摘要:

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.

ISSN:0366-9033    

DOI:10.1039/DF9511000001

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

AUTHOR INDEX * Anderson, R. D., 136. Aston, John G., 73, 119. Bartindale, G. W, R., 104. Bateman, L., 219,227, 250,313, 326. Baughan, E. C., 106. Bawn, C. E. € I . , 282, 331. Bell, E. R., 242. Benson, S. W., 218, 224, 232, 234, 310. Blekkingh, J. J. A., 120. Bowen, E. J., 224. Bradley, R. S., 127. Brook, J. H. T., 298, 335. Brown, J. I<., 118. Burawoy, A., 104, 107. Burton, M., 136, 221. Cox, E. G., 127. Cullis, C. F., 327. Davies, C. N., 124. Davison, S., 136. Egerton, A. C., 278. Egerton, Sir Alfred, 311, 329, 332, 334. Eider, B., 235. Emte, W., 278. Evans, Alwyn G., 109. Evans, M. G., I. Gaydon, A. G., 108, 311. Gee, G., 214, 250. Gibbs, Julian H., 122. Glockler, Geo., 26. Gordon, Manfred, 125. Gowenlock. B. G., 108, 229. Gray, Peter, 128, 310, 317, 3-29. Guggenheim, E.A., 116, 118, 226. Hall, G. G., 18. Harding, A. J., 317. Harris, E. I., 318. Hazebroek, P., 87. Henderson, G. M., 291, 334. Hinshelwood, C. N., 129, 21.5, 217, 218, 266. Horrex, C., 187, 230, 232, 233, 234. Hughes, Hilda, 3 I 3. Jenkins, A. D., 311. Kistiakowsky, G. B., 175. Kooyman, E. C., 163, 224. Lapage, Ruth, 233. Lennard-Jones, Sir John, 9, 18, Linnett, J. W., 119. Luft, N. W., 117. McCoubrey, J. C., 94, 127. McCrae, J. O., 234. McDowell, C. A., 53, 106, IIO 116, 103, 104, 106. 310, 322, 329. Magat, M., 113, 118, 126, 226, 235. Marcotte, Frank'R., 236. Matthews, J. B., 298, 335. Melville, H. W., 154, 225. Miles, S. E., 187, 230, 233. Minkoff, G. J., 108, 278, 319, 329. Morris, A. L., 250. Mulcahy, M. F. R., 259, 317, 333. Nickle, A. Gordon, 175. Norrish, R.G. W., 269, 323, 325, Noyes, Jr., W. A., 221, 236, 308. Oosterhoff, L. J., 79, 87, 122. Partington, R. G., 219. Pennington, A. A., 282. Pitzer, Kenneth S., 66, 119, 124, 127, 226. Pople, J. A., 9. Porter, George, 108, 115, 223, 326. Raley, J. H., 242. Robb, J. C., 154, 225. Robertson, A. J. B., 324. Rowley, D., 198. Rust, F. F., 242. Schissler, D. O., 46. Seubold, F. H., 242. Sheppard, N., 118. Sheridan, J.3 120. Small, Mr., 323. Spence, R., 309, 324. Steiner, H., 112, 198, 235. Stevenson, D. P., 35, 110, 113. Stubbs, F. J., 129, 215, 217, 218. Sxyle, D. W. G., 328. Szwarc, M., 143, 215, 228, 231, 336. Thompson, S. O., 46. Tipper, C. F. H., 282, 331. Torkington, P., 104, 108, 128, 213, 223. Trotman-Dickenson, A. F., 111, 128, Turkevich, John, 46. Tutton, R.C., 154, 225. Ubbelohde, A. R., 94, 103, 124, 127, 128, 309, 323. Uri, N., 309, 324, 334. Vaughan, W. E., 242, 314, 330. Walsh, A. D., 310, 320, 323. Warren, J. W., 53, 110, 116. Wasserman, A., 235. Waters, W. A., 231, 315, 319, 332. Watson, W. F., 250. Wibaut, J. P., 332. Wooding, N. S., 330. 330. 327. 221. _ _ ~ * The references in heavy type indicate papers submitted for discussion. 339AUTHOR INDEX * Anderson, R. D., 136. Aston, John G., 73, 119. Bartindale, G. W, R., 104. Bateman, L., 219,227, 250,313, 326. Baughan, E. C., 106. Bawn, C. E. € I . , 282, 331. Bell, E. R., 242. Benson, S. W., 218, 224, 232, 234, 310. Blekkingh, J. J. A., 120. Bowen, E. J., 224. Bradley, R. S., 127. Brook, J. H. T., 298, 335. Brown, J. I<., 118. Burawoy, A., 104, 107.Burton, M., 136, 221. Cox, E. G., 127. Cullis, C. F., 327. Davies, C. N., 124. Davison, S., 136. Egerton, A. C., 278. Egerton, Sir Alfred, 311, 329, 332, 334. Eider, B., 235. Emte, W., 278. Evans, Alwyn G., 109. Evans, M. G., I. Gaydon, A. G., 108, 311. Gee, G., 214, 250. Gibbs, Julian H., 122. Glockler, Geo., 26. Gordon, Manfred, 125. Gowenlock. B. G., 108, 229. Gray, Peter, 128, 310, 317, 3-29. Guggenheim, E. A., 116, 118, 226. Hall, G. G., 18. Harding, A. J., 317. Harris, E. I., 318. Hazebroek, P., 87. Henderson, G. M., 291, 334. Hinshelwood, C. N., 129, 21.5, 217, 218, 266. Horrex, C., 187, 230, 232, 233, 234. Hughes, Hilda, 3 I 3. Jenkins, A. D., 311. Kistiakowsky, G. B., 175. Kooyman, E. C., 163, 224. Lapage, Ruth, 233. Lennard-Jones, Sir John, 9, 18, Linnett, J.W., 119. Luft, N. W., 117. McCoubrey, J. C., 94, 127. McCrae, J. O., 234. McDowell, C. A., 53, 106, IIO 116, 103, 104, 106. 310, 322, 329. Magat, M., 113, 118, 126, 226, 235. Marcotte, Frank'R., 236. Matthews, J. B., 298, 335. Melville, H. W., 154, 225. Miles, S. E., 187, 230, 233. Minkoff, G. J., 108, 278, 319, 329. Morris, A. L., 250. Mulcahy, M. F. R., 259, 317, 333. Nickle, A. Gordon, 175. Norrish, R. G. W., 269, 323, 325, Noyes, Jr., W. A., 221, 236, 308. Oosterhoff, L. J., 79, 87, 122. Partington, R. G., 219. Pennington, A. A., 282. Pitzer, Kenneth S., 66, 119, 124, 127, 226. Pople, J. A., 9. Porter, George, 108, 115, 223, 326. Raley, J. H., 242. Robb, J. C., 154, 225. Robertson, A. J. B., 324. Rowley, D., 198. Rust, F. F., 242. Schissler, D. O., 46. Seubold, F. H., 242. Sheppard, N., 118. Sheridan, J.3 120. Small, Mr., 323. Spence, R., 309, 324. Steiner, H., 112, 198, 235. Stevenson, D. P., 35, 110, 113. Stubbs, F. J., 129, 215, 217, 218. Sxyle, D. W. G., 328. Szwarc, M., 143, 215, 228, 231, 336. Thompson, S. O., 46. Tipper, C. F. H., 282, 331. Torkington, P., 104, 108, 128, 213, 223. Trotman-Dickenson, A. F., 111, 128, Turkevich, John, 46. Tutton, R. C., 154, 225. Ubbelohde, A. R., 94, 103, 124, 127, 128, 309, 323. Uri, N., 309, 324, 334. Vaughan, W. E., 242, 314, 330. Walsh, A. D., 310, 320, 323. Warren, J. W., 53, 110, 116. Wasserman, A., 235. Waters, W. A., 231, 315, 319, 332. Watson, W. F., 250. Wibaut, J. P., 332. Wooding, N. S., 330. 330. 327. 221. _ _ ~ * The references in heavy type indicate papers submitted for discussion. 339

