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A kinetic study of the addition of the ethyl radical to conjugated dienes and related compounds Brown, Alistair Chalmers Ramsay 1962

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A KINETIC STUDY OF THE ADDITION OF THE ETHYL RADICAL TO CONJUGATED DIENES AND RELATED COMPOUNDS by ALISTAIR CHALMERS RAMSAY BROWN B.Sc. (Hon. Chem.), The University of St. Andrews, 1958 A thesis submitted in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1962 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without ray written permission. Department of The University of British Columbia, Vancouver 3, Canada. Date //^ OcX , /nfrck PUBLICATIONS 1. A k i n e t i c study of the addit i o n of the ethyl r a d i c a l to conjugated dienes. A.C.R. Brown and D.G.L; James, Proc. Chem. Soc., 1962, 81. 2. A k i n e t i c study of the metathetical and addition reactions c h a r a c t e r i s t i c of a l l y l polymerization. A.C.R. Brown and D.G.L. James, Can. J . Chem., 40, 796 (1962) . The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ALISTAIR CHALMERS, .RAMSAY BROWN B.Sc. (Hon.Chem.) Univ e r s i t y of St. Andrews, 1958 WEDNESDAY, OCTOBER 10, 1962 AT 1:30 P.M. IN ROOM 261, .CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: F.H. Soward L.G. Harrison E.A. Ogryzlo D.G.L. James R.E. Pincock C.A. McDowell R. Stewart C.P.S. Taylor External Examiner: R.G.W. Norrish, F.R.S. Cambridge U n i v e r s i t y A KINETIC STUDY OF THE ADDITION OF THE ETHYL RADICAL TO CONJUGATED DIENES AND RELATED COMPOUNDS ABSTRACT A k i n e t i c survey of the reactions of the ethyl r a d i c a l with conjugated c y c l i c d e f i n e s and r e l a t e d compounds has revealed a great v a r i e t y of r e a c t i v i t y with respect both to addition and metathesis. An attempt to correlate r e a c t i v i t y with molecular structure has been presented both in the language of polymerization k i n e t i c s and of molecular o r b i t a l theory. In p a r t i c u l a r , the correla-t i o n of the energy of a c t i v a t i o n for the addition reaction with free valence and with l o c a l i z a t i o n energy has been pursued with some measure of success. The r e s u l t s of t h i s survey indicate that c h a r a c t e r i s t i c values e x i s t for the weighted A factors of both the addition and metathetical reactions. I f the measured A factor i s divided by the number of equivalent most-reactive s i t e s i n the molecule, values of the quotient l i e within a narrow range. A c h a r a c t e r i s t i c value of this quotient appears to be common to molecules of diverse s t r u c t u r a l types. The r e s u l t s of t h i s survey c l o s e l y p a r a l l e l the r e s u l t s of other investigators i n r e l a t e d f i e l d s . In p a r t i c u l a r , rate constants for the addition of the ethyl r a d i c a l i n the gas phase are l i n e a r l y r e l a t e d to rate constants for the addition of the methyl and the poly-s t y r y l r a d i c a l i n s o l u t i o n . The few deviations observed i n the comparison with the p o l y v i n y l acetate and the p o l y a c r y l o n i t r i l e r a d i c a l s may be explained i n terms of polar e f f e c t s by reference to the general equations for r a d i c a l r e a c t i v i t y proposed by Bamford, Jenkins and Johnston and by Schwan and P r i c e . The s i g n i f i c a n c e of the r a t i o of rate constants for addition and metathesis of a given compound with the ethyl r a d i c a l has been considered as an index for r e a c t i v i t y i n homopolymerization. The values of the r a t i o accord well with the published data on the degree of poly-merization of these compounds. F i n a l l y the k i n e t i c measurements have provided further information on certain s p e c i a l topics including the reactions of the cyclohexadienyl r a d i c a l , the electron a f f i n i t y of cyclooctatetraene and the structure of cycloheptatriene. GRADUATE STUDIES F i e l d of Study: Chemical K i n e t i c s Chemical k i n e t i c s Special topics i n inorganic chemistry Physical-organic chemistry S t a t i s t i c a l mechanics Surface chemistry D.G.L. James H.C. Clark R. Stewart R.F. Snider J. Halpern Related Studies: D i f f e r e n t i a l equations Atomic physics E l e c t r o n i c s C. Froese M. Bloom R.D. Russell ABSTRACT A kinetic survey of the reactions of the ethyl radical with conjugated cyclic olefines and related compounds has revealed a great variety of reactivity with respect both to addition and to metathesis. An attempt to correlate reactivity with molecular structure has been presented both in the language of polymerization kinetics and of molecular orbital theory. In particular, the correlation of the energy of activation of the addition reaction with free valence and with localization energy (representing stages preceeding and following the exis-tence of the activated complex) has been pursued with some measure of success. Polar and steric effects play a special role in certain cases; thus a significant polar contribution to the transition state appears necessary and reasonable to account for the reac-t i v i t y of cyclooctatetraene. This survey facil i t a t e s a reconsideration of the question of the existence of characteristic values of the A factor for the addition and metathetical reactions respectively. In each case, a f a i r l y constant value is obtained by dividing the A factor by the number of equivalent most-reactive sites in the molecule. This characteristic value appears to be almost independent of structural type with the possible exception of i i i the A factor for addition to non-terminal monoolefines for which a low value has been postulated. The results of this survey closely parallel the results of other investigators in related f i e l d s . In particular, rate constants for the addition of the ethyl radical in the gas phase are linearly related to rate constants for the addi-tion of the methyl and the polystyryl radical in solution. The few deviations observed in the comparison with the polyvinyl acetate and the polyacrylonitrile radicals may be explained in terms of polar effects by reference to the general equations for radical reactivity proposed by Bamford, Jenkins and Johnston and by Schwan and Price. The significance of the ratio of rate constants for addition and metathesis of a given compound with the ethyl radical has been considered as an index for reactivity in homopolymerization; in detail for a l l y l alcohol, and where possible for the other substrates. The values of the ratio accord well with the published data on the degree of polymerization of these compounds. The planar conjugated triene structure proposed by some authors for cycloheptatriene i s inconsistent with the observed value of the energy of activation for addition to this compound. A kinetic study of the cyclohexadienyl radical, comprising i t s formation from each of the cyclohexadiene isomers and i t s reactions with the ethyl radical, has revealed that the dispro-portionation reaction (yielding benzene) accounts for only 28% of the cyclohexadienyl radicals, the remainder forming CgH by combination. x i i i ACKNOWLEDGEMENTS I wish to thank Dr. D. G. L. James for his guidance and encouragement in the course of this investigation. I wish to thank Dr. J . E. Bloor for his advice and assis-tance in the molecular orbital calculations. I am also grateful to the National Research Council of Canada for Studentship awards covering the period June 1960 to September 1962. V TABLE OF CONTENTS Page INTRODUCTION 1 A. The Abstraction of Hydrogen by Alkyl and Other Radicals 2 B. The Addition Reactions of Alkyl and Other Radicals . 12 EXPERIMENTAL METHODS 30 A. Apparatus 30 B. Reactants 35 C. The Photolysis of Diethyl Ketone 40 D. The Photolysis of Diethyl Ketone in the Presence of Unsaturated Compounds 43 E. Polarography 50 RESULTS 52 DISCUSSION 81 A. The Photolysis of Diethyl Ketone 81 B. The Reactions of the Ethyl Radical with Unsaturated Compounds 86 C. The Reactions of the Ethyl Radical with Octene-1 . . 90 D. Accessible Upper Limits for Abstraction and Addition 91 E. The Calculation of Values of A^, A^, E^ and E^ . . . 92 F. Comparison of Intrinsic Radical Reactivities . . . .100 G. The Reactions of the Ethyl Radical with Cyclohexadiene-1,4 115 v i Page H. Benzene 121 I. 2,3-dimethylbutadiene-l,3 125 J. 2,5-dimethylhexadiene-2,4 127 K. Cyclohexadiene-1,3 131 L. |2,2,ljbicycloheptadiene 134 M. Cycloheptatriene 139 N. Cyclooctatetraene 143 0. Cyclooctadiene-1,5 149 P. A l l y l Alcohol 150 Q. A Kinetic Study of the Metathetical and Addition Reactions Characteristic of A l l y l Polymerization . .153 R. The Interpretation of Reactivity in Terms of the Electronic Properties of the Molecule 161 CONCLUSIONS 177 APPENDICES 179 A. Standard Volumes of Gas Burette 179 van der Waal's Corrections for Butane' '"' 179 B. Transmission of Neutral Density Fi l t e r s 180 C. Table of Perkin Elmer Columns and Retention Times. .181 D. Quantitative Calibration of Perkin Elmer Vapor Fractometer for Mixtures of Ethane and Ethylene. . .183 E. Quantitative Calibration of Perkin Elmer Vapor Fractometer for Mixtures of Ethylene and Acetylene .186 • * V l l Page APPENDICES (Continued) F. Quantitative Calibration of Perkin Elmer Vapor Fractometer for Mixtures of Benzene and Cyclohexadiene-1,4 188 G. Tables of Molecular Dimensions, Secular Matrices, Eigenvalues and Eigenvectors 190 BIBLIOGRAPHY 218 • • a V11X LIST OF TABLES Table Page I. The photolysis of diethyl ketone 53 II. The reactions of the ethyl radical with octene-1 . . . 54 III. The reactions of the ethyl radical with a l l y l alcohol. 55 IV. The reactions of the ethyl radical with 2,3-dimethyl-butadiene-1,3 57 V. The reactions of the ethyl radical with 2,5-dimethyl-hexadiene-2,4 60 VI. The reactions of the ethyl radical with cyclohexa-diene-1,3 61 VII. The reactions of the ethyl radical with cyclohexa-diene-1,4 ( f i r s t series) 63 VIII. The reactions of the ethyl radical with cyclohexa-diene-1,4 (second series) 64 IX. The reactions of the ethyl radical with [2,2,l]bicyclob heptadiene 65 X. The reactions of the ethyl radical with cyclohepta-triene 66 XI. The reactions of the ethyl radical with cyclooctate-traene 67 XII. The reactions of the ethyl radical with cycloocta-diene-1,5 68 ix Table Page XIII. Comparison of the results for octene-1 with those of James and Steacie 69 XIV. Abstraction of the hydrogen atom by the ethyl radical 70 XV. Addition of the ethyl radical to the double bond. . .71 XVI. The disproportionation and combination of ethyl and cyclohexadienyl radicals 72 XVII. The reactions of the ethyl radical with benzene . . . 73 XVIII. Polarographic half-wave potentials 74 XIX. The abstraction of hydrogen from 2,3-dimethyl-butadiene-1,3 93 XX. The abstraction of hydrogen from j^2,2,lj bicyclo-heptadiene .94 XXI. The addition of the ethyl radical to cyclohexa-diene-1,4 95 XXII. The addition of the ethyl radical to cycloocta-diene-1,5 96 XXIII. Accessible upper limits for the reactions of the ethyl radical with benzene 97 XXIV. Absolute values of the A factor and activation energy for abstraction . 98 XXV. Absolute values of the A factor and activation energy for addition 99 X Table Page XXVI. Correlation of the rate constants for the addition of the ethyl radical with the methyl a f f i n i t i e s of various substrates, each at 65°C 102 XXVII. Calculation of values of ft at 60°C for various monomers, and comparison with values of 13-flog (k ?/k 2S also at 60°C 107 XXVIII. Correlation of the rate constants for the addition of the ethyl radical with monomer reactivity ratios, each at 60°C I l l XXIX. A comparison of predicted and observed values of the degree of polymerization at 60°C 162 XXX. Comparison of the energy of activation for the addition of the ethyl radical with the free valence at the reaction centre 169 XXXI. Comparison of the energy of activation for the addition of the ethyl radical with the atom localization energy at the reaction centre 171 x i LIST OF FIGURES Figure Page 1. Apparatus 31 2. The nuclear magnetic resonance spectrum of 2,5-dimethylhexadiene-2,4 37 3. The ultra-violet spectrum of cyclohexadiene-1,3 and l-ethylcyclohexadiene-2,4 48 4. The abstraction of hydrogen from diethyl ketone 75 5. The reactions of the ethyl radical with octene-1 . . . . 76 6. The reactions of the ethyl radical with acyclic dienes . 77 7. The abstraction of hydrogen from cyclic dienes and polyenes 78 8. The addition of the ethyl radical to cyclic dienes and polyenes 79 9. The reactions of the ethyl radical with a l l y l alcohol. . 80 10. Correlation of the rate constant for the addition of the ethyl radical with the methyl a f f i n i t y 103 11. Correlation of the addition rate constant with the value of (3 . .108 12. Correlation of the addition rate constant with the rate constant for addition of the polyvinyl acetate radical 112 Figure Page 13. Correlation of the addition rate constant with the rate constant for addition of the polyacrylonitrile radical 113 14. Correlation of the activation energy for addition with the free valence 170 15. Correlation of the activation energy for addition with the atom localization energy 172 16. Correlation of the rate constant for the addition of the ethyl radical with the atom localization energy. . .173 INTRODUCTION An ethyl radical can react with an olefinic molecule by abstracting a hydrogen atom or by adding at one of the unsatu-rated carbon atoms. For a "terminal" d e f i n e , these reactions can be represented, C0H ' + RCH„CH = CH0 > C0H, + R-CHCH = CH n...abstraction Z _> Z Z Z o z C H * + RCH.CH = CH —> RCH-CHCH C H ...addition 2 5 2 2 2 2 2 5 The rate constants of these reactions are governed by the Arrhenius relationship, k = Ae and, in general, both A and E w i l l change when the nature of the radical or the olefine is changed. Thus the attack of a single free radical on a series of defines w i l l proceed at different rates which w i l l depend on the different molecular properties of the defines. In this way, the attack by the chosen radical can be used to measure the relative reactivities of a series of defines; the effect of structural variations can be observed, and an interpretation sought. This concept of reactivity is best considered in terms of the separate contributions of frequency factor and energy of activation by the measurement of rate constants over a range of temperatures. Unfortunately, most of the experimental methods previously employed have not encompassed more than a 2 narrow range of temperature and, in these cases, i t has been customary to assume that the frequency factor is constant for the attack of the same radical on similar reaction centres, in which case log k is linearly related to E. However, any compari-son of reactivities where variable steric factors may be involved is necessarily unsound and must be treated with caution. The reactions of simple free radicals with hydrocarbon substrates have been studied by a number of workers. Although abstraction and addition can often be observed simultaneously, i t is simpler to discuss these alternative processes under separate headings. A. The Abstraction of Hydrogen by Alky! and Other Radicals  1. The methyl radical The abstraction reactions of the methyl radical in the gas phase have been studied by Trotman-Dickenson, Birchard 1 2 3 and Steacie and Trotman-Dickenson and Steacie. ' The results of these and other investigations have been reviewed 4 by Trotman-Dickenson. Methyl radicals were generated by the photolysis of ace-tone between 25 and 340°C. In this temperature range, i t is assumed that the only important reactions of the methyl radicals are, (1) 2CH* 3 (2) 3 CH* -i* CH3COCH3 —>'CH 4 + CH^OCRj (3) From the relative rates of formation of methane and ethane, and knowing k.j/k2x, i t i - s possible to calculate k^/k^,2. A general pattern of reactivity was discovered in this study. In the alkane series, differences in reactivity were attributed to the characteristically different energies of activation for abstraction of hydrogen from primary, secondary and tertiary carbon atoms, respectively. 4 The energies of activation (E) and the bond dissociation energies (D) for primary, secondary and tertiary carbon-hydrogen bonds were shown to f i t the relation, E = 0.5D - 33.5 A relation of this type was f i r s t proposed for a series of reactions by Evans and Polanyi"* who stated that, where there i s no resonance stabilization in the transition state or a constant amount of resonance stabilization throughout a series of reactions of the type, X + YZ —> XY + Z i t may be expected that E = oC H const., where E i s the activation energy, H is the heat of reaction and CX has a value between 0 and 1. That oc is 0.5 in the correla-tion of Trotman-Dickenson i s in accord with the similarity of the 4 bonds being broken and formed. In the alkene series Trotman-Dickenson demonstrated the 4 activating effect of the double bond by showing that the energy of activation for abstraction from butene-1 was 7.6 kcal./mole compared with 8.3 kcal/mole for n-butane. The reactivities of butene-1 and pentene-1 were identical confirming that abstraction was from the cC-methylenic group only. Theoretically, the resonance energy of the a l l y l i c radical^'^ formed by abstraction of an oQ hydrogen may be expected to lower the energy of activation for this abstraction reaction. In contrast to the alkane series the relative reactivities of primary, secondary and tertiary hydrogens were attributed to the variation in the A factor. For propene, butene-1 and -10 3-methylbutene-l the values of 10 A per reactive hydrogen were 2, 7 and 23 mole ^ c.c. sec *7atom respectively, while activation energies were equal within the limits of experimental error. No explanation for this trend could be advanced. Szwarc and Binks have discussed hydrogen abstraction reactions by methyl and ethyl radicals in solution and methyl o radicals in the gas phase. If the driving force of the hydrogen abstraction reaction arises from the energy of the new C-H bond formed between the attacking radical and the hydrogen atom, then a decrease in activation energy would be predicted for an increase in radical-hydrogen dissociation energy. This i s supported by a comparison of the relative rates of abstraction of hydrogen from isooctane by methyl and ethyl radicals. The bond dissociation energy in methane is 3-4 kcal./mole 5 higher than D(C2H^-H). Accordingly the exothermicity of the hydrogen abstraction reaction involving methyl radicals must also be higher by 3-4 kcal./mole than that of the reaction involving ethyl radicals. In view of the symmetry of such a reaction (a OH bond is broken and another formed), the dif-ference in exothermicity should be divided equally between the difference of activation energies of the forward and back-ward reactions. Therefore, the ratio of the rate constants for abstraction by methyl and ethyl radicals should be of the order exp (1500/RT) to exp (2000/RT), i.e., between 10 and 20 at 65°C. Binks and Szwarc have interpreted the experimental results as indicating a value of approximately 11 for this ratio. In the above comparison the abstraction of hydrogen from isooctane by two different radicals was considered. A similar argument has been applied to a series of hydrogen abstraction g reactions involving the methyl radical and different substrates. The relation observed by Trotman-Dickenson for abstraction of primary, secondary and tertiary hydrogens in the alkane series, E = 0.5D — 3.3.5 is equivalent to the statement that differences in activation energy are given approximately by half the differences in the appropriate C-H bond dissociation energies. In the alkene series Trotman-Dickenson observed that variations in reactivity were not reflected in the experimentally determined activation g energies. (See above.) However, Szwarc and Binks have calculated 6 differences in activation energy from the rate constants at 182°C assuming that the value of A/n, where n is the number of reactive hydrogens, is constant. The values obtained were in good agree-ment with the expected pattern. Similar differences in activation energy were obtained by Szwarc and Binks by applying a similar treatment to abstraction rate constants for the methyl radical in isooctane at 65°C. 2. The trifluoromethyl radical The abstraction reactions of the trifluoromethyl radical have attracted some interest in recent years 0'""^'^ and the results have been summarized bri e f l y by Pritchard and Miller.''""' Sources of the trifluoromethyl radical have included the Q photolysis of hexafluoroazomethane, the photolysis of hexa-1 A * | i "1 Q *1 / 1 7 fluoroacetone * » » * and the photolysis of trifluoro-12 acetaldehyde. Of these methods, the photolysis of hexafluoro-acetone seems to offer the advantage of a simple photolysis , • 14,16 mechanxsm. ' Energies of activation for abstraction from hydrocarbons by trifluoromethyl radicals are generally lower than those for abstraction by methyl radicals by 2 to 3 kcal./mole.*'"* As D(CH3-H) = D(CF3~H), the theory of Szwarc and Binks is inade-quate, and i t has been proposed that the main contributing factor i s the greater electron a f f i n i t y of the trifluoromethyl radical.^ 3. The ethyl radical The abstraction reactions of the ethyl radical have been 18 studied by James and Steacie in the gas phase. Ethyl radicals were generated by the photolysis of diethyl ketone at tempera-tures varying from 50 to 180°C. The rate of abstraction was compared with the rate of dimerization of the ethyl radicals, C2H5* + RH ^- C 2H 6 + R' (6) 2C2H5* ->C 4H 1 0 (2) Values of k^/k.^ were measured and used to calculate Er-%E0 6 2 6 Z and A^/A^. The activating influence of bond multiplicity was demonstrated by comparing n-heptane, heptene-1 and heptyne-1. (E^-%E 2 = 10.6, 8.3 and 7.6 kcal./mole respectively.) A compari-son of the reactivities of hexene-1, heptene-1 and octene-1 revealed no significant difference which fact is in agreement 4 with results of Trotman-Dickenson et a l . The frequency factors were found to be approximately proportional to the number of hydrogen atoms available for abstraction in each molecule. Thus for n-heptane, heptene-1 and cyclohexene the values were approxi-mately in the ratio 10:2:4 respectively. 4. The polystyryl and trichloromethyl radicals Gregg and Mayo*"°/ studied the abstraction of hydrogen from a number of hydrocarbons by the polystyryl radical. Each hydro-carbon was used in turn as solvent for the polymerization of styrene and the molecular weight of the polymer was measured. Hence the a b i l i t y of the hydrocarbon to participate in chain 8 transfer was observed. The abstraction of hydrogen from several of the same hydrocarbons (toluene, cumene, ethylbenzene, diphenylr 2 0 methane and triphenylmethane) was studied by Kooyman using the trichloromethyl radical. The trichloromethyl radicals were generated in solution at 91.5°C by the reaction of benzoyl peroxide with carbon tetrachloride. The rate of abstraction from each hydrocarbon was calculated from the retardation of addition to cetene. The rate constants thus obtained were compared with the transfer constants of Gregg and Mayo. It was shown that a plot of the relative rate constants for abstraction by the trichloromethyl radical against the transfer constants was linear, i.e., . = (const) x k _ CC13* v ' transfer Kooyman used the same method to measure the abstraction rate 20 constants for a series of defi n e s . It was observed that abstraction was very slow when the oc position was f u l l y sub-stituted. The abstraction reactions of the trichloromethyl radical 21 have been studied by Huyser for a series of substituted toluenes. The radicals were obtained by the photolysis of bromo-trichloromethane at 50°C. The rate of abstraction from each substituted toluene was compared with the rate of abstraction from toluene. The relative reactivities were found to be linearly related to the Hammett (S values of the substituents 9 (methyl, methoxy, chloro etc.)» electron donating groups favour-ing rapid abstraction. Poor correlation was obtained when the <r values were used. On the basis of this observation, Huyser has postulated a polar contribution to the transition state in abstraction reactions, involving the trichloromethyl radical. . . . h . . . c c i ^ Ar Huyser has also studied the addition and abstraction reac-tions of trichloromethyl radicals with a number of to Cg 22 linear and cyclic defines. „ Unfortunately the experimental method yields ratios of addition and abstraction rate constants ka/kt . The value of the method i s therefore limited as i t may not be possible to distinguish between slow addition and rapid abstraction when a low ratio is observed. However, the results for butene-2, peiifeene-2 and 4-methylpentene-2 seem to indicate that the rates of abstraction of hydrogen are in the order tertiary> secondary > primary. This order of reactivity of hydrogen atoms towards abstrac-tion very li k e l y is related to the relative dissociation energies of the carbon-hydrogen bonds concerned. However, Huyser has postulated a polar contribution to the transition state similar 21 to that for abstraction from toluene. Transition states A, B and C might be suggested for abstraction from butene-2, pentene-2 and 4-methylpentene-2. JCH -CH-^—CH—^-CHCH .. .H.. .CCl B As the order of stability of carbonium ions is tertiary> secon-dary > primary, the ease of attaining these transition states would be A < B <: C. It i s interesting to observe that the trichloromethyl radical i s not regarded as showing pronounced electronegative character in i t s addition reactions, and is regarded as similar to both the methyl and the ethyl radical in contrast to such electrophilic reagents as oxygen atoms. 5. The hydrogen atom The abstraction reactions of hydrogen atoms have been 25 26 studied by Trost and Steacie and Schiff and Steacie. The hydrogen atoms were generated in a discharge tube and the abstraction of hydrogen from some alkanes was studied. In the homologous series ethane to n-hexane values of activation energy varying from 8.5 to 9.1 kcal/mole were observed. The abstraction reactions of hydrogen atoms have been studied 24 o by Hardwick at 23 C in n-hexane solution using radiolysis of the solvent to form atomic hydrogen. The defines were classified according to structural type, RCH=CH2, RCH=CHR, R2C=CH2, etc. It was found that the rate of abstraction was the same for a l l 11 defines of a given structural type, but varied between the different structural types. As the investigation was conducted at one temperature only, i t i s not possible to attribute the variations in reactivity to variations in frequency factor or energy of activation. To explain the formation of products of the type R2C=CHR in the abstraction of hydrogen from the structural group 2 7 RCH=CHR, Hardwick has made the novel suggestion that olefinic hydrogen is removed in the abstraction process. That abstraction from tetramethylethylene was too slow to be detected is cited 24 as further evidence for this mechanism. 6. Conclusions In the light of present knowledge, i t may be concluded that in the process of abstraction by methyl, ethyl and similar radicals, the activation energy is controlled predominantly by the strengths of the bonds broken and formed. Some modifica-tion of this theory may be necessary when the radical formed by abstraction has considerable resonance energy. The polar contribution to the transition state, suggested for abstraction by the trichloromethyl radical i s probably less important for the methyl and the ethyl radicals in view of the lower electron af f i n i t y of these radicals. Although the results obtained by the various investigators using different radicals are generally in agreement, some anomalies are apparent. The abstraction of olefinic hydrogen 12 by the hydrogen atom is in sharp contrast to the abstraction from the OC-methylenic group by alkyl radicals and no explanation has been advanced for this behaviour. The conflicting conclusions of Trotman-Dickenson and Szwarc and Binks on the activation energies and A factors in the alkene series remain unresolved in the absence of further evi-dence. The importance of accumulating further evidence by measuring these quantities accurately is thus demonstrated. B. The Addition Reactions of Alkyl and Other Radicals The addition reactions of free radicals have been the subject of many investigations and a large number of papers have attempted to interpret the pattern of reactivity which is observed when a series of substrates are studied with a chosen reference radical. A wide diversity of methods have been used to measure addition rate constants and, in the f i r s t part of this section, these methods w i l l be outlined and any immediate conclusions indicated. However, a general survey of the results and their implications w i l l be postponed u n t i l the contributions of a l l workers have been described as several of the early results do not appear to demonstrate any clear pattern of reactivity u n t i l they are combined or compared with the results of more recent investigations. 