I. HYDROCARBON STRUCTURE AND BOND PROPERTIES Introductory Paper BY M. G. EVANS Received 27th July, 1951 In this general introduction I wish to refer to several points which I think may be the basis of some aspects of our discussion. In chemical kinetic studies one is frequently interested in the activation energy’ of some primary step involving the rupture of a particular bond : or one may be interested in relating the activation energy of some primary bimolecular step to the heat of the reaction. Such connections involve a knowledge of, or the measurement of, bond dissociation energies. In this connection I would recall that in certain classes of simple bimolecular reactions there is a close parallelism between the change in activation energy of the reaction and the change in heat of reaction or bond dis- sociation energy.Thus, for example, in the sodium flame reaction R-C1 + Na -+ R + Cl-Na+ (Activation energy E ) R-C1 + R + C 1 (Bond dissociation energy D) . It has been found that d E = dD. A change in the bond dissociation energy is closely paralleled by a change in the activation energy. Another example of such a parallelism was remarked upon by Steiner and Watson for the homopolar reaction involving hydrocarbons and halogen atoms : and attempts have been made to find similar correlations in reactions such as R-H + C1+ R + HCl, R-H+H 4 R + H , R-H + CH, -+ R + CH,. It may be that in the later part of this discussion we shall see how far such generalizations are possible in hydrocarbon reactions. But the point I wish to emphasize is that from the point of view of the energetics of primary reactions it is important that we have good values of bond dissociation energies.On the other hand, for all theoretical considera- tions of the factors influencing the electronic stability of molecules and radicals it is also necessary that careful measurements and definitions of bond dissociation energies should be made. We realize now that the energy change involved in rupturing a par- ticular type of bond, say a G-C bond or a C-H bond, is very dependent upon the molecular environment of that bond, and the range of energy changes with which we might be concerned with are shown in the following Table. Together with the term bond dissociation energy, which is the heat of a bond fission reaction, the term bond energy or bond energy term has been used.This is a quantity derived from heats of formation of A I2 INTRODUCTORY PAPER TABLE I Molecule I-I-- I CH3-H . . . C,H,--H . . . PhCH2-H . . CH,= CH-CH2-H - CC13-H . . . 101'0 98.0 77'5 76.5 89.0 Ph-Ph . . . . . CHS-CH, . . . . PhCH,-CH,Ph. . . . CH2= CH-CH2-CH2-CH = CH, Ph3C-CPh3 . . . . mole -I- =I I -76 molecules but we should be clear how bond energy term differs from bond dissociation energy. We can measure the heat of formation, say of hydro- carbons, from the elements in their normal standard states ; this is the therrnochemical quantity Qj" nC (solid)+ (n + 1)H2 --> CnHBnf2 We can in principle measure the heats of formation of hydrocarbons from the gaseous atoms C and H in the standard and electronically- defined state From the cycle Qfo.ncg + (2n + 2)Hg - C,H2n+2 QP. NCg + (2% + 2) H g Qp" t 1- -nL 1 1 4% + I ) D 9 c n H 2 n + 2 , nC (solid) + (n + I)H, QfO the two thermochemical heats are related, i.e., Qf" = nL + (n + I)D(H-H) + Qf". This is in principle only, because unfortunately the latent heat of vapor- ization L of carbon to a defined atomic state is not yet known with cer- tainty. On this basis we should find, for example, Qf(CH,) = 17-89 kcal. Qj(C,H,) = 20.24 kcal. Qf(CH,) = (L + 225.9) kcal. Qf(C,H,) = (2L + 332.2) kcal. The bond energy term is derived from the thermochemical quantity Qf. It has to do with partitioning the total heat of formation of the molecule from the atoms Qf" among the bonds in the molecule. For a homo- bonded molecule such a process is quite unequivocal.In CH, there is no doubt about the method of