ISSN:0366-9033    

DOI:10.1039/DF95110BX003

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

M. G, EVANS 9 A SURVEY OF THE PRINCIPLES DETERMINING THE STRUCTURE AND PROPERTIES OF MOLECULES PART I.-THE FACTORS RESPONSIBLE FOR MOLECULAR SHAPE AND BOND ENERGIES BY SIR JOHN LENNARD-JONES AND J. A. POPLE Received 19th March, 1951 In this paper a general account of the basic factors determining the structure of molecules is presented. It is pointed out that previous theories used to ex- plain the structure of molecules are inconsistent in certain respects and tend to obscure the nature of the forces operating. Here i t is shown that a satisfactory qualitative picture of the structure of a molecule can be obtained by considering only electrostatic repulsions operating in conjunction with the antisymmetry principle. This is applied t o the relative position of bonds and lone pairs inI 0 STRUCTURE OF MOLECULES molecules and then t o the interaction of two electrons in a bond.In the con- cluding sections, i t is shown how the same qualitative ideas can be applied to strained hydrocarbons and to simple free radicals. 1. Introduction.-The wave theory of chemical valency has had a curious history. The first applications were naturally made to the simplest diatomic molecules. Even for such systems different methods of calculation were devised, some based on the original treatment of the hydrogen molecule by Heitler and London,l others based on the concept of orbitals extending throughout the whole Most of the attempts to deal with the theory of bonds have been approximate in treatment and only in one or two cases, such as in the elaborate treatment of the hydrogen molecule by James and C~olidge,~ and by Hylleraas,* have the calculations been pushed through to a stage of satisfactory accuracy. Such calculations have, however, served to establish the validity of wave mechanical methods and to inspire the belief that, when properly applied, they are capable of accounting satisfactorily for all molecular properties.The surprising feature about the subsequent developments is that the main successes have been achieved not with simple molecules but with conjugated hydrocarbon systems. It is true that there have been attempts to deal in detail with molecules like ~ a t e r , ~ methane and ethylene,7 but even in such comparatively simple systems the quantitative treatment is heavy and elaborate.It was the study of the oxygen molecule by the molecular orbital theory that led Hiickel to consider the molecules of formaldehyde 8 and ethylene and then to show how benzene and other conjugated systems could be dealt with on an approximate basis.10 This led the way to extensive calculations of the resonance energies and bond lengths of a wide variety of conjugated hydrocarbons.11 The essential step in all this theoretical work WAS the recognition of the part played by n-electrons in molecules of this type. The assumption was made that they could be treated separately from all the other electrons whether these were in ordinary single bonds ( 0 bonds) or in the inner shells of the atoms. While this assumption has never been rigorously justified, it is believed to be true because of the difference in the symmetry properties of the n-electrons and those of the rest of the molecule.I t is not proposed to deal in this short paper with the various successes and limitations of the theory of conjugated hydrocarbons, because this field has been adequately reviewed in a Discussion recently organized by the Royal Society.12 Some indication will, however, be given in the paper which follows this l3 of the reasons for the success of the theory in this field. It appears that by a curious coincidence the equations used in the theory are the same as those obtained by a more complete treatment, though the equations and the parameters which appear in them have a different interpretation. The theory of the structure of saturated hydrocarbons cannot be said to have attained a comparable degree of success.All attempts to deal Heitler and London, 2. Physik, 1927, 4, 255. Lennard- Jones, Trans. Faraday Soc., 1929, 25, 668. James and Coolidge, J . Chem. Physics, 1933, I, 825. Hylleraas, 2. Physik, 1930, 65, 209. 5 Van Vleck and Sherman, Rev. Mod. Physics, 1935, 7, 167. 6 Van Vleck, J . Chem. Physics, 1933, I , 177, 219 ; 1934,~~ 20. 7 Penney, Pvoc. Roy. Soc. A , 1934, 14, 166. Hiickel, 2. Physik, 1930, 60, 423. lo Hiickel, 2. Physik, 1931, 72, 310. 11 Pauling and Wheland, J. Chem. Physics, 1933, I, 362 ; Pauling and Sherman, l2 Lennard- Jones, Coulson, Longuet-Higgins, et al., Proc Roy. SOC. A , 1951 l3 Lennard- Jones and Hall, this Discussion. Hiickel, 2. Physik, 1931, 70, 204. J . Chem. Physics, 1933, I , 606, 679.(to be published shortly).SIR JOHN LENNARD-JONES AND J. A. POPLE 1 1 with them have been based on the method of electron pairs. In this treatment the polyvalent atoms such as carbon are first “ prepared ” in the sense that the occupied atomic orbitals are superimposed to give other orbitals with directional properties. These are then used in precisely the same way as Heitler and London dealt xith the interaction of hydrogen atoms. An electron in each directed orbital is assumed to interact with an electron of another atom to form a bond. In the calculation of the interaction, however, the terms in the normalization factors, usually described as overlap integrals, are neglected. This is a serious limitation because the directed orbitals are adjusted to give the maximum overlap with the orbitals of the interacting atom and i t is inconsistent to neglect quantities which have been given a maximum value.The omission of these quantities from the formulae usually used in the theory of electron pairs renders i t difficult to understand clearly the physical interpretation of the various terms which ossur in the formulae or to see what the effect would be of a change in the directed orbitals of the atoms concerned. In other words, the formulae leave obscure which properties of a molec- ular system remain invariant when the system of representation in terms of directed atomic orbitals is changed, and which properties vary in a significant way. This distinction is necessary if we are to understand the factors which determine the shapes and energies of molecules.In view of the unsatisfactory nature of existing theories, this paper will be concerned more with the general principles which determine the structure and properties of molecules than with a detailed account of calculations which have been made for particular molecules. The account is based on a series of papers, published recently,14-21 which have aimed at providing a more systematic formulation of the molecular orbital theory of molecular structure than has hitherto been available. 2. The Factors Determining the Relative Positions of Bonds .-The electronic wave function of a molecule has to be a solution of the appropriate Schrodinger equation and must be antisymmetric for inter- changes of the co-ordinates (including spin) of any pair of electrons.This antisymmetry principle does not appear important in the problem of two electrons in a bond for then the antisymmetry occurs in the spin part of the wave function, but for systems of three or more electrons it intro- duces restrictions on the relative distribution of the electrons in space. To assess the part played by the antisymmetry principle in deter- mining the structure of molecules, we need an approximate quantum- mechanical wave function which can be interpreted in simple chemical terms. The most convenient way of doing this is to assign each electron to an orbital, associated with CI or /I spin functions and combine these into a determinant, so that the total wave function is automatically’ antisymmetric.If the space orbitals are $1 . . . z,h~ and each orbital is doubly occupied, the total wave function is where only the diagonal elements of the determinant have been included inside the brackets. This is the general form of the molecular orbital approximate wave function.l*~ 15 Now since a determinantal function such as (I) is only multiplied by a numerical factor if the rows or columns are replaced by 1inea.r com- binations of themselves, it is usual to restrict the orbitals to be normalized l4 Lennard-Jones, Proc. Roy. SOL. A , 1949, 198, I. 15 Lennard-Jones, Proc. Roy. SOC. A , 1949, 198, 14. 16 Hall and Lennard-Jones. Proc. Roy. SOC. A , 1950, 202, 156. 17 Lennard-Jones and Pople, Proc. Roy. SOC. A , 1950, 202, 166. 18 Pople, Proc. Roy. SOC. A , 1950, 202, 323.19 Hall, Proc. Roy. SOC. A , 1950, 202, 336. 2 o Hall and Lennard-Jones. Proc. Roy. SOC. A , 1951, 205, 357. 21 Hall, Proc. Roy. soc. A , 1951, 205, 541.I 2 STRUCTURE OF MOLECULES and orthogonal. This is not a further approximation; it is merely a convenient mathematical device for simplifying the physical interpretation. Even with this restriction, however, the orbitals . . . *N are not fixed uniquely. It is still possible to apply certain linear transformations to #l . . . $N without altering the total wave function Y . This leads to alternative ways of describing the electronic structure of molecules in terms of orbitals. Two particular sets of orbitals have been found to be of particular significance. The first set, called molecular orbitals, each have a sym- metry determined by the nuclear framework and are generally spread throughout the molecule.It can be shown that these are particularly significant in connection with spectroscopic processes l6 ; if an electron is removed from a molecule, i t should be regarded as removed from a molecular orbital. The other important set of orbitals, called equivalent orbitals, give rise to more localized distributions of charge corresponding to the various bonds or lone pairs of the molecule. A symmetrical molecule such as methane, for example, could be described either in terms of orbitals spread throughout the molecule OY in terms of four equivalent orbitals, identical with each other except for orientation. It is possible to find the transformation from the molecular to the equivalent orbitals, or vice versa, by group theory.15 To find the way in which electrostatic attractions and repulsions influence the relative positions of the various parts of a complex molecule, we divide the total energy into the following parts : (i) the kinetic energy of the electrons, (ii) the potential energy due to the electrostatic repulsion of the (iii) the potential energy due to the electrostatic repulsion of the (iv) the potential energy due to the attractive forces between the nuclei, electrons, nuclei and the electrons. This can be done using the determinantal wave function (I), and explicit expressions can be obtained for the energies in terms of the molecular orbitals or of the equivalent orbitals.16,17 We find that each of the four parts is invariant under the transformation from molecular to equivalent orbitals, as we should expect.Although it might appear at first sight as though no advantage could be gained by a transformation, further exam- ination shows that the equivalent orbital description permits a closer understanding of the part played by electron repulsions, that is of the con- tribution (iii) to the energy. Suppose we denote the molecular orbitals by I,&, # z . . , and the cor- responding equivalent orbitals by xl, xZ . . . . notation for two electron integrals If we use the following - (4 we find that the electron-electron potential energy divides into two parts which are not separately invariant, although their sum is. These parts may be writtenSIR JOHN LENNARD-JONES AND J.A. POPLE r3 for molecular orbitals, and PY v J for equivalent orbitals. In these expressions z’ means summation over both suffixes omitting the terms for which m = n. Now, if we examine the individual terms in these expressions, we see that the first term in J (or j ) gives the repulsive potential energy between two electrons in the same molecular (or equivalent) orbital. The second term represents the repulsive potential energy between electrons in different orbitals. We may therefore refer to J or i as the Coulomb part of the interelectronic potential energy. Finally, the part (- K ) or (- k ) gives a contribution which cannot be so easily interpreted ; it is referred to as the exchange energy. This latter part only differs from zero because the distributions $I (or X) overlap one another to a certain extent ; if there were no overlap, there would be no exchange energy.We expect, therefore, the exchange part to be small when the orbitals are well localized and so to be less im- portant for equivalent orbitals than for molecular orbitals. This is amply confirmed for the ( z s ) ( z p ) configuration of an atom such as beryl- lium, each orbital being singly occupied. The ‘‘ molecular orbitals ” are the 2s and z p functions themselves, and the equivalent orbitals are localized on opposite sides of the nucleus. The latter are the digonal hybrids used by Pauling. It is found that, using molecular orbitals, the exchange energy (- K ) is about 28 yo of ( J - K ) , whereas if equivalent orbitals are used, the corresponding paxt (- K) is only 2-4 Yo of the total.The general conclusion to be drawn from this discussion is that molec- ular structure can most conveniently be described in terms of pairs of electrons in equivalent orbitals, interacting according to ordinary electro- static forces. The exchange part of energy’, though not negligible, will then be small relative to the Coulomb part. On this view there are two important factors determining molecular shape. One is the exclusion principle, which demands that the occupied equivalent orbitals shall be orthogonal to each other. The other in the principle of minimum energy. This requires that subject to all other conditions the repulsion of the electrons shall be a minimum. We are now in a position to discuss the relative orientation of bonds in hydrocarbons, and the significance of the tetrahedral valency of carbon.The structure and stability of the methane molecule can best be under- stood by comparison with the neon atom which has the same number of electrons. The structure of neon is usually represented by the configura- tion (1s)2(2s)2(2~,)2(2PZ)8. These are the symmetrical “ molecular ” orbitals of the atom. The last four, however, can be tra.nsformed into four equivalent orbitals in tetrahedral directions (usually described as tetrahedral hybrids). With neon i t is the wZative orientation of these four orbitals that is significant; the total electron density, or course, is spherically symmetric. Now i t can be shown that if we use the equiv- alent orbital description, go yo of the electron-electron repulsion energy arises from the Coulomb part of (4).The methane molecule can be regarded as obtained from a neon atom by removing four unit positive charges from the nucleus along the directions of the four tetrahedral equivalent orbitals. As these positive charges will, to some extent, draw the electrons in the corresponding equivalent orbital with them, charge distributions in these orbitals will become more localized and the Coulomb part of the interaction of pairs of electrons in equivalent orbitals will account for more than g o yo of the total electron-electron potential energy. We may thus conclude that both the electrostatic m, 12I4 STRUCTURE O F MOLECULES repulsion betweenthe electrons in different orbitals and the antisym- metry principle operate in such a way that the pairs of electrons get as far away as possible from other pairs.These are the chief factors underlying the tetrahedral structure of methane. In addition, we have the repulsion between the protons which has a similar effect, and, of course, a partly cancelling term arising from the attraction of a proton for the electrons of other bonds. All these are significant terms in the total energy. The point we wish to make, however, is that from the arguments outlined above, the exchange part is expected to be comparatively unimportant. Electrostatic repulsions also play a vital part in determining the structure of molecules with lone pair electrons, such as water and am- monia.l* Although these are not hydrocarbons, it is worth while ex- amining their structure briefly, for we shall find in a later section that certain hydrocarbon free radicals are somewhat analogous.The ammonia molecule has the form of a triangular pyramid with three equivalent N-H bonds inclined to each other at an angle of about 107O, so that the structure is nearly tetrahedral. The equivalent orbital picture of this molecule describes it as having three equivalent orbitals associated with the N-H links, each doubly occupied, and a fourth orbital, also doubly occupied, symmetrically related to them, corresponding to the lone pair of electrons. Again the tetrahedral structure is preferred because of the repulsion between pairs of electrons. It has been found 18 that it can best be described as having pairs of electrons in two equivalent orbitals associated with the OH links and pairs of electrons in two other different equivalent orbitals projecting out (backwards) from the oxygen atom so that the whole forms an approximately tetrahedral system.Some other ways in which the repulsion between bonding orbitals or lone pairs is likely to be an important factor in determining molecular structure may be noted. The rotation about a single carbon-carbon bond in molecules such as ethane will depend on the repulsion between electrons in C-H bonding orbitals on different carbon atoms. We should expect the ‘ I staggered ” configuration (Dsd) to be the most stable form, as this would allow the bonding electrons to keep farther apart than in the D3h configuration. Similar factors will operate if the C-H bonds are replaced by lone pairs, as in the hindered rotation of the OH bonds about the C-0 single bond in alcohols.3. The Factors Determining the Energy of a Bond.-In the previous section we have seen how the molecular orbital theory in its equivalent orbital form gives a satisfactory qualitative picture of the interaction be- tween electrons in different bonds or lone-pair orbitals. Where the theory is incomplete is in the way it treats the interaction of a pair of electrons in the same equivalent orbital. This is of great importance, for it is the interaction of two electrons in a bonding orbital which determines the energy of that bond. We consider the case of two electrons in a symmetrical bond (e.g. a homonuclear diatomic molecule, or the C-C bond in ethane).Accord- ing to the molecular orbital theory described above, the distribution of the two electrons is described by a wave function where f, is a n equivalent or localized orbital embracing both nuclei. The factor in brackets represents the spin part of the wave function. If the nuclei are similar, the function fs will, in general, be symmetrical in the two nuclei. According to this wave function each electron moves in the smoothed-out field of the other. In an actual molecule, of course, the motions of the two electrons are strongly interrelated, for each repels the other. The approximation (5) is quite inappropriate for large inter- nuclear separations, for it predicts too large a probability of dissociation The water molecule also has this type of structure.= fS(1)fS(2){a(1)fl(2) - a(2)fl(1)>J * - ( 5 )SIR JOHN LENNARD-JONES AND J. A. POPLE 15 into ions. To take into account the interrelation of the two electrons in the same orbital it is necessary to improve the representation ( 5 ) by adding other terms. Thus the tendency of the electrons to keep apart and there- fore to be on opposite sides of the centre of symmetry of the bond can be represented by adding a term involving antisymmetric functions fa If, in particular, certain symmetric and antisymmetric linear combinations of atomic functions +a and +b are used for f, and fa the function (6) takes the form which is just the form of electron pair function originally used for the hydrogen molecule by Heitler and London.1 This is a particular case of the generalized molecular orbital function (6).Another way of increasing our understanding of the chemical bond, and particularly of the effect of electrostatic forces, is to divide up the energy of the system in a way similar to that used for the many electron problem in The results of doing this for the hydrogen molecule are given in Table I. Also given in this Table are the corresponding energies for two separate hydrogen atoms. = {f*(Ilf8(4 - fa(Ilfu(2)) { + ) 8 ( 4 - 42)8(1)) - - (6) ?P = {+U(I)+b(4 + + b ( I ) + U ( 2 ) H . ( I ) B ( 4 - 42)8(1)), * - (7) 2. TABLE I.-ENERGIES FOR THE HYDROGEN MOLECULE 22 AND Two HYDROGEN ATOMS Total energy . . I - 1-16 Contribution to 1 (Atom%nits) 1 (Atomic 'H Units) 1 Binding (kcal.) Energy - 1'0 I - 9s) I I I Kinetic energy .Nuclear repulsion . Electron repulsion . Electron-nuclear 1-15 0.59 3'63 94 455 - 2-0 - I018 368 co I16 STRUCTURE OF MOLECULES Although figures such as those of Table I have only been worked out for two electrons in the presence of two bare nuclei (assumed to be protons), there is not much doubt that similar results apply for other chemical bonds ; that is, three of the contributions listed in the table above will be positive and only one negative. This analysis of the results is inter- esting, because i t shows that to achieve accuracy in the calculations it is necessary to represent a bond by such a wave function that not only is the average electrostatic attraction between electrons and nuclei as large as possible, but also the average electrostatic repulsion of the electrons is as low as possible.It is the second part which causes difficulty in the calculations. To obtain it accurately other terms must be included in the wave function (6) to represent to the full the tendency of the electrons to avoid each other. It is hoped to publish a fuller discussion of this problem elsewhere. 4. Strained Bonds in Hydrocarbons.-In all the systems discussed so far, we have been able to describe the electronic structure in terms of equivalent orbitals which have been concentrated mainly on the line joining the two nuclei connected by the bond. These may be described as straight or normal bonds. In many molecules, including some hydro- carbons, however, there are bonds whose electrons are most probably to be found off the internuclear line.In other words, they are bent or strained. A simple example is the molecule cyclopropane C,H,, in which the three carbon nuclei form an equilateral triangle. As the angle between adjacent C-C lines is only 60°, we can see that the bond orbitals mainly concentrated along the internuclear lines would be abnormally close to each other. Both the exclusion principle and electrostatic repulsion between the electrons tend to open out the angle between the bonding orbitals, so that i t is considerably larger than the angle between the internuclear lines. This effect has been investigated quantitatively by Coulson and Moffitt. 23 Another simple example of a strained bond system is the ethylene molecule. This is of particular interest, as it affords a striking illustration of the relation between the two types of molecular description referred to earlier.In recent years it has been customary to describe the double bond of ethylene in terms of two orbitals, one symmetrical in the plane of the molecule (0-bond) and the other with a node in this plane (n-bond). Alternatively, we can describe the structure in terms of two equivalent orbitals, These two orbitals are concentrated in regions on opposite sides of the molecular plane. It should be emphasized that these two pictures of the double bond are equally valid, and the choice of the one to be used should be deter- mined by the type of property under discussion. The equivalent orbital picture is more useful when we wish to discuss the electron distribution or the parts of the molecule which are likely to be reactive.Our description of the double bond in terms of two bent orbitals has retained the approximate tetrahedral relation of the four valencies of carbon. There is a modification, however. The two orbitals of the double bond emanating from one carbon atom are drawn together by the field of the other carbon nucleus. The angle between them, therefore, will be some- what less than that characteristic of tetrahedral valency’. It may be expected, as a result, that the p-character of these orbitals near the carbon atoms will be increased. It then follows from the orthogonality conditions 2s Coulson and Moffitt, Phil. Mag., 1949, 40, I. One further point about the ethylene molecule is worth noting.SIR JOHN LENNARD-JONES AND J.A. POPLE 17 that the bonds of the CH orbitals should have more s-character and conse- quently be inclined at an angle greater than the tetrahedral value. This is confirmed by the experimentally determined value of the HCH angle in ethylene which is in the neighbourhood of IZOO. The triple bond between two carbon atoms can also be described in terms of bent orbitals. The triple bond is usually described in terms of a single o-bond, and two r-bonds with nodes in two perpendicular azimuthal planes. These three bonds can be superimposed so as to pro- duce three equivalent bonds, localized about different planes through the CC axis. The angles between these planes is IZOO. This picture therefore corresponds to the model often shown in text-books of chemistry’ of three bent springs connecting the carbon atoms as in acetylene.It can be shown that these two sets of orbitals are related to each other by a transformation which leaves the total determinantal wave function invariant. The triple bond differs from the double bond in one respect, however. Whereas the equivalent orbitals of ethylene are uniquely defined, there is a rotational degree of freedom in the corresponding orbitals of acetylene. It is only the relative azimuthal angles of the three bonds that is important. The actual position of any one may be taken in an arbitrary azimuthal plane, but the system as a whole is axially symmetric. 5 . The Structure of Radicals.-Up to this point we have been con- cerned with molecular systems in which the structure was determined by the interaction of pairs of electrons, each pair occupying a different orbital.Although this gives a satisfactory description of the ground state of almost all stable molecules, it will not apply to free radicals with an odd number of electrons or to a system with an even number of electrons not com- pletely distributed in pairs. The theory of the structure of these radicals has not yet been dealt with satisfactorily. We shall not attempt to de- velop such a theory here, but we give only some general indication of the lines along which it might proceed, using simple hydrocarbon radicals as examples. Before we can discuss the effect that electrostatic repulsion has on the structure of such systems, it is necessary to review briefly the modifications of the orbital theory when some orbitals are singly occupied.Two cases will be considered :- (i) One orbital singly occupied.-It turns out that this configuration can be described by a single-determina.nt wave function, provided that the singly occupied orbital belongs to one of the irreducible representations of the symmetry group of the molecule.16 It must, in fact, be a molecular orbital. (ii) Two orbitals singly occupied-This type of configuration can give rise to two distinct molecular states, a triplet and a singlet. The triplet state can be represented by a single-determinant function if all the singly occupied orbitals are associated with the same spin. The singlet state cannot be represented by one determinant, but this is not a serious limita- tion as the triplet always has a lower energy.I f we examine the details of possible transformations within the determinant representing the triplet state, we find that it is possible to transform from molecular to equivalent orbitals within the set of doubly occupied orbitals and within the set of singly occupied orbitals, but not by using linear combinations of the two. The significance of this becomes clearer when simple examples are con- sidered. This system has an odd number of electrons and will belong to class (i) above. If we suppose that the three C-H bonds are equivalent, then the radical can either be planar with the carbon at the centre of the equilateral tri- angle of the three hydrogens, or it can have a pyramidal form like ammonia.In either case the three bonds will be represented by three localized equiv- alent orbitals and there will be one other “ lone electron” in a singly As a first example we will consider the methyl radical CH,.18 STRUCTURE OF MOLECULES occupied orbital. If the radical is planar, this singly occupied orbital will have a node in the molecular plane, and if it is pyramidal, the orbital will probably be directed much as the lone pair in ammonia. We cannot say which configuration will have the lower energy without making detailed calculations, but it is worth noting that the same factors which cause ammonia to be non-planar are operative also in the CH, radical, viz. the electrostatic forces between electrons in different equivalent orbitals, but to a less extent. As there is only one lone electron, this may not suffice to counteract the mutual repulsion of the three CH bonds and so the CH, radical may be planar or very nearly planar. If a further hydrogen atom be removed from CH, we are left with the methylene radical with six outer electrons. The electrons may be arranged in three doubly occupied orbitals (singlet state) or in two doubly and two singly occupied orbitals (triplet state). Again it is not possible to predict which of these is the more stable without lengthy calculations. We may, however, say something about the electronic arrangements in both states. The triplet state is analogous to the ground state of the water molecule, except that the two lone pair orbitals in water are replaced by two singly occupied orbitals. The configuration which has the lowest energy will be determined by electrostatic repulsions between the orbitals. We may note that the repulsion between electrons in non-bonding orbitals is smaller -than in water and as this is one of the principal factors which prevents water from becoming linear, we may expect the corresponding barrier for CH, to be smaller and possibly non-existent ; that would imply a linear CH, radical. The singlet state of CH, will have its shape determined by similar factors. As we now have three localized orbitals (two bonding and one lone pair) tending to get as far apart from each other as possible, the equilibrium configuration is likely t o be one in which the three orbitals point from the centre towards the vertices of an equilateral triangle. The shape of CH, would then be triangular. Department of TheoreticaZ Chemistry, University of Cambridge.