13 1. The methyl radical 28 29 Raal and his co-workers ' have studied the addition of methyl radicals to a series of olefines at 300°C in the gas phase. Methyl radicals, generated by the photolysis of acetalde-hyde, initiated the polymerization of the d e f i n e being investi-gated. No clear pattern of reactivity was observed. Buckley and Szwarc have pointed out that the calculation of rate of addition was based on the assumption that a l l the olefines poly-merized to the same degree.^ As this is not necessarily true, the results must be accepted with some reserve. Mandelcorn and Steacie"^ investigated the addition of methyl radicals to ethylene, propylene, acetylene and butadiene in the gas phase at temperatures varying from 140 to 240°C. Methyl radicals were generated by the photolysis of acetone. A low concentration of methyl radicals was employed in this investigation and i t was believed that the termination of the adduct radical did not involve the consumption of a methyl radical. The validity of this assumption is somewhat doubtful. Rate constants were calculated in two ways. In the f i r s t method, the lowering of the material balance due to the addition reactions of the methyl radicals was measured. In the second method the rate of consumption of the olefine was measured. The possible errors were discussed by these investigators who concluded that the two alternative methods for the calculation of addition rate constants would give low values for energies of activation in the 14 f i r s t method and high values in the second. For ethylene, propylene and butadiene, the values of energy of activation were 7.0, 6.0 and 2.5 kcal./mole respectively. The method i s inapplicable when rapid abstraction occurs. Szwarc and his co-workers have published a considerable number of papers on the addition reactions of the methyl radical 31a in solution. The methyl radicals are obtained by the thermal decomposition of acetyl peroxide in isooctane solution and the method is essentially a comparison of the rate of addition to the d e f i n e with the rate of abstraction of hydrogen from the 32 solvent. CH3* + A -^CH 3A* (2) C H3* + C 8 H 1 8 - ^ C H4 + C8H17 ( 1 ) Unfortunately, the radical source imposes temperature limits as the decomposition procedes too slowly below 60°C and too o 3 3 rapidly above 90 C. For this reason results are usually quoted as "methyl a f f i n i t i e s " ( = k ^ k ^ at 65°C. Using the photolysis of azomethane to generate methyl radicals, Feld and Szwarc have extended the temperature range to 6 - 95°C and have shown that the value of A2/A^ is approxi-mately constant for a series of compounds having the same reac-34 tion centre (ethylene, propylene, isobutene, styrene, etc.). However, a methyl group attached to the reaction centre usually a reduces the reactivity by a factor of 7 to 11. This is 15 presumably, in part, a steric effect. The addition of methyl radicals to propylene has been 55 studied by Miyoshi and Brinton. From a detailed product analysis i t was concluded that addition to w a s approxi-mately 9 times as fast as to C ( 2 ) ' The reactivities of a number of unsaturated compounds towards ethyl, n-propyl and isopropyl radicals have been determined in isooctane solution. The interrelations of these radicals w i l l be discussed later in this section. 2. The trifluoromethyl radical Stefani, Herk and Szwarc have studied the addition reactions of trifluoromethyl radicals at 65 C in isooctane solution. The radicals were generated by the photolysis of hexafluoroazo-methane and the rate of addition to each olefine was measured relative to the rate of abstraction from the solvent. The results were consistent with the high electronegativity of the trifluoromethyl radical and relative reactivities showed a high dependence on the polarity of the reaction site. In view of the probable strong contribution of the structure olefine e -CF^ to the transition state, an increase in reactivity with decrease in ionization potential was predicted and observed. A plot of ionization potential against the logarithm of the trifluoromethyl a f f i n i t y was linear for a number of terminal olefines. The addition of the trifluoromethyl radical to some aromatic compounds has been studied by Charles et a l . ' and Holmes-and Kutschke*7 3. The ethyl radical The addition reactions of the ethyl radical were studied by James and Steacie in the gas phase over the temperature o 39 range 50 to 180 C. Ethyl radicals were generated by the photo-lysis of diethyl ketone and the rate of addition to the olefine was compared with the rate of dimerization to form butane. C2H5* + A —> C2H5A' (7) 2C 2H 5' C 4H 1 ( ) (2) The 1- substituted ethylenes (hexene-1, heptene-1 and octene-1) were found to have the same activation energy within the limits of experimental error (E^-%E 2 =7.0 kcal./mole). For 1,1- disubstituted ethylenes a lower value (5.6 kcal./mole) was observed. The A factor was constant in the absence of structural features which could lead to steric blocking of the reaction centre but in 2,3,3-trimethylbutene-l the A factor was low, due presumably to the presence of a tertiary butyl group close to the reaction site. The ethyl radical does not add to cyclohexene and trans-octene-4 at a detectable rate. It was suggested that the double bond was shielded from radical attack by substituents at the reaction centres giving an A factor lower than the normal value for the 1-alkenes. The results of some early investigations which did not in 17 themselves display any clear pattern of reactivity have been reconsidered recently:-4. The hydrogen atom Melville and his co-workers^>41>43 s t u c j i e d the reactions of hydrogen atoms with a number of olefines in the gas phase using the rate of attack on a molybdenum trioxide surface as a measure of the hydrogen atom concentration. In this method the sum of abstraction and addition rate constants was measured although i t was later decided that for ethylene and propylene 44 addition was the predominant reaction. The results indicated that the reactivity of the double bond towards attack by hydrogen atoms was not markedly dependent on the amount of substitution. 5. The trichloromethyl radical Kharasch and Sage generated trichloromethyl radicals by the photolysis of liquid bromotrichloromethane and measured the rate of addition to a number of o l e f i n e s ^ Recently, Hardwick has measured addition rate constants for hydrogen atoms in solution. The atomic hydrogen was gene-rated by the radiolysis of n-hexane. He concluded that the rate of addition was constant for a given structural type and differed for varying structural types. Hardwick has pointed out that this fact is consistent with the results of investigations involving other radicals, e.g. e t h y l J 7 and methyl radicals. Hardwick has shown that his results, obtained in solution, are consistent 43 with those of Melville et a l . in the gas phase. Comparison of the addition of hydrogen atoms and trichloromethyl radicals 45 (as measured by Kharasch and Sage), showed that rapid addi-tion of hydrogen was paralleled by rapid addition of trichloro-methyl radicals. As the addition of oxygen atoms to defines shows a different dependence of reactivity on structure, Hard-wick has concluded that hydrogen atoms and trichloromethyl radi-cals are to be compared with alkyl radicals such as ethyl and methyl, rather than electrophilic reagents such as oxygen atoms. 6. The RS* radical The addition reactions of the RS* radical have been studied by Sivertz and his co-workers."^ 7. The polymer radicals An important example of a radical addition reaction is the propagation step in polymerization by a radical mecha-57a nism. 8. Reactivity and molecular properties 46 Kooyman and Farenhorst measured the relative reactivities of aromatic hydrocarbons towards the trichloromethyl radical and observed a linear correlation between the logarithms of the relative rate constants (k r) and the highest free valences of the hydrocarbons. An increase in the rate of addition was matched by an increase in the maximum free valence. If the free valence is regarded as a measure of the potential free radical character, then some intuitive j u s t i f i c a t i o n may be found for such a relationship. 19 47 It was observed by Coulson that the methyl a f f i n i t i e s of aromatic hydrocarbons, as measured by Szwarc and his co-workers, could be similarly correlated with the maximum free valence. As free valence and atom localization energy are linearly related to a good approximation in the aromatic series, Coulson could show that methyl a f f i n i t i e s are also related to atom localization energies. In this case an increase in atom localization energy is accompanied by a decrease in the methyl a f f i n i t y . The free valence is a property of the unreacted molecule and is concerned, therefore, with the i n i t i a l stages of the reaction, prior to the formation of the transition state complex. The atom localization energy is the energy to isolate a Ii electron on a particular atom in a conjugated system and repre-sents a condition which approximately describes the later stages of the reaction, subsequent to the formation of the transition state complex. The gradient of the correlation of the logarithm of the methyl a f f i n i t y against localization energy corresponds to a value of -11 kcal. for /5 (the resonance integral). This suggests that localization has not proceded far at the . . 31b transition state. As values of log (methyl affinity) and log k r (as measured by Kooyman and Farenhorst) both correlate with localization energies, a linear correlation of log (methyl affinity) and 20 AO log k r is predictable and has been observed by Levy and Szwarc. It was pointed out that in this correlation a variation in methyl a f f i n i t y of 4 powers of 10 was equivalent to a variation in k r of 6 powers of 10. It was proposed that this fact reflects the difference in intrinsic reactivities of the two radicals. An extremely reactive radical w i l l be relatively insensitive to the reactivity of the substrate. Therefore the slope of the line was defined as the ratio of the intrinsic reactivities of the methyl and the trichloromethyl radicals and on this scale the intrinsic reactivity of the methyl radical is 1.8 times that of the trichloromethyl radical. Similar comparisons of the intrinsic reactivities of methyl, ethyl and n-propyl radicals showed that these radicals had equal intrinsic reactivities? It was concluded that they probably had very similar rates of addition to the same substrates. As ethyl a f f i n i t i e s are approximately 11X methyl a f f i n i t i e s , this conclusion implies that the rate of abstraction from isooctane by a methyl radical is HX/the rate of abstraction by an ethyl radical at 65°C. Szwarc and Binks have suggested that this ratio is consistent with the bond energies involved. A comparison of the methyl and polystyryl radicals has shown that the methyl radical has an intrinsic reactivity which i s 58 1.7 times that of the polystyryl radical. The lower intrinsic reactivity of the latter has been ascribed to the resonance stabilization of the substituted benzyl radical. 21 In the reactions of the methyl radical with a hydrocarbon, the methyl radical i s usually regarded as a weak electron donor, 49 Matsen has considered a process in which the unpaired methyl electron enters i n i t i a l l y into the lowest unoccupied orbital of an aromatic hydrocarbon without binding the methyl to a particular carbon atom. The electron a f f i n i t y should have the effect of reducing the repulsion between the aromatic molecule and the methyl group. A plot of log (methyl affinity) against the apparent electron a f f i n i t y shows that these quantities are linearly related and that an increase in electron a f f i n i t y is accompanied by an increase in the rate of addition. Matsen has pointed out that this correlation does not prove that the hypo-thetical transition state is correct since a l l the electronic properties of an aromatic molecule, such as electron a f f i n i t y , free valence, etc. are related. Szwarc has demonstrated that an increase in singlet-triplet excitation energy in the aromatic series is accompanied by a . decrease in methyl a f f i n i t y , the logarithm of the methyl af f i n i t y being linearly related to the frequency of the transi-tion. The possible physical significance of this correlation was considered by Szwarc who discussed the energy barrier to reaction in terms of the energy required to uncouple a pair of electrons in order to make one available for bond formation. The simple relationships between maximum free valence, 22 localization energy, excitation energy, etc. which are found in the aromatic series do not apply to olefines and the number of correlations is more limited. The relative rates of addition of electrophilic radicals (e.g. oxygen atoms) correlate with the properties of the double bond such as excitation energy, bond order and ionization potential, whereas these quantities do not control the rate of attack of ethyl, methyl and similar 23 radicals. It is believed that the nature of the transition state complex is different for the two classes. For electro-p h i l i c radicals, a transition complex in which the radical attacks the bond rather than a particular carbon atom has been 23 suggested. Preliminary discussions have indicated that free valence or atom localization energy may be regarded as the index of 23 51-53 reactivity for the addition of methyl and similar radicals. ' Sato and Cvetanovic compared the reactivities of a number of terminal and internal olefines for the addition of methyl, ethyl and trichloromethyl radicals and concluded that free valence and not atom localization energy was the controlling property.^ Binks and Szwarc, on the other hand, concluded that methyl a f f i n i t i e s of terminal olefines correlated with atom localization energies provided allowance was made for the varia-tion of resonance integral with bond length. Deviations from this correlation were observed for internal olefines and were attributed to steric hindrance. The effect of methyl substituents on the reactivity of aromatic and conjugated hydrocarbons can be accounted for in terms of hyperconjugation. Binks and Szwarc have shown that i f the methyl substituent i s located on a carbon atom which is not the reaction centre, then the effect on the methyl a f f i n i t y can be calculated to a f a i r degree of accuracy. When the methyl substituent is attached to the reaction centre the steric effect outweighs the hyperconjugative effect. 53 Pullman and Effinger have attempted to explain the observed differences in the reactivities of aromatic and unsatu-rated hydrocarbons in terms of localization energy. Binks and Szwarc"^ do not regard the results of Pullman and Effinger as accurate and have pointed out some discrepancies between their calculations and observed values. To investigate further the factors controlling the rate of 52 addition, Jennings and Cvetanovic studied the addition of hydrogen atoms to mono-olefines at 23.5°C in the gas phase. Since hydrogen atoms are very small, i t was hpped that complica-tions due to steric factors would be minimized. The results were found to correlate with atom localization energy but not with the maximum free valence, and therefore stand in contrast to Sato and Cvetanovic 1s conclusions. Q Szwarc and Binks have described a simple model to account for the dependence of activation energy on localization energy. This model may be discussed in terms of a potential energy 24 diagram which relates the energy of the system composed of a radical (R*) and a molecule (A) to the distance between R* and A. The approach of the radical to the. "real" molecule A results in a repulsive force and the energy of the system increases with decreasing R*-A distance. If, however, the molecule A is converted to a "residual" A with one of the electrons completely isolated from the (7 system and localized on a carbon atom, then the interaction of this localized electron and the p electron in the radical w i l l result in an attractive Morse curve leading to the formation of a chemical bond. Energy of the system Distance R-A At i n f i n i t e separation, the energy difference of the two systems, R* + real A and R* + residual A, is equal to the localization energy of A. It i s proposed that the transition state corres-ponds to the intersection of the two lines. The energy of the 25 transition state w i l l l i e slightly below the intersection because of resonance, but this effect is assumed to be constant for a series of substrates similar to A. It is important to keep in mind that the shape of the attraction curve must be independent of the nature of the remaining conjugated system since, by definition, i t i s isolated from i t . Now the reaction of R* with two similar substrates A and A' is considered. It is assumed that eaeh has the same type of reaction centre ( = C or C-H ). H The same attractive curve applies in each case and i t can be reasoned that the repulsive curve is also the same in each case. Hence the respective potential energy diagrams differ only in the positions of the repulsion curves relative to the attraction curve. Assuming that those portions of the attraction and repulsion curves which are pertinent to this problem may be approximated by straight lines with slopes ^ and X_, a simple geometrical treatment shows that the difference in a c t i -vation energy for two substrates A and A' is proportional to the difference of the corresponding localization energies and L ', i.e., r E-E'=(l + K / Ik)" 1 (VV* ( a ) This proportionality i s , in fact, observed for the addition of methyl and similar radicals to aromatic compounds or terminal olefines. 26 It is instructive to consider the effect of a change in the repulsive force on the activation energy of the addition process. Energy of the system Distance R-A Such a change can be effected by changing the nature of the radical (e.g. CH^ ' to CCl^) . For radicals R^  and R* i t can be deduced, from equation (a), that ( E - E ' ) = OC ( E - E ' ) K l K2 x R_ / R-i >. R-i CC = (1 + If a  l l OJya + JTa V L-') The significance of oC has already been discussed. It was defined as the intrinsic reactivity of R^  relative to R^ . In the abstraction process i t was suggested that the driving force of the reaction came from the energy of the new C-H bond. In contrast, the strength of the new bond is 27 believed to play a minor role in controlling the energy of the addition process. For example, i t has been concluded that methyl and ethyl radicals add at the same rate although D(A-CH3) > D(A-C 2H 5). This may be interpreted in terms of 54 a potential energy diagram: Distance R-A However, i f the strength of the newly formed bond changes considerably, this w i l l affect the rate of the addition reaction, by changing the slope of the attraction curve. For example, the rate of addition of; the methyl radical to ethylene, styrene and 1,1-diphenylethylene is affected by the sta b i l i t y of the new radicals formed by addition.^ 9. Conclusions It may be concluded that in the process of addition to an olefinic hydrocarbon, the activation energy is closely controlled by the repulsion between the p electron of the radical and the 28 77 electrons of the hydrocarbon and by a property of the hydro-carbon i t s e l f . Whether this property is the atom localization energy or the maximum free valence is not yet clear. The work of Szwarc and his co-workers and Jennings and Cvetanovic strongly supports the claim of localization energy, although the conflic-ting conclusion of Sato and Cvetanovic cannot be ignored. However, in correlations of the types which have been dis-cussed above, i t has been assumed that the frequency factor is constant for a l l members of a reaction series, and log k i s regarded as a linear function of E. There is very l i t t l e reliable experimental information on the temperature coefficients of the rates of addition reactions and, for this reason, the relative importance of energy of activation and frequency factor is often unknown. This applies particularly to non-terminal olefines so that theoretical calculations cannot be tested accurately for this class. It seems desirable, therefore, to measure accurate values of activation energy and frequency factor for the addition of a simple radical to a number of selected substrates. In this investigation a number of linear and cyclic dienes and polyenes were studied. These are representative of a variety of struc-tural types. The experimental work was carried out in the gas phase to avoid the possible disturbing influences of solva-tion effects. In the measurement of rate constants over a range of temperatures an upper limit is imposed by the thermal decomposition of the adduct radical. Consequently, the ethyl radical was chosen as the photolysis of diethyl ketone is a f a i r l y simple and carefully studied mechanism at temperatures from 50 to 180°C. 30 EXPERIMENTAL METHODS A. Apparatus Kinetic measurements were conducted on a conventional high vacuum apparatus (Figure 1). Mercury cut-offs were used instead of stopcocks throughout the storage, preparation, photolysis and analysis sections. In this way errors arising from the absorption of reactants and products in stopcock grease were avoided. 1. Preparative system Reactant pressures were measured on the manometer (M) by a cathetometer. This manometer also served as a cut-off and was opened to pump out the reaction c e l l and preparation line. 2. Optical system A British Thomson-Houston ME/D 250 W. mercury arc lamp provided an intense source of illumination from a small area and a single quartz lens (f = 7 cm.) gave a parallel beam which just f i l l e d the reaction c e l l . The lamp was operated on the 230 volt A.C. supply through a control circuit consisting of a fixed resistor (35 ohms), a rheostat (20 ohms), a voltmeter and an ammeter. The lamp was allowed to warm up on an i n i t i a l current of four amps, and the circuit resistance was gradually reduced u n t i l the normal working conditions of 65 volts and F I G . I A P P A R A T U S A N A L Y S IS 7=->H.V F I G . I A P P A R A T U S 32 3.6 amps, were observed. It has been reported that no radiation can be detected from this source between 2482 and 2752 A* owing 0 18 to reversal of the 2537 A li n e . Consequently, the possibility of mercury photosensitization could be discounted. The optical f i l t e r was a 0.5% solution of potassium hydrogen phthalate contained in a cylindrical quartz c e l l of 7 cm. diameter and 2 cm. length. This f i l t e r does not transmit wavelengths of less than 3000 A* and transmits about 70% of the 9 59 incident radiation at 3130 A. The effective radiation was limited to the region 3000 to 3200 A* by the f i l t e r and by the transparency of the ketone to longer wavelengths. The solution was renewed for each photolysis. The intensity of the incident radiation could be reduced by neutral density f i l t e r s of aluminium deposited on quartz (Appendix B). The fused quartz reaction c e l l was a cylinder 10 cm. long 3 and 5 cm. diameter with an illuminated volume of 196 cm. The quartz to pyrex connection was through a mercury sealed B12 ground joint. The c e l l was housed in an electric resistance furnace and i t s temperature was measured by means of three copper-constantan thermocouples which were distributed over the surface. 3. Fractionation system In the analysis section the reaction products were divided into three fractions, volatile at -215, -170 and -120°C respectively. The lowest temperature was obtained by means of a solid nitrogen trap and the higher temperatures using a Ward-Le Roy s t i l l . The solid nitrogen trap was constructed of 6 mm. tubing in the form of a spir a l . This was surrounded by a Dewar vessel and sealed to i t by a B34 ground joint. By pumping on the liquid nitrogen i n i t i a l l y contained in the Dewar vessel, a temperature of -215°C was obtained. The vapour pressure of the nitrogen was observed on a small U tube manometer. In the presence of solid nitrogen a pressure of 0.5 cm. was indicated. After use, rapid melting of the solid nitrogen was achieved by passing a current through a few turns of resistance wire wound on the lower spirals of the trap. The modified Ward s t i l l was constructed to the pattern of Le Roy.^^ A central trap, into which the gas was condensed, was made from a 12 mm. tube and a 6 mm. tube. The column was ring sealed to a jacket tube which was provided with a B34 ground joint. The diameter of the jacket tube was 30 mm., and the length of the column below the ground joint approximately 30 cm. Three copper-constantan thermocouples were attached to the outer surface of the central trap. One was placed at the bottom and the others were 8 and 16 cm. from the bottom. The central trap was then covered with a layer of lead f o i l followed by a layer of glass tape and f i n a l l y a heating c o i l of 10 feet of 33 s.w.g. "Advance" was wound over the glass tape. The total resistance was about 90 ohms. In use the outer jacket was evacuated and surrounded by liquid nitrogen. Temperatures above that of liquid nitrogen were obtained by passing a current through the heating c o i l . This current was controlled by a Variac and observed on an ammeter (0.5 amp. f.s.d.). The Variac was connected to the secondary winding of a transformer which reduced the 230 volts supply to 23 volts. Fractions were pumped into the gas burette by a Toepler pump (T^) assisted by the mercury diffusion pump. The pressure of each fraction, confined in one of four calibrated volumes (Appendix A), was measured on a mirror scale and the temperature was measured simultaneously on a thermometer suspended close to the burette. When significant, a van der Waal's correction was applied to the pressure (Appendix A). The second Toepler pump (T 2) was used to transfer gases to the sample tube of the gas chromatography unit. 4. Gas chromatography Chromatographic analyses were carried out on a Perkin Elmer Vapor Fractometer 154C. Columns used were 6 f t . by % in. and the carrier gas was helium except when i t was desired to detect hydrogen, in which case nitrogen was used. Detection was by means of a thermal conductivity c e l l connected to a Leeds and Northrup Speedomax G 1 mV. recorder. The sampling system for gases consisted of a sample tube 35 and bypass tube between two double-oblique taps. These taps could be turned to pass the carrier gas through either tube. The gas was pumped into the evacuated sample tube by a Toepler pump (T 2 in Figure 1) with the carrier gas flowing through the bypass. The inlet double-oblique tap was turned momentarily to admit carrier gas to the sample tube, thus equalizing the pressures in the sample tube and helium line. This caused a considerable disturbance of the recorder baseline followed by a further disturbance after approximately two minutes. The two double-oblique taps were then turned simultaneously to sweep the sample into the column with only a very slight flow disturbance. Liquid samples were injected through a septum by a hypo-dermic syringe. The columns used and the retention times of various com-pounds are l i s t e d in Appendix C. B. Reactants Except where otherwise specified, compounds were purified on the Beckman Megachrome Preparative Gas Chromatograph, using helium as carrier gas. Purity was then checked on the Perkin Elmer Vapor Fractometer Model 154C. Immediately after purification, compounds which were to be used in kinetic measurements were transferred to the reaction system, degassed and d i s t i l l e d from one bulb to 36 another with retention of the middle third. Diethyl ketone, the White Label grade of Eastman Organic Chemicals, was purified on the Ucon Polar column at 105°C and 8 p.s. i . inlet pressure. Octene-1, obtained from the Phillips Petroleum Company, was purified on the Apiezon column at 110°C and 10 p.s.i. inlet pressure. A l l y l alcohol was the Chemically Pure grade of Eastman Organic Chemicals. It was purified on the Ucon Polar column at 110°C and 8 p.s. i . inlet pressure. 2.3-dimethylbutadiene-l,3. obtained from the Borden Chemical Company, was d i s t i l l e d on a good fractionating column in an atmosphere of nitrogen. The middle fraction, boiling between 68 and 69°C, was collected. 2<5-dimethylhexadiene-2.4. obtained from the Borden Chemical Company, was purified on the Ucon Polar Column at 130°C and 8 p.s. i . inlet pressure. Only one peak was observed in the subsequent analysis on the Perkin Elmer Vapor Fracto-meter but some doubt was f e l t as to the true identity of the compound as the melting point (approx. 