the N and H atoms of residue i (denoted by Ni and €&) are parts of peptide unit i - 1 ; if a polypeptide were described in terms of peptide units, the first peptide unit would begin only

+i

108

HAROLD A . SCHERAGA

at the Ca atom of the first residue. By specifying the rotational angles t,hi, and wi, the positions of the following atoms are defined: C!, C;, Oi,Ni+l,Hi+*,and Ci.,,. The angles #, #, and o are positive for a righthanded rotation; when looking along any bond, the far end rotates clockwise relative to the near end. The choice of the zero angle for rotation is made so that = $i= wi = 0 for the fully stretched polypeptide chain. As an aid in determining the angles of rotation for various conformations, the angles are listed in Table 1 for a number of conformations for specific geometrical arrangements of neighboring peptide units. Table 2 lists the rotational angles for several regular structures. TABLE1 Angles of Rotation in the Backbonefor Various Conformationsin Polypeptides of L-Amino Acid+,* (Edsall et al., 1966)

4 0"= 360' 60" 120°

180" 240' 300"

Rotation around N-Ca Ca-C' Ca-H Ca-R Ca-C' Ca-H Ca-R

bond

q5

Rotation around Ca-C'

Oo= 360" bond cis t o N-H bond bond trans to N-H bond 60' bond cis to N-H bond 120' bondtrans to N-H bond 180" bond cis to N-H bond 240" bond trans to N-H bond 300'

Ca-N Ca-R Ca-H C-'N Ca-R Ca-H

bond

bond cis to C'-0 bond bond trans to C'-0 bond bond cis t o C'-0 bond bond trans to C'-0 bond bond cis to C'-0 bond bond tram to C'-0 bond

I n the fully stretched polypeptide chain, the peptide bond is in the trans conformation bond is trans to the N-H bond. * For the description of D-aminoacids, interchange Ca-H and Ca-R in the table. a

(wc = 0 ) ,i.e. the C'-0

TABLE2 Angles of Rotation for Some Regular Structures (Edsall et al., 1966)

4

Structure Fully extended chain Right-handed a-helix Left-handed a-helix Parallel-chain pleated sheet Antiparallel-chain pleated sheet Polyglycine I1 Collagen

O0 132" 228' 61" 38'

looo

N

120°

* 0" 123' 237" 293' 325' 330" N 340'

I n designating side chains, the bonds are numbered from the C" atom to the end of the side chain, as shown in Table 3. For unbranched side chains, the angle of rotation around thejth bond is denoted by xj, where

CALCULATIONS O F CONFORMATIONS O F P O L Y P E P T I D E S

109

TABLE3 Numbering of Atoms and Bonds in the Commonly Occurring Amino Acids I n branched chains, the two branches are defined according to the convention shown in Fig. 3. They are shown here for the naturally occurring configurations of threonine, isoleucine, and hydroxyproline. I n allothreonine and alloisoleucine the numbering of the two branchesis interchanged. The configuration around the branch carbon atom in valine and leucine is the same as in Fig. 3. In arginine, NVl is cis to C8.

Alanine

Valine

Loucine

Isoleucine

Methionine Cysteine Cystine Serine

Threonine

Lysine

Arginine

Histidinc

Aspartic acid

Glutamic acid

110

HAROLD A . SCHERAOA TABLE3 (contl:nued).

Asparagine

GIlutamine

Phenylalanine

Tyrosine

Tryptophan

Proline

Hydroxyproline

j = 1 for rotation around the C'-Cfi bond, j = 2 for rotation around the @-Cr bond, etc. For branched side chains, an extension of the subscript, adding the numbers 1 or 2, is used to distinguish the branches, i.e. xjland xj2. Branch 1 is defined according to Fig. 3 in non-planar branches (tetrabonded carbon atoms). When looking along the bond leading to the atom on which branching occurs, the next atom of Branch 2 is located 120" counterclockwisefrom the next atom of Branch 1. With this nota-

CALCULATIONS OF CONFORMATIONS OF P O L Y P E P T I D E S

111

tion, the longer branch in isoleucine, the hydroxyl group in threonine, and the ring in hydroxyproline (Greenstein and Winitz, 1961) are designated as Branch 1. I n other branched side chains, the longest branch is usually designated as Branch 1, except where this would lead to an inconsistency or conflict with the conventions already established (Table 3). Successive letters of the Greek alphabet are used as superscripts on the chemical symbol of the atom, with the superscript number 1 or 2 added in the case of branched chains (see Table 3). Hydrogen atoms, not shown in Table 3, are indicated according to the heavier atom to which they are attached, as follows. The hydrogen carries the superscript symbol (a,p, y , etc.) of the heavier atom, with an additional superscript (1, 2, 3, etc.) if there is more than one hydrogen atom attached to the heavier atom. The

from backbone

(9 FIQ.3. Conventions used to define the numbering of bonds in side chaina branching at a tetrahedral carbon atom as seen (a)perpendicularlyto and (b)looking along the bond leading to the Branch point. If the bonds leading from the branching carbon atom toward the backbone and toward Branch 1 are in the plane of the drawing, the bond leading to Branch 2 is below this plane, and the hydrogen atom is above this plane (a). (Edsdl et al., 1966).

numbers increase counterclockwise, as in Fig. 3. The notation for the hydrogen atoms is illustrated by the examples in Table 4. As in the definition of rotations for the backbone, the sense of rotation is such that a right-handed rotation about any side-chain bond, looking in the direction of numbering, is taken to be positive. The choice of zero angle of rotation is such that the planar eclipsed (cis) conformation is denoted by xj = 0 (Fig. 4). For the C"-@ bond, the N-C" and the CP-CY bonds are used to define the angle xl. I n branched chains, Branch 1 is always used to define the angle of rotation. In the description of helices, the following parameters and symbols are used : n = number of residues per turn

h =unit height (translation per residue along the helix axis)

112

HAROLD A . SCHERAQA

t=unit twist (angle of rotation around the helix axis per residue), where t = 360"/n. These parameters define the spatial arrangement of the residues, for fixed bond lengths and bond angles. However, helices may be characterized in other ways besides n and h, e.g. in terms of and t,4 or by means of the notation SR,where S is identical with n, and R is the number of atoms in a

+

TABLE 4 Examples of Nomenclature for Hydrogen Atoms

(a)

(b)

FIG.4. Definition of the angle of rotation x for rotation around single bonds in side chains as seen (a)perpendicularly to the bond being rotated and (b)looking along the bond being rotated (Edsall el al., 1966).

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

113

hydrogen-bondedring (Bragg et al., 1950). There is a definite correlation between, say, n and h, on the one hand, and 4 and t,h, on the other (Mizushima and Shimanouchi, 1961 ; Miyazawa, 1961 ; Ramakrishnan, 1964; Sugeta and Miyazawa, 1967; Kijima et al., 1967). If attentionis centered on the hydrogen-bond arrangements, the 8, notation of Bragg et al. (1950) is useful. I n describing hydrogen-bond arrangements, care should be taken in observing the definition of a residue. For example, in the &-helix,the N-H of residue i is hydrogen-bonded to the C'=O of residue i - 4. Thus, in terms of the standard notation, the a-helix is described as having i to i - 4,or 5 to 1, hydrogen bonding. TABLE5 Selected Values of Bond Distancesa-b Bond

_____

Bond Length, d

Backbone cu-C' N-CU C'-N C'=O N-H Ca-H

1.53 1.47 1.32 1.24 1.00 1.00c

Side Chain Ca-Cb (and all aliphatic C-C) C-Car (aliphatic to aromatic, as in tyrosine) Cp-H (and all aliphatic C-H) C=O (carboxyl, smide, ester) C=O (carboxylate) (C0)-0 (single bond in ester to carbonyl carbon) C-0 (carboxyl) C-0 (alcohol) C-0 (single bond in ester to alcohol R group) C-N (amide) C-N (amine) N-H (amide and amine) Car-Car (aromatic ring) Ca-0 (aromatic ring t o phenolic O H ) 0-H (tyrosine, alcohol, carboxyl) C-S (cysteine) C-S (methionine) C-S (cystine) S-S (cystine)

1-53 1.54 1.00c 1.23 1-25 1.36 1.29 1.42 1.45 1.32 1.47 1.00 1.40 1.36 1.00 1.82 1.78 1.86 2.04

*Used by Sasisekharan (1962), Ramachandran et al. (1963a,b), Brant and Flory (1965c), Leach et al. (1966a,b), Gibson and Scheraga (1966), Scott and Scheraga (1966c), Ooi et al. (1967), and based on survey of literature, as reported for example by Pauling (1960), and by G . Vanderkooi in this laboratory. b Amide group taken as planar ( W = O " ) . c This value should probably be increased to about 1.10 A, according t o electron diffraction data on aliphatic hydrocarbons (Bonham et al., 1959).

114

HAROLD A. SCRERAGA

111. GEOMETRICAL DATA Computations of polypeptide conformation must be based on accurate values of bond distances and bond angles. From a survey of the literature, it appears that, whereas these parameters may vary from compound to compound, there is a general consensus of accepted values; these are listed in Tables 5-1 1. TABLE 6 Selected Values of Bond Anglesa,* Bond Angle

Backborne T[C%'N] T[OC'N] T[C%'o] T [ C'NCa] r[C'NH] T[HNC~] T[xcuY] (for X and Y in both backbone and side chain) Side Chain

T[ccc] T[cco] (alcohol) T[cc=o] (amide, ester, and acid) T[cc-o] (ester and acid) T[oc=o] (ester and acid) T[cco](carboxylate, both oxygens being equivalent) T[oco] (carboxylate, both oxygens being equivalent) ~[ccN] (amide)

T[OCN] (amide) T[CCN] (amine) T[C&&ar] (aromatic ring) T[coc](ester) T[ccs](cystine, cysteine, methionine) T[css](cystine) T[CSH] (cysteine) T[csc](methionine) T[COH] (tyrosine) T[COH] (serine and threonine) T[COH] (acid)

Value, degrees

114' 125" 121O 123" 123' 114' 109.5' 113' (unless noted otherwise)a lloo 120° 115O 126' 118' 124' 120° 120' 113O 120° 114' 113' 104' 96' lloo lloo 105°-1100 116"

"Used by Sasisekharan (1962), Ramachandran et al. (1963a,b), Brant and Flory (1965c),Leach et al. (1966a,b), Gibson and Scheraga (1966),Scott and Scheraga (1966c), Ooi et al. (1967),and based on survey of literature, as reported for example by Pauling (1960),and by G. Vanderkooi in this laboratory. b Amide group taken a s planar ( W = 0"). C The effect of variations in the backbone angles on sterically allowed conformationswaa considered by Leach et al. (1966a,b). d For example, in calculations on polyamino acid helices, T[ccc]has been taken in the range 113-115' (Ooi etal., 1967)in side chains.

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116

It should be emphasized that these parameters should not be regarded as fixed, i.e. polypeptide structures are not necessarily rigid. However, departures from these values (and from the assumed planar trans conformation of the backbone amide group) can be taken care of by introducing appropriate energy terms t o allow for such departures (seeSection VE). TABLE7 Selected Values of Bond Angles Involving Hydrogen Atoinsa Bond Angle

Value, degrees

T[CCH] (aliphatic) T[CCH] (aromatic) T[HCH] (diphatic) T[CNH] (amide) T[HNH] (amide) T[cNH] (amine) T[HNH] (amine)

108.6" 120° 1095' 120° 120° 109.6" 109*6°

a Basis for selection of angles involving hydrogen atoms: the two H atoms are placed in the perpendicular bisecting plane of the T[ccc]angle, which is set a t 113'. If T[HCH] is set equal to 109.6", then T[CCH] = 10843". These assumptions may have to be changed.

TABLE8 Geometrical Data for Proline (Leung and Marsh, 1968) (from L-leu-L-pro-gly) Bond Distanoes Bond C'leu-C'Ieu C'leu-olen C'-N N-C' Clx--cB CP-CY

cy-ca C6-N

Bond Angles

Bond Length, A 1-60 1-27 1.34 1.46 1-50 1.6la l*60a 1.46

Bond Angle T ~ ~ u ~ ' ~ ] l e u

~[C~C'Nlleu T[C'NCu] T[NC'CD]

T[c'cpcy] T[cDcyc8] T [ CyCSN]

T[C'%C']

Value, degrees 119" 119O 121" 104" 107" 106'a 103" 126"

0 Average of the two sets of values given for Cy. The value of T[cBcyc8] is given as 11 1' by Saaisekharan (1969).

A particular case which should be pointed out is that of the bond angle around tetrahedral carbon atoms. Very often, all of the angles around a given carbon atom are assigned the value of 109.5". However, in some cases, such as for aliphatic carbon chains, the value of 7[CCC] has been observed to be as large as 115". I n calculations on poly-1;-valine (Ooi,

116

H A R O L D A . SCHERAQA

TABLE9 Geometrical Data for Argininea (Mazumdar and Srinivasan, 1964; Ramachandran et al., 1966a) (Charged guanidino group) Bond Distances Bond

Bond Angles Bond Angle

Bond Length, b

Cs-NE NE-H NE-CT CT-N' N-'H

Value, degrees 118' 124' 118' 121° 124' 115' 120° 120"

1.47 1.00 1.34 1.34 1.00

a The values in this table were selected froin those of Table 1 of Ramachandran et al. (1966a), in which the crystal data for L-arginine.HBr.Hz0, L-arginine.HCl.Hz0, L-arginine.HCI, and L-arginine-2H20 are summarized.

TABLE10 Geometrical Data for Histidineas 0 (Donohue and Caron, 1964) Bond Distances Bond

Bond Length, A

Bond Angles Bond Angle

Value, degrees

T[cwNq T[CBCYC*2] T[C*~CYN~~] T[cyNslcE1] 7[Ns1CE1NE2] T[C~~N~~C'~] T[N'~C*~C~]

122O 132" 106' 108' 109" lloo 10'7'

a From structure of histidine hydrochloride monohydrate. No structural data are available for neutral histidine; hence, it is tentatively assumed that the only geometrical difference between the charged and uncharged forms is the presence or absence of a hydrogen atom on either one or the other of the two ring nitrogen atoms [see Poland and Scheraga (1967) for a similar dilemma about the partial charges]. b The ring hydrogen atoms are placed in the plane of the histidine ring, on the lines bisecting the 7[CNC], T[NCN], and ~ [ N c cangles. ]

et at., 1967), +r[CaCBCrl]and 7[CaCBC@]were set at 113' instead of 109*5°; the angle +r[CW%y2] was also set at 113', and the hydrogen atom on CF was placed along the threefold symmetry axis defined by the C", Cyl, and Cr2 atoms [Scott and Scheraga (196610)give a recipe for computing all the angles consistently with whatever set of assumptionsis made].

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

117

The data for proline, arginine, histidine, and tryptophan are not included in Tables 5 , 6 , and 7, and are listed separately in Tables 8-1 1. Various geometrical data for proline have been reported by Mathieson and Welsh (1952), Leung and Marsh (1958), Sasisekharan (1959), and Rich and Crick (1961). The bond lengths and bond angles for L-leu-Lpro-gly are given in Table 8. The hydrogen atoms on CP, Cr, and C8 of the proling ring were placed on the perpendicular bisecting plane of the T[ccc]or T[CCN]angles, and positioned so that T[HCH]= 109.5" (Scott et al., 1967). TABLE11 Geometrical Data for Tryptophana (Pasternak, 1956) (glycyl-L-tryptophandihydrate) Bond Distances Bond

Bond Angles

Bond Length, d

Value, degrees

1.53 1.34 1.42 1.43 1.31 1.39 1.40 1.41 1-35 1.39 1.40

127' 126' 108' 107" 109" 109O 107" 134' 1190 117' 122" 1210 116" 123' 1280

The ring hydrogen atoms are all placed in the plane of the tryptophanring, on the line bisecting the T[CCN], T[CNC], and T[ccc]angles.

From the data for L-leu-L-pro-gly, it appears that the Cr atom of the prolyl ring can lie either above or below the plane of the ring. I n computations on proline, the Cr atom was placed half-way between the two positions given by Leung and Marsh (1958) (not quite in the plane), but the two hydrogen atoms were placed in the two extreme positions, above and below the plane, corresponding to those they would occupy when the Cr atom is in the observed positions above and below the plane, respectively (Scott et al., 1967). The bond lengths and angles which result from this placement of the Cr and H ( 0 ) atoms are artificial; however, this does correctly represent the volume occupied by the side chain.

118

HAROLD A . SCHERAGA

IV. TRANSFORMATION OF COORDINATES From the set of geometrical parameters given in Section 111, it is possible to compute the Cartesian coordinates of each atom of an amino acid residue in a coordinate system fixed on the particular residue. But, since the position of every residue with respect to every other one in a polypeptide chain can be varied by varying all of the +'s, tfs, and xi's (see Fig. 2), a particular set of these dihedral angles will specify a particular conformation of the chain. Before the energy of a given conformation can be computed, however, it is necessary to express the position of every atom in the same coordinate system. For this purpose, various coordinate-transformation procedures have been described [see, for example, Nemethy and Scheraga (1965), modified by Ooi et al. (1967), or Brant and Flory (1965c)I. I n the particular case of regular, or helical, structures simple procedures are available to relate the dihedral angles (which repeat in every residue of a regular structure) to the parameters n and h (Mizushima and Shimanouchi, 1961; Miyazawa, 1961; Sugeta and Miyazawa, 1967; Kijima et al., 1967).

CONTRIBUTINGTO V. TERMS FOR THE

THE EXPRESSION TOTAL ENERGY

While early calculations of polypeptide conformation were carried out with very simplifying assumptions about the internal energies, it seems preferable to present here the present status of the attempts to obtain as reliable a set of energy functions as possible. I n later sections we will present resuIts obtained both with the simplified and with the more complete expressions for the energy. As intramolecular contributions to the total energy, we recognize the following :torsional barriers to internal rotation about single bonds, nonbonded interactions, electrostatic interactions, hydrogen bonding, bond stretching, bond angle bending, and torsion about the peptide bond; also included are inter-molecular solvent-polypeptide interactions, which involve free energy contributions, such as those from hydrophobic bonding. Expressions for these energies have been deduced from various types of physico-chemical data on low-molecular-weightmodel systems. More recently, the expressions for most of these contributions have been refined by using them to compute known crystal structures of small molecules. We shall first present here the original expressions, and then discuss their subsequent refinement. Further discussion of these topics may be found in the books by Volkenstein (1963) and by Birshtein and Ptitsyn (1966).

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119

A. Torsional Energies

A method for calculating the barriers to internal rotation has recently been proposed (Scott and Scheraga, 1965). It is based on the concept that the barrier arises from two effects, exchange interactions of electrons in bonds adjacent to the bond about which internal rotation occurs, and nonbonded or van der Waals interactions, The exchange interactions are represented by a periodic function, and the nonbonded interactions either by a Buckingham “6-exp” or Lennard-Jones “ 6-12 ” potential function, the parameters of which are determinod semi-empirically. (The parameters of the nonbonded potential energy functions are discussed in Section VB.) While such a procedure is generally accepted, a problem arises as t o the numerical values to assign to the parameters in the periodic potential functions. The ranges of values used by Brant and Flory (1965~) and by Scott and Scheraga (1966~) for the barriers to rotation about the single bonds of the backbone reflect this difficu1ty.l These differences are probably not too significant, since the barriers are probably not very large and do not contribute as much to the total energy as other factors do (see below). The barriers to rotation about the side-chain single bonds, e.g. the aliphatic C 4 bond, are higher, but there seems to be less difficultyin assigning parameters to these rotations. Consider first the potential functions U(+)and U(r$)for rotation about the Ca-C’ and N-C” bonds, respectively, of the backbone. Since no direct information (accessible principally from microwave spectroscopy) is available for the barriers to rotation about the bonds in the polypeptide backbone, it is necessary to estimate these quantities by analogy with small molecules for which experimental information is available. For rotation about the Ca-C’ bond, the best analogous small molecules are those having the structure CH,. CO .X, where X can be H, F, C1, Br, CN, OH, CH,, or CzH6. The potential U(+)for rotation about the G - C bond in all of these molecules is known to have three-fold periodicity, with three minima of equal energy and three maxima of equal energy, with the barrier heights shownin Table 12 (Herschbach, 1962). The three minima in the rotational potential always occur when the C - X bond is staggered with respect to the C-H bonds of the methyl group (i.e. when the C= 0 bond eclipses a G-H bond of the methyl group) and the maxima occur when the G-X bond eclipses one of the G-H bonds of the methyl group (i.e. when the C=O bond is staggered with respect to the C-I3 1 As a possible way of circumventing this problem, Gibson and Soheraga (1967a)have considered an alternative approach, in which the barrier (includingboth the exchange interactions and near-neighbour nonbonded interactions) is taken m that of a similar model compound (see Table 13).

120

HAROLD A. SCHERAOA

TABLE12

.

Barriers to Internal Rotation for CH3. CO X

Barrier

Compound CH3CHO CH3CFO CHSCC10 CH3CBrO CHaC(CN)O CHsCOOH CHaCOCH3 CH3COCzHs

(koalmole-1) 1.17 1.04 1.30 1.30 1.27 0.48 0,76 0.50

bonds of the methyl group). On the basis of the data in Table 12, it is assumed that the potential for rotation about the Ca-C' bond in the polypeptide chain should also be threefold with minima at # = 0", 120°, and 240" and maxima at 60°, 180", and 300". From the data in Table 12, it would seem that the barrier height should fall in the range 0.48 to 1.3 kcal mole-l. However, following a suggestion of Schellman and Schellman (1964),Scott and Scheraga (1966~) selected acetic acid as the closest rotational analog to a polypeptide of any of the molecules in Table 12, since the C-OH bond in acetic acid probably more nearly resembles the C'-N bond in the polypeptide than do those in any of the other molecules (i.e. the C'-N bond in polypeptides has about 50 yodouble-bond character). They then subtracted from the value of the acetic acid barrier that portion estimated as arising from nonbonded repulsions between the methyl hydrogens and the two oxygen atoms. This led to the following equation for the inherent torsional contribution to the potential function :

U(#)= ( q d 2 ) ( 1 -

3#) (1) where U+= 0.2 kcal mole-l. Actually, if this barrier lies anywhere in the range of 0 to 1.0 kcal mole-l, the effect on the results of polypeptide conformational calculations is found not to be very significant. De Santis et al. (1963, 1965) neglected this barrier altogether in their calculations, while Brant and Flory (19654 used the value 1 kcal molep1 but found that their results for the mean-square unperturbed end-to-end distances were not particularly sensitive to this choice. I n eq. 1, the N-Cu bond eclipses the C'-0 bond at # = 0", a position of minimum energy. Concerning internal rotation about the N-C" bond in the polypeptide backbone, Brant and Flory (19654 have pointed out that the nature of this rotational barrier is more difficult to understand than that for the COB

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121

C"-C' bond because of the lack of microwave spectral data for appropriate small molecule analogs. If one considers the N-C' bond as a double bond, then the situation would be similar to that of the molecules in Table 12, with the N-C' bond playing the role of the C=O bond and the N-H bond that of the C-X bond. Minima would then be expected when the N-H bond was staggered with respect to the bonds C"-H, Ca-R (or H for glycine) and C"-C' [i.e. when the N-C' bond eclipses The total barrier might then bonds Ca-H, C"-R (or H), and C"-C'J. be expected to lie in the range 0.48 to 1.3 kcal mole-l. However, since the N-C' bond has only about 50 % double-bond character, the barrier might not be as high as 1.0to 1.3kcal mole-l, as in the first few compounds of Table 12. Regardless of whether or not the N-C' bond is considered as more like a single bond or more like a double bond, the potential should be threefold since the only sixfold potentials known are for molecules like methyl boron difluoride (CH3BF2)and nitromethane (CH3N02)(Hershbach, 1962) where the two substituents (i.e. the fluorines and the oxygens) are the same. It seems reasonable to treat the N-C' bond in this case as more like a double bond relative to the N-H bond, and assume that the maxima occur at 4 = 0", 120", and 240" and the minima at 60", 180", and 300". Hence, the inherent torsional contribution to the potential for the N-C" bond is represented by the equation

U(4)

= (U$/2)(1+COB 34)

(2)

Because of the 50 %double-bond character of the peptide bond, Scott and Scheraga (1966~) took U4 about halfway between the value for acetaldehyde (where the C=O bond is a double bond and the barrier height is 1.17 kcal mole-l) and the two sixfold cases (wherethe threefold contribution is zero) ;hence they used a value of 0.6 kcal mole-I. Brant and Flory (1965~) used a value of 1-5kcal mole-l, and found that neither interchanging the positions of maxima and minima in the potential function, nor varying U+ had much effect on their calculations. De Santis et al. (1963, 1965) neglected this barrier altogether. According to the above discussion, the N-H bond has a cis position with respect to the C"-C' bond at t$ = 0",a position of maximum energy. Regardless of the lack of our present knowledge concerning the nature and heights of these two barriers in the polypeptide backbone, two important points seem evident, viz. these barriers are not as high as the barriers to rotation about C-C bonds in hydrocarbons where the barriers are of the order of 3 kcal mole-I or greater, and the potentials are probably threefold rather than sixfold, because sixfold potentials occur in only a few cases where the symmetry is such that the threefold contribution cancels. 5

122

HAROLD A. SCHERAOA

The possibility of rotation about the peptide bond will be discussed in Section VE. We turn now to the potential function U(x) for rotation about the side-chain bonds, considering first the C-C bonds for which the following equation is used.

U(X) = (U,/2)(1 +cos 310

(3)

where U x= 2.8 kcal mole-l, the remainder of the barrier, as in the case of the backbone barriers, coming from additive contributions from the nonbonded interactions. When x = 0", the N-C" bond eclipses the CP-CY bond, or the C"-CP bond eclipses the Cr-CS bond and so on; these are positions of maximum energy. I n side-chain ester groups, Ooi et al. (1967) regarded the CP-CY bond of aspartate (and the CY-CS bond of glutamate) as analogs of the C"-C' bond of the backbone, and hence used the value U+=O.2 kcal mole-l for U x for these bonds. Torsional potential functions for rotation in side-chain ester groups have been suggested by Yan et al. (1968). A twofold potential function of the form (Ux/2)(1-cosx), with a barrier height of 8.75 kcal mole-I, was assigned to the (C=O)-OC bond. The value of U ( x ) for rotation about the (COO)-C bond was taken as zero for all values of x. I n the absence of data for the rotation of the phenolic group of tyrosine around the CB-CY bond, Ooi et al. (1967) selected the following sixfold potential, on the basis of symmetry considerations :

where U x = 0 . 5 8 kcal mole-l. The minima occur at x=30°, go", 150°, 210", 270", 330". When x = 0", the Cr-CS bond eclipses the V-CP bond at a position of maximum energy. For benzyl esters, Yan et al. (1968) used eq. 4 with a value of Ux= 0-50 kcal mole-l for rotation around the CH2-C6H5 bond, based on the value of Ux for the small molecule H3C-C6H, (Volkenstein, 1963). Equation 4, with Ux= 0.50 kcal mole-l bond of p-methyl was also used for rotation around the C,H5-CH, bond of benzyl-aspartate (Yan et al., 1968). For the C,H5-NO, p-nitro benzyl-aspartate, Yan et al. (1968) used a function of the form ( Ux/2) (1 - cos 2x), with Ux= 7.8 kcal mole-l (Trotter, 1959); the minima of this function occur in the planar conformation (x = 0" and 180").

It must be emphasized that, as shown by Scott and Scheraga (1965),

CALCULATIONS OF CONFORMATIONS OB POLYPEPTIDES

123

the barriers to internal rotation can be accounted for by the sum of two terms : the electron exchange interactions described above, and the nonbonded interactions to be described in Section VB. It appears that rotational barriers cannot be accounted for by nonbonded interactions alone. I n view of the intimate relation between observed rotational barriers and the torsional and nonbonded energies,it is not surprising that the ranges reported for potential functions show up in both the torsional end nonbonded contributions ; see Section V F on crystal energy calculations for a possible resolution of these uncertainties. I n contrast t o the above treatment, in which the barrier height was regarded as being made up of explicit additive contributions from the torsional and nonbonded terms, Gibson and Scheraga (1967a) did not make this separation explicitly, and took the rotational barriers for side chains from experimental data on analogous small molecules (Table 13) ; the backbone rotations (and bond 4 of the arginine side chain, with an TABLE13 Side-Chain Rotational Barriersa (Gibson and Scheraga, 19678)

Aromatic Branched Serine Other Leucine, isoleucine Aromatic Serine

Asparagine Aepartate Other Methionine

300 180,300 300 300 180,300

60, 180, 300 60, 180,300 180 180

60,180 60 60, 180 60, 180 60

0.40 0.40

0.20 0.20 0.75

3.50a 3.80 1.00 3.50d 3.50d

0.00' 2.00f 60,300 60,300

0.75 0.40

0.508 0.00e

3.50h 2.00(

a Barriers not shown i n this table wero the same as for some analogous bond in the table ; e.g., bond 3 of glutamine is analogous to bond 2 of asparagine, bond 3 of lysine or arginine is analogous to bond 2 of lysine, etc. b Barrier height relative t o the trans position. c Assignment of trans and gauche minima and choice of A U for bond 1 were based on data of Pachler (1964). d Analogous t o iso-butane (Wilson, 1959; Lin and Swalen, 1959; Green, 1961). e Sixfold potential considered negligible. f Analogous to ethanol (Wilson, 1959; Lin and Swalen, 1959; Green, 1961). Analogous to acetic acid (Wilson, 1959; Linand Swalen, 1969; Green, 1961). h Analogous t o propane (Wilson, 1959; Lin and Swalen, 1959; Green, 1961). Estimate.

124

HAROLD A . SCHERAGA

intrinsic torsional barrier of 0-5 kcal mole-l) were treated as described above. Thus far, the torsional barriers for rotation about the S-S and C - S bonds of cystine have been treated only by the method of Gibson and Scheraga (1967a), described in the previous paragraph, i.e. the nearneighbor nonbonded interactions were included with the intrinsic torsional energy. Thus, Gibson and Scheraga (1967b)have taken the total potential for rotation about the S-S bond as twofold with minima at x = 90”and x = 270”and a barrier height of 12.0 kcal mole-l (Bergsonand Schotte, 1958). The total potential for rotation about the C-S bond was taken as threefold, with minima at x= 60”, 180°, 300” and an estimated barrier height of 2-00kcal mole-l; in this connection, the data of Rudolph et al. (1966),giving 1.48 kcal mole-I for this barrier, will be useful. B. Nonbonded Interactions The nonbonded interactions are usually expressed as a sum over all pairwise interactions between atoms i and j of the molecule. These, in turn, are functions of the dihedral angles 4, $, and the x’s. Reviews of the subject of nonbonded potential functions have been given by Westheimer (1956), Pitzer (1959), and Fitts (1966). Initial work by Sasisekharan (1961, 1962), Ramachandran et aZ. (1963a, b), Schellman and Schellman (1964), Nemethy and Scheraga (1965), and Leach et al. (1966a, b) was carried out by assuming that there was no attractive interaction between atoms i a n d j for r > r o ,but only an infinite repulsion for r 6 r o (the hardsphere potential), where r ois the sum of the van der Waals radii of atoms i a n d j (see Fig. 5 ) . At the present time, more realistic potential functions (usually Buckingham or Lennard-Jones) have been used (see Fig. 5 ) (Liquori, 1963, 1966; Brant and Flory, 1 9 6 5 ~Gibson ; and Scheraga, 1966, 1967a; Scott and Scheraga, 1966c; Ramachandran et al., 1966b; Ooi et al., 1967 ; Venkatachalam and Ramachandran, 1967). Nevertheless, it is worthwhile to mention the hard-sphere potential since it already provides fairly realistic information about steric hindrance in the polypeptide chain. Also, as we shall see, it is a fairly good first approximation for more refined calculations involving more realistic energy expressions. The main problem in the use of the hard-sphere potential is the selection of values of the van der Waals radii of the atoms. Much has been written on this subject, and the difficulty lies primarily in the fact that the concept of a “van der Waals radius’’ is itself a nebulous and inexact one. Also, since the radii are assigned to spherical atoms, no consideration is taken of the angle at which the two atoms approach each other. Thus, it is not surprising to find large ranges of values in the literature for the

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

125

same atoms. To circumvent this difficulty, the workers referred to above have always varied their values of van der Waals radii within the ranges found in the literature so as to assess their influence on the h a 1 computed results. Ramachandran et al. (1963a, 1966b)and Leach et al. (1966a, b) have presented calculations to show the influence of ranges of van der Waals radii on the allowed conformations of dipeptides and of helical structures. We present in Table 14 a list of “selected” van der Waals contact distances. These values were selected intentionally to lie toward the low-value end of the range reported. I n this way, the computations would be less likely to exclude peptide conformations in which certain

E

IE Lennard -Jones 6-12 Potential

Hard -Sphere Potent i o I

Fra. 5. Schematic drawing, comparing the hard-sphere and Lennard-Jones 6-12 potentials. The symbol E is the same as Ugj of eq. 6,

pairs of atoms are in unusually close contact due to the direction in which they approach each other. On the other hand, the use of small radii has probably led to the admission of certain conformations which would have been disallowed on steric grounds. The values of Table 14 are essentially those used by Nemethy and Scheraga (1965)and Leach et al. (1966a,b). More refined treatments of the potential function have made use (primarily) of the Buckingham “ 6-exp” or Lennard-Jones “6-12” forms. These are Buckingham :

uij = a,.. exp ( - b..r..)- c../rG. 21

(5)

u.. v - d..lr!2 $3 v - e..lrG. v

(6)

tj

23 23

23

Lennard-Jones : 23

126

H A R O L D A . SCHERAOA

where rij is the internuclear distance of atoms i a n d j , and aij,b,, cij, dij, and eij are constants independent of rij. TABLE 14

___ C' 0 N H CH Car NH.2 OH

Selected Valuesn of van der Waals Contact Distances (A) (Leach et al., 1966a) C'

0

N

H

CH

Car

NH2

OH

2.9

2.7 2.6

2-7 2.6 2.6

2.4 2.2 2.3 2.0

3.2 3.0 3.0 2.7 3.6

3.1 3.0 3.0 2.7 3.4 3.4

3.1 3.0 3.0 2.7 3.4 3.4 3.4

3.0 2.9 2.9 2.6 3.3 3.3 3.3 3.2

* C H refers to CHs, CH2, and CH, C' to carbon atoms in the carbonyl groups of backbone or side-chain amide groups, 0 t o carbonyl oxygen atoms, O H to alcoholic or phenolic hydroxyl groups, N t o amide nitrogen atoms in the backbone, NH2 to amide N H 2 groups in side chains, H to hydrogen atoms in the backbone amide NH groups only. The value for Car takes account of the thickness of the aromatic ring.

The Lennard-Jones potential is the one most commonly used at present since the Buckingham form has an additional parameter, exhibits a physically unrealistic maximum at very short internuclear distances, and approaches --a, as the internuclear distance approaches zero. While these artifacts can be eliminated by proper computer programming, they increase the time of computation. Nearly the same curves result in the region of rij of interest if eqs. 5 and 6 are made to coincide a t their minima. Hendrickson (1961) and Scott and Scheraga (1965, 1966a, b, c) have developed procedures for obtaining the constants of eqs. 5 and 6. The coefficients cij or eij of the attractive terms are obtained by using the Slater-Kirkwood equation

where e is the electronic charge, m the electronic mass, cti and ajthe atomic polarizabilities of atoms i a n d j (taken from Ketelaar, 1953),and Xi andNj are the effective values of N , the number of outer-shell electrons [replacing the real values of N , as suggested by Pitzer (1959)l. Using data from Pitzer (1959), Scott and Scheraga (1965) have presented a curve for the dependence of N,, on atomic number 2 for the inert gases. This curve is assumed to hold for any other atom, and provides values of Nefffor any

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

127

value of 2. Hendrickson (1961)and Scott and Scheraga (1965)have also provided a procedure for obtaining aijand b, of eq. 5 from data on molecular beam scattering; however, only the procedure for obtaining dij of eq. 6 is presented here. These parameters were obtained from the condition that Uij be a minimum at rmin,the sum of the van der Waals radii. The values used for the parameters are given in Table 15. Brant et al. (1967)and Gibson and Scheraga (1967a) obtained dij by minimizing Uij at rijequal to the sum of the van der Waals radiiplus 0.2 A. This is equivalent to enlarging the van der Waals radii [see Brant et al. (1967)for justification of the inclusion of the 0.2 A increment]. TABLE 15 Parameters for Calculating Nonbonded Potentialsa.b van der Waals radius (A)

1024 x a

Atom

C

1.70

N

1.55

H

1.62 1-20 1.80

0.93 0.87 0.84 0.42 0.34

0

S

(-3)

Nerr 6.2 6.1 7.0

0.9 16.0

a These values differ somewhat from those selected by Brant and Flory (1966~) and by Brant et al. (1967). b Gibson and Scheraga (19678) used an alternative procedure in order to reduce the amount of computation. Hydrogen atoms were not considered individually unless they can take part in a strong hydrogen bond. Instead, they were regarded a8 part of an extended “atom” such ES a methylene group, etc. See Table 1 of Gibson and Scheraga (19674 for the values of the van der Waals radii, 01 and Neil for these extended “atoms”.

A typical set of nonbonded potential functions (Scott and Scheraga, 1966c; Ooi et al., 1967) obtained by the procedure described above is given in Table 16. Those of Brant and Flory (1965~) and of Brant et al. (1967),obtained by essentially the same procedure, differ somewhat from these because of the different values selected for the parameters of Table 15. Liquori (1966) has used a combination of Lennard-Jones and Buckingham functions, based primarily on work of Mason and Kreevoy (1955). Equation 6 is used for all pairs of atoms for which the internudear distance can change as a result of a variation in the dihedral angles. Hence, it is used, in general, for all pairs of atoms separated by three or more bonds. Further, since the contribution of nonbonded interactions to the total energy falls off very rapidly with increasing internuclear distance, the nonbonded interaction generally can be ignored if rii > 7.0 A.

128

HAROLD A . SCHERAGA

TABLE16 Constants for Nonbonded Potential Functions (Scott and Scheraga, 1966c; Ooi et al., 1967)

47 370 363 367 367 366 128 365 I24 125

2.40 3.40 3-10 3.04 3.22 3.25 2.90 3.07 2.72 2.75

4.5 286 161 I45 205 216 38 153 26 27

a Ooi et al. (1967) investigated the effect of variation of the van der Waals radius of the hydrogen atom (hence of dtj) on the computations for homopolymer helices.

Several other functional forms, besides the Lennard-Jones and Buckingham potentials, have been used to describe the non-bonded interactions. For example, Kihara (1953) used a form in which the repulsive potential becomes i n h i t e at very short distances, about 46 that at which the minimum of the function occurs; if the distance, at which the potential becomes infinite, is reduced to zero, then the Lennard-Jones form results (Rowlinson, 1965). Kitaigorodskii (1961) derived another function from the Buckingham form. By defining ro as the distance between the atoms at which U is a minimum, and letting z = r / r o , a=bro, and U2/3be the value of U at r = 2ro/3 he obtained

Kitaigorodskii (1961) assumed that (Uij)2/3= 3.5 kcal mole-l and a= 13 for all atom pairs, and reduced eq. 8 to

U,

=

3-5(8600exp ( - 13zij)- 0-04/ztj}

(9)

Selection of ro,for any atom pair, then gives Uij as a function of rij,according to eq. 9. Kitaigorodskii (1961) applied eq. 9 to C . * -C, C - 'H, and He * H interactions. Venkatachalam and Ramachandran (1967) deh e d ro so that U , = 0 at a value of rij equal to the sum of the van der Waals radii of the two atoms, and referred to this Kitaigorodskii function as Kl. They also obtained a function, referred to as K 2 ,by requiring that Uij be a minimum at a distance of separation equal to the sum of the van

-

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

129

der Waals radii of the two atoms, but otherwise satisfying eq. 9. Venkatachalam and Ramachandran (1967)then selected values of ro (on both the K , and K z basis) for all atom pairs in polypeptides and obtained, thereby, appropriate forms of eq. 9 for each atom pair. Aside from the variety of functional forms for the nonbonded interactions, there is a range of values reported for the parameters of these functions, especially for those involving hydrogen atoms (see, for example, Bartell, 1960; Scott and Scheraga, 196613; Bixon and Lifson,

FIG.6. Nonbonded potential curves computed by Venkatachalam and Ramachandran (1967) for the interactions (a) N . . . H and (b) N . . . N for the various functions: (K1); -x-x(Brent and Flory, 19650);- - - - - (De Santis et al., 1966); ( K z ) ; . (Scottand Scheraga, 1966~).

... .

-a_--

1967; Huggins, 1968). An example of the variation in some of these functions is shown in Fig. 6. It should be emphasized that all of these functions are based on limited data and assumptions whose validity is difficult to substantiate. Also, it is possible that two sets of functions may be required, one for near-neighbor interactions and another for interactions between remotely connected parts of the chain (Scott and Scheraga, 1966~).Therefore, recent attempts have been made to refine these functions by using them to compute the known structures of small molecules from electron diffraction data and the known crystal structures of small molecules from X-ray diffraction data. Jacob et al. (1967), 5*

130

HAROLD A . SCIIERAGA

Kitaigorodskii (1965, 1966), Rabinovich and Schmidt (1966), Williams (1966), Giglio and Liquori (1967), and Damiani et al. (1967) have made some progress in this direction; further work along these lines is in progress (see Section VF). Venkatachalam and Ramachandran (1967) and Mark (1 968) have evaluated the various functions presented here; their conclusions are given in Section IX.

C . Electrostatic Interactions Arridge and Cannon (1964)and Brant and Flory (1965a, c) have emphasized the importance of including dipole-dipole electrostatic interactions between the polar amide groups in conformational energy calculations. I n addition to the polar amide group with a dipole moment of 3.7 D (Brant and Flory, 1965c),Ooi et al. (1967)took into account the dipole interactions involving the polar ester groups in aspartate and glutamate side chains (p= 1.7 D) and the polar phenolic group in the tyrosyl side chain (1.5 D) ; such effects should be taken into account for all polar side chains (Yan et al., 1968). The dipole moments are represented by partial charges (the so-called monopole approximation) to reproduce the bond moments and over-all dipole moments (Scott and Scheraga, 1966c; Brant et al., 1967; Ooi et al., 1967). By using partial charges, the dipoledipole interactions can be calculated with a Coulomb’s law type potential function between the partial charges qi and qj separated by a distance

.

rij

u€!,=

c all

qi9jlDrij

(10)

partial charges

where D is the apparent dielectric constant. It is difficult to make a reliable estimate of the magnitude of D. When two charges are close enough so that there are no solvent molecules or other atoms of the polymer chain between them, D is determined by the atomic polarizabilities of the interacting atoms and by the influence of the reaction field of the environment. For these distances, Brant and Flory (1965~) selected a value of 3.5 for non-polar solvents after examining the effect of variation in D on their results. Scott and Scheraga (1966~) and Ooi et al. (1967) have used values in the range from 1 to 4 without significantly affecting their results. Gibson and Scheraga (1967a, b) used a value of 3.0 to reflect the effect of the aqueous solvent in their calculations ;at very large separations, the effective dielectric constant of this solvent probably rises to 80, thereby greatly reducing the electrostatic interactions. Since this large value of D is approached rapidly for charge separations greater than the width of one water layer (Griffithand Scheraga, 1966), electrostatic

CALCULATIONS O F CONFORMATIONS O F P O L Y P E P T I D E S

131

interaction energies are taken to be zero at these distances, thus saving considerable computer time. Of course, for nonpolar solvents, in which D is low, the electrostatic interactions are not negligibly small at these distances; hence, since they are sufficiently long-range, they cannot be ignored as in the water case (Ooi et al., 1967). The values of the partial charges are usually selected to reproduce bond moments and the over-all dipole moment, i.e. the vectorial sum of the bond moments must agree with the experimental dipole moment, and the algebraic sum of the partial charges must be zero for uncharged groups. An example of a typical set of bond moments is given in Table 17. These, together with the set of partial charges of Ooi et al. (1967) in Table 18, reproduce the amide, ester and phenol dipole moments. Table 18 compares the values of the partial charges, chosen as described above and used by Ooi et at. (1967), with those of Brant et al. (1967) and others. It can be seen that the sets of data differ somewhat, depending on the criteria for assignment of the charges. TABLE17 Bond Moments and Bond Distances (Ooi et al., 1967) Bonda

Distance (A)

0-H (phenol) O=C (peptide and ester) N-H (peptide) 0-C (ester end phenol) O-cH3 (ester) N-C (peptide bond)

1.00 1.24 1.00 1.36 1.46 1.32

Bond Moment (D) 1.6 2-48 1.31 0.7b 0.66b 0.20

a The first atom of each pair is the negative end of the bond dipole. b Adjusted to give the known dipole moment of esters (1.7-1.8 D),

assuming a planar

structure.

A different approach to the assignment of partial charges has been taken by Poland and Scheraga (1967). They compute the total charge on any atom as the sum of the u and T charges. The u charges are computed by the MO-LCAO treatment of Del Re (l958,1963a, b), and depend on the complete connexity of at1 atoms in the molecule, i.e. the method requires that all atoms carry partial charges. The T charges, based on MO calculations, are taken from Pullman and Pullman (1963) and Berthod and Pullman (1965) for side chains, and evaluated from the magnitude and direction of the total dipole moment for the amide and carboxyl groups. The data for the neutral molecules formamide and methyl formate are shown in Table 19; these reproduce the magnitude and directions of the dipole moments of these compounds (shown in

132

HAROLD A . SCHERAOA

TABLE18 Partial Charges in Units of e, the Electronic Charge Charge

Atom Amide group C' 0 N

H

Schellman and Oriel (1962)

Ooi et uI. (1967)

+ 0-43 - 0.30

+0.318 - 0.422 - 0.202 0.204

- 0'394 - 0.281

+

+ 0.26

Poland and Scheraga (1967)5

+0.394

+0.450 -0.417 - 0.304 0.271

- 0.39

Eater group C (carbonyl) 0 (oarbonyl) 0 (single bond) C (single bond) Phenolic group CT

+

+ 0.281

+0.517 -0.417 - 0.202 +0*102

+ 0.100 + 0.340

- 0.440

0 H a

Brant et aZ. (1967)

The treatment of Poland and Scheraga (1967) differsfrom the others (seetext). TABLE19

u, T , and Totai Charges (in units of e, the electronic charge) on Two Neutral Molecules (Poland and Scheraga, 1967)

Formantide H' C' 0 N H(N) H(N) Methyl formate C H

H H 0 C' 0' H'

0

T

Total

+ 0.063 + 0.070

+ 0.208

-

+ 0.063 + 0.278

- 0.348 +0-140

-0.413 - 0,376 0.224 0.224

- 0.065 -0-616 0.224 0.224

+ +

- 0.024

- 0'024

+ 0.054 + 0.064 + 0.054 - 0.254

+0-107 - 0.058 0.067

+

+ +

+0.189 0-036 - 0.225

+

+ 0.054 + 0.054 + 0.054

- 0.065 +0.143 - 0.283 0.067

+

Fig. 7). Using the n- charges of Table 19, and u charges computed for amino acids by the method of Del Re (1958, 1963a, b), Poland and Scheraga (1967)obtained the partial charges for the amide group shown in Table 18. I n this treatment, the amide group carries a net charge of -0.102, counterbalanced by a charge of +0.102 on each side chain

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

133

(includingthe Ca and Haatoms). Somewhat different values are obtained for proline and hydroxyproline. The paper of Poland and Scheraga (1967) may be consulted for a listing of the u and 7~ charges on all the amino acid residues1 which commonly occur in proteins. Gibson and 8cheraga (1967a,b) used essentially this set of charges in their computations. 0' p=1*77Il

0

FIQ.7. Direction and magnitude of the total dipole moment in methyl formate (Curl, 1969)and in formamide (Kurland and Wilson, 1967)(from Poland and Scheraga, 1967).

It is hoped that current efforts at evaluating energy parameters from crystal structure calculations will provide a basis for resolving the apparent discrepancies between charge assignments, which appear in Table 18. D. Hydrogen Bond A variety of potential functions have been used for the hydrogen-bond interactions between the NH and CO groups of the backbone. For 1 After the paper of Poland and Scheraga (1967)was published, these authors became aware of an earlier paper by Del Re et aZ. (1963)on the calculation of the partial charges in amino acids. These two papers differ in several respects. Del Re et al. computed only the (I charges, and used parameters from saturated molecules in their computations. On the other hand, Poland and Scheraga used parameters of Berthod and Pullman (1966), based on molecules in which saturated and unsaturated groups were next to each other, t o compute the (Icharges; in addition, Poland and Scheraga also added in the T charges. Finally, the data of Del Re et aZ. pertain to the free (ionized and un-ionized)amino acids (where the partial charges are influenced by the neighboring a-amino and a-carboxyl groups), whereas those of Poland and Scheraga pertain to amino acid residues in a long chain (where the residues are bordered by peptide bonds).