partitioning the heat of formation among the four identical bonds and so we obtain a derived quantity 4" = Qf/n for a homobonded molecule. For methane we can write qa = (L + z25.9)/4 = (L/4) + 56.5 kcal. When, however, a molecule contains different types of bonds, the par- titioning of Qja among the various types of bond is very uncertain. We think we can write, say, for ethane QF = 6q'(C-H) + I~'(C-C), but to go further involves us in assumptions. the p(C-H) in ethane is the same as qa(C-H) in methane when Thus we can assume that (2L + 332.2) = 6(L/4) + 56.5 + P(C--C) p(C-C) = (L/2) - 6.8 kcal. p(C-H) = (L/q) +- 56.5 kcal.,M. G. EVANS 3 or that the value of q"(C-C) in ethane is the same as p(C-C) in diamond when (2L + 332.2) = 6qa(C-H) f (L/2), p(C-C) = L / z kcal.4"(C--H) = (U4) + 55'4 kca1.2 and in some cases larger uncertainties than these can arise from our choice of assumption in partitioning the heat of formation among non-identical bonds. Bond dissociation energies have a perfectly definite meaning if defined as the heat of the reaction : R, - R, -+ R, + R2 - D(R1 - R2) under defined conditions; and this heat of reaction can be referred to the heats of formation of radicals and molecules D(Ri - R2) = Qf(Ri) + Qf(RJ - Qf(Ri - RJ. There are very few cases in which the heat of the reaction can be measured directly by therrnochemical or equilibrium measurements, and a number of ways have been used for evaluating the energy changes in reactions of the above kind.R .P U ( R - I ) k c d . ,40 145 ,so I55 FIG. I. One method which originated in the work of Polanyi and Butler and has been extended by Dr. Szwarc, identifies the activation energy of the reaction involving bond fission with the bond dissociation energy. The method involves the assumption that for a reaction of the type above there is no activation energy for the recombination of the radicals. Changes in bond dissociation energy of a particular bond, say a C-C bond (the A values in Table I), may arise from changes in the heats of formation of the radical Qf(R), or the molecule Qf(R-H), or Qj(R-R). Sometimes i t is possible to feel confident that changes in bond dis- sociation energy or heats of formation arise from some overwhelmingly large electronic effect.electrons are involved, such as the change in bond dissociation energy between P h . CH,-H and CH,-H. Here the difference in bond dis- sociation energy has been ascribed to the stabilization of the benzyl radical by the delocalization energy of the T electrons of the benzyl radical. This is particularly true in molecules where4 CH 3-H CH 3CII 2-H CH3 \CH-H CH ,/ tert.-Bu-€3 INTRODUCTORY PAPER I01 101; 103 f 3 97 97 94 89 89 86 In this case we can split up the electronic energy of the molecule E (Ph CH,) = z'E (C-H) + FE(C-C) + E , E (Ph CH,) = z'E (C-H) + pE(C-C) + E,, and, although one is aware that the energy contributions from the o(C-H) and 0 (G-C) will be different in the two molecules, one is neglecting these differences compared with the much larger contribution arising from the energy of the v electrons ; and indeed the broad successes of the molec- ular orbital treatment of T electronic structures has given great justifica- tion for this belief.Although a useful concept, and a word in common use, the term resonance energy is very difficult both from the theoretical and thermo- chemical points of view. The definition of resonance energy is implied in these equations : Qf- Q f = R or D(R,--R2) = Qf(R1) + R(Ri) + Qf(R2) + R(R2) - QfWl-R,) - R(Rl-R2) = Ds(R,-R2) + R(RJ + R(RJ - R(R1-Rz). I t involves the choice of a standard heat of formation Qf of a hypothetical molecule with localized bonds or standard bonds. Apart from increasing the heats of formation arising, say, from elec- tronic energy in the molecules or radicals, changes in bond dissociation energy may arise from steric effects between non-bonded groups. In- dications of this effect are given in the comparison : kcal./mole. kcal . /mole. D(CHa-H) . . I01 D(CHS-CH3) . * 87 D(Ph,G-H) . * 75 D (Ph 3C-CPh 3) . . I1 A1 = 26 The low bond dissociation in CC13-Br has recently been discussed by Szwarc in terms of the stability of the CCl, radical and the steric effects in the CC13-Br molecule ; and we are aware of the low heats of polymer- ization found in I : I-disubstituted vinyl compounds-perhaps we have too easily neglected these factors in our past work. Alkyl Radicals.