15°C) and boiling point o 61 (135 C) were higher than those l i s t e d . Consequently, the N.M.R. spectrum was measured on the Varian A60 instrument. Two peaks were observed corresponding to methyl and ^ tnylic". hydrogens (Figure 2). The peak areas were in the ratio 6.2/1 in good agreement with the theoretical 6/1. Slight s p l i t t i n g o o CM O o to o o 37 The nuclear magnetic resonance spectrum of 2,5-dimethylhexadiene-2,4. 38 was observed in the methyl peak. This is consistent with the slight difference in environment for the methyl groups A and B: (B) Me H > = .Me (A) (A) Me^ > = C^ H xMe (B) Since this experiment was carried out the compound 2,5-dimethylhexadiene-2,4 has been l i s t e d by Eastman Organic Chemicals. The boiling point quoted by this company is 132-136°C. Cyclohexadiene-1,3, obtained from Columbia Organic Chemicals, was d i s t i l l e d on a good fractionating column in an atmosphere of nitrogen. The middle fraction, boiling at 80°C, was analysed on the Perkin Elmer Vapor Fractometer and was found to contain approximately 170 benzene. In view of the low reactivity of benzene relative to cyclohexadiene-1,3 no significant correction need be applied for this impurity in the calculation of the addition and abstraction rate constants. Cyclohexadiene-1,4, obtained from the Aldrich Chemical Company, was purified on the Apiezon column at 110°C and 10 p.s . i . inlet pressure. The compound used in the f i r s t series of runs was found to be pure when analysed on the Perkin Elmer Vapor Fractometer. The compound used in the second series on runs was found to contain 0.1% benzene and, where necessary, a correction was applied for this impurity. {2,2,l]bicycloheptadiene, obtained from the Aldrich Chemical Company, was purified on the Ucon Polar column at 39 105°C and 10 p. s . i . inlet pressure. Cycloheptatriene, obtained from the Shell Chemical Company, was purified on the Apiezon column at 120°C and 10 p.s.i. inlet pressure. Cyclooctatetraene. obtained from Columbia Organic Chemicals, was purified on the Ucon Polar column at 105°C and 14 p . s . i . inlet pressure. The original material contained some styrene and the "purified" cyclooctatetraene was found to contain about 0.2% of this impurity. The styrene content was not reduced when the purification step was repeated. Calculation showed that no significant error would result from the presence of this impurity. A number of unidentified impurities also occurred in the "purified" cyclooctatetraene. These a l l had much shorter retention times than cyclooctatetraene and were removed by bulb-to-bulb d i s t i l l a t i o n in the reaction system. Cyclooctadiene-1.5. obtained from Petroleum Chemicals Inc., was purified on the Apiezon column at 115°C and 14 p.s.i. inlet pressure. The "purified" compound contained some impurity with a relatively short retention time. This was removed by bulb-to-bulb d i s t i l l a t i o n in the reaction system. Benzene, the Reagent grade of A l l i e d Chemicals, was puri-fied on the Apiezon column at 100°C and 10 p.s. i . inlet pressure. Styrene, obtained from Columbia Organic Chemicals, was purified on the Ucon Polar column at 130°C and 14 p.s. i . inlet 40 pressure. Acrylonitrile, the chemically pure grade of Eastman Organic Chemicals, was purified on the Ucon Polar column at 100°C and 10 p.s . i . inlet pressure. Crotononitrile, obtained from Peninsular Chemresearch Inc., was purified on the Ucon Polar column at 110°C and 14 p.s. i . inlet pressure. The cis isomer was eluted f i r s t and the cis/trans ratio was approximately 35/65. Anthracene was the Chemically Pure grade of Eastman Kodak. It was used only as a standard substance in checking the polarographic technique and no purification was carried out. C. The Photolysis of Diethyl Ketone  1. Kinetic measurements Diethyl ketone was admitted to the preparation line and reaction c e l l u n t i l the required pressure was obtained. The c e l l temperature was measured by the c e l l thermocouples, the c e l l was isolated and the reactant pressure was measured accur-ately on the manometer (M). The photolysis was timed by stop-watch and the temperature was calculated from the mean of several e.m.f. readings taken at regular intervals during the run. After the photolysis the contents of the c e l l were admitted to the analysis line where the bulk of the diethyl ketone was condensed by the dry-ice trap and the products were divided 41 into fractions using the solid nitrogen trap and the Ward-Le Roy s t i l l . Carbon monoxide was separated from the higher boiling constituents at -215°C and measured on the gas burette. Various gas-chromatographic analyses of the carbon monoxide fraction verified that i t was free from methane, hydrogen, ethane and ethylene. Ethane and ethylene were transferred to the gas burette as a single fraction with the Ward-Le Roy s t i l l at a temperature of -170°C. The ethane-ethylene fraction was free from carbon monoxide, propene and butane. A trace of propane was occasion-a l l y observed but the quantity was much too small to be s i g n i f i -cant. The ratio ethane/ethylene was measured on column J ( s i l i c a gel) at a temperature of 80°C and a helium pressure of 12 p.s . i . The area of each peak was measured by dividing i t into elemental trapezia each with a height of 0.01 mV. The instrument was calibrated by running standard mixtures of ethane and ethylene and the response to ethane was found to be greater by a factor of 1.08 (Appendix D). Butane was removed and measured at a s t i l l temperature of -120°C. Analysis confirmed the purity of this fraction. The results for the photolysis of diethyl ketone are recorded in Table I and plotted in Figure 4. 42 2. Analysis for products involatile at -120°C Following the analysis of the low boiling fractions as described above, the dry-ice trap and Ward-Le Roy s t i l l were allowed to warm up to room temperature and the compounds remaining in the analysis line were condensed out of the appara-tus through the sample admission stopcock. Additional diethyl ketone was condensed out to increase the bulk of the sample to about 40 microlitres. The resulting drop of liquid was injected into the gas chromatograph using a Hamilton Microliter syringe. Analysis was on column R at 100°C and 15 p . s . i . helium pressure. The retention time of diethyl ketone was 6.5 minutes (air = 0) and a small product peak was observed at 17 minutes. The accepted mechanism for the photolysis of diethyl ketone predicts the formation of 3-methylhexanone-4. Efforts to obtain this compound for a direct comparison of retention times were unsuccessful. It does not appear to be l i s t e d by any of the usual suppliers and Eastman Kodak were not prepared to undertake a custom synthesis. In an attempt to obtain enough of the product for spectro-scopic analysis, several long photolyses were conducted on diethyl ketone and the cumulative reactant-product mixture was injected into the gas chromatograph. As the compound under investigation passed through the outlet from the detector i t was frozen out in a cold trap and transferred to a 10 cm. infra-red c e l l . The absorption spectrum, measured on the 43 Perkin Elmer Model 21 Infra-Red Spectrophotometer was too faint to be of any value. D. The Photolysis of Diethyl Ketone in the Presence of Unsatu-rated Compounds 1. Standard procedure Diethyl ketone was measured into the reaction c e l l as described in "The photolysis of diethyl ketone" and the excess ketone pumped out of the preparation line. The ketone in the c e l l was then frozen into the temporary storage vessel (S4 in Figure 1). The substrate was then admitted to the c e l l and the temperature and pressure measured. After the excess substrate had been pumped out of the preparation line the ketone and substrate were frozen out together into the c e l l cold finger. The reactants were allowed to vaporize into the c e l l and were mixed by lowering and raising the mercury in the mixing vessel several times. The photolysis and analysis were conducted as described for the photolysis of diethyl ketone. Carbon monoxide was separated from the higher boiling fractions at -215°C, and measured, the C 2 hydrocarbons at -170°C and butane at -120°C unless a very volatile substrate was present in which case a temperature of -125°C was used. Analysis of ethane-ethylene fractions was carried out on column J at 80°C and a helium pressure of 12 p.s.i. 44 2. Special observations and experiments on individual  substrates In the cases of octene-1, 2,3-dimethylbutadiene-l,3, 2,5-dimethylhexadiene-2,4, £2,2,l)bicycloheptadiene and cyclo-octadiene-1,5 the fractions were free from contaminants and no further measurements were necessary for the calculation of rates of abstraction and addition. However, in the cases of a l l y l alcohol, cyclohexadiene-1,3, cyclohexadiene-1,4 cyclooctatetraene, cycloheptatriene and benzene abnormal behaviour was observed. These observations and special experi-ments are described under the individual headings below. A l l y l alcohol Analysis of the ethane-ethylene fraction revealed traces of propane and propene. The quantities ob-served were very small and no correction was necessary. The butane fraction contained pentene-1. Only in the highest temperature run was the quantity greater than 0.5% and in most runs i t was much less than this. Consequently, no correction was attempted. A mechanism for the formation of pentene-1 is proposed in the Discussion. Cyclooctatetraene Preliminary experiments on cyclo-octatetraene revealed that i t was decomposed by the ultra-violet radiation to benzene and acetylene. The latter appeared in the ethane-ethylene fraction and i t was necessary to c a l i -brate the gas chromatograph for relative response to acetylene using the standard mixture of ethylene and acetylene (Appendix E). 45 This appeared to be the only anomalous reaction and other decom-position products were not observed. Cyclohexadiene-1,4 The photolysis of diethyl ketone in the presence of cyclohexadiene-1,4 gave benzene as one of the products. Calibration of the gas chromatograph by a standard mixture of cyclohexadiene-1,4 and benzene, injected as small liquid samples, showed that there was no significant difference in response (Appendix F). Therefore, benzene could be measured by comparison of i t s peak area with that of cyclohexadiene-1,4. In these measurements, i t waa necessary to allow for the volume of the tubing between the c e l l and the cut-offs. Two series of results were obtained for the rate of formation of benzene. In the f i r s t series, the products were introduced into the gas chromatograph using the Toepler pump to compress the gas into the sample tube. This method had the advantage of simplicity of technique. However, only a fraction of the gas could be analysed as condensation took place i f the pressure was too great. Furthermore, considerable adsorption of the reactants took place in the stopcock grease of the sampling system resulting in pronounced t a i l i n g of the gas-chromatographic peaks. The results obtained by this method are recorded in Table XVI and show a large scatter. In an attempt to improve on this method a few experiments were conducted using the absorption spectrum of benzene in the 2 6 0 0 A region as a method of measurement. This was found to be too insensitive. The use of infra-red absorption was also considered. Calculations showed that the sensitivity in this region would s t i l l be inadequate. In the second series of runs on cyclohexadiene-1 ,4 , the reactant-product mixture was condensed out of the apparatus through the sample admission stopcock. Some diethyl ketone was passed through the analysis system to flush i t out and to increase the bulk of the sample. The resulting drop of liquid was injected into the gas chromatograph by a Hamilton Micro-l i t e r syringe and analysed on column R at 50°C and a helium pressure of 1 5 p . s . i . Analysis of the cyclohexadiene-1,4 showed that benzene was present as a trace impurity ( 0 . 1 7 o ) and i t was necessary to apply a small correction for this. Analysis of the diethyl ketone showed that i t was free from any impurity having a retention time similar to that of benzene. The results obtained in the second series of runs are recorded in Table XVI. Identification of the reaction products arising from  cyclohexadiene-1.4 The reactant-product mixture from an experiment conducted on cyclohexadiene-1,4 was analysed on column R at 1 0 0°C and 1 5 p . s . i . helium pressure. Two products other than benzene were observed. One of the peaks was shown to arise from the photolysis of diethyl ketone alone (p. 1+2) while the other was observed only when diethyl ketone was 47 photolysed in the presence of cyclohexadiene-1,4. The retention time of this peak was 14 minutes (air = 0), compared with 5.5 minutes for benzene and 6.5 minutes for diethyl ketone and cyclohexadiene-1,4. In an effort to identify the reaction product, four runs were conducted at a temperature of about 90°C and with a photo-lysis time of three hours, so that a considerable accumulation of the product took place. The cumulative reactant-product mixture was condensed out of the system and injected into the gas chromatograph. When the product peak was being observed to pass through the thermal conductivity c e l l , the effluent carrier gas stream was diverted through a hypodermic needle dipping into 5 mis. of 1007o ethanol. The resulting solution was analysed in a 1 cm. quartz c e l l on the Cary Model 11 Spectro-photometer. A strong absorption band was observed at a wave-length of 2600 A* (Figure 3). A similar band was observed for cyclohexadiene-1,3 and i t w i l l be postulated in the Discussion that the reaction product from cyclohexadiene-1,4 was, in fact, l-ethylcyclohexadiene-2,4. Unfortunately, efforts to obtain this compound for direct comparison were unsuccessful. Accord-ing to the Custom Synthesis Department of Eastman Kodak Ltd. the compound is d i f f i c u l t to prepare and the starting materials unobtainable. Further experiments were conducted to ascertain whether there was, in fact, only one product arising from cyclohexadiene-1,4. 0 Q U Z (/)-[->- » - 6 o 1 I I I — I I I I I I I I h i L _ J I I I I I I 1 F I G . 3 43 O Q U Z (/) - h ) - » _1 o o _ ] I I 1 I 1 1 1 I I I I F I G . 3 The u l t r a - v i o l e t spectrum o f cyclohexadiene-1,3 and the r e a c t i o n product b e l i e v e d to be 1-ethyl-cyclohexadiene-2,4 49 Accordingly the reactant-product mixture was analysed on column B at 100°C and 12 p . s . i . helium pressure and on an Apiezon column (Appendix C) at 100°C and 8 p.s . i . helium pressure. In neither case was any other product observed. It seems unlikely, therefore, that either product peak was inhomogeneous. Cyclohexadiene-1,3 I n i t i a l experiments on the reactions of the ethyl radical with cyclohexadiene-1,3 showed that benzene occurred as a product. In theory the rate of formation of benzene could have been measured in these experiments. However, in the gas-chromatographic analysis (column R, 100°C and 12 p. s . i . helium pressure), the benzene appeared on the t a i l of the much larger cyclohexadiene-1,3 peak and accurate measurement of the benzene peak area was not possible. For this reason, the corrections in k^ and ky were calculated from the results obtained in experiments on cyclohexadiene-1,4. The validity of this method of calculation w i l l be j u s t i f i e d in the Discussion. Cycloheptatriene A careful analysis of the reaction-product mixture from experiments conducted on cycloheptatriene showed that traces of benzene and toluene were present. The quantities were very small. Benzene Benzene was found to possess very low reactivity towards the ethyl radical and definite evidence of abstraction or addition could not be obtained. In an effort to obtain qualitative evidence of reaction, a mixture of diethyl ketone and benzene was photolysed and the resulting mixture analysed 50 for ethylbenzene on column R at 100°C and 15 p.s.i. helium pressure. This compound was not present in detectable quantity and the significance of this fact w i l l be considered in the Discussion. Polarography A Sargent Model XXI d.c. Polarograph was used to measure half-wave potentials. The output voltage of this instrument was calibrated against a General Radio Vacuum Tube Voltmeter Type 1800B and a l l results were corrected for the voltage drop across the measuring and damping resistors. Freshly d i s t i l l e d mercury was used in the dropping mercury electrode. The mercury pressure head was 35 cms. and the dropping rate was 3.0 seconds per drop on open c i r c u i t . Compounds under investigation were dissolved in acetonitrile containing 0.1M tetrabutylammonium iodide as supporting electro-lyte. The acetonitrile was the Spectro grade and the tetrabutyl-ammonium iodide was the White Label grade, both of Eastman Organic Chemicals. Each was used without purification. Before the half-wave potential was measured, the solution was deoxygenated by bubbling nitrogen through i t for twenty minutes. The nitrogen was purified by passing i t through alkaline pyrogallol solution, cone, sulphuric acid and aceto-n i t r i l e . Measurements were conducted at 25°C in a thermostat. A ImM solution was used in cases where the half-wave potential was not close to the decomposition potential of the supporting electrolyte. In cases where the decomposition of the supporting electrolyte began before completion of the polarographic step, a blank run was carried out f i r s t and then the measurement was carried out on the same chart using a 5mM solution of the compound being investigated. In this way the difference in the two traces was accentuated and an approximate value of the half-wave potential could be estimated. The results are shown in Table XVIII. 5 2 RESULTS The values of [d] and [b] quoted in the following tables are i n i t i a l values. Where significant, a correction was applied for the changes in these quantities due to the consump tion of diethyl ketone or substrate. A l l limits of error are calculated at the 57o probability level. TABLE I The photolysis of diethyl ketone. 10" 1 2 R z (om^mol73 s"3) temp. (°K) time (sec) (mole cm 3) (mol. cm " 3 a"1) 10 1 3k A 10 1 3k 4" 10- 1 7 M CO C 2H 6 C2 H4 C4 H10 M k 5/k 2 1 k 3  K2 1 k 2 327 900 7.39 16.42 2.29 1.71 14.39 1.016 0.119 2.08 -534 600 8.88 52.0 6.87 5.49 45.3 1.003 0.121 2.34 -334' 900 8.685. 70.2 8.733 7.38 61.9 1.006 0.119 1.98 -340 3600 6.29 3.666 0.727 0.370 2.948 1.002 0.125 3.37 2.76 362 1200 6.35> 11.66 2.35 0.847 9.37 1.004 0.090 7.76 2.71 364 900 7.80 15.24 3.31 1.436 11.95 1.002:' 0.120 6.96 5.54 365 7200 2.09 1.312: 0.286 0.1279 1.034 1.006 0.123 7.65 6.36 366 1800 6.86 6.26 1.652 0.593 4.67 1.008 0.127 7.15 6.58 405 3600 4.13 12.31 3.44 1.135 8.97 1.009 0.127 19.61 18.24 426 600 6.86 53.4 17.48 4.79 37.4 1.028 0.128 30.3 28.9 473 720 5.90 34.47 23.8 3.05 15.90 1.150 0.192 88.0 95.6 495 600 5.46 46.8 32.9 3.39 19.16 1.112 0.177 123.4 130.0 •Sr - Calculated using the relation:-: -=0.136 Rc 4H 1 0 TABLE II Reactions of the e t h y l r a d i c a l with. octene-1. -12 10 Rr (cm mol. s ) temp* ( ° K ) times (sec) (mol. cm ^ , ) (mol. - 3 -1, cm s ) 10 1 3k 6 13 * 13 10 Jk7 10 1 3k —1 l O ^ ' f o l l o " 1 ' [ B] CO °2 H6 C 2 H 4 C 4 H10 M k 5 / k 2 k 3  K2 K2 339 7200 1.66 3.66 2 . 8 9 2 0.447 0 . 2 9 1 2.237 0 . 9 2 8 0.130 1.54 (1.039) 3 . 8 2 4.07 342 5400 2.11 3 . 6 5 3 . 9 9 9 0.643 0,393 3.10 0.935 0.127 2.02 (1.15) 4.O6 4.48 348 5400 2e35 3 . 6 3 4.77 0.797 0 . 4 6 9 3.63 0 . 9 2 8 0 . 1 2 9 2.16 (1.42) 4 . 9 8 5.31 356 7200 2 . 2 4 3.30 1.390 0.325 0.127 0.877 0,864 0.145 2 . 8 2 3.32 6.13 5 . 8 9 364 5400 2.00 3 . 0 6 4.65 0.874 0.435 3.32 0.902 0.131 3 . 6 0 2 . 9 8 8.22 8.50 3 7 3 5400 2.49 3.32 5 . 7 6 1 . 1 9 2 0.534 3.86 0 . 8 7 8 0 . 1 3 8 3.85 4.05 10 . 8 4 10.66 3 7 7 7200 1.98 3 . 5 5 1 . 2 9 0 0.384 0.102 0.616 0.776 0 . 1 6 6 4.66 5.97 (10.40) (9.71) 388 3600 1.96 2.74 5.56 1.297 0.495 3.47 0 . 8 5 7 0.143 6 . 6 1 7 . 5 1 15.7 15.1 394 3000 2 . 0 9 3.00 6.24 1.569 0 . 5 3 6 3.64 0 . 8 3 5 0.147 7 . 7 1 9 . 0 6 1 8.2 17.4 403 3600 2.48 3.04 7.22 2.05 0.596 3 . 9 1 0 . 8 2 5 0.152 9.16 11.2 21.4 20.0 415 1 8 0 0 2.22 2.68 1 3 . 6 1 3 . 6 2 1.156 7 . 7 5 0 . 8 3 5 0.149 12.8 1 5 . 4 30 . 5 2 8 . 9 425 1 8 0 0 1.96 2.70 13 . 3 1 3 . 8 2 1.071 6.88 0 . 8 0 4 0.156 1 6.8 20.6 3 7.2 3 5.0 1 - C a l c u l a t e d u s i n g the r e l a t i o n :- ~RQ^^=0,\36 RQ^H^Q Values i n br a c k e t s were excluded on s t a t i s t i c a l grounds. TABLE I I I geactions of the ethyl radical with a l l y l alcohol temp. (°K) time (mole i o " 1 7 W -3, cm ; I O - 1 7 [ B ] 10* (mol. •12 R Z -3 -1 cm s ) (cm mol. s 13 * 13 10 kg 10 k ? i i (sec) GO C2Hg C2H4 C4 H10 M M * IC3A2 k 2 k 2* 323 8100 3.10 6.00 1.653 0.328 0.1468 1.134 0.885 0.880 0.129 1.72 3.11 327 10800 2.68 6.30 0.931 0.225 0.0772 0.545 0,827 0.830 0.141 (2.45) 3.40 332- 12600 3.36 5.24 0.927 0.249 0.0669 0.530 0.840 0.835 0.126 (2.93) 4.01 332 9000 3.20 5.85 2.112. O.46O 0.165 1.372 0.867 0.857 0.121 2.35 4.41 333 5400 3.14 6.89 2.757 0.565 0.245 1.820 0.865 O.864 0.135 2.25 4.04 333- 12600 3.26 6.59 0.874 0.229 0.0634 0.498 0.833 Oo827 0.128 (2.11) (3.25) 334 2400 3.12 6.60 10.64 1.816 1.058 7.94 0.917 0.915 0.133 2,64 4.86 343 54OO 2.97 5.88 4.04 0,852 0.342 2.575 0.849 0.847 0.133 3.49 6.55 350 4500 2.90 5.64 4.14 0.918 0.339 2.558 0.839 0.837 0.133 4.01 7.53 353 4500 2.59 4.94 3.643 0.854 0.287 2.175 0.831 0.829 0.132 5.03 8.55 36O 3600 4.34 4.26 7.51 1.749 0.636 4.64 0.851 0,852 0.137 6.17 12.1 367 1800 3.15 3.68 14.77 2.79 1.424 10.19 0.879 0.881 0.140 6.07 15.0 371 2700 2.63 4.22 3.661 1.028 0.268 1.973 0.820 0.820 0.136 7.63 (11.1) TABLE III (cont.) 10 -12 R Z (cm mol. s ) temp. (°K) time (sec) (mol. cm"3) (mol. -3 • cm s -1) 13 * 10 \ 6 1 01 3k? I O - 1 7 [ D ] i o - 1 7 [ i i] CO C 2 H 6 C 2 H 4 C 4 H 1 0 M M* k3/k2 k 2* k 2* 378 1200 2.56 4.03 1 3 . 3 4 2 .94 1.155 8 . 2 0 0 . 8 3 5 0 . 8 3 8 0 . 1 4 1 9 .82 I8.7 379 3600 4.29 4 .15 8 . 0 2 2.23 0 .606 4.24 0 .806 0 . 8 0 9 0 .143 9 .16 17.9 388 900 2 . 8 2 3 .83 26.33 5 .67 2.24 1 6 . 7 1 0 . 8 5 0 0 .849 0 . 1 3 4 11.9 25.4 400 900 2 . 3 9 2 .66 13 .59 3 .54 1.081 7.92 0 .843 0 8 8 4 4 0 . 1 3 7 1 6 . 8 28.3 402 1200 2 . 5 9 2 . 7 3 15.85 4 .16 1.238 9 .00 0 . 8 3 0 0 . 8 3 1 0 . 1 3 8 18.3 32.7 404 1200 2 . 4 5 3.05 25 .01 6 .02 2 . 0 0 14.72 0 .829 0 .829 0 . 1 3 6 19.2 36 .6 415 600 2 . 4 7 2 . 3 8 2 6 . 5 6 6 .94 2 . 0 7 15 .8 0 . 8 5 6 0 . 8 5 3 0 . 1 3 1 23.6 41.2 438 600 2 . 0 6 2.33 23.89 7 .73 1.69 1 2 . 0 6 0 . 8 2 8 0 . 8 3 0 0.140 (39 .6) (50.2) Values in brackets were excluded on s t a t i s t i c a l grounds. Calculated using the. relation F ^ H ^ 0.136 ^C^Hxo V-Tt O N TABLE IV Reactions of the ethyl radical with 2,3-dimethylbutadiene-l ,3> temp. (°K) time (mol. cm"3) 10 (mol. " 1 2 R -3 • cm s -1) (»* molT* 1 0 1 3k 6 I 0 1 3 k ? (sec) I O " 1 7 [ D ) I O " 1 7 [ B ] CO C 2 H 6 C 2 H 4 C 4 H 1 0 M IC3A2 k 2 s 306 600 8 . 2 1 0.330 27.64 3 .12 2 . 8 4 2 1 . 8 1 0 .902 0 . 1 3 0 (180 . ) 318 600 7 .71 0 .268 32 .17 3 .67 2 .95 2 4 . 2 8 0 . 8 7 0 0 . 1 2 1 15.6 3 1 7 . 320 1200 8 . 7 3 0 .134 24.91 3 .09 2 . 4 6 1 9 . 7 6 0 . 9 1 7 0.124 8.3 382* 322 600 8.47 0 .269 3 7 . 1 9 4 .28 3 .53 2 8 . 2 8 0 . 8 7 5 0.125 341« 323 900 7 .61 0 .222 25.28 2 . 9 0 2 .28 1 8 . 6 9 0 . 8 5 4 0 .122 4 1 5 . 324 900 8 . 1 2 0 .182 29.78 3 .64 2 . 8 1 23.30 0 .905 0 . 1 2 1 346 . 329 600 6.27 0 .268 36 .91 4 .20 3.35 27.39 0 . 8 5 6 0 .122 402. 332 606 8.48 0 .238 55.6 6.48 5 .14 43.3 0 . 8 9 6 0 . 1 1 9 398. 333 600 8 . 6 5 0.247 51 .1 6 .06 4.47 3 8 . 2 0 . 8 6 7 0.117 485. 339 600 7.89 0 .248 57.8 6 .78 5 .22 43 .2 0 .865 0 . 1 2 1 4.6 527. 339 600 8.15 0.239 58.9 6.42 5.50 44.2 0 .859 0.125 585. 341 600 7.44 0 . 1 8 4 33.74 4 .30 2 . 9 5 25.03 0 .869 0 . 1 1 8 518 . 341 600 8.27 0.300 56.5 6 . 7 8 4.85 40.5 0 . 8 3 7 0 . 1 2 0 10.7 5 3 1 . TABLE IV (cont.) tempo (°K) time (mol. - 3 , cm ) 1 0 ' (mol. ~ 1 2 H - 3 Z cm s - 1) V 1 1 , ^ ~ 2 "S {cm mol. s 13 13 1 0 k 6 1 0 v k ? (sec) I O - 1 7 [ D ] I O " 1 7 [ B ] C O C 2 H 6 C 2 H 4 - G 4 H 1 0 M k 3 / k 2 K 2 349 6 0 0 8 . 0 3 0 . 2 0 8 4 8 . 5 6 . 2 2 4 . 2 2 3 5 . 1 0 . 8 5 2 0 . 1 2 0 3.7 6 4 7 . 3 5 6 6 0 0 7 . 6 4 0 . 2 1 7 5 7 . 7 7 . 5 7 4 . 9 5 41 . 0 0 , 8 4 3 0 . 1 2 0 1 . 4 7 4 3 . 3 6 1 4 8 0 7 . 5 3 0 . 1 6 7 5 6 . 0 7 . 5 3 5 . 1 0 40 . 5 0 . 8 5 7 0 . 1 2 6 8 5 2 . 3 6 1 6 0 0 7 . 7 6 0 . 1 7 6 5 8 . 7 8,09 4 . 9 2 42 . 0 0 . 8 5 5 0 . 1 1 7 1 . 8 8 6 5 . 372 3 6 0 6 . 2 2 0.139 6 0 . 3 8 . 8 6 5 . 1 8 4 3 . 2 0 . 8 6 2 0 . 1 2 0 1 0 2 1 . 3 7 3 3 6 0 7 . 3 5 0 . 1 6 9 70 . 7 1 0 . 1 0 5 . 8 7 4 9 . 4 0 . 8 4 2 0 . 1 1 9 1 0 6 7 . 3 8 0 3 6 0 6 . 8 1 0 . 1 3 5 6 5 . 9 1 0.40 5 . 3 7 46.8 0 . 8 6 8 0.115 1 0 6 5 . 3 8 1 6 0 0 6 . 8 9 0 . 1 3 0 5 7 . 2 9 . 4 5 4 . 7 7 40 . 7 0 . 8 7 6 0 . 1 1 7 13 . 9 1027. 3 8 6 3 6 0 6 . 9 6 0 . 1 8 6 6 7 . 4 1 0 . 3 8 4 . 9 0 4 5 . 3 0 . 8 2 7 0 . 1 0 8 1051. 3 8 7 6 0 0 6 . 8 2 0 . 1 5 0 4 9 . 0 7 . 9 1 3.75 32 . 4 0 . 8 2 4 0 . 1 1 6 105. 1 2 1 0 . 3 9 6 3 6 0 6 . 9 3 0 . 1 8 3 7 4 . 8 1 3 . 0 0 5 . 7 1 4 6 . 9 0 . 8 0 2 0 , 1 2 2 1 3 8 0 . 402 3 6 0 6 . 8 4 0 . 1 3 9 6 6 . 7 1 3 . 1 1 4.86 41 . 5 0 . 8 1 9 0 . 1 1 7 1 5 9 0 . 4 0 9 3 6 3 6 . 5 9 0 . 1 1 6 6 8.7 14.23 5.32 4 3 . 4 0 . 8 3 9 0 . 1 2 2 1 7 5 0 . TABLE IV (cont.) 10 Rz (cm mol. s z) temp. (6K) time (sec) (mol. -3, cm ) (mol. -3 cm s - 1) i o 1 3 k 6 10 1 3k 7 k 2* i o - 1 7 | > ] I O " 1 7 [ B ] CO C2Hg C2 H4 C4 H10 M k 3/k 2 k 2* 412 600 6.43 0.112? 6O.5 13.65 4.72 38.2 0.857 0.124 71.0 1620. 414 600 6.51 0.059 59.8 14.69 5.12 40.3 0.920 0.127 156. 1700. 415 600 6.42 0.101 57.9 13.76 4.44 36.5 0.869 0.122 (1590.) 427 360 6.59 0.136 66.1 18.22 4.65 35.8 0.817 0.130 (1770.) 440 300 6.11 0.132 69.1 20.2 4.64 36.3 0.818 0.128 (1850.) 474 600 5.02 0.077 67.3 28.4 4.73 32.8 0.909 0.144 (1800.) 503 360 5.24 0.139 77.4 41.3 4.00 24.74 0.854 0.162 (1890.) 506 360 4.97 0.130 71.4 38.3 3.67 21.75 0.842 0.169 (2200.) Values in brackets were not included in the s t a t i s t i c a l analysis. V J 1 vO TABLE V Reactions of the ethyl radical with 2,5-dimethylhexadiene-2,4. -12 10 RZ (cm mol. s ) ( m o l . cm-3) (mol. cm 3 s 1) 10 1 3k, a3. temp. (°K) time (sec) 10 '[D] -17, 10 | [B] /CO C 2H 6 °2 H4 C4 H10 M k 5/k 2 *2 3 k 2* 326 21600 3.78 2.06 0.563 0.1246 0.0469 0.377 0.890 0.124 2.57 (4.91) 328 14400 3.37 2.07 0.2604 0.0693 0.0168 0.143 0.810 0.119 3.20 6.36 339 8100 3.29 1.93 2.025 0.390 0.179 1.439 0.903 0.124 3.95 8.47 343 1200 8.18 2.21 14.90 2.59 1.368 11.82 0.967 0.116 45- (6.49) 351 5400 3.05 1.97 1.844 O.442 0.1386 1.168 0.873 0.119 6.96 11.0 362 3600 3.83 1.63 5.44 1.211 0.443 3.71 0.904 0.119 9.68 16.6 377 4500 2.86 1.65 4.56 1.151 0.334 2.777 0.862 0.120 13.0 22.9 383 4200 2.74 1.43 4.07 1.125 0.289 2.364 0.858 0.122 15.9 26.2 392 1800 2.83 1.58 9.68 2.48 0.687 5.98 0.875 0.115 20.5 31.3 412 2700 2.41 I.46 11.46 3.29 0.788 6.40 O.846 0.123 30.8 47.9 420 1800 2.57 1.52 15.16 4.68 1.001 8.09 0.842 0.124 37.4 55.3 * - Conditions unfavourable for the calculation of k 6/k 2 1 2 ON O Values in brackets were excluded on s t a t i s t i c a l grounds. TABLE V I Reactions of the ethyl radical with cyclohexadiene-1,3• 10 Rg (cm mol. s ) -3 -3 -1 13 13 (mol. cm ) (mol. cm s ) 10 k> 10 k 7 temp. (°K) time (sec) I O _ 1 7 [ D ] I O " 1 7 [ B ] GO C 2 H 6 C 2 H 4 C4H10 M k 3/k 2 k 2 k 2* 316 600 9.11 0.766 30.53 4.44 2.94 23.36 0.910 0.126 19.2 (80.1) 322 600 8.52 0.970 25.27 3.86 2.26 17.42 0.842 0.130 19.2 104.9 323 600 8.16 0.845 27.51 4.10 2.37 20.14 0.881 0.118 22.9 94.0 326 600 8,34 1.064 29.62 4.53 2.48 20.25 0.836 0.122 21.7 109.1 335 600 7.20 1.26 31.73 5.19 2.39 19.75 0.785 0.121 27.3 132. 339 600 8.57 0.773 37.81 5.94 3.37 26.44 0.856 0.127 24.4 147. 342 600 7.88 0.776 40.7 6.66 3.25 27.62 0.841 0.118 38.9 174. 345 600 7.95 0.526 37.30 6.09 3.11 26.91 O.884 0.116 40.9 170. 349 600 7.39 0.601 43.4 7.04 3.55 30.6 0.866 0.116 42.1 192. 359 600 7.27 0.625 45.9 8.09 3.46 30.5 O.84O 0.113 55.4 236. 362 600 7.31 0.469 42.4 7.60 3.32 29.17 0.866 0.114 56.2 248. 369 480 7.35 0.550 54.6 10.20 4.10 36.0 0.844 0.114 66.2 287. TABLE VI (cont.) 10" 1 2 RZ (cm mol. 1 1 3 s~a) (mol. cm"3) (mol. cm -V1) 10 1 3k 7 temp. ( ° K ) time (sec) I O " 1 7 [ D ] I O " 1 7 [ B ] ••1—II., J_ • —1 CO C2H6 C2H4 C4H10 M k 5/k 2 k 2* k 2 s 379 480 7.61 0.520 51.6 10.71 3.84 31.9 0.824 0.120 66.7 341. 382 480 7.07 O.458 48.7 10.10 3.71 30.9 0.841 0.120 63.1 335. 389 480 6.86 O.47O 60.2 12.Q2 4.36 37.0 0.829 0.118 85.0 404. 412 360 7.07 0.385 67.4 18.85 4.30 37.5 0.835 0.115 149. (540.) 427 360 6.51 0.254 72.6 22.4 5.14 41.4 0.876 0.124 159. (611.) .1 i In calculating k g / ^ 2 and k^/^*3, a correction was applied for the benzene formed in the disproportionation of ethyl and cyclohexadienyl radicals. Values in brackets were not included in the s t a t i s t i c a l analysis. ON ro TABLE V I I Reactions of the e t h y l r a d i c a l w i t h cyclohexadiene-1,4* F i r s t s e r i e s . -12 \ - i _ i 10 R z (cm mol. 2s 2) (mol. cm" 3) (mol. cm"3 s" ) 10 kg temp, time 1 7 . 