134

HAROLD A . SCHERAQA

example, Liquori (1966) has used the following potential function, proposed by Stockmayer to calculate pairwise interactions between polar gas molecules :

The Lennard-Jones term describes the nonbonded interaction between the hydrogen atom of an N-H group and the oxygen atom of a C=O group. The second term describes the electrostatic interaction between two point dipoles centered on the oxygen atom and the hydrogen atom and having the orientation of the C=O and N-H bonds. ) Ooi et al. (1967) have used a form of the Scott and Scheraga ( 1 9 6 6 ~and potential function of Lippincott and Schroeder (1955) and Schroeder and Lippincott (1957), modified to take account of the angular dependence (Moultonand Kromhout, 1956). The form used by Ooi et al. (1967) is

U,,

=

Ae-bR- (A/2)(Ro/R)"XP (-bRo)

([1 + (6)1/2cos 8,]

-D*

1

+ (6)'12 1 + (6)'12 cos O2

* R-r-ro*)2

1+(6)1/2

(~(R-T)

+[

] )exp[-n

where the adjustable parameters are (for U=, in kcal mole-') : A = 4.941 x lo8, b = 4.8, D*= 82.4, n* = 13.15, r = 1-01 A, ro* = 0.97 A, Ro= 2.85 it. The variables are: R (the N-0 distance in angstroms), and 8, and O2 (the angles which the line HO makes with the directions of the lone-pair orbitals of the 0 atom, taken as 120' with respect to the C=O bond and lying in the NCO plane). This function is used only within a certain range of 8, and B2, within which a good hydrogen bond may be expected to form; if both cos8, and were less than 0.1, or if the OHN angle was less than 30°, the interaction energy of the N - - 0and H. -0pairs was calculated using eq. 6 instead of eq. 12. Equation 12 gives a reasonable representation of hydrogen-bond strength under conditions which are favorable for hydrogen bond formation. It is not well suited for representing the interaction energy for the borderline cases between a poor hydrogen bond and no bond at all, and a discontinuity is introduced when the shift is made from using eq. 12 to eq. 6. To avoid these difficulties, and to avoid the use of so many parameters of the LippincottSchroeder function, Poland and Scheraga (1967) developed a new hydrogen bond potential function. Its use in trial calculations on poly-L-alanine has given satisfactory results.

-

-

CALCULATIONS O F CONFORMATIONS OF POLYPEPTIDES

135

I n a sense, the Poland-Scheraga function resembles the LiquoriStockmayer one, except that the electrostatic portion is evaluated from the partial charges described above. The criteria on which the calculation is basedis that UHBshould have the followingproperties : (a)the potential should have a minimum at the experimentally measured distance, rm (where r is the distance between the hydrogen and the acceptor atom), (b)the value of the potential at rm should be the experimental energy of formation of the hydrogen bond, - E , and (c) the long-range, attractive part of the potential should be the known total dipole-dipole interaction

FIG.8. Schematicrepresentation of the hydrogen-bondpotential. The solid line (dipoledipoleinteraction potential) and thedot (positionof minimum,and energy at the minimum) are the only features that are known. The dashed line is an empiricalpotential constructed to fit th&fZwn data (Poland and Soheraga, 1967).

potential for the molecules taking part in the association. Figure 8 illustrates, by the heavy line and the dot, what is known with reasonable certainty about the hydrogen-bond potential ;this is the informationutilized by Poland and Scheraga (1967). The electrostatic part of the potential is given by the monopole approximation (with partial charges computed as described above), which gives the correct dipole-dipole interaction at large distances. The potential UHB is written as the sum of the electrostatic part plus an empirical function (of the Buckingham or LennardJones form), e.g. for the Lennard-Jones form

136

HAROLD A . SCHERAOA

The electrostatic function S(r) is computed from the partial charges. Application of conditions (a) and (b) leads to an evaluation of the parameters d and c. The angular dependence arises from the electrostatic interaction of the partiaI charges (in the S ( r ) term). Once d and c are

rH...O, Angstrom units Flu. 9. Potential function [ U ( r ) ,which is the same as U H B ] for the amide hydrogen bond, with ~ = 5 - 5kcal mole-1. Curve A is the analogue of eq. 13, using a Buokingham potential with repulsive part Arep and attractive part Curve B is eq. 13. In both cases, S ( r ) is added to either the Buckingham or Lennard-Jones terms to obtain V ( r ) (Poland and Scheraga, 1967).

known for a particular donor-acceptor pair, UHBis then determined in each conformation for the given donor-acceptor pair by computing the appropriate values of X(r). Using available data for the amide hydrogen bond (fromN-methyl acetamide), Poland and Scheraga (1967) computed the function shown in Pig. 9 ; from Fig. 9, it can be seen that differences

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

137

between the Buckingham and Lennard-Jones parts of UIIBare negligible. Poland and Scheraga (1967) also made an estimate of the strength of possible C-H - 0 hydrogen bonds, which are thought to occur in polyproline, collagen and polyglycine. It is hoped that crystal structure calculations, now in progress, will provide a r e h e d set of parameters for the function of eq. 13, as well as for all the other energy contributions discussed in this section (See Section

--

VF).

E. Distortion of Geometry The possibility exists that the portions of the polypeptide backbone and side chains can undergo distortions of their geometry through bond stretching, bond angle bending, and torsion about the peptide bond. Such effects have been considered by Bixon and Lifson (1967) for cyclic alkanes, by Jacob et al. (1967) for linear alkanes, and by Gibson and Scheraga (1966) for a dipeptide. Such flexibility reduces the repulsive non-bonded interactions in some conformations, and may have to be taken into account to explain the conformations of some proteins. To allow for flexibility, all atoms are assumed to be executing simple harmonic oscillations around their equilibrium positions, the latter corresponding (for peptides) to the geometry discussed in Section 111. Force constants for all vibrational modes have to be estimated from spectroscopic data, and the potential energy of these harmonic motions added to the contributions already discussed. The total potential energy is then minimized. At the present time it is difficult to obtain reliable values for all of the force constants required. Estimates of these force constants for hydrocarbons have been made by Bixon and Lifson (1967), and Jacob et al. (1967), and for polypeptides by Gibson and Scheraga (1966). I n the particular case of polypeptides, the vibrational modes considered by Gibson and Scheraga (1966) included bond stretching, bond-angle bending and torsion about the peptide bond. It is hoped that, by comparing conformational energy calculations on single molecules in the gas phase (now in progress) with experimental results from electron diffraction data, reliable values for the required force constants will be found. At this time, the question of whether such distortions of geometry have to be taken into account in conformational energy calculations for polypeptides is still unsettled. On the basis of the small amount of information now available, it is expected that inclusion of the possibility of distortion of geometry in the calculations will not make much difference in the positions of local minima in the energy surface, but may make a considerable difference in the relative energies of these minima.

138

HAROLD A . SCHERAGA

F. Role of Crystal Energy Calculations ir, ReJinement of Energy Parameters All of the energy contributions described above play a role in the intraand intermolecular interactions which determine the most stable conformations of crystals of small molecules. If the parameters of the various energy contributions are regarded as unknowns, to be determined by the requirement that the total potential energy be a minimum at the known equilibrium’ conformation of the crystal, then it should be possible to obtain reflned energy functions for use in conformational energy calculations. Furthermore, X-ray crystallographic data, and electron diffraction data on molecules in the gas phase, provide additional information about intramolecular interactions. Jacob et al. (1967) have recently carried out calculations of this kind, using electron diffraction data, and Kitaigorodskii (1965, 1966), Rabinovich and Schmidt (1966), Williams (1966), Giglio and Liquori (1967), and Damiani et al. (1967) have done similar calculations on crystals. It should be noted that the energies thus calculated can be put on an absolute scale by using them to compute the heat of sublimation (Bixon and Lifson, 1967). Conformational energy calculations on model compounds for polypeptides, both for single molecules and for crystals, are now in progress, but it is premature to discuss the results. Hopefully, these calculations will provide a reliable set of potential energy functions.

G. Free Energy of Hydration There is one additional contribution, which cannot be obtained from calculations on dry crystals, which must be taken into account, viz. solvation. Qualitatively (and also from the X-ray results on myoglobin and lysozyme) we know that solvation plays a very important role in determining protein conformation. If the solvent is water, we expect the nonpolar groups to lie preferentially in the interior of the molecule and the polar ones on the surface, in contact with the water; if the solvent is non-polar, the reverse situation is expected. Focusing attention here on water as the “natural” solvent for proteins, we shall discuss the assignment of free energy parameters to reflect the behavior suggested above. These parameters should make it difficult for polar groups to shed their water and enter the non-polar part of the interior of a protein molecule, but make it easy for nonpolar groups to do so. As will be discussed further in Section VIB, whereas it is the potential energy which must be minimized for all the contributions discussed above, it is the free energy

CALCULATIONS O F CONFORMATIONS OF POLYPEPTIDES

139

which must be taken into account when dealing with solvation. The following considerations provide the basis for obtaining an expression for the free energy of hydration. Calculations of the thermodynamic properties of aqueous solutions of nonpolar solutes (Nemethy and Scheraga, 1962)and of alkali halide ions (Griffith and Scheraga, 1966) show that the nearest-neighbor solvent molecules in the first shell around the solute molecule contribute very much more than all other solvent molecules to the free energy of solvation of these substances; the same is probably true of polar nonionic solutes. Hence, unless two atoms approach each other to within a distance equal to the sum of their van der Waals radii plus the diameter of a water molecule (designated here as T O ) , the solvent that is displaced is assumed not to contribute to the free energy. Also, as soon as an atom has approached another atom within this distance, it will displace a certain amount of solvent, which should be roughly proportional to the volume of the displacing atom; further approach of the two atoms, up to their van der Waals distance, should not greatly increase the amount of solvent displaced. To describe this behavior, Gibson and Scheraga (1967a) have expressed the amount of water qij removed from nearest-neighbor contact with the ith atom by the approach ofjth atom as Here rij is the distance between the atoms, and g(r) is a cut-off factor which provides a continuous function to make qij vanish at rij = ro.

This function is very nearly equal to 1.0 when r < 0.9 ro, then drops to a value of 0.5 when r = 0.95 ro, and to zero when r = ro; furthermore, it is continuous and has a continuous derivative (which are required properties for computing gradients). The quantity V, is a factor proportional to the volume of t h e j t h atom. The total amount of solvent removed from the ith atom by the approach of all other atoms will then be

In practice, the values of Vj were set equal to the volumes of the atoms in A3, as given by Bondi (1964), divided by 30. A further consideration in

140

HAROLD A . SCHERAQA

computing the solvation free energy is that there is a maximum solvation number for any atom; when this number of solvent molecules has been removed, there can be no further contribution to the free energy from the removal of solvent molecules from the first shell around that atom. If the maximum solvation number of the ith atom is Ai,then the free energy contribution arising from the removal of solvent from this atom is

X GP$(Wi,Ai)

(17) where Gfis the free-energy change when one solvent molecule is removed from the ith atom and $( W,,A,)is a function which is equal to zero when W,= 0, to Ai when W i2 Ai,and is continuous in between. The total solvent free energy is then obtained by summing over all atoms : Gi =

c w = xci i

(18)

The function for rj selected by Gibson and Scheraga (19674 was

[

rj(W,A) = A 1-exp

(--A

9 1

This is nearly linear up to W = 0.75A, then turns sharply but smoothly to a constant value of A . A simpler function, consisting of two polynomials TABLE20 Data for Evaluating Solvent Free Energies (Gibson and Scheraga, 1967a)

A

Go

solvent molecules in first shell)

(Free energy for removing one solvent molecule) (kcal mole-1)

(Number of Atom type _~~~_____ H 0 (carbonyl) 0 (hydroxyl) 0- (carboxyl) N (amide) NH3+ (amine) N+ (imidazole) N+ (guanidine) CH (aliphatic) CH2 (aliphatic) CH3 (aliphatic) C (aromatic) CH (aromatic) S

2 4 6 5 2 6 3 6 2 3 8 2 3 6

0.31 0.94 0.84 4.80

0.63 15.40 3.30 1.20 -0.13

-0.13 -0.13 0.11 0.11 -0.17

CALCULATIONS OF CONFORMATIONS O F POLYPEPTIDES

141

pieced together, has also been used, with essentially the same results. A more realistic form for the function, 4, however, would involve several step-like changes in the value of 4, to reflect the fact that the solvent is removed discontinuously. An appropriate function is now being investigated. Values for A, were deduced with the aid of Corey-Pauling-Koltun space-filling models ; those of G: were computed from data of Nemethy and Scheraga (1962) for nonpolar groups and were calculated for ionic groups by the method of Griffith and Scheraga (1966). For nonionized polar groups, approximate values were deduced from thermodynamic data for organic compounds containing polar groups (Frank and Evans, 1945). The values of Ai and G: are shown in Table 20. It should be emphasized that the Gio's, and hence also Gw,are free energies. Experience to date shows that the most pronounced effect of the solvent free energy is to cause charged ionic groups to stick out from the surface of small polypeptides into the water; we would expect that, in larger structures, the solvation contribution will also cause many of the nonpolar groups to lie preferentially in the interior of the macromolecule.

H. Loop-Closing Potential For conformational energy calculations on structures involving loops and peptide (e.g. the loop of gramicidin-S involving only N-Ca, C"-C' bonds, or the loops in proteins involving closure by the S-S bonds of cystine), it is necessary to assure that the loop will closeproperly to satisfy all the requirements (proper bond distances, bond angles, etc.) of the covalent structure. For this purpose, an empirical loop-closing potential is required. For gramicidin-S (Scott et al., 1967), where the loop involves the bonds of the polypeptide backbone, closure of the ring was effected at the C"-C' bond of an arbitrarily selected residue, together with the following potential function to close the gap : u,a*

-

Alr-rol +B(2- cosal- c0sa2)

(20)

where ro is the equilibrium length of the Ca-C' bond (1.53 A), and r is the actual distance in angstrom units between the C" and C' atoms ; a1 and az are the angles 7[D1CaC'] and T[D~C'C~], Dl and Dz being dummy atoms attached to the C" and C' atoms, respectively, in the directions of the bonding orbitals. The angles al and a2 become zero when the correct bond angles obtain. The parameters A and B are adjustable ones, which must be large enough to close the loop, but not so large as to dominate completely the total energy. Scott et al. (1967) examined the effect of varying A and B, and selected the values of A = 12 and B = 100 (for UgeD

142

HAROLD A . SOHERAOA

in kcal mole-I). The value of Ueapwill differ from zero if there is any deviation from the proper bond distance or bond angles at the C"-C' bond. This function can also be used to close a gap at any other bond, such as a disulfide bond, by changing the value of ro,e.g. r0= 2.04 A for an S-S bond. An alternative function, which includes six terms, has been used by Gibson and Scheraga (1967b) for closing the S-S bond of cystine. Two of these terms are torsional potentials for rotation around the C-S bonds ; these potentials include non-bonded interactions and were described in Section VA. The third term is a torsional potential for rotation about the S-S bond, and is also described in Section VA. The remaining energy terms consist of one to close the bond gap between the sulfur atoms and two terms to bring the C-S-S bond angles to their correct value. To close the gap, the simple harmonic function

is used, where rssis the S-S distance and rois its equilibrium value, 2.1 A (Yakel and Hughes, 1954;Bergson and Schotte, 1958) ;actually, a shorter distance of 2.04 4 may be more correct (see Table 5). Again the force constant Ksshas to be large enough to close the gap but not so large as to make this term dominate all others. A value of 1000 kcal mole-l is satisfactory. For the C-S-S angle terms, the formula ucss = (1/2)Hcss[l-

COB (0-

80)l

(22)

is used, where 8 is the C-S-S bond angle with equilibrium value O0= 104' (Yakel and Hughes, 1954). An argument similar to that above leads to a value of 100 kcal mole-1 for Hcss. When rss > 5-6A, only eq. 21 is used, and the remaining five terms set equal to zero. When rssc 5.7 A, the remaining five terms are included, but multiplied by an empirical factor to preserve continuity as r s sis varied. From a mathematical point of view, the presence of a loop in a polypeptide chain having rigid geometry simply adds a set of constraints to the function to be minimized; the use of a special loop-closingpotential is analogous to the use of Lagrange multipliers. Since the only purpose of this potential is to ensure that the loop is closed at the energy minimum, its exact mathematical form is not of any importance. If non-rigid geometry is allowed, the potentials for bond stretching and bond-angle bending accomplish loop closure (in addition to their other roles); hence, it was not necessary for Bixon and Lifson (1967) to include a special loopclosing potential in their calculations for the cycloalkanes. However, for rigid geometry, some sort of energy term must be added to close each loop.

'

CALCULATIONS O F CONFORMATIONS O F P O L Y P E P T I D E S

143

VI. METHODSOF ENERGY CALCULATION AND ENERGY MINIMIZATION

As mentioned in Section IV, the position of every atom is first expressed in the same coordinate system, and then the calculations of the conformational energies are carried out. The calculations have been basically of two types, depending on whether only the hard-sphere potential or the more complete energy expressions (described in Section V) are used.

A. Hard-Sphere Potential Using only the hard-sphere potential, the calculations are very simple. One merely compares the interatomic distance with the van der Waals contact distances of Table 14 for every pair of atoms in the molecule. If the former is less than the latter for any pair of atoms, an overlap has occurred and the whole conformation is rejected (see p. 376 of Leach et al., 196f3a, for modification of this procedure for atoms separated by only three bonds). If no overlaps occur, the conformation is said to be sterically allowed. This test is applied over the whole range of the $'s, @s, andx's, these angles being varied in small increments. This procedure has been applied to dipeptides, to helical structures, and to some polypeptides of known sequence. I n the case of dipeptide and helical structures, the results are expressed as maps, showing which regions of #I and t,b are allowed and disallowed as a result of steric overlaps. Of course, this procedure cannot distinguish among allowed conformations ; thus, it cannot lead to a determination of the most stable conformation, i.e. the on0 of lowest energy of all of the allowed conformations.

B. Complete Energy Expression If one includes some or all of the contributions to the energy expression, described in Section V, then two types of calculation are possible, in both of which the energy is regarded as a sum over all pairwise interactions. First, since the total energy can be expressed as a function of all of the dihedral angles, one can compute the energies for all possible conformations. This has been done for dipeptides and for regular structures such as homopolymers; the results are expressed as energy contours in the +t,b or x2-xj planes. Also, the energies can be computed for the particular conformations of polypeptides of known sequence, which are found to be sterically allowed by the criterion involving only the hard-sphere potential (Vanderkooi et al., 1966). Secondly, using any one of a variety of procedures, one can vary the dihedral angles to minimize the energy. Combinations of both procedures have also been used; for example, after

144

HAROLD A . SCHERAGA

obtaining contour diagrams for various polyamino acid helices, say in a plane for fixed xj’s, Ooi et nl. (1967) then minimized the energy with respect to all of the dihedral angles to obtain the conformations of lowest energies. Gibson and Scheraga (1968a)have shown that it is the sum of the intramolecular potential energies plus the solvent free energy which must be minimized with respect to the coordinates of the polypeptide to obtain the equilibrium conformation. The same conclusion, based on a less general argument, was also reached by Lifson and Oppenheim (1960). Since many local minima exist, one has to face the following additional questions: (1) How can one reach the various minima from a given initial conformation? ( 2 ) How can one compute the partition function for the system over states around each local minimum, and thereby compare the relative stabilities of the different “equilibrium ” conformations corresponding to each minimum? (3) How can one estimate the fluctuations of the conformation about each minimum? (4) Which minimum corresponds to the native conformation of a protein? The first question is discussed below. The last three questions have recently been considered by Gibson and Scheraga (1968a) who have shown how to compute the vibrational partition functions which will determine the relative stabilities (free energies or statistical weights) of the different minima (yielding also the mean-square deviation of the conformation from that at each energy minimum). They have also shown, by means of an example, that the statistical weight of a protein can be highest (i.e. be in its native conformation) in a potential energy minimum which is not the global minimum, although it must be a minimum with a relatively low energy. As far as the minimization procedure itself is concerned, allowance is made for the variation of all of the dihedral angles of the backbone and side chains. At present, the only known way to locate the global minimum is to try to find all local minima and choose the one with the lowest energy. Gibson and Scheraga (1967a)have evaluated many of the procedures reported in the literature for finding local minima. These are the method of steepest descents, conjugate gradients (Fletcher and Reeves, 1964),the variable metric method (Davidon, 1959; Fletcher and Powell, 1963) (all of which require the computation of gradients as well aa energies), Rosenbrock’s method (Rosenbrock, 1960; Fletcher, 1965), Powell’s method (Powell, 1965), Smith’s method (Smith, 1962), and a version of the simplex method (Nelder and Mead, 1965) (none of which requires gradients) ;the most satisfactory one was found to be Davidon’s (1959) method. A crude procedure for rapidly searching the energy

+-+

CALCULATIONS O F CONFORMATIONS OF POLYPEPTIDES

145

hypersurface from a large number of starting conformations, in order to explore local minima, has been reported by Scott et al. (1967). Bixon and Lifson (1967) used the method of steepest descents to minimize the conformational energies of cycloalkanes. Recently, Gibson and Scheraga (1968b) have made some progress in being able to move from one energy minimum to a lower one, and so on, by alternating between searches for local minima and searches for any conformationof lower energy; this procedure has not yet been sufficiently extensively evaluated to know whether it is capable of providing the global minimum, but it has been used successfully to obtain a series of local minima with descending energies. WITH HARD-SPHERE POTENTIAL VII. RESULTS

The first calculations reported for a polypeptide, using the hard-sphere potential, were those of Ramachandran et al. (1963a)for the “dipeptide” structure shown in Fig. 2 and referred to as “glycyl-L-alanine”. This nomenclature is retained, even though the structure of Fig. 2 would propionamide. If properly be described as a-(N-acety1)-amino-N-methyl the p-methyl group of the structure in Fig. 2 is replaced by another R group, thereby forming another amino acid X, the dipeptide is referred to as glycyl-L-X. Figure 10 shows the conformational map for glycyl-L-alanine, using two different sets of van der Waals contact distances (Ramachandran et al., 1963a). Even though this is a map for a dipeptide, one can represent on it the positions of regular structures in long polyamino acid chains, i.e. those for which the values of the angles t,hi are the same for every residue. Thus, in Fig. 10, &R and crL refer to the positions of the right- and left-handed a-helices,respectively; the fully-stretched chain is located at the origin. Leach et al. (1966a) extended these calculations to various dipeptidelike and tripeptide-like structures, involving all of the different amino acids which normally occur in proteins. I n this way, the effects of variations in the size and shape of the side-chain groups on the allowed conformations were studied. A summary of some of the results is presented in Fig. 11. Steric restrictions, due to the backbone atoms alone, permit the peptide groups adjacent to glycyl residues to assume only about 50 % of all conceivable conformations. An alanyl side chain limits these to 16% and, with further side-chain complexity, restrictions increase so that the backbone adjacent to valyl or isoleucyl side chains can take up only about 5 % of all possible conformations. Leach et al. (1966a) also examined the influence of variation in the amide geometry and in the

146

HAROLD A . SCHERAGA

7[NCaC’] bond angle on the allowed conformation ; Ramachandran et al. (1965), Ramakrishnan and Ramachandran (1965), and Ramachandran and Lakshminarayanan (1966) have reported similar calculations. These computations, with a hard-sphere potential, were extended to helical pentapeptide and hexapeptide structures of the type gly-X4 and gly-X, in order to determine the additional steric restrictions which arise

FIG.10. Conformational map of glycyl-L-alanine. The locations of the right- and lefthanded or-helices are denoted by OIRand OIL,respectively. The fully-stretchedchain is located at the origin. The full and dashed lines represent the boundaries of sterically allowed regions for this dipeptide,as calculatedby Ramachandran et d.(19634 with two different sets of assumptions about van der Wads contact distances.

when complete turns of various helical structures are constructed (Leach et al., 1966b; Ramachandran et al., 1966b). I n such computations, the dihedral angles #i, k, and the xj’s are assumed to be the same in every residue. It should be recalled that, as mentioned in Section 11, equations exist to convert n,h to #, and vice versa. These relations exist, independent of the question as to whether or not steric overlaps occur at any given ftilues of d, and #. Leach et al. (1966b, c) have shown that, in general, there are

+

CALCULATIONS OF CONFORMATIONS O F P O L Y P E P T I D E S

+

147

two solutions, i.e. two pairs of angles and #, both for right-handed and for left-handed helices, corresponding to any n, h (in a limiting case, however, the two solutions for each handedness may coincide, and for some choices of n and h no solutions exist). I n the case of the a-helix, the 3,,-helix, or any other helix, one of the pairs of dihedral angles corresponds to the helix as originally described (Pauling and Corey, 1951; Donohue, 1953) [designated by Nemethy et al. (1967) as a I , (310)1, etc.]

FIG.11. Allowed meas of the steric map for various dipeptidea. In area 0 no conformstiona are allowed. Conformationsin areas 1 to 4 are allowed for glycyl glycine, in arem 2 to 4 for glycyl-L-alanine,in areas 3 to 4 for higher straight-chainhomologs, while only area 4 is allowed for glycyl-L-valineand glycyl-L-isoleucine. T h e circles marked R and L indicate the location of the standard right- and left-handed a-helix on the steric map (Nemethy et al., 1966a,b).

-

with nearly straight C=O * -H-N hydrogen bonds of normal length. For the other solution (designated as a I I , (3,0)11, etc.), the planes of the peptide groups are tilted in such a manner that, while n and h are maintained constant, the N-H groups point toward the helix axis and the C=O groups point away from it ;hence no hydrogen bonds can be formed between adjacent helical turns and, therefore, no stable helices corresponding to the second set of solutions exist. If, however, any one or more of the last three peptide units at the C-terminus of an a-helix were in the conformation correspondmg to the aII-helix, with the rest of the helix

148

HAROLD A. SCHERAGA

retaining the cq-helical conformation, then the N-H groups of the tilted terminal peptide units would point approximately midway between the C=O groups of the third and fourth preceding residues, as shown in Fig. 12. Thus, the hydrogen-bonding arrangement of these residues is

c CO’

ial

H-Bonds

Bifurcat,ed

t H-Bonds

-

No

H-Bonds

FIG.12. Transition region in an a-helix from the a1- to the aII-helical conformation. The helix is represented as being wrapped around a cylinder, for the sake of clarity, so that only the front half is shown. The change from the dihedral angles corresponding to the ar-helix to those for the aII-helix occurs at the carbon atom marked by an asterisk. The straight hydrogen bonding directions on each amide H and 0 atom are marked by a dashed line. The bifurcated hydrogen bonds in the transition region are indicated by dotted lines. No such bonds can form in the cxII-helix(lowerpart of figure) (Nemethy et al., 1967).

intermediate between that of the a,-helix and the (3,&-helix, while the helical parameters n and h are still those for the a-helix. This structure represents an example of “bifurcated hydrogen bonds ” discussed by Baur (1965). At the residue where the transition from the a,- to the aIIhelix occurs, there is a slight distortion of the helix, i.e. a displacement of

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

149

one C=-atom,because of restrictions on the bond angles. Examination of the crystal structures of myoglobin and lysoeyme indicates that the uII conformation occurs in this manner (Nemethy et al., 1967). Because of the variations which occur in the arrangement of the hydrogen bonds, as described in the previous paragraph, the (n,h)and S, nomenclature for classifying various types of helices do not always coincide. Thus, whenever observed structures are said to have an u-

36

-

300v

-0 240

0

60

I20

180

240

300

360

(P(N-Ca) FIG.13. Conformational map for helices with i to i - 3 hydrogen bonding (variants of the 310-helix). The shaded areas represent those conformations which allow acceptable hydrogen bonding. Conformations inside the area (marked by 1) enclosed by the line are sterically allowed for single-strandedhelical polyglycine. The positions of the right- and left-handed“standard” 3lo-helixare indicatedby circles (Leach et al., 1966b).

helical or 310-helical character, it is advisable to state which of the two criteria is being used for the classification. We shall usually use the n,h nomenclature (expressed in terms of and #) in this chapter; however, occasionally, it will be advantageous to use the S, nomenclature, especially when attention is focused on the hydrogen bonding. I n light of the above discussion on helical structures, let us consider the results of Leach et al. (1966b)in which steric overlaps in gly-X, and gly-X, were examined over the +-#plane. I n addition to the steric requirement, Leach et al. (196613) introduced simplified and rather arbitrary criteria

+

150

HAROLD A . SCHERAGA

for the formation of acceptable hydrogen bonds, and examined the influence of amide group geometry on steric overlaps and on hydrogen bonding. The sterically allowed area for polyglycine helices is shown in Figs. 13 and 14. As compared with the dipeptide glycylglycine (Fig. l l ) , only a narrow additional band of conformations is excluded, cutting off the a-helical areas from the remaining allowed area. The excluded band I

300

-

A

-

I

I

L

I

I

I

‘it

-

240 1

7

‘-L

L

-

0

0 180-

Y

3 120

60

L

L

\?

-1

-

I

I

I

7

I

1. I

I

-

r

FIG.14. Conformationalmap for helices with i to i - 4 hydrogen bonding (variants of the a-helix). The shadedareas represent those conformationswhich allow acceptablehydrogen bonding. Conformationsinaide the area (marked by 1)enclosed by the line (as shown more distinctly in Fig. 13) are sterically allowed for single-stranded helical polyglycine. Only conformations lying inside both areas satisfy simultaneously all criteria. The positions of the right- and left-handed “standard” a-helicesare shown by circles, those of the w-helices are shownby triangles (Leach et al., 1966b).

corresponds to helices with very low axial translation (Ramakrishnan, 1964);the small values of h do not allow sufficient spatial separation between atoms on adjacent turns of the helix. Using their criteria for hydrogen bonding, Leach et al. (1966b) found that good i to i-3 (i.e., 310-type)hydrogen bonding could exist in only a narrow range of values of and I)(seeFig. 13). It is seen that the areas of good hydrogen bonding do not coincide particularly with the arew in which no steric overlaps occur. On the other hand, as shown in Fig. 14for i to i-4 hydrogen bond-

+

CALCULATIONS O F CONFOR1\IATIONS O F POLYPEPTIDES

151

ing (i.e., .-type) these are88 do coincide, in agreement with the frequent observation of cr-helical structures in polypeptides. A comparison of the +-$ maps of Figs. 15 and 16 illustrates similar additional steric restrictions on a poly-L-alaninechain, as one passes from a dipeptide (Fig. 15) to helical structures (Fig. 16). Further discussion of steric effects in small polypeptide structures can be found in the recent review of Ramachandran and Sasisekharan (1968). 360

300

240

--

-

180

au

3 I20

60

0

FIG.16. Energy contours for an alanyl residue (Scott and Scheraga, 1966~).The units of energy are kcal mole-’. The circles marked R and L indicate the locations of the standard right- and left-handed a-helix. The steric map (Leach et al., 1966a) is superimposed on the energy contours (Scheragaet al., 1967a).

The hard-sphere potential has also been used to compute the aterically allowed conformations of small polypeptides of known amino acid sequence, viz. an octapeptide loop of ribonuclease (Nemethy and Scheraga, 1965) and the cyclic decapeptide gramicidin-S (Vanderkooi et al., 1966). We shall use the calculation for gramicidin-Sto illustrate the method. This decapeptide consists of two identical pentapeptides joined into a ring by peptide bonds, the amino acid sequence being (L-Val-L-Orn-L-Leu-D-Phe-L-Pro)a

152

HAROLD A. SCHERAOA

+

Only those values of 9 and which lie within the allowed regions of the steric map for each amino acid residue (of the type shown in Fig. 11) were used in the computation. Several q3-+ values in the allowed areas for each amino acid were selected at random, the number of such points being approximately proportional to the allowed area for each amino acid. Having selected a discrete set of q3-+ values for each amino acid, and regarding the atoms as hard spheres, all sterically-allowed conformations

FIG.16. Energy contours for poly-L-alanine helices (Scott and Scheraga, 1966~).The units of energy are kcal mole-1. The circles marked R and L indicate the location of the standard right- and left-handed a-helix. The steric map (Leach et al., 1966b) is superimposed on the energy contours (Scheraga et al., 196%).

of half of the backbone of the molecule were generated. The remaining half of the backbone of the molecule was obtained by symmetry, since the gramicidin-S molecule is believed to have a twofold axis of symmetry (Schmidt et al., 1957). Side chains were then added to these backbones; backbone conformations which could not fit side chains were discarded. Also, those conformations in which the ring closure was imperfect (within an arbitrary tolerance) were discarded. This procedure was repeated twice, with two independent sets of values of q3 and $. I n all, 282 allowed conformations were obtained by these criteria. If a larger number of q3-i,h

CALCULATIONS OF CONFORMATIONS O F P O L Y P E P T I D E S

153

values had been selected for each amino acid originally, additional sterically allowed conformations could have been obtained. The results reported here are illustrative of the information which can be obtained from the hard-sphere potential. Of course, while this approach provides some indication of the stereochemical restrictions in a polypeptide chain, it should be regarded as giving only a first approximation to the most stable structure. Further progress requires the use of more complete energy expressions, as discussed in the next sections.

VIII. APPLICATION OF COMPLETEENERGY EXPRESSION TO RESULTS OBTAINEDFROM THE HARD-SPHERE POTENTIAL Before discussing the calculation of the energy as a function of the dihedral angles, and the minimization of this function to obtain the conformations of lowest energy (see Section IX), it is of interest to compute

FIG.17. View down the axis of symmetry of the low-energyconformation of gramicidinS, with most side-chain atoms omitted (Vanderkooiet al., 1966).

the energies for those conformations which have been found to be sterically allowed by the criteria discussed in Section VII. For this purpose, we will continue with the illustrative calculation of the conformations of gramicidin-S. We have already seen that many conformations are ruled out by the criteria discussed in Section VII. Using the complete energy expression 6

154

HAROLD A . SCHERAGA

discussed in Section V, it was possible to compute the total energy of each of the 282 allowed conformations of gramicidin-S. The backbone energies were computed fist, and the distribution of energies among these conformations found to be quite broad. The backbone conformations with low energies were subjected to minor variations in q3 and $ to further lower their energies. All possible sterically allowed combinations of sidechain conformations were then generated on the backbones of low energy,

D-Phe

FIQ.18. View of low-energy conformation of gramicidin-Sfrom 80" away from the axis of symmetry, with the side chains included. The apparent asymmetry of the molecule in this figure is due to the angle of observation (Vanderkooiet al., 1966).

and the energy contributions due to the side chains were calculated. The conformation with the lowest total energy could thus be chosen out of the entire list of sterically allowed conformations (Figs. 17 and 18) (Vanderkooi et al., 1966; Scheraga et al., 1966a). The energy of the conformation of Figs. 17 and 18 could not be lowered by the variational procedure described above. Therefore, it is probably near an energy minimum. This conformation (designated GSI) has two across-the-ring hydrogen bonds, and the backbone dihedral angles listed in parentheses on the left side in Table 21. As will be described in Section IXE, this structure has been used as a starting point for energy minimiza-

a

b F

2 F

P

?i 0

TAI~LE 21

x

Dihedral Angles of Conformations Obtained by Energy blhimization from GSI and GSII (Scott et al., 1967)

m 0 4

L-Valine L-Ornithine L-Leucine D -Phenylalanine L-Prolin6 L-Valine L-Ornithine L-Leucine D-Phenylalanine L-Proline

63.1(60) 69*4(70) 243.7(230) 309.1(320) 123.0(120)e 74*0(60) 71.3(70) 243.2(230) 317*1(320) 123.0(120)e

303-8(310) 231*8(240) 240-O(230) 118.8(100) 303.0(320) 307.2(310) 226-3(240) 230.0(230) 108.6(100) 326.1(320)

303.9 300.6 311.9 37.6

181-8 302.7 62.3

63.5

308.8 303.1 310-7 49.9

179.8 3024 61.6

60.1

The backbone dihedral angles of GSI are given in parentheses The energy of GSI, is - 96 kcal mole-1. c The backbone dihedral angles of GSII are given in parentheses. The energy of G S ~ Iis I - 98 kcel mole-1. e Fixed angle of proline, i.e. set at 123". 5

b

106*7(120) 126-O(120) 1 0 4 q120) 321*0(300) 123.0(123)e 107-8(120) 128*9(120) 106*3(120) 327.3(300) 123*0(123)C

148.4(140) 146-6(140) 120.0(140) 117*2(110) 2764(300) 144.1( 140) 146.0(140) 128.0(140) 116.3(110) 277-9(300)

298-5 63.0 178.9 166.7

185.2 186.2 296.9

59.5

297.4 62.0 178.2 166.0

186.8 186.5 296.9

69.6 cd

0

156

HAROLD A. SCHERAOA

tion by the procedures mentioned in Section VI. Further discussion of Table 21 will be deferred until Section IXE.

IX. USE OF COMPLETEENERGY EXPRESSION FOR CONFORMATIONAL ENERGY CALCULATIONS, INCLUDING ENERGY MINIMIZATION

A. Hydrocarbons Before presenting results on polypeptide structures, it is worthwhile to consider a few typical papers on hydrocarbons, which make use of similar methods and include two atoms, viz. C and H, present in polypeptides. Consider f i s t the calculation of the rotational isomeric states (potential energy minima) of the normal hydrocarbons (Scott and Scheraga, 1966a, b ; Scheraga, 1965b). The geometry was fixed, but allowance was made for departure of the T[CCC] angle from the tetrahedral value by using experimental values for this angle. The energy terms included the intrinsic torsional potential around C-C bonds and nonbonded interactions. The parameters for the torsional potential and the nonbonded interactions were obtained by fitting the theory (i.e. minimizing the energy) to experimental data for the barriers to rotating a methyl group in ethane and propane, for the difference in energy between the trans and the two gauche forms of butane, and for the location of the gauche minima in butane. These parameters were then used, along with known bond lengths and bond angles, to calculate the location and energies of the various rotational isomeric states for pentane, hexane, and heptane. However, as pointed out by Jacob et al. (1967),these calculations, as well as the similar ones of McCullough and McMahon (1965),overweight the H * * .H interactions by requiring a rigid geometry. I n calculations on cycloalkanes, Bixon and Lifson (1967) took into account internal rotation barriers, nonbonded interactions, bond stretching and bond angle bending during the course of energy minimization. Best agreement with experimental data was obtained by taking the observed values of T[CCC] from the normal alkanes as the zero strain angle, rather than the tetrahedral value; also, the T[HCH] angle was assumed to vary linearly with the T[CCC] angle. Calculations were also carried out for the translational, rotational, and vibrational contributions to the enthalpy, using spectroscopic data ;these contributions were a small but significant part of the computed enthalpy, in comparing theoretical with experimental enthalpies. Besides the above examples of hydrocarbons, conformational energy calculations have also been carried out for synthetic polymers (De Santis et al., 1963), perfluoroalkanes (Bates, 1967), nucleotides (Sasisekharan et al., 1967; Scott, 1967),and polysaccharides (Rao et al., 1967).

CALCULATIONS O F C O N F O R M A T I O N S O F POLYPEPTIDES

157

B. Dipeptides Returning to dipeptides, we consider first the calculation of energy contour diagrams for the dipeptides glycyl-glycine and glycyl-L-alanine, the same structures to which the hard-sphere calculation of Figs. 10, 11, and 15 was applied. Such calculations, for the amide group in the planar trans conformation, have been reported by Brant and Flory (1965c), Gibson and Scheraga (1966), Scott and Scheraga (1966c), and Rama-

i0

$ ' (N-CO)

FIG.19. Energy contours for a glycyl residue. " h e units of energy are kcal mole-'. The symbols R and L indicate the locations of the standard right- and left-handed a-helical conformations (Scott and Scheraga, 1966~).

chandran et al. (1966b). Figure 19 shows the contour map for glycylglycine (Scott and Scheraga, 1966c);it was basedon torsional, nonbonded and electrostatic energies, and is seen to resemble the steric map of Fig. 11. Pigures 20 and 2 1, obtained by Brant and Flory (1965c),illustrate the influence of omission of the amide-amide dipole-dipoleinteraction on the energy contours for glycyl-L-alanine (the remaining contributions being torsional and non-bonded energies). Besides contributing to a different appearance of the contour diagram, the inclusion of this dipole-dipole interaction was required in order to obtain agreement between calculated

158

HAROLD A . SCHERAGA

and experimental values of end-to-end distances for random coil conformations of some polyamino acids (see Section IXC). A similar diagram for glycyl-L-alanine,using slightly different energy functions is shown in Fig. 15, superimposed on the results based only on the hard-sphere potential (Scott and Scheraga, 1966c; Scheraga et al., 1967a). From the similarity of the steric map and the contour diagram, it can be seen that the repulsive parts of the nonbonded interactions play a very important role in determining the energy contours (Brant and 360

300

-Y

240

-

-

"* 180 3 I20

60

-*

-

I

S\

I

z<

(N-Ca) FIG.20. Contour diagram of total potentid energy of glycyl-L-alanineat 1 kcal mole-1 intervals (for 1)= 3-5). On the basis of this potential surface o/npZg=9.13 (Brant and Flory, 1965~).

E'lory, 1966c;Scheraga et ab., 1967a). One interesting difference between the two is that, whereas the steric map is divided into separate regions in the neighborhood of 4=0-150" and #=lSOo, the energy contours in these two regions are separated by a relatively low-energybarrier. Since some of the dihedral angles of myoglobin (Watson, 1965), and lysozyme (Phillips, 1965) lie in this region, and would be disallowed on the steric map, it is gratifying that they are allowed on the contour diagrams. Presumably, the energy required to cross this barrier is compensated by other interactions in the protein molecule. If distortion of the geometry is permitted, a8 described in Section VE,

UALCULATIONS OF CONFORMATIONS O F POLYPEPTIDES

159

then the region of accessibility (i.e. of low energy) is increased. This can be seen by comparing Fig. 22a for a rigid model with Fig. 22b for a flexible model (Gibsonand Scheraga, 1966). Small discrepanciesbetween Figs. 22a, 15,20, and 21 are due to alight alterations in the energy parameters. The comparison of the rigid and flexible models is facilitated by Fig. 22c, in which the energy is plotted as a function of # for a fixed value of # = 260". 360

-

I I\

I

60 -

zz-%%

I

A?

I

5;

(N-Ca) FIG.21. Total potential energy of glycyl-L-alanineat intervals of 1 kcal mole-1 using the same values of the parameters as in Fig. 20, but ignoring the dipole-dipoleenergy (i.e., D = a).This potential surface yields
C . Random Coil; End-to-end Distance Brant and Flory (1965c), Brant et aZ. (1967), and Miller et al. (1967) have used the data of Fig. 20 (and similar data) to compute the unper~ , the random coil. The turbed mean square end-to-end distance, ( T ~ ) of where results are expressed in terms of the dimensionless ratio (r2)O/npZ~, np is the number of virtual bonds of length lp in the polypeptide chain.' 1 As pointed out by Nemethy and Scheraga (1965)and Brant and Flory (196Bc),if the amide group is in the planar trans conformation, then the distance between neighboring a-carbonatoms is independent of the intervening values of and$,;I hence, the polypeptide chain may be treated as a sequence of np virtual bonds of length Zp joining the a-carbon atoms.

+

1

360

240

..u d0 180

A

5 3

*

I

120

5

w 03 0

6oi

/I

I

0

60

60

120

120

I80

240

300

360

Cp"-C) m

L-

\

I

P

I 0

I

180

240

300

I

360

+(N-Ca)

FIG.22. Energy contours (at intervals of 1 kcal mole-1) for glycyl-L-alanine. (a) Rigid model; (b)flexible model; (c) a plot of the energy as a function of 4 for a fixed value of $=260° (solid curve: rigid model; dashed curve: flexible model) (Gibson and Scheraga. 1966).

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

161

Since Brant and Flory (1965~) computed the unperturbed dimensions of the chain, and their related experimental work on some polyaniino acids verified that long-range effects did not contribute in the unperturbed state (Brant and Flory, 1965b),only the near-neighbor interactions (i.e. Fig. 20) were taken into account in computing (r2)o/npZifor the random coil. This ratio depends on the average matrix used in the transformation of coordinates (seethe procedure mentioned in Section IV). The average matrix is evaluated in terms of the partition function for each pair of bonds (which is expressible in terms of the potential energy of Fig. 20 for the dipeptide). Brant and Flory (1965~)showed how the computed values of (r2>o/nplivaried with different parameters for the energy functions. By suihble selection of these parameters within reasonable ranges (those used to obtain the data of Fig. 20) it was shown that (P)o/npZ:= 9-13, in agreement with the experimental result of 9.0 & 0.5 (Brant and Flory, 1965b). Omission of the dipole-dipoleinteraction (i.e., use of the data of Fig. 21) led to the much lower value of (r2)o/npli= 3-95, demonstrating the importance of including the dipole-dipoleinteraction energy. Aside from the important contribution of the electrostatic interaction, the calculations of unperturbed dimensions of the polypeptide chain are insensitive to the details of the potential energy functions (Brant et al., 1967). On the other hand, in the special case of random polyglycine chains, the calculated dimensions are found to be little infiuenced by such electrostatic terms, the conformation being influenced predominantly by the symmetry of the residue. For polyglycine, (r2),,/npZ;r2, a value differing very little from that expected for a polypeptide chain having free rotation about all N-C" and C"-C' bonds. Brant et al. (1967) found that the conformational entropies of randomly coiling polyglycine and poly-L-alanine are nearly equal, despite the for these two polymers; appreciable difference in the values of (r2)o/npZ~ they, therefore, concluded that the less extended character of the polyglycine chain results from the chain symmetry rather than from a greater number of accessible chain conformations. For the case of poly-Lalanine, Brant and Flory (1965~) have shown that the values of (r2),,/np2: for the polypeptide chain converge more slowly, with increasing np,to the limiting value at infinite npthan do the values for polyethylene and polydimethylsiloxane ;this behavior is due to the relatively greater stiffness of the polypeptide chain. Calculationsof end-to-end distances of random coil conformations have also been carried out for polypeptide copolymers (Milleret al., 1967). The values of (r2)0/npZiwere found to vary markedly with composition and amino acid sequence in the copolymers. For example, the introduction of glycine residues randomly into poly-L-alanine led to a monotonic decrease 6*

162

HAROLD A . SCHERAGA

in thc valuc of this ratio (from 9 to 2) as the percentage of glycine increased. The end-to-end distance is also very sensitive to the degree of regularity of L- and D-residues in a copolymer of L- and D-alanine. Preliminary experimental results on copolymers of glycine and L-glutamic acid and on copolymers of L- and D-glutamic acid tend to confirm the main predictions of the calculations (Miller et al., 1967). N

60

120

N

180

240

300

O

FIG.23. Energy contour diagram for single-stranded helical polyglycine. The units of energy are kcal mole-'. The symbols R and L indicate the locationof the standard rightand left-handeda-helicalconformations, B that of the B helix of myoglobin, w that of the w-helix, 310 that of the 310 helix, and I1 that of the polyglycine I1 structure (Scott and Scheraga, 1966~).

D. Helical Structures Conformational energy diagrams (similar to those of Figs. 13, 14, and 16, based on the hard-sphere potential) may be obtained for regular (i.e., helical) structures of polyamino acids, if the assumption is made that the set of dihedral angles is the same in every residue. Such diagrams have been reported by Liquori (1966), Scott and Scheraga (1966c), Ooi et al. (1967),and Ramachandran et al. (1966b).

CALCULATIONS OF CONFORMATIONS OF POLYPEPTIDES

163

The contour diagram for single-stranded polyglycine, based on torsional, nonbonded, hydrogen-bonding and electrostatic energies, is shown in Fig. 23. The symmetrical character of the map arises, of course, because of the absence of a substitutent in the L-position on the a-carbon atom. The contour diagram of Fig. 23 resembles the steric diagrams of Figs. 13 and 14. The symmetry of Fig. 23 is also reflected in the fact that the two lowest points on the diagram, both having the same energy, are in the regions of the right- and left-handed a-helices, respectively. This

0

60

120

180 +(N-Ca)

240

300

360

FIG.24. A re-plot, in standard convention, of the poly-L-alanine energy contour diagram of Liquori (1966). The contours are drawn at intervals of 1 kcal mole-1.

result cannot be compared with experiment, since polyglycine does not occur as a single-stranded structure. It remains to be seen whether calculations on multiple-stranded polyglycine, now in progress [along with similar calculations on other multiple-stranded structures such as ,$-structures and the collagen-like poly-(gly-pro-ah)], will show that the multiple-stranded structure, of say polyglycine I1 (indicated by the I1in Fig. 23), is more stable than the single-stranded structure because of intermolecular hydrogen bonding and other intermolecular interactions, which were not included in the calculations on which Fig. 23 was based.