ISSN:0366-9033    

DOI:10.1039/DF9511000009

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

18 STRUCTURE OF MOLECULES A SURVEY OF THE PRINCIPLES DETERMINING THE STRUCTURE AND PROPERTIES OF MOLECULES PART 11.-THE IONIZATION POTENTIALS AND RESONANCE ENERGIES OF HYDROCARBONS BY SIR JOHN LENNARD-JONES AND G. G. HALL Received 19th March, 1951 The theory of molecular orbitals provides a suitable method of calculating the ionization potentials of molecules. In this paper the method is applied to saturated hydrocarbons and i t is found to account satisfactorily for the change in the ionization potentials of paraffin molecules as the length of the chain is increased. The theory is applied also to unsaturated hydrocarbon molecules and an examination is made of methods previously used to calculate resonance energies. It is shown that the results of earlier work can be given a different interpretation from that usually accepted.In this new theory ionization potentials play an important part.SIR JOHN LENNARD-JONES AND G. G. HALL I 9 1. Introduction.-In the preceding paper 1 a discussion has been given of the properties of chemical bonds in terms of equivalent orbitals. The object of the paper was to discuss the factors which determine the disposition of bonds relative to one another and the strength of the bonds; that is, the paper was concerned mainly with the shapes and energies of molecules. This treatment was shown to be one aspect oi a generalized theory of orbitals, given elsewhere, which lends itself to trans- formations from one type of orbital to another according to the problem considered. The equivalent orbitals used for the study of bonds were ob- tained as transforms of molecular orbitals and were so designed as to be confined to particular regions of a molecule.Such a point of view is useful in the study of the chemistry of molecules, for then attention is usually focused on the localized properties, but when molecules are sub- ject to the interaction of light or a beam of impinging electrons, it is the whole of the molecule which is concerned, and not any particular part. The interpretation of the results of spectroscopy must thus be sought in terms of molecular orbitals, for these have the appropriate property of being symmetrically related to the whole system. In this paper we con- sider methods of calculating the ioniza.tion potentials of molecules and show that while these quantities are properties of the whole molecule, they can none the less be expressed using equivalent orbitals.The theory is applied to some saturated hydrocarbons and satisfactorily accounts for the change in ionization potentials as the length of the paraffin chain is increased. An attempt is then made to extend the theory to calculate the ioniza- tion potentials of unsaturated hydrocarbons, but the experimental evidence available is not sufficient to justify detailed calculations. This leads to an examination of the methods previously used to calculate the total energies (and thus by inference the resonance energies) of conjugated hydrocarbons. Equations are obtained for these energies which have precisely the same form as those used in earlier theories but their interpretation is different ; in fact, it appears that the success of earlier work is due to a series of coincidences in that approximate methods led to equations of the correct type and the deficiencies of the theory were concealed by the use of certain parameters (usually denoted by a and p).These parameters were obtained not by direct calculation but by a comparison with experiment. They thus provided connecting links between one set of experimental results and another, and served to correlate the properties of conjugated mole- cules among themselves. The method developed here has the advantage of providing a precise interpretation of the parameters ( a and j3) and, though these may not be calculable directly, it may be possible to trace their variation from one molecule to another and so to resolve some of the difficulties which surround the theory of unsaturated molecules in its present form.It may, for example, provide a starting point for an ex- tension of the theory to heterocyclic molecules, which have not so far been amenable to satisfactory treatment. 2. Molecular Orbitals and Equivalent Orbitals.-In the orbital theory of valency the electronic structure of a molecule is described in terms of orbitals each of which describes the motion of one electron alone. These orbitals have to be combined with one another in the form of a deter- minant to obtain a wave function for the molecule as a whole which conforms to the Pauli principle. In order to be the best possible, these orbitals must satisfy equations which, for a state with paired spins, can be written (H + v + 4 d J n = 2 EmndJ,,, ??& 1 Lennard- Jones and Pople, this Discussion.2 Lennard-Jones, Proc. Rqy. SOC. A , 1949, 198, I , 14.20 STRUCTURE O F MOLECULES where H is the Hamiltonian for an electron in the field of the bare nuclei, V and A are the Coulomb and exchange operators representing the effect of the remaining electrons and Em, is defined as These equations do not define the orbitals uniquely, so that the motion of the electrons can be described equally accurately using several different types of orbital.* One possible type is the equivalent orbital which is explained and illustrated in the previous paper.l In many respects this is the most convenient description of a molecule, but for certain purposes it is essential to use the molecular orbital description.A molecular orbital 4, is defined by the condition that Em, = 0, w + n. * ( 3 ) From this definition it can be proved that each molecular orbital belongs to one or other of the irreducible representations of the symmetry group of the molecule. This means that they cannot usually be localized in a particular part of the molecule but are spread throughout it. On the other hand, equivalent orbitals are identical with each other except for their position and orientation in space. They satisfy the orbital equations above, for the operators V and A are unaltered by a transforma- tion from molecular orbitals to equivalent orbitals ; (in fact, these operators are invariant under any orthonorm transformation).The quantities Em, are replaced by em,, defined as where x, and X, denote any two orbitals in the equivalent orbital set. These quantities enan have the property of depending only on the velative orientation of X, and x,. Thus, if X, is equivalent to X, and X, to xu and if x, and x, have the same relative positions as X, and xY, then emn = ew. . * ( 5 ) The diagonal elements en% are all equal for a set of equivalent orbitals, and the non-diagonal elements are equal when they involve pairs of orbitals similarly distributed and similarly related in position. The total energy of the molecule can be expressed equally conveniently using either kind of orbital. In terms of molecular orbital qua.ntities the total energy is where the last term is the sum of the internuclear repulsions and Hnn = [JnH+ndx. .J In the equivalent orbital description it is where (7) Methods have been given elsewhere of passing from one set of such symbols to another. a Hall and Lennard-Jones, Proc. Boy. Soc. A , 1950, 202, 155.SIR JOHN LENNARD-JONES AND G. G. HALL 21 This new orbital theory not only provides two alternative descriptions of a molecule in terms of orbitals but also shows how these orbitals may be transformed into one another. Thus the equivalent orbital description is directly related to the molecular orbital one, and any statement or equation made in one set of terms can be translated into the other set. If, for example, the magnitudes of the equivalent orbital parameters e, are known, the molecular orbital parameters En, may be found by dia- gonalizing the matrix ern,. 3.Ionization Potentials of Saturated Molecules.-The removal of an electron from a molecule is one of the simplest phenomena involving primarily the electronic structure of the molecule. When considered on the orbital theory 3 it is found that the effect of ionization is to remove an electron from a molecu1a.r orbital without serious changes to the remaining orbitals. Ionization is not, therefore, the removal of an electron from one particular part of a molecule such as a lone pair or a bond, but rather from a molecular orbital spread over the whole molecule. The vertical ionization potential corresponding to a molecular orbital I& is equal to - En, to a good approximation. Since these vertical ionization potentials are directly observable quantities, the form of the molecular orbitals and the magnitude of their parameters become a matter of considerable ex- perimenta 1 significance.Conversely, the importance of the experimental ionization potentials in elucidating the electronic structure of molecules can hardly be over-emphasized (see Mulliken 4)). Quantities such as heats of formation, internuclear distances and dipole moments depend on many occupied orbitals. They only yield information about individual orbitals after an extensive analysis. Ionization potentials, on the other hand, give direct and unambiguous information about single molecular orbitals. There is a very close parallel between the theory of molecular vibrations and the orbital theory of ionization potentials.Vibration frequencies and their normal co-ordinates correspond to ionization potentials and their molecular orbitals. The matrix of force constants corresponds to the equivalent orbital matrix em,,. This suggests that, just as vibrational spectra can be analyzed and the magnitude of the frequencies calculated in terms of force constants, the ionization potentials can be interpreted and calculated using the ern, parameters.6 The ionization potentials of methane may’, for example, be calculated in the following way. In the equivalent orbitals corresponding to the four CH bonds. Because of the equivalence, the em, matrix has the form a b b b b b a b b b b a and the ionization potentials are found by diagonalizing this matrix. diagonalization of this matrix leads to the equation The I emn - E8,n I = 0, .* (11) just as the diagonalization of the force constant matrix leads to a deter- minantal equation for the vibration frequencies. For methane this equation becomes a-E b b b b a-E b b b b a-E b b b b a-E = 0. * (14 Mulliken, J . Chern. Physics, 1935, 3, 517. Hall, Proc. Roy. SOC. A , 1951, 205, 541.2 2 STRUCTURE OF MOLECULES The roots of this equation are (a + 3b) and (a - b), the latter appearing three times, so that the ionization potentials are The values of the parameters u and b are not known initially, just as the force constants of a vibrating system are not known initially, but when a sufficient number of molecules have been analyzed it should be possible to predict suitable constants for any particular molecule.4. Saturated Hydrocarbons.-In practice it is much more difficult to determine ionization potentials than vibration spectra, because usually only one ionization potential, that of the most loosely bound electron, is available. Until it becomes possible to measure the inner ionization potentials experimentally, it will be necessary, therefore, to consider homo- logous series and not individual molecules. Unfortunately very few of these series have been studied experimentally to date. Another difficulty is that the outer ionization potentials are not very sensitive to changes in structure, so that very accurate determinations are required. The easiest series to consider in this way is the normal paraffin s e r i e ~ . ~ All its CC bonds and all its CH bonds may be taken as chemically equivalent, so that the number of enan parameters required is small.Since i t is only the form of the equations that is known, these parameters have to be deter- mined from the observed ionization potentials. Once the parameters are known, the ionization potentials may be calculated for the whole series. Table I shows the agreement between the calculated and the observed6 potentials. TABLE I.-~ALCULATED AND OBSERVED IONIZATION POTENTIALS &(Al) =- (u + 3b) ; 12{T2) =- ( a - b). . - (13) 11.394 12.72~ I I'sg3 I I 6-08, Propane . Butane . Pentane . Hexane . Heptane . Octane . Nonane . Decane . Calculated 11'2 I4 10.795 10'554 10.41~ 10.32~ 10.26~ 10'224 10-1g4 Observed 11'21 10.80 10.55 10.43 10.35 10.24 10'2 I 10.19 From the same parameters some of the inner ionization potentials may also be calculated.This application of the method will be of increasing importance as the inner potentials come to be studied experimentally. Not all the potentials can be calculated, for some of the molecular orbitals have symmetry properties such that their potentials involve a different set of parameters. As an illustralion some of the ionization potentials of normal octane are given in Table 11. TABLE II.-SDME CALCULATED IONIZATIOX POTENTIALS OF NORMAL OCTANE 10.795 I 1.87~ 12.36~ 15'46, I I - 7 1 ~ 13'534 - - These ionization potentials, arranged in order of increasing magnitude, correspond to the removal of electrons from different molecular orbitals. The first and last rows refer to molecular orbitals involving mainly (but not exclusively') the CC links, while the second and third rows refer to orbitals involving mainly the CH, groups.Honig, J . Chem. Physics, 1948, 16, 105.SIR JOHN LENNARD-JONES AND G. G. HALL 23 5. The Ionization Potentials of Conjugated Hydrocarbon Molecules.- It is characteristic of conjugated molecules that, although their structure may still be described in terms of equivalent orbitals, the equivalent orbitals representing the double bonds are not localized between two atoms. In butadiene, for example, in addition to the equivalent orbital representing the central CC single bond, there are four equivalent orbitals corresponding in pairs to the outer CC double bonds of the classical formula. These double bond equivalent orbitals are not localized strictly between a pair of carbon atoms but spread partly over the central bond. This means that the e-parameters of these equivalent orbitals are not constant from the double bond of one molecule to the double bond of another molecule and so the ionization potentials cannot be calculated in the same way as for saturated molecules.The difficulty of finding suitable parameters has been overcome 8 by considering, instead of the ground state, an excited state of the molecule, referred to as the standard excited state, in which the T electrons are in singly occupied orbitals with parallel spins. These singly occupied w orbitals can be transformed among themselves into equivalent orbitals localized around a single atom, so that the ionization potentials may be calculated in the same way as for saturated molecules.Provided the internuclear distances are the same, the ionization potentials and molec- ular orbitals of the ground state are equal, to a good approximation, to those of the lower members of the set corresponding to the excited state, so that the ionization potentials of the ground state can be found in this indirect way. To illustrate the method the ionization potentials of benzene may be considered. In the standard excited state there is one singly occupied equivalent orbital, antisymmetrical in the plane, around each carbon atom. If the parameters are denoted by e = en,, f = enn*l and the remainder taken to be negligibly small, the ionization potentials are found by solving the secular equation e-E f f f e--E f f e--E f f 8--E f f e-E f f f e-E - - 0.. (14) The roots of this are e + 2f; e + f (twice) ; e - f (twice) ; e - 2f, . (15) so that the ionization potentials of the electrons in the occupied orbitals of the ground state are Unfortunately the ionization potentials for conjugated molecules are not yet sufficiently accurate to justify detailed calculations. It will be neces- sary, for example, to take into consideration the variation of the parameter f with internuclear distance and this will call for a large amount of em- pirical data. 6. The Calculation of the Energies of Conjugated Hydrocarbon Molecules.-The contribution of the v electrons to the total energy of a conjugated molecule can be expressed, according to the orbital theory, as the sum of two terms.The first term is the sum of the ionization poten- tials and so can be calculated by the method of 5 5. The second term cannot be calculated directly, but, if the molecular orbitals are known, it 7 Hall and Lennard-Jones, Proc. Roy. SOC. A , 1951, 205, 357. W L U ) = - (8 + 2f) ; = - (e + f). - . (16) Hall (to be published shortly).24 STRUCTURE OF MOLECULES can be expressed 9 in terms of a second set of parameters hmn. These h,, are the matrix elements of the bare nuclei Hamiltonian with respect to the equivalent orbitals X, and x, of the standard excited state and so can be taken as constant whenever the emn are constant. For convenience we may include the internuclear repulsion into the h,, so that the energy, as in (8), becomes additive.Since the molecular orbitals are easily found in terms of these equivalent orbitals, the total 7 electronic energy can be calculated in terms of two sets of parameters. It has become usual not to compare this energy with experimental quantities directly but to do a similar calculation for a state corresponding to a single structural formula with definite single and double bonds. The difference in energy between the actual state and this hypothetical " reference state '' is regarded as the empirical resonance energy. We note in passing that this procedure is not very satisfactory either experimentally or theoretically. The present method of calculating resonance energies has several features in common with the molecular orbital method used by Huckel l o for conjugated hydrocarbons and extended by Lennard- Jones l 1 (for a general account and further references, see Lennard- Jones 1 2 ) .The molecular orbitals were expressed as linear combinations of atomic orbitals and the coefficients in the expansions determined by minimizing the energy. This led t o a determinantal equation for the energies of the molecular orbitals and it happens to have the same form as the one used in $ 5 to calculate ionization potentials. The quantities appearing in this determinant, usually denoted by a and fl, were not calculated theor- etically but were expressed in terms of experimentally known quantities.'l Despite the great difference between this procedure and that used above it can be shown that, as applied to conjugated hydrocarbon mole- cules, the equations used are similar and, since both methods use experi- mental data to determine their parameters, their results will coincide. The definition of the parameters according to the theory developed here is a = +(en, + hnn) ; P = i(enn+i + hnn+i)- * * (17) The coincidence between the old theory and the new one does not take place generally but depends on such accidents as the neglect of second- neighbour interactions and the use, in the older theory, of only two para- meters a and fl.For hetero-molecules, therefore, the two methods yield different results, Thus the agreement between the theories is confined to that part of the older theory which has given the best agreement with experiment. In earlier theories it was found very difficult to give an exact definition of a and 8.They were regarded as matrix elements of a suitable self- consistent Hamiltonian with respect to the atomic orbitals, but this Hamiltonian was not defined precisely. This lack of exact definition led to some ambiguities. For example, the definition of fl differed according as it was assumed that the atomic orbitals were orthogonal lS or not. Thus, whereas Hiickel estimated fi as I 5-20 kcal. /mole, Lennard- Jones allowed for the variation of fi with distance and found fl = 35 kcal./mole for Y = 1.33 A, and Mulliken and Rieke, by making allowance for the overlap integral and hyperconjugation, find p = 44.5 kcal./mole at the same distance. It is probable that this theory will lead to a value rather larger than these. We note in passing that to relate the orbital theory to the earlier molec- ular orbital theory we must distinguish between the interpretation of a and j? for conjugated hydrocarbons as matrix elements with respect to equivalent orbitals and the corresponding interpretation for saturated Hall (to be published shortly).l o Hiickel, 2. Physik, 1931, 70, 204. l1 Lennard-Jones, Proc. Roy. SOC. A , 1937, 158, 280. l2 Lennard-Jones, Proc. Roy. SOC. A , 1951 (in press). l3 Mulliken and Rieke, J . Amer. Chem. SOC., 1941, 63, 1770.SIR JOHN LENNARD-JONES AND G. G. HALL 25 molecules. The equivalent orbitals, in the latter case, may be CC bonds or CH bonds (or, in hetero-molecules, lone pairs). It thus appears as though in such molecules the parameter a is closely related to a bond property, but b, which is a matrix element relative to two equivalent orbitals meeting on a common centre, is rather to be associated with a particular atom.In conjugated molecules, on the other hand, the equiv- alent orbitals are localized in the neighbourhood of a particular atomic centre, so that a should be associated with an atom and with two neighbouring atoms. The differences between this orbital theory and the previous molec- ular orbital one are best illustrated by showing that many of the as- sumptions and approximations of the older theory, as discussed by Coulson and Dewar,l* are now unnecessary. In the previous theory the approximations were made of expanding the molecular orbitals as linear combinations of a small number of atomic orbitals and of assuming that these atomic orbitals were orthogonal.The errors introduced by these approximations are undoubtedly appreciable. On the other hand, in this theory the molecular orbitals are expressed as transforms of an orthonormal set of equivalent orbitals. This does not involve any approximations, for the determinantal wave function for the molecule as a whole is invariant under such transformations. For con- jugated molecules, however, there is an approximation involved in equat- ing the molecular orbitals of the ground state with those of the standard state described above, but the error thus introduced can be estimated using perturbation theory. Frequently the older theory used a wave function for the molecule as a whole in the form of a product of orbitals.Such a wave function does not satisfy the Pauli principle and consequently omits the exchange con- tribution to the energy and over-estimates the probability of the electrons being simultaneously around one atom. To reduce these errors a deter- minant of T orbitals has sometimes been used for conjugated molecules, as for example, by Goeppart-Mayer and SkIar,l6 by Craig l6 and by Parr and Mulliken,17 but even this is not antisymmetrical with respect to the interchange of u and T electrons. When the total wave function is made fully antisymmetrical, the theory loses much of its simplicity and does not lead to the usual secular equation.l% 5 None of these difficulties arise in the present form of the theory, since it is based on a wave function of the correct determinantal form.Then again, in the older theory there was some difficulty in isolating the contributions to the total energy from the internuclear repulsions, the electrons in symmetrical orbitals (U bonds) and those in antisymmetric orbitals (T bonds). This seems to have been due to confusion between the Schrodinger equation for the molecule as a whole and the equation for the T-orbitals. Now that the equations for the orbitals have been derived explicitly, this difficulty disappears. In both theories the approximation is made of using a single deter- minant as a wave function in contrast with the electron pair theory which uses a linear combination of determinants. The closeness of this ap- proximation is to be judged by the flexibility of the wave function and it is obviously better to use orbitals chosen a so as to make the approximation as good as possible than to use orbitals in which only a certain number of parameters can be varied.Indeed, it is probable that, unless a large number of determinants are used, the wave function of the electron pair theory, in which only the coefficients of the determinants are varied, will not be as good an approximation as the wave function of this theory. l4 Coulson and Dewar, Faraday SOC. Discussion, 1947, 2, 54. l5 Goeppart-Mayer and Sklar, J. Chem. Physics, 1938, 6, 645. l6 Craig, Proc. Roy. SOC. A, 1950, 200, 474. l7 Parr and Mulliken, J. Chem. Physics, 1950, 18, 1338. 18Moffitt, Proc. Roy, SOC. A, 1949, 196, 510.26 BOND RESONANCE ENERGIES The previous molecular orbital theory had the severe limitation that, jn order to be self-consistent in the sense introduced by Coulson and Rushbrooke,lg the v electron distribution had to be uniform.This meant that hetero-molecules could not be considered quantitatively, and that variations in the parameters due to changes in bond length, etc., could only be treated approximately. This particular difficulty does not arise in this theory, since the equations for the orbitals of the standard excited state are self-consistent in the iullest sense. As already mentioned, there is an approximation involved in the use of the standard state, but the error can be estimated and is unlikely to be large. In practice, owing to the difficulty of obtaining the necessary ionization potentials, it is necessary to make a number of working assumptions as to the magnitude and vari- ation of the parameters emn and h,,, but these are not necessary to the validitj of the theory and can be refined considerably as more data become available. Finally, it may be remarked that hyperconjugation appears in a new aspect in the equivalent orbital theory. In the theory developed by Mulliken,l3 for example, hyperconjugation is a consequence of the expan- sion of molecular orbitals as linear combinations of atomic orbitals. Thus, in ethane, there are four antisymmetrical orbitals of the 7~ type corre- sponding to localized molecular orbitals of each of the CH, groups. The interaction of these T type orbitals gives to the C-C bond a certain triple bond character. The disadvantage of this treatment is that it becomes difficult to understand what a normal CC link is. On the other hand, in this orbital theory the phenomenon known as hyperconjugation is included in the general treatment. There is no need to separate out this factor from the others which determine the energy of a molecule. Department of Theoretical Chemistry, University of Cambridge. 1 9 Coulson and Rushbrooke, Proc. Camb. Phil. SOC., 1940, 36, 193.