1 7 R N ^ • - ^ / \ - N s — ( ° K ) (sec) 10 X ' [ D ] 10 X ' [ B ] CO C 2Hg C 2 H 4 C 4 H 1 0 CgHg M l^orr, V K 2 K 2 3 327 600 5 . 9 7 0 . 5 0 6 35.15 6 .43 3 .62 29.25 0 . 3 1 9 1 .015 1.006 0.124 6 7 . 9 332 600 6 . 1 4 1.33 42.0 1 1 . 9 9 3 .82 32.1 2 .02 1.050 1 .002 0 . 1 1 9 71.6 346 1200 3 .20 1 .01 13.92 5 . 7 0 1.033 9 . 2 0 0 . 9 4 1.070 1 .002 0 . 1 1 2 1 1 2 . 347 1200 2 . 9 4 4 .44 14.70 1 2 . 9 8 O.46O 4 . 02 2.51 1.156 0 . 9 8 5 0 . 1 1 4 1 1 1 . 355 900 3 . 1 8 0 . 6 9 1 24.92 7.91 2 . 0 9 I8.14 1.03 1.045 1 .004 0 . 1 1 5 1 4 3 . 372 900 3.30 0 . 8 6 27.22 1 1 . 8 2 2 . 0 6 17-48 1 .97 1.076 1.004 0 . 1 1 8 1 9 1 . 388 600 2 .64 0 .455 2 4 . 7 4 9 . 7 1 1 .95 16.55 1 .37 1 .061 1.005 0 . 1 1 8 277. 406 600 2.50 0 .688 22.83 14-24 1 .410 11 .56 3-01 1 .131 0.999 0 .122 358 . 416 600 5.00 O.434 48 .8 23.6 3.52 29.24 3.03 1 .082 1 .020 0 .120 464. M, R C 2 H g + R C 4 H 1 0 - R C 6 H 6 c o r r • = R c o TABLE VIII Reactions of the ethyl radical with cyclohexadiene-1,4 Second series 1 9 ^fe. -J- i 10 R z (cm.mol. V * ) :emp. :°K) time (sec) (mol. cm. "^) (mol.cm. A,. V1) 13 1 0 k6 10-«[ D] 10"i7fB~ \ CO C2 H6 C2 H4 C4 H10 C6 H6 M * M corr. k 3/k 2 k * k2 327 1800 4.04 2.15 18.90 8.44 1.437 12.28 1.42 1.097 1.022 0.117 72.1 333 1800 2.94 1.28 13.54 5.31 1.086 9.20 0.88 1.071 1.006 0.118 82.3 351 1800 2.86 0.99 16.40 6.76 1.287 10.81 1.09 1.072 1.005 0.119 127. 357 1800 1.73 0.98 10.42 5.36 0.723 6.10 0.97 1.100 1.007 0.118 147. 368 1800 2.94 1.31 17.32 10.75 1.043 8.90 1.90 1.135 1.024 0.117 192. 391 1200 2.97 1.07 21.71 15.06 1.199 10.00 2.74 1.155 1.028 0.120 307. 407 600 4.21 0.487 37.06 18.47 2.61 21.76 2.77 1.086 1.011 0.120 416. Rp u *i"Rp u —-Rp u ^2-6 L4 H10 L6 H6 corr. R c o ^ 4> TABLE IX Reactions of the ethyl radical with [2,2,ifrbicycloheptadienet 10" 1 2R Z (cm^molT* s~^) temp. (°K) time (sec) (mol* cm"3) (mol. -3 -1, cm s ) 13 10 k 6 13 10 ky I O ~ 1 7 [ D ] I O " 1 7 [ B ] CO C 2 H 6 C2 H4 C4 H10 M k 3/k 2 k 2 3 323 1200 6.18 5.62 19.36 2.35 1.89 14.49 0.869 0.131 0.19 11.9 336 900 5*83 4.78 24.26 3.02 2.31 17.57 0.848 0.132 0.04 18.5 341 1800 5.46 3.01 14.95 1.993 1.388 10.47 0.854 0.133 0.09 22.0 349 910 5.75 4.14 30.44 3.89 2.83 21.25 0.826 0.133 0.25 27.9 360 900 5.12 2.88 29.80 4.12 2.72 20.83 0.837 0.131 0.36 37.3 366 900 4.62 2.45 30.12 4.21 2.72 20.93 0.835 0.130 0,19 44.7 382 600 4.59 1.17 35.75 5.80 3.29 26.15 0.894 0.126 2.0 63.9 398 600 4.O4 I.23 31.26 5.79 2.69 20.38 0.837 0.132 0.28 93.1 404 600 4.45 1.12 36.82 7.20 3*27 23.75 0.841 0.138 6.27 109.0 O N TABLE X Reactions of the e t h y l r a d i c a l w i t h c y c l o h e p t a t r i e n e . -12 \ 10 R z (cm mol. s ) temp. (°K) time (sec) (mol. -3, cm ; (mol. cm -3 -lx s ) 13 10 \ 13 10 ^ k ? I O " 1 7 [ D ] I O " 1 7 [ B ] CO C 2 H 6 C 2 H 4 C4 H10 M k 3 / k 2 k 2 s kf 323 3600 6.67 0.96 3.649 0.640 0.303 2.487 0.857 0.122 (10.04) 35.1 324 3000 6.56 1.17 1.907 0.353 0.155 1.107 0.766 0.140 (16.2) 36.5 328 1800 6.59 1.54 11.96 1.852 1.018 8.31 0.849 0.123 9.84 41.1 339 900 6.50 2.23 24.85 3.83 1.94 16.29 0.809 0.119 12.2 53.4 351 900 3.51 0.757 20.48 2.94 1.76 15.15 0.883 0.116 19.5 82.8 352 1800 3.03 0.850 10.14 1.598 0.802 6.74 0.822 0.119 19.6 83.7 364 600 5.78 1.59 32.16 5.72 2.28 19.18 0.774 0.119 24.6 105.9 372 600 5.61 1.10 39.38 7.01 2.98 25.45 0.824 0.117 29.7 128. 392 600 2.96 0.689 24.77 4.65 1.72 14.91 0.790 0.116 49.1 201. 403 600 2.66 0.374 23.54 4.63 1.79 15.22 0.843 0.117 62.1 263. 414 900 1.83 0.309 17.96 3.66 1.322 11.29 0.833 0.117 (85.8) 306. 426 900 1.54 0.275 15.38 3.46 1.020 9.16 0.820 0.112 (121.) (354.) Values i n bracket s were excluded on s t a t i s t i c a l grounds. O N O N TABLE X I Reactions of the e t h y l r a d i c a l w i t h r c y c l o q c t a t e t r a e n e . -12 , \ - i -* 10 R 7 (cm mol.~ s S ) (mol. - 3 , - l x 13 13 cm ) (mol. cm s ) 10 kg 10 k ? temp. ( ° K ) time (sec) I O " 1 7 [ D ] i o " 1 7 | s>— 1— [B] CO C 2 H 6 C 2 H 4 C 2 H 2 ""N C 4 H 1 0 M k 3 / k 2 k 2 k 2 324 3600 3.20 1.40 5.07 0 .626 0.458 0.402 3.64 0 .842 0 . 1 2 6 2 . 1 0 30.4 328 3000 2 .88 1.23 5.74 0 .686 0.514 0.489 4 . 1 1 0 . 8 3 6 0.125 1.97 3 8 . 2 334 3600 3 . 1 7 1.12 5.83 0.741 0.513 0 .382 4 . 0 9 0 . 8 2 8 0.125 2.75 45.2 344 2400 2.37 1.00 6.46 0 .807 0.554 0 . 6 0 5 4.47 0 . 8 1 7 0.124 3.57 5 6 . 9 350 1800 3 .46 1 .31 13.47 1.802 1.183 0.754 9 . 3 7 0 . 8 3 0 0 . 1 2 6 3 . 8 7 5 8 . 1 354 1800 3 .02 1.27 14.53 1.869 1.192 0 .969 9 . 9 7 0 . 8 1 5 0.119 5.13 6 8 . 5 356 1800 3 . 1 9 1 .34 14.23 1.920 1.188 0 .859 9 . 4 1 0 . 7 9 6 0 . 1 2 6 5 . 2 6 72.2 365 1800 2 . 9 3 0 . 6 9 1 4 . 3 9 2.04 1.275 0.649 10.23 0 . 8 5 3 0.125 5 . 6 7 98.3 371 1200 2 . 6 2 0 . 7 7 15.84 2 . 3 0 1.275 0 . 9 5 4 1 0 . 9 0 0 . 8 3 3 0.117 12 .8 106 .8 378 1200 2 . 9 9 0 . 7 9 10 .56 1.838 0 . 8 1 1 0 . 6 1 0 6 . 6 7 0 . 8 0 5 0 .122 1 2 . 3 103.1 382 900 2 . 6 1 0.73 15.79 2.53 1.332: 0 . 9 6 0 1 0 . 6 2 0 . 8 3 2 0.125 1 0 . 6 7 114. 392 960 3 . 6 7 0.50 26 .68 4 . 9 6 2.25 0 . 6 2 7 18 .62 0.884 0 . 1 2 1 2 0 . 0 149. 405 900 3.83 O.51 26.92 5 .88 2 . 1 6 0.643 17.65 O.874 0 ,122 24.9 ( 1 6 4 . ) * # Not i n c l u d e d i n the s t a t i s t i c a l a n a l y s i s . ON -<1 TABLE XII Reactions of the ethyl radical with ::cy'cloo>ctadiene-l,5» 10 Rg (cm mol. s ) temp. ( ° K ) time (sec) (mol. l0'1?fD] cm"3) I O " 1 7 [ B ] (mol. cm " 3 s"1) i o 1 3 k 6 £0 C 2H 6 C 2H 4 C4H10 M k 3 / k 2 k 2 330 7200 2.80 1.01 1.560 0.311 0.155 1.241 0.995 0.125 7.51 343 7200 3.15 1.02 1.940 0.432 0.177 1.517 1.005 0.117 9.51 350 7200 2.92 0.97 1.781 0.456 0.162 1.320 0.997 0.123 13.2 361 900 2.66 0.Q2 15.11 2.54 1.479 12.53 0.996 0.118 15.0 372 3600 2.96 0.94 2.648 0.770 0.235 1.882 1.001 0.125 (14.4)* 373 7200 2.42 0.92 1.829 0.618 0.151 1.213 1.001 0.124 23.4 384 2400 2.81 0.96 9.64 2.50 0.832 7.03 0.989 0.118 31.3 402 1800 2.14 0.85 8.36 2.55 0.710 5.73 0.991 0.124 44.4 The value in brackets was excluded on s t a t i s t i c a l grounds ON 00-TABLE XIII Comparison of the results for octene-1 with those of James and Steacie. ABSTRACTION :-James and Steacie this work this work number of runs. 12 9 12 k 3/k 2 C B 0.136 5.595 1.824 CTB 13-f i O g 1 0 J L E 6 - i E 2 0.136 5.728 1.876 0,054 O.323 0.125 measured 5.053 I.64I O.O33 0.133 0.050 A2' 5.6i 0.3 5.7*0.7 5.05i 0.3 8.3-0.5' 8.6i 1.3 7.5* 0.5 ADDITION :-James and Steacie this work this work number of runs. 14 11 11 k^Ag B ex cr 0.136 4.990 1.471 C 13-f i o g l 0 _ i A 2 £ 5.0 + 0.2 0.136 5.199 1.558 0.0209 0.084 0.0314 5.2± 0.2 measured 5.485 I.664 0.0116 O.O47 0.0174 5.5+ 0.1 Ey--gE2 6.7i 0.3 7 . l i 0.3 7.6± 0.2 B and C are the coefficients of the straight lines 13 + log-L0(kr/k2a)=C-103B/T f i t t e d to the data of table II. c r k , o " c and CT B are the standard deviations in 13-+- logio(k r/k2i), C and B respectively. The limits of error are calculated at the 5% probability level. The units of A are cm mol7 s ; the units of E are kcal. mole . ON TABLE XIV Abstraction of the hydrogen atom by the ethyl radical substrate No. of runs C B tfk 13+log 1 0A 2% E 6-%E 2 ft diethyl ketone 16 5.505 1.697 - - - 5.5t0.1 7.8t0.2 octene-1 12 5.053 1.641 0.033 0.133 0.050 5.05±0.3 7.5+0.5 cyclohexadiene-1,3 17 4.967 1.175 0.052 0.154 0.054 5.0^0.3 5.4to.5 cycloheptatriene 8 5.316 1.422 0.022 0.120 0.044 5.3+0.3 6.5+0.5 cyclooctatetraene 13 6.011 1.872 0.076 0.318 0.117 6.0±0.7 8.6+1.2 cyclohexadiene-1,4 ( f i r s t series) 9 5.714 1.272 0.0173 0.072 0.026 5.7to.2 5.8+0.3 eyelohexadiene-1,4 (second series) 7 5.7E4 1.270 0.0074 0.038 0.0137 5.7to.l 5.8to.l cyclooctadiene-1,5 7 5.328 1.480 0.031 0.189 0.068 5.3to.4 6.8*0.7 2,5-dimethyl-hexadiene-2,4 10 5.532 1.658 0.026 0.095 0.035 5.5+0.2 7.6t0.35 a l l y l alcohol 17 5.385 1.665 0.027 0.087 0.032 5.4+0.2 7.6+0.3 * Results of James and Steacie. B and C are the coefficients of the straight lines 13-Mogi0(k6/k2^) = 0-103B/T fitt e d to the data of tables II-XII. C^, & G and 0"B are the standard deviations in 13+logio( k6/ k2^), C and B respectively. The limits of error are calculated at the 5% probability level. The units of A are cm3 mol."*- s"*-; the units of E are kcal. mole"*-. o TABLE XV Addition of the ethyl radical to the double bond substrate No. of runs C B O'c tf-B 13+log 1 0 A 2 % E 7-%E 2 octene-1 11 5.485 1.664 0.0116 0.047 0.0174 5.5to.l 7.6to.2 cyclohexadiene-1,3 14 5.552 1.145 0.0180 0.080 0.028 5.55*0.2 5.2to.3 cycloheptatriene 11 5.857 1.391 0.0163 0.060 0.021 5.9to.l 6.4+0.2 cyclooctatetraene 12 5.271 1.216 0.032 0.161 0.057 5.3to.35 5.6+0.6 [2,2,l] bicyclo-heptadiene 9 5.811 1.526 0.0070 0.033 0.0117 5.8t0.1 7.0t0.1 2,3-dimethy1-butadiene-1,3 27 5.643 0.9913 0.031 0.072 0.026 5.6t0.15 4.5+0.2 2,5-dimethy1-hexadiene-2,4 9 5.164 1.435 0.0160 0.067 0.025 5.2t0.15 6.6+0.3 a l l y l alcohol 18 5.739 1.695 0.034 0.102 0.037 5.7t0.2 7.75t0.35 B and C are the coefficients of the straight lines 13+logiQ (k 7/k 2^) = C-103B/T f i t t e d to the data of tables II-XI. c/^, Cq and Cg are the standard deviations in 13+log^Q(ky/k2^) , C and B respectively. The limits of error are calculated at the 5% probability level. The units of A are cm mol. s ; the units of E are kcal. mole 72 TABLE XVI The disproportionation and combination of ethyl and cyclohexadienvl radicals  First Series Second Series k6d k6d :°K) k6a T(°K) k6a 327 0.214 327 0.364 332 0.617 333 0.395 346 0.391 351 0.381 347 0.342 357 0.390 355 0.336 368 0.362 372 0.418 391 0.388 388 0.377 407 (0.450) 406 0.565 416 0.424 Average = 0.4lt0.26 Average = 0.38+0.03 TABLE XVII The reactions of the ethyl radical with benzene (mol.cm." ) (mol.cm."" s~ ) (cm ' molT^s"2) temp, time ' ^ N ^3 ^g ^7 (°K) (sec.) 10- 1 7j- D~j 10" 1 7[ B-] CO C 2H 6 C 2H 4 g 4H 1 0 M ^ 1 0 l 3 k ^ " " k ^ 337 2,400 5.60 8.13 34.40 4.579 3.456 26.65 0.995 0.117 +0.47 0.39 360 1,800 2.60 2.88 15.69 2.158 1.605 13.51 0.998 0.119 -0.02 1.5 360 10,800 2.77 8.35 1.150 0.282 0.107 0.882 1.012 0.122 +0.21 -362 5,400 3.36 7.64 2.862 0.629 0.282 2.249 1.006 0.125 -0.185 -374 23,400 1.25 14.1 0.3621 0.1014 0.0321 0.2577 0.992 0.168 +0.17 0.05 377 21,600 1.07 13.4 0.3599 0.0977 0.0452 .0.2327 0.918 0.194 +0.03 0.46 386 21,600 1.19 13.8 0.3442 0.1110 0.0328 0.2334 1.001 0.141 +0.11 -403 21,600 1.32 12.9 0.429 0.1751 0.0394 0.2610 1.017 0.151 +0.11 -CO 74 TABLE XVIII Polarographic half-wave potentials A. Compounds for which complete polarographic wave was observed (cone. ImM) compound half-wave potential (volts) 135 cyclooctatetraene -1.28 (cf. -1.12) cycloheptatriene -1.96 styrene -1.98 (cf. -1.96) 1 4 0 acrylonitrile -1.67 (cf. -1.94 S.C.E. ) 1 5 8 cis-crotononitrile -1.94 trans-crotononitrile -1.95 1 S Q anthracene -1.47 (cf. -1.48) B. Compounds for which the polarographic wave was not completed before decomposition of the supporting electrolyte began (cone. 5mM) approximate half-wave  compound potential (volts) 2,3-dimethylbutadiene-l,3 -(2.25-2.45) 2,5-dimethylhexadiene-2,4 -(2.25-2.45) cyclohexadiene-1,3 no wave observed [2,2,£] bicycloheptadiene no wave observed 75 2«0 CD O -J + ro 1*0 1 1 1 1 1 1 1 1 1 1 1 — ON. — o e \ 1 1 1 1 1 1 1 1 1 1 1 2-0 1 0 3 / T F I G . 4 3*0 The a b s t r a c t i o n o f hydrogen from d i e t h y l ketone. S o l i d c i r c l e s : - c a l c u l a t e d u s i n g measured v a l u e s o f R C 2 H 4 ' Open c i r c l e s : - c a l c u l a t e d u s i n g the r e l a t i o n , R c2 H4 = 0 , 1 3 6 R c4 H10* I C P / T F I G . 5 76 F I G . 5 The r e a c t i o n s o f the e t h y l r a d i c a l with octene-1. S o l i d c i r c l e s : - c a l c u l a t e d u s i n g measured val u e s of Rq^^ Open c i r c l e s : - c a l c u l a t e d u s i n g the r e l a t i o n ^ c ^ H ^ =0.136 Rc^H ]_o Dotted l i n e s : - c a l c u l a t e d by James and S t e a c i e . F I G . 6 77 IE _ o o _) F I G . 6 The reactions of the ethyl radical with acyclic dienes. Solid circles:- addition Open circles:- abstraction. DMB:- 2,3-dimethylbutadiene-l,3 DMH:- 2,5-diraethylhexadiene-2,4 Oc :- octene-1 1— 1—I— T—I— 1—I—I—1— 1—1—I—I—I—f 7S F I G - 7 The abstraction of hydrogen from cyclic dienes and polyenes. CHD-1,4 (1)^- cyclohexadiene-1,4 ( f i r s t series) CHD-1,4 (2):- cyclohexadiene-1,4 (second series) CHD-1,3 cyclohexadiene-1,3 CHT :- cycloheptatriene COT :- cyclooctatetraene COD :- cyclooctadiene-1,5 79 F I G . 8 A d d i t i o n o f the e t h y l r a d i c a l to c y c l i c dienes and polyenes. BCH: - [2,2,l] b i c y c l o h e p t a d i e n e . For other a b b r e v i a t i o n s see f i g u r e 7. so i l i i i — i — I — i — i — i 1 1 1 — i — r 2 - 5 3 3 - 0 1 0 / T F I G . 9 The r e a c t i o n s of the e t h y l r a d i c a l w i t h a l l y l a l c o h o l . S o l i d c i r c l e s : - a d d i t i o n . Open c i r c l e s : - a b s t r a c t i o n . 81 DISCUSSION A. The Photolysis of Diethyl Ketone The mechanism for the photolysis of diethyl ketone, f i r s t proposed by Dorfman and Sheldon, has been confirmed by 63 64 18 subsequent investigations. ' ' C2 H5" C O" C2 H5 * h ^ " — > 2C2H^ * CO 1. 2C 2H 5 -— > C, H„ _ 4 10 2. 2C2H- -— ^ C2 H6 * C2 H4 3. C2H* + C2H5-CO-C2H5 - C 2H 6 + CH3CH-CO-C2H5 4. At higher intensities and below 520°K the pentanonyl radical is removed from the system by the reaction, C0H*C + CHoCH-C0-CoHc > C.H -C0-CoHp 4a. Id 3 £• j 4-9 2 5 In this mechanism, one molecule of carbon monoxide is equivalent to two ethyl radicals, and hence to one molecule of either ethane or butane. The material balance (M) is defined by the relation, M m RC 2H 6 + RC 4H 1 Q R c o where denotes the rate of formation of the species Z in mole--1 -3 cules s cm of illuminated volume. Previous investigators -i- -+• 18 have measured M as 0.98810.02 and 0.997T0.03. The results of this study given in table I show values of M ranging from 1.002 at lower temperatures to 1.150 at 473°K, suggesting that 82 reactions 1 to 4a account adequately for a l l the products between 327 and 405°K approximately, while other reactions become increasingly important at higher temperatures. Neglecting the values obtained at 426°K and higher temperatures, M is equal to l.OOotu.Ol. The deviation of M from unity at higher temperatures may be explained as follows. As the rate of abstraction is rela-tively high at higher temperatures, i t is possible that the concentration of pentanonyl radicals was high enough for mutual termination of a significant proportion of these radicals to take place. The only effect of this process would be an increase in M. The measured rate of abstraction would be unaffected. The value of k^ /k,^  ^ a S ^ e e n e s t i n t e d by Kutschke as 0.139+0.01 using the hydrogenation technique, 1 8 and 0.136+0.02 18 by James and Steacie, who used a mass spectrometer to analyse the ethane-ethylene fraction from the photolysis products of diethyl ketone. This latter method of determination assumes that k 3/k 2 - R C 2 H 4 / R c 4 H 1 0 ' In an investigation of the photolysis of diethyl ketone at 298°K, Weir has obtained a value for k 3/k 2 = 0.135.65 This value was obtained by assuming that reaction 4 was much slower than reaction 3 and that the ethane-ethylene fraction would therefore contain 50% of each constituent. As reactions l-4a are inadequate below 320°K, an accurate calculation cannot be applied in assessment of this claim. However, the high 83 concentration of diethyl ketone (2.5 cms pressure) and the low 12 intensity of illumination (Rqo = 1.1x10 approximately) would seem to favour a moderate rate of abstraction. In this event a value less than 0.135 is indicated by Weir's measurements. The interactions of ethyl radicals, generated by the photolysis of propionaldehyde, have been studied by Kerr and Trotman-Dickenson who found k^ /k,, to be 0.15 and independent o 66 of temperature between 323 and 588 K. Thynne has reported a value of 0.14-0.01, independent of temperature, in the photolysis of diethyl ketone between 350 and 440°K and the photolysis of ethyl formate.^7 In this investigation, values close to 0.12 were observed at 327-426°K, increasing to 0.19 at the higher temperatures (473 and 495°K). The low temperature values are in good agree-ment with the temperature independent value of 0.12 reported by Brinton and Steacie who explained the higher values at low intensities and higher temperatures on the basis of additional ethylene formed by the thermal decomposition of the pentanonyl radical, CH3CH-CO-C2H5 > C 2H 4 + CO + C ^ 5. The net effect of this reaction is to raise the apparent value of k2/k£, but i t does not affect M. Consequently, the high values of M referred to above are not accounted for by this reaction. It has been suggested that the formation of vibrationally 84 excited radicals in the primary process could lead to high values of k^/k^.^8'^^ It can be shown that, r 1 k 4 RC 2H 6 " RC 2H 4 R C 2 2k 3 C4 H10 Rr H ko C4 H10 1 C4 H10 where [ D ] i s the concentration of diethyl ketone in molecules cm . The results obtained in this investigation are l i s t e d in table I and plotted in figure 4. The straight line parameters were not calculated as several of the results were obtained under unfavourable conditions, and, consequently, some weighting process would have been necessary. However, the results are 18 seen to l i e close to the line of James and Steacie, k 4 / k ^ - 10 (" 7* 5- 0- 1 )exp(-7800 +200)/RT cm 3 / 2 mol."^ s'^ and may be regarded as essentially confirming this relation which applies between 320 and 490°K. It follows from this that the results of this investigation are also in agreement with the results obtained by Kutschke and Steacie, Wijnen and 18 Steacie and Ausloos and Steacie. A conflicting value for E^-*^ of 8.9 kcal./mole has been 67 reported by Thynne. The reason for this discrepancy is not clear. It should be noted that the results of James and Steacie were calculated using the relation k 3/k 2 = 0.136. However, as the conditions of reaction had been chosen such that 85 Co 2ko 2 » 3 R C 4 H 1 Q k 2 the values of the abstraction rate constant are insensitive to variations in k^/k^. It is significant that the values of the abstraction rate constant obtained in this investigation by setting ko/k2 = 0.136 l i e below the line in figure 4 when X 2 ^ 2k 3 R c4 H10 k2 The compound 3-methylhexanone-4 formed in reaction 4a has not been identified but has been postulated by analogy with the 62 1 photolysis of acetone, CH3 * CH3-CO-CH3 > CH4 * CH2-CO-CH3 CH* + CH -C0-CHo > C_H -C0-CHo J 2. 3 ^ 5 3 In this investigation, only one product could be detected which had a retention time greater than that of diethyl ketone. As described in the Experimental section, only a faint infra-red spectrum could be obtained for this product. The compound could not be obtained for a direct comparison of retention times. The results of this investigation suggest that the photo-lysis of diethyl ketone is adequately represented between 320 and 405°K by the reactions 1 to 4a, and that the values of k^/ky 2 and E 4~%E 2 as measured by James and Steacie are consistent with the values of the abstraction rate constant obtained in this investigation. It is concluded, therefore, that diethyl ketone 86 is a suitable source of ethyl radicals for a study of the abstraction and addition reactions discussed below. B. The Reactions of the Ethyl Radical with Unsaturated Compounds  1. Abstraction Ethyl radicals w i l l abstract hydrogen from a hydrocarbon in the reacting system. In the case of the general alkene-1, R-CH2-CH=CH2, the reaction w i l l probably take the following 18 course at higher intensities: C0H* + R-CH -CH=CH. — ^ C_H, + R-CH-CH=CH0 6. 2 5 2 2 2 6 2 C2H^ + R-CH-CH=CH2 > R-CH-CH=CH2 6 a ^2^5 These reactions are analogous to reactions 4 and 4a in the previous section and the material balance i s not changed by the inclusion of reactions 6 and 6a or the alternative sequence: R-CH-CH=CH2 + C2H5-CO-C2H5 R-CH^CH^^+C^-CO-C^ 6b. C2 H5 + ^2 H4" C 0" C2 H5 > C4 H9" C O" C2 H5 4 a ' In each case the overall reaction s t i l l requires that the consumption of two ethyl radicals w i l l lead to the formation of one molecule of ethane. It can be deduced that, k6 _ R c 2 H 6 " R c 2 H 4 fD] k4 -2 C4 H10 2 £2 2k3 R r * u k o °4 H10 2 where [B] represents the concentration of the hydrocarbon in molecules cm"3. 87 By photolysing diethyl ketone in the presence of n-heptane, •4-James and Steacie have obtained a value of M equal to 1.00-0.03. Similar results were obtained for trans-octene-4 and cyclohexene (addition to these compounds is too slow to be detectable). It is concluded that reactions 6-6b are adequate and that reactions of the type, R-CH-CH=CH0 + C0H" —> C.H, -h R-CH=C=CH 2 I 0 2 o 2 are excluded as this reaction would raise the material balance above unity. 2. Addition Simultaneously with the abstraction reactions described above, the ethyl radical can add to the double bond of an alkene °2 H5 + R " C H 2 ~ C H = C H 2 * R-CH2-CH-CH2-C2H5 7. C0H* + R-CH -CH-CH -C0H,. 5> R-CH0-CH-CH0-C0H_ 7a. ID 2 2 2 D 2 | l i b C 2H 5 As two ethyl radicals are consumed without the formation of either ethane or butane, the material balance f a l l s below unity and i t is easily shown that, k ? _ RC0 " ( RC 2H 6 * RC 4H 1 Q) _ ( I " M ) RC0 k 2 % " f B ] R c H " f B 3 RC H i J C4 H10 C4 H10 As the abstraction reaction does not affect M and as the addition reaction does not produce ethane, values of both the abstraction and addition rate constants can be measured simul-taneously in a single experiment provided that addition and 88 abstraction proceed at comparable rates. The validity of the expression for the addition rate 39 constant has been investigated by James and Steacie for the compound heptene-1. Values of the addition rate constant were found to be independent of intensity, concentrations of reactants, wavelength and time of photolysis, provided M did not f a l l below 0.8. Lower values of M correspond to a low concentration of ethyl radicals and this condition favours reactions of the type, The kinetic consequence of this reaction would be an increase in M and hence a low value for the addition rate constant. This effect has been observed in the present investigation. A low concentration of ethyl radicals w i l l raise the mean lifetime of the adduct radical. In cases where a very unstable adduct radical is formed, reversal of the addition process may be possible. Some evidence for reversible addition of the ethyl radical has been obtained in this laboratory. Preliminary experiments on the addition of the ethyl radical to cis and trans crotononitriles suggest that some interconversion of the geometrical isomers may occur simultaneously Sivertz has reported similar behaviour for the addition of the CH-S radical to cis butene-2. >^ R-CH2-CH-CH2-C2H5 R-CH -CH-CH -C0H, 7b. 3 89 3. Excluded reactions It is necessary to consider reactions of the type, R-CH-CH=CH„ 4- C0H* => C_H. + R-CH -CH=CH0 6c. 2 2 5 2 4 2 2 R-CH0-CH-CH -C H + C H* > C0H. + R-CH -CH 0-CH„-C 0H C 7c. Z 2 2 5 2 5 £ 4- Z Z Z £ 5 As M would not be affected, the expression for the addition rate constant would s t i l l be valid. However, apparent values of k^/k^ would be high and values of the abstraction rate constant would be low. An examination of the results for [z,2,l] bicycloheptadiene shows that values of k-j/^ a r e higher than those obtained by photolysing diethyl ketone alone under similar conditions. Addition to this hydrocarbon i s readily observed; however, i t w i l l be suggested later in this Discussion that abstraction from [2,2,l]bicycloheptadiene should take place very slowly. The fact that values of the abstraction rate constant are very close to zero, rather than significantly negative, indicates that reaction 7c is not important in this system. The results for cyclohexadiene-1,4 provide further evidence. If reaction 6c occurs, then the following reactions would be observed, C2 H5 + C6 H8 — * C2 H6 + C6 H7 6-C2 H5 + C6 H7 - * C2 H4 + C6 H8 6 c ' The C-H_ formed in reaction 6c would be, mainly, the energetically 6 8 favoured cyclohexadiene-1,3. That this isomer has not been detected in experiments on cyclohexadiene-1,4 is evidence that 90 reaction 6c can be neglected. Whether the exclusion of reactions 6c and 7c in these particular cases j u s t i f i e s their exclusion in the general case is a valid question. However, the constancy of abstraction rate constants when intensity and concentrations are varied at constant temperature, coupled with the linearity of the Arrhenius plots, is encouraging evidence that reactions 6c and 7c are relatively slow and that the expression for the abstraction rate constant is valid. C. The Reactions of the Ethyl Radical with Octene-1 As the results of previous investigations have been cal-18 39 71 culated assuming that k^/k^ = 0.136, i t was desirable to reexamine the reactions of the ethyl radical with a typical alkene-1 to establish a basis for comparison of the results of this investigation with those obtained previously. The results for octene-1 appear in table II and are compared with the results of James and Steacie in table XIII and figure 5. Values of the abstraction and addition rate constants were calculated by two methods: 1. In the f i r s t method of calculation, the results of the ethane-ethylene analyses were used to calculate values of R-C^ Hg and R p u . C 2 H 4 2. In the second method, i t was assumed that k^/k^ = 0.136 and the proportion of ethylene in the ethane-ethylene mixture 91 was calculated from the yield of butane. It is seen that the results of James and Steacie are in good agreement with the results obtained in this investigation by setting k^/k^ = 0.136. However, values obtained using the analysis of the ethane-ethylene fraction lead to significantly different straight line relationships, k^/k * = 1 0 ( " 7 - 9 _ 0 - 3 ) exp(-7500-500)/RT cm 3 / 2 s~* mol."*. o Z + k ?/k 2* = 10("7.5-0.1) e x p (. 7 6oot 200)/RT cm 3 / 2 s~* mol."*. To maintain internal consistency, these values w i l l be adopted as standards for comparison in this Discussion. D. Accessible Upper Limits for Abstraction and Addition The rapid addition of the ethyl radical to certain compounds necessitates conditions which are unfavourable for the measurement of the rate of abstraction. In cases where true abstraction rate constants could not be measured, i t is interesting to estimate, for each experiment, the maximum value that the abstraction rate constant could have while remaining undetectable. Intuitively, i t is suggested that the rate of abstraction should be detectable i f The quantity on the right is calculated for each run in tables XIX, XX and XXIII. This upper limit is then compared with the corresponding rate constant for octene-1. Conversely, in cases where abstraction was so fast as to preclude the measurement of addition rate constants, i t is interesting to estimate upper limits for the addition rate constant. Even allowing for slight experimental error, i t seems established that values of M are greater than 0.98 and true values of the addition rate constant are therefore less than 0.02 R C 0 RC,H, 'Vl10 This quantity has been calculated in tables XXI, XXII and XXIII and compared with the corresponding values for octene-1. It must be noted that the upper limits may be greatly in excess of the true values. The significance of these upper limits w i l l be discussed in the sections dealing with the respective compounds. E. The Calculation of Values of A6, A7, E6 and E7. Formally, the tables of results obtained in this investi-gation are not complete without a statement of values for A,., A,, E, and E-,. These values are l i s t e d in tables XXIV 6 7 6 7 72 and XXV and were calculated using the expression for k 2 > k 2 = 5.06X10""10 exp (-2000+1000)/RT cm3 mol." 1 s" 1. However, the probable errors in values of A and E are increased by this operation and, for purposes of comparison, the relative values of A and E are preferable. 93 TABLE XIX The abstraction of hydrogen from 2,3-dimethylbutadiene-l,3 ( 3/2 -i -% -h, (cm ' mol. 2 s z) temp. (°K) 101 3 k 4/k 2^ 12CD] k4 l O 1 3 " ^ : for octene-1 ratio 318 1.472 4.24 0.780 5.4 329 2.219 5.19 1.16 4.5 341 3.370 13.6 1.74 7.8 361 6.372 28.1 3.22 8.7 386 12.82 48.0 6.33 7.6 412 24.34 148. 11.8 11.9 94 TABLE XX (cm 3/ 2 mol. * (cm 3^ 2 mol. * s -*> 1 0 1 3 \ io12M \ & V 10 1 3 \ for temp. (°K) (X) for octene-1 (Y) cyclohexadiene-X/Y (Z) 1,4 X/Z 323 1.782 0.196 0.939 0.21 63.1 0.0031 336 2.849 0.348 1.48 0.24 89.6 0.0039 341 3.370 0.611 1.74 0.35 102. 0.0060 360 6.176 1.098 3.12 0.35 160. 0.0069 366 7.392 1.39 3.71 0.38 183. 0.0076 382 11.54 4.53 5.71 0.79 255. 0.018 398 17.40 5.72 8.50 0.67 347. 0.016 404 20.18 8.02 9.81 0.82 388. 0.021 95 TABLE XXI The addition of the ethyl radical to cyclohexadiene-1,4 (10~ 1 3 cm 3/2 , • mol. 2 s "S (10" 1 3 v., cm3^2 mol. ^ 0.02 R C 0 V k 2 % : for k 7/k 2^ for temp. (OK) C4 H10 (X) octene' (Y) -1 ratio X/Y BCH* (Z) ratio X/Z 327 25.7 2.49 10.3 14.0 1.8 327 5.02 2.57 2.0 14.4 0.35 332 11.1 2.97 3.7 16.4 0.68 333 6.96 3.08 2.3 16.9 0.41 346 9.10 4.74 1.9 25.2 0.36 347 3.30 4.89 0.67 25.9 0.13 351 10.07 5.55 1.8 29.1 0.35 355 16.9 6.27 2.7 32.5 0.52 357 8.61 6.67 1.3 34.4 0.25 368 8.87 9.20 0.96 46.2 0.19 372 15.1 10.28 1.5 51.1 0.30 388 26.9 15.7 1.7 75.5 0.36 391 12.8 16.9 0.76 80.7 0.16 406 19.5 24.4 0.80 113. 