164

HAROLD A . SCHERAGA

Another important point to note is that the so-called standard 310 helix is outside the range of stability; this result is also obtained €or poly-~alanine (Scott and Scheraga, 1966c) and, presumably, accounts for the fact that no 310 helices have been observed. I n contrast to polyglycine, most other polyamino acids exist as singlestranded structures, and the calculations for single-stranded structures

0

$(N-C") FIG.25. Energy contoursfor poly-L-alaninehelices, in kcal mole-1. The symbols R and L indicate the positions of the right- and left-handed a-helices; the symbols and fia designate the positions of the parallel and antiparallel pleated-sheet structures (Ooi et al., 1967).

can be compared with experimental data. Liquori's (1966) original diagram for helical poly-L-alanine,based only on nonbonded interactions, is shown in Fig. 24. Using torsional, nonbonded, hydrogen bonding, and electrostatic energies, Scott and Scheraga (1966~) obtained the contour diagram for helical poly-L-alanineshown in Fig. 16. As in the case of the dipeptide diagram in Fig. 15, the steric map for poly-1;-alanine is superimposed on the contour diagram, and again it can be seen that the repulsive parts of the nonbonded interactions play a very important role in determining the energy contours; a similar superposition of Fig. 23 on Fig. 13 or 14 would lead to the same conclusion. The unique positions of

C A L C U L A T I O N S O F C O N F O R M A T I O N S O F POLYPEPTIDES

165

the right- and left-handed a-helicesmay be noted. By carrying out energy minimization calculations within the zero kcal contours, both in the right- and left-handed regions, it was found that the right-handed a-helix of poly-L-alaninewas more stable than the left-handed one by a few tenths this energy difference of a kcal per residue (Scott and Scheraga, 1966~); (if real, and not due to small errors in energy parameters) is large enough to favor the right-handed form (observed experimentally) if the chain

#

(N-Ca) FIG.26. Energy contours for poly-L-valinehelices, in kcal mole-'. The energy at each value of 4 and #represents the minimum value for side-chain-to-side-chainand side-ohainto-backbone interactions. The symbols R, L, 81, and /?2 have the same meaning as in Fig. 25 (Ooi et al., 1967).

were more than 10-20 residues long. Using only his non-bonded potential functions, with no other contributions to the total energy, Liquori (1966) reached a similar conclusion for poly-L-alanine. However, the importance of the electrostatic interactions is emphasized in a comparison of the helical senses of aspartate and glutamate polymers (see below). Similar calculations have been carried out for a variety of other homopolymer helices (Ooi et al., 1967; Scheraga et al., 1966b, 1967b; Scheraga, 1967a, c; Yan et al., 1968), each of which has presented an interesting structural problem in polyamino acid chemistry. The energy contributions included in all of these calculations were : torsional, nonbonded,

166

HAROLD A. SCHERAGA

electrostatic, and hydrogen bonding, and the energy was expressed as a function of the dihedral angles, both of the backbone and of the side chain. The contour diagrams of poly-L-alanine and poly-L-valine are oompared in Figs. 25 and 26 (the absolute values of the energies in Figs. 25 and 26 should not be compared, since the number of interactions differs for the two polyamino acids). I n both cases, the right-handed a-helix is the most stable form. The energies in Fig. 26 are minimum values for Right-handed

FIG.27. Side chain and backbone conformation for the right-handed a-helix of poly-Ld i n e of minimum energy. 4 = 132', t j = 123O, xi = 290' (Ooi et al., 1967).

rotation of the side chain at each value of $ and 4. The energy is quite dependent on the backbone conformation. For example, in the region of $ = 60°, 4 = 320°, almost all values of x1 are attainable without overly large increases in energy; on the other hand, in the region of the righthandeda-helix ($= 132",1,h=123°),onlyvaluesof~1inthevic~tyof290" are attainable at reasonable energies, the energy rising very steeply if x1 changes significantly from 290". This prediction of the possible existence of poly-L-valine in an a-helical form has been verified experimentaJly (Ooi et al., 1966). The calculated conformation of the side chain, relative

CALCULATIONS O F CONFORMATIONS OF POLYPEPTIDES

167

to the backbone, in the right-handed a-helical form of poly-L-valine is shown in Fig. 27. Poly-j?-methyl-L-aspart ate and poly-y-methyl-L-glutamate have been studied in the range of values of # andh,z near the right- and left-handed a-helicalregions (Ooi et al., 1967). Energy minimizations were carried out in these two regions with respect to four single-bondrotations (two backbone and two side-chain) in the asprtrtate polymer, and with respect to five single-bondrotations (two backbone and three side-chain) in the case of the glutamate polymer. The left-handed a-helix was found to be more stable than the right-handed form for the aspartate polymer, but the Left-handed

FIG.28. Side-chain and backbone conformations for the (a) right- and (b) left-handed a-helices of poly-8-methyl-L-aspartate of minimum energy, with D = 1. (a) 4==129", #= 126",x1=306', x ~ = 1 6 1 ~(b) . +=229", +=237", x1=176', xz=23So (Ooi etal., 1967).

reverse was true for the glutamate polymer. The dipole-dipole interaction of the ester group with the amide group of the backbone is the cause of the difference in screw sense; this interaction stabilizes the righthanded form in the glutamate polymer, but destabilizesit in the aspartate polymer. A low dielectric constant ( D< 3) must be used in order for the magnitude of the dipole-dipoleinteraction in the aspartate polymer to be great enough to overcome the non-bonded energy, which favors the righthanded form in both polymers. These calculations provide an explanation for the well-known difference in screw-sense between the two polymers ;even though their side chains differ only by an extra CH2group in the glutamate polymer, this extra methylene group is sufficient to change the orientation and distance between the amide and ester dipoles. The

168

HAROLD A . SCHERAQA

orientation of the side chain groups in the aspartate and glutamate polymersisshowninFigs. 28 and 29. Goodman et al. (1963) have shown that, whereas benzyl-L-aspartate forms a left-handed a-helix, a nitro group in the para position of the benzyl group converts this helix to a right-handed one. Hashimoto (1966), Hashimoto and Aritomi (1966), and Hashimoto et al. (1966) have reached similar conclusions for nitro, cyano, chloro, and methyl substituents in the para position. The above calculations were repeated, using the benzyl instead of the methyl ester, and allowing for rotation about all of the single bonds of the side chain (Yan et al., 1968). The results for the unLeft-handed

Right-handed

@ . .

--. -. ---B 00

0 '

0 0, 00,

@---

0

B',

FIG.29. Side-chainand backbone conformations for the (a)right- and (b)left-handed

+=

of minimum energy, with D = 1. (a) 129", a-helices of poly-y-methyl-L-glutamate I+$=126', x1=172", xz=285', ~3=144O. (b) +=230°, I+$=236., x1=3Og0, xz=7O0, x3=68' (Ooi et al., 1967).

substituted benzyl ester were the same as for the methyl ester. Further, the nitro, cyano, chloro, and methyl aspartate polymers were all found t o be right-handed, in agreement with experiment. It appears that the additional non-bonded and electrostatic interactions of the para substituents with its near neighbors changes the orientation of the ester group in such a way that the relative stabilities of the right- and left-handed a-helices are reversed. Besides the above examples, the influence of dipole-dipoleinteractions between polar side chains (containing a heteroatom in the y position) and backbone amide groups has been shown for polymers such as poly-Lserine (Birshtein and Ptitsyn, 1967). I n such cases, the p-structure is energetically more favored than the a-helix.

CALCULATIONS OF CONFORMATIONS O F POLYPEPTIDES

169

Similar calculations have been carried out for poly-L-tyrosine (Ooi et al., 1967). Keeping 4 and $ fixed at values corresponding to the rightand left-handed a-helical forms, one obtains the contour diagrams (on a xz us x1plot) shown in Figs. 30 and 3 1. These figures show that one of the gauche positions of the CY atom with respect to the N atom (xl= 60') is not permitted, meaning that x1 must lie in the vicinity of either 180" or 300" for both the right- and left-hand helices. For the case of poly-L-

36 -4 -5

I

0

I

60

1

I

I

120.

180

240

300

I

360

FIG.30. Energy contours (involving all possible interactions of the side chains) for the right-handed a-helix (+= 132' and $=123") of poly-L-tyrosine, with D = 4 , in kcal mole-l/residue. The position of lowest energy is indicated by the small cross near XI= 300, X Z = 150 (Ooi et al., 1967).

tyrosine, Ooi et al. (1967) carried out compIete energy minimizations with respect to 4, #, xl and xzfor all local minima of the contour maps for both the right- and left-handed helices (with x3 fixed, i.e. with the OH group fixed with respect to the benzene ring). The conformations of lowest energies are indicated by crosses on Figs. 30 and 31, and illustrated in Fig. 32. The calculations indicate that poly-L-tyrosine is right-handed, which is in agreement with some experimental results (Fasman et al., 1964; Beychok and Fasman, 1964; Pao et al. 1965) but not with others (Applequistand Mahr, 1966). Ooi et al. (1967) have suggested a possible

170

HAROLD A . SCHERAOA

re-interpretation of the results of Applequist and Mahr (1966) which could bring their experimental results into agreement with those of Fasman et al. (1964), Beychok and Fasman (1964) and Pa0 et al. (1965). The conformation of poly-L-phenylalanineof minimum energy is approximately the same as that of poly-L-tyrosine,with the right-handed a-helix being the more stable one (Yan et al., 1968). I n the case of poly-L-proline I1 (the amide group being in the planar trans conformation), the angle 4 is fixed by the rigid geometry of the pyrrolidine ring ; hence, the conformational energy depends only on 3.

XI FIG.31. Same as Fig. 30, but for the left-handed a-helix ( + = Z 2 S 0 and $=237') of poly-L-tyrosine,with D = 4 (Ooi et aE., 1967).

The energies computed by Schimmel and Flory (1967) are shown in Fig. 33. Except in the range 3 = 275-370' (or loo),steric repulsions give rise to energies more than 7 kcal mole-l above the minimum which occurs a t 304'. With #restricted to the range of 276'-370°, rotations about each Ca-C' bond are essentially independent of rotations about adjacent bonds. Interactions dependent on two # angles are significant only when one (or both) of these hz, angles is well outside the sterically accessible range (275-370'). This fact simplified the computation of (r2)o/n,Z~ (Schimmeland Flory, 1967), as outlined in Section IXC. Energy-transfer

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

171

experiments (Stryer and Haugland, 1967),employing oligomers of polyL-proline I1 as spacers between energy donor and energy acceptor, confimed these calculations of the dimensions of short chains. Aside from minor differences due to differences in the geometry and in the energy parameters, the curve of Fig. 33 of Schimmel and Flory (1967) is similar to the one obtained by De Santis et al. (1966) on the assumption of regularity (i.e. that $is the same in every residue). A polymer related to poly-L-proline, in the sense that the amide nitrogen is substituted and, therefore, cannot take part in hydrogen bonding, is poly-N-methyl-L-alanine. Conformational energy calculations for this Left-handed

FIG.32. Side-chainand backbone conformations for the (a)right- and (b) left-handed a-helices of poly-L-tyrosine of minimum energy, with D = 4 . (a) 4= 130°, $= 124O, x1=302", xz=163". (b) +=228O, #=238O, xl=171", xz=227O(OoietaZ., 1967).

polymer (Mark and Goodman, 1967a, b ; Liquori and De Santis, 1967) indicate that the preferred conformation is either a right-handed, approximately threefold helix, or a slightly distorted, left-handed u-helix. Further calculations have been carried out on a variety of homopolymers and copolymers of amino acids, with and without the regularity requirement, i.e. that the set of dihedral angles be the same in every residue, and also on polyamino acids of discrete length, i.e. with amino and carboxyl end groups included (unpublished results in our laboratory). However, the results of these calculations are still incomplete. From the above examples, it is clear that the nature of the side chain influences the helical sense of polyamino acids. The side-chain-to-side-

172

HAROLD A. S C H E R A O A

chain and side-chain-to-backboneinteractions also cause variations in the dihedral angles of the backbone (Ooi et al., 1967) and in the optical rotatory dispersion properties of a-helices (Vournakis and Scheraga, 1968). Recent experimental studies of Fraser et al. (1967)confirm this predicted influence of side chains on the geometry of the a-he1ix.l Venkatachalam and Ramachandran (1967) have evaluated the various nonbonded potential functions described in Section VB, by using them to calculate nonbonded potential energy contours for the dipeptide glycyl-L-alanine and for helical poly-L-alanine. The functions considered were those of Brant and Flory (1965c),De Santis et al. (1965),Scott and

280

300

320

+, degrees

340

0

20

FIG.33. Relative conformational energy of poly-L-proline I1 as a function of q5 (Schimme1 andFlory, 1967).

Scheraga (1966c), and the two Kitaigorodskii functions designated K 1 and K , (see Fig. 6). While the absolute values of the maps differed, the general shapes for the dipeptide and for the polymer were all similar with one exception, viz. the functions of De Santis et al. (1966)yielded an extra minimum in the region of 4 = 40", i,L = 350". Since none of the data for myoglobin and lysozyme fall in this region, Venkatachalam and Ram&chandran (1967) have suggested that at least some of the functions of De Santis et al. (1965) need revision.2 As indicated in Section VF, it is hoped that the use of electron and X-ray diffraction data will clarify the problem as to which are the appropriate parameters for the nonbonded potential functions. 1

See note 1 added in proof on p. 183.

2

See note 2 added in proof on p. 184.

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

173

E. Gramicidin-X The rapid minimization procedure, mentioned in Section VIB, has been applied in conformational energy calculations of gramicidin-S, using two special starting conformations and 27 randomly selected ones (Scott et al., 1967; Scheraga, 1967d). The two special conformations were those suggested by Vanderkooi et al. (1966)and described in Section VIII (designated as GSI) and by Liquori et al. (1966), shown in Fig. 34 (designated as GSII). Structure GSII was obtained by use of an assumed “stereochemical code” (Liquori et al., 1966),in which the allowed conforVal

n

FIG.34. View of gramicidin-S structure G&I. The y-axisis the one of twofold symmetry (Liquori et al.,1966).

mations of any amino acid residue are assumed to be those corresponding to the minima in the conformational map of helical poly-L-alanine (with a different conformation for proline) ;the same twofold symmetry requirement, used to obtain GSI, was also used to obtain GSII. Scott et al. (1967) carried out the energy minimization without making use of the symmetry requirement, and obtained structures quite similar to those of Figs. 17 and 34, and of comparable energies ; however, after energy minimization, the structure of Fig. 34 lacked a-helical hydrogen bonds, but was stabilized by nonbonded and electrostatic interactions. Thus, this structure is designated as GSIII. The slight variations in the structure of Fig. 17 led

174

HAROLD A. SCHERAGA

D

Fro. 35.

CALCULATIONS O F CONFORMATIONS O F POLYPEPTIDES

175

to its rc-clcaignation as GSI,. The dihedral angles of the starting conformations (GSI and GSII), and those of minimum energy (GSI, and GSIII), are shown in Table 21. The values of xr 60" for ornithine in GSIII may seem strange, at first sight, since the a-helix cannot accommodate a side chain in this position (Ooi et al., 1967; see also Fig. 30). However, this conclusion of Ooi et al. (1967) pertains to a-helices with # 125", whereas the values of # for ornithine in GSIII are 145"; the increase in # from 125" to 145' involves a departure from the a-helical conformation, and permits the side chain to take on the gauche conformation corresponding to X I 60". Although GSI, and GSIII are of comparable energies, there appears to be more looseness (hence, presumably more entropy) in GSI,. This may increase its stability in solution. No crystal data are yet available to check whether either structure is compatible with that of the solid. It will be of great interest to make this comparison, not only as a check on the computational procedure, but also to see whether intermolecular interactions in the crystal (neglected in the above calculations) influence the conformation. None of the 27 randomly selected starting conformations led to a structure having an energy as low as that of GSI, and GSIII. Figure 35 illustrates the course of energy minimization from one of these randomly selected starting conformations.

-

-

-

N

F. Oxytocin and Vasopressin I n contrast to the calculations described above for gramicidin-S, several recent calculations on open-chain and cyclic structures of known amino-acid sequence have taken into account the free energy of hydration (Gibson et al., 1967a, b); Davidon's (1959) method was used for energy minimization. For the open-chain structures, the calculations showed that, even without imposing the condition of regularity, irregular helical structures close to the regular ones represent structures of energy minima. Thus, the presence of many different side chains need not by itself provide enough of a perturbation to overcome the cooperative interactions that occur in a regular structure. These calculations also focused FIQ.36. Illustration of the conformational changes which occur during energy minimization from a random starting conformation of gramicidin-S. The Roman numerals correspond to three stage8 of the computation. The side chains (except for proline) were truncated to the p-carbon position for Stage I, but complete side chains were used for Stages I1 and 111. In order to increase the clarity of the illustration, one of the ornithyl side chains was omitted from the drawing in 11, and one of the valyl side chains waa omitted in I11 (Scott et al., 1967).

176 HAROLD A . SCHERAGA

FIG.36. Computed structures of vasopressin (A) and oxytocin (B),obtained by energy minimization,starting from the /I-conformation (Gibson and Soheraga, 1967b). These are the f i s t two conformations listed in Table 22.

TAESE 22 Minima of Oxytocin and Vasopressin=(Gibson and Scheraga, 1967b)

ogytocin Vasopressin

Peptide :

Final structure: Residue 1. +-Cysthe 2. Tyrosine 3. Isoleucineb 4. Glutamine 5. Asparagine 6. 4-Cystine 7. Proline 8. LeucineC 9. Glycined Final energy (kcal mole-1) 1. +-Cystine 2. Tyrosine 3. Isoleucineb 4. Glutamine 5. Asparagine 6. &Cystine 7. Proline 8. Leucinec 9. Glycinea Final energy (kcal mole-1)

c

#

c

-

327.2 7.5 266.1 6.6 239-5 325.1 289.2 258.8 292.9

120.8 132.7 22.1 86.0 95.2 120.3 87.8 119.8

110.0 106.6 31.8 86.1 91.6 120.1 76.9 105.0

-

-

214.2 141.4 109.5 243.7 112.5 126.9 1376 118.4 84.0

85.8 137.6 351.1 62.7 111.2 120.4 127.2 109.1

(no solvent ; 0~3.0)

*

+

315.4 334.4 276.8 7.5 238.5 324.9 298.9 326.4 295.6

121.9 135.2 25.5 84.5 93.5 120.2 90.5 90.2

-

10.86

-6.17

30.96

a Starting conformation,upper group:

Phenylalanine in vasopressin. c Lysine in vasopressin. d C-terminal amide in both peptides. b

oxytocin

- 45.32

Oxytocin (no solvent; D = 1.0)

#

+

306.9 339.4 276.9 6.0 234.4 324.8 297.9 321.5 327.6

122.6 132.7 21.3 91.8 37.2 120.5 77.9 124.6

-

# 288.8 352.5 279.0 355.8 266.2 324.6 299.6 328.8 295.3 - 166.55

d 0

2

r

0

w

aP

z

0

-

286.9 121.6 104.9 242.0 144.2 126.3 146.2 344.8 142.0

43.1 95.2 18.8 83.8 111.3 120.3 258.0 125.3

93.3 97.5 6.4 82.7 110.6 119.9 254.5 90.0

66.14

+

- 16.35

+==60°, $J= 300°, except for proline, for which = 120°,

237.2 168.1 101.2 231.7 124.3 125.8 154.8 96.8 70.8

+= 300';

-

259.6 44.2 112.7 90.6 145.6 56.0 23.1 248.6 97.8 122.9 120.1 119.3 115.4 229.1 32.4 244.2 52.5 - 150.61 lower group,

+ = 120°, I)= 1.30".

Z m

0 4

M

cd

178

H A R O L D A . SCHERAGIA

attention on the main problem which must yet be solved, viz. the selection of the global minimum out of all local minima, and its relevance to the structure of the native polypeptide or protein. As representatives of cyclic structures, involving loops closed by disulfide bonds, oxytocin, vasopressin, and the octapeptide loop of ribonuclease were considered (Gibson and Scheraga, 1967b). Using selected starting conformations, oxytocin and vasopressin had minimum energies (not global minima) at similar conformations (Fig. 36 and Table 22). This result suggests that the main factor determining the conformation of the ring in these two peptides is the need to close it, and that other factors, such as the specific nature of the side chains, affect only the details of the structure. This conclusion is supported by the fact that omission of the hydration free energy led to similar structures, although the energies were considerably different than those obtained when hydration was included (see Table 22). However, these peptides are much smaller than proteins. I n the latter case, where one can identify an “inside” and an “outside,” one would expect a greater influence of hydration on the conformation, leading to a preponderance of nonpolar groups inside and polar ones outside, in water. X. CONCLUSIONS The procedures and calculations described in this chapter provide considerable insight into the factors affecting the conformations of polypeptides and proteins. The computer programs for gramicidin-S, 0x9tocin, vasopressin, etc., can also be used for larger structures-f the size of ribonuclease and lysozyme-although the required computer time is considerably increased. The major problem that remains to be solved is the relevance of the global minimum to the structure of a native protein, and the ability to select the global minimum from the various possible local minima. Related to this problem is the question of whether long-range interactions may make it very difficult to identify the energy minimum corresponding to the native conformation of a globular protein (Flory, 1967). These questions are actively under investigation, and it is hoped that progress along these lines will soon be forthcoming. A more limited objective that should be achievable involves the refinement of, say, 6 A resolution data for a protein down to atomic resolution. For example, if one can construct a rough model of a protein from 6 H X-ray data, then it is reasonable to assume that such a model might be in the potential energy well of the native globular protein. If so, the procedures used for the small peptides may yield the correct structure of the

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protein at atomic resolution. Such an approach is also in progress. Calculations on the crystal structures of small peptides (e.g. gramicidin-S and oxytocin) are also being undertaken. Severalrecent attempts have been made to analyze the limited existing crystal structure data of proteins to determine which amino acids may be classified as helix-breaking and which as helix-favoring (see,e.g., Bigelow, 1967, and Cook, 1967, and references cited therein). It is no doubt worthwhile to continue such an approach, especially as more X-ray data become available. However, the possibility should be kept in mind that a particular amino acid may be helix-breaking in one protein (or copolyamino acid) and helix-favoring in another. Our view would be that one must consider the free energy of the total system (protein plus solvent). Conclusions based on only near-neighbor interactions of specific amino acids may be valid in some cases, but may not have general validity. Actually, the relative importance of near-neighbor vs. long-range interactions is automatically provided by the computational procedures involving energy minimization, described in Section VIB ;however, it is too early to provide an answer to this question. REFERENCES Anfinsen, C. B. (1964). In “New Perspectives in Biology” (M. Sela, ed.), p. 42. Elsevier Publ. Co., Amsterdam. Applequist, J., and Mahr, T. G. (1966). J . Am. Chem. SOC.88,5419. Arridge, R. G. C., and Cannon, C. G. (1964). Proc. Roy.Soc. (Lodon),Ser.A278,91. Bertell, L. S. (1960). J . C h m . Phys. 32, $27. Bates, T. W. (1967). Trans. Far@ Soo. 63, 1825. Baur, W. H. (1965). Acta Cryst. 19, 909. Bergson, G., and Schotte, L. (1958). Arlciw Kemi 13,43. Berthod, H., and Pullman, A. (1965). J . Chim.Phys. 62,942. Beychok, S . , andFasman, G. D. (1964). Biochemistry 3,1675. Bigelow, C. C. (1967). J . Theoret.Biol. 16, 187. Bijvoet, J. M., Peerdeman, A. F., and van Bommel, A. J. (1951).Nature 168,271. Birshtein, T . M., and Ptitsyn, 0. B. (1966). “Conformations of Macromolecules.” Interscience, New York. Bimhtein, T. M., and Ptitsyn, 0. B. (1967). Biopolymers 5, 788. Bixon, M., and Lifson, S. (1967). Tetrahedron 23,769. Bondi, A. (1964). J.Phy8. Chem.68,441. Bonham, R. A., Bartell, L. S., and Kohl, D. A. (1959). J . Am. Chem.SOC.81,4765. Bragg, W. L., Kendrew, J. C., and Perutz, M. F. (1950). Proc. Roy. SOC.(London), Ser. A 203, 321. Brant, D. A., and Flory, F. J. (1965a). J . Am. Chem.SOC. 87,663. Brant, D. A., and Flory, P. J. (1965b). J . Am. Chem.SOC. 87,2788. Brant, D. A., andFlory, P. J. ( 1 9 6 5 ~ )J. . Am. Chem.Soc.87,2791. Brant, D. A., Miller, W. G., andFlory, P. J. (1967). J . MoZ. Biol. 23, 47. Cook, D. A. (1967). J . MoZ. BioZ. 29, 167. Curl, R. F., Jr. (1959). J . Chem.Phys.30,1529. Damitmi, A., Giglio, E., Liquori, A.M., andMazzarella, L. (1967). Natzlre 215,1161. Dmvidon, W. C. (1959). AEC Research and Development Report, ANL-5990. DelRe, a. (1968). J . Chem. Soc., 4031.

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Kitaigorodskii, A. I. (1965). Acta Cryst. 18, 585. Kitaigorodskii, A. I. (1966). J. Chim. Phye. 63, 9. Kurland, R. J., and Wilson, E. B., Jr. (1957). J. Chem. Phys. 27, 585. Leach, S. J., Nemethy, G., and Scheraga, H. A. (1966a). Biopolymers 4, 369. Leach, S. J., Nemethy, G., and Scheraga, H. A. (1966b). Biopolymers 4, 887. Leach, S. J., Nemethy, G., and Scheraga, H. A. (19660). American Documentation Institution Auxiliary Publ. Project (Library of Congress, Washington 25, D.C., Document 8862), cited by Leach et al. (1966b). Leung, Y. C., and Marsh, R. E. (1958). Acta Cryst. 11, 17. Lifson, S., and Oppenheim, I. (1960). J. Chem.Phys. 33, 109. Lin, C. C., and Swalen, J. D. (1959). Rev. Mod. Phys. 31, 841. Lippincott, E. R., and Schroeder, R. (1955). J. Chem. Phya. 23,1099. Liquori, A. M. (1963). Consiglio Nazionale Delle Richerche, p. 209. Liquori, A. M. (1966). J. Polymer Sci. Part C, No. 12, 209. Liquori, A. M., and De Santis, P. (1967). Biopolymers 5, 815. Liquori, A. M., De Santis, P., Kovacs, A. L., and Mazzarella, L. (1966). Nature 211, 1039. Mark, J. E. (1968). J. Phys. Chem., in press. Mark, J. E., and Goodman, M. (1967a). J . Am. Chem. Soc. 89, 1267. Mark, J. E., and Goodman, M. (1967b). Biopolymers 5, 809. 77,5808. Mason, E. A., and Kreevoy, M. M. (1955). J.Am. Chem.SOC. Mathieson, A. McL., and Welsh, H. K. (1952). Acta Cryst. 5,599. Mazumdar, S. K., and Srinivasan, R. (1964). Currents&. (India)33,573. McCullough, R. L., and McMahon, P. E. (1965). J.Phys. Chem. 69,1747. Miller, W. G., Brant, D. A., and Flory, P. J. (1967). J. Mol. Biol. 23, 67. Miyszawa, T. (1961). J. Polgmer Sci. 55,215. Mizushima, S., and Shimanouchi, T. (1961). Adw. in Enzymol. 23, 1. Moulton, W. G., andKromhout, R. A. (1956). J. Chem.Phys. 25,34. Nelder, J. A., and Mead, R. (1965). Computer J. 7, 308. Nemethy, G., and Scheraga, H. A. (1962). J. Phys. Chem. 66, 1773. Nemethy, G., and Scheraga, H. A. (1965). Biopolymers 3, 155. Nemethy, G., Leach, S. J., and Scheraga, H. A. (1966a). Abstr. of First Middle Atlantic Regional Meeting, A.C.S., p. 83, Feb. 3-4. Nemethy, G., Leach, S. J.,and Scheraga, H. A. (1966b). J.Phys. Chem. 70,998. Nemethy, G., Phillips, D. C., Leach, S. J.,and Scheraga, H. A. (1967). Nature 214, 363. Ooi, T . , Scott, R. A., Vanderkooi, G., Epand, R., and Scheraga, H. A. (1966). J. Am. Chem.SOC.88, 5680. Ooi, T., Scott, R. A., Vanderkooi, G., and Scheraga, H. A. (1967). J. Chem.Phys. 46, 4410. Pachler, K. G. R. (1964). Spectrochim. Acta 20, 581. Pao, Y .H., Longworth, R., and Kornegay, R. L. (1965). BiOpOly?nt??~ 3,519. Pasternak, R. A. (1956). Acta Cryst. 9, 341. Pauling, L. (1960). “The Nature of the Chemical Bond”, Cornell University Press, Ithaca, New York. Pauling, L., andCorey, R. B. (1951). Proc. Natl. Acad.Sci., U.S. 37,729. Phillips, D. C. (1965). Private communication. Pitzer, K. S. (1959). Adw. Chem. Phys. 2, 59. Poland, D., and Scheraga, H. A. (1967). Biochemistry 6, 3791. Powell, M. J. D. (1965). Computer J . 7, 303. Pullman, B., and Pullman, A. (1963). “Quantum Biochemistry.” Interscience, New York.

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Rabinovich, D., and Schmidt, G. M. J. (1966). Nature 211,1391. Ramachandran, 0.N., and Sasisekharan, V. (1 968). Adu. inprotein Chem.,in press. Ramachandran, G. N., and Lakshminarayanan, A. V. (1966). Biopolynzero 4,496. Ramachandran, G. N., Ramakrishnan, C., and Sasisekharan, V. (1963a). J. Mol. Biol. 7, 95. Ramachandran, G. N., Ramakrishnan, C. and Sasisekharan, V. (1963b). “Aspects of Protein Structure” (G. N. Ramachandran, ed.), p. 121. Academic Press, London. Ramachandran, G. N., Ramakrishnan, C., and Venkatachalam, C. M. (1965). Biopolymrs, 3, 591. Ramachandran, G. N., Mazumdar, S. K., Venkatesan, K., and Lakshminarayanan, A. V. (1966a). J . Mol. Biol. 15, 232. Ramachandran, G. N., Venkatachalam, C. M., and Krimm, S. (1966b). Biophye~cd J. 6, 849. Ramakrishnan, C. (1964). Proc. Ind. Acad. Sci. 59, 327. Ramakrishnan, C., and Ramachandran, G. N. (1965). BiophyoicalJ. 5,909. Rao, V. S. R., Sundarmajan, P. R., Ramrtkrishnan, C., and Ramachandran,, G . N. (1967). I n “Conformration of Biopolymers” (G. N. Ramachandran, ed.), p. 721. Academic Press, London. Rich, A., and Crick, F. H. C. (1961). J. Mol. Biol. 3, 483. Rosenbrock, H. H. (1960). Computer J. 3, 175. Rowlinson, J. S. (1965). Disc. Faraday SOC. 40, 19. Rudolph, H. D., Sutter, D., Wendling, P., Jaeschke, A., and Dreizler, H. (1966). Tram. Am. Crys. Assoc. 2, 197. Sasisekharan, V. (1959). Acta Cryst. 12, 897. Sasisekharan, V. (1961). Proc. I d . Acad. Sci. 53A, 296. Sasisekharan, V. (1962). In “Collagen” (N. Ramanathrtn, ed.), p. 39. Interscience Publishers, New York. Sasisekharan, V., Lakshminarayanan, A. V., and Ramachandran, G. N. (1967). In “ Conformationof Biopolymers” (G.N. Ramachandran, ed.),p. 641. Academic Press, London. Schellman, J. A., and Oriel, P. (1962). J. Chern. Phys. 37,2114. Schellman, J. A., and Schellman, C. (1964). I n “The Proteins” (H. Neurath, ed.) 2nd ed., Vol. 2, pp. 14,24. Acdemic Press, New York. Scheraga, H. A. (1965a). Proc. Welch Found. Conf. on Chem. Res. VIII. Selected Topics in Modern Biochemistry (Nov. 16-18, 1964), p. 149. Scheraga, H. A. (1965b). Abstr. of Mtg. of the British Biophysical Society. Scheraga, H. A. (1966). “Molecular Architecture in Cell Physiology” (T. Hayashi and A. G. Szent-Gyorgyi, eds.), p. 39. Scheraga, H. A. (1967a). Abstr. of Second Middle Atlantic Regional Meeting, A.C.S., p. 104, Feb. 6-7. Scheraga, H. A. (1967b). J. General Physiology 50, 5. Scheraga, H. A. (19670). Abstr. of 153rd A.C.S. meeting, Miami, Florida, p. 415, April. Scheraga, H. A. (1967d). Proc. VIIth International Congress of Biochemistry, Tokyo, p. 171. Scheraga, H. A., Leach, S. J., Scott, R . A., andNemethy, G. (1965a). Discus&ns Faraday SOC.40, 268. Scheraga, H. A., Nemethy, G., Leach, S. J., Scott, R. A., and Poland, D. (1966b). FederationProc. 24,413. Scheraga, H. A., Scott, R. A,, and Gibson, K. D. (1966a). FederationProc. 25,346.

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Notes added in proof (pertaining to text on p. 172) 1. G6 et aZ. (1968) have recently shown how the data of Sections IXB and IXD may be used to compute the parameters [e.g. u and s of Zimm and Bragg (1959)l of the helix-coil transition in polyamino acids. Heretofore, it had been necessary to rely on a comparison of the results of the statistical mechanical theory with experimental data in order to obtain these parameters. However, with the aid of the aforementioned calculations of the conformationd energies of dipeptides and helices, it h w been possible t o formulate a theory for computing u and 8. It remains to be seen how well the computed values of these parameters agree with those evaluated from experimental data on the melting of polyamino acid helices.

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2. These same potential functions were evaluated by Mark (1968), who used t,hem to calculate the geometric isomerization energy of butene-2. He concluded that “the functions employed by Brant and Flory (196%) and Scott and Scheraga (1966~) were quite successful in reproducing tho experimental result, whereas those recommended by Venlratachalam and Ramachandran (1967) were significantly less so; the functions employed by De Santis et al. (1965) gave exceedingly poor agreement with experiment

”.

STE REOSELECTJON IN THE ELEMENTARY STEPS OF ORGANIC REACTIONS SIDNEY I. MILLER Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois, U . S . A . I. Introduction . 11. The Shape of Simple Species

.

A. Some Valence Bonds Ilesults . €3. Some Molecular Orbital Results . 111. Bonding Theory and Stereoselection . A. Electrocyolic Reactions €3. Cycloadditions . C. Sigmatropic Migrations . D. Sigma-Sigma and Sigma-Pi Switch . . E. Substitution at Saturated Atoms . F. Substitution at Unsaturated Atoms. G. Addition and Elimination . K. Rearrangements IV. Miscellaneous Factors and Stereoselection A. Excited States and Molecular Vibrations . B. Magnetic Resonance Data . C. Collinearity and Coplanarity of Reacting Centers D. Principles of Least Motion (PLM) E. Electrical Effects V. Stereoselection Deriving from Steric and Conformational Factors A. Steric Effects B. Conformational Analysis . VI. Conclusions References

.

.

.

.

. .

.

.

. . . . . . . . . .

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

185 188 188 191 201 202 217 235 243 246

265 272 287 293 293 295 296 301 303 308 308 313 321 323

I. INTRODUCTION REACTIONSfollow some paths in preference to others. Among these paths there are often stereochemical alternatives. Why there is selectivity has intrigued and provoked the chemist, since he became aware of stereoisomers. Based on their vast store of observations, facts, errors, artifacts, and prejudices, chemists have produced a variety of speculations, theories, principles, etc. to explain this selectivity. With the veritable publication explosion in matters stereochemical, it seems appropriate to collect a few key observations and describe current views of stereoselection. 7

185

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S I D N E Y I . MILLER

Our overall plan in this paper is this. Initially, we shall set down a few definitions, and a point of view. We shall then describe a number of “principles ’’ or causes of stereoselection associated with bonding, steric, thermodynamic, electrical, mechanical, etc., factors, inherent in the stereoprocess. The relation between the properties of intermediates, e.g. carbanion or syn-anti isomers, etc., rate and equilibrium conditions and stereoselectivity will be dealt with. Throughout, we shall examine representative systems and reactions to see how relevant the principles of stereoselection are. No attempt will be made to venture into several important areas, e.g. enzyme stereospecificity, stereoregular polymers, etc. At the instant Pasteur recognized the existence of stereoisomers (objects), he also accepted the existence of stereoprocesses (operations). For the notion of “isomer ’’ carries with it criteria of distinguishability; among these is the possibility that a given isomer can be formed, separated, or altered in a way which differentiates it from other isomers. This applies equally to isomers with many properties in common, e.g. optical antipodes, or to those with essentially all different properties, e.g. cis-trans,syn-anti, gauche-anti, erythro-threo, or axial-equatorial pairs. Now, the stereo-path may be part of an overall conversion which, if described in some detail, we term a mechanism. Our present task is to attempt to understand those elementary or single-step processes by which stereochemical choices are made. That different things differ is obvious or trivial. Nevertheless, it seems worthwhile to focus attention on the stereo-process. Stereoelectronic axiom 1 : Provided that a distinction i s possible, a single elementary step must be stereospecijic. Stereoselectivity axiom 2: If two or more stereoisomers of different free energy can enter into or result from similar elementary processes, the rate of one will be preferred. The first axiom is an observation about the uniqueness of a single chemical act at the molecular level. The second axiom is based on the fact that the path of lowest free energy of activation is favored. Another question regarding stereo-paths involves terminology. Following Mislow (1965), we write

Stereoselectivity =SS -

A=

a - (b+c+* * .) (a + b + c + - - )

where a , b, c, etc., are the concentrations of A, B, C, etc., being formed or consumed competitively in a given reaction. When SS, = 0 or 1, the reaction is termed stereospecific. We agree with Eliel (1962) that specificity should be used in an absolute sense, and only SSshould be qualified,

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e.g. with “more”, “partial”, “predominant ”, etc. Unlike Eliel, we shall take the view that if the process

-

dl-RCHBr CHBrR +I- + trans-RCH=CIFR

+IBr

(2)

goes as written (SS= 1-00),then it is termed stereospecific, even though a syn rather than the usual anti process has occurred. Another kind of measure of## is given by the difference,[SS(kinetics)-SS(equilibrium)], in which the degree of kinetic over equilibrium control is indicated. Total equilibrium control would lead to stereoconvergent product ratios. The reader should be aware of the fact that definitions of SS and specificity (Zimmerman et al., 1959, 1963), may differ somewhat among organic chemists, but that the same words may have entirely different meanings to inorganic chemists (Gillard, 1967). Before we come to grips with current problems in the field, it seems appropriate to close this section on an historical note. If any one individual should be singled out as the “father” of stereoselectivity, that man should be Arthur Michael (1895). It was he who pointed out that 1,2-eliminations (or additions) are favored when groups depart (or arrive) in the anti sense.

In this he had to oppose the strong tradition of van%Hoff and Wislicenus (1887), whose ideas of structure were sound, but whose notions about the stereochemical course of reactions were often erroneous. After a vigorous polemic with Wislicenus, Michael emerged victorious on the trans rule of stereoselection (Pfeiffer, 1904). It is interesting that Walden’s work (Ingold, 1953) on substitution reactions and Michael’s work on addition-elimination appeared a t the same time. By 1912, Frankland could sense that trans processes and the Walden inversion (equations 4b, d) were related, and an underlying explanation would eventually be found for both. D-RCHOH.CO2H

t

d Aga0,HaO

L-RCHCl*COaH

9

I

D-RCHC1-COgH b Aga0,HaO

(4)

L-RCHOH*COaH

Inasmuch as rate and stereochemical studies were available, and made a consistent picture, the issue of anti or trans mechanisms, e.g. equation

(3), seemed “settled”. There was one notable application of Michael’s

188

SIDNEY I. MILLER

rule in the 1920’s, when the incorrectly assigned structures of syn and anti oximes were reversed, and the mechanism of the Beckman rearrangement was corrected, on the basis of observed anti eliminations (Meisenheimer and Theilacker, 1932). By contrast, the stereochemical outcome of apparently simple substitutions, as in equation (4), had no convincing rationale for many years. This provoked ever increasing attention after 1900, and the Walden displacement processes became a dominant interest among many organic chemists. Finally, by the 1930’s, the mechanism of a three-center displacement, H + H,, was described in quantummechanical terms (London, 1929). Stereochemically speaking, displacement now became the key process, and theoretical developments centered on and flowed from it (Olson, 1933; Ingold, 1953). This brings us to the modern era.

11. THESHAPEOF SIMPLE SPECIES Both valence bond (VB) and molecular orbital (MO) theories have been used to “explain” the observed shapes of molecules. What we wish to know here is the shape of a transition state containing m atoms and n electrons. Fortunately, the preferred shapes of the simple species are known or can be guessed from the numbers and kinds of bonding and nonbonding electron pairs (Gillespie, 1967). Therefore, we must examine the preferred shape of clusters of three, four or more atoms. For, to envision the topology of a transition state is tantamount to a description of the stereochemical result of an elementary process. A. Some Valence Bond Results The first application of quantum mechanics to a rate process was made by London (1929; Eyring et al., 1944). For a two-electron diatomic molecule A-B, there are two allowed wave functions, $c Relative t o the separated atoms, the corresponding energies are

E,

=

Q+J 1+ 5 2

For our purposes, it will be sufficient to note that Q , the coulomb integral, and J , the exchange integral, are negative, have theunitsof energy, and fall off with interatomic distance, TAB. The overlap integral,

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189

takes on values between zero and unity. (In approximate work, S -N 0; Q/J.: 0.1-0.2.) I n the state i,bz, the appropriate energy is E-, and atoms A and B repel one another at all internuclear distances; in the other state t,hl, S is positive and the energy E , has a minimumvalue at the AB bonding distance, re. Following London, others developed the VB method for three-atom and higher species (Eyring and Polanyi, 1931; Eyring et al., 1944). Consider a four-atom, four s electron species ABCD; this may be represented, without any geometrical implications, as

Then, for the six possible diatomic molecules, we can write the energy as

The energy of the lowest energy state is given by

E

= (1 +S2)-’(Q

+ (+[(a-p)’ + (P-y)’

-t- ( y - a)2]}1’2)

(8)

in which 5’ = a = J,,+J,,

C S& Q = p = Jae+JM,

Qij

=

J d + J a O

For a three-center molecule ABC, we simply drop all terms involving D, e.g. Qad =Jd = 0, and the form of (8) is preserved. This is the London (1929) equation. Similarly, one recovers the appropriate expressions (7) for diatomic molecules by removing one atom from ABC. The energy of ABCD (or ABC) in any configuration can be found by inserting the values of Qij,Jij andSij at the appropriate rij in (8). Qualitatively, even the overlap-independent (5= 0) energies will indicate the most favorable shape. For the molecule A4, E (tetrahedral)N- Q and E (square)21 Q + (Jlz-J l , ) . For A,, E (equilateral)-N 0 and E (linear) N Q + (J12 - J l s ) ; in this connection, London (1929) points out that equilateral H, would constitute a violation of the Pauli principle. Since fJlzf - IJ1,l > 0, square A4 and linear A, are energetically favored. Currently, Ellison is using VB theory, “diatomics-in-molecules” (Pfeiffer et al., 1967) on small species. Companion (1967) has looked into this approach and found that several predictions made in earlier versions

S I D N E Y I. M I L L E R

190

of VB theory, or in other ways, have been confirmed. One of the novel predictions is that Li,H, should be in the form of a tetrahedron, two of whose corners have been pushed together slightly. As one goes to higher species, VB theory rapidly leads to formidable expressions. For qualitative discussion, however, one can use the cc perfect-pairing approximation ”, which is intuitively reasonable but crude and difficult to justify rigorously (Eyring et ul., 1944). The binding energy is given by

E

=

C Q.ij+X Jij-4 C Jij-4 paired nonpaired orbitals

orbitals

(9)

Jij

orbitals with parallel spins

Here, every bonded electron pair, in atomic or hybrid orbitals, contributes Jij; every pair of bonds (or bonds involving nonbonded atoms) with spin-independent electrons contributes - +Jij;every electron pair with parallel spins contributes - i J i j . This expression tells us that bonding lowers the energy, and nonbonded atoms or nonpaired electrons raise the energy. Increased stability will therefore be found when the negative terms in (9) approach zero, as they must when the relevant atoms or electrons move apart. Among other assumptions, one considers only a single set of bonds or electron-pairing scheme when one uses (9). Therefore, it is best applied to frameworks for which a single covalent structure can be written. Under these conditions, it is easy to see why :for a four-atom six s-electron system, the order of energies is E(1inear)< E(trans)< E(skew) < E(ci8);

A-A-A-A

A \ A-A

A

A \A-A’.

.A

\

A-A

A /

‘A

for a six-atom twelve s-electron system, the hexagon is the favored shape. Many of the transition states examined according to the HeitlerLondon method, should be of continuing interest for years to come (Glasstone et al., 1941). The stereochemical legacy of the period may be summarized explicitly as follows : two-electron three-center (Hi), triangle ; three-electron three-center (H3,H,C1, HCH in CH,), linear; four-electron four-center (H, + C=C, Br, + C=C, C=C+C=C), coplanar cycle ; six-electron six-center (Br, + C=C-C=C, C=C + C=C-C=C), coplanar cycle ;

STEREOSELECTION I N STEPS O F O R G A N I C REACTIONS

six-electron six-center (catalytic hydrogenation, H 2+ C=C coplanar bicyclic.

191

+Ni-Ni),

The influence and impact of these semi-empirical calculations and absolute reaction rate theory on the thinking of physical organic chemists was profound. It makes clear, for example, the electronic basis for some of Ingold’s broad generalizations, e.g. “ I n bimolecular eliminations, E2, in systems H-Cfi-C,-X, where X may be neutral or charged, the p-CH electrons, independently of the electrostatic situation, enter the C, octet on the side remote from X, because repulsive energy between electron-pairs in the transition state can thus be minimized: the result is anti-elimination, independently of the structural details of the system” (Ingold, 1953). Thus far, no mention has been made of a directional bias in the available orbitals of A, in the London-Eyring-Polanyi approach. When there are p-electrons on the atoms, the J’s of the VB expressions become sensitive to interatomic angles as well as distances. The first calculations on the reaction of chlorine atoms with hydrogen assumed that the transition state, HzC1, was linear (Glasstone et al., 1941). Magee (1940), using two s and one p orbital, concluded that H2Clwas triangular. More recent calculations on deuterium and tritium isotope effects on this reaction did not indicate a strong preference for either geometry (Bigeleisenet al., 1959). Of course, the three-electron model is unrealistic for this system. It turns out that we can make more progress with the MO approach, but in more complex systems.

B. Some Molecular Orbital Results In the course of our discussion we shall draw heavily on MO terminology and results but shall avoid MO calculations as such. I n the primitive aspect of the theory, n one-electron MO’s, k,are constructed by a linear combination of atomic orbitals (LCAO):

Compilations of the results of Huckel MO (HMO) calculations for a variety of polyene systems are available (Coulson and Streitwieser, 1965; Heilbronner and Straub, 1966). These include the coefficients c, in any MO, and the MO energies

Ei = cL+mi/3

192

S I D N E Y I . MILLER

in which a is the one-electron coulomb integral and /3, the resonance integral, falls in the range - 1 to - 3 e.v., depending on the kind of polyene. The overlap integral S has the same form as in VB theory, and the AO’s are usually chosen identical, equispaced, and properly aligned in simple HMO theory to maximize 8.In Fig. I we have abstracted the a-B a

a+@

7%-

+ + a

--+ o -

+ + +

+ - + + - - +

at::;; al U

a

+ 0,628

a-B

+ o - o +

a

+ - c - c + +

+ + + - + + +

+ + +

+ - + + + - + - + + - - + + + - - + + + +

U

a-0.62p

+ - + - + + - o + + + o - -

--/+I-

a - 1.628

I

+@

a+B a+

dS8

a- 1.88

a- 1.258

a

a - 0.4458

a

+ 0.4458

-0-

FIG.1. Schematic Hiickel molecular orbital energy levels and signs of amplitude plots for wave functions #. The energy increases from lower levels to upper ones. Left, open chains; right, rings. The orbitals $i making up these MO’e may be all 8, all p , etc.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

193

forms of the MO’s and their energies, for several acyclic and cyclic species. The scale of energies is in 8 units relative to a. According to the aufbau idea and Pauli principle, as in atoms, the electrons are fed into these orbitals to a maximum of two per orbital in order of increasing energy, preferring single occupancy of orbitals of identical energy (degenerate),where available. Molecular orbitals whose energies are negative, zero or positive relative to the AO’s are designated as bonding, nonbonding, and antibonding. The sum of the one-electron energies of (10) gives the total bonding energy, Etot. This will be E,, or En,depending on the original 4’s. For a three-atom system consisting of three identical $ orbitals, which may be s or p , the MO’s are given as follows :

The ground state of linear A, (four electrons) is indicated as Yl=@+I while the first excited state may be written as Y2= $!$2$3. By reference to the levels for cyclic A,, it is seen that, because of degeneracy, the With the aid of the energy ground state of A; is given by Yl= @ $ 2 + 3 . levels in Fig. 1, we have an immediate answer to the preferred shape of three-center species, A;, As, and A,. The lowest orbitals are at 2 / 2 8 for the linear and 28 for the cyclic species. For two electrons, Etotof cyclic A; is favored by 1.1 7/3; for three electrons, cyclic A, is favored by 0.178; for four electrons, linear A, is favored by 0.838. It is gratifying that these HMO answers are in accord both with VB theory and the recent sophisticated calculations on triatomic hydrogen (Conroy and Bruner, 1967). With regard to the shape of the MO’s themselves, consider a set of four parallel and equally spaced p-orbitals of a carbon chain, as a model 7+

S I D N E Y I. M I L L E R

194

for cis-l,3-butadiene. After these AO’s are suitably combined, one obtains four Huckel MO’s, of which #1 and t,h2 are each doubly occupied. The latter has the form $2

= 0 . 6 0 ~ 1 +0.37112

- 0.3711, - 0.60114

(13)

The amplitude of 9h2 can be traced in schematic fashion from its approximate shape to several idealizations in Fig. 2 &d. The convention of 2d is used in Fig. 1 . Likewise, the corresponding MO formed from a set of s-orbitals is

+

= 0 . 6 0 ~ 0.3782 ~ - o*37S3- 0.60~4

(1 3 4

The amplitude function is given schematically in Fig. 2, e and f. The basis for much of our discussion depends on an understanding of the coefficients ci in t,hi. I n 4, of butadiene, for example, the signs simply reflect the direction along a coordinate axis (usually x ) in which the p orbitals are making their contribution. The squares of the coefficients (ci) measure the charge density or, roughly, the contribution of a particular A 0 to the MO. An index of the bonding contributed by the AO’s $E and $j to the one-electron MO is given by cjck; the total bond order is given as a sum over all occupied orbitals

PjE=

c

CjCk

occup.

in which there is a term for each electron in each MO. At the nodes, where $i= 0, the MO is nonbonding. As Pjkis positive, zero or negative, the two AO’s are bonding, nonbonding or antibonding in the molecule. Later, we shall use a similar criterion for overlap between suitable orbitals of different molecules, namely that they have a net positive Pjb for bonding. Another useful way to look at the #’s is at their symmetry. Subscripts g (gerade) and u (ungerade) are labels specifically associated with the presence or absence of the inversion symmetry element in the given orbital. In (11)and Fig. 1, the three MO’s t,hl, $2, #3 of allyl, a r-system, may be designated as u, g, and u, respectively. We shall designate MO’s antisymmetric ( b ) or symmetric ( a ) ,as they do or do not change sign when a specific symmetry operation is performed on the molecule. For the MO of (13) and Fig. 2b, there are two symmetry planes a,,, )a,, both of which are b ; there is an a two-fold symmetry axis G2(z) and an a mirror plane aYz.Inspection of the #i’s of any acyclic polyene in Fig. 1 with respect to a,, indicates the order #l(a), #2(b), #3(a), #4(b), etc., in which the MO’s are symmetric for i=odd and

I

-*

-*

a

u

P

m

STEREOSELECTION I N S T E P S O F ORGANIC REACTIONS

I

+-m

+ - d

6'

1

FIQ.2. The molecular orbital #z constructed from four atomic orbitals. Upper, a-d: (62, of four p orbitals, pictured in different ways. Lower, e-f : (12 of four s orbitals pictured in different ways.