ISSN:0366-9033    

DOI:10.1039/DF9511000018

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

26 BOND RESONANCE ENERGIES ESTIMATES OF AVERAGE BOND ENERGIES AND RESONANCE ENERGIES OF HYDROCARBONS BY GEO. GLOCKLER Received 8th March, 1951 Average bond energies of hydrocarbons are estimated on the basis that the heat of sublimation of carbon L(C) = 169-7 kcal. It is assumed that the experi- mental values of the CC- and the CH- distances of the three molecules ethane, ethylene and acetylene yield a relation between these distances which also holds for all other hydrocarbon molecules. It means that carbon-carbon bonds of relatively high average bond energy associate with carbon-hydrogen bonds of relatively high average bond energy. These average bond energies are used to calculate resonance energies. It is emphasized that these latter quantities depend on the reference state chosen.The method of calculating resonance energies from heats of hydrogenation is analyzed and i t is found that this pro- cedure must be amplified by also considering the resonance energies and other effects which tend to change the average bond energies of the intermediate struc- tures. The hydrogenation of butadiene t o butene and butane and of benzene to I : 3-cyclohexadiene, cyclohexene and cyclohexane are discussed as examples. Introduction.-The heat of sublimation of carbon L(C) is still in This dispute as can be seen from an excellent review by Springall-l Springall, Research, 1950~ 3, 260.GEO. GLOCKLER 27 quantity is necessary for the calculation of average bond energies of hydro- carbon molecules and the latter quantities are needed to calculate reson- ance energies.There are now three experimental determinations 2* 3 9 * of L ( C ) which check satisfactorily' and the value L ( C ) = 7-36 eV (169.7 kcal.) is adopted here. For comparison the average bond energies of hydro- carbons based on L(C) = 5.888 eV (135.8 kcal.) are also given in Table I. In order to make the calculations described below' it is assumed that the experimental values for the internuclear CC- and CH- distances (R(CC) and R(CH)) for acetylene, ethylene and ethane can be used to establish a general relation between R(CC) and R(CH) for hydrocarbon molecules. It means that CC- bonds of relatively high CC- average bond energy associate with CH- bonds of relatively high CH- average bond energy. Methane and its radicals, the nonnal paraffins, I-olefins, di-olefins and benzene are considered in detail as examples.Similar studies have been made earlier by Skinner,G Roberts and Skinner and Glockler.* The system of bond energies used here (based on L(C) = 169.7 kcal.) fits better into a larger scheme involving CC, CN, CO, NO, 00 and NN bonds, than thc similar set based on L(C) = 135-8 kcaL8 Methyl Radical .-The bond dissociation energy of methane (D(CH,-H)) is known to be IOI kcal.99 lo The heat of formation of TABLE I.-HEATS OF FORMATION Q,, ATOMIC HEATS OF FORMATION Qa, AND INTERNUCLEAR DISTANCES R(CC) AND R(CH) ESTIMATED cc- BOND ENERGIES B(CC), AND CH- BOND ENERGIES %(CH), Qj kcal. - 54'33 - 54'33 - 204.1 - 187.6 - 14-52 - 14.52 - 24.00 - 2 4-00 0'00 0'00 I 6.52 16-52 15-99 15-99 - 128.8 - 107.4 Q, kcal.388-3 320'5 (135.4) 84-0 531'5 463'5 1304'2 I 100-4 169.8 135.8 665'9 598.0 392'4 358.4 (92'3) 80.0 I 1.207 1-207] 1.316 1.316 1'353 1.353 1'39 1'39 1'545 1'545 ( 1'5 4 7) (1'547) - - - 181.5 118.9 84.0 125.0 77'5 I 16.4 85.1 84.9 67.9 84-5 67.7 (135.4) - I - R(CH) A 1.060 1-060 - - 1-071 1-071 1.075 1.075 - - 1'100 1'100 1.092 1.092 1.131 1.131 &CH) kcal . 103.4 100.8 - - 101.6 96.5 98.3 96.9 88.4 98.1 89.6 80.0 101'0 I - (92'3) Rcmarks U b a b b a b ac bc a b b ad bd U U (a) Based on L(C) = 169.7 kcal. (b) Based on L ( C ) = 135.8 kcal. ; D(H2) = 103-2 kcal. ( c ) B(CC in diamond) = +L(C). (d) The value B(CH, radical) is obtained by extrapolation. Brewer, Gilles and Jenkins, J . Chem. Physics, 1948, 16, 797. Simpson, Thorn and Winslow, A .E.C.General Chemistry Report A NL-4264 Marshall and Norton, J . Amer. Chem. Soc., 1950, 72, 2166. Hagstrum, Physic. Rev., 1947, 72, 947. Skinner, Trans. Faraduy Soc., 1945, 41, 645. Roberts and Skinner, Trans. Faraday Soc., 1949. 45, 339. Glockler, J . Chem. Physics, 1948, 16, 842 ; 1951, 19, 124. Anderson and Kistiakowsky, J . Chem. Physics, 1943, 11, 6. (Argonne Nat. Laboratory, 1949). lo Kistiakowsky and Van AItsdalen, J . Chem. Physics, 1944, 12, 469.28 BOND RESONANCE ENERGIES methane (Qf = 15-98 k~a1.l~) yields Qa(CH4) = 392-4 kcal. (Table I). The heat of atomization of methyl radical must then be Qa(CH,) = Qa(CH4) - D(CH, - H) = 291-4 kcal., whence B(CH in CH,I = 97.1 kcal., (L(C) = 169.7 kcal. ; Table 11) These values lead to the CC- bond dissociation energy of ethane : D(CH, - CH,) = 83-5 kcal.while Szwarc la gives 80 f 6 kcal. based on the work of Rice and Do01ey.l~ Methylene Radical .-The CC- bond dissociation energy of ethylene into two CH, radicals is less than 160 kcal.l2. l4 Using D(CH, - CH,) = 150 kcal. yields the set D(CH,-H), D(CH,-H), D(CH-H) and D(CH) of Table 11. B(CH in CH,) and B(CH in CH,) are more nearly equal in the set based on L(C) = 169.7 kcal. This equality may be expected since in both structures the carbon atom used sp3 hybridization. It is also seen that B(CH in CH,) = 95-4 kcal. is nearer to B(CH in C2H4) = 104.8 kcal. than when L(C) = 135.8 kcal. is taken as a base. This feature is also expected since the carbon atom uses spz hybridization in both the CH,- radical and in C,H, (Walsh 15).The bond dissociation energies based on L ( C ) = 135.8 kcal. show erratic behaviour, as for example D(CH-€3) =76-3 kcal. would be less than the bond dissociation energy of CH- radical (80 kcal.). The first set in Table I1 seems to be the more acceptable. Hence the average CH- bond energy in methylene radical is estimated to be 95-4 kcal. and the CH- bond dissociation energy of CH, is taken to be 98.5 kcal. - - TABLE II.-AVERAGE BOND ENERGIES AND BOND DISSOCIATION Energies of Methane and its Radicals (kcal.) ; based on D(CH,-H) = IOI kcal. ; D(CzH4) = 150 kcal. ; assuming L(C) = 169.7 or 135.8 kcal. CH4 CH, . CH, . CH I &CH) 98.1 97'1 95'4 92'3 89.6 85.8 78.4 80.0 Qa 392'4 291.4 190.8 92'3 358'4 257'4 156.8 80.0 D(R-H) 101'0 100.6 98.5 92'3 101'0 100.6 76.8 80-0 11 Bichowsky and Rossini, The Thermochemistry of the Chemical Substances l2 Szwarc, Chem.Rev., 1950, 47, 75. l3 Rice and Dooley, J . Amer. Chem. Soc., 1933, 55, 4245. l4 Price, Physic. Rev., 1934, 45, 843 ; 1935, 47, 444. 15 Walsh, J . Chem. Soc., 1948, 398. (Reinhold Publishing Corp. New York, 1936).GEO. GLOCKLER 29 Methine Radical (CH, X217).-The heat of dissociation of CH(217) radical is given by Herzberg l6 as D(CH) = 3-47 eV (80.0 kcal.) based on the work of Shidei.17 This value depends on the interpretation of a missing line in the spectrum of CH as indicating a predissociation. It might, however, be a perturbation. In that case D(CH) = 4-00 eV (92.3 kcal.) obtained by extrapolation of a B(CH) against R(CH) curve (from the data of Table I) is a good estimate, considering also the fact that a linear Birge-Sponer extrapolation yields 5-31 eV (122.5 kcal.).16 The value D(CH) = 92-3 kcal.also fits better into the sequence HF, OH, NH and CH (Table 111, column 4). The values B(OH in H,O) and B(OH) are from Dwyer and Oldenbergla D(HF) is 145.6 or 132.6 kcal. depending on D(FJ being 60 or 40 kcal.ls. a. D(NH) is 96.9 or 78.4 kca1.l6- 21 The larger value fits the sequence given in column 4 of Table 111. The value of B(CH in C,H,) is related to the dissociation of acetylene into CH radicals or with the breaking of the CC- bond : C,H, + ZC + zH ZC + zH + 2CH C,H, -+ zCH - 388.3 or - 320-5 kcal. 184.6 or 160.0 kcal. - 203.7 or - 160.5 kcal. whereas Szwarc la mentions < 187 (?) kcal. The higher value (based on L(C) = 169.7 kcal.and D(CH) = 92.3 kcal.) is nearer to the questionable figure which was obtained by Price l4 and Hilgendorff 2 2 from a Rydberg series in acetylene. It is based on the interpretation of a diffuse band at 1520 as a predissociation. TABLE 111.-AVERAGE BOND ENERGIES g(MH) OF MH- BONDS M = F, 0, N and C ~~ 132.6 109-2 92-7 89.6 135'0 78.4 80.0 100'1 145.6 109.2 98-1 145.0 96.9 92-2 100'2 100'1 Remarks D(F,) = 34 or 60 kcal. Ref. (18) D(N2) = 225.1 or 272.1 kcal. L(C) = 135.8 or 169.7 kcal. D(F,) = 34 or 60 kcal. Ref. (18) Ref. (16) Ref. (IS), (21) Paraffins.-The heat of atomization of the normal paraffins a t oo K) based on Q, values from Selected Vulues 2s is given by Q~.(C,Hanca) = 112~20 + 276.64n ; n > 4 (kcal.), where 276.64 kcal. = increment per CH,- group.The bonds of the end methyl groups are stronger than the bonds within the carbon chain. The end CC- bond energy B(CC of CH,) = 83.8 kcal. from propane on. The next CC- bond energy is 83-5 kcal. from butane upwards and the other CC- bond energies are all equal to 83.3 kcal. The CH- bond energies 1 6 Herzberg, Molecular Spectra and Molecular Structuve, I . Spectra of Diatomic Molecules, 2nd edn. (D. Van Nostrand Co. Inc., New York, 1950). 1' Shidei, Japan J . Physics, 1936, 11, 23. la Dwyer and Oldenberg, J . Chem. Physics, 1944, 12, 351. so Eucken and Wicke, Naturwiss., 1950, 10, 233. 21 Glockler, J . Chem. Physics, 1948, 16, 602. 2z Hilgendorff, 2. Physik, 1935, 95, 781. 23 Selected Values of Properties of Hydrocarbons (Nat. Bur. Stand., Cir.461, Simon, FZuorine Chemistry, Vol. I (Academic Press Inc., New York, 1g50), Chap. 10. 1947).30 BOND RESONANCE ENERGIES are : B(CH in CH,) = 96.8 and B(CH next to CH,) = 96-73 kcal. The CH- bond energy of the CH- bond on the third and fourth carbon atom are 96-70 and 96.68 kcal. respectively. These values will reproduce the Q,, values satisfactorily. Ethane.-The heat of formation is 16-52 kcal.2, yielding Qa = 665.9 kcal. It is of interest to point out that the distances mentioned in Table I fit the moment of inertia of the Ethyl Radical.-Anderson and Van Artsdalen give 98 & 2 kcal. for D(C,H,-H) as an upper limit and the values summarized by Szwarc 1, range from 97 to 102 kcal. From Qa(C2Hs) = 665-7 kcal. and adopting D(C,H5-H) = 97 kcal. yields Qa(CaH5) = 568.7 kcal.and B(CH in C2H5) = 96.8 kcal. if B(CC in C,HJ = B(CC in CZH,) = 84-5 kcal. g(CH in C,H,) = 96-9 kcal. and hence B(CH in CZH,) and D(C2H5-H) are nearly the same showing that there is very little reorganization involved when an ethane molecule loses one hydrogen atom and becomes an ethyl radical. Olefins .-Q,, (propene) = 810.5 kcal. whereas a propene molecule which has ethylene and ethane-like bonds would have Q,, = 802.6 kcal. Hence some of the bonds have been strengthened. It is assumed that the single bond located near the double bond is mostly affected by hyper- conjugation.26 In order to obtain an estimate of this effect it is assumed that the ethylene portion of the molecule is as in ethylene (2B(CH as in CaH,) and B(C = C as in C,H,) = 2 x 101.6 + 125-0 kcal.) and that the remainder of the heat of atomization (482.3 kcal.) is distributed over the CC- single bond and the attendant CH- bonds.The estimated average bond energies in propene are : B(HC=) = 101.6, B(C=C) = 125.0, B(C-C) = 89-2, B(=CH-) = 99.7 and B(CH in CH,) = 97-8 kcal. The corresponding internuclear distances are : R(HC=) = 1.071, R(C=C) = 1.353, B(C-C) = 1-52, R(=CH-) = 1.082 and R(CH in CH,) = 1-094 A. The CH- bond on the middle carbon atom is taken to have the average bond energy of B(=CH) and B(CH in CH,). The I-butene molecule is treated in a similar manner with the as- sumption that the propene-end of the mclecule is a s in propene itself. Labelling the CC- double bond CCI ", the CC- single bond adjacent to the double bond " CC I1 " and the CC- single bond of the CH,- group " CC I11 " it is found that : - CH I : zB(CH as in C2H4) CC I : B(C=C as in C2H,) = 125.07 ,, cc 11 : ~(c-c as in propane) = 89.21 ,, CH I I1 : B(CH near C=C) = 99.68 ,, CH I1 I11 : 2g(CH betw.C-C) = 194.65 ,, CH I11 : 3B(CH of CH,) = 290.60 ,, = 203.19 kcal. CC I11 : B(C-C of CH,) = 84-53 Y ? ~~ Q,, (actual) = 1086.78 ; 1086.93 ,, The normal increment of Qa of the I-olefins is reached between I-hexene and I-heptene. Di-o1efins.