0.17 407 32.6 24.9 1.3 115. 0.28 416 41.6 30.5 1.4 139. 0.30 * BCH = 2,2,1 bicycloheptadiene TABLE XXII The addition of the ethyl radical to cyclooctadiene-1,5 3/2 (cm ' mol. temp. (°K) 10 1 3* M 0.02 R c o  C4 H10 i o 1 3 ', k 7/k 2^ for octene ratio 330 0.995 2.77 2.82 0.98 343 1.005 3.07 4.24 0.72 350 0.997 3.22 5.32 0.61 361 0.996 9.30 7.42 1.25 372 1.001 4.09 10.28 0.40 373 1.001 3.64 10.52 0.35 384 0.989 7.63 , 14.4 0.53 402 0.991 8.27 22.1 0.37 TABLE XXIII Accessible upper limits for the reactions of the ethyl radical with benzene temp, (°K) 337 360 360 362 374 377 386 403 (cm 3 / 2 mol."* s"*) 0.02RCO I0' 3k 7/k 2^ for R* octene-1 (q) 1.55 3.53 2.96 7.28 0.293 7.28 0.500 7.74 0.101 10.85 0.111 11.8 0.103 14.9 0.130 22.7 ratio p/q 0.44 0.41 0.040 0.064 0.0093 0.0095 0.0069 0.0057 (cm' 3/2 10 4 k 2 2.95 6.18 6.18 6.58 9.27 10.07 12.8 19.7 mol. z s I p l A ">'V k2 % ratio . " i ——.— W k h x/y for octene-1 (x) (y) 0.203 1.53 0.13 0.558 3.12 0.18 0.205 3.12 0.066 0.289 3.32 0.087 0.0820 4.62 0.018 0.0804 5.00 0.016 0.111 6.33 0.018 0.202 9.59 0.02 98 TABLE XXIV Absolute values of the A factor and activation energy for abstraction (cm3 mol." 1 s" 1) substrate 13+log A6_ A 2^ 13+log v— 10 1 3 A 6 (kcal./ -mole) E6 diethyl ketone 5.5*0.1 4.9*0.1 7.2 8.8*0.7 octene-1 5.05-0.3 4.75*0.3 2.5 8.5*1.0 cyclohexadiene-1,3 5.0*0.3 + 4.4-0.3 2.1 6.4-1.0 cycloheptatriene 5.3*0.3 + 5.0-0.3 4.7 7.5*1.0 cyclooctatetraene + 6.0-0.7 5.1-0.7 23. 9.6*1.7 cyclohexadiene-1,4 ( f i r s t series) + 5.7-0.2 5.1*0.2 11.5 6.8*0.8 cyclohexadiene-1,4 (second series) 5.7+0.1 + 5.1-0.2 12. 6.8*0.6 cyclooctadiene-1,5 5.3-0.4 4.4*0.4 4.8 7.8*1.2 2,5-dimethy1-hexadiene-2,4 5.5+0.2 4.4*0.2 7.6 8.6*0.8^  a l l y l alcohol + 5.4-0.2 5.1*0.2 5.4 8.6*0.8 * n = number of reactive hydrogen atoms per molecule. 99 TABLE XXV Absolute values of the A factor and  activation energy for addition (cm3 mol.s"^-) substrate 13*log A 2% 13+log s— \ A 2 % N / 10 1 3 A ? (kcal./ mole) E7 octene-1 5.5-0.1 5.5*0.1 6.8 8.6*0.7 cyclohexadiene-1,3 5.55*0.2 5.25-0.2 7.9 6.2*0.8 cycloheptatriene 5.9-0.1 4-5.6-0.1 16. 7.4*0.7 cyclooctatetraene 5.3*0.35 4.4*0.35 4.2 6.6*1.1 bicycloheptadiene 4-5.8-0.1 5.2*0.1 14. 8.0*0.1 2,3-dimethyl-butadiene-1,3 5.6*0.15 5.3-0.15 9.8 5.5-0.7 2,5-dimethy1-hexadiene-2,4 5.2*0.15 4-4.9-0.15 3.2 7.6*0.8 a l l y l alcohol 5.7-0.2 5.7*0.2 5.4 8.75-0.85 * n = number of reaction centres per molecule. 100 It should be noted that the temperature dependence of has been rejected by some workers on the grounds that no significant activation energy has been detected in the dimeriza-tion of other simple alkyl radicals.^8»69 ^ case values of E^-%E>2 would equal E^, and a l l values of and A^ quoted here would be high by a constant factor of 2 approximately.^7 It has been found convenient to include in tables XXIV and XXV values of the quantity 13+log ' A r l \ —r x — where n is the number of reactive sites per molecule. Considering these values in the light of the limits of error, i t may be concluded fAr l \ that 13-Mog — £ x —J is f a i r l y constant in each series. These l A 2 ^ NJ values w i l l be discussed further in the sections dealing with the respective compounds. F. Comparison of Intrinsic Radical Reactivities  1. The ethyl and methyl radicals The work of Szwarc and his school has been discussed in the Introduction and i t was pointed out that relative rate constants, measured at 65°C in iso-octane solution are reported by these workers rather than activation energies. Consequently a comparison of rate constants must suffice and should not introduce too much error as the variation in A factor for attack by the methyl radical should follow roughly the same pattern as for attack by the ethyl radical. 101 The work of Szwarc and his co-workers differs in two respects from this investigation: (a) the methyl, rather than the ethyl, radical has been chosen for the general survey of reactivity, and (b) the reactions are studied in solution. It would be simpler to compare two systems differing in only one of these respects and the consequences of (a) and (b) w i l l be examined in turn. (a) The addition reactions of the ethyl radical have 35 been studied in iso-octane solution by Smid and Szwarc. The logarithm of the methyl a f f i n i t y was plotted against the logarithm of the ethyl a f f i n i t y for a variety of substrates. The points were observed to l i e closely about a line of unit gradient, i.e., CH3 C 2H 5 AE y - AE y where AE^j is the difference in activation energies for addition to two substrates i and j . It was concluded that the methyl and the ethyl radicals possess equal int r i n s i c reactivity and that the rate constants for the addition of these radicals to a single substrate are probably very similar. (b) Values of the methyl a f f i n i t y and ky/k22, both at 65°C are compared in table XXVI and the logarithms of these values are plotted in figure 10. As the logarithms of the methyl a f f i n i t i e s are linearly related to the logarithms of the ethyl a f f i n i t i e s , this is equivalent to a correlation between the rate of addition of the ethyl radical in solution and in 102 TABLE XXVI Correlation of the rate constants for the addition of  the ethyl radical with the methyl a f f i n i t i e s  of various substrates, each at 65°C substrate 13 + log (k 7/k 2^) log (methyl affinity) (ref.32,33,42,79,91,92) octene-1 0.56 1.41* 2,5-dimethylhexadiene-2,4 0.92 1.33 71 vinyl acetate 0.91 1.57 39 2,4,4-trimethylpentene-l 1.06 1.56+ cis-crotononitrile 7^ 1.38 1.87 trans-crotononitrile 7^ 1.55 1.87 cyclohexadiene-1,3 2.16 2.82 styrene 7 2.30 2.91 2,3-dimethylbutadiene-l,3 2.71 3.35 73 acrylonitrile 2.89 3.24 * the value for heptene-1 •f the value for isobutene 103 ~~ I 2 3 1 3 + L O G ( K T / K / * ) F I G . 10 C o r r e l a t i o n o f the r a t e constants f o r the a d d i t i o n o f the e t h y l r a d i c a l with the methyl a f f i n i t i e s o f v a r i o u s s u b s t r a t e s , each a t 65°C. 104 the gas phase. A line of unit gradient has been drawn and the scatter of points about the line is small enough to support the linear relation. This correlation implies that the methyl radical in solution, and the ethyl radical in solution or in the gas phase, have similar intrinsic reactivities. This conclusion is in accord with the prediction that repulsion between a methyl radical and a substrate should not differ appreciably g from the repulsion for an ethyl radical. In view of the small, and similar, polar effect in the addition reactions of the methyl and ethyl radicals, i t would be interesting to compare the ethyl radical with radicals which show a more pronounced polar effect in addition. 2. The control of monomer reactivities by resonance and ele c t r i c a l factors Considerable attention has been focussed on the addition reactions of growing polymer radicals, both in polymerization and copolymerization. In the copolymerization of two monomers and M2 the possible propagation reactions are, P^  + ML — > k l l + M2 — > *2 k12 P 2 + Mx — * i k21 P 2 + M2 —> *2 k 2 2 105 The reactivity ratio is defined, r l = k l l / k 1 2 a n d r2 = k22^ k21 and a quantitative expression for the reactivity ratio has 74 75 been developed by Price and his co-workers. * RT I n U / r p - ( q ^ ) + 7.23*1020 E±( £ ±- £ 2) (x) To demonstrate the significance of this expression, consider the reaction, M CH_ CHY + CH0 = CHX —> M CH0 CHY — C H 0 — CHX n 2 2 n 2 2 q represents the relative resonance stabilization conferred upon the new radical by the substituent X and £ may be repre-sented as the charge induced by X or Y on either of the carbon atoms forming the new C - C bond in the transition state. 3. The equation of Bamford, Jenkins and Johnston The equation derived by Bamford, Jenkins and Johnston, also expresses reactivity in terms of polar and non-polar 76 effects. log k = log k T + CT + /3 (a) 0 The rate constants k g and k-r refer respectively to the reaction of a given radical RCH^ -CHX with a substrate S and to metathesis of the same radical with toluene, C is the Hammett constant for the group X, and dC and ft are constants for the substrate S. The quantity cC is a measure of the extent to which the reaction rate is influenced by polar substituents. If either cC or CT is zero, the equation reduces to log k - log k-r + /3 (b) 106 4. Comparison of the q- t scheme and the equation of  Bamford, Jenkins and Johnston The two equations are, to a large extent, equivalent, and the reactivity ratios calculated from the equation (x) can be used to calculate values of /3 in equation (a), which may be written in the form log ( l / r x ) = log ( k T / k u ) + + /3 This has been done for a number of monomers in table XXVII. ML is styrene and a temperature of 60°C has been adopted. These values are plotted against the values of 13+log(k^/k2 ) at 60°C for these monomers in figure 11, and a line of unit slope has been drawn. The small scatter of points about this line shows that the modified equation (b) i s adequate in this case as Cf is very small. 5. The ethyl and polystyryl radicals With the exception of the point for acrylonitrile the correlation of log (ky/Vi^) and (3 is equivalent to a comparison of log (k^/k2*) and log (1/r^) where i s styrene. This i s because |S was calculated from the expression, /S - log (1/r^) - const, where the constant i s log (k-f / k^) a t 60°C. In the case of acrylonitrile an additional term oCC (= +0.03) was included. Only in acrylonitrile i s high enough to be significant as Of for polystyryl i s very low 76 (-0.01). TABLE XXVII Calculation of values of 15 at 60°C for various monomers and comparison with experimental values of 13+log(k7/k2 ) also at 60°C 13+log log (1/rj) A b ) substrate/substitute (a) (k 7/k 2^) (M^:styrene) occr (75) (76) octene-l/hexene-1 0.49 -1.95 0 2.85 hep t yne -1^9/ hexyne -1 0.25 -1.98 0 2.82 vinyl butyl ether 7 3/ vinyl isobutyl ether 0.77 -1.67 0 3.13 a l l y l alcohol/ a l l y l acetate 0.65 -1.67 0 3.13 2,3-dimethylbutadiene-l,3/ butadiene 2.66 +0.33 0 5.13 vinyl acetate 7 vinyl acetate acrylonitrile / acrylonitrile 71/ 0.84 2.86 -1.41 +0.40 0 +0.03 3.39 (cf. 5.17 (cf. 3.0) 7 6 5.3) 7 6 styrene / styrene 2.26 39/ 0.93 0.00 0 4.80 (cf. 4.85) 7 6 2,4,4-trimethylpentene-l isobutene -1.85 0 2.95 a The f i r s t compound in each pair is the substrate for which ky/k-^ has been measured. The second compound is a related monomer for which values of q and E have been measured.?5 b Calculated from the expression: j3 = log(l/r ) + log J^ ljL -oCC where log k l l = 4*80. 1 k T k T 108 3 « £ ) 4 - 0 5 ' 0 F I G . 11 C o r r e l a t i o n o f the a d d i t i o n r a t e constant a t 60°C with the value o f /3 109 A linear relationship of this type is to be expected whenever c£or cf is zero as the equation (x) reduces to the simple form (y). This is vi r t u a l l y the case for the ethyl and polystyryl radicals for which cf is zero (by definition) and -0.01 respec-tively. If the equation applies in both gaseous and liquid phases and as ft depends only on the substrate, the linear corre-lation between the addition rate constants for the ethyl and polystyryl radicals follows directly. Applying Szwarc's concept of intrinsic reactivity, i t i s concluded that the ethyl and polystyryl radicals have equal intrinsic reactivity. As i t has been concluded above that the intr i n s i c reactivity of the ethyl radical in the gas phase is equal to that of the methyl radical in the liquid phase, i t would be expected that methyl and polystyryl radicals should have equal intrinsic reactivities. This i s in contradiction of the results of Leavitt, Stannett and Szwarc, who observed 58 the relation, CH3 p AE - 0.59 AE i j i j where the superscript p refers to the polystyryl radical. No explanation for this discrepancy can be found. 6. The ethyl and polyvinyl acetate radicals Values of log (1/r^) at 60°C, where is vinyl acetate, have been calculated in table XXVIII for a number of substrates. As values of q and £ do not exist for every monomer the values 110 for a closely related species have been used in a few cases; for example, the values for a l l y l acetate serve for a l l y l alcohol. The values of log (1/r^) are plotted against values of lS+logCk^/k^ ) in figure 12. The point for a l l y l acetate is denoted by an open ci r c l e as i t w i l l be necessary to consider this compound again in a later section (Q). A line of unit gradient has been drawn to show that the ethyl radical and polyvinyl acetate radical do not differ appreciably in intrinsic reactivity. The scatter of points about the line i s small except, possibly, in the case of acrylonitrile. It has been pointed out above that such a linear relation would be expected i f oC cf in the equation (a) is very small or zero. As d - 0.31 for the polyvinyl acetate radical, the required condition i s that cC = 0 for a l l the substrates. This is approximately true except in the case of acrylonitrile ( <£. = -3.1) and the point for this monomer consequently shows by far the greatest deviation from the straight line. 7. The ethyl and polyacrylonitrile radicals In table XXVIII and figure 13 a similar comparison is shown for = acrylonitrile. In this case the point for a l l y l 78 alcohol represents a direct measurement of 1/r^, and an open ci r c l e has been used in figure 13 to identify the point for this compound. The value of cf for the polyacrylonitrile radical is 0.66.7 TABLE XXVIII Correlation of the rate constants for the addition of the ethyl radical with monomer reactivity ratios. each at 60°C * substrate 13+log logU/ri) l o g d / r i ) q2. 10 1 0 a. substitute (k 7/k 2i) (M^.V.A.) (M^ .AN) (kcal./mole) (e.s.u heptyne-l 3 9 hexyne-1 0.25 -0.42 -0.51 -0.25 -0.34 octene-1 hexene-1 0.49 -0.36 -0.31 -0.40 -0.40 a l l y l alcohol a l l y l alcohol 0.65 - -0.60 - -a l l y l alcohol a l l y l acetate 0.65 -0.14 -0.33 -0.64 -0.29 vinyl butyl ether? 3 vinyl isobutyl ether 0.77 -0.20 -0.35 -0.68 -0.55 vinyl acetate^l vinyl acetate 0.84 0.00 -0.57 -0.72 -0.11 2,4,4-trimethylpentene-l 3^ isobutene 0.93 -0.24 -0.15 -0.60 -0.42 styrene?^ styrene 2.26 +1.49 +1.20 -3.10 -0.24 2,3-dimethylbutadiene-l,3 butadiene 2.66 -1-1.82 +1.52 -3.60 -0.24 ac r y l o n i t r i l e ? 3 acrylonitrile 2.86 +1.53 0.00 -2.70 +0.34 * The f i r s t compound in each pair is the substrate for which ky/k^ has been measured. The second compound is a related monomer for which values of q and £ have been measured. V.A. = vinyl acetate; AN = acrylonitrile 1 , V S i * 2 I 3 + L 0 G ( K 7 / K 2 A ) F I G . 1 2 112 I 3 + L 0 G ( K 7 / K 2 A ) F I G . 12 C o r r e l a t i o n o f the a d d i t i o n r a t e constant with the r a t e constant fgr the a d d i t i o n o f the p o l y v i n y l a c e t a t e r a d i c a l , each a t 60 C. * 2 1 3 + L O G (K7/K2*) F I G . 1 3 113 C o r r e l a t i o n o f the a d d i t i o n r a t e constant w i t h the r a t e constant f o r the a d d i t i o n of the p o l y a c r y l o n i t r i l e r a d i c a l , each a t 60°C. 114 A linear relationship is observed for eight of the substrates but the deviation is correspondingly larger than before for acrylonitrile. It has been pointed out that the two equations (a) and (x) are equivalent in many respects. Consequently the deviation of acrylonitrile can be considered in terms of the q- £. values of the monomers involved. The values of q and £ for vinyl acetate, a l l y l acetate and hexene-1 (table XXVIII) do not differ greatly so the corresr ponding radicals resemble each other and the ethyl radical both in the small degree of resonance stabilization and in the a b i l i t y to act as weak electron donors. In contrast, the large negative value for q (-2.7) and the positive value for £. (+0.34) li s t e d for acrylonitrile mean that the polyacrylonitrile radical is stabilized by resonance to a considerable degree and is also strongly electrophilic, therefore this radical and the ethyl radical differ completely in these important qualities. The reaction C ^ + CH2 = CH-CN — > C^-C^-CH-CN appears to be abnormally fast in consequence of the appreciable ionic contribution to the stabilization of the activated complex.^1 Clearly, the comparison of 13+log(ky/k22) with log (1/r^) is a much more severe test of the val i d i t y of a correlation when M1 is acrylonitrile than when is vinyl acetate. 115 G. The Reactions of the Ethyl Radical with Cyclohexadiene-1,4 The additional experimental procedure required for cyclo-hexadiene-1,4 is described in the experimental section. The results are tabulated in tables VII, VIII, XIV and XVI and plotted in figure 7. The presence of benzene in the products coupled with values of M which are greater than unity, suggest that the usual reactions, C2 H5 + C6 H8 — * C6 H7 + C2 H6 6" C2 H5 + C6 H7 - * C8 H12 6 a -are supplemented by C„H* -i- C,H* > C,E, + C0H^ 6d. 2 5 6 7 6 6 2 6 As the "extra" ethane formed in reaction 6d is equivalent to the benzene, a corrected material balance may be defined by the expression, R + R - R M = C2 H6 C4 H10 C6 H6 corr. RC0 Values of M l i e close to unity suggesting that addition corr. is too slow to be detected. This is in agreement with the 79 results for the attack of the methyl radical in solution. The modified mechanism is thus confirmed and i t can be shown that, k6_ _ RC 2H 6 * RC 2H 4 ~ RC 6H 6 j ^ i k4_ k 9% [ B ] R % [B] k k 2 C 4H 1 0 2 It should be noted that the alternative reaction path, 116 C£H* — * C,H. +H 8. 6 7 6 6 C_Hl + H* — ^ C„H, 8a. is not acceptable. The ethane formed in reaction 8a would have considerable vibrational energy and Steacie and Parlee have shown that, at the low pressure in this system, decomposi-tion would predominate over deactivation:^> 8^-c/6 — » 2 C H; The main reactions of the methyl radicals would be, CHl + CoH.-CO-CLH, > CH. + C0H. -C0-CoH,-3 2 5 2 5 4 2 4 2 5 C H 3 + C6 H8 _ CH-3 + C2H; -™3 + C2 H5 -As methane and propane were not detected in the reaction products the reaction 8 can be excluded. It should be noted that hydrogen atoms would form molecular hydrogen by abstraction from diethyl ketone and cyclohexadiene-1,4, H*+ CoH_-C0-CoH, > C_H.-CO-C0H_ + H_ 2 5 2 5 2 4 2 5 2 H " + C6 H8 * C6 H 7' + H2 Hydrogen was not detected in the products. 1. Abstraction (kcal./mole) compound 13»log(A6/A2*) V^2 cyclohexadiene-1,4 5.7*0.1 5.8to.l octene-1 5.05*0.3 7.5*0.5 > CH, + 4 C2H4-CO > CH, + 4 C6 H7 C3 H8 CH, + 4 C2 H4 117 Cyclohexadiene-1,4 has two non-conjugated double bonds while the cyclohexadienyl radical has a planar conjugated system extending over five carbon atoms. Consequently a low activation energy for abstraction would be expected and is observed. Rapid abstraction from pentadiene-1,4 by the methyl 82 radical has been reported. Once again the group -CH^ CH-CH^ -CH=CH- is present in the substrate. If the A factor is divided by the s t a t i s t i c a l factor of two and compared with the value for octene-1, then i t is apparent that the A factor for cyclohexadiene-1,4 i s high. It is possible that the cyclic molecule permits the approach of an ethyl radical without steric hindrance while the alkyl chain in octene-1 may shield the reactive methylene group to some extent. 2. Addition The upper limits for addition to cyclohexadiene-1,4 do not differ significantly from the corresponding addition rate constants for octene-1 (table XXI). As cyclohexadiene-1,4 has four positions where addition can take place, compared with one in octene-1, i t may be argued that the ratio x/y should be divided by four. In this case the reactivity of cyclohexadiene-1,4 is concluded to be lower than that of octene-1. This behaviour towards addition has been observed for other 1,2-39 substituted ethylenes, v i z . cyclohexene and trans octene-4. 118 A more conclusive result is obtained when the upper limits for addition to cyclohexadiene-1,4 are compared with the corresponding addition rate constants for [ 2 , 2 , l j b i c y c l o -heptadiene. Clearly, the rate of addition to cyclohexadiene-1,4 is slower than to [2,2,l]bicycloheptadiene. 3. The identification of reaction products The adduct formed in reaction 6a can exist in two isomeric forms, (A) (B) As described in the experimental section only one product other than benzene was detected and the near ultra-violet spectrum of this product was similar to that of cyclohexa-diene-1,3 (figure 3). This evidence points strongly to the presence of the conjugated structure (A). In the cyclohexadienyl radical, 119 i t would seem reasonable to expect the atom localization energy at c(2) t o ^ e ^ o w e r t n a n at Therefore the forma-tion of l-ethylcyclohexadiene-2,4 would be energetically favoured. It must be recorded, however, that the addition of hydrogen atoms to benzene results in the formation of cyclohexadiene-1,3 and cyclohexadiene-1,4 in the ratio 1:2. 8 3  4. The reactions of ethyl and cyclohexadienyl radicals It has been suggested above that cyclohexadienyl radicals are removed from the system by the reactions, C2 H5 + C6 H7 C8 H12 6 a -C2 H5 + C6 H7 - * C6 H6 * C2 H6 6 d " By analogy with other radical-radical reactions, we may expect, C2H; + C6H7' — C 2H 4 + C 6H 8 6c. However, the C^ Hg formed in reaction 6c would be, mainly, the energetically preferred cyclohexadiene-1,3. This compound was not detected and i t may be assumed that reaction 6c is much slower than 6a and 6d. For the same reason the reactions, C6 H7 + C 2 V C ° - C 2 H 5 — * C6 H8 + W ^ V s C.H* + C,H_ > C,HQ + C.H* 6 7 6 8 6 8 6 7 can also be excluded. It should be noted that the reaction, C,H' * C\H, + H* 6 7 6 6 does not take place at a detectable rate (see above), and that mutual termination by pairs of cyclohexadienyl radicals w i l l be 120 a rare event as C\H* <^ C0H*|. [ 6 7J I I 5} It is concluded therefore that cyclohexadienyl radicals are removed predominantly by the reactions 6a and 6d, and that the alternative reactions proceed at a much slower rate. The ratio k,,/k. could not be evaluated by measuring od oa the relative rates of formation of benzene and 1-ethylcyclo-hexadiene-2,4. The gas chromatographic separation of benzene and cyclohexadiene-1,4 could be achieved only under conditions in which the adduct had a very high retention time. Consequently, this compound appeared as a broad f l a t peak which could not be measured accurately. However, i f reactions 6a and 6d represent the exclusive fate of the cyclohexadienyl radical, then, R, = R. - R,-. 6a 6 6d The quantities on the right hand side of this equation are measurable and R, can be calculated. 6a The values of k^/k^ obtained in this way are reported in table XVI for two series of experiments. The more consistent results obtained in the second series arise from the improved experimental technique described in the experimental section. •4-It is concluded that k,,/k, is equal to 0.38.0.03. The low 6d 6a value of the ratio in this particular case where reaction 6d is especially favoured on energetic grounds supports the assump-tion that this reaction is of negligible importance in the general case. 121 H. Benzene 1. Abstraction and addition The reactions of the ethyl radical with benzene were too slow to be detected and, for this reason, upper limits for both abstraction and addition were determined in table XXIII. At higher temperatures the rate constant for abstraction is not more than 2% of the value for octene-1, while the rate constant for addition is less than 1% of the value for octene-1. Very slow addition is expected in view of the high resonance energy of benzene (36 kcal./mole) 8 4 and slow abstraction is consistent 85 with the high C-H bond dissociation energy (103 kcal./mole). The methyl a f f i n i t y of benzene at 65°C is 1.1% of the 35 42 value.for heptene-1. ' A similar relative reactivity would be predicted for the addition of the ethyl radical in the gas phase at 65°C. However, the rate of addition to benzene should be strongly temperature-dependent and i t is surprising that the true addition rate constants do not exceed the upper limits at the higher temperatures. The work of Trotman-Dickenson has suggested that methyl radicals w i l l abstract hydrogen readily from benzene with an 4 activation energy of 9.2 kcal./mole, while trifluoromethyl radicals w i l l abstract hydrogen from benzene with an activation energy of 7.7 kcal./mole. 9 This apparent abstraction by trifluoromethyl radicals has been studied by Charles and his c o - w o r k e r s . ^ ' T h e reaction conditions were such that the 122 probable reaction path would be, CF* + C.H, > CF0H + CJll 3 6 6 3 6 5 2C,H " > C.H -C,H 6 5 6 5 6 5 CF' + C H* » C H CF, 3 6 5 6 5 3 The product analysis showed that diphenyl was not present and that CF^H and CF^C^H^ were present in approximately equimolar quantities. To explain the loss of trifluoromethyl radicals from the system i t was suggested that the primary reaction was that of addition only: CF' + C,H, > CF C.H * (a) 3 6 6 3 6 6 and that a certain fraction of the CF^C^H^ radicals would react with another trifluoromethyl radical CF_C,H* + CF ' » CF0H 4- CF„C,H, (b) 3 o o 3 3 3 6 5 These reactions are kinetically indistinguishable from the process of abstraction but have been j u s t i f i e d by Charles and Whittle on thermochemical grounds.^ For "normal" abstraction, a C,H -H o D bond must be broken requiring 101 kcal./mole. In reaction (b) however, the C-H bond is weaker because aromatic s t a b i l i t y is gained when i t i s broken. The dissociation energy of this bond has been estimated as approximately 64 kcal./mole. 1^ The formation of an efficient hydrogen donor by the addition of the methyl radical to benzene in iso-octane solution has been 35 reported, and Levy, Steinberg and Szwarc have discussed the possibility of abstraction after addition in the reaction of the 86 methyl radical with benzene. Wilen and E l i e l have shown, 123 by using ring deuterated toluene, that ring abstraction occurs with the methyl r a d i c a l 8 7 and have suggested that the reaction proceeds through the formation of a substituted cyclohexadienyl radical. The results of Charles and Whittle suggested that the reaction, C F 3 + C F 3 C 6 H 6 — f C F 3 > 2 C 6 H 6 ( c ) proceeded at approximately the same rate as reaction (b). The addition of the trifluoromethyl radical to benzene has also been studied by Holmes and Kutschke. 1 7 As these workers used a lower concentration of trifluoromethyl radicals than did Charles and his co-workers, reactions (b) and (c) were relatively slow and the CF^C^H^ radical formed high molecular weight products. The true rate of abstraction from benzene was found to be very slow. If i t is assumed that addition of the ethyl radical to benzene is followed by reactions analogous to (b) and (c), then the true addition rate constant w i l l be equal to the sum of the apparent addition and apparent abstraction rate constants, and ethylbenzene should be a reaction product. That this compound was not detected suggests that the apparent abstraction is very slow. This, of course, is in agreement with the observed values of k^/k^2. It is interesting to compare the adduct radical formed by the addition of the ethyl radical to benzene with the 124 cyclohexadienyl radical; An investigation of the fate of the cyclohexadienyl radical has shown that addition of an ethyl radical is slightly favoured over abstraction of hydrogen by an ethyl radical. The effect of replacing one hydrogen of the methylene group by the ethyl group is d i f f i c u l t to predict but rates of addition and abstrac-tion should be s t i l l of the same order of magnitude. A new approach to this problem is anticipated using benzene-dg as substrate. In this case the apparent abstraction reaction w i l l form C^ H^ D which can be measured by mass spectro-meter. The rate of addition could then be estimated i f the rela-tive rates of disproportionation and combination for the reaction of an ethyl radical and C2^^C^B.'^ radical were known. 2, Polymerization The polymerization of styrene in the presence of benzene OQ on 0 yields a copolymer. > y At 50 C the value of r^ was found to be 100-400. A copolymer of vinyl acetate and benzene has also 90 been reported. From the experimental data i t is possible to 3 estimate that r^ is of the order of 10 . From an inspection of figure 12 i t is concluded that 10 k /k 2 for benzene at 125 60°C is of the order 10 . This i s the order of magnitude which may be predicted from the methyl a f f i n i t y . I. 2,3-dimethylbutadiene-1.3  1. Addition The activation energy for the addition of the ethyl radical to 2,3-dimethylbutadiene-l,3 i s considerably lower than the value for octene-1. This is due, at least in part, to the smaller change in derealization energy accompanying addition to the conjugated diene. The a l l y l i c adduct radical is stabilized by resonance. An il l u s t r a t i o n of such a l l y l i c s t a b i l i t y is found in the kinetic study of the polymerization of methyl a e r y l a t e . T h e addition of a small quantity of butadiene w i l l retard the propagation. Presumably the resonance stabilized radical R-C^-CH-CH-C^ i s slow to add to the monomer. The activation energy for the addition of the ethyl radical can be discussed in terms of the resonance energy of the adduct radical relative to that of the substrate and also in terms of the polarity of the new carbon-carbon bond.