-I would now like to turn to some points in connection with the alkyl radicals. Here our information on bond dissociation energies and heats of formation of radicals rests on thermochemical data, rates of pyrolysis, and Dr.Stevenson's work on appearance potentials. The connection between appearance potentials A and the thermo- chemical quantities we have been discussing can be illustrated by the energy diagram (Fig. 2). A = D(R1--R2) + m,) A = Qf(R2) + Qf(Ri) - Qf(Ri--Rz) = Qf(R2) + Qj(Ri) - Qf(Ri-R2) + TABLE 11 Molecule Value of D in kcal./mole from Appearance Potential Pyrolysis I IM. G. EVANS 5 and either from a knowledge of I(R,) from separate experiments or from an elimination of I(R,) by using two different reactions producing the same ion, heats of formation of radicals or bond dissociation energies can be obtained. In general the agreement obtained by this method and other chemical methods, say, pyrolysis, is very good.Let me illustrate this bp three examples. X = H ___- I01 97 89 86 € Br -- 67'5 64.0 62.5 60.0 1 A 101 97 94 89 Didance R,- R, 81.0 67.5 55'0 79.0 51.0 51.0 82.0 67.5 53.0 77'5 63'5 47'5 FIG. 2. There does appear t o be a small but disturbing discrepancy, however, in the series : CH3 >H-H CH3-H CH3-CH,-H CH, This discrepancy is illustrated in the following Table :- TABLE III* R Me . Et . iso-Pr . tert.-Bu . D(R ~ X) (Based on Work of Stevenson) (kcal.) D(K- X) (Based on Work of Polanyi and Butler) (kcal.) c1 81 79 77 74 * I am indebted to Dr. Skinner for this Table and for helpful discussions on this section. In other words the monotonic trend of bond dissociation energies in the sequence primary, secondary, tertiary, has been Iost in the halides, and the bond dissociation energy of the zso-propyl-X is slightly greater than6 INTRODUCTORY PAPER for ethyl.Now this is interesting, first from the experimental stand- point. Referring back to Fig. I, in which the activation energy of the Na flame reaction is plotted against the bond dissociation energy given by Polanyi and Butler, we see that the rate of reaction is very nearly identical for isopropyl and n-butyl and that this point falls off the curve using the Polanyi-Butler bond energy. It seems as though the Polanyi- Butler value of D(R-Cl) is too low ; on the other hand, I would suggest from the reactivity t h a t the value of D(iso-Pr-C1) of Stevenson is slightly too high. TABLE IV kcal. I Baughan, Evans and Skinner and Roberts Experimental values from appearance potential .Polanyi . D(R-H) . Et--H kcal. 7'0 (4.0) 4'0 Pr-H 1 sec.-Pr-H kcal. kcal. I - 1 7'0 _ _ ~ tert.-Bu-H kcal. 21'2 11.0 12'0 There is another very interesting point in connection with this series of radicals. The decreasing bond dissociation energy of the R-H bond has been attributed to the increasing stability of the radical arising from the increased stability of the free electron in hyperconjugation with the CH, group. Several attempts have been made to treat this : Baughan, Evans and Polanyi made a naive approach, using the method of bond eigenfunctions, and obtained values agreeing with the trend discussed above. Skinner and Roberts made a more careful estimate. using the Molecule CH3--H .CH3CHZ-H \C-H CH3 CH,/ CH3/ CH3\ CH ,-C-H TABLE V D (homo) kcal. (0) 4 7 I 2 D (ionic) kcal. (0) 38 69 86 method of Mulliken, and reachedvery similar conclusions. Theoretically, there seems to be no doubt about this effect, although a theoretical estimate of the value is very uncertain. An