-The heat of formation of butadiene at oo K is 30-2 kcaL2' whence Q,, = 958.5 kcal. If the molecule had ethylene-ethane-like bonds, its Q,, would be 939.5 kcal. The middle single CC- bond is known to be shorter (1-46 %i compared to 1-55 A) and hence stronger than usual. It will be assumed that the two end portions of the molecule are " ethylene like " and that all of the change in bond energy is located in the middle 24 Smith, J .Chem. Physics, 1947, 17, 139. 25 Anderson and Artsdalen, J . Cliem. Physics, 1944. 12, 479. 26 Mulliken, Riecke and Brown, J . Amer. Chem. SOC., 1941, 63, 41. Aston, Szasz, Wooley and Brickwedde, J. Chem. Physics, 1946, 14, 67.GEO. GLOCKLER 31 CC- bond. The attendant CH- bonds are expected to be affected to a degree as determined by the CC bonds which emanate from the carbon atom to which they are attached. In the manner indicated with I-butene it is found that 4B(CH as in C,H,) = 406.374 kcal. ; R = 1.071 8, 2B(C=C as in C2H4) = 250.143 kcal. ; R = 1-353 B(C-C, middle) = I O O - ~ O Z kcal. ; R = 1-457 A zB(CH, middle) = 201-065 kcal.; E? = 1-077 Qa (base) 939'53 kcal. Qa (actual) Butadiene . 958.51 kcal. Butene . . 1086.77 ,, Butane . . 1218.51 ,, 1222.23 Qa = 958.48 kcal. ; 958.514 kcal. It should be noted that the bond distance of the single CC- bond has been determined from the bond energy data used here and is an inde- pendent check on the electron diffraction value cited above (1.46 When on the other hand, the system of bond energies based on L(C) = 13543 kcal. is used to make the same calculation then it is found that 4B(CH as in C,H4) = 386.08 kcal. ; R = 1.017 8, zB(C=C as in C,H,) = 154.98 kcal. ; R = 1-353 A B(C-C, middle) = 86.37 kcal. ; R = 1.288 A zB(CH, middle) = 195.25 kcal. ; R = 1.068 A Qa = 822-78 kcal. ; The single CC- bond distance is now calculated to be 1-288A which would make this bond even shorter than a C=C bond and it does not check the electron diffraction value (1.46 A).Hence this point is taken as a piece of circumstantial evidence against L(C) = 135.8 kcal. Resonance and hyperconjugation.-By resonance energy is meant the usual strengthening of the bonds of a molecule due to the fact that the actual total energy of atomization of the molecule is found to be greater than the same quantity when calculated on the basis of some preconceived notion regarding the bonds in a given structure. This hypothetical molecule is then used as the base for calculating the resonance energy of the molecule. For example, it will be assumed here that the basic forms of butadiene, butene and butane have ethylene-like double CC- bonds and ethane-like single CC- bonds. From this point of view it is necessary to include all forms of reorganization energy such as hyperconjugation, near-bond effect, Van der Waals' interaction, London dispersion effect, inductive effect, etc., etc.The three molecules mentioned show the following differences between their Qa (actual) and Qa (ethylene-ethane- like) values : 822.67 kcal. n 18-98 kcsl. 5-89 I, - 3'72 9 , If butadiene is referred to a " butene-like " base then the dii'ference is 958.51 - 945.08 = 13-43 kcal. This quantity differs markedly from 3.5 kcal. given by Wheland 29 and obtained as the difference of twice the heat of hydrogenation of butene to butane and the observed heat of hydrogenation of butadiene to butane. In this case, this difference or resonance energy of butadiene is referred 28 Schomaker and Pauling, J .Amer. Chem. Soc., 1939, 61, 1769. 29 Wheland, The Theory of Resonance (John Wiley and Sons, Inc., New York, 1944).32 BOND RESONANCE ENERGIES to a butene-like base, rather than to a common " ethylene-ethane-like " reference structure. Since butene does not show resonance, i.e., there is only one basic structure, it is quite proper to use it as a resonance reference. However, it seems better to employ a common base such as ethylene- ethane-like bonds. It is true that then aEZ the effects which weaken or strengthen bonds will be involved along with resonance. However, in a large enough molecule it may well happen that the other effects besides the possibility for resonance may produce numerically as large changes in bond energy as does resonance.A detailed study of the hydrogenation of butadiene to butene and butane shows that the following relationships exist. Each molecule is referred to an ethylene-ethane-like base. Let QO1, QOZ, Qos = energy of atomization of butadiene, butene and butane Q1, Q2, Qs = actual energy of atomization of these molecules (based REi, RE2, RE3 = resonance energy or hyperconjugation energy or It is proposed to study first the hydrogenation of butadiene and butene, assuming them to be ethylene-ethane-like. The processes, buta- diene + H2 --f butene, and butene + H, + butane, are alike in the sense that the same bond changes occur. respectively referred to an ethylene-ethane base. on L(C) = 169.7 kcal.).near bond effect, etc., for these molecules. BUTADIENE : Qol = 939.53 kcal. 2 X 101.59 99'24 99'24 2 X 101.59 H H 125.07 84-53 125.07 H2- b C C F - H, BUTENE : Qot = 1080.88 kcal. 2 X 101.59 99-24 2 X 96-87 3 x 96.87 H H2 125.07 84'53 84'53 Q o a - Q o i = (2 x 96-87 - 99-24} + (84.53 - 125.07) H, b C C d - H , and and similarly + (3 x 96.87 - 2 x 101.59) = 141-37 kcal., BUTANE : Qo3 = 1222-23 kcal. 3 x 96.87 2 x 96-87 2 x 96-87 3 X 96-87 H Z H, Ha= C- C- C C HS 84'57 84'57 84'57 so that Qos - Qo2 = (3 x 96-87 - 2 x 101.59) + (84.53 - 125.07) + (2 x 96-87 - 99-22) = 141-37 kcal. These differences refer to the hydrogenation of butadiene to butene and butene to butane by hydrogen atoms C4Ht + 2H + C,H,* + 141.37 kcal. C4H$ + ZH -+ C,H,$ + 141-37 kcal. C,H$ + H, + C,H,* + 38-18 kcal.C4H$ + H, + C4H,*, + 38-18 kcal. The hydrogenations by molecular hydrogen are (0" K) C,H,* etc. represent the ethylene-ethane-like molecules. It is seen that or Q02 - QOI = Q o S - Qos, * ' (1) ~ ( Q o s - Q o z ) = Qos - Qol,GEO. GLOCKLER 33 i.e. twice the last step of hydrogenation equals the total hydrogenation from butadiene to butane, which is obviously true €or the starred struc- tures. If the bond energies of the real molecules and the basic reference structures are different either by resonance or otherwise, then the following relations exist where BEi are the resonance energies or other bond energy changing effects. (3) The differences in the Q's now refer to the hydrogenation of the actual molecule?, and it is seen that twice the diflerence in hydrogenation energy of the last step from butene to butane minus the total hydrogenation energy from butadiene to butane equals the resonance energy of butadiene (RE,) only if RE, = RE3 = 0.Qi = Qw + REi, * (2) Putting eqn. ( 2 ) into (I) yields 2(Ra - Q2) - (Qs - Qi) = 2(RE3 - BE,) - (RE3 - RE,). - The real molecules are represented as follows : BUTADIENE : Q1 = 958.50 kcal. 2 X 101.59 100.53 100.53 2 X 101.59 H H H , ~ C ~ C - C - C C - - - - - - - - H , 125.07 roo-go 125.07 BUTENE : Qa = 1086.77 kcal. 2 X 101.59 99.68 2 x 97'33 3 x 96-87 H H, H 2 C- G-------C- C H3 125.07 89.21 84.53 BUTANE : Q3 = 1218*51 kcal. 3 X 96.75 2 X 96.73 2 X 96-73 3 X 96-75 Ha Ha 83'77 83-51 83'77 H3=C--C-C- The hydrogenations (at oo K) are and The experimental values 3 O are 26.72 and 30.45 kcal.respectively (at 82' C). The usual calculation for the resonance energy of butadiene (using the values at oo K) is RE, = 2 x 28.48 - 53-53 = 3-43 kcal. This difference is, however, a(Q3 - Q2) - (a3 - $21) = 2VE3 - RE,) - (RE3 - J w 9 or 3-43 = z(- 3-72 - 5.89) - (- 3-72 - 18-98). Hence the resonance energy of butadiene referred to an ethylene-ethane base is 18.9 kcal. and on a butene base it is 958.50 - 945.07 = 13-43 kcal. The three resonance or strengthening or weakening effects of butadiene. butene and butane when referred to the ethylene-ethane base are 18.9, 5-9 and - 3-7 kcal. It is seen that the resonance energy 18.9 kcal, is only about three times the second value (5-9 kcal.). The latter effect 3O Kistiakowsky, Ruhoff, Smith and Vaughan, J .Amer. Chem. SOL, 1936, B 58, 146.34 BOND RESONANCE ENERGIES is due to some other influence than resonance and the impression is gained that the changes brought about in bond energies due to resonance effects and other features such a s hyperconjugation, etc., are only different in degree and not in kind. After all, were it possible to solve the wave equation without approximations, the concepts of resonance, Van der Waals' forces, etc. would not be needed. Benzene .-The average bond energies of benzene fit into general B(CC) against R(CC) and B(CH) against B(CH) curves based on the data of Table I using L(C) = 169.7 kcal. This is not the case for L(C) = 135.8 kcal. It is conceivable that several of these curves may be necessary for different kinds of bonds.The ordinary heat of formation 23 is 24 kcal. a t 0" K leading to Q,, = 1304.2 kcal. If the structure were Kekulk-like then this value would be 1224.2 kcal. The difference is the resonance energy of benzene of 80 kcal. The difference from the accepted value (39 k~al.~o. 3 l ) is due to the use of another set of bond energies (based on L(C) = 125.0 kcal.) 31 and because the heats of hydrogenation in steps from benzene to cyclohexane are to be interpreted in a manner analogous to the butadiene case mentioned above. I n the present instance there are three stages : Again Qoi refers to the ethylene-ethane base and Qi to the actual molecules. The quantities BEi represent the resonance energies of the molecules or any effect that causes them to be different from their basic reference structure.Since the steps of hydrogenation of the base struc- ture refer to the additions and subtractions of the same kind of bonds - C6H6 --f C6H8 4 C6Hlo -+ C6H12. Q02 - R o i = Qos - 9 o a = Qo4 - Qosj - (4) or 3(!?04 - Q03) = 9 0 4 - Qo1J which is obvious if all steps are alike. Qi of eqn. (2) where i(C6H6) = I, i(C6H8) = 2, i(C6H10) = 3 and i(C6H1,) = 4 yields 3@4 - Q3) - (94 - Qi) = 3(RE4 - RE31 - (RE4 - RE,). ( 5 ) The left side of eqn. (5) refers to three times the heat of hydrogenation of cyclohexene to cyclohexane minus the heat of hydrogenation of benzene to cyclohexane. This difference is only equal to the resonance energy of benzene (BE,) when RE, and RE4 are zero. The heats of hydrogenation of benzene at 355" K in steps are known : 8 2 Replacing the Qoi by the respective - oOK i 355OK I I I - 5-57 kcal.27'78 I J 28*59 I J - 5-5 kcal. 20-8 28.7 IS The corresponding heats of formation at 355°K are: Qr(C6H6) = - 19-10, Q,(C6H,) = - 24-67, Qt(C6Hlo) = 2-11 and Q,(C6Hlz) = 30.7 kcal. These values are known for benzene and cyclohexane at 0" K : Qf(c6H6) =- 24.0 and Qf(C6Hl,) = 20.7 kcal. The Q, values for C,H8 and C6H,, at 0" K were found by graphic interpolation to be : Q,(C6H8) = -29.5 and 9,(C6Hlo) =- 8.7 kcal. These data lead to the hydrogen- ation values at 0°K given above. On the usual basis it would be said 91Pauling, The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, 32 Kistiakowsky, Ruhoff, Smith and Vaughn, J . Chem. Physics, 1936, 58, N.Y., 1940). 137 and 146.GEO. GLOCKLER 35 that the resonance energy of benzene is 3 x 28-7 - (28.7 + 20.8 - 5.5) = 42.1 kcal., whereas this quantity equals the combination of RE-factors mentioned above. They can be found from the corresponding Qa values : Qa(C&) = kcal. and the similar values of their ethylene-ethane-like bases : g2(C,H6) = 1224-2, ax(C6H8) = 1372.6, Qg(C6HlO) = 1521.oandQ~(C,H,,) = 1669.5 kcal. The result is IZE(C,H,) = 80.0, RE(C,H,) =29-3, RE(C,H,,) = 4-9 and RE(C,H,,) = - 11.7 kcal. These values also yield 42-1 kcal. when placed in eqn. (5). In conclusion it should be said that no c l a h is made that the present set of bond energies is satisfactory in every respect. After all the heat of sublimation of carbon is not definitely settled. Even more important, the very definition of the term " average bond energy " is in question as pointed out recently by Szwarc and Evans.33 The main thesis of the present remarks is to emphasize that some acceptable system of bond energies must be invented if resonance energies are to be calculated and that the method involving heats of hydragenation must be applied properly. 1304'2J Qo(C6Ha) = 1401.9, Qa(C6H10) = 1525.9 and Qa(c~H12) = 1657.9 Financial support was received from ONR Contract N8 onr 79400. Department of Chemistry and Chemical Engiwerifig, Iowa City, Iowa. The State University of Iowa, 33 Szwarc and Evans, J . Chem. Physics, 1950, 18, 618.