^ 1'^ The ethyl radical is a weak electron donor (its ionisation potential 94 is 8.78 volts ), and a polar effect may be expected when the substrate is an electron acceptor. However, the compound Wlog(A 7/A^) 2,3-dimethylbutadiene-l,3 5.6-0.15 + octene-1 5.5-0.1 126 behaviour of the polystyryl radical in chain transfer studies 95 has shown that i t is a weak electron donor and i t has been concluded that the polar effect is not important in the addition 91 of the ethyl radical to styrene. There is evidence that a similar conclusion should apply to 2,3-dimethylbutadiene-l,3. The polarographic half-wave potential of styrene is -1.98 volts w.r.t. the mercury pool, while the value for 2,3-dimethylbuta-diene-1,3 is below -2.2 volts. Further evidence is obtained from copolymerization data as interpreted by Price and his co-workers (section F). The value of £ for 2,3-dimethylbuta-diene-1,3 is not available but the value for butadiene is equal to that for styrene (-0.24x10 ^ e.s.u.).^** Therefore, i t is concluded that the polar effect is not important in the addition of the ethyl radical to 2,3-dimethylbutadiene-l,3. As there are two potential reaction centres in each molecule, an A factor which is twice that for octene-1 would be predicted. Inspection of the measured logarithmic values and the associated probable errors shows that, although i t is impossible to distinguish between these values, the limits of error would not be inconsistent with a difference of 0.3 in the logarithms, that i s , a factor of two in the numerical values. 2. Abstraction In table IV values of the abstraction rate constant for 2,3-dimethylbutadiene-l,3 have been calculated for a few runs. Because of the high values of the ratio [ D I / F B I , the values are 127 comparable with the possible experimental error. An inspection of table XIX shows that the accessible upper limits of the rate constants for abstraction from 2,3-dimethylbutadiene-l,3 are greater than the corresponding abstraction rate constants for octene-1 by factors varying for 4.5 to 12. The high values of this ratio show that, although the rate of abstraction is too slow to be measured, i t is not necessary to postulate an abnormally low reactivity. This conclusion s t i l l holds when allowance i s made for the six available hydrogens in 2,3-dimethyl-butadiene-1,3 compared with two in octene-1. 3. Polymerization 2,3-dimethylbutadiene-l,3 polymerizes by a radical mechanism 96 to a predominantly 1,4 polymer (9170) . Although the polymer radical is resonance stabilized, propagation w i l l be facilitated by the high reactivity of the monomer. The high value of the ratio kj/Vi^ observed in this investigation would suggest that propagation would take place much faster than chain transfer. Consequently a high degree of polymerization would be predicted. J. 2,5-dimethylhexadiene-2,4 2,3-dimethylbutadiene-l,3 2,5-dimethylhexadiene-2,4 2,5-dimethylhexadiene-2,4 compound abstraction addition reaction addition 13+log(Ar/A2^) E r-%E 2 5.5*0.2 7.6-0.35 5.2*0.15 6.6*0.3 5.6*0.15 4.5*0.2 128 1. Addition The low reactivity of 2,5-dimethylhexadiene-2,4 towards addition compared with that of 2,3-dimethylbutadiene-l,3 arises mainly from the comparatively high energy of activation assisted 97 by the low A factor. It has been suggested, albeit somewhat tentatively, that in the addition process the approach of the radical is along the C=C axis, in which case the methyl substi-tuents could lower the A factor by steric hindrance. The relatively high activation energy may result from the energy required for the passage of the ethyl radical between the methyl substituents on i t s approach to the reaction centre. A possible alternative explanation is that the transition state is dis-torted, that i s , the approach of the ethyl radical is not along the C=C axis, but along some less favourable line of approach. It has been observed that the activation energy for the addition of the methyl radical to hexadiene-2,4 is not s i g n i f i -cantly different from that for butadiene-1,3 although the A factor 82 is low. Apparently a single methyl group on the reaction centre w i l l exert a steric effect without increasing the energy requirements for the approach of a radical to the reaction centre. The energy of activation for addition of a methyl radical to 2,5-dimethylhexadiene-2,4 was 2.35 kcal./mole higher than the value for butadiene-1,3. In this work the difference in activation energies for 2,5-dimethylhexadiene-2,4 and 2,3-dimethylbutadiene-1,3 is 2.1 kcal./mole. 129 Rajbenbach and Szwarc have discussed the possibility that addition takes place at rather than *-n 2,5-dimethyl-hexadiene-2,4 and have concluded that the activation energy 82 for addition at this site would be higher than that observed. However, Pullman has calculated the atom localization energy at C. . to be-2.48p (cf.—1.78/3 for the reactive position in 2,3-dimethylbutadiene-l,3) and has shown that this value is consistent with the correlation of localization energy and 98 methyl a f f i n i t y . As no value was reported for the atom localization energy at c(2) » i , t w o u l d b e wise to obtain further evidence and this matter w i l l be examined further in section R. The analysis of the products from the addition of mercaptans to 2,5-dimethylhexadiene-2,4 by a radical mechanism has shown 101 that the RS- group is attached to C(2)* However, this evi-dence is of limited value as the radical is presumably electro-p h i l i c in which case the i n i t i a l point of attack w i l l be at the 23 double bond. 2. Abstraction The energy of activation for abstraction from 2,5-dimethyl-hexadiene-2,4 is lower than that for octene-1. It is concluded that the activating influence of conjugation outweighs the superior dissociation energy of a normal primary carbon-hydrogen bond. The A factor for abstraction should be considered in the light of the number of reactive hydrogen atoms in the molecule. 130 Dividing the A factors for abstraction from octene-1 and 2,5-dimethylhexadiene-2,4 by 2 and 12 respectively, the values become: Inspection of the limits of error shows that these values are in agreement. The low A factors observed by Trotman-Dickenson for abstraction from a methyl group in the alkene series should be 4 considered here. However, 2,5-dimethylhexadiene-2,4 can not be regarded as an ideal molecule with which to test this claim in view of the possible steric effects. Slow abstraction from cis-99 butene-2 by the methyl radical has been observed and attributed to a low A factor arising from crowding of the methyl groups. Such an effect should be more pronounced here where two methyl groups are attached to the same carbon atom. Unfortunately, the limits of error do not allow any clear conclusion on this point for 2,5-dimethylhexadiene-2,4. The use of the expression A/n, where n is the number of reactive hydrogen atoms in each molecule, has been c r i t i c i z e d by some workers on the grounds that the hydrogen atoms in a methyl group are so close together that the chance of abstraction on co l l i s i o n is probably less than 3 times the chance for a reaction site with only one hydrogen atom. 1^ Possibly a compound octene-1 4.75*0.3 2,5-dimethylhexadiene-2,4 4.45-0.2 131 st a t i s t i c a l factor between 1 and 3 would be appropriate. K. Cyclohexadiene-1,3 1. Correction for the "extra" ethane The abstraction of hydrogen from cyclohexadiene-1,3 w i l l form the cyclohexadienyl radical. The fate of this radical has been discussed in section G and the only important reactions were shown to be, C2 H5 + C6"7* C8 H12 6 3 • C2 H5 + C6 H7 — > C2 H6 + C6 H6 6 d ' The ratio k g ^ / k ^ a has been measured as 0.38-0.03, independent of temperature, and this value was used in calculations on cyclo-hexadiene-1,3. It is easily deduced that, k6 , x k6 , s <k6a * k6d) ^ (corr.) = ^  (apparent) x ^ + 2 ± 6 d ) k 7 k 7 k 6 k 6 d ^5 (corr.) = ^5 (apparent) + (corr.) x ^TY^ The results reported in table VI are corrected in this way. The effect of the correction is small in both cases and i t is concluded that reaction 6d is unimportant, both in this system where i t is specially favoured, and in general throughout this study. 132 compound reaction 13+log (A r/A 2*) 2,3-dimethylbutadiene-l,3 cyclohexadiene-1,3 octene-1 cyclohexadiene-1,3 cyclohexadiene-1,4 abstraction abstraction abstraction addition addition 5.55*0.2 5.6*0.15 5.0*0.3 5.7*0.1 5.05*0.3 5.8-0.1 2. Addition A comparison of the results for cyclohexadiene-1,3 and 2,3-dimethylbutadiene-1,3 shows that the difference in reactivity of these compounds arises from a difference in activation energy rather than any significant difference in the A factor. Addition to cyclohexadiene-1,3 w i l l be accompanied by the release of some strain energy. This may contribute to a lowering of the activation energy for addition. 3. Abstraction (comparison with cyclohexadiene-1,4) The energy of activation for abstraction from cyclohexa-diene-1,3 does not differ significantly from the value for cyclo-hexadiene-1,4. In each case the radical formed by abstraction is the cyclohexadienyl radical, therefore the difference in net energy change for abstraction from these substrates w i l l be equal to the difference in energy of the two substrates. Here i t w i l l be assumed that the major contributing factors w i l l be electronic and strain energies. In the case of cyclohexadiene-1,3, the molecule is resonance 133 stabilized by about 2 kcal./mole, 8^ while the cyclohexadiene-1,4 molecule w i l l have l i t t l e or no resonance energy. The cyclohexadiene-1,3 molecule i s , presumably, almost 102 planar and some angular steric strain should exist at the methylene groups. This would be partly released on abstraction by changing the equilibrium bond angle to approximately 120° . The strain energy of cyclohexadiene-1,3 has been estimated as 4 kcal./mole relative to cyclohexane. It is l i k e l y that cyclohexadiene-1,4 is folded so as to 104 reduce the angular strain at the methylene group to a low value. As strain and electronic energy effects w i l l oppose one another, the overall energy change on abstraction w i l l be similar for the two compounds. Assuming that a trend in the overall energy change is paralleled by a similar trend in activation energy, i t is concluded that the activation energy for abstrac-tion of hydrogen from cyclohexadiene-1,3 should be similar to the value for cyclohexadiene-1,4. No reasonable explanation can be found for the widely differing A factors for abstraction from cyclohexadiene-1,3 and cyclohexadiene-1,4. It is possible, but unlikely, that the line of approach of the ethyl radical which is favourable for abstrac-tion from cyclohexadiene-1,3 is also favourable for addition and that addition is the preferred reaction. Alternatively, the close proximity of the four hydrogen atoms available for abstrac-tion in cyclohexadiene-1,3 may lower the A factor. 134 L. [2,2.l] bicycloheptadiene compound [2,2,lJ bicycloheptadiene cyclohexadiene-1,3 reaction ^-Hog^/A,, «) 5.81*0.07 5.55*0.2 V*E2 4-7.0-0.1 5.2*0.3 addition? addition |^2,2,lj bicycloheptadiene abstraction 4-cyclohexadiene-1,4 abstraction 5.7 -0.1 The behaviour of ^2,2,l]bicycloheptadiene (I) towards both abstraction and addition contrasts sharply with that of cyclo-hexadiene-1,4 (II) to which i t bears some structural similarity. high 5.8*0.1 ( I i ( I D 1. Abstraction The rate of abstraction of hydrogen from [2,2,l| bicyclo-heptadiene is slower than the rate of abstraction from cyclo-hexadiene-1,4 by a factor of at least 50 (table XX). This may be explained by considering the conformation of the cyclohexa-dienyl radical in which five carbon atoms (including the one attacked) are presumably coplanar. 135 The derealization of five H electrons results in consider-able resonance stabilization of the radical which accounts for the low dissociation energy of the C^ H^ -H bond. In the case of j^2,2,l]bicycloheptadiene, the trans-annular methylene group would not permit the corresponding planar conformation and the stabilization of the radical would be much less important. Furthermore, the stable configuration of single bonds around a 2 trivalent carbon atom in sp hybridization i s presumably planar (or very nearly so), and such a planar configuration would not be expected at the bridgehead carbon atom. In this way, the resis-tance of the C-H bond towards attack is increased. 2. Addition The rate of addition to {^2,2,l]bicycloheptadiene is greater than the rate of addition to cyclohexadiene-1,4 by a factor of more than two throughout the temperature range investigated. The high reactivity towards addition arises from a low activation energy and the A factor is normal for a molecule with four reac-tive centres, i.e. A^ for |^2,2,lJ bicycloheptadiene is approxi-mately twice that for cyclohexadiene-1,3. 136 Gresser, Rajbenbach and Szwarc have observed a high methyl a f f i n i t y for both [2,2,l]bicycloheptadiene and |i2,2,l] bicyclo-heptene and have suggested that the release of steric strain is an important factor in controlling the energy of activation for addition to these compounds. Although the Raman spectrum suggests an almost planar molecule, 1^ 7 i t seems more li k e l y that cyclohexadiene-1,4 is folded with a dihedral angle of approximately 1 4 0 ° . 1 ^ In this conformation the angular strain would be very small. As the methyl a f f i n i t y of [2,2,lj bicycloheptadiene (115.) is only slightly greater than twice the value for [2,2,l]bicyclo-heptene (50.2), i t has been concluded that these values differ 79 in reactivity only by a s t a t i s t i c a l factor of two, and that homoallylic resonance does not contribute any significant stabilization energy to the adduct radical. The reasoning behind this conclusion assumes that the strain energy released by adding a radical to these compounds w i l l be the same in each case. This assumption may be inaccurate. There is no evidence for 2-6 overlap of II electrons in calculations predict a derealization energy of zero and this is the ground Theoretical in agreement with the heat of hydrogenation. 109 Some interaction of the il electrons occurs in the lowest excited state. The 108 C/o\~C/£L\ bond order has been calculated as 0.12. Moreover, (2) (6) when an ethereal solution of ^2,2,ljbicycloheptadiene is irradiated with a high pressure mercury lamp, the valence r ? 6 ^ si tautomer, quadricyclo12,2,1,0 » 0 » Iheptane is formed. 113 Radical addition reactions to |~2,2,lJbicycloheptadiene can produce products with a ring. Thus the addition of bromotrichloromethane produces the compound: CC1, (III) On the other hand, the addition of p_ thiocresol does not yield 111 products analogous to (III). However, this does not exclude 138 homoallylic resonance in the intermediate radical. Obviously, more work is necessary to resolve this conflict. It would be interesting to analyse the products from the addition of the ethyl radical to j^2,2,l]bicycloheptadiene although the experimental d i f f i c u l t i e s would be considerable. 3. Polymerization The polymerization of j^2,2,ljbicycloheptadiene and i t s deri-112 vatives yields further evidence for a 2-6 interaction. 2-carbethoxy- j^2,2,ljbicycloheptadiene polymerizes readily by a free radical mechanism to a polymer with the repeating unit: Under the same conditions, [2,2,ljbicycloheptadiene also gives high polymer, but at a slower rate and i t was suggested that the carbethoxy group may activate the double bond towards attack and stabilize the adduct radical by resonance. 2-carbethoxy-[2,2,lj bicycloheptene did not polymerize under the conditions of these experiments and i t was suggested that the greater ring strain in the [2,2,l]bicycloheptadiene system may be responsible for the greater reactivity. 139 M. Cycloheptatriene 1. Formation of toluene A trace of toluene was observed in the product analysis following a run on cycloheptatriene. This could possibly arise 119 from the thermal decomposition of the substrate. A further possibility is the intramolecular rearrangement of the cycloheptatrienyl radical. C,HCCH0 6 5 2 2. Electronic structure and geometry The structure of cycloheptatriene has been the subject of considerable discussion. The compound has been represented by the different structures: (I) (II) (III) An equilibrium between I and II has been postulated while i t has also been suggested that I and II are canonical forms contribu-114 ting to III (a quasi-aromatic structure). The two main questions are: (a) Is the molecule planar? (b) Is there significant 1-6 overlap of TT electrons as assumed 140 in III? Methods of approach to this problem have included the study of cycloheptatriene and related compounds by the following methods, 1. Nuclear magnetic resonance.11"* 2. Ultra-violet, infra-red and Raman spectroscopy. 1 1 6 3. Chemical methods. 1 1 6' 1 1 7 Unfortunately, some doubt exists as to the true significance of the rather complicated N.M.R. spectra which have been observed. An attempt to study cycloheptatriene by X-ray crystallo-118 graphic analysis below i t s melting point (-80°C) failed. The phase was found to be highly disordered. However, an X-ray investigation of the compound CyHgMo(C0).j has shown that the six carbon atoms, other than that of the methylene group, are 120 very nearly in the same plane. In the triene system a pattern of alternate single and double bonds is clearly established and the C^.-C,,. distance of 2.52 & suggests that any overlapping (1) (6) of i t electrons must be very weak. This conclusion contradicts the earlier suggestion that the N.M.R. spectra of cycloheptatriene 121 and C_H0Mo(CO)0 supports a quasi-aromatic system. 7 o 3 A structure in which only the methylene group is out of 121 plane is in agreement with the vibrational spectrum. . 84 The resonance energy of cycloheptatriene is 7 kcal./mole. 141 compound reaction 13+log(Ar/A2*) E r-%E 2 cycloheptatriene abstraction 5.3*0.3 6.5*0.5 octene-1 abstraction 5.05*0.3 7.5*0.5 eyelohexadiene-1,3 abstraction 5.0*0.3 5.4*0.5 cycloheptatriene addition 5.9-0.1 6.4*0.2 octene-1 addition 5.5*0.1 7.6*0.2 cyclohexadiene-1,3 addition 5.55*0.2 + 5.2-0.3 3. Abstraction The energy of activation for abstraction is lower than that for octene-1 but higher than the value for cyclohexadiene-1,3. The A factor for abstraction is normal for a molecule with a single reactive methylene group. Assuming a planar triene system without 1-6 interaction, then the moderately high activa-tion energy could be attributed to the deviation of the methylene group from the plane of the triene system. If such a conforma-tion were maintained in the cycloheptatrienyl radical then the unpaired electron could only overlap weakly with the conjugated system. It is more li k e l y that the radical is almost planar, in which case i t w i l l possess considerable strain energy. A non-planar triene system could also account for the moderately high activation energy for abstraction. If a similar geometry were maintained in the cycloheptatrienyl radical then the s t a b i l i t y would be diminished by the reduced TT electron overlap. 142 4. Addition As in the process of abstraction, the activation energy for addition l i e s between the value for octene-1 and that for cyclohexadiene-1,3. This value seems rather high for a planar triene system without significant overlap of TT electrons across the ends of the conjugated system. If such 1-6 inter-action were present then the st a b i l i t y of the quasi-aromatic system would increase the energy of activation for addition. The reactivity of a non-planar triene system towards addition cannot be predicted accurately. The reduced overlap of the 7T electrons would contribute to a f a i r l y high energy of activation. The half-wave reduction potential of cycloheptatriene was found to be -1.96 volts. By comparison with styrene i t is concluded that a polar contribution to the transition state is not li k e l y to be important in the addition reaction. The 122 ionisation potential of 8.55 volts further supports this view. The A factor for addition to cycloheptatriene is approxi-mately twice the value for octene-1. This is consistent with the presence of two reaction centres in the cycloheptatriene molecule. 5. Conclusions The reactivity of cycloheptatriene towards addition does not appear to be consistent with the planar triene system without a 1-6 overlap of TT electrons. The results are more easily 143 interpreted in terms of either a quasi-aromatic system or a non-planar triene system. N. Cyclooctatetraene 1. Photoinitiated decomposition The photolysis of cyclooctatetraene was shown to produce benzene and acetylene in approximately equimolar quantities, C8Hg + h» - > C 6H 6 + C 2H 2 This reaction has been observed previously and is attributed to the decomposition of a metastable t r i p l e t state 125 molecule. Cyclooctatetraene absorbs f a i r l y strongly at 1.29 3130 & (log £ =? 2.4), and a quantum yield for benzene and 128 acetylene of 0.1 has been reported. Photoisomerisation to styrene has also been observed with a quantum yield of 4x10 . Small quantities of additional, unidentified, products have been detected. Some of these products are 128 polymers. The mean lifetime of the excited molecule has -8 -7 125 been estimated as 10 to 10 seconds. In calculating values of the abstraction and addition rate constants, i t has been assumed that this decomposition reaction takes place independently of the normal addition and abstraction reactions. It is interesting to note that Bryce-Smith and Lodge have reported the synthesis of substituted cyclooctatetraenes by the irradiation of mixtures of benzene and substituted acetyl-144 130 enes. For example, methylcyclooctatetraene carboxylate was formed by the action of ultra-violet radiation on a mixture of benzene and methyl propiolate. However, only a trace of cyclo-octatetraene was formed on irradiation of a mixture of benzene and acetylene. The results for cyclooctatetraene must be accepted with caution. The possibility that electronically excited molecules may participate can not be ignored, although the concentration of excited molecules would be very much smaller than the concen-tration of ground state molecules. It must also be pointed out that the rate constants for both abstraction and addition show more scatter than is normally observed. This could arise from an undetected imperfection in the mechanism or from the increased complexity of the analysis due to the presence of acetylene in the C 2 fraction. In the case of abstraction, the scatter can be attributed, in part, to the d i f f i c u l t y of measuring the abstraction rate constant when i t is much smaller than the rate constant for addition. 2. Geometry The cyclooctatetraene molecule is non-planar and non-aromatic. The most stable conformation is a "tub" (I) with Z.C=C-C = 126.46°, C-C = 1.462 X and C=C = 1.334 ft.132 (I) The rather large bond angle (126.46° compared with 121° in ethylene) corresponds to a slight flattening of the molecule. This increases the overlap of ^ orbitals and the resulting resonance energy (4 kcal./mole approximately) balances the slight angular strain. Evidence for this overlap is found o 131 in the single bond length of 1.462 A. This is shorter 9 134 than the normal value for C 0 - C „ of 1.506 A. compound cyclooctatetraene cycloheptatriene cyclohexadiene-1,3 octene-1 cyclooctatetraene octene-1 reaction 13+log(Ar/A2*) E r-%E 2 addition 5.3*0.35 5.6*0.6 addition 5.9*0.1 6.4-0.2 addition 5.55*0.2 5.2*0.3 addition 5.5*0.1 7.6-0.2 abstraction 6.0*0.7 8.6*1.2 abstraction 5.05*0.3 7.5*0.5 146 3. Addition A low energy of activation is observed for the addition of the ethyl radical to cyclooctatetraene. This may be discussed in terms of the high electron a f f i n i t y of this compound. It i s interesting to compare the polarographic half-wave potentials of cyclooctatetraene (-1.28 volts) and acrylonitrile (-1.68 volts). The low activation energy for the addition of the ethyl radical 73 to acrylonitrile (E^-%E2 4= 4 kcal./mole) has been attributed to lowering of the energy of the activated complex by the partial donation of an electron from radical to substrate. This polar contribution is probably even more important for addition to cyclooctatetraene. The adduct radical may have some a l l y l i c resonance s t a b i l i -zation. However, the odd electron could only overlap weakly with the 77 electrons of the adjacent double bond. The high electron a f f i n i t y of cyclooctatetraene has been attributed to the presence of considerable resonance energy 135 in the dianion. It has been shown that the dianion is planar with a 10 TT electron system which confers aromatic st a b i l i t y 135 as predicted by the Huckel molecular orbital theory. The electronic st a b i l i t y of the planar form outweighs the increased strain energy. It is probable that the radical ion is also planar. In contrast, cyclooctatetraene would not gain aromatic st a b i l i t y in the planar conformation and adopts the less strained "tub" form. 147 The A factor for addition to cyclooctatetraene is lower than the A factors for addition to octene-1 and cyclohexadiene-1,3 when allowance i s made for the s t a t i s t i c a l factor of eight in the case of cyclooctatetraene. It has been observed that addition to cyclohexene and trans-octene-4 proceeds too slowly to be detected and a low A factor has been postulated to 39 account for this fact. As the double bonds of cyclooctatetra-ene are almost isolated, i t is possible that the A factor should be compared with that of a cyclic d e f i n e . 4. Abstraction The A factor and activation energy for abstraction from cyclooctatetraene are subject to large limits of error which do not permit any distinction between this compound and octene-1. However, i t is interesting to discuss these values as they stand. A high activation energy for abstraction from cycloocta-tetraene would be in agreement with the high value for abstrac-4 tion from ethylene by methyl radicals (10 kcal./mole). The length of a C 9 - H bond (1.086 A ) , 1 3 ^ is shorter than a sp^ 137 C o - H bond (1.108 A*). Consequently a higher dissociation sp-3 energy for the former would be predicted. However, this reason-ing would predict a value for the activation energy for abstrac-tion from cyclooctatetraene which is higher than the value for 18 abstraction from n-heptane (10.6 kcal./mole). Possibly a polar effect (similar to that suggested above for addition) 148 lowers the energy of the activated complex. Huyser has suggested a polar contribution to the transition state for abstraction from 21 substituted toluenes by the trichloromethyl radical. If the A factors for abstraction are divided by the number of equivalent hydrogen atoms in cyclooctatetraene and octene-1, then i t may be inferred that the "relative A factor" for cyclo-octatetraene is not significantly different from the value for octene-1. In view of the large limits of error which apply in the case of cyclooctatetraene, i t is by no means certain that this agreement is not purely fortuitous. 5. Polymerization Cyclooctatetraene vapour has been polymerized to a white transparent solid by a free radical mechanism. Initiation was 138 by a thermal activation process. Polymer has also been prepared in solution by heating cyclooctatetraene and sodium to 90 to 130°C. 1 3^ In this way compounds with molecular weights up to 1200 have been formed. compound octene-1 cyclooctatetraene 5.1*0.7 4.75*0.3 149 0. Cyclooctadiene-1,5  1. Abstraction compound 13*log(A 6/A-ft E g - ^ cyclooctadiene-1,5 5.3*0.4 6.8*0.7 octene-1 5.05*0.3 7.5*0.5 The energy of activation for the abstraction of hydrogen from cyclooctadiene-1,5 by the ethyl radical does not differ significantly from the value for octene-1. Similarly, the A factor is consistent with a s t a t i s t i c a l factor of four compared to the A factor for octene-1. In the following table, values of lS+logCk^/k^z) for cyclo-o octadiene-1,5 and octene-1 are compared at 60 and 100 C. compound temp. (°C) 1 3 * l o g ( k 6 / k 2 % > cyclooctadiene-1,5 60 0.89*0.07 octene-1 60 0.13*0.03 cyclooctadiene-1,5 100 1.36-0.07 octene-1 100 0.65*0.03 If the values for cyclooctadiene-1,5 are reduced by 0.6 (to allow for the s t a t i s t i c a l factor of four) and compared with the values for octene-1 in the light of the limits of error, then i t is observed that the difference in reactivity of these com-pounds is just significant at the 5% probability level. This difference is very small and may arise from minor energetic differences in the two molecules or the radicals derived from 150 them by abstraction. 