1'36

196

S I D N E Y I. MILLER

antisymmetric for i =even. Apart from the degenerate MO’s which are labeled e , the MO’s of the coplanar cyclic polyenes of Pig. 1 can be termed a or b with respect to a symmetry plane perpendicular to the ring. Group theoretical arguments (Jaff6 and Orchin, 1965; Cotton, 1963) are used to categorize the total symmetry of an MO more specifically, e.g. with various superscripts and subscripts on a,b, and e , but we shall be concerned with their use rather than their origins. To obtain a state symmetry, say, of s-cis-butadiene, we note that y/1 -- $2$2 1 2 -- a2b2 =

and

Y2 =

+&b&

=

(1)2(-1)2

a2ba = ( 1 ) 2 ( - 1 ) ( 1 )

=

1

= -1.

That is, we insert + 1 or - 1 for each $ in the given state as it is symmetric or antisymmetric. To designate state symmetries, we shall use upper-case Ietters A and B. Thus, Y, is A and !P2is B for cis-butadiene. State symmetries involving degenerate $’s are not so obvious, and simply will be given where required (Jaff6 and Orchin, 1965; Cotton, 1963). The relation between the shapes, spectra, and MO’s of simple molecules was first investigated systematically by Walsh (1953). His work was a natural development of the familiar view that the states (orbitals) of diatomic molecules correlate with those of the separated atoms. The energy levels are “connected ” so that states (orbitals) pass adiabatically from atoms to molecules or molecules to molecules. That is, levels of the same symmetry, u, rr, g, u, do not cross. This non-crossing rule is basically a statement of the Pauli restriction for atoms, molecules, and their interconversions. It has been pointed out that in polyatomic molecules the non-crossing rule may not hold in special cases (Herzberg and Longuet-Higgins, 1963) ; these involve level crossings in one (some) but not all of the coordinates of the potential energy surface. Walsh first made the MO’s from AO’s consistent with the symmetry of a given species. Then, drawing on spectral and structural data, theoretical calculations, experience, intuition, etc., he ranked the MO’s according to their energies in a given geometry. Electrons were then fed into the orbitals in the usual way, the final shape being determined by the occupied orbitals. Figures 3 and 4 are typical. Examples of both experimental fact and/or prediction, with the number of electrons indicated in parentheses, are: HC2 (9), linear; C3 (12), linear; HOz (13), bent; HOCl (14), bent; HFF (16), linear; NCN (14), linear; NF2 (17), bent; C13 (21), bent. By analogy with the isoelectronic triatomic molecules, one can guess the probable shape of higher species, e.g. H2C=CH and HCO (11) are bent, and H,C=C=CH+ and CO,+(15) are linear.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

197

The original Walsh diagrams have been discussed critically and corrected or modified for special applications (Coulson and Neilson, 1963; Hansen, 1966). I n Pig. 3c, the effect of d-orbitals is tentatively

I

b HAB

I

1 E

I

90"

I

HAB angle, degrees

I€

a

HAH

I ISO"

I

9 0"

135' HAH angle, degrees

180°

90"

BAB angle, degrees

FIU.3. Walsh correlation diagrams. a: State energy levels for methylene (Jordan and Longuet-Higgins, 1962). b : MO levels after Wahh (1953). c: MO levels after Atkinsand Symons (1967) and Hayes (1966); above the break, d-type orbitals have been included; their effect on the energy of some MO's is indicated by the smdl arrows.

incorporated (Hayes, 1966). When the d-orbital symmetry coincides with any MO, the energy of the latter may be raised or lowered, as indicated by the arrows along the ordinate. Unfortunately, the generalized

198

SIDNEY I . MILLER

levels tend to be uncertain, since all of the levels undergo relative shifts as each electron is fed in. Walsh realized that accurate spectral data and calculations would eventually require a unique level diagram for each species. Figure 3a represents an attempt in this direction, where the individual MO energies have been estimated and summed for each electronic state, as indicated by the state symbols at the right of Fig. 3a. This is Jordan

Tux

A-A

dg

FIG.4. Walsh (1953) diagram of the shape of HAAH and the energies of the molecd,br orbitals (Murrell, et al., 1965). The fifth, sixth, and seventh filled BIO’s correspond:to H-&CH, H-NsN-H and H-0-0-H, respectively. Two high energy A-H u* orbitals we not shown.

and Longuet-Higgins’ (1962) description, tailored to fit the species CH2 and NH,. The ground state of triplet methylene is linear (s,Zg), its first excited state is a bent singlet (lAg).The amine ground state is bent. By extension, BH,, like CH,, would be linear and HzO, like NH,, would be bent. Concerning the shape of HAAH in Fig. 4, we take only the bonding AO’s, i.e. 1s orbitals from each hydrogen and 28 and 2p orbitals from each atom A. Therefore, there are ten MO’s that can be filled. When

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

199

five of these are occupied, we have H-CzC-H, which is most stable as a linear molecule. Murrell et al. (1965) point out that different excited states (4~:) will have different shapes, with the energy increasing in the order planar (T;T&), skew (T;T&)and linear (n&7&). Their qualitative arguments are based primarily on the necessity for increased orbital overlap of bonding MO’s and decreased orbital overlap of antibonding MO’s. For this reason, a planar form is predicted for diimide, H-N=N-H, and a nonplanar form is predicted for hydrogen peroxide, H-0-0-H, where the vgorbitals are being Bled. I n both cases, antibonding is diminished by distortion of the m-type MO from 180”. Since aeo compounds RN=NR favor the trans coplanar form and H202is skew, these predictions are in accord with experience. Two reports of quantum calculations on the relative stability of cis and trans diimide (HN=NH), however, are contradictory (Wheland and Chen, 1956; Alster and Burnelle, 1967); it has been observed that cis-difluorodiimide is the more stable form (Bohn and Bauer, 1967). We shall have occasion to refer to the Walsh diagrams in discussing certain transition states. Pictorial representation of some of the orbitals given in Figs. 3, 4 have been given by Atkins and Symons (1967), and some of the analytical functions have been given by Gray (1964). As an illustration of the latter, we shall outline Jaff6’s (1953) MO description of the three-center substitution process (15). Jaff6 assumed that the three A-R bonds were sp2 and lay in the xy plane. For a reaction of carbon (A), he

X+D-R,AX -+ X * * . R 3 A . * * X -+ L-XAR,+X

(15)

assumed that its p z orbital interacted with the orbitals and c $ ~ from the X groups, the latter were assumed to be cylindrically symmetrical about the z axis and could be s, p or hybrid orbitals. The MO’s of (16) are pictured in Fig. 5 . A more complete treatment of a three-center

1 =

$2

--

(41+42)

model of C1. - CH, - C1 has been given by Carr&et al. (1969). Clearly, these orbitals are similar to those given previously for the three-center system A, in (11). By changing p z of this set to a suitable

200

S I D N E Y I. MILLER

hybrid orbital and assuming a cyclic AX2,one would obtain a set similar to (12) for cyclic A,. Whether the attacking X is a cation, radical or anion, $z will hold zero, one, or two electrons in addition to the two electrons in To choose between the linear and cyclic forms, we refer to the correlation diagram in Fig. 3. If the effect of the substituents is ignored, then the transition state will have 2O(AX<), 21(AX,) and 22(AX,) valence electrons. Accordingly, the prediction would be that the cation is angular, while the radical and anion would be linear. lt is reassuring that the bent molecule OFz is a plausible analog for the twenty-electron

PI

$1

9e

FIG.5 . Molecular orbitals for the transition state X.. .A . . .X deriving from orbitals $1, $2, and p , in X.. RsA.. X.

.

.

system; and the presumably linear (Atkins and Symons, 1967) radical F, is an anaIog for the twenty-one electron system. Provided that we can extrapolate from A, to X-..AR,...X, the transition state energies can also be deduced from HMO theory. Note that three s rather than p z orbitals are appropriate here. From Fig. 1, E, can be compared for linear and triangular transition states with the following results: when X is a cation, XAX is angular; when X is an anion, XAX is linear ;when X is a radical, XAX might be bent or linear. This extrapolation to a many-electron system may be unsafe-we cannot be wholly satisfied with these predictions until the results of more realistic calculations become available.

STEREOSELECTION I N STEPS O F O R G A N I C REACTIONS

201

If instead of carbon, the central element were in the third row, e.g. silicon, one presumably could use hybrid orbitals with d participation (Gillespie, 1952; Dewar, 1953). This would lower the energies of the linear and bent transition states (Hayes, 1966). On the basis of the several approaches used to this point we anticipate that : all transition states R,AXi should involve retention of configuration; all transition states R3AXg should involve inversion of configuration. The geometry of the corresponding radical is less certain. We can still hedge on an absolute decision at this point, because the changes in the A-R bonds have been ignored. I n practice, however, these predictions are in accord with many observations of carbon, silicon and phosphorus chemistry (Ingold, 1953; Sommer, 1965; McEwen, 1965). This question will come up again. The same MO methods can be applied t o four- and five-center additions and eliminations, subject to certain restraints. Thus, the synchronous addition of X-X to a double bond in any unsaturate must be syn. The termolecular addition of X and Y to an unsaturate can be q n or anti. Provided that X and Y are nonbonded, VB theory, the Walsh-type correlations (Fig. 4), and extended HMO theory (Hoffmann, 1963) suggest an anti preference. I n the next section, the powerful application of symmetry restrictions will confirm these predelictions. Some years ago Stewart and Eyring (1958) enunciated a principle of “minimum bending of orbitals ”. On examining the wave equation, they concluded that the electron cloud behaves like a “fluid of high surface tension in that it will seek minimum curvature of the boundary surface consistent with minimum potential energy ”. This is done by expanding over as many nuclei as possible, by smoothing the orbital surface and avoiding corners. Although Eyring et al. were concerned with the barrier in ethane (1958b) and “diabatic” reactions (1958a), they believed that they had uncovered a principle which could account for rotation barriers in ethane, the preference for chair cyclohexane over other conformations, favored anti-processes in organic reactions, the trans-effect in coordination compounds, and the trans-effect in nuclear magnetic resonance (Stewart and Eyring, 1958). Unfortunately, the relation between this theory and applications of interest here has remained obscure and has not been exploited.

111. BONDING THEORY AND STEREOSELECTION I n a series of communications, Woodward and Hoffmann (1965; Hoffmann and Woodward, 1965; Woodward, 1967) gave a beautifully simple solution to the problem of stereoselection in molecular reactions.

202

S I D N E Y I. M I L L E R

By molecular reactions, we mean that group of concerted reactions which are neither ionic, nor radical, and which have “no mechanism ” (Rhoeds, 1963). The basic idea is that those reaction paths are favored in which orbital symmetry is conserved. Their work quickly provoked contributions from theoreticians and experimentalists alike. Fukui (1965, 1966; Fukui and Fujimoto, 1965, 1966), for example, must be credited with extending their ideas to include heterolytic and homolytic reactions. All of this work will be considered in detail. We shall discuss several types of “no-mechanism ” reactions first and “ some-mechanism” reactions second. From an orbital viewpoint, all heterolytic rearrangements would be subsumed under sigmatropic reactions; heterolytic substitutions and additions (eliminations) turn out to be versions of cycloadditions (cycloeliminations). Nevertheless, we have retained categories on the basis of mechanism, because these are familiar, and because the trend is from the relatively simple to the complex mechanism.

A. Electrocyclic Reactions I n their first paper, Woodward and Hoffmann (1965a) explained the ateric course of ring opening or closing, i.e. electrocyclic reactions of the type (17). Such a reaction involves a net change of one CJ and one T bond. A frontier orbital representation of this process is given in Fig. 6

T i

B E 1

4

(Fukui, 1966a). Depending on k, the highest occupied molecular orbital (HOMO) will be symmetric (a) or antisymmetric ( b ) , with respect to a symmetry plane ( 0 ) perpendicular to the plane of the carbon chain of 1. Thus, l a is a (4n + 2 ) r and l b is a 4n7r electron system (Fig. 6). Now, in order for the ring to close and form a a-bond, the ends of the 7r-system of l a must rotate in opposite directions or in a disrotatory mode, while the ends of l b must rotate in the same direction, or in a conrotatory mode. I n either case, rotation occurs so as to maximize orbital overlap or bonding as measured by PGjin (14).

-

c

conrotatory

disrotatory

ggk -

lb

2

3b

3a

4q

J \

B

C

uq 4q A

disrotatory

D

J \

conrotatory

-

B

D

FIQ.6 . Stereoselection in electrocyclic processes.

A

C

204

SIDNEY I. MILLER

I n order to see all of the stereochemical consequences, we have put a marker group M on the original compound 1 (Fig. 6). By a disrotatory process, 3a must give 4a or 4b; by a conrotatory process, 3b must give 4c or 4d. The choice between the kinds of reaction path is, in principle, absolute. Moreover, although we have given an explanation of ring closure, we need only reverse the arguments to account for ring opening on identical paths. The pyrolysis products of the cis- and trans-2,3-dimethylcyclobutenes are illustrative of the conrotatory mode (Criegee et al., 1965):

The allowed paths are indicated by unbroken arrows. Ring opening of the trans-isomer favors 5 rather than 6. I n the present context, the choice between two conrotatory paths as in (19) (Freedman et al., 1965) is of secondary interest, although the rationale of such conformational Ph

Br

___f

B r p v & , Ph Ph

Ph

100%

preferences will be discussed later (see (214)).

+

P

h

v

P

Br Br

0%

h

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

205

Both the conrotatory and disrotatory modes are indicated in the following reaction sequence which involves a tetraene, a triene, and a diene in ring opening or closing (Marvell and Seubert, 1967).

By implication, reactant and product were taken to be in their ground states, i.e. the electrocyclic processes were thermal in Fig. 6. Obviously, if the reactions proceed between excited states, e.g. as a result of photochemical excitation, then we have to consider rr to rr* transitions from the HOMO to the lowest vacant molecular orbital (LVMO). Because of the alternation in orbital symmetry in a polyene chain, the new HOMO is b for a (4n+2)- or a for a (4n)-polyene in its excited state. Assuming that the state of highest energy will be most effective in process 1 , we can again use Fig. 6 to describe the reactions. That the molecules l a and l b are now in excited states is assumed to be irrelevant. What matters is that the incipient a-bond of 2 is made from the proper

206

S I D N E Y I . MILLER

overlap of la and lb. I n effect, a polyene which cyclizes by a conrotatory mode thermally, will cyclize by a disrotatory mode photochemically ;if it cyclizes by a disrotatory mode thermally, it will cyclize by a conrotatory mode photochemically. Two different systems illustrate these alternatives nicely : the fourcenter reaction (22) (Dauben and Cargill, 1962; Shumate et al., 1965);

cis,cis

cis,traas

the six-center reaction (23) (Fonken, 1962; Vogel et al., 1965);

conrot.

CHs

I n reaction (24), the assignment of the configuration of the nonatriene is speculative, but consistent with the processes involved. Electrocyclic reactions are also possible when the i-r system exten& over a carbon chain containing an odd number of atoms :

The essential aspects of reaction (25) are depicted in Fig. 6. Huisgen et al. (1967) have provided a beautiful example of an “odd” electrocyclic change in (26). The aziridine opens up to a dipolar four-electron allylic species. Since the HOMO is b (Fig. l),the thermal change is conrotatory and the excited state process is disrotatory. To avoid equilibration of the dipolar ions, these workers trap them with an acetylenic ester in a stereospecific cycloaddition, which we shall discuss presently. I n their first paper, Woodward and Hoffmann (1965a) make a prediction based on orbital properties favoring one of two disrotatory paths in (27). The process of ionization to produce a cyclopropyl cation also produces a negative ion, X-. (We can also think of the reversal, namely, the attack of X- on a, three-atom cyclic cation.) Here, is a and t+b2is b (Fig. 1). From either point of view the two u orbitals involved in the

S T E R E O S E L E C T I O N IN S T E P S O F O R G A N I C R E A C T I O N S

207

Ar

Ar

I

I

Cis

trans

N

trans

cis

change have different symmetries and should move in opposite directions, as indicated by the small arrows in (27). Baird and Reese (1967) and Ando et al. (1967), have found systems in accord with these predictions, e.g.

endo

em

S I D N E Y I. M I L L E R

208

and Parham and Sperley (1967) have provided another (28). Later, we shall discuss a recipe for predicting relative reactivities of systems such as (27) (Schleyer et al., 1966).

The predictions one can make about electrocyclic processes are given in Table 1 . Although this is a Table of both allowed and forbidden one-step processes, this does not rule out other reaction paths, e.g. via several steps by free radicals. Furthermore, “forcing ” conditions may provide sufficient energy so that a forbidden path may become allowed. Considering the type of system, there are perhaps more predictions in the Table than experimental facts. Nevertheless, the success of the Woodward-Hoffmann rule has been remarkable. TABLE1 Electrocyclic Reactions of Polyenes (C=C),

or (C=C),C ~

Polyene (C=C)C+ (C==C)C. (C=C)C(C=C)z (C=C)2C+ (C=C)zC. (C=C)2C(C==C23 (C=C)4 (C=C)5 (C=c)B

n Electrons

Thermal p a t h

2

Disrotatory Conrotatory Conrotatory Conrotatory Conrotatory Disrotatory Disrotatory Disrotatory Conrotatory Disrotatory Conrotatory

3 4 4 4 5

6

6 8

10

12

Photochemical path Conrotatory Conrotatory Disrotatory Disrotatory Disrotatory Disrotatory Conrotatory Conrotatory Disrotatory Conrotatory Disrotatory

Q

.____

a

See text and Fig. 9 with regard t o this stereopath.

When the reactant molecules have built-in restrictions, certain alternatives are precluded. A conrotatory cyclization is thermally allowed for butadiene but is not possible in cyclopentadiene, because it would lead to a trans ring junction; photochemical excitation must

S T E R E O S E L E C T I O N IN STEPS O F O R G A N I C R E A C T I O N S

209

be used to make the bicyclo-compoundby a disrotatory closure (Brauman et al., 1966). On standing, this unstable substance reverts relatively slowly and only in part to cyclopentadiene. The failure to convert dihydronaphthalene photochemically into the

thV

hv

it

conrot.

(30)

“elusive” compound, cyclodecapentaene (van Tamelen and Pappas, 1963) may in part be ascribed to the fact that the “allowed” conrotatory process is sterically improbable. The reverse reaction, namely, cyclization is both allowed and probable (30). The apparent photochemical path from trans- t o cis-dihydronaphthalene becomes all the more plausible if the decapentaene is an intermediate (van Tamelen and Burkoth, 1967). It is interesting that none of these restraints indicated for (29) or (30) seem to apply when ring closure or opening occurs at nitrogen (Battiste and Barton, 1967) :

+ c6~.&

;>c6H5 N

c6HS

N-N

aH5

__f

CoH5

C6H5

(31)

This is consistent with the notion that these restrictions are steric rather than electronic.

210

S I D N E Y I. M I L L E R

I n some processes, the cyclopropyl group behaves as though it were functionally equivalent to a double bond (Hoffmann and Woodward, 1965b). I n (29), we have an excited state disrotatory process to one cyclopropyl ring and one double bond. With one more double bond in

(32), we have a disrotatory thermal process (Ciganek, 1967). With still another double bond, we speculate that the disrotatory process goes in the excited state : H

Finally, the photochemical mechanism of bullvalene formation in (30) “substitutes ” two cyclopropyl groups for two double bonds in an allowed disrotatory process (Schroder and Oth, 1967). It should be pointed out that our description of electrocyclic reactions thus far has been qualitative. Woodward and Hoffmann (1965a)do refer to unpublished HMO calculations which back up the almost intuitive symmetry arguments. Nevertheless, Fukui (1965,1966)and Zimmerman (1966) outlined HMO treatments in which they obtained changes in energy for conrotatory and disrotatory processes. On the basis that paths involving minimum energy between reactants and transition states were favored, their predictions were in essential agreement with those of Woodward and Hoffmann. I n the second paper on the subject of orbital symmetry and stereoselection, Longuet-Higgins and Abrahamson (1965) succeeded in answering several questions : (1)Why should ring-opening be in%uenced by the structure of the polyene? (2) Why should extended HMO calculations and the symmetry of the HOMO give the same answer? (3) What does orbital overlap in a single molecule mean quantummechanically (Fukui, 1966a)l Their discussion is based on the premise that in the transformations of (17), (18), etc., the orbitals or electronic states pass adiabatically from reactant to product: that is, orbital symmetry is conserved. In effect, this is an application of the non-

(1,3-cyclohexadiene)*

(1,3,5-hexatriene)*

FIQ.7. Disrotatory electrocyclic ring opening of 1,3-cyclohexadieneto 1,3,5-hexatriene.The excited state process, “forbidden ” in the disrotatory mode, as indicated on the right, is allowed in the conrotatory mode (not shown).

20

Z m

E3 c

c

S I D N E Y I . MILLER

212

crossing-rule to syininetry correlation of reactant(s), transition state and product(s). To begin with, let us consider the correlation diagram in Fig. 7 from the frontier electron point of view (Fukui, 1966). Specifically, the level diagram corresponds to ring opening of a cyclohexadiene, as in (23), (30), and (32). The “reactants”, u and n orbitals, are in the same molecule. In this picture, the emphasis is on frontier HOMO and LVMO, and symmetry labels are assigned to the orbitals with respect to a mirror plane perpendicular to the plane of the polyene. Now, if their symmetry is right, the HO a(a) electrons “enter” LV n*(a), or HO n(b)electrons enter LV u*(b);the process is syn or disrotatory. I n the left half of Fig. 7,lines joining reactant and product orbitals indicate the conservation of orbital symmetry. The reaction is allowed in the ground state. On the excited state side of Fig. 7, the HO u (a)level of cyclohexadiene cannot feed into a LV n* (a) level in the cyclohexadiene of like symmetry, because none is available. (In other cases, an orbital of the appropriate symmetry may be of higher energy than the LVMO.) Now the transitions to product, which conserve symmetry and are indicated by the straight lines, would give a product in one of the higher excited states, rather than in the first excited state. To proceed from the first excited state of cyclohexadiene in disrotatory fashion to the first excited state of hexatriene involves a switch in symmetry. This is forbidden, or at least energetically costly. It turns out that a state level diagram, with symmetries appropriate to the conrotatory path, indicates an allowed excited state process of higher energy-see below. Longuet-Higgins and Abrahamson (1965) adopted a viewpoint which has been incorporated into Figs. 8 and 9. They first classify all of the orbitals according to the possible changes during reaction. On the conrotatory path to butadiene, cyclobutene has a twofold axis (C,) of symmetry, and in the disrotatory mode, a plane (ul)of symmetry. How the orbitals relate to these symmetry operations is indicated in Table 2. I n Fig. 8, the orbitals are arranged in order of increasing energy, but the symmetry labels refer either to the Cz or u1 operation. TABLE 2 Orbital Symmetries in the Electrocyclic Process: Cyclobutene ~~

f

Butadiene

~~

Symmetry Cyclobutene 8-cis-Butadiene Conrotatory Mode Disrotatory Mode

a b a‘

77, o*

b’

Tr*,

a, %-* a1 77

a*

*19

*4 $8

$19

$3

b.94

STEREOSELECTION IN STEPS O F ORGANIC REACTIONS

213

Clearly, the conrotatory mode is energetically favored. (In Fig. 7, only the 0 operation appropriate to disrotatory ring opening in cyclohexadiene was used.) Longuet-Higgins and Abrahamson (1965) also give a state correlation diagram (Fig.-& lowest portion). I n such a diagram, one arranges in Dierotatory Mode

Conrotatory Mode

CP

cyclobutene

I oyolobutene

butadiene

cyclobutene

butadiene

butadiene

FIG.8. Conversion of cyclobutene to s-cis-butadiene. Conrotatory changes are on the left; disrotatory changes are on the right. Upper section: alternative modes of ring opening of cyclobutene. Middle section : orbital correlation. Bottom section : symmetry state correlation.

ascending order the electronic states ?PI,Y2, Y3,etc. or ground state, first excited state, second excited state, etc. Group-theoretical arguments are then used to assign the symmetry designation to each orbital, and the state symmetries are obtained as described previously. From Table 2, we now find which orbitals and, therefore, which states in reactant and product are symmetry related. We connect these on an energy-level diagram (Fig. 8) by straight lines. The broken lines join

S I D N E Y I. M I L L E R

214

states of the same symmetry but involve symmetry “cro~sings’~ and are forbidden; under these conditions, a symmetry change must occur between reactant and product. Such a switch sometimes may appear to be favorable on an energy scale; but it is known that such nonadiabatic transitions are forbidden, a t least between electronic states of any molecule, and this same prohibition is assumed here. (In the present context, the word “forbidden” only indicates that the process in question requires relatively more energy than a comparable “allowed” process.) With regard to Fig. 8, ground state cyclobutene goes smoothly to ground state butadiene in the conrotatory mode; in the first excited state, the allowed change a2mr*(B)+ $1&$h4(B)would produce a product in the second excited state and therefore has a high energy requirement. I n the disrotatory mode, ground state cyclobutene is symmetry-related to the second excited state, I,@$:, of butadiene and would be energetically unfavorable; in the first excited state, 2nw*(A”), the change to the first excited state, $&b2$8(A”),of product is both energetically accessible and allowed. On the basis of state correlation diagrams we may occasionally make predictions a t variance with those based on orbital correlation diagrams, especially where radical species are involved. Consider the three atom electrocyclic process (34) with reference to Table 3 and Fig. 9. The most

(m=

+ ,*,

or -)

TABLE3 Orbital Symmetries in the Electrocyclic Process: Cyclopropyl + Allyl __.-

Symmetry Conrotatory Mode Disrotatory Mode

a b a’ a”

Cy clopropyl radical U

Allyl radical $2

m, a*

u,?I a*

*3

*I* $3

4s

favorable mode for thermal ring opening (or closing)is disrotatory for the cation and conrotatory for the anion. The most favorable mode for ring opening (or closing) of the first excited state is just the reveroe of those given for the ground state. Both orbital-symmetry and state-symmetry correlations lead to the same results, in these cases. Judging from the

STEREOSELECTION IN STEPS OF ORGANIC REACTIONS Disrotatory Mode

Conrotatory Mode

a*@")

oyclopropyl

cy clopropyl radical

216

ally1

allyl radical

-,

cyclopropyl

cyclopropyl radical

allyl

allyl radical

'f

E

oW(A)

cyclopropyl anion

.

#12#22(A)

allyl anion

cyclopropyl anion

allyl anion

FIG.9. Conversion of cyclopropyl species to dlyl species. Conrotatory changes are on the left; disrotatory changes are on the right. Upper section: alternative modes of ring opening and orbital correlation of cyclopropyl species. Middle section : symmetry state correlation of radical. Bottom section : symmetry state correlation of anion.

trend and pattern of energy levels, one must conclude that thermal conversions in the ions would occur more readily and be more stereoselective than those of the radicals. Longuet-Higginsand Abrahamson (1966) arrange the electronic states of allyl radical: +&b2 -+,bl@ < @t,h3 <@&. This order is not apparent from the energy-level separation one obtains by simple HMO theory,

216

S I D N E Y I . MILLER

e.g. Fig. 1 or the upper portion of Pig. 9 (Zimmerman, 1966). The order would be evident, however, if overlap were not neglected in the HMO procedure, since the gap between z,hl and i,b2 would be reduced and that between z,h2 and z,h3 would be enlarged (Coulsonand Streitwieser, 1965). I n both reaction modes, ground state reactants correlate with excited state product. The state symmetry correlation indicates that the thermal conrotatory process is slightly favored; the same result would presumably be obtained from extended Huckel calculations. The state-symmetry correlation also indicates that electrocyclic radical interconversion favors a conrotatory path from the first excited state and a disrotatory path from the second excited state. Because of the proximity of the energy levels and the violations of the noncrossing rule, it is probable that the excited state process will not be highly stereoselective. The same detailed considerations must be applied to the five-atom five-electron system and yield the results given in Table 1. Differences between the stereochemical predictions of Table 1 and those of others (Woodward and Hoffmann, 1965a; Fukuiand Pujimoto, 1966b; Zimmerman, 1966) tend to be limited to the excited-state reactions of odd-atom radicals. Occasionally, only several of the 7~ centers of a polyene are involved in reaction. I n these cases it is worthwhile to look into the orbital symmetry of the critical centers. (See Coulson and Streitwieser, 1965, or Heilbronner and Straub, 1966.) The tropone-benzene rearrangement was examined in this way (Mukai et al., 1967). A disrotatory electro-

Atom

1

2

3

4

5

6

7

8

HOMO

-

+

-

-

-

0

+ +

+

LVMO

+ +

+

0

cyclic reaction at atoms 2 and 7 is allowed in the ground state and forbidden in the first excited state. Not all electrocyclic reactions are stereoselective. It turns out that none of the three of the possible interconversions between triplet cyclopropylidene and allene should show SS, according to an analysis given by Borden (1967).

STEREOSELECTION IN STEPS O F O R G A N I C REACTIONS

217

B. Cycloadditions The chemical aspects of cycloaddition (i+j) reactions have been carefully defined and discussed (Huisgen et al., 1964; Rhoads, 1963; Warrener and Bremner, 1966). Here, they shall simply be regarded as intermolecular electrocyclic changes involving two or more charged or

neutral alkenes (Hoffmann and Woodward, 1965a). Taking the simple view fist, as in Fig. 10, we ask whether the HOMO of one reactant and LVMO of the other have the same symmetry. These are syn cycloadditions. If LVMO and HOMO are not compatible, a “forbidden” or highenergy process would normally be necessary to effect cyclization ; otherwise, anti cycloaddition (Fig. 1Oc) might be possible, as will be discussed shortly. It may be even simpler to imagine the reactants as they would appear in the transition state and inquire whether one has an incipient aromatic system, i.e. Huckel (4n + 2 ) cycle ~ (Dewar, 1966; Fukui, 1965, 1966). If so, the cycloaddition is thermally allowed; otherwise, forbidden. The nature of these predicted closures would normally be reversed for reactions of the fist excited states. Several examples of allowed gyn cycloadditions follow, but the reader may recall the 4 + 2 Diels-Alder and retro Diels-Alder processes in equations (20)and (21),parts c and d, and the 4 + 2 dipolar cycloaddition in (26). ( 2 + 2 ) (Rudolph, 1967; Zeldin et al., 1967):

(2

8

+ 2) (Warrener and Bremner, 1966):

syn

a

syn

b

anti

c

FIG.10. Cycloaddition of ( k + 1 ) and ~ (m+ 1)n polyenes. The energies of the highest occupied (HO) and lowest vacant (LV) orbitals are shown for an unfavorable thermal cyclization (upper left) and a favorable cyclizstion (upper right). Below, three possible modes of favorable orbital overlap between the two polyenes are shown: from left to right, aymmetric+symmetricor aa;antisymmetric +antisymmefric or bb ;M6biue twist of one polyene fo sttain -urn

overlsp. These hsve ale0 been termed nym. e n snd ad<*respeotively.

S T E R E O S E L E C T I O N I N STEPS O F O R G A N I C R E A C T I O N S

(2+3), ( 2 + 4 ) (McGreer and Wu, 1967): H&z\ /c=c /CH3 H \CO OCH3

.

-

1

II&=N=N

..

H5c2acH3 H

CO.OCH3

+

I

cis and trans

+ + 2) (Blomquist and Meinwald, 1959) :

(2 2

“WX x x (4 + 4) (Paquette and Slomp, 1963)

(6

+ 4) (Paquette and Barrett, 1966) :

130”

__t

& R’

I

R

219

220

S I D N E Y I . MILLER

(6+6) (Tezuka et al., 1967):

The stereospecific cis-addition of diboron tetrachloride to alkynes and alkenes (37) may be interpreted as an interaction of the empty a-orbitals of the boron atoms with the .rr-orbital of the organic species. According to this picture, boron-boron bond breaking would lag behind boroncarbon bond formation. The transition state is a 4n + 2 Huckel aromatic (n=0), and thermal addition is allowed. If bond making and breaking were synchronous, this four-center reaction would be more like the u-r exchange reactions, which we shall discuss later. With regard to (37), there is a discrepant case in which an apparent trans addition of diboron tetrachloride t o cyclopentadiene has been found (Saha et al., 1967). I n (39),we have an example of a stereospecific formation of a pyrazoline. When pyrazolines are photolyzed, the elimination of nitrogen, if concerted, should be syn. This stereospecific product has been observed (McGreer and Wu, 1967). The pyrolysis of pyrazolines, if concerted, should be anti. It is not clear why this process turns out to be complex: in (39), one alkene is formed stereospecifically by an anti hydrogen migration, but two isomeric cyclopropanes are formed. Crawford and Ali (1967), find rather different product patterns in the pyrolysis of 3-methyl and 3,4-dimethylpyrazolines, and give evidence for diradical intermediates. The general problem of unstable intermediates in a step-wise process will be discussed in a later section. The apparent bimolecular photoprocess of fourteen centers (44) would be even more remarkable, if it were concerted. Barltrop and Hwp (1965), who discovered it, write a stepwise mechanism for cyclieation:

S T E R E O S E L E C T I O N I N STEPS O F O R G A N I C R E A C T I O N S

221

Finally, the simplest cycloaddition (1 +j)involves a one-center p orbital, e.g. X=CH2, NH, 0, S, etc. Singlet state 0, S, and CH, might react with alkenes and the syn process would be expected. This stereochemistry has been found with the additions of CH, and s, although the latter appears to be par of a multistep process (Gunning and Strausz, 1966). Unlike the reactions in which two polyenes react, as in (36), there is no a priori steric problem in making syn or anti bonds, since X is monatomic. The orbital pictures of Fig. 20b,c were drawn for another purpose, but illustrate this point as well. We shall return to l + j additions, when carbenoid reactions are discussed. The preceding approach applies, in principle, to any concerted cycloadditions involving three or more reactants. If the number of rr-electrons, k + l + m in 5 or k + l + m + n in 6, is 4n + 2, reaction is allowed.

5

6

Few examples of such polymolecular processes are known, however. Trimerizations of alkynes appear to be 2 + 2 + 2 cycloadditions, but

concerted mechanisms are unverified, e.g. (45) (Clemo and McQuillen, 1935), while atepwise processes are known e.g. for acetylene (Fields, 1967) or t-butylfluoroacetylene (Viehe, 1965). The bimolecular reaction, alkene+norbornadiene, (40), does seem to be a genuine example following the 4n + 2 rule. Fragmentations or cycloeliminations, which are the reverse of cycloadditions, appear to be more common. Although it is not at all certain that the specific examples of (46) (Kirmse, 1960) and (47) (Rosenblum and Moltzan, 1956) are concerted, they are at least representative of

222

S I D N E Y I . MILLER

inherently more probable 2 + 2 + 2 processes than synchronous trimerizations. When a cyclic polyene is large enough, it can exist in both cis- and trane-forms. Our approach t o polyene cyclization has tacitly assumed an all cis T chain in the form of a band or ribbon that would slip smoothly on to the surface of a cylinder of appropriate diameter. Should the orbitals of the two polyenes in (36) have a mismatch in their orbital symmetries, a single twist in the m band of one of them could remedy this (Fig. 1Oc). Cycloaddition would now be allowed and the reaction would proceed, provided other factors were favorable. Such cases of Hobius (Zimmerman, 1966), anti (Fukui and Fujimoto, 1966b) or axisymmetric (Lemal and McGregor, 1966), as opposed to Huckel, syn, or sigmasymmetric ring closure are unknown (or, at least, rare). A Mobius form has, however, been proposed a~ the key intermediate in the photochemical transformations of benzene (Farenhorst, 1966) in (48) in place of the disrotatory cyclization proposed by van Tamelen (1965).

I n their excellent review of multicenter photochemical reactions, Warrener and Bremner (1966) classify reactions by the number of participating centers, e.g. nC. When orbital overlap’of nonadjacent centers is involved, the label XnC refers to orbital overlap in alternate centers. I n equation (48) or (49) (Srinivasan and Sonntag, 1965) there

-90%

-10%

is an X4C product, and in (50) (Prinzbach and Druckrey, 1965),an X6C product. These examples of “crossed” bond formation may be electrocyclic andlor cycloaddition reactions. I n particular, the X4C reaction of butadiene is nicely oonsistent with two discrete disrotatory motions

STEREOSELECTION I N STEPS O F ORGANIC REACTIONS

223

involving atoms 1 and 3 versus 2 and 4 (Fig. 11) in HOMO & ,I (Warrener and Bremner, 1966).

FIQ.11. An electrocyclic X4C reaction for excited state diene, which gives bicyclobutane.

($8)

trans& or cieoid buta-

The stereochemical consequences of XnC reactions can be examined by the usual orbital symmetry correlations. The predictions for transtrans-butadiene are indicated in (51); closures from #2 (thermal) or t,h3 A

~

&

hvord, A A

(61)

A

(excited state) were considered. Note that the thermal reaction from the transoid configuration is not excluded, for it must lead to a trans-fused

bicyclobutane (Wiberg, 1968)! The thermal path in (51) is unfavorable, because of the necessary distortion of a bonding orbital; in the excited state, it becomes a matter of the species falling into the potential energy valIey of one or other of the stabIe products of (49) and dissipating its excess energy. In a fixed transoid configuration, only the X4C product can be formed (Dauben and Willey, 1962). Clearly, in the general X4C case, it would always be well to check both symmetry and steric factors.

W”bv cholestadiene

(52)

S I D N E Y I. M I L L E R

224

The course of several possible cycloadditions is given in Table 4. Here, orbital symmetry predictions have generally been confirmed by calculations of the energies for alternate paths (Fukui and Fujimoto, 1966b). Hoffmann and Woodward (1965a) emphasize that the selection rules apply only to concerted reactions; other factors, e.g. spatial inaccessibility, loss of 7-conjugation through distortion, entropy or energy factors, etc., may interdict an allowed path. On the other hand, numerous “forbidden” cycloadditions, e.g. thermal dimerization of certain alkenes (Huisgen et al., 1966; Ulrich, 1967; Hamer, 1967) and photochemical Diels-Alder reactions do take place (Warrener and Bremner, 1966). If any of these exceptional reactions turn out to be concerted, one would be compelled t o improve on the present fairly naive orbital picture. TABLE 4 Stereochemistry of syw-Cycloaddition Reactions of n-Systems in one Plane

Species 1

Species 3

C: (singlet)

2

c=c c=c

4 4 5

C==C (C=C)C.

c=c C==C c=c

c=c

(C=C)C+ (C=C)C. (C=c)CC==C

c=c

(c==C)a (c==C)Z (C=Ch

C==C

c-c

c=c

(C=C)z (C=C)3

n Electrons Thermal path

c=c

(C=C)z

6 6 6 6 6 7 8 8 8 8

10 10 10 12 12

Allowed Forbidden Forbidden Forbidden Allowed Allowed Allowed Allowed Allowed Forbidden Forbidden Forbidden Forbidden Forbidden Allowed Allowed Allowed Forbidden Forbidden

Photochemical path Forbidden Allowed Allowed Allowed Forbidden Forbidden Forbidden Forbidden Forbidden Forbidden Allowed Allowed Allowed Allowed Forbidden Forbidden Forbidden Allowed Allowed

a The “forbidden ” cycloadditions may become “allowed ” anti closures if sterically accessible.

To predict and understand the course of some simple cycloadditions, it may often be necessary to examine the orbital symmetry changes in greater detail. Several examples wiII be treated at different levels to

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

225

illustrate the approach. First, let us do the Diels-Alder ( 2 + 4 ) cycloaddition :

A straightforward orbital correlation, made in Pig. 12, indicates that the thermal process is favored over any excited state process. This has been supported by an extended Huckel calculation (Hoffmann and Woodward, 1965a). An orbital correlation and energy level diagram have also beengiven for 1,3-dipolarcycloadditions (Eckell etal., 1967),e.g. (26).

FIQ.12. Orbital symmetry correlation for the Diels-Alder process, cis-s-butadiene+ ethylene.

The analysis of ethylene dimerization (2 + 2) follows (Hoffmann and Woodward, 1965a; Orchin and Jaff6, 1967). Two molecules of ethylene each possess two orbitals, r 1 and rZ. When the molecules are brought together to form “square” cyclobutane, two u and two u* orbitals are formed. The relation between the two sets of orbitals is indicated in Fig. 13. Both sets of orbitals can be classified as symmetric (a) or antisymmetric ( b ) , with respect to the two planes u1 and uz a t right angles, which bisect the plane of the carbon atoms. The ranking of orbitals in Fig. 14 according to their energies is critical; this is best deduced by MO calculations(Hoffmann,1963),from spectroscopic information (Jaff6 and Orchin, 1962),or kfy analogy and intuition. A key point is 8*

226

SIDNEY I . MILLER

that the occupied orbitals are aa and ab in the ethylenes and aa and ba in the dimer. After the orbital levels or electronic states (Fig. 14)for reactants and products are correlated, it becomes clear that the dimerization should be difficult from two ground-state ethylenes, but facile from one molecule of ethylene in the first excited state and another in the ground state. 01

a2

8

01

01

01

-

1 aa

s

> I

orbitals

1: ab

ba

bb

U

’ orbitals

FIQ.13. Orbitals in the cyclodimerizationof ethylene.

The dimerization of acyclic polyenes in which all T bonds are lost would lead to the open structures of (54) and (55). A schematic orbital correlation diagram (Fig. 15) for process (54) shows that ally1 dimerization is improbable. The cyclization of higher acyclic polyenes, e.g. to cis-or trans-7 in (55),is subject t o a similar prohibition, but the formation of 8 is allowed. I n general, processes in which the products retain elements of symmetry inherent in the reactants are symmetry-forbidden; the argument used to demonstrate this is analogous to that used for ethylene. One dimerization of 1,3-butadiene, namely to 9, is unique :this

STEREOSELECTION IN STEPS OF ORGANIC REACTIONS

227

product has no symmetry so that there are no orbital-symmetryrestrictions. Were it not for the fact that 9 is highly strained, and a Diels-Alder reaction path (see equation (64)) is of lower free energy, the allowed

FIG. 14. Orbital and state symmetry correlations for the dimerization of ethylene. The orbital symmetry designations in the upper diagram are with respect to the planes of symmetry uyzand uzr.

228

S I D N E Y I. M I L L E R A

uzv

FIG. 15. Orbital correlation for the dimerization, allyl radical + allyl radical. The process is symmetry forbidden (Hoffmann and Woodward, 1965b).

process to 9 might be observed. The reverse reaction, i.e., thermal decomposition of 9 would perhaps be more accessible for study. The dimerization of ethylene is the first of another group of dimerizations leading to closed structures, e.g. in (56) and (57).

All of these are symmetry-forbidden. Consider the formation of prismane. As pictured in Fig. 16, the reactant orbitals are properly aligned, but

STEREOSELECTION IN STEPS O F ORGANIC REACTIONS

ad*,

~

229

os*(e")

cyclopropenyl

.

+

prismane

cyclopropenyl

FIG.16. Orbital correlationfor the dimerization of cyclopropenyl radicals to prismane, a forbidden process.

have not yet interacted. For the dimerization process to occur, a change in orbital symmetry would be required. I n fact, one ground would have to be raised to its excited state cyclopropenyl, (r1)2r2, ) ~ process r ~ ,(56)is allowed. The formation of cubane is state, ( ~ ~before equally improbable from ground-state cyclobutadiene (equation (57) and Fig. 17). Indeed, it can be shown that ground-state dimerization is

I

E

-os*(bzu) U?*(aZu)

~

m*m*(eg,

"1

wr*(b)

---t--. _ __-_---_-'--.I

wg, w3(e)

+---I--

=1(4

_____________

I I 0 3 , u4(eu9 I)

-

--re OZ(b2g)

cyclobutsdiene

+

o l ( d

cyclobutsdiene cubane FIG. 17. Orbital correlation for the dimerieation of cyclobutadiene to cubane, a forbidden process.

230 S I D N E Y I. M I L L E R improbable on symmetry grounds for this whole family of hypothetical reactions involving closed polyhedra. I n cases of this type, the construction of state-symmetry correlations is not obvious. One must work out the symmetry designations and relative energies of electronic states which involve degenerate (e) orbitals (Cotton, 1963; Jaff6 and Orchin, 1965);here, our energy levels are purely schematic. Another kind of cycloaddition and cycloelimination is found in the general process (58) in which X = Y can be N2, CO, N20, SO2, Cs, etc.

X=Y,

AB(C=C)kDE

, -

;fr”. (C=C),+

-2

I n all cases a branched r-system is involved and in some, e.g. NzO, there may be a change in shape of X =Y in the reaction. There are ground-state singlet species here, e.g. NzO,SO2, and triplet species, e.g. SO. Reactions between singlet and triplet species generally involve at least two steps, namely bond formation and spin inversion; the intermediate(s) need not be sterically stable (Gaspar and Hammond, 1964). The fact that sulfur oxide, probably a triplet, is ejected from 2-butene episulfoxides to yield

both alkenes may be indicative of partial equilibration of intermediates; the process is syn-stereoselective, however (Hartzell and Paige, 1967). Lemal and McGregor (1966) have provided data and a correlation diagram for the decomposition of cis- and trans-diazenes (Fig. 18). The novel feature of Fig. 18is the use of a p orbital of nitrogen in the reactants and crN and rN, orbital of nitrogen in the product. (Alternative bookkeeping schemes of orbitals and their symmetries, e.g. inclusion of lone pairs, are unnecessarily complex.) On the basis of the level diagram, the prediction is that thermolysis of pyrroline will produce a diem by the dismt.

dII

tram-tram

fi+ Ne

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS Conrotatory (allowed.)

231

Disrotatory (allowed)

A

p1

N

lkl II

Q I

111

N

8-I

I

Conrotstory (forbidden) (Axisymmetric, CI)

Disrotstory (allowed) [Sigmasymmetric. 0 " )

FIG. 18. Stereoselection in cycloaddition or fragmentation. Upper: two modes of allowed orbital change. Lower: decomposition of the diazene obtained from 3-pyrroline (Lemal and McGregor, 1966). Thedisrotatorypathisallowed; theconrotatorypath would involve a change in orbital symmetry and is forbidden.

disrotatory path, which is observed. Similarly, the extrusion of sulfur dioxide from sulfones (Saltiel and Metts, 1967) follows the same course. On the other hand, the conrotatory mode is followed in the photolysis of the sulfones of (61). Along the same lines, Baldwin (1966) cites evidence for the nonconcerted thermolytic decarbonylation of cyclopropenones and cyclopropanones, as opposed to the concerted facile reactions of d 3-cyclopentenonesand A 3-2-oxacyclopentanones. For the general equation (58), the conrotatory mode is associated with

232

SIDNEY I . MILLER

?

trans

Cis

cis-trans

trans-trans

a symmetry axis (C2), and the disrotatory mode is associated with a plane of symmetry (uV). Disrotatory processes are thermally allowed for even k and conrotatory processes are allowed for odd k. Reference to Fig. 1 for orbital symmetries may again be helpful. I n the first excited state, the simple picture associates even k with concerted conrotatory and odd k with disrotatory processes. Apparently similar reactions do not, however, follow these orbital symmetry rules. According to Neureiter (1966), addition of sulfur dioxide to alkenes or its subsequent elimination appears to be synstereospecific instead of anti, as predicted. According to Freeman and

Graham (1967), reaction (62) is considered to go through a diazene intermediate, in which case, an anti process, instead of the observedsyn, would again be predicted. It is true, however, that the three-membered rings are unique in one respect-the syn product is essentially preformed in the reactant and no rotation is needed to get to the product ;the anti product requires a 180" rotation. If these apparently molecular reactions were homolytic or heterolytic, a syrt product (88# 1) would still be plausible. These are two among several factors that can be opposed or parallel to the symmetry factor. At this stage, more experience is needed with a variety of cyclic compounds, particularly with the exceptional threemembered rings, to sort out the complexities in process (58). For the concerted decomposition of N-nitroso compounds in (68), we require only that the orbitals labeled pNand crN can be deleted from Fig. 18. Now, a disrotatory change is allowed for the three-membered ring and forbidden for the five-membered ring. The elimination of dinitrogen oxide from N-nitrosoaeiridines is syn stereospecific (Clark and

S T E R E O S E L E C T I O N I N STEPS O F ORGANIC REACTIONS

233

Helmkamp, 1964), while the same reaction with N-nitroso-3-pyrroline appears to be slow and produces several products beside the alkene. Although McGregor and Lemal(l966) suggest that group interference as well as unfavorable effects on 7r-overlap would result from a conrotatory change in their system, these reasons are not convincing, since other conrotatory processes (61) do take place in five-membered rings. Beside the primary problem of whether or not a cycloaddition is allowed and with what orientation, there can be another stereochemical question. I n the Diels-Alder (4 + 2) cycloadditions, the preferred formation of endo adducts has long been recognized. It has been suggested that orbital overlap in the incipient bonds is simply more efficient in the

+

+

endo

exo

endo form (Herndon and Hall, 196713).Hoffmann and Woodward (1965b) propose that orbital symmetry can provide a rationale for the preferred endo product in some cycloadditions and the preferred exo product in others. Consider the Diels-Alder reaction of 1,3-butadiene with itself. From Fig. 1, we note that HOMO and LVMO are b and a respectively, or as pictured in Fig. 19. The two endo and one exo modes of forming product are also indicated. Only in the endo case is favorable overlap or “secondary interaction ” possible between non-bonding orbitals. I n the endo-2 transition states the secondary interactions could conceivably lead to full bonding, as discussed previously (55). That this does not happen may be a reflection of the steric strain in such a product; nevertheless a r need not involve appreciable strain. Herndon and weak ~ - 7 interaction Hall (1967a) and Hoffmann and Woodward (1965a)have used extended Huckel calculations in a few cases to show that this favorable secondary interaction contributes to a lower energy path. The LVMO of maleic anhydride and benzoquinone, or +,(MA) and +6(B&)respectively, are both b ; this pair are more reactive than two butadienes and of course favor endo addition. Similar reasoning would favor endo cycloaddition for a 2 + 2 + 2 system. By similar juxtaposition of orbitals, other allowed cycloadditions can

234

SIDNEY I . MILLER

favor either endo or exo products. The 6 + 4 cycloaddition is thermally allowed-see (42). Here, an ezo product would be favored, because the nonbonded interactions in the endo are repulsive-see Fig. 19: the orbital symmetries of t,h2(4) and t,ba(6) match at the ends of the chain but not in the middle.

endo-l(2

+ 4)

?( 4 + 4

undo (4

+6 )

FIG.19. Cycloadditions. Full lines between molecules represent incipient bonding; broken lines represent favorable secondary interactions. The endo (2+4) proceea is preferred over the ezo (2 + 4) process. The e r o (4 6) process, which is not shown, is preferred over the endo (4 + 6) procesa, which is shown.