ISSN:0366-9033    

DOI:10.1039/DF9511000026

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

GEO. GLOCKLER 35 IONIZATION AND DISSOCIATION BY ELECTRONIC IMPACT THE IONIZATION POTENTIALS AND ENERGIES OF SOME LIMITATIONS ON THE METHOD FORMATION OF SEC.-PROPYL AND TERT.-BUTYL RADICALS. BY D. P. STEVENSON Received 2znd January, 1951 It is shown that the mass spectrometrically measured appearance potentials of a variety of ions in a number of different substances are mutually consistent with the assumption that there are electron impact induced ionization and dissociation processes R, - R, + E -+ Rl+ 4- R, + ZE such that the appearance potential of R,, A(R,+), is given by the equality where I* ( ) and D( ) are the ionization potential and dissociation energy of the parenthetic substances, respectively. It is further shown that a necessary condition for the equality is I*(Rl) < I”(R,).If IS(Rl) > I*(R2), then i t is found that A(Rl+) > I*(R,) + D(Rl - R,) and probably the neutral product accompanying the formation of Rl+ is not R, but either R,* or F, + F, where the asterisk indicates electronic excitation and the F’s smaller dissociation fragments. The appearance potentials of C,H,,+, C3H,+, C,H,+ and C,H,+ in the mass spectra of a number of branched alkanes have been measured. It is found that in these cases that the condition, I*(R,) < P(R,), is satisfied, the appear- ance potentials of the ions C3H,+ and C,H,+ are mutually consistent and the A(R,+) = I”(R1) + wh- R,)36 IONIZATION POTENTIALS intercombination of the appearance potentials with the appropriate thermo- chemical data lead to D(sec.-C,H,-H) = 4-01 0.1 eV.D(tert.-C,H,-H) = 3-8, f 0.1 ,, P(sec.-C,H,) = 7*46 & 0.1 ,, P(tert.-C,H,) = 6.9, & 0-1 ,, It is thus found that the ionization potentials of the free radicals, CH,, C,H,, sec.-C,H, and tert.-C,H, do not parallel the ionization potentials of the cor- responding alkanes. It is suggested that i t would be of interest to determine whether the quantum theory offers an explanation of this lack of parallelism. It is shown that in certain mass spectrometers employing wolfram cathodes, there is insufficient differential pumping between the cathode and ionization chambers, and thus the apparent appearance potentials and intensities of certain ions in the mass spectra of some substances are falsified by the back diffusion of pyrolysis products in these mass spectrometers. The measurement of the so-called appearance potentials of the ions characteristic of the mass spectra of substances as excited by single electron impact in the dilute gas provides a potentially powerful means of studying the energetics of not only ions but also unstable molecules such as free radicals, The same difficulties are encountered in the interpretation of data obtained with mass spectrometers as are encountered in the inter- pretation of optical sFectra. These are the experimental ones of extra- polating observable intensities to limiting ones to determine character- istic energies and then associating the characteristic energies so determined with particular products and energy levels of the products.The mass spectrometric method has an advantage over optical methods in that in general the empirical formula of at least one of the products, the ionic one, is uniquely determined.This advantage is also a limitation on the method since it is thus required that only processes that lead to at least one ionic product can be studied. The experimental problem of extrapolating observations on ionization efficiency curves of ions in mass spectra to obtain the so-called appearance potentials that can be associated with definite energies has been solved by semi-empirical means. Methods of extrapolation have been found that not only yield reproducible limiting energies, the appearance potentials, but yield energies in agreement with those found by other methods. Thus extrapolating ionization efficiency curves for the molecule-ions in the mass spectra of a number of olefins in the manner found appropriate for agree- ment between the appearance potentials of rare gas ions and the spectro- scopically determined ionization potentials of the rare gases, leads to essential equality of the appearance potentials of the olefin molecule-ions and the ionization potentials of the olefins as determined from Rydberg series in their spectra in the vacuum ultra-violet., The interpretation of the appearance potentials of fragment ions in the mass spectra of complex substances involves the following problems.What are the neutral fragments that are simultaneously formed, and what are the states of electronic excitation of the neutral products and the ionic one ? I n addition to these problems the possibility arises that due to peculiarities of the potential hyper-surface of the state of the molecule-ion from which the fragments have been formed, i t has been necessary to endow the molecule-ion with more than the minimum energy necessary for the formation of the particular set of fragments in a par- ticular set of states. In the simplest case this would correspond to an activation energy for the formation of the molecule-ion, R,-R2+, from the radical R, and the ion R2+. It is the purpose of this discussion to show that in a number of cases the simplest set of assumptions suffice for the interpretation of the data to yield an apparently reliable determination of the energy of formation 1 Honig, J .Chem. Physics, 1948, 16, 105.D. P.STEVENSON 37 of the methyl radical. The methods employed for the determination of this energetic datum are employed to obtain the energies of formation and the ionization potentials of the sec.-propyl and tert.-butyl radicals from new experimental data on various Cs-cB alkanes. that the appearance potentials of certain ions in the mass spectra of propane and butanes could not be interpreted by means of a simple set of assumptions concerning their processes of forma- tion. Similar phenomena have been found with higher alkanes and a general rule is formulated for the prediction of those processes that may be interpretable through the simple assumptions. The origin of the failure of the simple assumptions has been explored by means of studies of isotopically labelled hydrocarbons.It has been found Experimental Measurements repoIted in this paper were made with a Westinghouse Type LV mass spectrometer somewhat modified in these laboratories. The modifi- cations and the method of measurement have been de~cribed.~~ The additive constant in the ionizing electron energy scale was determined by association of the initial break in the ionization efficiency curve of the argon ion, *OA+, with the spectroscopically determined ionization potential of argon, 15.76 eV.6 The possibility that the hydrocarbons might cause variation in the contact potentials associated with the electron gun was eliminated by making the measure- ments on argon simultaneously with those on the ions C,H5+, C,H6+, and C,H,+ in the mass spectra of the hydrocarbons.The contributions of the ion, C3H4+, to the m/q =. 40 current were corrected for by determining the relation between the ratios C,H4 +/C,H, + and C,H,+/C,E€, + as a function of apparent ionizing electron energy characteristic of the hydrocarbon mass spectrum in the absence of argon. The ratio C3H6+/C3H7+ was then used as a pseudo-energy scale for the determination of the contributions of C,H4+ to the m/q=40 positive ion current at any given apparent ionizing electron energy in the presence of argon. No detectable differ- ence was found between ionization effici- ency curves of argon as measured in the presence or absence of hydrocarbons. The appearance potentials were taken from the initial breaks of the ionization efficiency curves. The effects of range of the specific intensities of different ions were eliminated by the method of Smith,6 i.e.adjusting the intensity scale so that the linear portions of the ionization effici- IONIZING ELECTRON ENERGY-VOLTS FIG. I .--Ionization efficiency curves for the ions C4H,+ and C,H,+ of the 2 : 2 : 3-trimethylbutane mass spectrum. ency curve's were all of the same slope. The hydrocarbons upon which measurements were made were taken from the pure compound bank maintained by the Spectroscopic Department for calibration in spectrometric analyses. Linde Company spectroscopically pure argon was used. The appearance potentials that have been measured are given in Table I. Typical ionization efficiency curves are shown in Fig. 1-3. Stevenson and Hipple, J . Amer. Chem. Soc., 1942, 64, 1588.Stevenson, J . Chem. Physics, 1950, 18, 1347. Stevenson and Wagner, J . Chern. Physics, 1951, 19, 11. 5 Moore, Atomic Energy Levels (I Circular, Nut. Bur. Stand., c-467 (Washing- ton, D.C., 1949). 6 Smith, Physic. Rev, 1937, 51, 263.Molecule iso-C4Hl, . iso-C,HI2 . . z : 3-MeZ-Butane . z : 2-Me,-Butane . z : z : 3 : 3-Me4-Butane . neo-C,H,, . z : 2 : 3-Me3-Butane . FIG. 2.-Ionization efficiency curves for the ions C,H,+ and C,H5+ of the z : 2-dimethylbutane mass spectrum. A (CgHs') A (CSH6+) A (GH,') A(C4H8') A (CaH,') - 10.5~ f 0.1 11.0~ & 0.1 - - 13.2 0.2 10.2, f 0-1 10.8, f- 0-1 L - - 9.8, & 0'2 I0'Ys & 0'1 - - 13.6 & 0.2 I - 9'3 & 0'2 I0'Is & 0'1 - - - 10.32 f. 0.1 10.2~ & 0.1 I - 11.8, & 0 - 2 9'52 & 0-2 10'Oo 3 0'1 - - 9-24 0'1 9'79 & 0'1 - .O IONIZING ELECTRON ENERGY-VOLTS FIG. 3.-Ionization efficiency curves for the ions C3H,+ and C,Ho+ of the isopentane mass spectrum.Discussion The simplest assumption that can be made with respect t o the signifi- cance of the appearance potential of an alkyl ion in the mass spectrum of an alkane is that it corresponds to the energy of the process, - R, - R, + -+ Rl(X) + R,(X) + zE A (Rlf) = 'z(R,) f D(R1 - R Z ) J where X indicates the ground electronic state, A ( ) the appearance poten- tial, Iz() the ionization potential and D ( ) the dissociation energy. If such conditions obtain for the formation of an ion in the mass spectra of two substances, then the combination of the appearance potentials of the ion with the appropriate thermochemical data permits the determina- tion of a dissociation energy. For example, the appearance potentials of the ethyl ion in the mass spectra of ethane and propane in combination with the heats of formation of methane, ethane and propane, and theD.P. STEVENSON 39 dissociation energy of hydrogen into hydrogen atoms would yield the dis- sociation energy of methane, D(CH,-H), if C,He + Z? -+ C,H5+(X) + H(,.S+) + LF A(C2H5+) = Iz(C2H5) + D(C,H,--H), C,H8 + E +C2H5+(X) + CH,(X) + 2E The dissociation energy of methane, D(CH,-H), computed in this manner (termed the indirect method) could be in error if the two processes did not yield the ethyl ion in the same state, if the methyl radical were formed in an excited state or if either or both processes, and A (C,H5+) = IZ(CzH5) + D(CZHS-CH3).H + C,H5+ + CzH,+ CH, + C,H5+ + C3H8+ require an activation energy. It has been found that the appearance potentials of molecule-ions themselves can be reasonably accurately associated with the ionization potcntial of the molecule. Thus, the dissociation energy of methane, D(CH,-H), can be alternately calculated as the difference between the appearance potential of the methyl ion in the methane mass spectrum and the appearance (ionization) potential of the methyl ion in the methyl radical mass spectrum. Such a determination of D(CH,-H) would of necessity be greater than or equal to the true value, and it would be greater only bv virtue of an activation energy for the process H + CH,+ --f CH,+. This second method of obtaining dissociation energies from appearance potentials is termed " the direct method ".Agreement between deter- minations by the two methods would be strong argument for the validity of the simple assumption concerning these electron impact induced pro- cesses stated above. In the case of D(CH,-H), five pairs of processes have been examined and found to yield values that agree well within their experimental error. Furthermore, a direct measurement of the ionization potential of the methyl radical combined with either of two appearance potentials of the methyl ion gives D(CH,-H) in excellent agreement with the values deduced from the appearance potential pairs by the indirect method. These data and results are summarized in Table 11. There are also shown in this Table the results of determination of D(CH3-H) from the kinetics of photochemical reactions and pyrolyses. The complete agreement between the various determinations of D(CH,-H) shown in Table I1 can be taken as evidence that electron impact induced processes of the simple type described above do exist.It further suggests that the data in Table I may be similarly interpreted to yield dissociation energies of propane and isobutane, D (sec.-C,H,-H) and D (tert.-C,H,_H), respectively. The combination of the appearance potential, A(C,H,+) in the mass spectra of isobutane, isopentane and z : 3-dimethylbutane with the auxiliary data, z : 3-Me2-Rutane + CH, = iso-C,H,, + C,H,, = 0.18 eV,, z : 3-Me2-Butane -+ C,H, = iso-C,H,, + C,H,, AH:,, = 0.4 ell,, CH, = CH, + H C2H, = C,H, $- H D == 4-42 eV.D = 4.20 eV.8 7 Rossini et al., Selected Values of Properties of Hydrocarbons (Circular of the Nut. Bur. Stand., c-461, Washington D.C., 1947). See (a) of Table 11.40 IONIZATION POTENTIALS TABLE II.-TTARIOUS DETERMINATIONS OF D (CH,-H) Method Direct E.I. . Indirect E.I. . Electron Impact Average . Photochemical . Pyrolysis , ~ Process (a) CH, 3 CH,+ + (b) CH, -+ CH,+ + H + ( c ) CH,OH --f CH,+ + OH + E (d) C,H, -+ C,H6+ + H + E with C3H8 C,Hs+ + CH, + E (e) C,H8 -+ C,H7+ + H + 3 with 1 isoC,rI,, -+ C,H7+ + CH, + (f) C,H, 3 C,H6+ + H + with 7 isuC,H, + C,H,+ + CH, + (g) n-C,H7C1 -+ C,H7+ + C1 + with 7 (h) CH,OH 3 CH,OH+ + H + E with C,HsOH -+ CH,OH+ + CH, + E with I n-C4H,o + C3H7+ + CH3 + E J 3 (i) CH, + Br 3 CH, + HBr HBr -+ H + Br H I + H + I ( j ) CH,I -+ CH, + 1 D(CHI, -- H) eV (a) Hipple and Stevenson, Physic.Rev., 1943, 63, IZI. (b) Ref. (6) of text. (c) Cumming and Bleakney, Physic. Rev., 1940, 58, 787. ( d ) Stevenson, J. Chem. Physics, 1942, 10, 291. (g) Stevenson and Hipple, J . Amer. Chem. SOG., 1942, 61, 2766. (h) See (c). (i) Kistiakowsky et al., J . Chem. Physics, 1942, 10, 305 and 653 ; 1943, 1 1 , 6. ( j ) Polanyi et al., Nature. 1940, 146, 129 and 685 ; 1941, 147, 542 ; Trans. Famday SOC., 1941, 37, 377 and 648 ; 1943, 39, 19. result in D(sec.-C,H,-H) = 4-01 f 0-1 eV, Iz(sec.-C,H,) = 7*46 f 0-1 eV, while from A(C,H,+) in the mass spectra of neopentane, z : z-dimethyl- butane, z : z : 3-trimethylbutane and z : z : 3 : 3-tetramethylbutane and the auxiliary data z : z : 3 : 3-Me4-Butane + CH4= neo-C,H,, + iso-C,H,,, AH:,, = 0.03 eV,? z : 2 : 3 : 3-Me,-Butaiie+C2H,=z : 2-Me,-Butane+iso-C,H,,, AH:,, z : z : 3 : 3-Me,-Butane+C3H,=2 : z : 3-Me,-Butane+i~o-C~H,~, AH:,, and D(CH3-H) and D(C2H6-H) - -0*07,7 - 0-07, - D(tert.