2. Addition Addition of the ethyl radical to cyclooctadiene-1,5 was not detected. From an inspection of table XXII, i t may be concluded that the rate of addition to cyclooctadiene-1,5 i s slower than to octene-1. Slow addition is normal for a 1,2-39 disubstituted ethylene, other examples being cyclohexene, 39 trans-octene-4 and cyclohexadiene-1,4. It has been suggested that a low A factor is responsible for the low reactivity towards 39 addition of this class of substrate. P. A l l y l Alcohol 1. The formation of pentene-1 Pentene-1, observed in the reaction products from a l l y l alcohol, is probably formed by the reactions, C*2H5 + CH2=CH-CH2OH —> C2H -CH -CH-CH OH C2H5-CH2-CH-CH2OH —> C2H5-CH2-CH=CH2 + OH* The quantity of pentene-1 observed was very small at a l l except the highest temperature, and for this reason no correction was applied. In a series of experiments on a l l y l acetate an analogous reaction has been observed, 1 4 1 C0H* + CH =CH-CH -0-C0-CH_ > C0H -CH0-CH=CH0 + C0n + CH* 2 5 2 2 3 2 5 2 2 2 3 Carbon dioxide was found among the products and estimated by the method of gas chromatography. The subsequent reactions of 151 the methyl radicals produce methane and propane which have been detected by the same technique. 2. Abstraction and addition Values of k^/k^ observed in experiments on a l l y l alcohol were subject to some fluctuation. For both abstraction and addition, i t was found that the scatter of points about the straight line was considerably reduced by the use of the average value for k 3/k £ = 0.134*0.01. compound reaction 13+log(Ar/A2^) E r-%E 2 a l l y l alcohol abstraction 5.4*0.2 7.6*0.3 octene-1 abstraction 5.05-0.3 7.5-0.5 a l l y l alcohol addition 5.7*0.2 7.75*0.35 octene-1 addition 5.5*0.1 7.6*0.2 The limits of error of the Arrhenius parameters do not permit any distinction between the reactivities of a l l y l alcohol and octene-1 towards either abstraction or addition. However, a comparison of individual values of the rate constants for abstraction and addition is a more sensitive test. In the following table the logarithms of the rate constants for addition and metathesis with a l l y l alcohol are compared with the corres-ponding values for octene-1, at 60 and 100°C. 152 Abstraction compound a l l y l alcohol octene-1 a l l y l alcohol octene-1 temp. ( C) 60 60 100 100 13+log(k 6/k 2 2) 0.39*0.06 0.13*0.03 0.92*0.06 0.65*0.03 Addition compound a l l y l alcohol octene-1 a l l y l alcohol octene-1 134-log(k7/k2*) 0.65*0,08 0.49*0.04 1.20*0.08 1.02*0.04 temp. ( C) 60 60 100 100 It is observed that the rates of addition and metathesis with a l l y l alcohol are significantly higher than the corres-ponding values for octene-1 at both 60 and 100°C. The dif-ference in reactivity i s , however, a small one. As the induc-tive effect of the hydroxyl group should activate the molecule towards addition, i t must be concluded that the influence of this group i s considerable mitigated by the distance from the reaction centre. 153 Q. A Kinetic Study of the Metathetical and Addition Reactions  Characteristic of A l l y l Polymerization  1. Introduction A l l y l polymerization owes i t s distinctive character to a delicate balance between the rates of two competing reactions; addition and metathesis. Each of these alternatives involves the same reactants, a growing polymer radical, vinylic in nature, and an a l l y l i c monomer molecule: m! + CH?=CH-CH X — > M.-CH -CH-CH X addition M" 4- CH =CH-CH0X > M.H 4- CH =CH-CHX abstraction J 2 2 j 2 Addition forms another vinylic polymer radical, equal in reac-t i v i t y to i t s parent, and is thereby a step in the propagation of polymerization. Metathesis produces an a l l y l i c radical which is stabilized by resonance and has a reactivity decisively lower 142 than the vinylic radical. The a l l y l i c radical i s characteris-t i c a l l y too unreactive to add to the monomer molecule, and so 143 cannot propagate the chain. Indeed, i t may terminate the chain by combining with a growing polymer radical or i t may be removed by dimerization. In either case, metathesis results in both structural and kinetic chain termination, whereas addi-tion is the essential reaction of propagation in both a l l y l and vinyl polymerization. The experimental evidence for these views has been derived largely from kinetic studies on the polymerization of a l l y l acetate, initiated by benzoyl peroxide (C). Significant 154 observations i n c l u d e 1 4 4 (a) very inefficient catalysis, (b) a low degree of polymerization, insensitive to changes in [c]Q> (c) constancy of -d[MJ/d[c] during a given experiment. Bartlett 138 • and Altschul concluded that the unreactive radical CH^CH-CH-O-CO-CH^  was formed by metathesis, and termed this reaction "degradative chain transfer". Bartlett and Tate 1 4"* established that the oC-methylenic group i s the major site for metathesis by showing that when CH2=CH-CD2-0-C0-CH2 was polymerized, both -d[M]/d[c] and the degree of polymerization increased propor-tionately in relation to their values for normal a l l y l acetate, in accordance with the greater strength of the C-D bond. The ideal a l l y l monomer for this study is one which reveals most clearly the competition between metathesis and addition. Certain a l l y l monomers are unsuitable because they display either (a) vinylic reactivity, (b) effective chain transfer, or (c) radical displacement reactions. Thus; (a) the chlorine atom in a l l y l chloride makes the double bond 146 so reactive that a l l y l i c radicals can add to i t ; (b) meta-thesis with the acetoxy group of a l l y l acetate produces a radical reactive enough to add to the monomer; ' (c) displacement of the (CH^^C-COO radical from a l l y l trimethyl acetate by the polymer radical leads to structural chain termination.^ 4 7 A l l y l alcohol is suitable for this study because the hydroxyl group i s neither reactive in i t s e l f nor does i t confer abnormal reactivity upon the double bond. ^ y Thus a l l y l alcohol can be polymerized very slowly by peroxidic catalysts, but only an o i l with a degree of polymerization of five is obtained, and fresh catalyst must be added frequently to the system. 150,151 -j^g low reactivity makes the direct study of a l l y l polymerization d i f f i c u l t . Here the simple radical C2H^ has been chosen to attack the monomer and the reaction has been studied in the gas phase. In this way i t has been possible to avoid the variable influences of chain length and configuration of the polymer radical, and other problems arising from interactions in the liquid phase. A l l y l polymerization owes i t s distinctive quality to the restriction of the values of k /k £ to a narrow range of about P f 2 to 20. In this study i t has been found that k^/k^ = 1.8 for a l l y l alcohol at 60°C, but this ratio is relevant to the polymerization of a l l y l alcohol only i f k^/k^^k^/k^. This equality w i l l be j u s t i f i e d in the following sections. k k 2. The relationship between p and 7 In this section i t w i l l be shown that a simple relation-ship exists between k^ and k^, and, in fact, k ^ 2k_ at 60°C. P 7 Values of k^ for a l l y l alcohol and vinyl acetate may be calculated using the value of k 2 measured by Shepp and Kutschke k 2 = 5.06xl0' 1 0 exp(-2000*1000)/RT cm3 mol." 1 s" 1. Values of ky are compared with k^ for vinyl acetate at 60°C, and for this monomer, 156 k = 1.8 P k ? a l l y l alcohol: k7 = 2.2x10" •18 3 cm i -1 mol. s" 1 71 vinyl acetate: k7 = 3.5x10" •18 cm3 mol. 1 s" 1 vinyl acetate: 1"* 2 k P = 6.3x10" •18 3 cm mol. s"1 Vinyl acetate has been introduced because i t resembles a l l y l alcohol both in i t s reactivity towards the ethyl radical, and also in degree of resonance stabilization and electron donor power in polymerization. The correlations of the rate constants for the addition of the ethyl and polyvinyl acetate radicals may be recalled at this stage. (Figure 12.) The q- £. values of a l l y l acetate were used to calculate an approximate value for (1/r^) for a l l y l alcohol. The points were observed to l i e close to a line of unit slope. When the correlation was repeated for the ethyl and polyacrylonitrile radicals, only acrylonitrile showed a marked deviation and this was explained in terms of the considerably different q and £ values of acrylonitrile compared with the values for the other monomers. As the ethyl and polyvinyl acetate radicals are much more nearly matched in reactivity, i t seems reasonable to assume that the point for a l l y l alcohol would l i e close to the straight line of figure 12. This correlation may be expressed in the form, 157 k 2 1 P V a = ( c o n s t ) x k7 where ^ l ^ 3 is the rate constant for the addition of the poly-vinyl acetate radical. For = vinyl acetate, the term on the l e f t hand side becomes k„„ or k for vinyl acetate and this is equal to 1.8 22 p J n k P v a<=» 2 k, P 7 As the polyallyl acetate, and hence the polyallyl alcohol radical is very similar to the polyvinyl acetate radical in both resonance stabilization and polarity, i t is reasonable to propose the approximate relationship: k 2 ] P a a <» 2 k ? In the case of = a l l y l alcohol, the expression becomes, k paa ^ 2 k 4 x l 0-18 c m 3 m o l # - l s - l a t 6 0°c. P 7 3. The relationship between k7^ k6 and kp/ kf. In support of the proposition that k^/k^ ^ k^/k^, for a l l y l alcohol, the equation of Bamford, Jenkins and Johnston 7 ft w i l l be employed, log k g = log k,. -3-cCCf 4- ft As C i s zero for the ethyl radical, log k ? = log k'T + f$A log k 6 = log k'T + /3K where the subscripts A and M refer to addition and metathesis respectively. For the reactions of the polyallyl alcohol radical 158 log k p = log k'lr 4- O^ CT 4- |3A log k = log k'V + 4- /5M It therefore follows that, Since oC is a measure of the intrinsic polarity of the reaction, which is small in each case, i t follows that the difference is very small. As & for the -CtL^ COH) group is very small, the product (cf^ - oC~M)0' is negligible. The relationship k p/k^<» k^/k^ is therefore j u s t i f i e d and the latter ratio may be expected to predict the behaviour of a l l y l alcohol in poly-merizing systems. k k 4. The application of 6 and 7 to the polymerization  of a l l y l alcohol High polymer is readily formed from both vinyl acetate and methyl acrylate by the action of a trace of free radical i catalyst; whereas a l l y l alcohol is so unreactive that Staudinger originally believed that no polymer could be obtained from this monomer.1^4 This reluctance to polymerize is not due to the low reactivity of the double bond of a l l y l alcohol. It i s clear from the following rate constants, and from the relationship k p 2 k ? that the double bond of vinyl acetate is only slightly more reactive, methyl acrylate: vinyl acetate: a l l y l alcohol: .152 .153 k 7 = 12.4xl0" 1 3 exp(-8800/RT) cm3 mol." 1 s k p = 4.0xl0" 1 3 exp(-7300/RT) cm3 mol." 1 s k = 1.7xl0" 1 3 exp(-7100/RT) cm3 mol." 1 s The essential difference is the presence of a site for rapid metathesis in a l l y l alcohol, which causes degradative chain transfer to dominate the polymerization. No such site exists 71 in vinyl acetate and i t s polymerization proceeds unchecked by significant chain transfer. The number average molecular weight of polyallyl alcohol may be estimated from the kinetic results. This quantity is given by k^/k^, the ratio of the propagation and transfer constants,^ c and therefore approximately by k^/k^, which has the value of 1.9 at 100°C. This is considerable lower than the value of 5 reported for a mixture of 155 parts of a l l y l alcohol and 2 parts of hydrogen peroxide, held at 100°C for 116 hours with frequent replenishment of the hydrogen peroxide.^® However, in such a system we may expect extensive reactivation of the "dead" polymer by metathesis with the hydroxyl radicals present. By this means new reactive polymer radicals would be formed, and, in principle, the degree of polymerization could be increased indefinitely. The approximate equality of k^ and k ? for a l l y l alcohol explains the powerful inhibiting action of this substance upon the polymerization of certain other monomers. A l l y l alcohol inhibits the polymerization of butadiene so effectively that the corresponding copolymer must be prepared indirectly, 1"^ Reactivity in this system rapidly becomes transferred to the CH2=CH-CHOH radical, which is too unreactive to add to a l l y l alcohol or butadiene.7"* In contrast, a l l y l alcohol does form high copolymer with acrylonitrile; 1"' 1 clearly i t must be possible for the CH^CH-CHOH radical to add to the double bond of acrylonitrile. This difference in behaviour may be explained in terms of the lower-ing of the energy of activation for the addition by the contri-bution of ionic forms to the stability of the activated complex. The CH =CH-CHOH radical w i l l behave as a weak electron donor. 2 Acrylonitrile ( £. = -K».34xl0"1^ e.s.u.7-*) is strongly electro-p h i l i c ; i t is reduced at the dropping mercury electrode at the low half-wave potential of -1.68 volts, and is very readily polymerized by an anionic chain mechanism by such catalysts 156 as butyl lithium and a solution of sodium and naphthalene in tetrahydrofuran. 1"* 7 The polar effect should therefore be pronounced for acrylonitrile and very weak for butadiene ( 1. = -0.24xl0 - 1^ e.s.u.7"*). This situation closely resembles that of figure 13 where the apparently anomalous behaviour of acrylonitrile is also due to i t s electrophilic nature. 5. Conclusions Values of k^ and k^ are relevant to the study of the poly-merization of a l l y l alcohol in such varied aspects as the 161 magnitude of the propagation constant, the competition between propagation and chain transfer, the degree of polymerization, and propagation and inhibition in copolymerization. In each case the observed behaviour of the propagating system is con-sistent with predictions based upon the values of and k^. 6. Extension to other substrates Values of the addition and abstraction rate constants at 60°C are l i s t e d in table XXIX for several compounds. The predicted degree of polymerization is compared with the experi-mental value taken from the literature. R. The Interpretation of Reactivity in Terms of the Electronic  Properties of the Molecule  1. Introduct ion The attempts to correlate both the localization energy and the free valence of unsaturated molecules with the logarithm of the appropriate addition rate constant have been discussed in the Introduction. The purpose of this section is to present a method for the calculation of these quantities, and to assess c r i t i c a l l y the validity of a correlation of each with the measured values of the activation energy, or rate constant, for addition of the ethyl radical. The Huckel molecular orbital approach was adopted as being reasonably meaningful and simple in application. For unsaturated hydrocarbons, carbon 2p7T orbitals ( d> ) are involved. TABLE XXIX A comparison of predi cted and observed values of the degree of polymerization at 60°C 3/2 (cm ' mol. * s ^ ) substrate 10 1 3 k ?/k 2* i o 1 3 k 6/k 2* k ?/k 6 D.P. reference d i a l l y l ether 9.3 6.9 1.3 low 73, 155 octene-1 3.6 1.3 2.8 - -cis-crotononitrile 23- < 2.3 >10- not known 70 trans-crotononitrile 33- 0.3 >10- not known 70 acrylonitrile —1000- ~ o high high 73, 57d methacrylonitrile 830* low high high 70 2,3-dimethylbutadiene-l,3 470- low high high 96 eyelohexadiene-1,3** 520- 114- 4.6 3.8 105, 106 2,2,ljbicycloheptadiene 17. low high high 112 * Estimated from it s methyl a f f i n i t y . ** A l l values quoted are for 130°C. 163 Each molecular orbital (*>jfj) *-s expressed as a linear combination of the constituent atomic orbitals: n where n is the number of atoms contributing U electrons. It is required to find the best set of values for the c o e f f i c i -ents c j r > i.e., to find the set of coefficients which gives the most stable molecular orbital. This problem is solved by the application of the variation principle, which states that any wave function other than the correct one w i l l yield a value for 3 the ground-state energy algebraically higher than the true value. t = > E o It is therefore necessary to minimize £. with respect to each coefficient; TOr" = 0 This process yields n equations, 0 c l ( H 2 1 - S 2 1 £ ) 4- c 2 ( H 2 2 - S 2 2 0 + .... 4- ^ ( H ^ - S ^ O 0 C l ( H n f S n l ° + C 2 ( H n 2 " S n 2 ^ + • • • • 4* c (H -S € ) n nn nn 0 164 where H rs rs 5 fa *. d The term H^^ i s called the Coulomb integral and is represented by CC r r. The term H^, the bond integral, is represented by rs /3 r g. The term S is the overlap integral. For normalized atomic orbitals S =1 and to simplify the mathematics i t rr is assumed that S = 0 (r s). rs x The n equations now become, c 1 ( « u - O * c 2 / 3 1 2 + . . . . + c n ] 3 l n = 0 c x p 2 1 * c 2 < * 2 2 - £ ) - + C n P 2 n " ° n l * C2 h i + c ((* - I) = 0 n nn In this study the secular matrix was set up with the £_' s omitted: #11 21 h i 12 A In CC 22 P 2n Jn2 nn Values of the eigenvalues and the corresponding coefficients 165 (eigenvectors) were calculated on an "Alwac HIE" computer using a standard diagonalization program devised by Dr. P. N. Daykin of the British Columbia Research Council. 2. Molecular dimensions Values of (5 were calculated from the values of the / rs interatomic distance d . For several molecules, recently rs * J measured bond lengths and angles were available. In other cases the bond lengths used were based on the standard values quoted by L i d e . 1 6 3 These values of bond lengths and angles were used to calculate a l l values of d^ s using standard trigonometrical formulae. In the case of cycloheptatriene i t was assumed that the geometry of the molecule was that observed by Dunitz and 120 Pauling in the X-ray crystallographic study of the derivative CyHgMo(C0)3 and interatomic distances were calculated from the coordinates l i s t e d . As stated in section M, this molecular geometry does not appear to be consistent with the kinetic results and the purpose of adopting this model was to obtain further evidence on this point. 3. The calculation of oCrr and /3rs for 2p TT carbon orbitals Unless a carbon atom was attached to a heteroatom or a hyperconjugative group, oC rr w a s a s s u m e d t o D e zero. Prs w a s c a l c u l a t e d from the relation, P> = k S r rs rs Values of the overlap integral were expressed in units of P in which case k = 3.311. ,335 Values of S were obtained from the table of Mulliken, rs * Rieke, Orloff and Orloff. The values in this table were calculated for the Slater 2p"TT orbital of carbon taking the 1 fil effective nuclear charge as 3.09. The general equation for S is given by, TO S s rs = Sew cos O cos 6 ^ + S 77" TT sin 6 ^ sin 0 ^ c o s ^ 0^ and 62 are the angles between, the line joining the carbon atoms C and C , and the p orbitals of C and C respectively, r s r s r J ft" is the angle of twist looking along the C^-C^ bond. 4. Calculation of CCrr and /?rs for heteroatoms The approach of Fueno and his co-workers was adopted. The Coulomb integrals of heteroatoms were expressed as k p , , Expressed in terms of the standard bond integral X 1•3"/ adopted in this study, the Coulomb integral becomes 0.914 k ^1 335* V a l u e s °f k x f° r nitrogen and ethereal oxygen were taken as 1 in each case. A carbon atom adjacent to a heteroatom was assumed to have a Coulomb integral increment of 0.1 k x ^ (0*0914 k x 335) < As suggested by Fueno, vinyl acetate was treated as a conjugated system of three atomic orbitals, i.e., as vinyl alcohol, with a value of 2 assigned to the electronegativity parameter for the ethereal oxygen to allow for the large electron-withdrawing character of the acetyl group. 167 Values of S and S_ „ were obtained from the tables of C-0 C-N Mulliken, Rieke, Orloff and O r l o f f . 1 6 0 Fueno has adopted a s t n e value of the overlap integral for the C-0 bond in vinyl acetate and the C=N bond in acrylonitrile. These standard values were used in this study. In each case, >^ was assumed to be proportional to the overlap integral and values of /3 for the overlap of non-adjacent 2pTT" orbitals could thus be calculated. 5. Hyperconjuration The hyperconjugation parameters l i s t e d by Streitwieser were 3 Id adopted for the methyl group (conjugation model). The values l i s t e d were converted to the units of this study ( fi^ 3 3 5 ) * For the system, C(1)" C(2) = H 3 ° r C(1)" C(2) the following values were adopted: Coulomb integral bond integral CC 1 ] L = -0.0914 fi = 0.7615 = -0.0914 |3 2 3 = 2.7420 OCHH = - 0 ' 4 3 7 0 Molecular dimensions, secular matrices, eigenvalues and eigenvectors are tabulated in Appendix G. 168 6. The calculation of free valence The free valence index F is defined as r F = 1.732 - N r r where N r is the sum of the orders of a l l 77 bonds joining the atom r. The 7? bond order is given by, p = £.n. c. c. rs j j j r js in which n- is the number of electrons in the j*"* 1 molecular orbital. Values of F are shown in table XXX. r 7. The calculation of atom localization energy The atom localization energy (I<r) is defined as the energy required to isolate an electron at position r from the remainder of the "fT system. L was calculated as follows: r The eigenvalues were calculated for the molecule and the total TT electron energy was calculated by putting two electrons in each of the lower (occupied) levels. The eigenvalues were recalculated for the residual TT system with a TT electron isolated on the carbon atom to which addition takes place. The electrons were assigned in pairs to the lowest levels and the odd electron placed in the highest occupied level. The energy of the TT system was again calculated. 169 TABLE XXX Comparison of the energy of activation for the addition of  the ethyl radical with the free valence at the reaction centre substrate E7"* E2 F. r octene-1 7.6*0.2 0.754 heptyne-1 8.8*0.4 0.749 2,3-dimethylbutadiene-l,3 4.5*0.2 0.808 2,5-dimethylhexadiene-2,4 6.6*0.3 C ( 2 ) 0.435 ti C(3) ° * 4 8 4 cyclohexadiene-1,3 5.2*0.3 0.615 cycloheptatriene 6.4*0.2 0.724 cyclooctatetraene 5.6*0.6 0.561 £2,2,l| bicycloheptadiene 7.0*0.1 0.732 benzene High 0.399 71 styrene 4.0*0.6 0.796 vinyl acetate7^* 6.8*0.4 0.774 73 vinyl butyl ether 6.1*0.5 0.838 a c r y l o n i t r i l e 7 3 3.7*0.6 0.860 . ... 70 cis-crotononxtrile 4.0*0.8 0.687 70 trans-crotononitrile 5.7-0.8 0.685 39 2,4,4-trimethylpentene-l 5.7*0.9 0.776 1 F I G . 14 C o r r e l a t i o n o f the energy of a c t i v a t i o n f o r a d d i t i o n with the f r e e valence at the r e a c t i o n c e n t r e . 171 TABLE XXXI Comparison of the energy of activation for the addition of the ethyl radical with the atom localization energy at the reaction centre substrate E7"* E2 ^localization i (at 100°C) * ' 1.335' (k Alocaliza  — r x —) energy k 2 % - n)i- p. .„> octene-1 7.6*0.2 1.025 1.947 39 2,4,4-trimethylpentene-l 5.7*0.9 1.339 1.906 2,3-dimethylbutadiene-1,3 4.5*0.2 2.687 1.693 2,5-dimethylhexadiene-2,4 6.6*0.3 1.018 1.791 II 2.136 cyclohexadiene-1,3 5.2*0.3 2.184 1.760 cycloheptatriene 6.4-0.2 1.828 1.583 cyclooctatetraene 5.6*0.6 1.112 2.014 [2,2,ljbicycloheptadiene 7.0*0.1 1.120 1.909 benzene High low 2.206 styrene 4.0*0.6 2.555 1.723 • , 71 vinyl acetate 6.8*0.4 1.312 1.824 73 vinyl butyl ether 6.1*0.5 1.205 1.750 73 acrylonitrile 3.7*0.6 3.000 1.762 cis-crotononitrile 7^ 4.0*0.8 1.75 1.847 trans-crotononitrile 7^ 5.7*0.8 1.75 1.850 '<2)« :(3)" 1 * 6 1 * 8 2 * 0 F I G - 1 5 172 F I G . 15 C o r r e l a t i o n o f the energy o f a c t i v a t i o n f o r a d d i t i o n with the atom l o c a l i z a t i o n energy a t the r e a c t i o n centre, AN TCN CCN VA VBE S DMB CHT CHD-1,3 TMP COT BCH Oc DMH(2) • a c r y l o n i t r i l e • t r a n s - c r o t o n o n i t r i l e • c i s - c r o t o n o n i t r i l e • v i n y l a c e t a t e • v i n y l b u t y l e t h e r • styrene • 2 , 3-dimethylbutadiene-l , 3 - c y c l o h e p t a t r i e n e - cyclohexadiene - 1 , 3 • 2 ,4>4-tnmethylpentene-l • c y c l o o c t a t e t r a e n e 2,2,1 b i c y c l o h e p t a d i e n e • octene - 1 • 2 ,5-dimethylhexadiene -2 ,4 ; DMH(3):- 2 ,5-dimethylhexadiene -2 ,4 ; e l e c t r o n l o c a l i z e d a t C ( 2 ) . e l e c t r o n l o c a l i z e d a t C(3). 1 * 6 1 - 8 2 - 0 L r (-yS) F I G - 1 6 173 F I G - 1 6 Correlation of the rate constant for addition (at 100°C) with the atom localization energy at the reaction centre. For key to abbreviations see figure 15 174 No attempt was made to change the resonance integrals in the radical from the values used in the molecule although there is undoubtedly a change of interatomic distances on radical addition. A value of the localization energy for heptyne-1 could not be calculated by the simple method employed in this study. Values of the atom localization energy are shown in table XXXI. These values are plotted against values of E^-^E^ in figure 15 and against values of lS+logCk^/k^ x 1/n) at 100°C in figure 16. n is the s t a t i s t i c a l factor. 8. Discussion Correlation with the free valence The correlation with the activation energy for the addition of the ethyl radical with the free valence i s shown in figure 14. Conjugated dienes and polyenes are represented by closed cir c l e s , and monoolefines and vinyl monomers by open circles. The f i r s t class is seen to l i e on a line of gradient -7.2 kcal./ mole, while the points for the second class are grouped with no obvious correlation. Although the correlation of the conjugated compounds may be fortuitous, i t i s interesting to note that the 23 gradient obtained by Sato and Cvetanovic, when converted to the same units, becomes -7.7 kcal./mole. The agreement i s quite good when allowance is made for the different bond lengths and different method of calculation used by these workers. 175 Two values of F r were calculated for 2,5-dimethylhexadiene-2,4 corresponding to the value for the terminal carbon atom of the diene system a n <* the value for the non-terminal carbon atom C^^« I t : i s observed that F r^2) F r ( 3 ) ' P r e d i c t i n S that the non-terminal position should be more reactive towards addition. This matter w i l l be examined further in the section on the atom localization energy which follows. Correlation with the atom localization energy Values of the atom localization energy are plotted against the corresponding values of E ^ - ^ i ^ in figure 15, and against 13+log(k ?/k 2* x 1/n) in figure 16. The information contained in these two figures is essen-t i a l l y the same, but, as shown in section C, values of the a c t i -vation energy obtained in this study differ slightly from those which would be obtained by the method of calculation used in previous investigations, although individual values of the addition rate constant are in reasonable agreement. This fact explains the apparent paradox that the correlation of log (k^/k^* x 1/n) and localization energy shows less scatter than does the corresponding correlation of Ey-%E 2 and localization energy. Several conclusions may be derived from these figures. (a) The geometry assumed for cycloheptatriene is almost certainly inaccurate. The planar conjugated triene is predicted to be more reactive towards addition than is experimentally 176 observed. (b) Cyclooctatetraene and acrylonitrile are more reactive than would be predicted from the atom localization energies of these compounds. This is in accord with the postulate that a polar contribution lowers the energy of the transition state in the addition of the ethyl radical to these compounds. (c) The atom localization energy at l n 2,5-dimethyl-hexadiene-2,4 is in better agreement with the kinetic results than is the value at c ^ • seems l i k e l y , therefore, that addition is at C(2)* With this assumption, 2,5-dimethylhexa-diene-2,4 s t i l l shows a deviation from this line. It is possible that the method of calculation of localization energy is not adequate in this, case where two methyl groups are attached to the reaction centre. (d) The gradient of the line in figure 15 is equivalent The value which may be derived from the correlation of Fueno 162 and his co-workers is -8 to -9 kcal. (e>) The correlations suggest that the reactivity of |^2,2,lj bicycloheptadiene towards addition may be adequately explained by the localization energy and that the release of strain is of minor importance. (f) From figure 15, Ey-%E for benzene is predicted to be 10 - 11 kcal./mole. to an effective value of 177 CONCLUSIONS The energy of activation for the addition of the ethyl radical to conjugated dienes and polyenes is a function of the atom localization energy, and the electron a f f i n i t y , of the substrate. The former quantity is normally more important as the ethyl radical is only a weak electron donor. However, the polar effect appears to be of major importance in the addition of the ethyl radical to cyclooctatetraene. The energy of activation for the addition of the ethyl radical in the gas phase i s , in general, linearly related to the energy of activation for the addition of the methyl, ethyl, polyvinyl.,acetate and polyacrylonitrile radicals in solution. This relationship may be predicted from the correlation of energy of activation and localization energy. In the case of acrylonitrile, deviations are observed as a consequence of the higher electron a f f i n i t i e s of the polymer radicals relative to the ethyl radical. A similar deviation i s to be expected for cyclooctatetraene. The A factor for addition of the ethyl radical (relative to the number of reactive sites in the molecule) is approxi-mately constant for a variety of structural types. Consequently, the question of a low A factor for addition to non-terminal defines requires further examination. 