+

+

+

Hoffmann and Woodward (1965b) consider possible 2 2, 2 4, and 4 + 4 reactions of cyclobutadiene with itself. The fact is that the 2 + 2 and the 2 4 processes are not distinguishable, but the result is an endo favored cyclization (64). We have already discussed the forbidden 4 4

+

+

+

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

235

cycloaddition (57) which would lead to cubane. If, instead, the 4 + 2 cycloaddition occurs, orbital degeneracy is removed from the product orbitals. There would be no forbidden level crossing, as in Fig. 17; moreover, the nonbonding orbitals now overlap favorably, so that endo addition is favored. Thus far, orbital-symmetry requirements of any reaction have been met by changing the reaction conditions. Another possible approach is to change the orbital-symmetry requirements by adding a third reactant. Volger and Hogeveen (1967) effected the thermally forbidden 2 + 2 cycloaddition by adding transition metal catalysts,

while Mango and Schachtschneider (1967) showed how, in an orbital correlation diagram, such catalysts can raise the Woodward-Hoffmann prohibitions. The metal or metal ions may provide “ a template of

atomic orbitals ” through which symmetry- and energy-allowed changes can proceed. The uncatalyzed forbidden 2 + 2 + 2 + 2 reaction (66) becomes allowed when nickel is a co-reactant. The ability to turn the selection rules on and off at will is of obvious practical significance.

C . Sigmatropic Migrations Woodward and Hoffmann (1966b)d e h e a sigmatropic change of order [ i , j ] as the migration of a o-bond between X and Y in which one of

236

S I D N E Y I. MILLER

them usually has at least onedouble bond. Theconcerted Claisenrearrangement (Rhoads, 1963) is of order [3,3], the Sommelet reaction is of order [2,3], and the Stevens rearrangement is of order [1,2] (Zimmerman, 1963). We shall distinguish two different sigmatropic changes, which we represent schematically in Fig. 20, namely the migration of a group via a sigma orbital or by a pi orbital.

As an example of hydrogen migration [l,j] consider the transfer between the ends of an all cis polyene, in which the p atomic orbitals are given explicitly. If one imagines a uZ. plane through rr-orbitals of the transition state, the hydrogen atom may be transferred wholly on one side of the plane, suprafacially, or from one side to the other, antarafacially. The symmetry of the LVMO of the reactant rr system is critical in determining how the hydrogen is transferred (Fig. 20). The stereochemical predictions are indicated in Table 5, and the extension to the shift of a chain of i atoms is given in (70) :

The problem may be restated in terms of the symmetry of all of the orbitals involved. I n the transition state the pair of electrons forming the sigma bond to hydrogen may now be considered part of the rr system ; the hydrogen will move suprafacially or antarafacially depending on whether the HOMO is a or b. For (4%+ 2)rr electrons a thermal change is allowed, and for (4n)rr electrons a first-excited-state process is allowed. To include charged species in (69), the length of the chain must be appropriate. When j is odd, m=O; when j is even, ’m may be + (cation), (radical), or - (anion). The latter group of reactions comprise rearrangements of “some” as opposed to “no” mechanism. The predictions are included in Table 5. It will be noted that the vast number of 1,2-shifts in carbonium ions are included in the entry j = 2, m = + . A number of allowed thermal [1,5] rearrangements of the following types have been observed; (Ter Borg et al., 1967):

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

237

TABLE5 Stereoselection in Sigmatropic Reactions or Rearrangements: j

(p)T-I--C-M

1 + M-C--(p)Y-I.

-

C4jl

Symmetry-allowed u-orbital migration

m.

1,4

+

Thermal

1st excited state

Antara a Supra Antara Supra Antara Supra Supra Antaraa Antara a Antaraa Supra Supra

Suprab Antaraa Supra Antaraa Supra Antara Antara a Supra Supra Supra Antaraa Antaram

Symmetry-allowed n-orbital migration Thermal

1st excited state

Supra Antaraa Supra

Antarea Supra Antada

a A symmetry-allowed antara migration, which probably cannot proceed, because the migration terminus is inaccessible. * I n excited-state heptatriene, the allowed [1,3]reaction is antara (see footnote a).

(Crandall and Watkins, 1967) :

Go

e f J 0

/

(Keshelikar and Fanta, 1960; Roberts et ul., 1967):

+f H0 / /

(73)

HAoYN

Photochemically allowed processes have also been reported : [1,3], (Wehrli et ul., 1963):

L.A/-+w

0

0

1 Oa-testerone

(Borden et al., 1967):

(74)

238

S I D N E Y I. MILLER

It should be clear that the selection rules apply to concerted processes between spatially accessible parts of a moIecule. Antarafacid [1,3], [1,5], or [3,3] reactions involving a-orbital transfers between carbon atoms are not possible. Antarafacial migrations do become feasible when the transition state forms a cycle of at least 7 or 8 atoms; Woodward and Hoffmann (1965b) cite the [1,7] example (76).

precelciferol

calciferol

Sigmatropic reactions which need not involve hydrogen have already been indicated in (67) and (68). To these we add carbon migrations. (Schutte and Havinga, 1967):

(yo3 O

R

*

(&OR)

&coR

(77)

(Doering and Roth, 1962):

(Jones and Jones, 1967):

Woodward and Hoffmann (1965b)also pointed out the possibility of a sigmatropic change involving a v orbital. Figure 20 indicates the frontier orbital viewpoint. This sigmatropic shift can involve any migrating center which possesses a p orbital. We should expect, therefore, that in systems of the type 10 in which X has an accessible u or p orbital, that

10

x-cc=c-(i

c

1

E-1

S T E R E O S E L E C T I O N IN STEPS O F O R G A N I C

REACTIONS

239

all sigmatropic reactions should be allowed, as far as orbital symmetry is concerned. The decomposition of nitrosoamides (White and Dolak, 1966), which involves a [1,3] migration could be such a case, but there is no way to check this a t oxygen or nitrogen. O=N Ar-C-N-R

I __f

II 0

a

Ar-C

I

N-R

--+

Products

d

C

QV

suprafacial (syn)

suprafacial (syn)

antarafacid (anti)

(80)

antarafacial (anti)

FIQ.20. Orbital pictures of cycloaddition of order [l +f or sigmatropic changes of order [i,f. For the cycloaddition, the center orbital is on one atom, e.g. X of equation (68); it may be u or p , in 8 and b or p y in c and d. For the sigmatropic change, a u bond migrates in a and b and a u or a r bond migrates via a ?r orbital in c and d.

Berson and Willcott (1966) have used the all-carbon rearrangement of an optically active trisubstituted tropilidene (11) to formulate the

lla

llb

llc

oversus rr choice in intriguing style. Because of the ease of the tropilidenenorcaradiene interconversion as in equation (32) (Berson et al., 1967), it is assumed that the isomers of 11 actually arise from [1,5] sigmatropic changes in norcaradiene :

210

S I D N E Y I . MILLER

Depending on whether the starred carbon of 11 pivots so as to bond backside or frontside, there will be a 60" (82) or 120" (83) periodicity in the motion around the remaining carbons. The 60" pattern allows for racemization in two ways: if the starred carbon passes over the marker substituent M,the species develops a plane of symmetry; if the starred carbon never passes over M, it still leads to dl-pairs of nocaradiene or tropilidene. The 120" pattern does not allow for racemization so that optical activity in the isomers of 11 would be preserved. According to the orbital symmetry rules (Fig. 20a), the [1,5] suprafacial shift is allowed: the 120" pattern with retention should be the one observed, if the proposed mechanism is correct. Pending solution of the stereochemical puzzle of (82) versus (83), Berson and Nelson (1967)have found a [I, 31 sigmatropic reaction, which appears to proceed suprafacially with inversion. They point out that,

notwithstanding the complexity of the process and the distortions to attain the transition state, the orbital-symmetry requirement prevails. This complements and strengthens the whole concept of selection rules for sigmatropic shifts. Just as there are secondary interactions in cycloadditions, so too are there ancillary orbital-symmetry effects in sigmatropic reactions, In process (79), Jones and Jones (1967) find no products of [1,3] hydrogen or methyl shifts, e.g. 174,7-trimethylheptatriene,which ostensibly (Table 5 ) are photochemically allowed. They point out that in the first excited state of heptatrienyl radical, with # 5 ( + - - + - - +), the relevant reaction termini are not supra- but antarafacially related. In a similar case, [1,7] sigmatropic shifts occur in l-methoxycycloheptatriene, but subsequent [1,7] shifts do not. By including the p pair of electrons from the oxygen, Borden et al. (1967), show that suprafacial ( - 0 + - 0 + - ), of a ten-electron transfer in the first excited state eight-atom system is symmetry-forbidden in (85). A given sigmatropic migration may be allowed in a short polyene but forbidden in a longer one!

+

OR

STEREOSELECTION I N STEPS O F ORGANIC REACTIONS

241

The 3,3-shift, as in the Cope or in the Claisen, rearrangements provide

interesting stereochemical alternatives (Rhoads, 1963). Theoretically, six-center reactions may take place through a “chair” or “book” transition state. For both reactions, conformational and secondary

orbital symmetry factors suggest that possible “book” transition states are energetically less favorable than chair transition states. The conformational aspect of the problem is illustrated in a nitrogen analog of the Claisen rearrangement (Hill and Gilman, 1967). We need not belabor the point that the bulky groups prefer to be equatorial in the transition state. By constructing a correlation diagram, part of which is given in Fig. 15, Hoffmann and Woodward (1965b) showed that any tendency

10% (relative)

242

S I D N E Y I. M I L L E R

for orbital overlap between atoms 2 and 5 , as in the book forms, takes one on the high-energy path which ultimately leads to a bicyclohexane. On the other hand, the chair form minimizes such overlap; the orbital correlation for this transition state indicates a suitable low-energy path. They make the point that these are small secondary effects. I n fact, lower selectivity and even exclusive book-like transition states may be expected, especially where there are steric or spatial restraints, e.g. (Rhoads, 1963):

c-0 Fukui and Fujimoto (1966a) suggest that an overlap or bond-order criterion is another way in which secondary interactions may be examined. If benzene is assumed to be a crude model for the transition state of the [3,3]sigmatropic reaction, it is easy to show that P,,for the three orbitals is 2(pL5+p& +p&)= - 0.33. The negative bond order indicates repulsion. Therefore, the concerted [3,3] sigmatropic reaction prefers the chair transition state in which atoms 2 and 5 are as far apart as possible. I n the vinylogous Cope [5,5] rearrangement, Fukui and Fujimoto (1966a) find that the 2,2' and 4,4' antibonding character outweigh the 3,3' bonding character in the cisoid form. Therefore the chair transition

chair

cisoid

state is favored. This result had previously been obtained by Woodward and Hoffmann (1966b)from orbital correlation. Finally, there is an interesting example of a forbidden [1,3] sigmatropic change mentioned by Mango and Schachtschneider (1967),which proceeds because of the presence of cobalt hydrocarbonyl.

STEREOSELECTION IN STEPS OF ORGANIC R E A C T I O N S

243

In this work, some care was taken to verify the intramolecular 1,3 shift, and evidence was cited for an analogous catalysis of the isomerization of 2-methyl-1-pentene (Roos and Orchin, 1965).

D. Sigma-Sigma and Sigma-Pi Switch We complete molecular reactions with a group in which a-bond changes are prominent. This section will also serve to effect the transition from the no-mechanism to the some-mechanism categories. As indicated earlier, our classification serves mainly to divide up a large body of material. From the point of view of orbital correlations, there is nothing in a-IJand u-r exchange processes that restricts them to one mechanistic class or the other. This is illustrated by some of the possible reactions involving four centers, in which the formal similarities are stressed. ABCD

(4

+ BCDA A +BCD

(b)

AB+CD A+BC+D A+B+C+D A+BCD PABC+D AB+CD A+B+C+D AB+CD +AC+BD A+B+C+D

(c)

(4 (e)

(f) (8)

(91)

(h) (i) (j)

The 0-0 switch or exchange are terms we use for reactions such as (91), (92).

x-x

+

Y-Y

x..-x x x Fzi

i + J + J

Y...Y

Y Y

(92)

In (92), there is a four-center exchange of u bonds. I n principle, sixcenter trimolecular reactions involving three diatomic molecules could be in this group, providing only u bonds are permitted. Although several elementary reactions of the type (92) have been studied (Glasstone et al., 194l), there appear to be few gas-phase processes which follow this indicated mechanism. The once-classical example of a bimolecular reaction, i.e. hydrogen iodide decomposition (93),is actually a multistep RI+HI

+R H + I ~

(93)

process (Sullivan, 1967). Nevertheless, we shall need to refer to examples of (92) in discussions of polar gas-phase reactions (Benson and Haugen, 1966) and in certain condensed-phase heterolytic process, e.g. electrophilic substitution. At first sight the orbital changes in (92) appear to be similar to that in the dimerization of ethylene, or forbidden in the ground state.

S I D N E Y I. M I L L E R

244

But (92) is different. Since there are four u orbitals to consider, thereis an additional symmetry plane here. If the atomic orbitals are suitably combined pictorially, according to the general plan of Fig. 13, or analytically, one would find t,b2 and t,b3 to be degenerate. That is, the energy gap one has in the second and third MO's for the dimerization of ethylene (Fig. 14) vanishes ; the process becomes symmetry-allowed. The u-n switch is simply a four-center addition (elimination): there is a net loss (gain) of a n- MO and a gain (loss) of a u MO. Orbital symmetries have been indicated beside reactants and product in (94).

Evidently, symmetry is not conserved with respect to symmetry planes through coplanar reactants or products : the reaction is forbidden! An alternative mode of addition to that in (94) involves an orbital-symmetry switch about a C2 axis, and is forbidden as well. Y x=x I

I

-

Y

x+ y...'

.'

(95)

c';

Consistent with this prohibition, we do not have concerted reactions of the type

I I

+

-C=C-

I

R-R

-CR-CR-

I (96)

Moreover, most gas-phase additions of hydrogen or halogen molecules to alkenes appear to follow radical chain processes (Maccoll and Thomas, 1967). But there are a series of u-n exchanges, studied mostly as gas phase eliminations, in which the molecular component predominates, or can be made to predominate :

I I -c-cI I

d , c

I I

+

-C=C-

H-X

(97)

O=S=O

(98)

H X

R&-0

I

Cl-S=O

I

I3

c1-c=o

A __+

TL

R3CCl

+

I I

-C-CCl

I

-C=CI

'

I

+ o=c=o

+ HC1 f COI

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

245

Equations (97)-( 99) seem to involve violations of symmetry conservation, as in (94). There is, however, a basic difference between process (96) and (97)-(99), for in the latter a nonbinding orbital of X can bond to LVMO or t,h2 of the alkene. The orbital picture in 12 implies

12

a high degree of polarization in the transition state for the eliminations of (97), which in fact had been deduced from both experimental data and theoretical considerations (Maccoll and Thomas, 1967 ; Benson and Bose, 1963; Benson and Haugen, 1965). We know of no theoretical calculations which support the orbital switch inherent in 12, but it does seem to provide a plausible allowed path for certain observed processes. Another special kind of u-Z-switch involving a 5 MO and a Z- orbital is allowed. Taking singlet methylene as an example-any singlet atom will do-we note that its T LVMO can interact with HOMO of a carbonhydrogen bond. A typical insertion reaction is given in (100) (Kirmse, 1964) :

Elements of all of the previous reaction types, electrocyclic, sigmatropic, cycloelimination, o-exchange processes may be present simultaneously : R R

R R ,,-is

I 1

R'-C=C-B'

me80

I I

R'-C-C-R'

/

H

+ H

\

N=N

H

+ H /

\

(101)

S I D N E Y I. M I L L E R

346

I I I I

-c-c-

H 0-H

+

I I

__t

-C=C-

+

HBr

+

HOH

(102)

Br-H

Note that (104) (Barton and Brooks, 1961) is selective; the alternative %membered transition state was avoided. The extension of the Woodward-Hoffmann type of arguments to such examples should be simple at this point. It must be admitted that u-u and u-7r switch processes are of limited stereochemical interest. Given the prototypes (92) or (97), the reactions must be syn-stereospecific; any other stereochemical result would in fact be used as a criterion of a multi-step mechanism. This is also true of the “mixed” types, (101)-( 104). But these reactions are exceedingly useful as models for orbital-based calculations or estimates of free energies of activation, with the use of extended HMO theory. The four- or six-center process (92)-(104) does not appear to be more complex than the DielsAlder reaction, which has been investigated theoretically (Herndon and Hall, 1967).

E. Substitution at Saturated Atoms Fukui and Fujimoto (1966b) consider stereoselection in cases of u-7r interactions a t carbon. With respect to substitutions, the qualitative frontier-electron viewpoint is adequate for a general view of the field. It is of little help, however, in sorting out the numerous and subtle variations in the kinds of substitution a t a single center. The general equation for substitution is given by (105). I n the Y+(C=C)t-c-x

-+ Y . . *c,. . . x

--f

Y-(c=c)k+x

(105)

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

347

transition state, the entering and leaving groups are pictured as partly bonded to the ends of a conjugated system. Although the orbitals on the terminal carbon atoms interact with the T system and presumably are part u and part T at the transition state, it is convenient to look at the transition state as a T chain (Fig. 21). An electrophile will attack HOMO and a radical or nucelophile will attack LVMO.

--(ah

b syn

a

c anti

FIQ.21. Idealizedconcerted bond making and/or bond breaking in conjugatedpolyenes in substitution, addition and elimination.

The predictions based on this approach are given in Table 6, where 7r system-the corresponding terms used for displacements are usually retention and inversion. There is, of course, an overwhelming amount of data for two or three of the possible cases covered in this table and little or nothing syn and anti refer t o a symmetry plane through the

TABLE6 Stereochemistryin Displacement Reactions, Y + (C=C)&--C-X + Y ...Cj ...X j 1

3 6

I

T

electrons Y, electrophile 2 4 6 8

SYn Anti SYn Anti

7r

electrons 3 or 4 6 or 6 I or 8 9 o r 10

Y, radical or nucleophile Anti

SYn

Anti Syn

on the others. I n the limiting forms, unimolecular electrophilic (SEl), homolytic (SHl),or nucleophilic (S,l) substitutions produce unstable intermediates for which one or more counter-species compete. We shall not deal with these multi-step processes here in any detail, although some kinetic schemes will be examined later. For although individual molecular acts are stereospecific (stereoelectronic axiom l ) , it is still

248

S I D N E Y I . MILLER

difficult to predict which stereochemical course will be favored (axiom 2). It is interesting that the order and kind of complexity in the scheme that is needed for one kind of substitution, e.g. S,1 (Ford et al., 1967)is typical of all of them. In this section, we shall cite examples of what seem to be well behaved elementary processes and return to certain problem areas later. Bimolecular electrophilic reactions (S,2) involving hydrogen exchange a t a saturated center are rare. Although retention a t tetracoordinated H' (106)

nitrogen has been reported for (106) (Menger and Mandell, 1967), a corresponding reaction at carbon seems to be unknown (Reutov, 1967a). The relatively low proton affinity of a species such as CHI (Rutledge and Saturno, 1965) is certainly pertinent. Hogeveen and Bickel(l967) have discovered that a proton can displace a good leaving (CH3)sC--CH3

H+SbFe-

(CH3)3CC+CH4

(107)

carbonium ion. They raise the interesting question of a backside or frontside S, attack of the proton. By contrast, prototropy a t sp2 carbon, e.g. in polyenes such as in trans-$-ionone, 13, or a-ionone, 14 (Roest et al., 1967), is well known.

ia

14

Nevertheless, we are not aware of a displacement, e.g. (105)with Y = H+ displacing X = H+ in which SS is indicated. Complementary reviews on the subject of electrophilic displacements at a single carbon center agree that substitution with retention is the general rule (Reutov, 1967a and b ; Thorpe, 1966; Dessy and Kitching, 1966 ; Cram, 1965). These include carbonation of organolithiums, metal ion interchange, metal-halogen exchange, demetalation, etc. However, the mechanisms of these reactions are not always well defined : they are heterogeneous or take place within ion aggregates; they show complex kinetics; they are subject to medium effects, etc. When the transition states are cyclic, substitution with retention is unavoidable.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

249

Acidic deboronation (Brown and Murray, 1961), which goes with retention, probably involves a four-center transition state 15, in which HA

15

16

18

17

is the attacking acid. Likewise, mercury exchanges and demercurations often involve cyclic transition states 16-17 and go with retention. Demercurations with acid may involve cyclic transition states, but there is also evidence for an open one, 18. The rate constant for acid cleavage of allylmercuric iodide has the form (Kreevoy et al., 1967)

k

= kH(H+)

+ kHA(HA)

in which the first term corresponds to 18. The chlorination of optically active sulfides (Kwart and Strilko, 1967)

proceeds with retention in the absence of added salts, and with inversion and/or racemization in their presence. I n focusing on the first and simple process, we are oversimplifying an interesting sequence in which stereoselection may occur at several intermediates and/or ion pairs. The preceding SE2 examples have been in accord with the orbital symmetry prediction of Table 6. Matteson and Bowie (1965) give an S x example which is contrary:

* a+ \ / 8 7 D-C~HSCH. CHsB(OC4Hg)z % (Cl-Hg...C---B\)

I

-+

L-C~HS~H(CH~)H~CI

(110)

Although we have assigned a structure to the transition state so as to obtain the observed inversion, the coordination of solvent or chloride at boron and mercury is actually unknown. Ingold (1962) and Thorpe (1966) have suggested that S,2 reactions which go with inversion probably involve transition states in which bond formation lags bond 9

250

S I D N E Y I . MILLER

breaking; when this happens the orbital is rather more developed on the backside and the electrophile is directed there. This condition is sufficient but not necessary, as we shall show later. With regard to an allenic center, Matteson and Talbot (1965) have given the reaction ( 1 11) ;

consistent with the predictions of Table 6 the transition state is sixelectron, seven-center ( j= 5 ) . Here, a,bs of penta- or hepta-trienyl (Fig. 1) would be the significant orbital. This is symmetric so that both the entering and leaving groups should be exo (syn). This speculation should be tested. The orbital requirements for radical attack on any polyene are given in Table 6. If Hs, HC2and Cls (see Walsh diagram, Fig. 2) can be taken as models, then three-center transition states will be linear. If, however, cyclic transition states can be formed, HMO theory indicates a preference for them (Fig. 1). Unfortunately, attempted radical displacements have not been observed, simply because the radicals take other reaction paths (Pryor, 1966). The transition states may have been linear, but for abstraction from rather than displacement on carbon (Bujake et al., 1961). If the radical and molecule generated in these cases remain in I*

+ D-CH3.

I-I*

CH(CzH5)I

+ CH3.CH .CzH5

-#-+

__f

L-I*CH(CHs). CzHs

D, L--CH&H(CzH5)1*

+I +I

close proximity, e.g. in a solvent cage, overall exchange with retention would be a possibility. As it is, they presumably diffuse apart, the carbon radical inverts and loses configuration. According to Pryor (1966), chlorine radical attack on cyclopropane with ring opening could be an example of backside SHattack. It is interesting that energetic atoms such as chlorine CIS’ (n,r), ClS8, tritium, or carbon substitute for like atoms with predominant retention (Wai and Rowland, 1967 ; Wolf, 1964). These substitutions by “hot ” atoms probably involve head-on atomic displacements on

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

251

impact and are wholly beyond the energy range of the reactions we are considering. The state of the art and theory of bimolecular nucleophilic substitution (S,2) at carbon may be summarized: not all processes that go with inversion are SN2, but nearly all SN2 processes go with inversion. Over the past thirty years, Hughes, Ingold et al., took the view that "the exclusion principle would always defeat electrostatics " and produced a series of examples of various charge types in which SN2processes went with inversion (Harvey et al., 1960; Hoffmann and Hughes, 1964). DCeHtj*CH(CH3)CI+CHaS- + L-C@&*CH(CH3).SCH3+Cl-

+

(113)

L-C~H~*CH(CH~).S(CH~)Z+NT -+ D - C ~ H ~ * C H ( C H ~ ) N ~ + ( C H (114) ~)ZS D - C ~ H ~ . C H ( C H ~ ) B ~ + H Z N -+ C =L-CaH5.CH(CH3).SC(NH2)2+BrS (115)

+

D-CaH5'CH(CH3).S(CH3)2+H2NC=S

+

+

-+ L-CsH5'CH(CH3).SC(NHz)2 (CHa)2S(116)

Apart from overcoming coulombic repulsions, s N 2 reactions also proceed with inversion in the face of steric hindrance. By comparison, the stereochemical result of unimolecular nucleophilic substitution SN1 is variable. I n fact, nucleophilic substitutions at carbon with retention invariably follow other than s N 2 paths. I n its broad outlines, the Hughes-Ingold approach swept away the confusions of the period 1895-1933 and has not ceased to stimulate and provoke ideas in the area of substitution reactions. Surprisingly enough, the theoretical foundations of the SN2 process require reexamination and modification, as we shall see. There are few examples of sN2 reactions of stereochemical interest with j> 3 in (105). I n fact, Stork's examples seem to be the only ones known (Stork and White, 1956; Stork and Clarke, 1956).

R

R

This is a case of allowed syn entry and departure ;in Table 6,j= 3 and the number of electrons is 6. Oxotropy, a nucleophilic process (Mackenzie, 1964), could be stereoselective, but we are not aware of any relevant examples. . H AcO-+ ( C 4 ) e C O A c -+ AcOC--(C=C)k+HOAo +

(118)

S I D N E Y I. M I L L E R

252

Because of its overriding importance, we now wish to look more closely at substitution at a single center. Earlier, we indicated the bonding arrangements of a three-center system that result from VB or MO theories. According to bonding theory, the geometry of a pentacoordinate species is subject to any restrictions imposed by, or inherent in, orbital symmetry. Secondly, the Pauli principle is satisfied when the orbitals are properly chosen to form an orthogonal set. The hybridorbital approach is useful for specifying possible geometries (Gillespie, 1952; Dewar, 1953). These conditions are met in 20-24, in which the transition state for substitution at atom A in tetrahedral XAR1R2R, or 19 may have the entering (Y) and leaving (X) groups in any one of several configurations, e.g. 20-24. Y

I

19

22 Cb (sp”spd)

R

R

It is highly probable that transition states of carbon do not involve d-orbitals (Van der Voorn and Drago, 1966; Hudson, 1965). But the inaccessibility of bonding orbitals beyond four only restricts the average

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253

number of electrons around carbon to eight, without regard to coordination number and geometry. Subject to the conditions outlined, several pentacoualent transition states and 8, intermediates are allowed ;S , or SN intermediates are precluded. To choose the preferred path, one must compare transition state energies. The results of Van Der Voorn and Drago (1966) on phosphorus (V) chlorofluorides seem to be qualitatively applicable to trigonal bipyramids involving carbon, silicon, and sulfur. With reference to phosphorus, they say “Stabilization of certain isomers occurs as a result of CT bonding and is not due to more favorable rr bonding or d-orbital participation although both are present to some extent. It appears that the equatorial phosphorus orbitals are more electronegative than the axial orbitals because the phosphorus s orbital is concentrated in the equatorial orbitals. This gives rise to equatorial bonds which are stronger than axial bonds. I n the absence of steric hindrance, electropositive (electronegative) substituents prefer electronegative (electropositive) phosphorus orbitals giving rise to the observed isomers.” According to the HMO calculations, there is an increase in energy of at least 1 e.v. when an apical fluorine and an equatorial chlorine are interchanged in the phosphorus (V) chlorofluorides. One must ascribe the spatial preferences for bonding around the central atom to the symmetry properties of its contributing atomic orbitals! It is obvious, therefore, that nucleophiles should prefer axial entry and departure and that electrophiles should prefer equatorial entry and departure. Both of these are inversion paths! Following McEwen (1965), we have tabulated several cases in Table 7, with reference to attack on A in XAR1R2R,, 19. Attack of Y along a line perpendicular to the XR1R2 face leads most readily to Y and R, axial; attack of Y along a line perpendicular to the R1R2 edge leads to RIRz axial. Although Y presumably does not “reach” the original tetrahedron, these attacks are often named “on the face” and “ on the edge.” A tacit assumption in the change from tetrahedron to bipymmid is that the principle of least motion (PLM; see a later section) holds. On this basis, the choices in Table 7 were set up. According to the energy criterion supplied by Van Der Voorn and Drago (1966), symmetrical substitution with inversion, i.e. equatorial in-equatorial out, or axial in-axial out, should be the rule for trigonal bipyramidal transitionstates. Having outlined stereochemicalpreferences, we now draw on vibration theory to limit the choice in an absolute sense. Since the symmetry properties of the normal modes of a molecule are rarely considered in the context of stereoselectivity, we shall look into this question briefly.

254

S I D N E Y I . MILLER

TABLE7 Stereochemistry of Allowed Displacements of Y on Tetrahedral XAR1RzR3

Y entering, Y position

.

Y . .. A R I R ~ R.~X .

X leaving

Minimum no. of steps 01 b Stereochemistry @

Trigonal bipyramid

XR edge, equatorial Axial XRR face, axial Equatorial RR edge, equatorial Equatorial RRR face, axial Axial face or edge -

2 2 1 1 3

Retention Retention Inversion a Inversiona Racemization

Tetragonal pyramid

RR XR

1 or 2 1 or 2

3 2

Retention I nversion Racemization Racemization

1 or 2 1 or 2

Retention Retention

" "

C," model C," model

edge, basal edge, basal basal apical

RRR coplanar RXY coplanar

Basal Basal Basal Basal

a Multi-stage radical (SH)and nucleophilic attacks (SN)on A=carbon or nitrogen ar0 forbidden. b PLM (Principle of Least Motion) favors axial over equatorial entry and departure.

It is an old idea that in any cleavage process a bond is extended along a normal mode until it breaks. I n this mode, which is the critical one for reaction, not all of the atoms in the molecule are involved. It will be recalled that the normal modes of any molecule can be classified into subgroups or species according to the symmetry point group of the molecule (Nakamoto, 1962). For bipyramidal AY, or X2AY3the point group is D3,,, the number of vibrations is 18, and the vibrations are grouped 2(A;)+ 2(A9 + 6(E') + 2(E") (Condrate and Nakamoto, 1966). What is emphasized here is that all of the reacting centers of a transition state must be accounted for in the symmetry and the motions of the critical vibration mode. I n bipyramidal X2AY3,the motions of the X atoms and the Y atoms are independent, except in two degenerate modes u7 and u s ; but these vibrations cannot be related in any way to the critical mode. Otherwise, these are only three normal modes by which the motions of the incoming and outgoing groups can be coupled.

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255

In v3, the apical groups (X) move apart, while the equatorial groups (Y) are stationary; in the degenerate v 5 and v6 modes, one equatorial group moves against the other two, while the axial groups are stationary. Therefore, if the displacement is to be concerted, we need only consider changes at the axial positions or the equatorial positions. Again, the stereochemical result is inversion in both cases ! If substitution goes in two steps, there are several reaction paths via the trigonal bipyramid. Unless the probable structure of the transition state can be assigned, e.g. when the central atom is part of a cyclic structure or by the polarity of the substituents, Table 7 is now of little help in making stereochemical decisions. Again, in third-row elements such as silicon, and particularly phosphorus, in which relatively stable intermediates may be formed, pseudorotation may occur; in this case, the stereochemical result will depend chiefly on the favored equilibrium configuration. Here, substitution will be the result of at least three elementary steps. The preceding kind of analysis would have to be repeated for other possible transition states or intermediates, e.g. 22, 23 and 26. Some stereochemicaI results of having such transition states are given in Table 7. I n their critical review of pentacoordinated species, Muetterties and Schunn (1966) record few stable examples of the type 22 and 26 among non-transition elements. It would appear that structures such as XAR, might favor the tetragonal pyramid form, but this is not the case, at least among stable molecules. (Curiously enough, pentaphenyl antimony is a tetragonal pyramid.) Alkylphosphorus tetrafluorides or phosphorus (V) halofluorides which are bipyramidal pseudorotate ; the barriers to these internal motions are in the range 3-10 kcal/mole, and the probable transition state is the tetragonal pyramid 26. Other factors being equal, we would therefore be inclined to favor the trigonal bipyramidal over tetragonal pyramidal transition states and intermediates in substitution reactions of 19. Muetterties and Schunn (1966) suggest that certain boron hydride structures, e.g. 26 and 22 or 23 (C, symmetry, when X = Y ) , might be used as models for electrophilic substitution. I n general, if 21 or 22 were the preferred C, transition states or intermediates, the reaction would go with retention. Note that these are the analogs of the twoelectron three-center species A: discussed earlier by HMO theory. If, however, X, Y, and R were permuted, there would be several stereochemical possibilities, two of which are indicated in Table 7. To decide what kind of geometry is assumed in SE2 transition states, which are pentacoordinated and electron- and orbital-deficient, calculations on model species are needed to establish preferred geometries.

256

S I D N E Y I . MILLER

I n another approach, Sommer (1965) has argued that PLM would rule out certain modes of attack for the SN2 reaction. If the initial tetrahedral angle is taken as 110" and the bipyramid is formed, edge attack on 19 leads to six angle changes 7O0+4(2Oo)+1O0=160", while face attack on 19 leads to six angle changes 3( lo")+ 3(20")= 90". If the tetragonal pyramid with the angles pictured in 26 were formed, apical entry would lead to a change of 2(40°) + 4(24")= 176" while basal entry would lead to a change of 2(24")+ 40"+ 3(5")= 103". Without reference to the reaction type (S, versus SE),the PLM indicates an energy preference for forming the trigonal bipyramid by face attack and the tetragonal bipyramid by basal attack. Further reduction of the number of possibilities in this way is hazardous, because other factors, e.g. orbital overlap, non-bonding repulsions, etc., are not constant, and angle distortions contribute only a part of the total energy of activation. Indeed, a PLM argument would favor the C, models over the two trigonal bipyramidal models ! The allowed stereochemical alternatives in Table 7 are based on several lines of argument. It is interesting to see how our approach compares with that of Ingold's school (Harvey et al., 1960; Tobe, 1966; Ingold, 1953), e.g. "It has been shown that this form [20] of the transition state is required by the Pauli exclusion principle (there being no available empty orbitals of suitable energy), and not just to minimize steric and electrostatic interaction between entering and leaving groups " (Tobe, 1966). We have accepted the exclusion principle, but do not make it a proximate cause of the stereochemical course of the S,2 reaction. We believe that Ingold's (1953) energy criterion for the SN2reaction is more to the point: "the split bond X.. . C . . . Y holding the incoming and outgoing groups 11201 will have an approximately planar surface of zero electronic density (exactly planar if X = Y ) , in which the three bonds CR, can lie: this arrangement minimises the positive exchange energy between the altered and preserved bonds. State [21 or 221 admits of no such stable arrangement." It is not really obvious, however, why the exchange energies involving all five groups will be minimized in 20, even though they would be minimized in a three-center collinear system. The HMO calculations on the phosphorus (V) chlorofluorides (Van Der Voorn and Drago, 1966) do, of course, favor 20 over 24 and 25. Although there is little doubt as to the outcome of a more complete comparison, which would include 21 and 22 and carbon as the central atom, this has not been carried out. It must be admitted that we still have only a fairly qualitative, somewhat intuitive picture of substitution processes, and it would be desirable to have in hand a quantitative measure of the forces making for stereoselection.

S T E R E O S E L E C T I O N IN

STEPS OF ORGANIC

REACTIONS

257

No attempt will be made t o test all of the predictions of Table 7 on the substitutions at carbon, silicon, and phosphorus. These have been reviewed repeatedly. Only a few examples have been chosen to illustrate certain points. According to Sommer (19654, certain bridgehead silicon halides 27-29 compounds react readily with nucleophiles, e.g. water, hydrides ; these may be contrasted with their essentially inert carbon analogs. The order is k(27)> k(28)9 lc(29). He attributes this reactivity to the ability of silicon to utilize d orbitals and form almost strain-free pentacovalent species. It appears to us that compound 27 could react via a tetragonal pyramid, as Sommer (1965) suggests, but that compounds 28 and 29 should go via the C, model, as Hudson (1965) suggests (see Table 7). The chlorosilaadamantane 29 is relatively unreactive, both because of a strain-free ground state and the difficulty in distorting its locked structure to accommodate five groups a t silicon. These nucleophilic substitutions, which go with retention, seem to involve tangible examples of the tetragonal pyramid and C, species for third row elements. Whether these are transition states or transient intermediates is not obvious. c1 I

27

28

29

Although return to reactants from a pentacoordinated intermediate is possible, this behavior is uncommon. Sommer (1965)gives one example : H

*

D-RsSiF + CH30H

1

*

+ (R3SiF(OCH3))+ L-RaSiF+ CH30H

(119)

The intermediate he postulates is a tetragonal pyramid with methanol or methoxide a t the apex ; because of the large deformations involved in reaching such an intermediate, we propose that a pseudorotating trigonal or tetragonal bipyramidal species might be energetically more attractive (Gorenstein and Westheimer, 1967). Certainly, there is precedent for such an intermediate, since compounds with Sip; ions have been reported (Clark and Dixon, 1967). 9*

258

S I D N E Y I . MILLER

SN reactions of tetracoordinated phosphorus e.g. phosphine oxides, phosphine sulfides and phosphonium salts normally go with inversion (Hudson, 1965; McEwen, 1965). Wadsworth (1967) postulates diequatorial entry and departure in the following example :

G

c1

0

Reactions of phosphonium salts with hydroxide probably involve a pentacoordinated intermediate, since a third-order rate law is observed (Aksnes and Bergesen, 1966). Reaction via several intermediates was

found in the racemization of phosphonium salts by n-butoxide ion in butanol (Parisek et al., 1960) in which toluene formation is rapid compared to dibutyl ether formation. According to this mechanism,

(RO(R3’)PCHpCeHs) + ROPR3’++CaHsCHz-

OPR3’

+ ROR

alow f--

ROPRs’OR

+ CeH5CH3

the racemization is merely a complication following the main act; it is interesting, however, because it poses a problem which can be solved by having a pentacoordinated species in the mechanism. The mechanistic variations in these substitutions are sometimes unexpected. Cremer and Chorvat (1967) gave the stereoselective example, (123). I n view of the ring angle of ca. go”, the kinetic order of hydroxide in analogous attacks, and the single product, we speculate that 32 is the preferred intermediate. Compound 32 is presumably formed in one

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

32

259

33

I

HO 34

or more steps from 30 and 31 and is favored over 33 for steric reasons. I n 34, the diequatorial angle at phosphorus appears to be incompatible with the four-membered ring, The second mole of hydroxide ion attacks 32 to give the product. Steric interactions with the diagonal methyl group on carbon 2 are admittedly small-or so they seem-yet they appear to control the formation of the single product. Nucleophilic substitutions a t optically active sulfur sites in sulfinic esters, sulfoxides, sulfoxonium salts, sulfilimines proceed with inversion. Much of the previous literature is cited by Cinquini et al. (1967), who gives an interesting Walden cycle in (124). The actual inversion step is presumed to be the attack of water on the sulfoxonium intermediate, which is isolable (Hogeveen et al., 1966). For the most part, the similar stereochemicalresults in the SNreactions of ordinary sulfoxides, phosphoryl, sulfoxonium and phosphonium compounds is remarkable. Evidently the lone pair on sulfur is equivalent to one substituent (Gillespie, 1967). For this reason, the isolation of racemic product in (125) was unexpected (Andersen and Papanikolaou,

260

S I D N E Y I . MILLER

T

(1) AcaO-pyridine (2) Zn-pyridine

1966). Because the triaryl species is likely to be closer to coplanar than a trialkyl species (Scartazzini and Mislow, 1967), its barrier to inversion will be lower (Koeppl et al., 1967). For the present, then, backside attack on sulfur in SN reactions may be the usual course of substitution, but subsequent inversion may lead to a racemic product.

I

D

4- Ar”MgX Pi Ar Ar’

+ D,L-ArAr’Ar”S+

(125)

Three-, four-, five- and six-membered cyclic transition states as intermediates can be envisioned for substitution. These internal substitutions (S i) at a single center usually proceed stereospecifically with retention. We would expect retention when the angle at the central atom between incoming and outgoing groups is 90” or less, e.g. 21, 22, 23, 24, 26 and inversion when this angle is close to 120”, e.g. 20, 25. Of course, one must first ask whether a cyclic or acyclic species is expected to be on the reaction path. Because the answer to this question is often unknown, the stereochemical results of substitution can be confusing. This is not the case when the species participating in a reaction, their states of aggregation, and the kinetic order are defined, as in the field of demercuration (Thorpe, 1966; Reutov, 1967b). I n what follows, we examine both “settled” and “pending” cases. Optically active silanes of the type R,SiH react with lithium aluminum deuteride, halogens, oxygen bases, and perbenzoic acid stereoselectively, with retention. Generally, cyclic transition states have been proposed

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

261

by Sommer (1965; Sommer et al., 1967). These (35-38) are small rings consistent -with retention. Both SEi and SNi transition states are

R 35

I

H

37

36

38

represented here. It is understandable that “poor” leaving groups, e.g. hydride, fluoride, and alkoxide, require assistance in the form of coordination by the attacking reagent (Sommer, 1965). “Good” leaving groups, such as chloride, bromide, and carboxylate, are usually displaced by nucleophiles with inversion. The sequence in (126) illustrates the normal behavior, but also includes a surprise (Sommer et aZ., 1967c). The hydrosilylation, which proceeds with inversion, may be rationalized in several ways; but effectively, axial entry and axial departure, or

equatorial entry and equatorial departure of the alkene and hydride are indicated ; the platinum presumably mediates the transfer of hydride to the alkene, the critical transfers being made in three-center transition states. On the other hand, substitutions a t silicon by methoxide which

39

40

41

1

are promoted by palladium and nickel hydrogenation catalysts, are stereoselective with inversion (Sommer and Lyons, 1967). While the SS of these reactions involving hydrogen transfer from silicon might have been difficult to predict, the results are compatible with the SE character of the transfers in 39 and 40, and the SN character of the transfer in 41,

262

S I D N E Y I . MILLER

An exceptional case of displacement at phosphorus with retention was noted in the Wittig process (Homer and Winkler, 1964) : because of the

90” angle in the transition state, axial-equatorial departure from the betaine is most reasonable for internal displacement ; this is independent of the geometry of the alkene product. Day and Cram (1965) have found an unusual case of inversion at a sulfinyl center. They propose an S i process of diequatorial entry and departure : SOzAr

0

II

D-ArSCH3 (122) Ar

t

I1

NSOzAr

At carbon, most leaving groups are “good” in S,2 reactions: these go with inversion. At carbon, most leaving groups are “poor” in SE2 reactions; these go with retention. As for the SNireaction, this is usually strongly assisted, e.g. in (129) and (130) by the formation of sulfur dioxide (Mackenzie, 1964; de la Mare, 1963). The stereoR3COSOCl

RaCCl+ SOz

__f

(129)

R

I l l +R-C-CzCI c1

-+ 802 (130)

0

chemically interesting step in these four-electron four-center and six-electron six-center reactions seems wholly analogous to the molecular u-T exchanges discussed earlier.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

263

Electrophilic substitutions on exo- and endo-2-norbornyllithium present some unusual features : some are “normal ”,i.e. go with retention, while brominolysis favors inversion. Applequist and Chmurny ( 1967)

4

4

c1

ezo or endo

(131)

COOCHI

\

considered possible radical and carbanion mechanisms, but these did not appear to be relevant (131). They had to conclude that concerted electrophilic substitution can go both with inversion and retention in this case. We see no special virtue in the ad hoc proposals of a linear transition state, 42, for brominolysis of some organolithiums and a cyclic one for others, 43. It is known, however, that organolithiums are a\ / 8+ Br--Br -- 4--Li);-

I

42

-Brz 43

polymerized, e.g. into tetramers or higher polymers, which is indicated in 42, with “front side” shielding. At the same time, the activation

264

SIDNEY I . MILLER

energy for carbon-lithium ionization probably is low (Fraenkel et al., 1968). I n these circumstances, it may be easier for bromine to attack an organolithium backside than penetrate the aggregate frontside. If carbon-lithium bond-breaking runs far ahead of carbon-bromine bond making, this would be the sort of case envisioned for an SE2process with inversion by Ingold (1962) and Thorpe (1966). Some carbene reactions may be classed as displacements. It was pointed out in connection with equation (100) that the three-center insertion of singlet methylene into a single bond is an allowed 0-7r exchange. Excess energy would have to be dissipated in the product, but this should be relatively easy in solution (Gaspar and Hammond, 1964). On the other hand, a ground state triplet would presumably have to form a pentacoordinated intermediate, which would have to undergo spin inversion before the final product could be formed. If this electron-deficient species were something like 22, 23, 24, or 26, and long-lived, pseudorotation could lead to SS= 0 in the products. For condensed-phase reactions, Kirmse (1964) has used SS as a criterion of cyclic (singlet)versus acyclic (triplet)transition states and/or intermediates in these cases. When insertion is stereospecific with retention, a cyclic species is assumed; when insertion is unselective the acyclic species is assumed. We can, in fact, associate the singlet with a one-step, stereospecific process. On the other hand, one or more products could be formed from a triplet intermediate. (132)

CzHs .CHCl. CHI

CHa

,CHaCl CzH.5.CH, CHI (90% rtlcemic)

(134)

Kirmse, and Gaspar and Hammond (1964) have emphasized that the preceding stereochemical criterion is useful but uncertain, because the state of the initial methylene and the probable lifetime of possible intermediates are often unknown. One of the more interesting aspects of this research area is therefore centered on the identification of the state of the reacting species. A state diagram and orbital correlations have been given for cyanonitrene (Anastassiou, 1967).

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265

To complicate the issue further, there is now on record a stereospecific carbene displacement which looks very much like an SE2 reaction, with inversion (Landgrebe and Thurman, 1967) : H I CHs

H

CHs L-CzH5.

H

H

I I I I C .CH2HgCHz.C .CzH5 I- D-CzH5. C . CHz .CClzHgCHz. C .CzH5 I I I I

ClzCH

CHs

93”/0

(135)

CHs

CH3

7%

Since the first adduct to carbon in (135) would be electron-deficient,e.g. 25, one may write a stepwise process in which the first step is inversion (Table 7). To effect the internal proton transfer, additional steps involving pseudorotation, e.g. via 26, are needed. The minor product presumably arises from a conventional syn process involving axial entry and equatorial departure.

