Advances in Physical Organic Chemistry, Volume 06

Advances in

Physical Organic Chemistry

This Page Intentionally Left Blank

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.

This Page Intentionally Left Blank

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

This Page Intentionally Left Blank

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

.

.

. .

.

.

.

.

.

. . .

.

.

.

.

.

.

.

. . . .

.

.

. .

.

.

. .

.

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.

61

This Page Intentionally Left Blank

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

.

.

.

.

.

.

. . . .

.

.

.

. . .

.

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.

A-S,2

REACTIONS

99

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.

100

JOEL M. WILLIAMS, JR. AND MAURICE M. IEREEVOY

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.

A-S,2

REACTIONS

101

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.

This Page Intentionally Left Blank

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

. . . . .

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

.

.

.

.

.

.

.

. . .

.

.

.

.

. .

.

.

.

.

. . .

.

.

.

. . .

.

.

. .

.

.

. .

.

.

. .

.

.

. .

.

. . .

. . .

. . .

. . .

.

.

.

.

.

.

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.

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

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).

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

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

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

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