178 The results of this investigation demonstrate the importance of evaluating the energy of activation and the A factor as separate contributions to the reactivity of a substrate. r The successful interpretation of reactivity in terms of the atom localization energy of the substrate makes i t l i k e l y that further information w i l l be obtained by the combination of theoretical and experimental studies. APPENDIX A 1. Standard volumes of gas burette The volumes were measured by the standard technique of f i l l i n g with mercury which was then weighed. After assembly of the Toepler pump and gas burette, a sample of hydrogen was admitted to the gas burette and the pressure measured in each volume. The pressure ratios were consistent with the volumes as previously calculated. Volumes: A = 0.5133 mis. B = 1.219 mis. C = 3.613 mis. D = 9.76 mis. 2. van der Waal's corrections for butane 61b = nRT b correction not significant For butane: a = 14.47 (litres) atm. (moles) 2 = 1.10x10 9 (mis.) cms. (moles) 2 APPENDIX B Transmission of neutral density f i l t e r s F i l t e r N° 1 was a clear pyrex plate of 3 m.m. thicknes and the other f i l t e r s were made by depositing aluminium on pyrex. Transmissions were measured on a Cary Model 11 Spectro photometer. N° optical density I°/I 1 0.23 1.7 2 0.53 3.4 3 0.765 5.8 4 1.615 41. 181 APPENDIX C Table of Perkin Elmer columns and retention times Column J - S i l i c a gel pressure temp. retention time (p.s.i.) (°C) compound (minutes)(air=0) 12 80 carbon monoxide 0 ethane 1.4 ethylene 2.5 acetylene 6.5 butane 20. 12 110 ethane 0.8 ethylene 1.5 propane 2.5 propylene 6 butane 7.5 12 130 butane 5 12 150 butane 3.5 Column R - Polyethylene glycol 15 50 benzene 21 diethyl ketone 31 cyclohexadiene-1,4 26 [2,2,l]bicyclo-heptadiene 25 cyclohexadiene-1,3 23 butane 0.7 15 80 benzene 8 cyclohexadiene-1,4 11 diethyl ketone 14 reaction product from cyclohexadiene-1,4 28 reaction product from diethyl ketone 32 12 100 benzene 6.5 [2,2,1] bicyclo-heptadiene 7 diethyl ketone 7.5 toluene 13.5 cycloheptatriene 16 cyclooctatetraene 34 styrene 38 cyclooctadiene-1,5 44 APPENDIX C (Continued) pressure (p.s.i.) temp, I°ci compound Column R - Polyethylene glycol (continued) retention time (minutes)(air=0) 15 100 benzene diethyl ketone reaction product from cyclohexadiene-1,4 reaction product from diethyl ketone ethyl benzene Column B - di-2-ethylhexyl sebacate 12 12 50 100 Apiezon M (on firebrick) 8 100 butane pentene-}. a l l y l alcohol benzene diethyl ketone cyclohexadiene-1,4 reaction product from cyclohexadiene-1,4 reaction product from diethyl ketone diethyl ketone reaction product from diethyl ketone reaction product from cyclohexadiene-1,4 Molecular Sieve 5A 5 6.5 15. 17. 20.5 1.5 5 9 8.5 10 10 27 30 2 7 6 Retention times variable, depend on history of column. Order of elution: hydrogen oxygen nitrogen methane carbon monoxide 183 APPENDIX D Quantitative calibration of Perkin Elmer Vapor Fractometer for  mixtures of ethane and ethylene Ethylene was admitted to the apparatus, frozen out in the analysis line and any non-condensables were pumped off. The Ward s t i l l was set at -170°C and some ethylene was trans-ferred to the gas chromatograph for analysis. It was found to be pure. A sample of the ethylene was then transferred to the gas burette and measured. Ethane was purified and measured in a similar manner. Small samples of this standard mixture were analysed on column J at 12 p . s . i . inlet pressure and 80°C. The detector voltage was maintained carefully at 8.0 volts. Peak areas were measured by dividing them into elemental trapezia with a height of 0.01 mV. First standard mixture Pressure of ethane: 51.40 - 35.10 » 16.30 cms. Volume of ethane: 3.59 mis. Temperature of ethane: 21.8°C. Pressure of ethane 4- ethylene: 40.58 - 30.72 = 9.86 cms. Volume of ethane +• ethylene: 9.74 mis. Temperature of ethane 4- ethylene: 21.6°C. Molar ratio = 1.66 APPENDIX D (Continued) ethane peak ethylene peak area area (3xl0 3 attenua- area (3xl(P attenua- ratio minutes tion minutes tion C2 H6' / C2 H4 millivolts) value millivolts) value 111 64 156 64 1.74 837 16 479 16 1.75 645 16 722 8 1.78 491 16 520 8 1.79 456 8 511 4 1.79 617 8 696 4 1.78 359 8 409 4 1.76 Average area ratio - 1.77 Sensitivity to ethane 1.77 Sensitivity to ethylene 1.66 - 1.07 Second standard mixture Pressure of ethylene: Volume of ethylene: Temperature of ethylene: Pressure of ethane 4- ethylene: Volume of ethylene 4- ethane: Temperature of ethane 4- ethylene: Molar ratio 46.50 - 35.10 3.59 mis. 23.6°C. 59.80 - 35.10 3.59 mis. 24.5°C. 11.40 cms 24.70 cms C2 H6  C2 H4 = 1.15 185 APPENDIX D (Continued) ethane peak ethylene peak area area (3x103 attenua- area (3xl0 3 attenua- ratio minutes tion minutes tion . millivolts) value millivolts) value G2 H6 / L2 H4 426 32 343 32 1.24 657 16 530 16 1.24 509 16 826 1.23 499 8 790 4 1.27 485 8 383 8 1.27 Average area ratio = 1.25 Sensitivity to ethane 1.25 Sensitivity to ethylene 1.15 Average sensitivity ratio ! ' h a n e - 1.08 ethylene APPENDIX E Quantitative calibration of Perkin Elmer Vapor Fractometer for  mixtures of ethylene and acetylene The methods of purification, analysis and measurement of each compound were as described in Appendix D. Pressure of acetylene: 44.16 - 35.18 = 8.98 cms, Volume of acetylene: 3.613 mis. Temperature of acetylene: 21°C. Pressure of acetylene and ethylene: 54.36 - 35.18 = 19.18 cms, Volume of acetylene and ethylene: 3.613 mis. Temperature of acetylene and ethylene:22°C. True molar ratio — j ^ = 0.884 C2 H4 3xl0 3 minutes mil l i v o l t s acetylene peak ethylene peak area ratio* area on area on attenuation=4x attenuation=8x C2 H2 / L2 H4 678.5 446.4 0.756 791.4 513.2 0.767 1133. 741.2 0.760 1003. 666.2 0.749 840.6 549.7 0.761 834.7 550.7 0.754 747.6 490.0 0.759 1060. 701.6 0.752-* In calculating "area ratio", the area of the ethylene peak was multiplied by 2.01. APPENDIX E (Continued) Area ratio = 0.757*0.012 Sensitivity to ethylene _ 0.884 Sensitivity to acetylene ~ 0.757 188 APPENDIX F Quantitative calibration of Perkin Elmer Vapor Fractometer for  mixtures of benzene and cyclohexadiene-1,4 Standard mixtures of benzene and cyclohexadiene-1,4 were prepared by weighing out the pure components. Small quantities of these standard mixtures were injected into the gas chromatograph using column R at 50°C and 12 p.s . i . helium pressure. Peak area was measured as the product of peak height and peak width at half height. This method of area measurement was used in analyses of the reactant-product mixtures from experi-ments on cyclohexadiene-1,4. First mixture Molar ratio 19.8 Area ratios 20.3 19.8 19.8 Average area ratio 20.0 Sensitivity to CgHg 1.01 Sensitivity to Second mixture APPENDIX F (Continued) G6^8 Molar ratio = 5.71 C6 H6 Area ratios = 5.73 5.91 Average area ratio = 5.82 Sensitivity to C^ Hg Sensitivity to C 6H 6 = 1.02 These factors (1.01 and 1.02) are not significantly different from unity. 190 APPENDIX G Tables of molecular dimensions, secular matrices,  eigenvalues and eigenvectors Notes on the presentation of data in this section (a) Interatomic distances are quoted as values of d r g , the distance between the atoms r and s in Angstrom units. (b) The terms in the secular and diagonalized matrices have been multiplied by 10 4. Thus 1.0000 becomes 10000 and 0.0914 becomes 00914. (c) Diagonalized matrix (eigenvalues). High energy (unoccupied) molecular orbitals have negative values. Low energy (occupied) molecular orbitals have positive values. (d) The coefficients are tabulated in matrix form: c l l c12 c13 c l n c21 c22 c23" " " " c2n c n l cn2 cn3 cnn (e) The secular matrix for the "localized" molecule is derived from that for the true molecule by striking out the row and column corresponding to the atom at which the electron is localized. Octene-1 3 y a. Interatomic distances r s dj-s 1 2 1.335 1 3 2.461 2 3 1.506 b. Secular matrix 00000 10000 10000 -00914 01324 07615 00000 00000 01324 00000 07615 00000 -00914 27420 27420 -04570 c. Diagonalized matrix 26312. -10297. 8746. -31159. d. Coefficients .1306 .2487 .7177 .6372 -.6879 .7035 .0365 -.1746 -.7133 -.6404 .1244 .2561 -.0293 .1820 -.6842 .7056 e. Diagonalized matrix ("localized" molecule) -31135. - 1176. 25913. f. Coefficients ("localized" molecule) .1727 -.6854 .7074 .9631 -.0331 -.2672 .2065 .7274 .6544 2. 2,4,4-trimethylpentene-l a. Interatomic dist r 1 1 1 2 2 3 b. Secular matrix 00000 10000 01324 10000 -01828 07615 01324 07615 -00914 01324 07615 00993 00000 00000 00000 00000 00000 27420 c. Diagonalized matrix 1.335 2.461 2.461 1.506 1.506 2.608 01324 00000 00000 07615 00000 00000 00993 00000 27420 -00914 27420 00000 27420 -04570 00000 00000 00000 -04570 5" Ho \\v C* \ a-c = c . / 6 H 2 ances 2 3 4 3 4 4 28140. -10577. 7783. 24214. -30691. -31664. d. Coefficients .1583 .3109 .5079 .5078 .4257 .4257 -.6693 .6977 .0387 .0387 -.1765 -.1765 -.7247 -.5913 .1028 .1028 .2281 .2281 -.0000 .0000 -.5120 .5120 .4877 -.4877 -.0000 .0001 .4876 -.4878 .5121 -.5119 -.0416 .2588 -.4798 -.4795 .4853 .4855 e. Diagonalized matrix ("localized" molecule) -31615. 27488. -30691. 24214. - 2192. Coefficients ("localized" molecule) .2461 .2689 .0000 -.0000 -.9312 -.4812 .5176 -.4878 -.5120 .0223 -.4814 .5176 .4876 .5120 .0223 .4880 .4427 -.5119 .4877 .2568 .4879 .4427 .5121 -.4877 .2568 Heptyne-l \3 J L i C C = C // *H0 a. Interatomic distances rs 1 1 2 2 3 3 1.205 2.664 1.459 b. Secular matrix 00000 12118 03973 00000 12118 -00914 06622 00000 03973 06622 -00914 27420 00000 00000 27420 04570 c. Diagonalized matrix 26815. -12536. 10268. -30945. d. Coefficients .2252 .2669 -.6964 .7127 -.6806 -.6340 .0343 .1375 .7057 .6165 .0236 -.0812 .1748 .3230 -.6862 .7134 4. 2.3-dimethylbutadiene-l.3 C *~C \ / 3C C* / \ C 6 C • ^ 3 H 3s 164 a. Interatomic distances r s d r s 1 2 1.337 1 3 2.472 1 4 3.688 1 5 2.458 1 6 2.909 2 3 1.483 2 5 1.506 2 6 2.556 5 6 3.922 195 b. Secular matrix 00000 09999 01324 00728 09999 -00914 07615 01324 01324 07615 -00914 09999 00728 01324 09999 00000 01358 07615 01126 00530 00530 01126 07615 01358 00000 00000 00000 00000 00000 00000 00000 00000 01358 00530 00000 00000 07615 01126 00000 00000 01126 07615 00000 00000 00530 01358 00000 00000 -00914 00464 27420 00000 00464 -00914 00000 27420 27420 00000 -04570 00000 00000 27420 00000 -04570 c. Diagonalized matrix 28109. - 7929. -13784. 4651. 13202. 25299. -31372. -30973. d. Coefficients .1478 .2764 .2764 .1478 .4855 .4856 .4074 .4074 .5570 .4238 .4238 -.5570 .0123 .0122 -.1001 -.1001 .3841 -.5733 .5733 -.3840 -.0491 .0491 .1463 -.1463 .5906 -.3699 .3699 .5906 .0383 -.0383 .1138 -.1138 .4096 -.4801 -.4801 -.4096 .1735 .1735 .2676 .2676 .0537 -.1122 .1121 .0537 -.5128 .5128 -.4707 .4707 .0289 .1481 -.1482 .0289 -.4827 .4831 .4938 -.4942 .0126 .1161 .1160 -.0126 -.4839 -.4835 .5026 .5022 e. Diagonalized matrix ("localized" molecule) -12291. 27569. - 1969. -30968. 10992. 25220. -31349. f. Coefficients ("localized" molecule) 5. 2,5-dimethylhexadiene-2,4 " Rp C T v ¥ 3 C = C '3. H | E E C 8 a. Interatomic distances \ C 3. / 3 C 6 C = H 3 ' ° 196 .3985 -.7111 .5397 .0290 -.0491 -.1031 .1743 .2226 .2714 .1443 .4569 .5354 .3898 .4568 -.7790 -.0145 .5921 .0194 .0006 .2047 .0063 -.1156 -.1126 .0121 .4971 .4705 -.5163 -.4887 -.3749 -.6131 -.5781 .1038 .1601 .1828 .2821 .1116 -.0972 -.0461 .5571 -.4669 .5128 -.4297 -.1358 .1500 -.0286 .4709 -.4960 -.4822 .5079 r s d r s 1 2 1.337 1 3 2.472 1 4 3.688 1 5 1.506 1 7 4.950 1 8 4.250 2 3 1.483 2 5 2.459 2 7 3.850 2 8 2.882 5 6 2.600 5 7 5.124 5 8 5.149 b. Secular matrix -01828 09999 01324 00728 07615 07615 00033 09999 00000 07880 01324 01358 01358 00132 01324 07880 00000 09999 00563 00132 01358 00728 01324 09999 -01828 00099 00033 07615 07615 01358 00563 00099 -00914 01026 00033 07615 01358 00132 00033 01026 -00914 00033 00033 00132 01358 07615 00033 00033 -00914 00099 00563 01358 07615 00033 00033 01026 00000 00000 00000 00000 27420 00000 00000 00000 00000 00000 00000 00000 27420 00000 00000 00000 00000 00000 00000 00000 27420 00000 00000 00000 00000 00000 00000 00000 c. Diagonalized matrix - 8479. 27711. 29001. -13914. 13455. 24199. 2953. 24198. -31591. -30708. -31710. -30708. 00099 00563 01358 07615 00033 00033 01026 -00914 00000 00000 00000 27420 00000 00000 00000 00000 27420 00000 00000 00000 -04570 00000 00000 00000 00000 00000 00000 00000 00000 27420 00000 00000 00000 -04570 00000 00000 00000 00000 00000 00000 00000 00000 27420 00000 00000 00000 -04570 00000 00000 00000 00000 00000 00000 00000 00000 27420 00000 00000 00000 -04570 d. Coefficients . 5 5 6 5 - . 3 8 9 3 - . 3 8 9 3 . 5 5 6 5 . 0 1 9 3 . 0 2 0 0 . 2 0 1 3 . 0 6 9 7 - . 0 6 9 7 T V 2 G 1 2 . 3 5 9 9 . 3 6 6 8 . 2 4 8 5 . 1 8 9 5 . 1 8 9 5 . 2 4 8 5 . 3 5 3 1 . 3 4 1 6 - . 3 8 8 4 . 5 7 0 1 - . 5 7 0 1 . 3 8 8 4 - . 0 3 7 0 - . 0 3 3 8 - . 3 1 0 6 - . 5 5 8 6 - . 5 5 8 6 - . 3 1 0 6 . 1 2 2 4 . 1 1 2 4 - . 0 0 0 2 - . 0 0 8 4 - . 0 0 7 9 - . 0 0 0 2 - . 3 3 7 9 . 3 5 2 8 . 5 2 3 2 . 4 1 0 5 - . 4 1 0 5 - . 5 2 3 1 - . 0 4 3 9 - . 0 4 6 1 . 0 0 0 3 . 0 0 4 4 - . 0 0 5 1 - . 0 0 0 3 - . 3 8 1 L . 3 7 4 3 . 1 7 9 2 - . 0 2 2 1 - . 0 2 2 1 . 1 7 9 1 - . 3 4 0 3 - . 3 3 8 5 . 0 0 0 5 . 0 0 1 9 - . 0 0 7 8 . 0 0 1 2 . 4 8 6 3 - . 4 8 9 4 - . 1 8 7 1 . 0 3 9 4 - . 0 3 9 4 . 1 8 7 1 . 3 3 9 7 . 3 3 7 4 - . 0 0 1 1 . 0 0 7 8 - . 0 0 1 9 - . 0 0 0 3 - . 0 0 0 6 - . 0 0 0 7 . 0 2 0 0 . 0 1 9 3 - . 1 3 5 4 - . 1 4 0 3 - . 1 4 0 3 - . 1 3 5 4 - . 3 6 6 8 - . 3 5 9 9 . 3 0 5 7 . 3 1 1 6 - . 3 1 1 6 - . 3 0 5 7 . 3 4 1 6 . 3 5 3 1 . 2 8 8 4 . 2 7 9 0 . 2 7 9 0 . 2 8 8 4 . 0 3 3 8 . 0 3 7 0 . 1 0 8 7 . 0 9 9 2 - . 0 9 9 2 - . 1 0 8 7 . 1 1 2 4 . 1 2 2 4 . 1 8 6 1 . 1 7 1 0 . 1 7 1 1 . 1 8 6 2 . 3 8 4 7 - . 3 7 0 5 - . 3 2 2 1 . 3 3 6 2 . 3 6 6 7 - . 3 5 3 1 . 0 4 6 1 . 0 4 3 9 - . 1 5 9 9 - . 1 6 8 0 . 1 6 8 0 . 1 5 9 9 - . 3 4 1 4 . 3 4 9 5 - . 3 6 3 2 . 3 5 6 7 - . 3 2 5 4 . 3 3 3 1 - . 3 3 8 6 - . 3 3 9 9 . 3 4 5 3 . 3 4 3 5 . 3 4 3 6 . 3 4 4 9 . 0 0 0 4 . 0 0 0 6 - . 5 1 0 2 . 5 1 3 4 - . 0 0 0 4 - . 0 0 0 7 - . 3 3 7 6 - . 3 3 9 8 - . 3 4 3 2 - . 3 4 0 9 . 3 4 1 1 . 3 4 3 3 . 4 8 9 1 - . 4 8 6 6 . 0 0 0 6 . 0 0 0 8 - . 5 1 3 1 . 5 1 0 5 e. Diagonalized matrix (electron localized at a terminal carbon atom of the conjugated system) 2 8 3 4 5 . - 1 2 3 9 9 . 1 1 4 8 9 . 2 5 3 8 2 . 2 4 1 9 9 . - 2 1 0 6 . 2 4 1 9 8 . - 2 9 8 0 5 . - 3 0 7 0 8 . - 3 1 6 5 0 . - 3 0 7 0 9 . i—1 vO co f. Coefficients (electron localized at a terminal carbon atom of the conjugated system .0825 .1843 .3180 .0495 .0359 .4990 .5038 .0412 -.0299 .4157 .4197 -.3845 .7038 -.5583 -.0022 -.0054 -.0401 -.0420 .0078 .0188 .1404 .1472 -.4982 -.6758 -.4187 .0310 .0215 .1175 .1239 .0530 .0367 .2006 .2116 .0608 .0232 -.0124 .5202 .5162 -.0532 -.0412 .4762 .4726 -.0487 -.0377 -.0082 -.0082 -.0002 -.3553 .3684 .3691 -.3546 -.3386 .3512 .3518 -.3379 .7690 -.1070 -.5871 -.0030 -.0033 .0147 .0136 -.0335 -.0366 .1635 .1514 .0047 -.0047 -.0003 -.3644 .3593 -.3582 .3657 -.3474 .3425 -.3414 .3485 .0437 -.0009 .0024 -.4784 -.4783 -.0083 .0014 .5198 .5197 .0090 -.0015 -.0034 -.0048 .0011 .3813 -.3753 -.3083 .3078 -.4000 .3937 .3234 -.3229 .0101 -.0433 .2589 .0043 .0037 -.4783 -.4805 -.0044 -.0037 .4843 .4866 .0072 -.0064 .0005 .3044 -.3118 .3796 -.3770 -.3193 .3270 -.3982 .3955 g. Diagonalized matrix (electron localized at a non-terminal carbon atom of the conjugated system) -31572. -10595. 28260. - 2344. 24199. 7909. 24196. 27445. -30708. -31674. -30707. h. Coefficients (electron localized at a non-terminal carbon atom of the conjugated system) .2090 -.0198 .1314 -.4105 -.4105 -.2463 -.2539 .4168 .4169 .2501 .2578 -.0411 .6712 -.6953 -.0001 -.0022 -.0384 -?0385 .0003 .0099 .1749 .1750 .1008 .1609 .2992 .1729 .1607 .4788 .4797 .1444 .1342 .3999 .4007 .9237 -.0652 -.1062 -.0205 -.0206 .0026 .0024 -.2529 -.2542 .0315 .0292 .0001 -.0085 -.0004 -.5109 .5126 .0105 .0036 -.4870 .2886 .0100 .0035 -.1073 -.7190 -.5842 .0244 .0175 .1035 .1036 .0536 .0384 .2274 .2276 .0004 -.0001 -.0000 -.0049 .0020 -.5118 .5119 -.0047 .0019 -.4878 .4879 .2508 -.0238 -.0869 .4884 .4911 -.1690 -.1663 .4183 .4206 -.1447 -.1424 .0004 -.0073 .0011 .4878 -.4880 -.0018 .0028 -.5117 .5119 .0018 -.0030 -.1301 -.0353 .2227 .2512 .2506 -.4113 -.4070 -.2541 -.2536 .4161 .4118 -.0011 -.0001 -.0001 .0066 .0020 .4880 -.4877 -.0069 -.0021 -.5120 .5116 201 6. Cyclohexadiene-1,3 C / \ 8 H = C <o C * I I >r H == Cs C3 2 \ // C a. Interatomic distances r s d rs 1 2 1.337 1 3 2.461 1 4 2.880 1 5 2.589 1 6 1.506 2 3 1.483 2 5 2.911 2 6 2.489 5 6 1.540 b. Secular matrix 00914 09999 01324 00563 01026 07615 00000 00000 09999 00000 07880 01324 00530 01291 00000 00000 01324 07880 00000 09999 01291 00530 00000 00000 00563 01324 09999 -00914 07615 01026 00000 00000 01026 00530 01291 07615 -00914 07218 27420 00000 07615 01291 00530 01026 07218 -00914 00000 27420 00000 00000 00000 00000 27420 00000 -04570 00000 00000 00000 00000 00000 00000 27420 00000 -04570 c. Diagonalized matrix - 8101. 31059. -13798. 22182. 4113. 14540. -28235. -34556. d. Coefficients .5605 -.3995 -.3994 .5604 .1944 .1364 .1364 .1944 .3936 -.5806 .5806 -.3936 -.1546 -.0568 .0567 .1545 .5563 .3991 -.3990 -.5563 -.3545 -.5668 -.5668 -.3546 .1496 -.0242 -.0242 .1497 .1080 -.0204 .0204 -.1080 .0207 .0207 -.1610 -.1610 .5278 .5278 .4062 .4062 -.0284 .0284 .0844 -.0843 .4802 -.4802 .4922 -.4922 .0534 -.0534 .1686 -.1686 .1317 .1317 .1889 .1889 -.4513 -.4512 .5229 .5228 .5155 -.5155 -.4713 -.4714 e. Diagonalized matrix ("localized" molecule) 29995. -12237. - 1703. -34223. -27666. 12280. 21672. f. Coefficients ("localized" molecule) .0716 .1191 .2002 .5770 .4943 .4578 .3921 -.3965 .7136 -.5549 -.0415 -.0115 .1483 .0413 -.7784 .0676 .6039 -.0163 .0018 -.1559 .0170 .0100 .0184 -.1158 .5459 -.4833 -.5048 .4469 -.0332 .0341 -.1473 .4133 .4840 -.4907 -.5746 -.4797 -.6796 -.4764 .1485 .0126 .2417 .0205 -.0214 -.0929 -.1587 -.4173 .5362 -.4360 .5603 7. Cycloheptatriene a. Interatomic distances 203 120 ^ s 1 2 1.346 1 3 2.489 1 4 3.100 1 5 3.125 1 6 2.518 1 7 1.511 2 3 1.449 2 4 2.551 2 5 3.176 2 6 3.136 2 7 2.550 3 4 1.382 3 5 2.519 3 6 3.095 3 7 3.130 4 5 1.404 4 6 2.458 4 7 3.120 5 6 1.340 5 7 2.562 6 7 1.544 b. Secular matrix -00914 09834 01291 00364 09834 00000 08278 01126 01291 08278 00000 09271 00364 01126 09271 00000 00331 00298 01192 08940 01192 00331 00364 01358 04952 01600 00487 00487 00000 00000 00000 00000 00331 01192 04952 00000 00298 00331 01600 00000 01192 00364 00487 00000 08940 01358 00487 00000 00000 09933 01600 00000 09933 -00914 04713 00000 01600 04713 -00914 27420 00000 00000 27420 -04570 c. Diagonalized matrix -15087. 26829. - 6704. 10552. -11521. 17470. 2987. -30924. 204 d. Coefficients .2573 -.3978 .4840 -.5154 .4487 -.2726 .0010 -.0025 .1989 .1636 .1291 .1337 .1706 .2030 .6857 .5988 -.4860 .1868 .4731 -.4290 -.2498 .5086 -.0003 .0033 -.4289 -.5455 -.2469 .1851 .4965 .4201 .0066 .0120 -.4446 .5554 -.2141 -.2176 .5073 -.3648 -.0249 .0983 -.1900 -.3523 -.4718 -.4985 -.4098 -.2369 .2383 .2965 -.4778 -.2235 .4426 .4498 -.1879 -.5002 .0518 .1878 .1095 -.0017 .0044 .0036 .0011 .0997 -.6853 .7130 e. Diagonalized matrix ("localized" molecule) f. Coefficients ("localized" molecule) .2634 .4673 .5508 .4866 .2960 -.1790 -.2289 -.2192 .4601 -.5818 .5452 -.3195 -.0169 .0464 -.4665 .5485 -.1078 -.4707 .4966 .0074 -.0408 -.5082 -.5078 -.0575 .4650 .5052 -.0397 -.0870 .6313 -.0509 -.5737 -.0093 .5069 -.0127 -.1121 .0831 .0930 .1187 .1673 .2015 .7054 .6357 .0348 -.0014 .0054 -.0001 .1048 -.6843 .7208 8. Cyclooctatetraene a. Interatomic distances 16877. -14525. - 9549. 7921. - 1461. 25857. -30602. r s d. rs 1 1 1 1 1 1 1 2 3 4 5 6 7 8 1.334 2.497 3.214 3.349 3.072 2.497 1.462 205 b. Secular matrix 00000 10000 00620 00000 00654 01159 00620 04430 10000 00000 04430 00620 01159 00654 00000 00620 00620 04430 00000 10000 00620 00000 00654 01159 00000 00620 10000 00000 04430 00620 01159 00654 00654 01159 00620 04430 00000 10000 00620 00000 01159 00654 00000 00620 10000 00000 04430 00620 00620 00000 00654 01159 00620 04430 00000 10000 04430 00620 01159 00654 00000 00620 10000 00000 c. Diagonalized matrix 17483. -13695. 6143. - 7315. 9235. -10543. 9235. -10543. d. Coefficients .3536 .3535 .3536 .3535 .3536 .3536 .3536 .3536 -.3536 .3536 -.3536 .3536 -.3536 .3535 -.3535 .3535 -.3535 -.3535 .3536 .3536 -.3536 -.3536 .3535 .3535 .3535 -.3536 -.3536 .3536 .3535 -.3535 -.3535 .3535 -.4887 -.4843 -.1059 .1242 .4886 .4843 .1059 -.1242 .4922 -.4794 .0879 .1419 -.4922 .4794 -.0879 -.1419 .1059 -.1242 -.4886 -.4843 -.1059 .1242 .4887 .4843 -.0879 -.1420 .4922 -.4794 v0879 .1419 -.4923 .4795 e. Diagonalized matrix ("localized" molecule) 15718. - 393. -12872. 7270. - 8415. 9235. -10543. f. Coefficients ("localized" molecule) .1889 .3875 .4360 .4382 .4256 .3875 .3175 -.9113 .0320 .4008 .0247 -.0769 .0320 -.0173 -.1116 -.3642 .4427 -.4889 .4654 -.3643 .2655 -.1035 -.3086 -.1405 .5557 .5165 -.3087 -.4512 -.1016 .3477 -.1837 -.5095 .4789 .3477 -.4746 -.2240 -.5000 -.4470 .0000 .2240 .5000 .4470 -.2240 .5000 -.4470 .0000 .2239 -.5000 .4470 9. [2.2.1 bicycloheptadiene Interatomic distances 108 Secular matrix 1 1 1 1 2 2 2 2 2 3 4 7 3 5 6 7 1.522 2.328 2.329 1.558 1.333 2.718 2.369 2.296 00000 10032 01493 02947 02005 00000 10032 00000 02947 01493 02005 00000 01493 02947 00000 10032 02005 00000 02947 01493 10032 00000 02005 00000 02005 02005 02005 02005 -00914 27420 00000 00000 00000 00000 27420 -04570 c. Diagonalized matrix 13854. -11486. 5592. - 8578. 25524. -30391. d. Coefficients .4820 .4820 .4820 .4820 -.1484 -.2209 -.5000 .5000 -.5000 .5000 T.0000 -.0000 -.5000 -.5000 .5000 .5000 -.0000 -.0000 .5000 -.5000 -.5000 .5000 .0000 .0000 .1295 .1295 .1295 .1295 .7140 .6505 .0306 .0306 .0306 .0306 -.6843 .7267 e. Diagonalized matrix ("localized" molecule) 10654. - 802. -10141. 25171. -30365. f. Coefficients ("localized" molecule) .2647 .6798 .6612 -.0851 -.1533 -.9546 .1194 .2697 .0057 .0414 .1057 T.7148 .6913 .0013 -.0065 .0767 .1088 .1056 .7245 .6680 .0406 .0303 .0332 -.6839 .7270 Benzene a. Interatomic distances 1^ 3 r s drs 1 2 1.397 1 3 2.420 1 4 2.794 b. Secular matrix 00000 09039 01457 00662 01457 09039 09039 00000 09039 01457 00662 01457 01457 09039 00000 09039 01457 00662 00662 01457 09039 00000 09039 01457 01457 00662 01457 09039 00000 09039 09039 01457 00662 01457 09039 00000 c. Diagonalized matrix 21654. -15826. 6920. - 9834. 6920. - 9834. d. Coefficients .4082 .4082 .4082 .4083 .4082 .4082 -.4083 .4082 -.4082 .4082 -.4083 .4083 -.5262 -.0575 .4688 .5262 .0574 -.4688 .5177 -.4802 -.0375 .5177 -.4802 -.0375 -.2375 -.5745 -.3370 .2375 .5745 .3370 -.2556 -.3205 .5762 -.2556 -.3205 .5761 e. Diagonalized matrix ("localized" molecule) 18086. -14127. 6920. - 9834. - 1044. f. Coefficients ("localized" molecule) .3338 .4905 .5440 .4905 .3338 -.2595 .5061 -.5941 .5061 -.2595 -.5000 -.5000 -.0000 .5000 .5000 .5000 -.5000 .0000 .5000 -.5000 .5668 -.0572 -.5925 -.0572 .5668 209 11. Styrene a. Interatomic distances r s d r s 1 2 1.397 1 3 2.420 1 4 2.794 1 7 1.480 1 8 2.465 2 7 2.492 2 8 2.888 3 7 3.774 3 8 4.250 4 7 4.274 4 8 5.145 5 7 3.774 5 8 4.958 6 7 2.492 6 8 3.816 7 8 1.337 b. Secular matrix 00000 09039 01457 00662 01457 09039 07913 01324 09039 00000 09039 01457 00662 01457 01258 00563 01457 09039 00000 09039 01457 00662 00166 00099 00662 01457 09039 00000 09039 01457 00099 00033 01457 00662 01457 09039 00000 09039 00166 00033 09039 01457 00662 01457 09039 00000 01258 00166 07913 01258 00166 00099 00166 01258 00000 09999 01324 00563 00099 00033 00033 00166 09999 00000 210 c. Diagonalized matrix 23130. -16461. 4298. - 8022. 6925. - 9838. -12485. 12451. d. Coefficients .4678 .5110 .4161 .3687 .0272 .0298 .3480 .2970 .3964 .3998 .3339 .3164 .4860 .4848 .0167 .0041 .3535 -.3370 .1431 -.1203 -.5127 .5138 .3293 -.3022 .3403 .3177 .4475 .4111 -.0269 -.0294 -.4761 -.4309 .3520 .3348 .1960 .1788 .4858 .4844 .3487 .3185 .3933 .3949 .2934 .2750 .5129 .5140 .0120 .0192 .2798 .2762 .3022 .4143 .0039 -.0031 .5231 .5557 .1627 -.1422 .5280 -.5489 -.0216 .0228 -.3849 .4734 e. Diagonalized matrix ("localized" molecule) 22620. -16254. 9517. -11234. 6920. - 9834. - 1734. f. Coefficients ("localized" molecule) .4574 .4055 .3757 .3668 .3757 .4055 .2122 -.4928 .4093 -.3645 .3510 -.3646 .4094 .1818 -.5068 -.1455 .3278 .5383 .3278 -.1455 -.4428 .5357 -.1500 -.3436 .5633 -.3438 -.1498 -.3385 .0000 -.5000 -.5000 -.0000 .5000 .5000 -.0000 -.0001 -.5000 .5001 -.0001 -.4999 .5000 .0000 -.0647 -.3526 .0197 .3676 .0197 -.3526 .7818 Vinyl acetate a. Interatomic distances d r s 1 2 1.335 1 3 2.333 2 3 1.360 b. Secular matrix 00000 10000 01075 10000 01828 09140 01075 09140 18280 c. Diagonalized matrix -10241. 6763. 23585. d. Coefficients .6732 -.7112 .2025 .7005 .5257 -.4826 .2367 .4668 .8521 e. Diagonalized matrix ("localized" molecule) - 2243. 22351. f. Coefficients ("localized" molecule) .9135 -.4068 .4068 .9135 212 13, Vinyl butyl ether \ /• 0 3 a. Interatomic distances r s d r s 1 2 1.335 1 3 2.333 1 4 2.700 2 3 1.360 2 4 1.923 3 4 1.360 b. Secular matrix 00000 10000 01075 00828 00000 10000 00914 09140 03708 00000 01075 09140 08226 09140 00000 00828 03708 09140 00000 27420 00000 00000 00000 27420 •04570 c. Diagonalized matrix -11343. 29354. 2974. 14425. -30841. d. Coefficients .6132 -.7287 .3039 .0059 -.0237 .1236 .2631 .4108 .6720 .5432 -.6584 -.2650 .6803 -.0485 -.1763 -.4186 -.5730 -.5030 .2810 .4056 .0015 .0357 .1515 -.6834 .7133 213 e. Diagonalized matrix ("localized" molecule) - 5270. 28953. 11728. -30841. f. Coefficients ("localized" molecule) .8263 -.5583 -.0019 .0747 .2217 .4012 .6879 .5627 -.5165 -.7103 .2444 .4111 .0362 .1514 -.6834 .7133 14. Acrylonitrile N **• % C 3 \ c = c i A. a. Interatomic distances 1*^ d rs 1 2 1.339 1 3 1.426 1 4 2.590 2 3 2.426 2 4 3.470 3 4 1.164 b. Secular matrix 00000 09933 08609 00545 09933 00000 01424 00060 08609 01424 00914 09261 00545 00060 09261 09140 214 c. Diagonalized matrix 18238. -13003. - 4402. 9221. d. Coefficients .4498 .6906 ,1806 .5367 .2920 .4726 .6075 .5678 .5769 .5105 .6364 .0408 .6161 -.1978 -.4398 .6228 e. Diagonalized matrix ("localized" molecule) -10287. 3387. 16954. f. Coefficients ("localized" molecule) .5949 -.7319 .3322 .7342 .3266 -.5953 .3272 .5980 .7316 15. Cis-crotononitrile «, H 3 N r \ * C C \ / c = c 3i 3 167 a. Interatomic distances d r s 1 2 1.520 1 3 2.527 1 4 2.912 1 5 3.631 (continued) 2 3 1.340 2 4 2.412 2 5 3.474 3 4 1.445 3 5 2.604 4 5 1.159 b. Secular matrix 00914 07450 01192 00530 00060 27420 07450 -00914 09933 01490 00060 00000 01192 09933 00000 08377 00545 00000 00530 01490 08377 00914 09032 00000 00060 00060 00545 09032 09140 00000 27420 00000 00000 00000 00000 -04570 c. Diagonalized matrix -31128. -12864. 8478. - 4700. 17444. 26425. d. Coefficients .6840 -.1793 .0343 -.0124 .0016 -.7062 .0390 .4888 -.6889 .4846 -.1833 -.1288 -.0939 .5215 .5661 .0069 -.5998 -.1973 -.0007 -.5902 .1298 .6552 -.4301 .1431 -.1483 .2047 .4001 .5695 .6462 -.1847 .7070 .2582 .1639 .1063 .0640 .6255 e. Diagonalized matrix ("localized" molecule) -30245. - 9973. 3353. 16633. 24803. f. Coefficients ("localized" molecule) .6833 -.0256 -.0049 .0004 -.7297 .0026 .5965 -.7320 .3289 -.0134 -.0112 .7340 .3338 -.5900 -.0388 -.0412 .3194 .5922 .7367 -.0533 .7289 .0512 .0458 .0310 .6804 16. Trans-crotononitrile a. Interatomic distances r s d r s 1 2 1.520 1 3 2.527 1 4 3.845 1 5 4.955 2 3 1.340 2 4 2.412 2 5 3.474 3 4 1.445 3 5 2.604 4 5 1.159 Secular matrix -00914 07450 01192 00132 00000 27420 07450 -00914 09933 01490 00060 00000 01192 09933 00000 08377 00545 00000 00132 01490 08377 00914 09032 00000 00000 00060 00545 09032 09140 00000 27420 00000 00000 00000 00000 -04570 217 c. Diagonalized matrix -31124. -12878. 8472. - 4699. 17519. 26365. d. Coefficients .6841 -.1790 .0317 -.0029 .0005 -.7064 .0368 .4897. -.6891 .4854 -.1834 -.1215 .0942 .5200 .5646 .0070 -.6022 -.1981 .0007 -.5895 .1296 .6544 -.4296 .1515 .1366 .2111 .4044 .5728 .6453 -.1695 .7093 .2563 .1582 .0895 .0528 .6287 e. Diagonalized matrix ("localized" molecule) -30246. - 9971. 3355. 16651. 24780. f. Coefficients ("localized" molecule) .6832 -.0283 .0049 -.0007 -.7296 .0047 .5963 -.7319 .3289 -.0240 -.0101 .7340 .3338 -.5903 -.0351 -.0258 .3208 .5935 .7369 -.0333 218 BIBLIOGRAPHY 1. A. F. Trotman-Dickenson, J. R. Birchard and E. 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