F. Substitution at Unsaturated Atoms Substitution at certain unsaturated centers has little direct stereochemical interest, because there is no choice, e.g. substitution at aromatic, acetylenic, and carbonyl carbons must go with retention. On the other hand, stereoselection is possible a t ethylenic and allenic carbon, phosphorus (P=O, P=S) and sulfur (S=O) centers. There appear to be important mechanistic differences between substitutions at unsaturated carbon and phosphorus or sulfur. All SE, SH,SN substitutions a t such carbon atoms appear to proceed in a t least two steps, while those at phosphorus and sulfur may go in one or more steps. For the SN process, comparative data are available : here, substitution a t unsaturated carbon proceeds with retention, while at phosphorus and sulfur inversion predominates. Substitution a t unsaturated phosphorus and sulfur sites was sufficiently similar to other saturated centers that it was considered with them. Because of these mechanistic differences, we shall examine substitutions a t unsaturated carbon more closely. So effective was the collinear three-center transition state in clarifying the Walden inversion problem, that concerted backside attacks were proposed or considered for the Beckman rearrangement, isomerization of alkenes, etc. (Olson, 1933; Marvel, 1943), as well as substitution in alkenes (Gold, 1951 ; Ross et al., 1952). Since an appropriate arrangement of hybrid orbitals is available, some of the transition states did not

266

S I D N E Y I . MILLER

appear unreasonable, except for 47a and 47b,which have never been taken seriously. Although the relevant MO calculations which would allow an energy comparison of 4p47 with 4S51 have not been made, the first set can be rejected on several grounds. Among nontransition elements, the shape of their compounds is determined more by the number of bonding and nonbonding valence electrons than by the kind of atoms (Gillespie, 1967). For each acceptable transition state or intermediate, there is a known model species, e.g. amines or alkylborons for 48, alcohols for 49,imines for 50, and arenium ions (Olah et al., 1967) or Meisenheimer complexes (Grifh et al., 1967) for 51. The view that it should be easier for an attacking species to disrupt carbon r-bonds as in 48-51 rather than cr-bonds 44-47 is perhaps plausible, but also intuitive. Secondly, although the changes in bond angles to obtain any given species 48-51 are more numerous, they are smaller and less costly in terms of energy than the one 90' change in 44-47 (Allinger et al., 1967). For 44 and 47b, steric hindrance alone would preclude their formation (Miller and Yonan, 1957): in 44, the

45

46

47b

48

y,\,y' C

I

Om 50

49

51 171.=

Y

52

+,*,.or-

Y

YJ

Y'

53

54

S T E R E O S E L E C T I O N IN S T E P S O F O R G A N I C R E A C T I O N S

267

groups Y and A and Y' and B are closer to one another than they would be in any 1,a-alkene or eclipsed 1,2-alkane; the nonbonding interactions would be enormous (Allinger et al., 1967). The oxygen derivatives of three centers, carbon, phosphorus, sulfur, can be compared with respect to the AO's available for nucleophilic substitution. Unlike 45, participation of the r-system in the process is possible for 53 and 54. I n 49, we have sp3 bonds and the tetrahedral intermediate; in 53 and 54, which may be transition states or intermediates, we can have pd overlap between the orbital covering the three collinear atoms and sped orbitals to oxygen. We know of no basic restriction which requires alkenes and carbonyl compounds to undergo substitution in at least two steps e.g. through 48-51, rather than in one concerted step. Certainly, there seems to be no objection to an angular transition state per se. Nor are the angular distortions required to reach 48-51 particularly great. Incidentally, Dessy and Kitching (1966) give 51 in alternative forms, i.e. with the bonds to Y full (intermediates) or partial (transition states), as in 52 for electrophilic substitutions. These are presumably the analogs of SE transition states at saturated carbon. Evidence for intermediates in electrophilic or nucleophilic aromatic substitution suggests that transition state 52 is unnecessary, if not improbable; and if 52 is to be an intermediate, the conventional VB representation of 51 seems most appropriate. Over the last two decades Russian workers have uncovered a host of interesting SE reactions with retention at an alkene center (Reutov, 1967b). These have involved exchanges with mercury, lead, tin, thallium, etc. attached to an alkene carbon:

Numerous other stereospecific conversions have been reported, e.g. (137) (Zweifel and Steele, 1967). To examine the stereochemistry of the BE process, we use the conformational notation. The intermediate 55 is formed by attack of an electrophile on the n-system. Not all of the possible conformations of

268

S I D N E Y I . MILLER

intermediates (55 and 56) need be given, but the existence of a rotational barrier between 55 and 56 should be noted. Diversions of 55 and 56 into other reactions, e.g. addition, rearrangement, as well as the kinetics of scheme (138)and some of its ramifications, are not considered here.

55

56 Ym=E+, R*,or N

We use the term “substitution” with scheme (138)in the sense that it is used for aromatic compounds. “Addition” is reserved for processes in which a saturated intermediate is formed. To observe retention, we require only that k ( 2 ) k(3)in (138). By analogy with the S2, reactions at a saturated carbon (Kreevoy et al., 1967), it is probable that some demetalations with acid in a polar solvent proceed in this way. Certainly, the intermediates are wholly analogous to those proposed for the isomerization, hydration, or hydrogen halide addition to alkenes. The more usual intermediate in SE reaction is cyclic. For mercury

=-

c1

c1

I

I

c1

57

1

c1 58

S T E R E O S E L E C T I O N IN S T E P S O F O R G A N I C R E A C T I O N S

269

exchange with labeled mercury we propose species 57 ;Reutov postulates 58, by analogy with an SE reaction at saturated carbon. It is not clear what bonding in 58 is intended, but since the double bond is retained, all four groups attached to the &-carbonare presumably coplanar and share three sp2 orbitals. As we have pointed out for species 44,steric interference between the substituents would be large and 58 would be improbable. Although scheme (138) is the "standard" mechanism for the radicalcatalyzed isomerization of isomeric alkenes, kinetic data for both substitution and isomerization are sparse. Using cis- or trans-diiodoethene and labeled iodine atoms, Noyes et al. (1945) demonstrated that iodine atoms exchanged with predominant retention ; isomerization was the slower process, the barrier being <'4 kcal/mole. Corresponding studies with dibromoethene and bromine atoms indicate a barrier of ca. 3 kcal/mole (Steinmetz and Noyes, 1952) in which bromine-atom departure from and isomerization of the intermediate were competitive. Qualitative selective or stereospecific radical-initiated additions to alkenes have since indicated that radical intermediates probably have stereostability, but the studies cited are definitive. The kinetic analysis provided the essential model for XX in mechanistic schemes such as (138), whether for SE, SHor SN processes. Nucleophilic substitutions at alkene carbons also proceed with retention in cases which are not obscured or complicated by competing addition, elimination, rearrangement, etc. (Patai and Rappoport, 1964). Apart from two studies (Jones et al., 1960; Miller and Yonan, 1957), the major contributions were first made in Italy (Landini and Montanari, 1967), e.g. RCO C1

I I c=c I I H H

RCO SAr ArS4

H H

H SAr

H C1

I 1 c=c I I

RCO H

I 1 c=c I I

ArS__f

(139)

I I c=c I I

RCO H

Numerous synthetic applications with high XX,e.g. CsH6CH=CHAs(C,H,), (Aguiar and Archibald, 1967), have been recorded subsequently. Although nucleophiles do isomerize alkenes, the rates are generally lower than substitution rates (Miller and Yonan, 1957; Huett and Miller, 1961).

S I D N E Y I. M I L L E R X-

270 cia-p-OzN.

CeH4. CH=CHBr

, &

cis-p-OzN

.C&4.

CH=CHI

Consistent with the proposed intermediate, 48, steric effects on substitution are probably negligible. Rates of substitution of cis- or trans- species do not differ greatly (Ghersetti et al., 1965), e.g. (141) ArSOzCH=CHBr

+RNHz

+ ArSOzCH=CH.NHR

(141)

Electronic effects are also similar : Hammett p values for cis- and transseries e.g. ArSO2CH=CHC1 are almost identical at p ~ l . 5(Modem et aE., 1959). These polar and potential steric effects would tend to rule out a transition state such as 44. All of these data are consistent with scheme (138) in which 55 and 56 are carbanion intermediates. This scheme also combines the processes for isomerization and substitution, which only seem independent of one another in (140). Since the carbanions 55 and 56 are probably pyramidal, we consider their fate in detail in the context of an iodide-bromide exchange in (142). Assuming anti attack, we have placed the electron pair trans to the Cia-1

trans-2

60a

H

R 60c

lk-

60a

J F-

60b

t

x'-/

cis-2

STEREOSELECTION

IN

STEPS O F O R G A N I C R E A C T I O N S

271

incoming group. Accordingly, all of the rotamers formed from cis differ from those formed from trans. Further, if the group leaving and the electron pair are assumed to be anti periplanar, then substitution on cis with retention goes through 60b. According to this scheme rotation (across (142)) leads to halide-exchange with isomerization, while ,&carbon inversion (up and down (142))leads to halide-exchange with retention (terminology can be awkward: “inversion” may be used for “ D ” to “L” isomerization of the /3-carbon and for cis-trans isomerization at the a-carbon). Information on the relative heights of rotation versus inversion barriers in carbanions is not definitive. Rotational barriers for substituted ethanes, amines, and hydrazines (Miller, 1964; Dale, 1966) are normally in the range 3-5 kcal/mole, unless the substituents are large, in which case the barrier is higher. Inversion barriers for CR, have been estimated as ca. 6-10 kcal/mole (Koeppl et al., 1967) ; for large electron-withdrawing substituents, which tend to flatten the carbanion, this barrier should be even lower. Since substitution with retention predominates, we must assume that inversion barriers have dropped below rotation barriers. That is, the paths 59a to 60b for the cis-1 to cis-2 and 60a t o 59b for trans-1 t o trans-2 are favored. The assumption of a definite location for the negative charge on the /3-carbon requires that 59a and 60a both be on the lowest energy path for substitution and isomerization. That this location should be formed anti derives from orbital symmetry, i.e. y52 of ethylene. This in turn precludes substitution with retention by syn-clinal loss of bromine in 59a or 60a, for microscopic reversibility suggests that anti entry of one halide and syn-departure of the other are improbable. We deduce, therefore, that the substitutions in (142)require at least three elementary steps, e.g. cis-1 -+ 59a --f 60b --f cis-2; isomerizations with exchange require at least three steps, e.g. cis-1 -+ 59a + 59b -+ trans-2; isomerizations without exchange require at least four steps, e.g. cis-1 4 59a -+ 59b 460a -+ trans-1. I n scheme (142),59c and 60c are on high-energy detours and were not considered. One could, however, formulate an entirely self-consistent scheme involving preferred syn-entry and syn-departure through 59c and 60c. An economical two-step process could be given for exchange with retention. We reject this possibility, chiefly because of the strong anti preference in polar additions (see next section). Mechanism (142) applies to ordinary alkenes. Special alkenes, e.g. benzene, or special intermediates, e.g. 61-63, would have t o be treated on an individual basis. As applied to carbanions 61 and 62, mechanism (142)is simplified to (143),since the inversion barrier has become negligible, and the number of pertinent carbanion conformations has been reduced to two. A

272

S I D N E Y I . MILLER

63

62

61

rotation barrier, as in (138),would still make substitution with retention the favored process, as in (139). On the other hand, facile proton transfers involving 63 could provide low-energy paths for isomerization, as in (141). To summarize this section, we note that substitution with retention is a multistage process at unsaturated carbon centers. A concise mechanism

cis-forms

&yX

H H

F5

H & x H

-

, -

trans-forms

(143)

for SE,SH and a few SN reactions is given in (143). The generally applicable scheme for SN processes is given in (142).

G. Addition and Elimination The predicted stereochemistry of additions and eliminations, (144), of X and Y at the ends of a conjugated n chain is given in Table 8 (Fukui and Fujimoto, 1966b). The orbital overlap in these allowed processes is indicated in Fig. 21. It must be admitted that many of the X+(C)j+Y

+ x-(C)j-Y

(144)

entries in Table 8 are of academic interest. The available material dictates our bias and emphasis : additions and eliminations involving simple alkenes (j= 2) shall turn up repeatedly in several later sections and will be examined from different stereochemical vantage points. I n connection with 0-n exchanges of equations (94) and (96),we noted that certain additions or eliminations were forbidden. A typical orbital symmetry diagram for the forbidden four-center bromine addition to an alkene is given in Fig. 22. Apparently similar concerted additions are allowed, e.g. hydrogen halides in equation (97), because favorable orbital overlap is available. As indicated previously, the application of the selection rules of Table 8 or Fig. 22 requires discrimination. First, a check of LVMO of the atoms undergoing attack is always worthwhile (Coulson and Streitwieser,

S T E R E O S E L E C T I O N IN STEPS O F ORGANIC REACTIONS

273

TABLE8 Predicted Stereochemistry for the Concerted Additions and Eliminations : X+(C)j+Y + X-(C)j-Y T

chain

Chain length

‘IT

electrons

1 1

0 0

2 2

2 2 2 3

Allowed addition

4 4 4

5 6

6

C-C

Br-Br

c-c

I 1

Br Br FIG.22. Orbital symmetry correlation for the (forbidden) cis-addition of bromine to alkene.

1965). I n the HMO +6 of styrene, the coefficients at the CL and carbon atoms are ca. 0.4 and 0.6 respectively. I n the HMO t,h7 of acenaphthylene, the coefficients at carbon atoms 1 and 2 are ca. - 0.32 and 0.32. Therefore, the directive effect for addition is syn in styrene and anti in acenaphthylene! Second, MO calculations may be helpful in “new” or different systems. With respect to eliminations, Fukui and Fujimoto (1965) used frontier electron theory to provide reactivity indices for two model

274

S I D N E Y I. M I L L E R

substrates. I n accord with experimental fact, these calculations indicate that anti-elimination is favored in chloroethane, while syn-elimination is favored in exo-norbornyl chloride. Although carbene type insertions have been discussed as displacements and their reactions with alkenes could be treated as cycloadditions, both could just as easily fit into this section. Typical of the latter is the addition (145). Apart from a primary syn stereospecificity, there is a c1 (145)

selectivity preference for the chlorine atom to be syn to methyl groups (Moss and Gerstl, 1967). McConaghy and Lwowski’s (1967) data for the addition of carbethoxynitrene (C,H,O * CO -N)to 4-methylpentene in methylene chloride provide evidence for singlet-to-triplet competition with the addition.

trat1s

Their kinetic and product analysis is consistent with the working hypothesis indicated previously for insertions : the singlet process is stereospecific, while the triplet process is at best only selective. Here, as in the reaction of sulfur atoms with alkenes, (217), some progress has been made in separating the problem of the reacting species and their reaction rates from the observed SS in the product (Gunning end Strausz, 1966). I n general, however, interconversion rates of triplet cisoid and tramsoid diradicals are uncertain, and deductions from overall stereoselectivity are also uncertain.

STEREOSELECTION IN STEPS OF ORGANIC REACTIONS

275

Other electron-deficient species, which add to alkenes are more clearly heterolytic in flavor, e.g. three-center epoxidation (147) (Bordwell and Biranowski, 1967) and hydroboration (148). Although (148) looks very much like the forbidden u-7r exchange (96), Fukui (1966) postulated a,

(148)

preliminary allowed three-center cycloaddition, followed by hydride transfer within a highly polarized species. I n the example of asymmetric induction in 64 v e r w s 65 (Streitwieser et al., 1967), both intermediates

7

?,

H

'r

1

I

L

L

64

65

CLSM = (1R:25: 5R)-(-)diisopinoca,mpheyl

I -c-cI

o,&.-o I

I I

CH3 66

I

I -c-c-

I I

-7-o,Mn/o C-

I

I

67

I -c-c-

I

I I

/\ 0 0

0, / O I-OH /\ -0 O H

68

69

o,op

/\ 0 0-

I

70

are syn, but 64 is favored for steric reasons. Fukui's concept appears to be widely applicable, and we illustrate it with transition states, 66-69, and stereospecific additions, (149)-( 151).

S I D N E Y I . MILLER

276

(Zweifel and Whitney, 1967; Zweifel and Steel, 1967):

-

H Al(C4Hg)z

RCECH

I I C=C I I

HAl(C4Ho) n

R H

H CO-OH

H Al[C4Hg)zCH;Li+

I I ---+ c=c I 1 CHaLi

I I +c==c 2)H+ I I 1)COa

R H

R H

(149)

(Halpern et aZ.tl966):

(Ohno et al., 1965) :

0-

CHaCli

Cis

3 trum

Notwithstanding the fact that certain four-center additions to alkenes, e.g. equation (94) or Fig. 22, are forbidden, bromine addition to an alkene does occur. The orbital symmetry arguments which forbid cis addition to isolated bonds favor trans addition in equation (144), in which j= 4, X may be a nucleophile or radical and Y an electrophile or radical. Therefore, additions of molecular bromine or in general X-Y to alkenes, should proceed in at least two steps. Otherwise, separated X and Y, with one electron pair between them, add in concerted fashion to the alkene. Equation (144) is effectively the prototype of numerous ionic and radical u-rr exchange reactions. A wealth of information has beengecorded in excellent reviews covering special aspects of this general process, e.g. electrophilic additions (de la Mare and Bolton,

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

277

1966), nucleophilic attacks (Patai and Rappoport, 1964), and radical attacks (Cadogan and Perkins, 1964) on alkenes. Pollowing the orbital requirement, anti additions of the type (144) might (naively) be expected to follow third-order kinetics. It turns out that this is not general, nor is it a sufficient or necessary condition for anti 88. Over the past fifteen years, Shilov’s group has found interesting cases of nucleophilic participation in the addition of acids to alkynes and alkenes (Dvorko and Shilov, 1964; Dvorko and Mironova, 1965), e.g. d(adduct) - k(CH30 .CO *C=C.CO. -dt

OCH~)(KSCN)(CHS-CO * OH)

The reversible reaction (Miller and Noyes, 1952a) is kinetically of the I 2 + H C E C H + I-

cnsoH

(

,.;)

H-:

CHaO?

,CsC\

I - + tt~tns-ICH=CH1

I.-’I

(152)

70

third order forward, and second order back. This is one of the few examples in which the kinetics have been studied for both the addition and elimination under identical conditions. Microscopic reversibility suggests that the anti transition state 70 is highly probable. The rate law for formation of trans-3-chlorohexene from 3-hexyne (A), hydrochloric acid, tetramethylammonium chloride (TMAC) in acetic acid (Fahey and Lee, 1967) is fairly complex, by comparison. rate = k(A)(HCl)z.a+k’(A)(TMAC)(HCl)l.4

(153)

The following examples of stgreospecific or selective anti processes are typical of those 1,2-additions and eliminations which obey the selectivity rules. The much smaller group which violate or appear to violate the symmetry prohibition will be discussed later. A typical anti course of addition and elimination is given in (154) (Stevens and Valicenti, 1965) and (155) (Fowler et al., 1967). B ~

~

~ f~ \l/B z re2

L

Though a choice of paths is available, the additions and eliminations of (154) and (155) are anti stereospecific. Two different eliminations occur with the stilbene dibromides in (156) (Kwok and Miller, 1967b), but they are both anti ; which path is taken is determined by conformational energy factors to be discussed later.

It must be admitted that most of the preceding examples of additions (not eliminations) which appear to obey the symmetry rules are probably not concerted. Are they therefore fraudulent, deceptive, misleading, etc? Probably not. For most of these appear to be cases in which the shape originally impressed by orbit81 symmetry requirements is retained to the point at which a succeeding reaction step produces the stereoselective result. The mixed anti products found in some halogenations (157) suggest that there is an intermediate for which anions can compete Bra

ArCH=CHz

__j

slow

6+

Br-

ArC.H-QH2 -*.

‘.Br’ I

*fast

ArCHBrCHzBr (157)

ArCHNOsCHaBr

(Yates and Wright, 1967). Bimolecular nucleophilic attack on an acetylene (Miller, 1956) (158) or radical attack on an alkene (Readio and Skell, 1966) (159) are illustrative of both stepwise processes and overall stereoselectivity.

We consider the anti process (144) as the normal, if ideal, course of addition. Closer to reality is the stepwise process. If we begin with the schemes (138) or (142) for substitution at an alkene carbon, and divert the first intermediates as in (160), we acquire a basic scheme for addition. Now, the attacks of nucleophiles, radicals and eleotrophiles on aJ.kenes and of nucleophiles and radicals on alkynes produce trans-oriented intermediates, in which the ‘rmemory” of their parents is impressed. If k4 ks,and k3N k-3 and k4 k6,the path to product should be stereoselective (stereoelectronic axiom 2). Indeed anti attack of the gegen

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

279

(169

SCH3

mcle"' &IHs 1

88:;

10% CHsS'

CH3S--,-

+

CHaSH

SCH3

3

cis ___+ 55 or 59a

C 56 or 6Oa ttrans -3

I4

adduct 1

l6

(160)

adduct 2

species on the intermediates of (160) is conformationally preferable to syn attack so that SS should be high: no special or unusual effects need to be introduced to obtain anti additions and eliminations. Within the context of a stepwise mechanism, electrophilic attack on an alkyne should yield a carbonium ion free from stereochemical bias, 0.g. Rb=&Rt E'

In this case, relative product stability could determine SS. If in scheme (160), k 3 > k 4 , SS becomes dependent on the steric stability of the intermediates. This general problem will be taken up later. There have been proposals to the effect that anti SS derives from the formation of syn-shielded, complexed or bridged intermediates, e.g. 71-75. These, of course, would be a suficient cause for anti addition.

280

S I D N E Y I . MILLER

x+

x71b

71a

C-C

c--c:

c-g

s

x

I

I

I + x 73

72

71c

74

75

Theoretically, the question of the intervention of 71-75 is analogous to the one involving the shape of a three-center intermediate e.g. C;, C;, and Cy. HMO theory suggests that the positive species would be cyclic and relatively stable, the negative species linear and somewhat less stable and the radical species would be least stabilized with a small preference for the cyclic shape-see also Table 9. Since bridged analogs of 75 are rarely invoked, unless substituents on the ring can delocalize the charge, we need not consider them further. Because the electron octet is exceeded, the existence of bridged radical species 72 is unacceptable to some (Cadogan and Perkins, 1964)whereas it is taken for granted by others (Readio and Skell, 1966). I n a preparative study, Eberhardt (1967) considered that the product distribution as well as the delayed appearance of 2-phenyl-1-iodoethane in (161) was

yll_

2C6H5.CH=CHz

Ia

l l / /(2CoH5.CH?Hz) ..

0

___f

\ __f

CeH5. CH. CHaI

I

5.CH*CHz1

(161)

CeH5. CHI. CH3

CoH5. CHZ* CHZI

C~JHS. CHI. CH2T

indicative of a bridged intermediate. On the other hand, LeBel and De Boer (1967)account for SS in thiolacetic acid addition to 5-t-butyl-lchlorohexene by invoking stereoelectronic control. The fact that radical rearrangements, e.g. (162),are possible and that bridged transition states must exist suggests, but does not require, that

STEREOSELECTION IN STEPS OF ORGANIC REACTIONS

281

some species could acquire enough stability to become intermediates. Similarly, Readio and Skell’s (1966) examples (163) and (164) of unsymmetrical radical-bridging that account for positional and configurational stereoselectivity are plausible but not required. Microscopic H3C

H3C

I

( + )--CzH5. C .CHzS

Br.

+

I :.\

CzH5. C-CHz

H3C Bra

( - )-CzH5.

__f

I

I

q.CHzX I Br

H (X= C1 or Br)

(163) I

CZH5C-X

&/

CHzBr

+ Br,

rB&

H

&Br

Br

(164)

reversibility requires that radical additions and eliminations go through the same preferred configuration : if stereospecific addition is possible through an unbridged intermediate, then elimination on the same path is probable. Whether or not bridging ever occurs is not at issue here; what we wish to convey is that the stereoselectivity implicit in bridging mechanisms can be obtained without bridging. Electron-deficient boron and aluminum compounds are models for onium bridging in carbon. It seems generally agreed now that positive species bridged with X=C1, Br, OR, SR, NR2 are respectable intermediates (Olah and Bollinger, 1967; Olah, 1967); to these one can add a few speciaI carbon-bridged species, namely p-anisonium, pentamethylphenonium, and cyclopropenium ions (Olah et al., 1967). Species bridged with hydrogen or alkyl groups have not been observed directly yet, and debate over their existence continues to rage (Brown, 1967; Olah et al., 1967). Therefore, it seems essential to consider whether there is any need to invoke the cyclic onium species in any given case. de la Mare and Bolton (1966) and Dewar and Fahey (1964) have indicated a number of cases in which r-complexes or bridged species are highly probable, e.g. E+=If, RS+, AsCl+,,etc. But evidence based on stereoselective anti products is only consistent with but does not prove their existence. Yates and Wright (1967) have produced one possible criterion for the intervention of a cyclic bromonium species. They obtained p E - 2 for 10

282

S I D N E Y I . MILLER

reaction (157)and noted that the addition of 2,4-dinitrobenzenesulfenyl chloride to styrenes, for which a cyclic sulfonium intermediate was also plausible, had a similar p = - 2.3. By contrast, several bona fide carbonium-ion reactions, e.g. solvolysis of 2-phenyl-2-propyl chlorides, had p~ -4 to -4.7. Clearly, the p value for bromine addition is more consistent with a bridged intermediate than with an “open” ion ArCH+.CH,Br. The link between bridging and the magnitude of p is somewhat weakened by the fact that there are exceptional cases that require special explanations : one solvolysis has a p N - 2.2, and one halogenation has p 2~ - 4 (Yates and Wright, 1967). Cabaleiro and Johnson (1967)report that the addition of chlorine to trans-methyl cinnamate in chloroform or acetic acid is syn-selective, SS 21 0-75, in chloroform and acetic acid; acetoxychloro derivatives are produced as well. Again, Dewar and Fahey (1964)argue that the “normal course of addition of hydrogen halides onto olefins is a polar electrophilic process involving classical carbonium ions as intermediates and leading mostly but not exclusively to cis-adducts.” A synpreference was found in the additions of deuterium bromide to acenaphthylene, indene, and cis- and trans-phenylpropene. I n the case of indene, phenylpropene and methyl cinnamate, which are styrene analogs, concerted syn addition is symmetry-allowed (see bottom of p. 273). I n species such as these, carbonium ions are probable intermediates (Dewar and Fahey, 1964). Therefore, syn collapse of an ion pair in competition with other processes determines SS. Two rival completion steps are indicated in 76 for a cis-alkene; besides the conformational R

&-’

R‘

H

.f Br I

H 76

factor which is discussed in connection with (198),the formation of solvent-separated ion pairs, anti-ion pairs, etc. all may be important (Cabaleiro and Johnson, 1967). Thus, bromine addition to cis-stilbene is chiefly anti (Buckles et al., 1967) and deuterium bromide addition t o acenaphthylene yields mostly cis-adduct (Dewar and Fahey, 1964): in both cases, reactions in more polar solvents become less selective, presumably because the intermediates live longer and have time to isomerize. Added bromide ion does tend to restore the high anti-selectivity in the bromine addition to stilbene.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

283

Nickon and Westeriuk (1967) have given an interesting analysis of 1,3-eliminations and cyclopropane ring cleavages. (These are a180 examples of the similarity in cyclopropanes and alkenes, with respect to

n

x

z

U

x W

(“”

exo-8

X I I

X

5 Z

czpo-s

FIG.23. Concerted 1,3-eliminationsand cyclopropane ring cleavage.

orbital symmetry.) The descriptive notations (8= sickle) for transition states are given in Fig. 23. The scheme has been applied or extended to stepwise processes, e.g. El or EIcB, or the Pavorski reaction (181). The first four arrangements in Fig. 23 can be found in cyclohexanes, while the apo-S form can be found in some strained bicyclo systems. If ionization of Z or X precedes the formation of the cyclic transition state, the latter may be designated as “semi”. (The transition-state configurations for fragmentation of 82 and 83-85 of equation (172) or 87 and 86 obviously are analogous to the semi-U and semi-exo-X,respectively, of Fig. 23.) Bimolecular elimination of suitably labeled exo-norbornyl tosylate

284

S I D N E Y I . MILLER

indicated a preference for exo-S over W elimination in (165). The exo-8 process is a clear analog of anti elimination and hardly needs further

(165)

justification. For the record, note that the orbital of the departing proton can “displace” tosylate anti. This, incidentally, is analogous to the internal SNprocess involving the sulfoxonium salt in equation (124). Bimolecular elimination of suitably labeled endo-norbornyl tosylate

indicated a U over endo-S preference in equation (166), this despite the favorable anti orbital geometry for endo-S elimination. Because of orbital symmetry, the orbital of the endo proton should not displace the tosyIate. Nevertheless, the U or syn elimination does take place. Nickon and Westeriuk suggest that a quasi-cyclic transition state, e.g. 96, may facilitate this front-side displacement. (See also discussion of (195).) It is interesting that syn addition to a 1,3-dienewas considered, in the early 1950’s,to be the result of two coupled anti processes (Eliel, 1956). This useful, intuitive notion is contained in the general orbital symmetry scheme of Fig. 21, X and Y, with one bond or electron pair between them, react with LVMO of the 7~ chain. For concerted reactions, this could be termolecular anti for an alkene, bimolecular or termolecular syn for a 1,3-diene, termolecular anti for a 1,3,5-triene, and etc. For an all-cis triene, bimolecular anti addition of molecular bromine becomes possible -the Mobius chain of eight atoms mentioned earlier would also be appropriate here. There are few examples of additions to 1,3-dienes which bear on the stereochemical problem at hand. Syn attack on an open 1,3-diene is allowed, bimolecular in the cisoid (77) or trimolecular in the transoid (78) conformations; in one case, at least (Hellman et al., 1954), chlorine attack yields the trans 1,4-adduct (79).

77

78

79

STEREOSELECTION IN STEPS O F ORGANIC REACTIONS

285

Although the additions to 1,a-dienes in equations (167) (Hammond and Warkentin, 1961) and (168) (Young et al., 1956) illustrate the syn preference, their mechanisms are more complex than is indicated here. The 1,4-elimination in (169) (Cristol et al., 1955) does appear to be a straightforward example of syn preference.

'H PhCOO

x

x (leg)

Depending on the point of view, fragmentation reactions may be considered to be eliminations or u-TI and u-u exchanges. They are heterolyses involving five centers or more that yield three or more fragments (Grob and Schiess, 1967). Such reactions are sufficiently close to eliminations in an extended chain, e.g. (169), so that they can be considered with them (Banthorpe, 1963). The fragmentations of aminoketoximes (Grob et al., 1963) in (170) or 4-haloamines in (171) (D'Arcy et al., 1966; Bottini et al., 1966) are

S I D N E Y I. MILLER

286

80

81

typical. As six-electron, five- or six-center systems the symmetry requirement is that the HOMO orbital have two nodes; in terms of electron-pushing, there should be two anti eliminations in the molecule amounting to a syn elimination overall. I n the 3-chlorotropanes, this shows up in a rapid fragmentation of 80 as compared with 81. Finally, Wharton and Hiegel (1965) treated four 1,lo-decalindiol monotosylates, 82-85, with potassium t-butoxide in t-butyl alcohol a t 40' for 1 hour. The results were in accord with stereospecific concerted fragmentation in 83-85 where there were antiperiplanar (180') bonds. I n 82 the changing bonds are syn-clinal (SO') and none of cis-product is formed; the trans-product is presumed to arise from a stepwise process. __f

0-

OTs

complex mixtures

< 6% trans -076 C k

0 cis

S T E R E O S E L E C T I O N IN STEPS O F O R G A N I C REACTIONS

287

H. Rearrangements I n a rearrangement, /7.

E+O ‘M

T-L

__f

E-0

c

,T+L

(173)

M

a migrating group (M) shifts from the origin (0)down a chain to a terminus (T). The timing of the various bond-making and breaking steps all may affect the stereochemical outcome of the overall process. Of necessity, we shall be concerned chiefly withSS of the individual steps. The orbital symmetry requirements of elementary steps in a rearrangement have been discussed in various guises, under sigmatropic reactions, displacements in allylic or polyene systems, addition reactions, etc. The general equation for a sigmatropic transfer in a polyene is given in (173), the orbital pictures are in Fig. 20, and the selection rules are in Table 5. I n view of their importance, the energy requirements of 1 3 rearrangements are also given here. Zimmerman (1963) and Phelan et al. (1967), used HMO calculations to find the energy change for carbon to carbon migrations from the “open” to the half-migrated cyclic forms.

(174)

As indicated in Table 5 , the [1,2] reaction of carbonium ions is allowed and is energetically favored (Table 9). The migration of alkyl groups to TABLE9 Stabilization energies (in 8) and Activation Energies (in e.v.) for 1,2 Migrations or [1,2] Sigmatropic Shifts According to HMO Calculations: fl units are data of Zimmerman (1963); e.v. units are data of Phelan et aZ. (1967).

m=

+, . , o r -

Number Energy in Energy in e.v. of Migrating electrons Cation Radical Anion Cation Radical Anion group 2+n 2+n 8+n 8+n 14+n 20sn 8+n 8+n

8+n

-0.40 -1.18 -0.98 -1.46 -1.87

0.41 1.22 -0.86 -0.62 -0.45 0.08 -1.17 -0.88 -1.61 -1.67

12.24 9.42 6.22

16.10 13.28 7.84

19.96 17.14 9.46

6.30 2.88 6.30

7.37 6-92 7.60

9.44 10.96 8.70

288

S I D N E Y I. M I L L E R

adjacent radical or anionic sites is energetically unfavorable, but it becomes more probable if aryl substituents delocalize the charge. The migration of aryl groups is allowed and favorable, as in 51; here the bridging carbon is tetrahedral, as the phenyl group moves. To chemists that favor bridged species as intermediates, the calculations relate directly to the free energy of their formation; to chemists that abhor bridged intermediates, the calculations give the relative free energies of reaching the transition states, when the transition state of process (173) is a cycle of seven or fewer atoms; a syn migration is mandatory. At the same time, an asymmetric center M normally shifts with retention of configuration. However, equatorial entry or exit at the center M or T would lead to inversion, as in equation (128)for sulfur. Whether the leaving group L will be displaced “frontside” or “backside ’’ presumably depends on the same factors considered in our previous section on substitution. Concerning Wagner-Meerwein and pinacolic rearrangements, Pocker (1963)says, “Reactions which show stereospecificity need neither be necessarily concerted nor proceed via a bridged ion. Stereospecificity is indeed a requirement of concerted migrations and also of those reactions which involve bridged ion intermediates, but the converse is not true.” Here Pocker had in mind a whole reaction sequence in which optional paths could be followed by unstable intermediates. By insisting that every step is stereospecific, we avoid this problem and almost bypass the troubled territory of classical versus non-classical ions and bridged versus unbridged intermediates. The acetolysis at 75” of L-threo-3-phenyl-2-butyl tosylate yields 25.5% L-threo, 25.2yoD-threo and 2% erythro acetates along with several alkenes. The predominant attack by acetic acid is on the same side as the departing tosylate, and anti to the migrating phenyl group. According to the mechanism of Brown et al. (1965),which is given in scheme (175),the carbonium ions interconvert rapidly within the ion pairs. Acetic acid would prefer to attack on the least hindered side, i.e. anti to phenyl. To account for the conformations as given in the scheme (175),the preference for the one in which phenyl and tosylate are anti had to be assumed. Cram and Thompson (1967)would write a single phenonium ion in place of the equilibrating species, and acetic acid would have to attack anti to phenyl. I n forming the phenonium ion, an SN process with inversion at the terminus is involved. Both mechanisms are intended to rationalize the same stereoselectivity : the former emphasizes conformational control (see discussion of 108a in a later section), the latter conformational and electronic control.

S T E R E O S E L E C T I O N IN S T E P S O F O R G A N I C R E A C T I O N S

289

D-threo

L-threo

H

H

Since there are now on record examples of both open and bridged ions formed from phenylethyl compounds (Olah, 1967), the either-or aspects of the polemic are fast disappearing. Kingsbury and Best (1967b), for example, prefer t o believe th.at "bridged ions and open ions can indeed coexist peacefully; " their conclusions are based on the overall stereoseIectivity in the reactions of hydrogen chloride-lithium chloride with threo- or erythro-alcohols corresponding to the tosylates of (175). Stereoselective radical rearrangements are rare. The free-radical intermediates in the following [1,2] (Riichardt and Trautwein, 1965)and [1,3] (Montgomery and Matt, 1967) reactions presumably live long enough to racemize :

10*

290

SIDNEY I . M I L L E R

1

Cis and tmns (2-hexenes-k 2-methylpentenes)

The possible dilemma here is that a stereoselective or stereospecific radical reaction may be indistinguishable from a no-mechanism reaction. Although [I ,2] rearrangements to an electron-rich center are forbidden by the Woodward-Hoffmann rules (Tables 5, 8) there appear to be both real and apparent violations. The following desilylation goes with retention at carbon (Brook et al., 1967); large Hammett p values (3.4 to 4.14) for substituents in Ar indicate a high degree of carbanionic 0-

\*

*

(178)

D-(C8H5)3Si--CArR -+ D-(CeHs)&OCHArR

character in the slow step. The superiority of silicon over carbon in participating in a three-membered cyclic anion can be ascribed to d-orbital participation. Indeed, silicon shifts much more readily than a phenyl group, when compared in anions of substituted hydrazines (West et al., 1967). Pasto and Hickman (1967) give an interesting sequence,

9 '

J

(179)

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

291

(179), in which there are several stereospecific steps; the novel one is a [1,2] double syn shift involving nucleophilic substitution with inversion

at both ends.

Incidentally, the oxidation step presumably involves a standard syn shift to an electron-deficient oxygen with retention at carbon. The [1,2] Stevens rearrangement also goes with retention of the migrating group (Zimmerman, 1963). CH3 * CH .CsH5

CH3 * CH * CaHs

It is interesting that the alternative allowed five-center Sommelet reaction often dominates, when it can compete with the Stevens rearrangement. Since systems such as these often become much more complex than we have shown (Lepley and Giumanini, 1967), these mechanisms should be reappraised in each new application. The Favorski rearrangement normally goes with inversion a t the terminus, as in 86 (semi-em-8) rather than 87 (semi-U). Reusch and Mattison (1967) have verified this for the pulegone oxides of which onIy one of the optically active forms is given in (181). It is of interest that the cyclopropanone intermediate opens abnormally, that is with retention. These authors note that their conditions are similar to those for electrophilic substitution with retention, namely frontside proton transfer from a polar aggregate (Cram, 1965).

Ullti

sy11

86

87

S I D N E Y I . MILLER

292

Base-catalyzed [1,3] proton transfers with retention of optical activity are given here to illustrate the persistence of stereochemical pedigree in an apparently labile species. Guthrie et al. (1967) heated the imine (equation (182)) with base and were able to obtain rates of proton exchange with solvent (lee), racemization (kJ and isomerization (ki). It was found that the proton transfer was stereoselective across one face of the carbanion; collapse of the solvated ion aggregate favored starting material over product; collapse was accompanied by proton exchange with solvent and retention of optical activity. Now, these results require a specific configuration of the azaallylic anion, whether isomerization occurs or not. The orbital-symmetry requirement, which would be anatarafacial for a concerted [1,3] shift, need not be retained for protonation from the bulk solvent; however, the overlap requirement of a T system would tend to keep the ion planar, and the conformational preference would keep the bulky groups remote from one another. It is left for the medium t o freeze the oriented intermediate as it forms, perhaps by forming a locally asymmetric solvated sheath around it. The detailed manner in which t-butoxide-t-butyl alcohol perform this holding operation is not clear, but the fact is that in this medium a variety of processes proceed with retention e.g. electrophilic displacement (Cram, 1965), elimination (188), ring opening (181), etc. Rearrangements to a carbene site or intramolecular insertion or addition reactions by a carbene may be stereoselective. The distribution

N,NHTs

@ -

diglyme 135-140"

+

'

.(l84)

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

293

of products in processes (183) (Doering and Kirmse, 1960) and (184) (Bird et ak., 1967) is determined by conformational energy, or other factors. Since the alternative paths are allowed, SS,as we are discussing it here, is not a t issue. The transannular insertions (Kirmse, 1964) proceed with retention, giving cis-fused ring systems. N-NHTos

Provided that we are dealing with intramolecular concerted processes of carbenes, it is difficult to imagine nonstereospecific processes. Indeed, the latter would be identified with stepwise radical reactions. The stereoselective carbene-initiated fragmentation (1 86) (Sanderson

and Mosher, 1961) appears to require migration to an electron-rich center. Unlike the preceding examples, this reaction can be regarded as involving an allowed series of intramolecular SN backside attacks.

IV. MISCELLANEOUS FACTORS AND STEREOSELECTION I n this section we collect a number of disparate observations, speculations and theories. Any “effect” on reactivity is, of course, a factor that alters theSS, but only some of these have been specificallyassociated with SS. For the present a t least these effects cannot always be woven into a grand design. Nevertheless, we shall attempt to relate them to the two large factors, namely, orbital symmetry which precedes, and steric effects, which follow this section. A. Excited States and Molecular Vibrations The role of orbital symmetry in determining the stereo-paths of reactions of excited states has been discussed earlier. A related idea is the hypothesis that the shape of an excited state must influence stereoselectivity. For example, once it was recognized that the first excited state of acetylene was trans-bent, and the second was cis-bent (Ingold

294

S I D N E Y I . MILLER

and King, 1953), one had a possible explanation of preferred anti addition (Burnelle, 1964). Following his self-consistent field MO calculations on acetylene, Burnelle (1964) examined the role of excited states and molecular vibrations in determining SS of additions. He found that, when a proton is brought close to acetylene, the energy of the trans-bent structure falls below that of the linear form. For similar addition to ethylene, Burnelle (1965) found that the first stable intermediate derived from the 90” twisted form of ethylene. Since such a geometry could only lead to SS = 0-there is no preferred orientation for attackthis particular model was less successful for ethylene than for acetylene. Bader (1962) proposed that the symmetry of the normal modes of a species and the symmetry of its excited states could determine the course of a reaction. Consider the transition state X . . .CH3...X of the SN2 reaction (equation 15) for which the MO’s t,bl (a,”),t,b2 (al’),t,b3 (a,”) have been given (equation 16 and Fig. 5). The most readily imposed electronic excitation is to t,b3 or to an excited state Y = $ ~ 2 ~ # 2 t , b 3 , of symmetry Az”. The stretching frequency which leads to bond breaking in XCH,X is unsymmetric, A2”,and given as v3 for such molecules (Nakamoto, 1962). Bader treated the decomposition of an azo compound, R-R=g-R, in the same way. The Walsh diagram (Fig. 4) indicates the appropriate levels : ground state (lag)2( l b J 2 (2a,)2 (2bJ2 (la# (3a,)2; lAg fkst excited state (W2(3@,)(%*I; ‘Bg second excited state (la,)2( 3 4 (4a,*); I A g Such a species does not have any B, vibrations, but it does have A , vibrations (Nakamoto, 1962) corresponding to the second excited state. Therefore, the predicted mode of decomposition should be symmetric, which is, of course, the way azo compounds decompose : R-N=N-R

-+ R . + N d + R . or R-R+N=N

As a test of the method, we examined the dimerization of ethylene. The first and second excited states are A , and Al, respectively (Fig. 14). For a four-center square species, the normal vibrations which could lead to dimerization are v1 (Alg)and v2 (Big) (Herzberg, 1945). Accordingly, dimerization would be possible but difficult, since the symmetry of v1 matches that of the second excited state. This conclusion agrees with the results of orbital-symmetry arguments.

S T E R E O S E L E C T I O N IN S T E P S O F O R G A N I C R E A C T I O N S

295

I n our second test, the ndve extension of Bader’s approach was unsuccessful. Consider favored anti addition to acetylene. The lowest vibrational modes of acetylene have the symmetry 7rg and .rr, corresponding to trans and cis distortions respectively (Burnelle, 1964). The first and second excited states of acetylene are trans A,, and cis-B1, respectively. Because an appropriate symmetry match is made in the second excited state, syn-addition is indicated. To obtain agreement with observed fact, Burnelle proposed that under the influence of an attacking reagent, the 7rg vibration is excited, the ground state acetylene (Alg) undergoes a forbidden radiationless transition to AIU, and the anti reaction can proceed. According to Burnelle’s calculations, perturbation of the acetylene by the approaching proton makes the desired transition increasingly probable. I n this case, the properties of the transition state, rather than those of the reactant, are critical. It appears that Bader and Burnelle’s approach to reaction SS may be difficult to apply generally, but it does seem to merit further evaluation. B. Magnetic Resonance Data Dixon (1967) has proposed that nmr coupling constants ( J ) and esr hyperhe splittings may indicate or correlate with preferred stereopaths. He has given empirical correlations of log k or Eactwith J values. Proton-proton spin-spin coupling constants JH,CHI in typical alkanes are : CH3CH2H,8 c/s; (CH3)2CH2,7.3 c/s; (CH3),CH; 6.8 c/s. The larger the vaIue of J , the less the delocalization at a given bond. Therefore, the activation energy of a process in which this bond is ruptured should increase roughly as J . This is found for sN1, E l , E2, ElcB and radical abstraction reactions, but not s N 2 reactions of primary, secondary and tertiary halides. Dixon (1967b)also suggests that anti elimination should II 4 c/s) but syn be favored in cyclohexyl halides (Jt,a,,8II 12, JBauche elimination should be favored when vicinal atoms are eclipsed e.g. in cyclopropanes ( J c i s ~ 9Jeasche-5 ; c/s). Since they are the reverse of elimination, the direction of additions to unsaturates can readily be deduced ; moreover, the orientation follows Markovnikoff’s rule. Inasmuch as spin-spin coupling constants reflect the state of the molecule and the charge distribution of its parts, they may be useful in characterizing ground states. It seems improbable that nmr data can tell us much about transition states. I n Fig. 24, we give a Karplus (1963) plot for the theoretical angular dependence of J , , 2 on the torsion or dihedral angle T of an ethane. It is interesting that the three properties of substituted ethane portrayed in this Figure, namely J , half wave potentials and elimination rates estimated by PLM, all appear to be

296

S I D N E Y I . MILLER

w

Jl,2

,

0"

45O

90"

;I

135'

I

0

dihedral angle

FIG.24. Schematic effect of dihedral angle: the magnitude of the coupling constant for vicinal protons, J 1 , g ; or the half-wave potentials for the reduction of cyclic vicinal dibromides (polarographicdebromination), A = --Ell2 (volts w8. S.C.E.); or A=,ZDz, the sum of the squares of the displacement of the atoms in dehydrochlorination of ethyl chloride by PLM.

similarly related to T. It must be admitted, however, that the plots in Pig. 24 are schematic and/or idealized and their value may be more theoretical than practical.

C. Collinearity and Coplanarity of Reacting Centers This so-called stereoelectronic factor operates to maximize or minimize orbital overlap, as the case requires, to obtain the most favorable energy. This was evident from the three- and four-center systems we have discussed by the VB and HMO methods. It was also implicit in favored anti-l72-additions, 1,3-cyclizations (Fig. 23), fragmentations (e.g. (174)), etc. Here we have selected several reaction types to illustrate the principle. I n this and other sections, we show that the tendency for reaction centers to be collinear or coplanar stems largely from orbital symmetry (bonding), but may also derive from steric and electrostatic effects, as well as PLM. The syn-periplanar eliminations by pyrolysis of esters, xanthates, sulfoxides and amine oxides are symmetry-allowed. With respect to the alkene portion of the transition state, the centers presumably are or

STEREOSELECTION IN STEPS O F ORGANIC REACTIONS

297

would prefer to be close to coplanar. The five-center pyrolyses of Rand S-steroidal sulfoxides (Jones and Green, 1967) show this preference clearly in four pairs of compounds (Ror S, and e or a, and cc or B), in which axial sulfoxide departs more readily than equatorial sulfoxide. This is idealized in 88 to emphasize the conjugation between sulfoxide and incipient alkene; in R-4P and S-4& the molecular framework is pictured fairly close to the product cholestene. As between 89 and 90, the latter is far less reactive because of the nonbonding repulsions

H/ 88

89

R-4g

91

between phenyl and methyl. Evidently, it becomes much more difficult for 90 to achieve the favored transition state geometry. It is well known that in many brominations and protonations of cyclohexenols (91) axial entry is favored (Eliel et aZ., 1965). This is attributed to the parallel alignment of the n orbitals on the three centers. The overlap preference is well illustrated in the oxidation of allyl vs. saturated alcohols. Normally, axial alcohols are oxidized more rapidly by chromic acid than equatorial alcohols. In the absence of large strain factors, equatorial allyl alcohols are oxidized faster than axial alcohols by chromic acid; hydrogen is abstracted in the rate-determining step. The contribution of u-p ketonic resonance lowers the activation energy,

298

S I D N E Y I . MILLER

when hydrogen is removed from the allylic axial position (Burstein and Ringold, 1967). Relative oxidation rates with chromium (11)oxide in 90% acetic acid are given below. rel. rate

rel. rate

4.0

H

H HO

Three-center SN2 displacement and anti-eliminations from unsaturates are obvious examples of the coplanarity principle. DePuy et al. (1965) noted that when anti eliminations cannot have coplanar reacting centers the syn coplanar-transition state may become more favorable. Syn bimolecular eliminations had been noted in various systems previously, e.g. haloethenes (Miller, 1961), but these were generally slower than anti eliminations. There were, however, syn bimolecular eliminations whose rates approached that of the anti form or exceeded it. The relative rates of elimination of 2-phenylcyclopentyl and cyclohexyl tosylates with t-butoxide in t-butyl alcohol at 50" are as follows : syn-cyclopentyl, 3 ; anti-cyclopentyl, 26 ; syn-cyclohexyl, 0 ; and anti-cyclohexyl, 2. I n the cyclopentyl system in which the torsional angle ( r ) between the leaving groups approaches zero the syn rate is close to the anti rate. I n the cyclohexyl system in which r of the stable form is cu. 60" the syn rate is 0. LeBel et al. (1964),report that in the reactions of t-butoxide with the 2,3-dihalobornanes, 92-95, N

N

Br

92 relative rates

113

93

94

95

17

3

1

the syn elimination is favored over anti elimination by factors of ca. 30 or more. Here there is a dihedral angle of ca. 0" for syn-leaving groups and angles of ca. 120" between anti leaving groups. Moreover, exo-cisin 93. dehydrochlorination is favored over endo-cis-dehydrobromination Apart from the favorable frontier electron densities on the exo departing

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

299

atoms (Fukui and Fujimoto, 1965), this unusual preference may be ascribed to the greater accessibility of exo protons to base attack and to the relief of nonbonding 1-6 and 2-4 interactions as the endo groups (X, H) move up in 93. Other steric factors will be mentioned presently. I n the polarographic reduction of a variety of 1,2-dibrornides,Czech workers found an interesting pattern of E l l z versus the dihedral angle T between the two C-Br bonds. This is given in somewhat idealized form in Fig. 24 (Zuman, 1967). The reduction appears to go most readily with antiperiplanar dibromides ( r > 150")) or those which can take up that ' ) reduction is of intermediate difficulty, and it conformation; syn (T = 0 becomes increasingly difficult is more negative) from T in the range 0'-60' to T 60"-120". Although the transfer coefficient does vary systematically between the readily reducible and the less reducible compounds, this does not appear to involve a change in mechanism. Czech workers have also found several competitive anti- and syneliminations (PbnkovA et al., 1967; Zhvada et al., 1967). threo op

H Bu-n I' I t-Bu. CH2.C-c--H

I

erythro

I

t-Buo-* I350

cis-

and trams-[t-Bu.CHz.CH=CH.Bu-n + t-Bu.CH2.CF=CD.Bu-n]

(CH3)3N+D

CHz-

I

CHN(CH3)3+

I

(CH2)n-4 -(CHz)z

%=5-14,16

(188) RO___t

$'

(189)

c k - and truna-(CHz),-2 L

C

H

The erythro compound shows little or no kinetic isotope effect, but the threo compound has a moderate one, k,lk, 2.3-3.3, for both syn and anti processes. This suggests that an E2 process is involved. Eliminations from the cyclic bromides may produce trans alkenes by syn eliminations or by anti eliminations, if n 2 8 in( 189). I n the reaction of menthyltrimethylammonium ion with strong bases up to 27% of menthene-3 is obtained (190). Baldwin et al. (1967) believe that an anti-like elimination from a skew conformation or a syn elimination from a carbanion species can account for this result; anti elimination from the other chain isomer, in which all substituents were axial, would be energetically less favorable overall. Concerted syn 1-2-eliminationis in violation of the orbital symmetry rules. Extenuating circumstances as well as valid exceptions have been indicated on several occasions. One need not abandon the orbital view, however, if the molecule as a whole is considered. I n an orbital comelation diagram, e.g. Fig. 22, the higher energy syn path becomes more

300

S I D N E Y I. M I L L E R __f

C3H7-i

OH8Un

H3cT5L C3H7-i

O

anfi Y

I

X

accessible if the alkene and alkane HOMO and LVMO levels are pushed together. This presumably happens to the 0-orbitals in an eclipsed conformation, e.g. in cyclopentane, norbornane, or in equation (191) (Cristol and Hause, 1952). It is usually in these cases that coplanarity of the reacting centers cannot easily be achieved. Certain strong bases in ion-pairing solvents, e.g. t-butoxide in t-butyl alcohol, appear to be more favorable to the syn process than ethoxide in ethanol (Zhvada et al., 1967). Although 96 is analogous to another proposed syn favored transition state (Cristol and Bly, 1961), 97, there is no direct evidence that cyclic transition states are really involved.