-C,H,-H) = 3.8, -& 0-2 eV, Iz(tert.-C,H,) = 6.9, & 0.2 eV, as summarized in Table 111.These dissociation energies for secondary and tertiary C-H bonds are in approximate agreement with the values given by Butler and Polan yi, D(sec.-C,H,-H) = 3.86 eV and D (tert.-C,H,-H) = 3-73 eV.D. P. STEVENSON 41 Process TABLE III.-VARIOUS INDIRECT ELECTRON IMPACT DETERMINATIONS OF D (sec.-C3H,-H) AND D(tert.-C,H,-H), AND OF IZ(sec.-C,H,) AND I* (tert.-C,H,) D(R-H), I*( R) ~ s o - C ~ H ~ O -+ C3H7+ + CH3 + E - } 2 : 3-Mez-Butane --f C3H,+ + C,H, + E iso-CsHlz -+ C3H7+ + C,H, + - } 2 : 3-Mez-Butane --r C,H7+ + C3H, + E 4.Oz 4'Il 7'54 - neo-C,H,, .+ C4Hs+ + CH, + E 2 : 2 : 3 : s-Me,-Butane --f C4H9+ + C4H9 + E } 2 : 2-Me-Butane 3 C4H9+ + C,Hs + z : z : 3 : 3-Me,-Butane --f C,H,+ + C,H, + E -} 7'36 3-89 3437 av.R = sec.-C,H, I 4-07 f 0.1 7'46 z t 0'1 av. R = tert.-C,H, 2 : 2 : 3-Me3-Butane + C,H,+ + C3H7 + 2 : 2 : 3 : 3-Me4-Butane -+ C4H9+ + C,H, + E "} 3.8, & 0.1 6-90 Jr 0-1 D(sec.-C3H7-H)-D(tert.-C,H9-H)=0~2 vs . 4-07 - 3.8,=0.1, 6.8, 6.9, The electron impact values for the dissociation energy of alkyl-hydrogen These bonds differ in several respects from those from pyrolysis kinetics. differences are : (i) a smaller range between D(CH,-H) and D(tert.-C,H,-H) according to the electron impact method, i.e.0-54 eV compared with 0.72 eV and (ii) the electron impact method gives less difference between D(C,H,-H) and D(sec.-C,H,-H) and greater difference between D(sec.-C,H,-H) and D(tert.-C,H,-H), respectively, than does the pyro- lysis method. According to Steacie the activation energies for the react ions CH3 + C2H6 +CH4 + CZHS CH, + C3H8 --f CH4 + C3H7 CH3 + iso-C4H1,3 + CH4 + C4H9 are 8, 6-8 and 4-2 kcal./mole, respectively. To the extent that these activation energies reflect the strengths of the primary, secondary and tertiary carbon-hydrogen bonds, they suggest the order of the inequalities, D(C,H,-H) > D(sec.-C,H,-H) > D(tert.-C,H,-H), by the electron im- pact method t o be preferable t o that given by the alkyl iodide pyrolysis method.It may be noted in this connection that the difference between the ionization potentials of propane and isobutane (0-9-1.0 eV) lo is greater than the difference between the ethane and propane ionization potentials (0.4 eV).% l o The ionization potentials of the alkyl radicals, CH,, C,Hs, sec.-C,H, and tert.-C,H,, IO-O,, 8.6,: 7*4s and 6-9, eV, respectively, roughly parallel those of the corresponding alkanes, namely, 13.3,~ 1.1-7,z 11.3 lo and I 0-4 2 eV, respectively. However, the free radical ionization potentials do not show the discontinuity of trend between C, and C, shown by the alkane ionization potentials. It is not obvious to the author whether or not exact parallelism would be expected to exist between the ionization potentials of these two homologus series on theoretical grounds.New York, 1946), p. 520. 9 Steacie, Atomic and Free Radical Reactions (Reinhold Publishing Corp., lo Delfosse and Bleakney, Physic. Rev., 1939, 56, 256,42 IONIZATION POTENTIALS Comparison of the mass spectrum of ordinary propane with those of n-propyl deuteride and sec.-propyl deuteride 4 has conclusively shown that in the formation of C,H,+ in the propane mass spectrum it is one of the secondary hydrogens that dissociates. The sum of the ionization potential of the sec.-propyl radical and the dissociation energy of the secondary carbon-hydrogen bond given above is 11.5~ & 0.1 eV. This agrees within experimental error with the value found for the appearance potential of C,H7+ in the propane mass spectrum, 11.67 & 0.1 eV.” It has also been shown that in the formation of C4H0+ from isobutane, it is the tertiary hydrogen that dissociates.The sum of the ionization and dissociation energies, Is(tert.-C,H,) and D (tert.-C,H,-H), given above, is 10.8 f 0.3 eV. This is considerably less than the value found for the appearance potential of C4H9+ in the isobutane mass spectrum, I 1-57 fo.2 eV.2 Since there are no sufficiently low states of the hydrogen atom, the difference between the calculated and observed appearance potential must be associated with excitation of the butyl ion. If the previously found appearance potential of C4Hg+ in the mass spectrum of tert.-butyl chloride, 10.2, & 0.1 eV,12 is combined with the heat of formation of tert.-butyl chloride (- 1-83 eV) and the dissociation energy of HCl (4.43 eV),13 the energy required for the formation of C4Hs+ + H from isobutane is calculatcd to be 10.8, & 0-1 eV, in excellent agreement with the value from the sum of ionization potential, I*(tert.-C,H,), and of dissociation energy, D(tert.-C,H,-H), given above.Since the appearance potential of C4Hg+ in the tert.-butyl chloride mass spectrum is thus shown to be compatible with the data reported in this discussion, the dissociation energy of the tertiary carbon-chlorine bond may be taken as the difference between this appearance potential and the ionization potential of the tert.-butyl radical, D(tert.-C4Hs-C1) = 10’2, - 6.9, = 3 ~ 3 ~ eV. It may be noted that neither the appearance potential of C2H,+ in the isopentane or z : 2-dimethylbutane mass spectra nor that of C,H,+ in the z : 2 : 3-trimethylbutane mass spectrum has been employed to deduce dissociation energies.The reason for these omissions will now be discussed. It was found that the appearance potentials of the methyl ion in the mass spectra of propane and the butanes 2 were considerably greater (ca. 5-8 eV) than the minimum values to be expected from the sum of the ionization potential of the methyl radical (10.0, eV) and the dissociation energy of the carbon-carbon bonds being broken, if the processes of forma- tion were C,Hs + .i? --f CH,+ + C,H,(X) + zE, - Thus, we may conclude the processes are not represented by the equations a s written, although the seemingly complementary processes giving ethyl and propyl ions, respectively, are represented by the equations C,Hs + E -+ CH,(X) + C,H,+ + 2E C,H,, + or C4HIo + E + CH,+ + C,H,(X) + zE.- --f CH,(X) + C,H, + 2E Examination of the mass spectra of the monodeutero-propanes and butanes reveals the processes yielding CH,+ must be quite different from those yielding C,H,+ (propane) or C,H7+ (butanes). The intensities of the ions C,H,D+ in the mass spectra of the isotopic propanes, n-C,H,D and sec.-C,H,D are approximately those to be expected from their molec- ular structure, and similarly for the intensities of the lions C,H,D+ in the mass spectra of the monodeutero-butanes.4 However, contrary to 11 Stevenson and Hipple, J . Amer. Chem. Soc., 1942, 64, 2769. 12 Ref. (g) of Table 11. 1, Herzberg, Molecular Spectra and Molecular Structure (Prentice Hall, hTew 1-ork, 1939).Closer scrutiny of the mass spectra of the various isotopic propanes and butanes suggests a possible reason for require- ment of an excited state of the molecule-ions, C,H,+ and C,H,,+ for the formation of CH,+.Al- 3 though the intensities of C,H,+ g and C,H,D+ in the mass spectra ; of n-propyl deuteride, and of 2 C,H,+ and C,H,D+ in the mass 5 spectra of the butyl deuterides were approximately those to be L~J expected from the molecular structures, it was found that B and similarly for n-butyl deuter- ide.4 Since such a large fraction ,.oo 5 0.80- o.40- n-C3H7D C,H,D+z 1.2 C,H,+ 0.20- of the propane and butane mole- 00- - - - 20.0 40.0 60.0 80.044 IONIZATION POTENTIALS and while and It is seen that extra energy of the magnitude of 1.2-1-7 eV is required.It may be of significance for the nature of the process that in these cases the extra energy is approximately that required for reactions of the type These results suggest the phenomenon first observed in the formation of the methyl ion in the mass spectra of propane and the butanes is indeed a general one and that there exists the general rule that for IS(R,) > 18(R,), the process R, - R, + E -+ R,+ + R, + ZE Iz(C,H,) - Ia(tert.-C,H,) = 8.67 - 6.9, = 1 . 7 ~ eV, triptane, A (C,H,+) - A (CIHO+) = 1-7, eV, Is(sec.-C,H,) - Is(tert.-C,H,) = 0.5, eV. alkyl radical = olefin + H. A H = 1.6 - 1.8 eV. requires A(%+) > WR,) + D(R,-R,), while for the complementary process R,-R, + E -+ R, + R,+ + 2 E The existence of this rule greatly limits the potential of the electron impact method of determining dissociation energies.Having reliable values for the ionization potentials of the methyl and ethyl radicals, it was hoped that measurements of the appearance potentials of either CH,+ or C,H,+ in the mass spectra of CH,-R or C,H,-R would suffice to determine the energy of formation of the radical R by the formulae D(CH,-R) = A (CH,+) - Is(CH,) or D(C,H,-R) = A (C,H,+)-18(C,H,). However, for this direct procedure to be applicable, it is necessary that P(R) > I"(CH,) or I'(R) > Is(C,H,). These conditions make the method inapplicable to all C, and higher alkyl radicals. The appearance potentials of the olefin ions, C3Ha-f- and C4H8+, in the mass spectra of the iso-alkanes, Table I, present an interesting example of a difficulty that may beset electron impact studies.In agreement with previous findings 2 the appearance potential of C,Ha+ in the mass spectrum of isobutane, 10.5 f 0-1 eV, equals the sum of the ionization potential of propylene 1 (9.80 & 0.05 eV) and the heat of the reaction, iso-C4H,, = C,H, + CHI, AH& = 0-80 eV. However, this appearance potential in the isopentane mass spectrum is lower than the least energy for the formation of C,H,+ from isopentane, iso-C,H,, + E -+ C3H6+ + C,Ha + zE, A(C,H,+) > 9.8 + 0.92 = 10.7 eV, and this appearance potential ( A (C,Ha+)) in the 2 : 3-dimethylbutane mass spectrum equals the ionization potential of propylene 1 It can only be concluded that isopentane to a small extent and z : 3-dimethylbutane to a greater extent pyrolyze at the wolfram cathode to give propylene among other substances, and that this propylene diffuses back into the ionization chamber and thus falsifies measurements of C ,HI+.The appearance potential of C4H8+ in the neopentane mass spectrum, A(C,H,+) = 10.3 0.1 eV is equal to the sum of the ionization potential of isobutylene (9.35 eV) 1 and the heat of the reaction, neo-C,H,, = iso-C,H, + CH,, AH,,, = 0.80 eV. For z : 2-dimethylbutane, 2 : 2 : 3- trimethylbutane and z : 2 : 3 : 3-tetramethylbutane, the appearance potential of C,H,+ is essentially equal to the ionization potential of isobutylene. Hence, here, too, pyrolysis and back diffusion must occur.* It does not seem likely that these pyrolytic reactions can lead to pro- ducts that would cause error in the measurements of the appearance potentials of the alkyl ions.This belief is based on the observation that * I t should be noted that these appearance potentials of C4H8+ strongly support Honig's determination of the ionization potential of isobutylene and his conclusion that the value found by Stevenson and Hipple ( J . Amer. Chem. Sot., 1942. 64, 2769), 8.9 eV, is in error. A (%+) > Is(%) + D(R,-R,).D. P. STEVENSON 45 with decreasing molccular weight the appearance potentials of alliyl ions increase. The low pressures obtaining in the mass spectrometer preclude association reactions that could lead to higher molecular weight substances which might cause low apparent appearance potentials. Furthermore, such substances would have been detected in the recordings of the com- plete mass spectra.If the pyrolyses lead to appreciable quantities of alkyl radicals C,H, and C4Hs, and these are sufficiently long lived to diffuse through the four slits that separate thk cathode from the ionization chamber, it is conceivable that the appearance potentials of C,H,+ and C4Hs+ given in Table I1 are low in the cases other than isobutane and neopentane. However, the internal consistency of the appearance poten- tials indicates such effect, if any, must be less than the experimental error. It is to be noted that the pyrolysis and back diffusion is not unique to the Westinghouse Type L.V. mass spectrometer. Koffel and Lad,'" using a spectrometer of quite different construction, have reported for isopentane, A (C,H,+) = A (C,H,+) - 0.9 eV ; for 2 : 3-dimethylbutane, A(C,H,+) = A(C,H,+ ) - 1.7 eV ; for 2 : a-dimethylbutane, A(C4H8+) = A (C4H,+) - 1.0 eV ; and for 2 : 2 : 3-trimethylbutane, A (C,H,+) = A(C4Hs+) - 1.1 eV.These differences are quite like those reported in Table 11, and thus we conclude their mass spectrometer also suffers from insufficient differential pumping between the cathode chamber and the ionization chamber. In view of the above, it is apparent that the reported intensities of such ions as C,H,+, C4H,+ and the like in the mass spectra of branched alkanes, the A.P.I. 44 Catalog of Mass Spectra, are of no real significance as far as indicating the probability of the formation of such ions by electron impact induced dissociations. The fact that the appearance potentials of the propylene and butylene ions in the mass spectra of isobutane and neopentane, respectively, are essentially equal to the sum of the heat of the reaction ; alkane = olefin plus methane and the ionization potential of the olefin indicates the absence of significant activation energy for the reverse reaction, olefin ion plus methane equals alkane ion. The absence of activation energy for this reaction indicates there may well be no activation energy for a re- action of the type, n-alkane ion -tsec.-alkyl ion plus sec.-alkyl radical. Thus it seems likely that the electron impact method is inapplicable to the evaluation of energies of formation and ionization potentials of C, and higher normal alkyls. Incomplete interpretation of data on the appear- ance potentials of C,H,+ and C4H,+ in the mass spectra of n-pentane, n-hexane, n-heptane and n-octane appears to substantiate this conclusi~n.~~ The author wishes to express his deep appreciation of the late Dr. Otto Beeck's continued encouragement in the here-described and other research. Shell Develo$mend Company, California. Emeryville, 1" Koffel and Lad, J . Chem. Physics, 1948, 16, 420. These authors made an extensive investigation of electron impact induced processes in the C,-C, alkanes. However, their use of linear intercepts as measures of appearance potentials renders their data non-comparable with the present work. Further, it has been shown that (Physic. Rev., 1943, 63, 121 : J . Cham. Physics, 1950, 18, 1347) appearance potentials deduced in this manner (linear intercepts) are not the minimum energies for dissociation processes. However, the linear intercepts do provide an approximate measure of the difference between appearance potentials. "That such ambiguity as this might arise in the interpretation of alky ion appearance potentials has been suggested t o the author by Prof. S. Winstein, private communication.