even more striking effect is revealed when we compare the heats of homopolar dissociation of these hydrocarbons with those heats for ionic dissociation leading to the formation of a carbonium ion. The work of Dr. Stevenson makes this comparison possible, and Table V shows the changes in these two heats referred to methane as zero. I would say that, from thetheoretical point of view, we are somewhat a t a loss to understand these results quantitatively. The difficulty is revealed in the very approximate treatment based on a consideration of the radicals as electronic structures of the type :M.G. EVANS 7 The electronic energy levels will be y-h/8---- p-@- Q-P--- 7-- p+P -- p+L)3 -4- $7f//S---”c+-- and the total mobile electron energies €or the radicals : CH3 CH3CH2 (CH 3) ZCH (CH 3) 3c 4 34 + P 54 + dYP 74 + d5/3 0 24’ + 2P’ 44‘ + 2 d z p ‘ 6q‘ + 2 1/Tp’, and for the ions where p and /3‘ are the exchange integrals in the radical and the ion re- spectively, and q and q’ the corresponding Coulombic integrals. This crude treatment gives the right sense of the trend in stability, and suggests that the ionization potential of the radical should decrease by : 3 4 - 2 4 ’ - ( 2 ~ ’ - ~ ) 54-4q’- d;(zp’-p) 7q-6q’- 1/3(zp’-p) But comparison with the experimental results leads to the conclusion that /3’ in the ion is much larger than /3 in the radical, and also that q‘ of the ion is greater than the value of q in the radical.In these crude approximations we are taking into an empirically esti- mated /3 the errors due to the approximations, and indeed we should not expect the same values of /3 and q to apply to two such cases. I do not know if any measurements have been made on the ionization potentials of polyene radicals but these would be of great interest from the theoretical point of view. These radicals all have a zero energy orbital as the highest filled level, and one would expect little change in ionization potential with structure as a result.* Steric factors and configuration in hydrocarbon reactions.-I would like to refer to the problems of configuration in the reaction of hydro- carbons.Some confusion seems to have arisen here ; and the following, I think, is the present position. The experimental observable quantities arising from a kinetic investigation are E and the temperature-independent factor A ; i t has been the practice over the last years to interpret A in terms of collision theory or in terms of the theory of the activated complex. The first method involves using a collision diameter which is in keeping with the kinetic sizes of the molecules involved, and introducing a steric factor P, such that PZ = A . The exact calculation of the temperature-independent factor on the basis of the activated complex theory is not possible ; and this method involves an intelligent guess at the structure and mode of motion of the activated complex.Temperature-independent factors have been discussed in terms of the entropy of formation of the activated complex; and the broad principle has emerged that both for reactions involving molecules and those involving radicals increasing complexity, which implies increasing restriction of motion in the associated activated complex, involves a decreasing entropy of activation or a decreasing A factor. * I am indebted to Dr. Longuet Higgins for discussions on this section. I = q R=CH3 CH,CH, (CH3WH ( C W 3c CHp,=CH-CH,--, CHz=CH-CH=CHz-CHz-,8 INTRODUCTORY PAPER This general trend emerges in the following Table VI of results, to which Dr. Steacie * subscribes, and I have his permission to quote.But we are in no position to understand in detail the fine differences in temperature-independent factors which seem to emerge in radical reactions involving hydrocarbons. TABLE \‘I Reaction H + H 2 + H 2 + H . . D + NH3-+H + NH,D . D + PH, + H + PH,D . Br + CH, --f HBr + CH, Br + H, -+ HBr + H . Br + CH3Br -+ HBr + CH,Br CH, + CH3COCH3 + CH, + CH,COCH, . . CH3 + CzH6 3 CH4 + C2H5 - CH3 + n-C4HI0 3 CH, + C4H,. . CH3 + ~ s o - C ~ H , ~ 3 CH, + C4H9 . CH, + neo-C,H,, 3 CH, + C,HI, . (p-C6H5. C6H4) Bc + C6H,CH3 (p-C6H6 * C6H4) 3CH $. C~HSCH, (p-tert.