96

97

It should be noted that 96 and 97 are six-electron systems and the arrangement is symmetry-allowed.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

301

D. Principles of Least Motion (PLM) The possibility that reacting species prefer to react along those paths in which they undergo the least modification has always been intuitively attractive. At one time or another, so-called principles of minimum structural change or deformation, configurational change, and minimum atomic and electronic motion have been invoked (Wheland, 1960; Hine, 1966). To account for Michael’s rule of favored anti 1,2-addition, Pfeiffer formulated acetylenes as trans-bent structures in 1904! Frankland (1912) suggested that anti elimination is favored by “an inherent tendency to centric symmetry.” The more conscious applications of PLM by Muller after 1886, are probably misapplications of the principle, since they were usually concerned with complex pyrolytic reactions above 1000” (Muller and Peytral, 1924). Wheland (1960) made the point in several ways that these principles could lead to absurd errors. When ethyl chloride is treated with hydroxide ion, we obtain ethanol, not dimethyl ether; but when isobornyl chloride is treated in the same way we obtain camphene after a deep-seated skeletal rearrangement. Although nucleophilic substitution at an ethylenic center goes with retention (Miller and Yonan, 1957), the Walden inversion undercuts any general “principle of minimum configurational change.” Likewise, an early PLM representation of the R-C-R’

l 33

n

R-C-R’

N-OH

lll 3

98

99

N-OH

Beckmann rearrangement in 98 had to give way to 99 which is in accord with observation (Meisenheimer and Theilacker, 1932). Nevertheless, Hine (1966) believes he has found a variety of reactions whose course PLM appears to control. Moreover, we too have used PLM arguments in the section on substitution reactions (I11E). Initially, Hine (1966a) related PLM to the London-Eyring-Polanyi approach to three-center reactions. Since this method cannot easily be applied to most systems of interest, approximate methods have to be used. One of these minimizes bond motions and bond distortions. The geometric changes in pentadienyl or cyclohexadienyl anions brought about by protonation (Bates et al., 1967)in equation (192) are assumed to be roughly parallel to changes in bond order (BO). For deuteriation on the end carbons, C(B0)2= 2(2/3)2+ 2(1/3)’ = 10/9; for deuteriation

302

S I D N E Y I. M I L L E R

D

40%

6006

on the central carbon (B0)2=4(1/3)2=4/9(Hine, 1966a). The PLM prediction is in accord with the statistically corrected factor of three favoring deuteriation of the central carbon atom. Because the anions involved in such reactions are ambident (or polydent) and may be specifically solvated or even chelated, and because competing explanations are still current (Hoffmann and Olofson, 1966),we are not inclined to rely on small rate factors to confirm or refute alternative rationalizations of the product distributions (Bates et at., 1967). As another application of PLM, Hine (I966b) examined the atomic displacements ( D )for dehydrochlorination of ethyl chloride to ethylene. Assuming a four-center system with a fixed dihedral angle T , he minimized ,ED2 of the reacting centers with respect to translations or rotations between reactant and product. A plot of 2 D 2 versus T is given in Pig. 24. Since the activation energy depends on ED2, the predicted order of decreasing elimination rates is anti-periplanar (1SOo) > synperiplanar (0') > anti-clinal (lZO'), syn-clinal (60'). On the surface, this provides a theoretical basis for anti 1,2-processes; it accounts nicely for the observations in the preceding section on the occurrence of facile syn-eliminations. But it is not difficult to find examples which violate PLM with respect to the minimization of atom displacements. The geometric line of argument employed for the dehydrochlorination of ethyl chloride is basically a symmetry argument in which motions are minimized with respect to a center of inversion (i)and/or a plane ( 0 ) . Therefore, PLM favors symmetric bond cleavages, cyclizations, associations, etc. We have seen previously that 1,4-additions and eliminations tend to be syn rather than anti, important results which PLM would not predict. Other examples are : additions to 1,3-dienes may be 1,2 or 1,4 (de la Mare and Bolton, 1966); the reacting site of an ambident nucleophile is variable (House, 1965);the collapse of a pair of a-cyano-a-methylbenzyl radicals (CIGH,C(CH,)CN)gives more dl than meso (Peterson, 1967); the rates of hydrogen abstraction from n-butylbenzene by chlorine are higher for internal hydrogens than for those on the terminal methyl group (Russell et at., 1963);endo rather than ex0 Diels-Alder cycloadditions are favored. Beltrame et al. (1967) point out that the fast step of equation (193) is inconsistent with PLM.

CeH5.SOz. CH=C(OCHs)CHa

If chemical transformations were simply problems in classical mechanics, one could apply the methods of the calculus of variations, possibly as Hamilton's principle or the principle of least action (Page, 1935). It often does happen that minimum changes in the several factors, bond and angle deformatim, atomic motion, orbital reorganization, etc., may run parallel to or contribute to the path of lowest free energy. But the relevance of any one of these factors must be known before a cause-effectrelation can be assumed. Nevertheless, PLM is an intriguing concept. We cannot believe that the complementary shapes of plots of ZD2 versus 7 (Hine, 1966b)for dehydrochIorination of chloroethane and J1,2versus T for vicinal proton spin splittings (Karplus, 1963) can be accidental. (One would be hard put to account for J1,2in terms of PLM.) To retain PLM as a guiding idea rather than a principle, we would limit its scope and rename it, the Hypothesis of Least Motion (HLM). Given that other factors are constant, one should consider HLM. Of the elementary paths from A to B, for example, one is of lowest free energy and presumably involves the least motion. It becomes more hazardous to extend this idea to evaluate two elementary paths A to B versus A to C. Our own attitude to HLM is ambivalent : because of its simplicity, there should be no hesitation about applying HLM widely, even indiscriminately; having done this, one should assess the results critically.

E. Electrical Effects Although the interactions of charged, dipolar or polarizable groups have been investigated for various purposes, they have not often been utilized in the context of stereoselectivity. I n fact, when coulombic effects were considered in the SN2 or E2 processes, their role was regarded as unimportant (Ingold, 1953; Cristol, et al., 1951). I n view of the substantial electrostatic (field) effects estimated for polar substituents on the pK's of carboxylic acids (Tanford, 1958), metal-ion coordination (Basolo and Pearson, 1967),etc., it will be interesting to see what effects there may be on SS.

304

S I D N E Y I . MILLER

I n papers on the Walden inversion, Ingold’s group (Harvey et al., 1960) established that electrostatic forces do not contravene the normal

stereochemistry of S,2 reactions. Even in the favorable case of negative nucleophile (azide) and positive substrate (sulfonium salt), exclusive inversion occurs. Obviously, the quanta1 forces of orbital symmetry and energy obliterate the coulombic factor here. I n any case, the problem of extricating a single classical factor at an SN2 reaction site would be extremely difficult, as has been noted by Holtz and Stock (1965). These workers provide an estimate of remote dipolar acceleration in the displacement reactions of 4-substituted bicyclo[2,2,2] octylmethyl derivatives. For the transition state 100 they

I

100

calculate log[k(4-Br)/lc(4-H)]= 2*5/D, at 350°K; if the effective dielectric constant D, N 5 in 50% ethanol, they obtain a factor of ca. 3 in the rate, which is in reasonable accord with observation. Since there is an inverse dependence of the free energy on the square of the distance from the reaction site, an extrapolation to the compound in which the substituent were one or two bond lengths from the reaction site, would yield an enormous, if hypothetical, electrostatic effect. Anti-elimination also proceeds in the face of opposing electrostatic forces as in 101-103 (Banthorpe, 1963). With regard to 102, Cristol and Begoon (1952) have shown that the dehydrochlorination or dehydrobromination rates for halofumarates are 10-20 times larger than those for halomaleates at 70” in water or ethanol. These and similar observations were used as a basis for dismissing electrostatic effects. However, the superiority of anti over s y n elimination in haloalkenes is normally much larger than these factors. I n the almost “neutral” cis- and transl-chloropropenes, the factor is 102-103, and in the 1,Z-dichloroethenes, whose polarity favors a n t i elimination, the factor is 103-104 (Miller, 1961; Miller and Noyes, 1952b). Since the largest factor favoring the

STEREOSELECTION

IN

STEPS OF ORGANIC REACTIONS

305

anti process is found when the orbital requirement and the coulombic forces are aligned, and the smallest when they are opposed, we are compelled to recognize both. This is not to say that the isolation of either factor from one another and others present will be easy or even possible. 6-

6+

101

103

102

I n Fig. 25, we give scale diagrams for syn-periplanar, anti-periplanar, and syn-cyclic dehydrochlorination of chloroethane with potassium alkoxide. The standard expression for an ion-dipole interaction is given in (194) (Amis, 1966), in which the negative and positive signs are

to be applied to parallel and opposed effects, respectively. Assuming the same dielectric constant for both forms a and b and p (C-Cl) = 1.86 D, we obtain d W E 10/DEkcal mole-I. Using somewhat different assumptions, Cristol et al. (1951) obtained 7-2/OE kcal molep1 for a similar elimination from anti versus syn-clinal ( 60') forms. The effective dielectric constant is probably in the range D,=2-8 for aqueous and alcoholic solvents, with DE,anti > DE,syn(Tanford, 1958; Baker et al., 1967)or d W E 1-5 kcal mole-I. Although dipole-dipole and desolvation terms often cause concern (Amis, 1966), these would partially cancel in our application of (194).

a

b

c

F I G . 25. Electrostatic effect on dehydroohlorination by RO-K+ on HC-CC1: a, ayn; b, anti; C, syn-cyclic ion aggregate. The bond distances (A) are CC (1.54), C H (l.l), O H (1.0), CC1 (1*77),K+O- (2.8), K+Cl- (3.14);the bond angles (degrees) are CCH (IIO), CCCl(llO), C H O (180), CClO (76) in a, CClO (10) in b.

S I D N E Y I. M I L L E R

306

The introduction of ion-ion and ion-dipole attractive terms in the syn-cyclic form of Fig. 25 adds a term -15-2/0, kcal mole-l. The comparison of syn-cyclicand anti forms yields d W N - 5/0, kcal mole-*. These electrostatic factors favoring the syn-cyclic form are exaggerated, since there is probably some compensating ion-pairing in the anti transition state. I n view of the approximate nature of the model, and the complete neglect of nonelectrostatic factors, no great weight should be placed on the absolute values of d W . I n particular, comparisons between the anti and syn-cyclic transition states are the most suspect, since the assumptions that have to be made about them are different and are likely to introduce errors which do not cancel. Nevertheless, it appears that the crude figures do indicate that an electrostatic factor could accelerate some eliminations, e.g. 103, and retard others, e.g. in 102. Of course, whatever one might decide about the electrostatic influence of an electronegative substituent, just the opposite conclusions would apply if base-promoted elimination from onium species such as 103 were considered. Ion aggregation would, of course, favor syn elimination. The proportions of cis product formed in equation (195) provide a n-CaH9.CHX * C4Hg-n

RO-,ROH

3

n-CaH7.CH=CH.CaH9-n

(195)

test of these ideas. The data (Zhvada and Sicher, 1965) given in Table 10 are consistent with increasing syn-elimination of the bromide and decreasing syn-elimination of the onium salts, when the solvent changes from methanol to ethanol to t-butyl alcohol. Although ZAvada and Sicher considered that their eliminations were E 1cB-like,the available evidence on analogous systems is that they are E2 (Bourns and Smith, 1964; Saunders et al., 1966). More recently, the Czech workers have also been using the notion of ion pairs such as 96 in t-butyl alcohol to explain some oftheir observations (ZAvadaet al., 1967). This is wholly consistent TABLE 10 Per cent cis-Product of 5-Nonyl Derivatives (Zhvrtda and Sicher, 1965)with ROH-RO- in equation (195).

Per cent

X, in (n-C4Hg)&HX

Temp., "C

Br (CH3)&+ (CHshS+

100 70,120 100

R=CqHg-t R=CzHs

40 26

9

23 74 64

R=CHB

21 81 -

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307

with observations on other reactions in which potassium t-butoxide participates : ion pairs promote electrophilic substitution at carbon with retention (Cram, 1965, Ford et aZ., 1967); an ion triplet effects a-elimination and rearrangement of l,l-diaryl-2-haloethenes(Pritchard and Bothner-By, 1960). Since the E 2 syn-eliminations in low dielectric solvents are explicable by model c of Fig. 25, the electrostatic factors should be recognized independent of whether orbital symmetry, steric, etc. predictions can or cannot account for observed SS. Dipole-dipoleinteractions have been used to assess the conformational populations of 2-haloketones (Eliel et aZ., 1965). With respect to SS, however, there are few applications in which these and related effects are considered. It is interesting that dipole induction and London dispersion effects were used some thirty years ago to account for the high endo over exo preference in the Diels-Alder reaction (Wassermann, 1965). Although effects are small for any pair of atoms, there are many closely packed atoms in a Diels-Alder transition state. At a carbon-carbon distance of 2.0 d between the atoms to be bonded, the energy favoring endo addition is 2.7 for dipole induction and 3.4 kcal/mole for dispersion in the reaction of cyclopentadiene with p-benzoquinone (Wassermann, 1965). These nonbonding attractive energies cooperate with the secondary HMO effects discussed earlier to lead to an endo product. Because chemists now have much more experience with these induction and dispersion terms, and the tedious calculations can be done on a computer, we believe Wassermann’s work should be repeated and extended. It will be interesting to have more examples of aUowed 6 + 4 additions in which the secondary HMO bonding forces, which favor exo-cycloaddition, are pitted against the nonbonding forces, which favor endo-cycloaddition. As a final example of this section, we cite Benson and Haugen’s (1965) electrostatic model for the prediction of activation energies for fourcenter gas phase reactions. Of interest here are the additions of hydrogen, halogens, interhalogens and hydrogen halides to alkenes. T o obtain the calculated value of the activation energy for the addition reaction (196),

-

c2H5 CH=CH2

+BrH

--f

czH5 .CRBr.CHS

(196)

Benson and Haugen utilize the following energy terms (in kcal/mole) :

*+

t-

t-

t+

to form the semi-ion pairs C2H,CH.CH2, 9-03; and Br-H, 32.2; to account for dipole-dipole interactions, - 10.1 ; and in the change in polarization energy in BrH, - 1.1 ; in going to the transition state London dispersion energy terms were small, < 0.5 kcal mole-I, and were neglected. After correcting the activation energy from 0°K to 298”K, these workers obtain Et$=29*2 compared to E;’i* 26.9. Although

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S I D N E Y I. M I L L E R

the initial assumptions and semi-ionic models are arbitrary, they are consistently appropriate in a large number of additions. Of these, some twenty calculated activation energies check observed values reasonably well. Benson and Haugen's approach is sufficiently successful so that it could perhaps be adapted to solution reactions. Problems with D , and desolvation energies may not be overcome, but even rough estimates of the electrical factors affecting XX would be useful.

V. STEREOSELECTION DERIVING FROM STERICAND CONFORMATIONAL FACTORS Because there are several excellent sources (Hanack, 1965; Eliel

et al., 1965) which deal with steric effects and conformational analysis, we can limit our discussion to two topics related to SS, namely the qualitative and semiquantitative evaluations of steric effects and quantitative conformational analysis. In some cases, the origins of SS can be assigned unequivocally.

A. Steric Effects Matter being what it is, any effort to separate bulk effects cleanly from electrical effects is doomed to fail. For many years now, organic chemists have pragmatically tried to isolate steric factors, although these are usually specific, rarely additive, and often entangled with electronic effects. Nevertheless, there is a large mass of data in which the bulk factor, as steric hindrance or acceleration in rate processes, seems readily visible, e.g. racemization of substituted biphenyls or 1,l'-binaphthyls (Cooke and Harris, 1967). I n the classical type asymmetric reduction in which 64 is preferred to 65, the ethyl group (R) of cis-1-butene-d prefers to be as far as possible from the groups on boron. Now, there is no satisfactory theory of steric effects, although attempts to rationalize the barrier of ethane by quantum-mechanical calculations are appearing more frequently (Clementiand Davis, 1966). Furthermore, simple group-additivity schemes of various kinds have had limited success, a t best, e.g. for estimating rotational barriers in ethanes (Tang and Chen, 1962), correlating relative reactivities with Taft E, values (Wells, 1963), or evaluating asymmetric induction (Ugi, 1965; Ruch and Ugi, 1966). Semi-empirical calculations by equation (197) have

+ Ebend +Etors. + Enonbond.

(197) been used to generate reasonable estimates of relative isomer or conformer stability as well as energy barriers in a few interesting systems = Estretch

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

309

(Allinger et ul., 1967). The total strain energy is arbitrarily ascribed to a sum of effects, bond stretching, angle bending, bond rotation and nonbonding interactions ; electrical terms are added, if required. Two reactants approach one another and in addition to bonding, there will be nonbonding interactions. At shorter distances, the non-bonding effects could be accompanied by compressions, deformations or torsions, or all of these. I n fact, when other factors and the Enonbond. term are constant, minimization of Etotamounts simply to the PLM. This is one link between XX and (197). I n successful applications of (107), one should not lose sight of the fact that these are mainly to nonpolar molecules. The truth is that no satisfactory theoretical or even semiempirical approach can account for the greater stability of certain cisoid over trunsoid isomers, e.g. dihalo-

b

b

C

C

FIG.26. Scale diagram of 1,Z-dibromoethaneand &hone. cc, ethane CC; c’c’ ethene CC; bb, syn BrBr; b’b’, syn BrBr; hh, syn HH; bb,, syn-clinal (60’) BrBr.

alkenes, difluorodimide (Bohn and Bauer, 1967), 1,4-difluoro (or chloro)-l,3-butadiene (Viehe and Franchimont, 1964), or gauche over trans rotamers, e.g. 1,2-dicyanoethane, sym-tetrabromoethane, etc. (Lee and Miller, 1960). Although one may label the forces “polarizability”, London, van der Waals, etc., their evaluation seems uncertain, particularly as solvent effects are often superimposed on them (Lee and Miller, 1960). A measure of the delicate balance between attractive and repulsive forces is indicated graphically in Fig. 26. cis-1 ,2-Dibromoethene is ca. 0.5 kcal moleF1 more stable than trans-l,2-dibromoethene. I n sym-tetrabromoethane, the gauche form is more stable than the trans form (not shown) by cu. 1 kcal mole-’ (Kwok and Miller, 1967a). Relative to the guuche form (bb,), the eclipsed form (bb) is higher in energy by ca. 6-10 kcal molep1 (Tang and Chen, 1962). At the b’b’ distance of cis-dibromoethene the intramolecular forces are attractive ;

310

S I D N E Y I . MILLER

they are even more attractive at the bb, distance in gauche-tetrabromoethane, but have become repulsive a t the bb distance of syn-tetrabromoethane. Incidentally, all of these Br-Br distances are less than the sum of the van der Waals radii of two bromine atoms or ca. 3.9 A. Without inquiring into causes or origins, we note that all eclipsed ethanes, cis-alkenes with nonpolar substituents, and axial monosubstituted cyclohexanes are high-energy isomers. These rotational barriers and relative isomer stabilities may be regarded as the manifestation of “steric” effects; in eclipsed forms, these will be “cis ” effects. Clearly the intuitive association of bulk and nonbonding repulsions is sound. Even in Fig. 26, in which we have seen a striking energy reversal with polar substituents, the scale of nonbonding attractive energies is relatively small, while that of nonbonding repulsion is presumably unlimited. Some years ago one could point to an electronic factor (Ingold, 1953) or to a steric factor (Cram, 1956) and account for favored anti-elimination. I n a simple ethane, the latter cis effect would appear to be chiefly due to d&o,)bond. of equation (197). I n a cyclohexane, dEnonbond. for the boat ‘uersuschair form would be even higher. As pictured in (198), only the ground state repulsions of reactants are indicated. We can elaborate this older view. X

__f

B& A

A -X,Y

i)

zB& J

A A (198) B

Y

The steric and electronic effects which seem independent can be interrelated as follows. As X and Y leave the alkane, the T orbital begins to form ;X and Y move away from the carbon atoms in directions indicated X + X’, Y --f Y‘ in 104 and 105. Except for a few XY pairs, e.g. the lower hydrides, most X Y distances exceed the carbon-carbon double bond distance, even when the atoms are bonded. Moreover, since X and Y are generally not bonded to one another, the syn transition state will have a large nonbonded interaction. If 105 were an alkene or cyclohexane, the repulsions would be even larger in the planar form. We would also guess that in 105, the necessary reduction in the size of the solvation sheaths of X and Y in solution would be energetically costly (Amis, 1966). Therefore, the incursion of nonbonded effects both in the ground state and in the transition state of process (198) combines

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311

with a bonding (orbital symmetry) preference to produce favored anti over syn elimination.

104

105

106

I n a cyclopentane or norbornane, the steric factors change, for the initial choice in an elimination is between two eclipsed forms. We have already seen that, according to PLM, syn-periphnar (0’) elimination of X and Y syn is preferable to X and Z anticlinal(120°).I n 106, the possibilities are illustrated for a cyclopentane (or norbornane). Note that atoms y or 6 and X or Y are “skew”, while /3 and Z are eclipsed. For ezo-syn departure (as in 93) X and Y would move anticlockwise in the direction of the vertical arrow along the incipient r orbital, while Z and W would move away from /3 and ainto the horizontal position. Foranticlinal departture of X and Z in the direction of the incipient rr orbital, Z would suffer nonbonded syn repulsion of /3. Obviously the least favorable elimination is endo-syn, in which both Z and W would have to move toward the incipient 7~ orbital and encounter nonbonding repulsions from 18 and a. Without a detailed calculation, it is not clear to what extent the other and Ebend have to be considered here. terms of equation (197), e.g. Etors. But, it does seem clear that the relative rates (circledatoms depart) given by LeBel et al. (1964) for 92-95, are plausible for steric reasons. If this is so, the coplanarity principle also has a steric basis, in these eliminations. I n the preceding explanation, we have ignored bonding factors. I n the norbornanes (106), at least, frontier electron reactivity indices (Fukui and Fujimoto, 1965) actually appear to favor sy?z-exo elimination. Normally, syn-elimination is in violation of the orbital symmetry rule, and we are inclined to accept anti elimination as the standard. Even so, we believe that powerful steric factors may overcome apparently unfavorable bonding factors to produce novel 55, as in 92-95. The kind of argument just given also seems appropriate for 1,2rearrangements in which the migrating group inverts the terminus. Independently of the charge on the cyclic intermediate or transition

312

S I D N E Y I. M I L L E R

state, nonbonding interactions are minimized in 107-109 as they would not be in 110 and 111. Now, although Simonetta and Cam& (1963) consider alternatives in anti migration of 109 in their HMO treatment of the rearrangement, they ignore the syn form 110 completely, presumably because of the less favorable geometry for bonding. But here, too, as in 107 and 108, it would appear that both the steric and the electronic factors jointly favor anti rearrangement. R

k 107

109a

lOSa

10s

110

109

111

There are perhaps only two research areas in which the quantitative estimation of steric factors is routinely done, namely for hindered biphenyls (Cooke and Harris, 1967) and rotational or pseudorotation barriers in ethanes and cyclic compounds (Allinger et aE., 1967). There are indications, however, that this interest is widening. Simonetta and Favini (1966) performed conformational calculations on the Cope rearrangement via chair or boat transition states and indicated that the orbital preference emphasized in a previous section should be supplemented with a steric factor. Garbisch et al. (1965) examined the reactivity of a wide variety of alkenes with diimide. The observed range in reactivity of 38000 was Etors.,and a-alkyl substitution. ascribed chiefly to terms such as Ebend, Unfortunately, those reactivity differences pertaining to SS generally turned out to be small and could not be generated by this approach: the at 80" gave trans/& = 2-3. reduction of 1-methyl-4-t-butylcyclohexene An interesting correlative approach was used by Schleyer et al. (1966)

STEREOSELECTION I N S T E P S O F ORUANIC REACTIONS

313

to estimate rates of a reaction controlled by steric and electrocyclic (orbital symmetry) factors. I n equations (27)and (28),the concerted solvolysis and ring opening of cyclopropyl systems are disrotatory . By allowing an electronic factor of 70 in the rate for each methyl substituent in cyclopropane, neglecting entropy effects, and judging the steric factor from model compounds, these workers assessed relative rates in (199)by the formula (200). The O.S. (orbital symmetry factor) =unity

Rel. rate=O.S. x 70nx e - d H a t r d f f T

(200)

or zero, and n = t h e number of methyl groups. As a model for the reaction of 2,2,3,3-tetramethylcyclopropyltosylate, the “ U ” carbonium ion of (199)is considered to possess 7.6 kcal mole-l strain energy based on 1,8-dimethylnaphthalene. Since cis methyl t--) methyl and 1 ,I dimethyl t+ tosylate ground state strain terms amount to 2.8,AHstrain = 4.8 kcal mole-l. The calculated relative rate is (70)4x e-4’8/RT,38,000 at IOO”, which is within a factor of 5 of the observed rate. I n all, relative rates covering a factor of 48000 of seven cyclopropyl tosylates were estimated in this fairly intuitive fashion. In this paper, the electronic factor was related to methyl stabilization of a cation; the interesting problem of the degree of electrocyclic control, i.e. O.S. factors between zero and unity, were not considered. Gleicher and Schleyer (1967) used a more sophisticated approach based on (197) to investigate the rates of solvolysis of bridge-head polycyclic bromides. They computed the strain in going from ground to transition states and were able to estimate rate constants on the average to within a factor of 1010’8in a range of reactivity of Although SS was not involved here, we anticipate that the general method will be used to investigate other large SS factors.

B. Conformational Analysis Concerning “ conformation ”, we prefer to adopt a broader definition than has generally been used heretofore. Excluding normal molecular vibrations, relative atomic motion that breaks no bonds within a molecular framework generates conformations. A usual definition which specifies that conformations are attained by rotations about bonds is far too restrictive, considering that the conversion of one chair form of cyclohexane to another involves several complicated coupled rotations and 11

314

S I D N E Y I . MILLER

deformations. I n any case, intramolecular motions are not likely to be “ pure ” stretch, bend, or rotation, particularly when these interconversions are often used in a conventional conformational context. Our definition, then, includes the “ mixed” motions : rotation in ethanes and biphenyls, rotation and inversion at nitrogen in amines or hydrazines ; syn-anti bending (wagging) in imines ; bending in the inversion of trimethylamine; rotation and twisting in the “inversion” or “flipping ’’ of cyclohexane; bending and stretching in the “pseudorotation’’ of phosphorus pentaphenyl; rocking in the bridges of a cyclophane; coupled rotations in the uncoiling of an R-helix; folding in 5,lO-thianthrene (or 9,lO-dithiaanthracene) dioxides ; translations within the loops of a catenane or in the cavity of a clathrate. Our definition is intended to be an operational one, since it is based on detectable or observable molecular motions, or essentially energy transitions. At the lower end of the energy scale the energy transitions presumably shade into strongIy anharmonic vibrations. No upper limits on the energy barriers between conformations are set, since none are meaningful : rotational barriers span the range of several callmole to 20-30 kcal mole-l (Miller, 1964); inversion barriers starting with 1-2 kcal mole-l andincreasing beyond 50 kcal mole-l (Koepplet al., 1967) have been estimated. An inherent weakness in our (or any) definition of conformation stems from the fact that the existence or the nature of a chemical bond is often debatable, e.g. in an ion pair, clathrate, amide, etc., so that the notion of bond breaking is sometimes difficult to define. The second weakness in our definition, namely its breadth, can perhaps be remedied by having smaller sub-categories, e.g. rotamers, invertomers, etc. Conformational analysis is something one does to, with, on, etc. conformations (or stereoisomers) and amounts to an examination of the role of conformations (or stereoisomers) in any context as carefully as one can. With respect to S S , this usually pertains to energies of the conformations of species on the reaction paths. By its definition in ( l ) , 88 implies comparison. Thus, the barriers between and the relative energies of the pairs gauche-trans,cis-trans, meso-dl, chair-boat,R-S, etc., which, in fact, are not necessarily conformers, normally enter into a conformational analysis. Where the isomers are interconvertible and one lies on a reaction path, the energy barrier between them may determine 88 of an overall process. Although energy differences in the relatively stable forms of ethanes (Peterson, 1967 ; Kingsbury and Best, 1967a), alkenes (Bohn and Bauer, 1967), cyclic compounds (Eliel et al., 1965; Reeves, 1965), or motional barriers in ethanes (Dale, 1966), biphenyls (Badar et al., 1967), cyclic compounds (Eliel et al., 1965;

S T E R E O S E L E C T I O N I N STEPS O F O R G A N I C R E A C T I O N S

315

Reeves, 1965), pyramidal species (Koeppl et al., 1967), aziridines (Anet and Osyany, 1967), azo compounds (Talaty and Fargo, 1967), imines (Curtin et al., 1966), some trigonal bipyramids (Muetterties and Schunn, 1966), etc. are known, similar energies for radicals, carbanions, carbonium ions, are generally unavailable. Our quantitative approach follows the phenomenological treatment usually given for conformational isomers. Consider the free-energy --f PI and R2 + (T2)* -+ P2 (201) R1 + (TI)* profiles for two elementary reactions (Fig. 27) in which reactants, transition states and products are indicated. The expressions for the

(202) ACT = Gf-G(R,) and AG$ = GZ-G(R,) free energies of activation are given in (202). The basic comparison is given by

(GZ-Gt) = (AGZ -AG:)+(G(R,)-G(R,)) (203) Similar relations hold for the enthalpies and entropies. Clearly, there is no unique stereochemical content attached to this relation, and it may

FIG.27. Free energy profiles and stereoselectivity: Ri -+ Pi and Ra + Pa.

S I D N E Y I . MILLER

316

be used for any comparison whatsoever. Moreover, information obtained about the free-energy difference of the transition states in forward reactions can obviously be used to obtain information on often unobservable reverse reactions under the same conditions. The exact free-energy relations given above describe rather than account for stereoselectivity in conformationally interesting systems. If too many of the terms are missing in these equations, attempted interpretations, explanations, etc. of SS remain equivocal. Any single isomer or conformation may react by more than one path to yield different structural isomers, diastereoisomers, geometric isomers, etc. RI + Pi’+ Pi”+Pi”’ In general, for these products, (203) leads to (205):

(204)

(G*‘-G*‘‘) = (dG*’-dG*:”) (205) For mobile systems in which R1 and R2are in equilibrium throughout, R1 + R3 K = (R2)/(Rl) (206) a corollary can be deduced. The ratio of the rate expressions yields : ,(207) d(P,)/d(Pl) = k2(R2)r/kl(R1)r= K‘k2/kl Since r = 1 in most cases of interest, we need not carry it further; the treatment can easily be generalized to include any r . Substituting the appropriate free energies in (207), we obtain

-RTln[d(P,)/d(P,)] = (G(R,)-G(R,))

+ (ACT,+ -da:)

(208)

If (203) and (208) are compared, we obtain (209). -RTln[d(P,)/d(P,)] = (G,+ - Gf)

(209)

If one reactant of the pair yields several products (204), then any two products in this system may be compared in (209). This is the CurtinHammett principle, which states that the product ratio or the reactionrate ratio depends only on the transition state energies, provided the equilibrium in (206) is maintained (Eliel et al., 1966). Finally, there is an extra-thermodynamic assumption, which one can make about two molecules whose reactivity one wishes to compare. The basic idea is not unfamiliar, since it is inherent in the Bronsted linear free-energy relation. The assumption is that the free-energy differencein the transition states is bracketed by reactants and products. The factor O! provides a numerical index between zero and unity of the

(G- G f )

= 4 W 2 )

- G(R1))+ (1 - 4 MP2) - G(P1))

(210)

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317

progress of the reaction, of how much the transition states resemble reactants and how much they resemble products. The success of this relation depends on the monotonic increase or decrease in the free energy difference between the energy profiles being compared. This relation is not binding (Kwok and Miller, 1967a), but it may be useful where it applies. We shall begin with (210), a conformational relation of uncertain applicability and work towards those that hold rigorously. The simplest application of the a-idea is to reactions which begin with one compound

and follow different stereo-paths (211). Applied t o the protonation of nitronate ions formed from 4-t-butyl nitrocyclohexanes, (212), this relation is in accord with product-like transition states (Bordwell and 1 the ratio of the rates of Vestling, 1967). Since K = (113)(114)~ 4 1 and protonation is k( 113)/k(114)N 1/3,we find (1- a)1:3/4. Another example of this type is found in the aluminum hydride reduction of 3,3,5-trimethylcyclohexanone at 34' in (213) (Ayres and Sawdaye, 1967) for which we calculate Ct&, - G,",, N 1 kcal mole-l, while Eliel et al. (1965) 0

I -

.N-0

113

112

114

115

116

318

S I D N E Y I . MILLER

give Gl16- Gl15 N - 1.6 kcal mole-l. Since (1- a) cannot be negative, the extra-thermodynamic assumption (211) does not apply. We see that the proper transition states for this reduction are not bracketed by reactant and product(s). This failure and others like it (Lee and Miller, 1960; Kwok and Miller, 1967a) compel one to seek causes of the nonadditivity of free energies and to ask whether the terms "reactant-like" and " product-like " are meaningful. A more general application of (210) and (211)is found in unpublished data from the author's laboratory, on debrominations of the stilbene dibromides with lithium bromide or stannous chloride. Fig. 27 is a

scheme which gives the general pattern of free energies. The value of Gdl- G,, = 0-78kcal mole-l at 80"was obtained for the solvent benzene, but it is not expected to vary much with solvent. The figure Gcis- G,,,, = N 5.7 kcal mole-' was assumed equal to the reported enthalpy difference of the stilbenes (Williams 1942).Our rate data yielded dG$ - dG$,,,, from which the other quantities could be found. For eliminations in the anti sense with lithium bromide or stannous chloride, a$- G$,,,, = 4.4 4.6 kcal mole-' and a = 0.1-0.2. Judged by the magnitude of a, these eliminations have product-like transition states. With respect to stilbene chemistry the pattern of Fig. 27 is rather general. That is, the relative reactivity of the two stilbenes is often small, e.g. within a factor of two in some (not all) additions of bromine (Buckles et aZ., 1967), 2,4-dinitrosulfenyl chloride (Slobodkin and Kharasch, 1960) or trichloromethyl (Cadogan and Inward, 1962). A different effect of these product-like transition states is seen in the fact that the overall debromination of dl-stilbene dibromide with lithium bromide may proceed in the syn sense. That is, the rate ratio a t 59" k(meso)/k(dZ)= 50 is composite. I n the dl compound, electronic factors which favor anti elimination collide with steric or conformational factors, which favor either bimolecular syn eliminations or some other path to trans-stilbene. The rate ratio for production of transstilbene k(meso)/k(dZ)N 60, while that for anti elimination is k(meso)/k(dZ) N 310.

S T E R E O S E L E C T I O N I N S T E P S O F ORGANIC REACTIONS

319

An analogous case of a powerful stability (thermodynamic) factor (low a) is given in the system -0.OC. CHC1.CHCl .CO. 0-

OH__f

c1, ,co.o-0. oc/c=c‘H

(215)

meeo or dl

in which Hughes and Maynard (1960) propose an E2 mechanism for dl and an ElcB mechanism for meso. I n the meso compound all factors cooperate to favor anti-elimination. I n the dl compound, the electronic factor is opposed, and presumably overwhelmed, by a conformational and/or an electrostatic factor(s), so that a syn-elimination is observed. We turn now to a group of related reactions (216) in which approaches to SS have sometimes seemed intuitive or capricious. The kinetically controlled ketonization of an enol (or enolate) in (216) by bromination, protonation, reduction, etc., often gives the cis-ketone predominantly. Zimmerman’s (1963) rationalization of these results tends to neglect 119a; attack from the more exposed (equatorial) direction of 119b would make X equatorial and lead to 118b. Johnson and Malhotra (1966) worry about the cis interaction (A1*3, of R with the substituents on Y and begin with 119a ;to avoid the high energy conformation 117a, X attacks at the axial position to give 118a. I n the first case, the most favorable conformation 117b is avoided by hindrance to entry of X; in the second case, the least favorable conformation is avoided by a product-like transition state. These contradictory rationalizations cie-(a-R,e - Y) ilea

L

7

cis-(e-R,a-Y)

ll8b

R 119a

119b X

trans-(a-R,a - Y ) 117a

-

11 -

a-attack

trans- (e-R,e Y)

117b

Y=O, NO2-, CN, G(OH)R, C(O-)R

320

S I D N E Y I. M I L L E R

account for the same observation, namely, that the cis product usually predominates. Surprisingly, the actual rates of axial and equatorial entry of X in (216) need not be very different! This becomes understandable in the context of a conformational analysis (Bordwell and Vestling, 1967). We use proton abstraction from nitrocyclohexanes and the reverse reaction (see (212)) to investigate the origins of SS. The scheme of Fig. 27 may be helpful here. For the deprotonation of the 4-t-butylnitrocyclohexanes of (212), R=H and k(114)/k(113) N 5;the equilibrium 21 1/5 (Bordwell andvestling, 1967). Therefore, constant K = (114)/(113) the free energy difference for the transition states, G:& G&4N 0. Assuming that this transition state difference will not change appreciably with pH for protonation and deprotonation, we conclude that axial and equatorial entry is about equally probable in this medium at 25'. The relations become complex when all of scheme (216) must be 118) considered. When 2-arylnitrocyclohexanes are involved, K = (117)/( N 100, and the deprotonation rate ratio E(118)/k(117) 21 200 (Bordwell and Vestling, 1967). Again, near-equality within a factor of two is indicated in the transition-state free energies. To assign a probable mechanism, we must investigate the energy relations implicit in (216). I n Fig. 28, a scheme is formulated for compounds such as Z-arylnitrocyclohexanes. Note that. the tie lines connect readily interconvertible rotamers, that there are four potential reactants, four corresponding transition states and two nitronate intermediates. Our ordering of the conformational energies is in part speculative. Unless 33 is effectively larger than NOz,the deployment of the ground states (117,118) is sound. The a - R nitronate was assumed to be of lower energy than the e-R nitronate, because of an A1. interaction (Johnson and Malhotra, 1965). As for the transition states these were assumed to resemble the nitronates more than the reactants ; therefore the left-hand transition states were placed lower than those on the right-hand side. According to this picture, deprotonation and protonation would proceed only through the transition states on the left-hand side of Fig. 28. This chain of reasoning leads to the conclusion that axial and equatorial protonation of the nitronate would proceed chieflyfrom 119a,and the factor favoring 118a over 117a would be ca. 2 in the rate constant. Although deprotonation would therefore begin with 117a and 118a,the major species present in the reactants are 117b and 118a. The preceding analysis is weakest, of course, where the assumptions take over from the facts. The advantage of such an analysis is that it does attempt to take into account explicitly all of the relevant free-

-

STEREOSELECTION IN STEPS OF ORGANIC REACTIONS

321

4

ac(e-R)

+

aT(e-R)

+

~

aT(a-R)

*

. ac(.-R)

(e -R,NOz)

119b 119a

AG'

-R)

ll8b

?-R,a-NOZ) &(a-R,

e-NOz)

ll8a

trans(e-R, e-NOz)

lllb FIG.28. Conformation analyses for proton abstraction from 2-R-nitrocyclohexaneand the protonation of the nitronate ions. See also equetion (216).

energy terms. This may include a free-energy diagram even more complex than Fig. 28, that is one in which flexible (skew-boat) conformations are included. For reductions of the general type given in (213) (Landor and Regan, 1967) as well as in a variety of other reactions, the participation of flexible forms is an accepted hypothesis (Robinson and Theobald, 1967).

VI. CONCLUSIONS Every reaction a t the molecular level is stereospecific (axiom 1). For a collection of molecules the elementary reaction is stereoselective (axiom 2). When several elementary reactions make a sequence, the i

overall SS is a product of the type n(SS),. Apart from the remarkable stereospecificityof enzymes, many multistep processes fall into a pattern. An intermediate is formed; it may be trapped to give PI and/or P2, or 12

322

SIDNEY I. MILLER

it may isomerize to or equilibrate with a second intermediate, which may be trapped, etc. This isomerization may be a rearrangement, rotation, inversion, pseudoinversion, etc. High SS will arise when alternative paths are precluded, k(trapping)9 k(isomerization), or when (8~9)~ of individual steps is high. There are two distinct problems here, namely, the stereoselectivity of the elementary and/or trapping steps, which has been our chief concern, and the stereostabilities of intermediates. I n order to penetrate to the problem of SS in a reaction sequence, one must examine the detailed mechanism. General schemes were considered, in (26) for a molecular reaction, in (142) for substitution of an alkene carbon, in (175) for a carbonium ion rearrangement, in (216) in a conformational context, etc., but our attention to mechanism was, of necessity, limited. Consider the process in equation (217) (Gunning and Strausz, 1966; Lown et al., 1967). Additions of triplet (T)sulfur to butenes in the gas phase can be stereospecific syn. Here, overall SS depends on kz 9 k6 and k,(M) $ k8, in which M is the concentration of inert gas. The syn addition of sulfur

presumably gives an energyin the first excited state, or singlet (ID), rich episulfide; now, high SS depends on k,(M)%kE,. Other kinetic analyses of mechanism, in which overall SS was at issue have been given for electrophilic additions (de la Mare and Bolton, 1966), El and ElcB mechanisms (Lee and Miller, 1959), Wittig reaction (Johnson, 1966), the fate of benzhydryl benzoate ion pairs (Stedronsky et al., 1968), etc. I n all of these reactions, the intrinsic question of mechanism and S X are indistinguishable. I n setting down “rules” and generalizations about SS, we have undoubtedly played down or ignored exceptions and violations. This was not our intention. Some of these cases arise, where there is unrecognized mechanistic complexity ; the clarification of the mechanism of certain bromine additions, e.g. by an ion pair mechanism, made synaddition unexceptional. Some violations fall into the category of

S T E R E O S E L E C T I O N IN STEPS O F ORGANIC REACTIONS

323

apparently forbidden or high-energy reactions, e.g. (97), which are justified by a more careful examination of the orbital-symmetry relations. On the other hand, the “wrong” stereospecificity for certain molecular cycloeliminations (62) has yet to be explained. By relaxing the anti-rule, and defining large conformational and/or electrostatic factors, we could provide a rationale for some syn additions and eliminations, (188), (189) and (191), in polar media. Nevertheless, many observations still lack a theoretical basis, and many of the theoretical predictions of SS in our tables lack real examples. Although any complex reaction sequence may possess a unique combination of elementary steps, our major concern was with the SS of each step in isolation. Of the several major and minor factors that bear on this problem, it appears to us that orbital symmetry and energy establish the stereochemical norms. The other factors are less understood, but no less important. On the simplistic binary level, we can check the factors in turn: orbital allowed or forbidden; orbital energy, high or low; bulk effect, positive or negative; conformation favorable or unfavorable ;electrostatic and nonbonding forces, attractive or repulsive ; and etc. Unfortunately, it is not yet possible to weight and interrelate these factors with any precision. To evaluate these opposing forces would be a long step toward understanding chemical behavior in general. Following a recent admonition (Gleicher and Schleyer, 1967) the reader should, if the writer did not, distinguish between prediction and hindsight, sequence and consequence (post hoc ergo propter hoc), and conformity and truth. REFERENOES Aguiar, A. M., and Archibald, T. G. (1967). J . Org. Chew. 32,2627. Aksnes, G., and Bergesen, K. (1966). Acta Chem. Scad. 20, 2608. Allinger, N. L., Miller, M. A., Vancatledge, F. A., andHirsch, J. A. (1967). J . Am. C h m . SOC. 89, 4346. Alster, J., and Burnelle, L. A. (1967). J . Am. Chem. SOC. 89, 1261. Amis, E. S. (1966). “Solvent Effects on Reaction Rates and Mechanisms”, Academic Press, New York, Chapter 11. Anastassiou, A. G. (1967). J . Am. Chem.Soc. 89, 3184. Andersen, K. K., and Papanikolaou, N. E. (1966). TetrahedronLetters 6445. Ando, T., Yamanaka, H., and Funasaka, W. (1967). IPetrahedron Letters 2687. Anet, F. A. L., and Osyany, J. M. (1967). J . Am. Chm. SOC. 89, 362. 89, 876. Applequist, D. E., and Chmurny, G. N. (1967). J . Am. Chem. SOC. Atkins, P. W., and Symons, M. C. R. (1967). “The Structure of Inorganic Radicals”, Elsevier, Amsterdam, Chapter 7. Ayres, D. C., and Sawdaye, R. (1967). J . Chem. Soc. (B) 681. Badar, Y., Cooke, A. S., and Harris, M. M. (1967). J . Chem. SOC. (B) 1316.