-C,H,C,H,) , C+ C6H5CH3 -+ (p-tert.-C,H, . C6H4) ,CH + CBH6CH, . A = PZ (cm.3/mole sec.) 3-5 x 101~ 2 x 1013 1-5 x 1013 1.5 x 101~ 1’1 x 1 0 1 2 1.3 x 101, 5 x I011 2 x I011 I x 1011 I x I011 2 x I011 2 x I010 5 x 109 Reference a b b d e e e e e C C f f a.Farkas and Farkas, Proc. Roy. Soc. A , 1935, 155, 124. b . Melville and Bolland, Proc. Roy. SOC. A , 1937, 160, 384. c. Kistiakowsky and van Artsdalen, J . Chem. Physics, 1932, 12, 469. d. Jost, 2. physik. Chem. B, 1929, 3, 118. e. Trotman-Dickenson and Steacie, J . Anzer. Chem. Soc., 1950, 72, 2310. using Gomer’s ( J . Chem. Physics, 1950, 18, 998) value of 7 X 1013 cm.s/mole sec, for the velocity constant for the combination of methyl radicals. The activation energy of this reaction is assumed to be zero. f. Dobres and Selwood, J . Amer. Chem. Soc., 1950, 72, 5731. In ionogenic reactions we have seen that energy changes consequent upon structural changes are all important in determining trends in re- activity : in radical reactions on the other hand the energy changes seem to be less important and differences in steric factor, i.e.temperature- independent factor, play a larger part. I would suggest that this difference may be due to the difference in the reaction potential energy surface in the two cases. In Fig. 3 ( a ) shows the potential energy as a function of reaction configuration for an iono- genic reaction, and (b) for a radical reaction. Because of the sharp de- pendence of energy on reaction configuration in ionogenic reactions this configuration is closely defined, and changes in the energy all important : but in radical and atom reactions, because of the large splitting dile to resonance energy in the transition state, this state is less sensitive to overall energy changes ; and because of the insensitiveness of the energy to configuration in the region of the transition state the reaction con- figuration is not closely defined, and can vary much more with structural changes.Summary.-It is interesting to note in this Discussion that me are using a theoretical framework with which we are all familiar. Changes in the stability of radicals are discussed in terms of the resonance energy of those radicals. In the field of T electron molecules and radicals the theoretical treatment of mobile electrons has given the chemist a useful and powerful tool: and the application of this treatment, even in its * Thanks are also due to Dr. Swarcz and Mr. Trotman-Dickenson for this Table and for discussion of this point.M. G, EVANS 9 simplest form, has led to beautifully successful results. We are very much in need of a similar treatment of saturated molecules and radicals ; and I would suggest that, in the treatment of equivalent orbitals by Lennard-Jones, we may have the beginnings of such an approach. I have already’ shown how in its very simplest form i t can be applied to the stability of alkyl radicals and their ionization potentials, and leads to results of right sense. A E Reachn Coordinate Remhon Coordinale FIG. 3. In the field of steric factors, i.e. temperature-independent factors and their change with structure, as in the influence of bond characteristics on activation energies, we need more and more accurate experimental data. Dr. Steiner has shown us, I think, the limit to which the transition state method, based on intelligent guesses at the structure and modes of motion of the activated complex, can be taken. There are, however, many fields in which our knowledge is very meagre -both on the theoretical and experimental sides-and from the point of view of this Discussion I think one such field is the problem of energy transfer in these fast radical reactions, and its converse problem of energy flow in unimolecular decomposition.