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AUTHOR INDEX Numbers in italics refer to the pages o n which references are listed at the end of each article. Barbieri, R., 81, 98 Barlin, G. B., 94, 98 Abrahamson, E. W., 210, 212, 215, 328 Barltrop, J. A., 220, 324 Ackermann, T., 86, 98 Barrett, J. H., 219, 330 Aguiar, A. M.. 269, 323 Bartell, L. S . , 113, 129, 137, 138, 156, 179, Akasaki, Y., 220, 331 180 Aksnes, G., 258, 323 Barton, D. H. R., 246, 324 Albery, W .J., 91, 98 Barton, T. J., 209, 324 Mi, L. H., 220, 325 Besoombe, K. N., 86, 98 Allinger, N. L., 266, 267, 297, 307, 308, Basolo, F., 303, 324 309, 312, 314, 316, 323, 326 Bates, R. B., 301, 302, 324 Allred, A. L., 72, 87, 100 Bates. T. W., 156, 179 Alster, J., 199, 323 Battiste, M. A., 209, 324 Amis, E. S . , 306, 306, 311, 323 Batts. B. D., 63, 81, 84, 98 Anmtassiou, A. G., 264, 323 Bauer, S. H., 199, 309, 314, 324 Andersen, K. K., 259, 323 Baur, W. H., 148,179 Ando, T., 207, 323 Begoon, A., 305, 325 Anet, F. A. L., 315, 323 Beirne, P. D., 298, 312, 328 An6nsen, C. B., 104, 179 Bell, R. P., 66, 67, 70, 73, 86, 95,96,97, 98 Angyd, S. J., 297, 307, 308, 314, 316, 326 Beltrame, P., 199, 302, 324, 325 AN&, J. L., 6, 60 Benson, S . W., 243,245,308,324 Applequist, D. E., 263, 323 Bergesen, K., 258, 323 Applequist, J., 169, 179 Bergson, G., 124, 142, 179 Arakawa, S., 168,180 Berry, R. S., 2, 58 Archibald, T. G., 269, 323 Berson, J. A., 239, 240, 287, 324 Aritomi, J., 168, 180 Berthelot, A., 9, 54, 58 Arnett, E. M., 78, 98 Berthod, H., 131, 179 Arridge, R. a. C., 130,179 Best, D. C., 289, 314, 328 Agperger, S., 307, 330 Beychok, S., 170,179 Aten, C. F., 56, 58 Bickel, A. F., 248, 327 Atkins, P. W., 197, 199, 200, 323 Biemann, K., 6, 60 Ayres, D. C . , 316, 323 Bigeleisen, J., 70, 98, 191, 324 Bigelow, C. C., 179, 179 Bijvoet, J. M., 106, 179, 183 Biranowski, J. B., 275, 324 Badar, Y., 314, 323 Bird, C. L., 293, 324 Bader, R. F. W., 294, 324 Bimhtein, T. M., 118, 168, 179 Baird, M. S . , 206, 324 Bishop, B. M., 67, 98 Baker, F. W., 306, 324 Bittman, R., 275, 331 Baldwin, J. E., 232, 324 Bixon, M., 129, 137, 138, 142, 145, 156,179 Baldwin, M. A., 299, 324 Bjerrum, J., 81, 98 Baliga, B. T . , 63, 78, 92, 98 Blomquist, A. T., 219, 324 Banthorpe, D. V., 299, 305, 324 Bly, R. S., Jr., 300, 325 Bmtjes, A., 35, 61 Bodenheimer, E., 169, 170, 180 Barasch, 'W., 285, 325 Bohn, R. K., 199, 309, 314, 324 333

A

B

AUTHOR INDEX

334

Bollinger, J. M., 282, 329 Bolton, R., 276, 282, 302, 322, 325 Bommel, A. J., van, 106, 179 Bondi, A., 139, 179 Bone, N. A., 54, 58 Bonham, R. A., 113, 179 Borden, G. W., 237, 240, 324 Borden, W. T., 216, 324 Bordwell, F. G., 275, 316, 320, 324 Bose, A. N., 245, 324 Bothner-By, A. A., 307, 330 Bottini, A. T., 285, 324 Bourns, A. N., 307, 324 Bowie, J. H., 4, 58 Bowie, R. A., 249, 329 Bradley, J. N., 56, 58 Bragg, J. K., 183,183 Bragg, W . L., 113, 179 Brant,D. A., 113, 114, 118, 119, 120, 121, 124, 127, 129, 130, 131, 132, 157, 158, 159, 161, 162, 172, 179, 181, 184 Brauman, J. I., 209, 324 Brause, A. R., 168, 180 Bremner, J. B., 217, 222, 223, 224, 332 Bromels, E., 93, 98 Brnnsted, J. N., 67, 98 Brook, A. G., 290, 324 Brooks, C. J. W., 246, 324 Brown, H. C., 249, 282, 288, 324 Brown, R. D., 79, 81, 98 Brown, R. F. C., 3, 7, 32, 51, 58 Brune, H. A., 204, 325 Bruner, B. L., 193, 325 Buchanan, A. S., 79, 81, 98 Buckles, R. E., 283, 318, 324 Bujake, J. E., 250, 324 Bunnett, J. F., 74, 98 Bunton, C. A., 70, 87, 88, 98 Burkoth, T. L., 209, 331 Burnelle, L. A., 199, 294, 295, 323, 324 Burnstein, S. H., 298, 324 Burr, J. G., 11, 12, 59 Burton, M., 11, 59

C Cabaleiro, M. C., 282, 283, 324 Cadogan, J. I. G., 277, 280, 318, 324, 325 Caldin, E . F., 95, 96, 98 Cannon, C. G., 130, 179 Cagill, R. L., 206, 325 Carhart, N. W., 26, 60 Carlsmith, L. A., 2, 60 Carlson, M., 264, 326 Caron, A., 116, 180

CarrB, S., 199, 312, 325, 331 Cartwright, C. H., 86, 98 Cam, M. P., 8, 59 Challis, B. C., 73, 97, 98 Chambers, R. D., 5, 59 Chapman, 0. L., 237, 240, 324 Chen, P. S. K., 199,332 Chen, S., 309, 310, 331 Chiang, Y.,63, 68, 69, 73, 74, 77, 78, 84, 97,100 Chloupek, F. J., 288, 324 Chmurny, G. N., 263, 323 Chorvat, R., 258, 326 Ciganek, E., 210, 325 Cinquini, M., 259, 325 Clardy, J., 2, 58 Clark, H. C., 257, 325 Clark, R. A., 239, 324 Clark, R. D., 233, 325 Clarke, F. H., 251, 331 Clementi, E., 309, 325 Clemo, G. R., 221, 325 Cline, J. E., 12, 59 Cockerill, A. F., 307, 330 Colonna, S., 259, 325 Comisarow, M. B., 266, 282, 329 Companion, A. L., 189, 325 Condrate, R. A., 264, 325 Conroy, H., 193, 325 Cook, D. A., 179,179 Cooke, A. S., 309, 312, 314, 323, 325 Corbett, T. G., 23, 59 Corey, R. B., 147, 181 Cotton, F. A., 196, 230, 325 Cottrell, T. L., 56, 59 Coulson, C. A., 191, 197, 216, 272, 325 Coussemant, F., 63, 94, 98 Coward, H. F., 54, 58 Cram, D. J., 248, 262, 288, 291, 292, 307, 311, 325, 326, 327 Crmdall, J. K., 237, 325 Crawford, R. J., 220, 325 Cremer, S. E., 258, 325 Crick, F. H . C., 117, 182 Criegee, R., 204, 325 Cristol, S. J., 285, 300, 303, 305, 325 Crow, W. D., 7, 32, 58 Cullis, C. F., 22, 54, 59 Cunningham, J. A., 5, 59 Curl, R. F., Jr., 122, 133, 179 Curtin, D. Y., 315,325

D Dale, J., 271, 314, 325 Damiani, A,, 130, 138,179

335

AUTHOR INDEX

D’Angelo, P., 50, 60 D’Arcy, R., 285, 325 Dauben, W. G., 206, 223, 325 Davidon, W. C., 144, 175, 179 Davidson, M., 63, 94, 98 Davidson, W. B., 2, 59 Davis, D. R., 309, 325 Davis, R. E., 93, 98 Day, J., 262, 325 Deber, C. M., 168, 180 De Boer, A., 281, 328 De Boer, T . J., 248, 330 Dedio, E. L., 322, 328 DeJongh, D. C., 8, 59 de la Mare, P. B. D., 262, 276, 282, 302, 322, 325 Del Re,G., 131, 132, 133, 179, 180 De Maeyer, L., 85, 98 DePuy, C. H., 298, 325 De Santis, P., 120, 121, 129, 156, 171, 172, 173,180, 181, 184 Dessy, R. E., 81, 101, 248, 267, 325 Dewar, M. J. S., 201, 217, 252, 282, 283, 325, 326 Dickmson, R. G., 269, 329 Dilling, W. F., 23, 59 DinnB, E., 206, 331 Dix, D. T . , 264, 326 Dixon, K. R., 257,325 Dixon, W. T., 295, 326 Doering, W. v. E., 238, 293, 326 Dolak, L. A., 238, 332 Donohue, J., 116, 147, 180 Doorakian, G. A,, 204, 326 Dormisch, F. L., 54, 60 Doumani, T. F., 12, 59 Drago, R. S . , 252, 254, 256, 331 Dreizler, H., 124, 182 Drenth, W., 78, 100 Drews, H., 4, 60 Druckrey, E., 222, 330 Dunford, H. B., 85, 100 Durand, J. P., 63, 94, 98 Dvorko, G. F., 277, 326

E Eaborn, C., 63, 98 Eberhardt, M. K., 280, 326 Eccleston, B. H., 37, 59 Eckell, A., 225, 326 Edsall, J. T . , 106, 107, 108, 111, 112, 180 Eigen, M., 85, 98 Elder, F. A., 12, 59 Eliason, R. W., 66, 68, 71, 73, 90, 92, 99

Eliel, E. L., 9, 59, 186, 284, 297, 307, 308, 314, 316, 326 Ellis, L. E., 209, 324 Ellison, F. O., 189, 330 Epand, R., 166,181 Evans, M. W., 141, 180 Eyring, H., 93, 100, 188, 189, 190, 191, 201, 243, 326, 327, 331

F Fahey, R. C., 277, 282, 283, 326 Fainberg, A. H., 7 8 , 101 Falk, M., 86, 87, 98, 99 Fanta, P. E., 237, 328 Farenhorst, E., 222, 326 Fargo, J. C., 315, 331 Fasman, G. D., 169, 170, 179, 180 Favini, G., 312, 331 Felix, A. M., 168, 180 Fendley, T. A., 95, 98 Fields, E. K., 3, 4, 5, 7, 8, 13, 14, 15, 18, 20, 21, 22, 23, 24, 25, 26, 32, 36, 37, 38, 41, 42, 43, 46, 51, 53, 55, 57, 58, 59, 60, 221, 326 Fischer, H. P., 285, 327 Fisher, I. P., 2, 59 Fitts, D. D., 124, 180 Fletcher, R., 144, 180 Flory, P. J., 106, 107, 108, 111, 112, 113, 114, 118, 119, 120, 121, 124, 127, 129, 130, 131, 132, 157, 158, 159, 161, 162, 170, 171, 172, 178, 179, 180, 181, 183, 184 Fonken, G. J., 7, 59, 206, 326, 331 Forbes, G. S., 12, 59 Ford, T. A., 86, 98 Ford, W. T., 248, 307, 326 Foster, N. G., 37, 59 Fowler, F. W., 277, 326 Fox, J. J., 86, 99 Fraenkel, G., 264, 326 Franchimont, E., 310, 331 Frank, H. S . , 141, 180 Frankland, P. F., 187, 301, 326 Fraser, R. D. B., 172, 180 Freedman, H. H., 204, 326 Freeman, J. P., 232, 326 Frey, H. M., 293, 324 Friedman, L., 8, 17, 23, 60 Frye, C. L., 261, 331 Fuhrmann, G., 2, 61 Fujimoto, H., 202, 216, 222, 224, 242, 246, 261,272, 273, 326, 331 Fukui, K., 202, 210, 216, 217, 222, 224, 242, 246, 272, 273, 275, 326

336

AUTHOR

Funasaka, W., 207, 323 Funderburk, L., 95, 99

G Gaeumann, T., 12, 59 Gal, J., 322, 331 Garbisch, E. W., Jr., 312, 326 Gardner, D. V., 7, 51, 58 Gaspar, P. P., 230, 264, 326 Gatti, A. R., 217, 332 Gay, I. D., 56, 59 Gerstl, R., 274, 329 Ghersetti, S., 270, 326 Gibson, K. D., 113, 114, 119, 123, 124, 127, 130, 133, 137, 139, 140, 142, 144, 145, 151, 152, 154, 157, 158, 159, 160, 165, 175, 176, 177, 178, 180, 182, 183 Giglio, E., 120, 121, 129, 130, 138, 156, 171, 172, 179, 180, 184 Gigubre, P. A., 86, 87, 99 Gillard, R. D., 187, 326 Gillespie, R. J., 188,201,252,259,266,326 Gilman, N. W., 241, 327 Giumanini, A. G., 291, 328 Glasstone, S., 190, 191, 243, 327 Gleicher, G. J., 313, 323, 327 Glicenstein, L. J., 220, 330 G6. M., 183,180 G6, N., 183, 180 Gohlke, R. J., 5, 60 Gohlke, R. S., 6, 59 Gold, V., 63, 66, 67, 71, 72, 73, 74, 75, 81, 84, 87, 93, 98, 99, 265, 327 Goodall, D. M., 74, 89, 95, 98, 99 Goodman, M., 168, 171,180,181 Goon, D. J. W., 79, 80, 81, 82, 85, 99 Gordon, S., 11, 12. 59 Gorenstein, D. G., 257, 327 Gosselink, D. W., 301, 302, 324 Graebe, C., 53, 59 Graham, E. W., 248, 307, 326 Graham, W. H., 232, 326 Graahey, R., 217, 225, 326, 328 Gray, H. B., 199, 327 Green, J. H. S., 123, 180 Green, M. J., 297, 328 Green, S. I. E., 81, 101 Greene, E. F., 56, 58, 59 Greene, R. N., 237, 330 Greenstein, J. P., 111, 180 Greenwelt, E. M., 189, 330 Griffith, J. H., 130, 139, 141, 180 Grimme, W., 206, 331 Grob, C. A., 285. 324, 325, 327

INDEX

Grubb, H. M., 50, 59 Grubb, P. W., 239, 324 Grubbs, E. J., 315, 325 Gruen, L. c., 13, 99 Gunning, H. E., 37, 60, 221, 274, 322, 327, 328 Guthrie, R. D., 292, 327

H Hakka, L. E., 67, 97,100 Hall, H. K., 285, 332 Hall, K. L., 12, 59 Hall, L. H., 233, 234, 246, 327 Halpern, J., 78, 99, 276, 327 Hamer, J., 224, 327 Hammett, L. P., 74, 99, 101 Hammond, G. S., 93, 99, 230, 264, 285, 326, 327 Hanack, M., 308, 327 Hansen, K. H., 197, 327 Hansen, R. L., 94, 99 Hantzsch, A., 2, 59 Harborth, G., 2, 61 Harrap, B. S., 172, 180 Harris, M. M., 309, 312, 314, 323, 325 Harrod, J. F., 276, 327 Hartough, H. D., 35, 59 Hartter, D. R., 239, 324 Hartzell, C. El., 230, 327 Harvey, S. H., 251, 256, 304, 327 Hashimoto, M., 168, 180 Hassner, A., 277, 326 Haugen, G. R., 243, 245, 308, 324 Haugland, R. P., 171,183 Hause, N. L., 300, 303, 305, 325 Havinga, E., 238, 331 Hayes, E. F., 197, 201, 327 Heaney, H., 2, 59 Heilbronner. E., 191, 216, 327 Heimlich, B. M., 5, 60 Heinzinger, K., 72, 99 Hellin, M., 63, 94, 98 Hellman, H. M., 285, 327 Hellman, J. W., 285, 327 Hellman, M., 12, 59 Helmkamp, G. K., 233,325 Hendrickson, J. B., 126, 127, 180 Hendry, D. G., 302, 330 Herndon, W. C., 233,234, 246, 327 Herschbach, D. R., 119, 121, 180 Herzberg, G., 196, 294, 327 Hesp, B., 220, 324 Hey, D. H., 9, 60 Heyer, E. W., 237, 330 Hickman, J., 290, 330

AUTHOR INDEX Hiegel, G. A., 286, 332 Hill, R. K., 241, 327 Hine, J., 301, 302, 303, 327 Hirsch, D. E., 37, 59 Hirsch, J. A., 266, 267, 309, 312, 323 Hodgkin, D. C., 152,183 Hoegfeldt, E., 85, 99 Hoffmann, H. M. R., 251, 327 Hoffmann, R., 60, 56, 61, 201, 202, 206, 210, 216, 217, 224, 225, 228, 233, 234, 235, 236,237, 238, 242, 302, 327, 332 Hoffmeister, E., 15, 60 Hogeveen, H., 235, 248, 259, 327, 331 Holtz, H. D., 305, 327 Horner, L., 262, 327 Hou, K. C., 10, 54, 59, 60 Houff, W. H., 37, 59 House, H. O., 302, 327 Hoye, P. A. T., 251, 256, 304, 327 Huber, H., 206, 224, 328 Hudson, R. F., 252, 257, 258, 327 Huett, G., 269, 327 Huff, N. T., 189, 330 Huggins, M. L., 129,180 Hughes, E. D., 251,256,304,319,327,328 Hughes, E. W., 142,183 Huisgsn, R., 2, 60, 206, 217, 224, 225, 326, 328 Hulett, J. R., 78, 95, 98, 99 Humffray, A. A., 79, 81, 98 Husk, G. R., 290, 332

I Ingold, C. K., 187, 188, 191, 201, 249, 251, 256, 264, 294, 303, 304, 311, 327, 328 Inward, P. W., 318, 324 Ito, A., 302, 330

J Jackson, P. M., 63, 98 Jacob, E. J., 129, 137, 138, 156, 180 Jeaschke, A., 124,182 JaffQ,H. H., 196, 199, 225, 230,287,288, 328, 330 James, B. R., 276, 327 Jamsen, M. J., 82, 100 Jeger, O., 237, 332 Johnson, A. W., 322, 328 Johnson, F., 319, 320, 328 Johnson, M. D., 282, 283, 324 Jolly, W. L., 93, 99 Jones, D. E., 269, 328 Jones, D. N., 297, 328

337

Jones, L. B., 238, 240, 328 Jones, V. K., 238, 240, 328 Jordan, P. C. H., 197, 198, 328

K Kaczynski, J. A., 301, 302, 324 Kaffenberger, T.,285, 325 Kahlert, B., 1, 60 Kmpmeier, J. A., 15, 60 KankaanperB, A., 63, 78, 100 Karplus, M., 295, 303, 328 Kashelikar, D. V., 237, 328 Kasparien, M., 95, 96, 98 Katz, T. J., 56, 61 Kavanau, J. L., 86, 88, 99 Kayser, R. A., 79, 80, 81, 82, 85, 99 Kayser, W. V., 65, 66, 67, 68, 69, 71, 73, 75, 78, 85, 92, 95, 96, 99, 100, 249, 268, 328 KendaU, R. F., 37, 59 Kendrew, J. C., 106, 107, 108, 111, 112, 113, 179,180 Kessick, M. A., 63, 71, 73, 75, 93, 99 Ketelaar, J., 126, 180 Kettle, S. F. A., 198, 199, 329 Kharasch, N., 318, 331 Kibby, C. L., 93, 98 Kihara, T., 128, 180 Kijima, H., 113, 118, 180 Kimball, G. T., 188, 189, 190, 326 King, G. W., 294, 328 Kingsbury, C. A., 289, 314, 328 Kiprianova, L. A., 63, 99 Kirmse, W., 221, 245, 264, 293, 326, 328 Kistiakowsky, G. B., 56, 58, 59 Kitaigorodskii, A. I., 128, 130, 138, 180, 181 Etching, W., 248, 267, 325 Kl~sinc,L., 307, 330 Klein, F. S., 191, 324 Kloosterzeil, H., 237, 332 Knox, B. E., 56, 59 Koeppl, G. W., 260, 271, 314, 315, 328 Kohl, D. A., 113,179 Kolthoff, I. M., 91, 99 Kornegay, R. L., 169, 170, 181 Korte, W. D., 261, 331 Kovaccs, A. L., 173, 181 Kowitt, F. R., 93, 99 Kramers, J. C., 22, 60 Krasnobayew, V., 285, 325 Kreevoy, M. M., 65, 66, 67, 68, 69, 70, 71, 73, 75, 76;78, 79, 80, 81, 82, 85, 89, 90, 91, 92, 93, 94, 96, 99, 100, 101, 127,181, 249, 268, 328

338

AUTHOR I N D E X

Kresge, A. J., 63, 67, 68, 69, 72, 73, 74, 77, 78, 84, 87, 97, 100 Kretchmer, R. A., 67, 69, 70, 76, 78, 82, 84, 99 Krimm, S., 124, 146, 157, 162, 182 Krishnamurthy, G. S., 260, 271, 314, 315, 328 Kromhout, R. A., 134, 181 KrupiEka, J., 300, 307, 332 Krynitzky, J. A., 26, 60 Kuntz, I., 265, 330 Kurland, R. J., 133, 181 Kwart, H., 249, 328 Kwok, W. K., 277, 310, 316, 317, 328

L Labaye, J., 54, 60 Laidler, K. J., 67, 98, 190, 191, 243, 327 Lajunen, M., 63, 78, 100 Lakshminarayanan, A. V., 116, 146, 156, 182 Lamm, B., 63,100 Landgrebe, J. A., 265, 328 Landholm, R. A., 66,68,71,73, 75,90,92, 94,99 Landini, D., 269, 328 Landolt, R. G., 237, 330 Landor, S. R., 321, 328 Lawesson, S.-O., 4, 58 Leach, S. J., 105, 113, 114, 124, 125, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 158, 173, 181,182, 183 Leach, W. A., 265, 330 LeBel, N. A., 281, 298, 312, 328 Ledger, R., 172, 180 Ledwith, A., 63,100 Lee, D.-J., 277, 326 Lee, W. G., 310, 317, 322, 328 Leermakers, P. A., 50, 60 Le Grow, G. E., 290, 324 Lemal, D. M., 222, 230, 231, 233, 328, 329 Lepley, A. R., 291, 328 Leung, Y. C., 115, 117,181 Levy, L. A., 277, 330 Lewis, E. S., 95, 99 Lifson, S., 129, 137, 138, 142, 144, 145, 156,179,181 Lin, C. C., 123, 181 Lindblow, C., 169, 170, 180 Lindeman, L. P., 6, 60 Linden, H. R., 56, 60 Lindow, D. F., 8, 17, 60 Link, H., 285, 327 Lippincott, E. R., 134, 181, 183

Liquori, A. M., 106, 107, 108, 111, 112, 120, 121, 124, 127, 129, 130, 134, 138, 156, 162, 163, 164, 165, 171, 172, 173, 179, 180,181, 184 Lloyd, N. C., 261, 331 London, F., 188, 189, 328 Long, F. A., 63, 66, 67, 69, 72, 73, 74, 77, 84, 89, 97, 98, 99, 100, 101 Longridge, J. L., 63, 84,100 Longuet-Higgins, H. C., 196, 197, 198, 210, 212, 215, 327, 328 Longworth, R., 169, 170, 181 Lossing, F. P., 2, 59 Loudon, A. G., 299, 324 Lown, E. M., 37, 60, 322, 328 Lugli, G., 270, 326 Lumry, R., 93,100 Luz, Z., 88, 100 Lwowski, W., 274, 329 Lyons, J. E., 261, 331

M Maas, W., 82, 100 Maccagnani, G., 259, 327 McCarty, C. G., 316, 325 Maccoll, A., 244, 245, 329 McClellan, A. L., 86, 100 McCollum, J. D., 4, 50, 60 McConaghy, J. S., Jr., 274, 328 McCullough, R. L., 156,181 McEwen, W. E., 201, 253, 258, 329, 330 McGreer, D. E., 218, 220, 329 McGregor, S. D., 222, 230, 231, 233, 328, 329 Mach, G. W., 78, 98 MacKenzie, K., 251, 262, 329 McLafferty, F. W., 5 , 60 McMahon, P. E., 156, 181 McOmie, J. F. W., 7, 51, 58 McQuillen, A., 221, 325 McRae, D. M., 290, 324 Macrae, T. P., 172, 180 Madsen, J. 0.,4, 58 Magee, J. L., 191, 329 Mahr, T. G., 169, 179 Malhotra, S. K., 319, 320, 328 Mendell, L., 248, 329 Mango, F. D., 235, 242, 329 Manton, J. E., 22, 59 Mark, J. E., 130, 171, 181, 184 Marsh, R. E., 115, 117, 181 Martin, A. E., 86, 99 Martin, B., 96,100

339

AUTHOR INDEX

Marvel, C . S., 265, 329 Mawell, E. N., 205, 329 Marzo, A., 302, 324 Mason, E. A., 127, 181 Matesich, M. A., 77, 78, 97, 100 Mathieson, A. McL., 117, 181 Matt, J. W., 289, 329 Matteson, D. S., 249, 250, 329 Mattison, P., 291, 330 Maynard, J. C . , 319, 328 Mazumdar, S. K., 116, 181, 182 Mazzarella, L., 130, 138, 173, 179, 181 Mead, R., 144, 181 Meek, J. S., 303, 305, 325 Meiboom, S., 88, 100 Meinwald, Y. C., 219, 324 Meisenheher, J., 188, 301, 329 Meister, W., 292, 327 Melander, L., 88, 92, 100 Melloni, G., 270, 326 Melquist, J. L., 66, 67, 68, 69, 81, 82, 94, 96, 99, 249, 268, 328 Menger, F. M., 248, 329 Mesmer, R. E., 93, 99 Metts, L., 231, 330 Meyerson, S., 3, 4, 5 , 7, 8, 9, 13, 14, 15, 18, 20, 21, 22, 23, 24, 25, 26, 32, 36, 37, 38, 41, 42, 43, 46, 50, 51, 53, 55, 57, 58, 59, 60 Michael, A., 187, 329 Michael, J. V . , 8, 56, 59 Michael, K. W., 261, 331 Mignonac, M. G., 12, 60 Miller, J. L., 283, 318, 324 Miller, M. A., 266, 267, 309, 312, 323 Miller, R. G., 2, 7, 23, 60 Miller, S. I., 260, 266, 269, 271, 277, 278, 298, 301, 305, 310, 314, 315, 316, 317, 322, 327, 328, 329, 331 Miller, W. G., 127, 130, 131, 132, 159, 161, 162, 179, 181 Minkoff, G. J., 54, 59, 60 Moronova, D. F., 277, 326 Mislow. K., 186, 260,285, 327, 329, 330 Mitchell, M. J., 8, 59 Miyazawa, T., 113, 118, 181, 183 Mizushima, S., 113, 118, 181 Modena, G., 270, 326, 329 Moltzan, H., 221, 330 Montanari, F., 259, 269, 325, 327, 328 Montgomery, L. K., 289, 329 More O’Ferrall, R. A., 67, 97, 100, 322, 331 Morgan, K. J., 288, 324 Morris, G. F., 298, 325 Morris, R. O., 269, 328

Morrison, G. A., 297, 307, 308, 314, 316, 326 Mosher, H. S., 293, 330 Moss, R. A., 274, 329 Moulton, W. G., 134,181 Muetterties, E. L., 255, 315, 329 Mukai. T., 216, 220, 329, 331 M d e r , J.-A., 301, 329 Murray, K. J., 249, 324 Murrell, J. N., 198, 199, 329 Mylonakis, S., 97, 100

N Nakamoto, K., 254, 294, 325, 329 Nakamura, K., 168,180 Nakazawa, T., 216, 329 Namanworth, E., 266 282, 329 Neckers, D. C., 50, 60 Neilson, A. H., 197, 325 Nelder, J. A., 144, 181 Nelson, G. L., 240, 287, 324 Nemethy, G., 105, 106, 107, 108, 111, 112, 113, 114, 118, 124, 125, 139, 141, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 158, 159, 173, 180, 181, 182, 183 Nettleton, M. A., 54, 59 Neuman, P. N., 206, 331 Neureiter, N. P., 232, 329 Nevitt, T. D., 3, 60 Nickon, A., 283, 329 Niki, H. J., 56, 59 Nolde, C., 4, 58 Noyes, R. M., 250, 269, 277, 305, 324, 329, 331 Nukada, K., 276,329 Nyholm, R. S., 266, 326

0 Ohno, M., 276, 329 Okamoto, M., 276, 329 Olah, G. A., 266, 282, 289, 329 Oleari, L., 199, 325 Olofson, R. A., 302, 327 Olson, A. R., 188, 265, 329 Olsson, S., 63, 100 Onwood, D. P., 73,100 Ooi, T., 113, 114, 116, 118, 122, 124, 127, 128, 130, 131, 132, 134, 144, 151, 152, 158, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 175, 181,183

340

AUTHOR I N D E X

Oppenheim, I., 144,181 Orchin, M., 196, 225, 230, 243, 287, 288, 328, 330 Oriel, P., 132, 182 Ostman, B., 63,100 Osyany, J. M., 315, 323 Oth, J. F. M., 210, 331 Oughton, B. M., 152, 183

P Pachler, K. 0 . R., 123, 181 Page, L., 303, 330 Paige, J. N., 230, 327 Palmer, H. B., 10, 54, 56, 59, 60 PAnkovA, M., 299, 330 Pao, Y . H., 169, 170,181 Papanikolaou, N. E., 259, 323 Pappas, B., 209, 331 Paquette, L. A., 219, 330 Parham, W. E., 208, 330 Parisek, C . B., 258, 330 Parish, R. C . , 306, 324 Parker, G . A., 261, 331 Parlin, R. B., 201, 326 Pasternak, R. A., 117,181 Pasto, D. J., 290, 330 Patai, S., 269, 277, 330 Patterson, D. B.. 312, 326 Patterson, W. L., 56, 59 Pauling, L., 113, 114, 147, 181 Paust, J., 208, 312, 331 Pearson, R. G . , 303, 324 Pedersen, K., 67, 98 Peerdemm, A. F., 106, 179 Pentz, L., 72, 100 Perkins, M. J., 277, 280, 325 Perrin, D. D., 94, 98 Perutz, M. F., 113, 179 Peterson, L. I., 302, 314, 330 Peytral, E., 301, 329 Pfeiffer, G . V., 189, 330 Pfeiffer, P., 187, 330 Phelan, N. F., 287, 288, 330 Phillips, D. C . , 147, 148, 149, 158, 181 Pieper, G., 2, 61 Pimentel, G. C . , 86, 100 Pitea, D., 302, 324 Pitzer, K. S . , 124, 126, 181 Plyler, E. K., 86, 100 Pocker, Y., 288, 330 Poland, D., 105, 116, 131, 132, 133, 134, 135, 136, 137, 152, 165, 181, 182, 183 Polanyi, M., 189, 326

Porter, Q.N., 4, 23, 59, 60 Powell, M. J. D., 144,180, 181 Pratt, M. W. T., 250, 324 Preston, J., 67, 98 Prinzbach, H . , 222, 330 Pritchard, J. G., 307, 330 Pryor, W. A., 250, 330 P t i t s p , 0. B., 118, 168, 179 Pullman, A., 131,179,181 Pullman, B., 131, 133, 180, 181 Purlee, E. L., 70, 100

0 Quayle, A., 4, 60

R Rabinovich, D., 130, 138, 182 Ramachandran, G. N., 105, 106, 107, 108, 111, 112, 113, 114, 116, 124, 126, 128, 129, 130, 145, 146, 161, 156, 157, 162, 172, 180, 182,183, 184 Ramakrishnan, C., 105, 113, 114, 124, 125, 145, 146, 160, 156, 182 Ramsey, B., 266, 282, 329

REO,V . S . R., 166,182 Rappoport, Z., 269, 277, 330 Rayreux, J. M., 12, 59 Readio, P. D., 278, 280, 281, 330 Reddy, T. B., 91, 99 Rees, C . W., 31, 42, 60 Reese, C. B., 206, 324 Reeves, C . M., 144, 180 Reeves, L. W., 314, 315, 330 Regan, J. P., 321, 328 Reid, J . M., 56, 60 Rekaaheve, A. F., 63, 99 Renk, E., 285, 327 Reusoh, W., 291, 330 Reutov, 0. A., 248, 260, 267, 330 Reuwer, J. F., Jr., 71, 95, 101 Rhoads, S. J., 202, 217, 241, 242, 330 Rich, A., 117, 182 Riley, T., 66, 72, 100 Ringold, H. J., 298, 324 Ripamonti, A., 120, 121, 129, 166, 171 172, 184, 180 Rist. H., 2, 60 Roberts, J. D., 2, 60 Roberts, R. M., 237,330 Robertson, E. B., 85, 100

AUTHOR I N D E X

Robinson. D. L., 321, 330 Rodewald, P. G.,261, 331 Roest, B. C.,248, 330 Roos, L.,243, 330 Rosenblum, M.,221,330 Rosenbrock, H.H.,144, 182 Ross, S. D.,265, 330 Roth, W.,238, 326 Rowland, F. S.,250, 332 Rowlinson, J. S., 128, 182 Rubin, A. B., 15, 60 Ruch, E.,309, 330 Riichardt, C., 289, 330 Rudolph, H.D.,124, 182 Rudolph, J., 73, 87, 100 Rudolph, R. W.,217, 330 Russell, G. A,, 302, 330 Rutledge, R. M.,248, 330 Rylender, P.N.,3, 60

S Sagatys, D. S., 260,271, 314, 315, 328 S&a, H.K.,220,330 Saint-Aunay, R. V. de, 12, 60 Salomcte, P.,63, 78, 100 Saltiel, J., 231, 330 Sandel, V. R., 204, 326 Sanderson, W.A., 293, 330 Sa9isekharm, V., 105, 113, 114, 115, 117, 124, 125, 146, 146, 151, 156, 182 S ~ t o ,T.,113, 118,180 Sato, Y.,78, 97, 100 Saturno, A. F., 248, 330 Sauer, J., 217, 328 Seunders, W.H., Jr., 307, 330 Sawdeye, R., 316, 323 Saerborough, J. M.,11, 12, 59 Scartazzini, R., 260, 330 Scatchard, G.,86, 100 S c h d , L. J., 71, 96,101 Schachtschneider, J. H.,235, 242, 329 Schafer, M. E.,2, 58 Schdner, K.,237,332 Scheleger, L. L.,77, 100 Scheer, W.,206, 224, 328 Schellmen, C., 105, 120, 124,182 Schellman, J. A., 106, 120, 124, 132, 182 Soheraga, H.A,, 104, 105, 106, 107, 108, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 136, 137, 139, 140, 141, 142, 143, 144, 146, 146, 147, 148, 149, 150, 151, 162, 163, 164, 166, 166, k67, 168, 169, 160,

341

162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 176, 177, 178,180. 181, 182, 183, 183, 184 Schestakow, P., 53, 59 Schiess, P.W.,285, 327 Schildcrout, S. M.,312, 326 Schimmel, P.R., 170, 171, 172, 183 Schleyer, P.v. R., 208, 312, 313, 323, 327, 331 Schmidt, G.M.J., 130, 138, 152, 182, 183 Schtillkopf, U.,208, 312, 331 Schomaker, V.,269, 329 Schotte, L.,124, 142, lY9 Schroder, G.,210, 331 Schroeder, R., 134,181,183 Schroll, G., 4, 58 Schubert, W.M.,63, 100 Schulte, R. D.,37, 59 Schumacher, E.,285, 324 Schunn, R. A.,255, 315, 329 Schutte, L., 238, 331 Schwartz, G.,168,180 Schwarzenbach, G.,81, 98 Scott, R. A., 105, 113, 114, 116, 117, 118, 119, 120, 121, 122, 124, 126, 127, 128, 129, 130, 131, 132, 134, 141, 143, 144, 145, 151, 152, 153, 154, 156, 156, 157, 158, 162, 164, 166, 166, 167, 168, 169, 170, 171, 172, 173, 176, 181, 182,183, 184 Seebach, D., 204, 325 Seldner, D.,50, 60 Semenow, D.A., 2, 60 Seubert, J., 205, 329 Shames, P. M., 117, 141, 145, 155, 173, 175, 183 Sharma, R. K.,54, 60 Shida, S., 54, 60 Shih, C., 9, 60 Shilov, E.A., 277, 326 Shimanouchi, T.,113, 118, 181 Shiner, V. J., Jr., 70, 87, 88, 96, 98, 100 Shishido, T.,216, 329 Shudde, R. H.,12, 59 Shumate, K.M.,206, 331 Sicher, J., 300, 307, 330, 332 Sidhu, K.S., 37, 60 Sillh, L.G.,81,98 Simmons, H.E.,2, 60 Simonetta, M.,302, 312, 324, 331 Simpson, R. B.,81, 100 Singer, L., 187, 332 Skell, P.S.,278, 280, 281, 330 Slobodkin, N.R., 318, 331 Slomp, 0.219, 330 Smat, R. J., 298, 325

342

AUTHOR I N D E X

Smith, C. S., 144, 183 Smith, J. S . , 298, 325 Smith, P. J . , 307, 324 Smith, R. F., 201, 326 Solly, R. K., 3, 7 , 32, 51, 58 Sommer, L. H., 201, 256,257, 261,331 Sonntag, F. I., 222, 331 Sperley, R. J . , 208, 330 Spindler, E., 225, 326 Spokes, G. N., 2, 58 Sprecher, C. M., 312, 236 Srinivasan, R., 116, 181, 222, 331 Stamhuis, E. J., 78, 82, 100 Stedronsky, E. R., 322, 331 Steele, R. B., 267, 276, 332 StefanoviO, D., 307, 330 Steinmetz, H., 269, 331 Steinwand, P. J., 65, 71, 73, 75, 78, 85, 92, 93, 95, 96, 100 Stevens, C. L., 277, 331 Stevens, I. D. R., 293, 324 Stewart, F., 290, 332 Stewart, F. H . C., 172, 180 Stewart, G. H., 201, 326, 331 Stiles, M., 2, 7, 23, 58, 60 Stivers, E. C., 71, 95, 101 Stock, L. M., 306, 306, 324, 327 Stoermer, R., 1, 60 Stork, G., 261, 331 Storr, R. C., 31, 42, 60 Straub, P. A., 191,246, 327 Straub, T. S . , 66, 67, 68, 69, 71, 90, 93, 96, 99, 100, 249, 268, 328 Strausz, 0. P., 37,60,221,274,322,327,328 Streitwieser, A., Jr., 191, 216, 272, 275, 325, 331 Strilko, P. S., 249, 328 Stryer, L., 171, 183 Subramanian, P. M., 298, 312, 328 Sugeta, H., 113, 118, 183 Sullivan, J. H., 243, 331 Sundararajan, I?. R., 156, 182 Sustmann, R., 225, 326 Sutter, D., 124, 182 Suzuki, E., 172, 180 Swain, C. G . , 7 1 , 73, 95, 100, 101 Swalen, J. D., 123, 181 Swindell, R., 237, 240, 324 Symons, M. C . R., 197, 199, 200, 323

T Taft, R. W., Jr., 70, 94, 100, 101 Talaty, E. R., 315, 331 Talbot, M. L., 260, 329

Tanford, C., 303, 306, 331 Tang, A., 309, 310, 331 Taylor, R., 63, 98 Taylor, R. L., 56, 59 Tedder, J. M., 198, 199, 329 Ter Borg, A. P., 237, 331 Tezuka, T., 220, 237, 240, 324, 331 Theilacker, W., 188, 301, 329 Theobald, D. W., 321, 330 Thomas, P. J.,’244, 329 Thomas, R. J., 66, 67, 100 Thompson, H. B., 129, 137, 138, 156, 180 Thoreen, J. W., 76, 99 Thornton, E. R., 72, 73,100 Thorpe, F. G., 248, 249, 260, 264, 331 Thurmaier, R. J., 283, 318, 324 Thurman, D. E., 266, 328 Thyagarajan, B. S . , 187, 332 Tieman, C. H . , 285, 325 Tinker, H. B., 78, 99 Tobe, M. L., 256, 331 Todesco, P. E., 270, 326, 329 Tonti, S . , 270, 329 Toporcer, L. H., 81, 101 Trautwein, H., 289, 330 Trommel, J., 106, 183 Trotter, J., 122, 183 Tsuboi, M., 113, 118,180 Tsukuda, M., 54, 60 Turro, N. J., 50, 60 Tuttle, R. W., 117, 141, 145, 155, 173, 176, 183

U Ugi, I., 309, 330, 331 Ulrich, H . , 224, 331 Urry, G., 220, 330

V Valicenti, J. A., 277, 331 Vancatledge, F. A., 266, 267, 309, 312, 323 Vanderkooi, G., 113, 114, 116, 117, 118, 122, 124, 127, 128, 130, 131, 132, 134, 141, 143, 144, 145, 151, 162, 163, 164, 156, 158, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 181, 183 Van Der Voorn, P. C., 262, 264, 256, 331 VanderWerf, C. A., 258, 330 Van Dine, G. W., 208, 312,331 Van Dyken, A. R., 12, 59 Van Fossen, R. Y . , 8, 69

343

AUTHOR INDEX

van Tamelen, E. E., 209, 222, 324, 331 Vaughan, C . W., 2, 60 Veenland, J. U., 248, 330 Venkatesan, K., 116, 182 Venkatachalam, C. M . , 124, 128, 129, 130, 146, 157, 162, 172, 182, 183, 184 Verbit, L., 275, 331 Vernon, C. A., 269, 328 Vestling, M. M . , 316, 320, 324 Viehe, H. G., 221, 310, 331 Vitullo, V. P . , 67, 97, 100 Vivarelli. P., 270, 326 Vogel, E., 206, 331 Volger, H. C., 235, 331 Volkenstein, M. V., 118, 122, 183 Vournakis, J. N . , 172, 183

w Wada, A., 113, 118,180 Wadsworth, W. S., Jr., 258, 331 Wai, C. M . , 250, 332 Wallace, T. S . , 5, 60 Wallbillich, G., 225, 326 Waller, F. D., 299, 324 Walrafen, G. E . , 86, 101 Walsh, A. D., 196, 197, 198, 332 Walter, J., 188, 189, 190, 326 Warkentin, S., 285, 327 Warrener, R. N., 217, 222, 223, 224, 332 Wartik, T., 217, 332 Wassermann, A., 307, 308, 332 Waterman, D. C . A., 66, 71, 99 Watkins, R. J., 237, 325 Watson, D., 72, 100 Watson, H., 158, 183 Watson, J. T . , 6, 60 Wehrli, H., 237, 332 Wells, P. R., 309, 332 Welsh, H. K., 117, 281 Welvart, Z., 9, 59 Wendling, P., 124, 182 Wenger, R., 237, 332 West, R., 290, 332 Westeriuk, N. H . , 283, 329 Westheimer, F. H . , 124,183, 257, 327 Weston, R. E . , Jr., 72, 99, 191, 324 Westphal, Y. L., 237, 331 Whalley, E., 63, 78, 79, 92, 98, 101 Wharton, P . S., 286, 332 Wheland, G. W., 199, 301, 332 White, E. H . , 238, 332 White, R. F . M., 269, 328 White, W. N . , 251, 331

Whitney, C. C., 276, 332 Whitney, R. B . , 67, 98 Wiberg, K. B., 223, 332 Wilen, S. H., 9, 59 Willcott, M. R., 111, 239, 324 Willey, F. G., 223, 325 Williams, D., 86, 100 Williams, D. E . , 130, 138, 183 Williams, D. H . , 4, 58 Williams, G. H . , 9, 60 Williams, J. M., Jr., 90, 91, 92, 101 Williams, R. B., 317, 332 Wilson, E. B., Jr., 123, 133, 181, 183 Winitz, M., 111, 180 Winkler, H., 262, 327 Winstein, S., 78, 101, 285, 332 Winter, R. E . , 204, 325 Wislicenus, J., 187, 332 Witt, H., 2, 61 Wittig, G., 2, 23, 50, 60, 61 Wolf, A. P., 250, 332 Wolfsberg, M., 191, 324 Woods, H. J., 63, 100 Woodward, R. B . , 56, 60, 201, 202, 206, 210, 216, 217, 224, 225, 228, 233, 234, 235, 236, 237, 238, 242, 327, 332 Wright, W. V., 278, 282, 332 Wu, W.-S., 218, 220, 329 Wyman, J., 106, 180 Wynberg, H., 35, 61, 82, 100

Y Yakel, H. L., Jr., 142, 183 Yamanaka, H., 207, 323 Yan, J., 122, 130, 165, 168, 170, 183 Yates, K., 278, 282, 332 Yonan, P. K., 266, 269, 301, 239 Yonezawa, T., 133,180 Young, W. G., 286, 332

Z ZBvada, J., 300, 307, 330, 332 Zeldin, M . , 217, 332 Zergenyi, J., 285, 324 Zimm, B. H . , 183,183 Zimmerman, H. E., 187, 210, 216, 222, 287,288, 291, 319, 332 Zimmermann, H., 73, 87, 100 Zuoker, L., 74, 101 Zuman, P., 299, 332 Zweifel, G., 267, 276, 332

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CUMULATIVE INDEX OF AUTHORS Bell, R. P., 4, 1 Brand, J. C. D., 1, 365 Brown, H. C., 1, 35 Collins, C. J., 2, 1 Ferguson, G., 1, 203 Fields, E. K., 6, 1 Frey, H. M., 4, 147 Gilbert, B. C., 5, 53 Greenwood, H. H., 4, 73 Johnson, S. L., 5,237 Kohnstam, G., 5, 121 Kreevoy, M. M., 6, 63 Long, F. A., 1 , l Maccoll, A., 3, 91 McWeeny, R., 4, 73 Miller, S. I., 6, 185 More O’Ferrall, R. A,, 5, 331 Norman, R. 0. C., 5 , 5 3 Olah, G. A., 4,305 Parker, A. J., 5, 173 Perkampus, H.-H.,4, 195 Pittman, C. U., Jr., 4, 305 Reeves, L. W., 3, 187 Robertson, J. M., I, 203 Samuel, D., 3, 123 Schaleger, L. L., 1, 1 Scheraga, H. A., 6, 103 Shatenshtein, A. I., 1, 156 Silver, B. L., 3, 123 Stock, L. M., 1, 35 Symons, M. C. R., 1,284 Turner, D. W., 4, 31 Whalley, E., 2,93 Williams, J. M., Jr., 6, 63 Williamson, D. G., 1, 365 Wolf, A. P., 2, 201 Zollinger, H., 2, 183 Zuman, P., 5, 1

346

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CUMULATIVE INDEX OF TITLES Acid solutions, strong, spectroscopic observation of alkylcarbonium ions in, 4, 305 Acids, reactions of aliphatic diazo compounds with, 5, 331 Activation, entropies of, and mechanisms of reactions in solution, 1, 1 Activation, heat capacities of, and their uses in mechanistic studies, 5, 121 Activation, volumes of, use for determining reaction mechanisms, 2, 93 Aliphatic diazo compounds, reactions with acids, 5, 331 Alkylcarbonium ions, spectroscopicobservation in strong acid solutions, 4, 305 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 Arynes, mechanisms of formation and reactions a t high temperatures, 6, 1 A-S& reactions, developments in the study of, 6,63 Base catalysis, general, of ester hydrolysis and related reactions, 5,237 Basicity of unsaturated compounds, 4, 195 Bimolecular substitution reactions in protic and dipolar aprotic solvents, 5, 173 Carbon atoms, energetic, reactions with organic compounds, 3,201 Carbonium ions (alkyl), spectroscopic Observation in strong acid solutions, 4, 305 Catalysis, general base and nucleophilic, of ester hydrolysis and related reactions, 5,237 Carbonyl compounds, reversible hydration of, 4, 1 Conformations of polypeptides, calculations of, 6, 103 Conjugated molecules, reactivity indices in, 4, 73 Diazo compounds, aliphatic, reactions with acids, 5, 331 Dipolar aprotic and protic solvents, rates of bimolecular substitution reactions in, 5, 173 Directive effects in aromatic substitution, a quantitative treatment of, 1,35 Electron spin resonance, identscation of organic free radicals by, 1, 284 Electron-spin resonance studies of short-lived organic radicals, 5, 53 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, 187 Ester hydrolysis, general base and nucleophilic catalysis, 5, 237 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 Ges-phase pyrolysis of small-ring hydrocarbons, 4, 147 General base and nucleophilic catalysis of ester hydrolysis and related reactions, 5,237 347

348

C U M U L A T I V E INDEX

Heat capacities of activation and their uses in mechanistic studies, 5, 121 Heterolysis, gas-phase, 3, 91 Hydration, reversible, of carbonyl compounds, 4, 1 Hydrocarbons, small-ring, gas-phase pyrolysis of, 4, 147 Hydrogen isotope effects in aromatic substitution reactions, 2, 163 Hydrogen isotope exchange reactions of organic compounds in liquid ammonia, 1, 156 Hydrolysis, ester, and related reactions, general base and nucleophilic catalysis of, 5, 237 Ionization potentials, 4, 31 Isotope effects, hydrogen, in aromatic substitution reactions, 2, 163 Isotope exchange reactions, hydrogen, of organic compounds in liquid ammonia, 1, 160 Isotope exchange reactions, oxygen, of organic compounds, 3, 123 Isotopes and organic reaction mechanisms, 2, 1 Kinetics, reaction, polarography and, 5, 1 Mechanisms, organic reaction, isotopes and, 2, 1 Mechanisms, reaction, use of volumes of activation for determining, 2 , 9 3 Mechanisms of formation and reactions of arynes at high temperatures, 6, 1 Mechanisms of reactions in solution, entropies of activation and, 1, 1 Mechanistic studies, heat capacities of activation and their uses in, 5, 121 N.M.R. measurements of reaction 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. Nucleophilic catalysis of ester hydrolysis and related reactions, 4, 237 Oxygen isotope exchange reactions of organic compounds, 3, 123 Planar and non-planar aromatic systems, 1,203 Polarizability, molecular refractivity and, 3, 1 Polarography and reaction kinetics, 5, 1 Polypeptides, calculations of conformations of, 6, 103 Protic and dipolar aprotic solvents, rates of bimolecular substitution reactions in, 5, 73 Pyrolysis, gas-phase, of small-ring hydrocarbons, 4, 147 Radicals, organic free, identification by electron spin resonance, 1, 284 Radicals, short-lived organic, electron spin resonance studies of, 5, 63 Reaction kinetics, polarography and, 5, 1 Reaction mechanisms, use of volumes of activation for determining, 2, 93 Reaction mechanisms in solution, entropies of activation and,.~ 1. 1 Reaction velocities and equilibrium constants, N.M.R. measurements of, as a function of temperature, 3, 187 Reactivity indices in conjugated molecules, 4, 73 Refractivity, molecular, and polarizability, 3, 1 Resonance, electron spin, identification of organic free radicals by, 1, 284 Resonance, electron-spin, studies of short-lived organic radicals. 5,63 Short-lived organic radicals, electron spin resonance studies of, 5, 63 Small-ring hydrocarbons, gas-phase pyrolysis of, 4, 147 Solution, reactions in, entropies of activation and mechanisms, 1, 1 Solvents, protic and dipolar aprotic, rates of bimolecular substitution reactions in, 5, 173 Spectroscopicobservation of alkylcarbonium ions in strong acid solutions, 4,305 Stereoselectionin elementary steps of organic reactions, 6, 186 Structure of electronically excited molecules, 1,366

CUMULATIVE INDEX

349

Substitution, aromatic, a quantitative treatment of directive effects in, 1, 35 Substitution reactions, bimolecular, in protic and dipolar aprotic solvents, 5 , 173 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 Unsaturated compounds, basicity of, 4, 195 Volumes of activation, use of, for determining reaction mechanisms, 2, 93

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