ISSN:0366-9033    

DOI:10.1039/DF9511000035

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

BEHAVIOUR OF PARAFFIN HYDROCARBONS ON ELECTRON IMPACT SYNTHESIS AND MASS SPECTRA OF SOME DEUTERATED PARAFFIN HYDROCARBONS BY D. 0. SCHISSLER,* $ S. 0. THOMPSON? AND JOHN TURKEVICH * I- Received 26th February, 1951 A method of preparation of mom-, di- and tri-deutero paraffin hydrocarbons containing the deuterium on one carbon atom is described. The mass spectra are given for all the deuterated methanes, four deuterated ethanes and two deuterated propanes. A quantitative explanation is given for the mass spectra of the deuterated methanes. The study of the products produced on electron bombardment of various deuterated hydrocarbons in a mass spectrometer is useful for several reasons. It permits the determination of both the number and type of the various isotopic molecules present in a given system thus affording a means of using stable isotopes for the study of homogeneous and heterogeneous reactions.' Furthermore, the decomposition of a hydrocarbon into various ionic fragments on electron bombardment in the ionization chamber of a mass spectrometer is an example of a truly unimolecular process.A study of this process in a number of deuterated compounds will undoubtedly throw light on the primary act of a molec- ular decomposition. For this purpose deuterated hydrocarbons of known structure and purity must be synthesized and examined in a mass spectro- meter. In a previous publication from the Frick Chemical Laboratory,B the synthesis and mass spectra of monodeuteromethane, monodeutero- ethane and two monodeuteropropanes were reported. In the present communication, we wish to report a new method of introducing one, two, or three deuterium atoms on a given aliphatic carbon atom as exemplified in the synthesis of mono- di- and tri-deuteromethanes, mono-, asym- metrical di-, and asymmetrical tri-deuteroethanes, mono-deuteropropane, and 2 : 2-dideuteropropane.The mass spectra of these compounds are presented and a quantitative treatment of the deuteromethane spectra is given. Experimental The introduction of deuterium atoms into hydrocarbons has been previously effected by the use of Grignard reagents and Dz0,2* 3* 4 D 6 and by the reduction of alkyl halides either by lithium aluminium deuteride and D20,6 or zinc and C,H,OD.' The Grignard reaction is difficult to manipulate because of the * Chemistry Department, Princeton University.t Chemistry Department, Brookhaven National Laboratory. 3 Ethyl Corporation Fellow, 1950-51. Turkevich, Bonner, Schissler and Irsa, Faraday SOG. Discussion, 1950, 8. Turkevich, Friedman, Soloman and Wrightson, J . Amer. Chem. SOC., 1948, Wagner and Stevenson, J . Amer. Chem. Soc., 1950, 72, 5785. Evans, Bauer and Beach, J . Chem. Physics, 1946, 14, 701. Turkevich, McKenzie, Friedman and Spurr, J. Amer. Chem. SOL, 1949, 71, Dibeler and Mohler, J . Res. Nut. Bur. Stand., 1950, 45, 441. Benedict, Morikawa, Barnes and Taylor, J. Chem. Physics, 1937, 5 , I. 70, 2638. 4945. 46SCHISSLER, THOMPSON AND TURKEVICH 47 large amounts of solvent necessary to form the Grignard reagent and is reported by one set of workers to lead to the formation of considerable amounts of olefin by a disproportionation reaction., On the otber hand, lithium aluminium deuteride is not a readily obtainable reagent. The use of zinc and C2H,0D involves the previous preparation of isotopically pure C2H,0D.The method used in this work for the preparation of deuterated hydrocarbons consists of the reduction of the corresponding organic halogen compounds by metallic zinc in the presence of heavy acetic acid (CH,COOD). It has wider applicabilicy than the other methods and involves a relatively simple experi- mental technique. The reaction is carried out in a vacuum apparatus consisting of a reactor tube fitted with three side tubes for the storage of the organic halide, the heavy water and the zinc. An excess of redistilled acetic anhydride is placed in the reactor tube and some thoroughly out-gassed, granulated zinc added.Any evolved hydrogen gas is pumped off. The purified alkyl halide is then distilled into the reactor a t liquid nitrogen temperature. The mixtuxe is warmed to room temperature and any hydrocarbon, produced by the moisture in the system, is pumped off. A small portion (0.5 ml.) of de-aerated heavy water (99.8 yo D20) is distilled into the reactor. The reaction is allowed to proceed to exhaustion of the acid and the deutero hydrocarbon so formed is collected in a sample bulb. Successive small portions of D20 are added t o the reaction mixture and the deutero hydrocarbon evolved after each addition is collected as a separate sample. In this way, the major portion of the protium contamination in the system is removed.Examination of the mass spectra of successive samples shows in- creasing deuterium content which reaches a constant value. The isotopic purity of the product after the third addition oj D,O is usually greater than 95 yo. No measurable quantity of deuterium gas or olefins is produced by this reaction. A controllable reaction with a minimum of side reactions is obtained by the use of mono-iodidesJ dibromides and trichlorides. The halides used in the preparations are the following : for CH,D, CH,I ; for CH,D,, CH,Br, ; for CHD,, CHBr, and CHCl, ; for CH,CH,D, CH,CH,I ; for CH,CHD,, CH,CHBr, ; for CH,CD,, CH,CCl, ; for CH,CHDCH, CH,CHICH, ; and for CH,CH,CH,, CH,CBr,CH,. The method is not applic- able t o the preparation of tertiary deuterides or to cases when the halide atoms are not on the same carbon atom because of the formation of olefins.The tetradeuteromethane was made by the Fischer-Tropsch synthesis of D, and CO over cobalt thoria kieselguhr catalyst and was isolated from the reaction products by distillation through a low temperature Podbielniak column, The hexadeuteroethane was made by reaction of dideutero acetylene with deuterium over a 5 yo Pd on charcoal catalyst a t oo C. The unsaturates were removed by bromine vapour treatment €or 36 hours and the product was dis- tilled through a soda lime tube to a trap a t liquid nitrogen temperature. The 2 : 2-dibrompropane was prepared from g g yo.propylene by means of the following intermediates : I : z-dibrompropane (bromine and propylene), methyl acetylene (I : a-dibromide and butyl alcohol + KOH),s z : 2-dibrompropane (methyl acetylene and HBr on activated charcoal a t 180O C).s The mass spectrometer is an all-metal 60' sector Nier type instrument.The accelerating potential is 2000 V and magnetic scanning is employed. The bombarding electron voltage is usually 75 V and the trap current is 40 PA. There is no pusher or drawing out potential in the ionization chamber. The positive ion currents are amplified by a Victoreen 5803 miniature tube with a grid leak of 2 x 10l0 ohms. The output of this tube is amplified through two stages and fed into a Brown electronic recorder. We wish t o thank Mi. W. Higinbotham for the design of the amplifying circuit. The isotopic purity of the compounds was determined in the following way.The presence of impurities of higher deuterium content was shown t o be neglig- ible in all our preparations by the absence of masses higher than the parent of the desired deutero compound. The amount of compounds of lower deuterium content was determined by measuring mass spectrum a t electron bombardmeat voltages just necessary to produce the ion of the parent mass.l0 (Olefin content of all preparations was shown to be negligible in the same way.) The impunties when present (usually less than 10 yo) and a CIS correction of 1-15 yo per carbon atom was subtracted t o give the results presented below. Hurd, Meinert and Spence, J . Amer. Chem. SOL, 1930, 52, 1138. Wilson and Wiley, J . Chem. SOC., 1941, 14, 596.10 Stevenson and Wagner, J . Amer. Cheun. SOC., 1950, 72, 5612.48 MASS SPECTRA - - - 100.0 73'4 16.9 4-02 1-80 1-06 - - Results Methane .-The mass spectra of all the deuteromethanes are presented in Table I. These patterns can be compared with those of protium methane in the following way. To the first approximation, the probability of a given process, e.g. the removal of a hydrogen atom, is the same in all the deuteromethanes. One can therefore calculate the abundance of ions of various masses on a pure statistical basis. The formulae for the various masses are given in Table 11, if one sets the constants a and b equal to one. An evaluation of how nearly the calculated spectrum approximates the experimental spectrum is obtained by TABLE I - - 100'0 59.0 27'5 3'53 3-56 0-94 1-01 195.54 2 400 - Mass - 20 I9 18 I7 16 I5 14 I3 Sum Sens div., mm.I2 CHZDS calc. z = 1.48 b = 0.65 CHDI calc. & = 1-80 b = 0.76 - 100'0 35'8 46.6 4-82 2-32 0'34 1-07 2'10 - - 1'02 % :I'I yo CD4 calc. b = 0.90 CH4 expt. CHDS expt. - 100'0 36.2 46'3 3'05 1-91 0'44 1-07 191.07 2-10 2200 CDa expt . 100.0 - 72.8 - 4'24 1-60 - - 1-10 179'74 - CHsD expt. - - 100'0 73'5 17'3 3'52 1-65 0.8 7 196.84 2830 b = 0.55 -I- ~~ - - 100'0 58-9 28.8 5-10 2-62 0.89 1-06 - - 1-14 "/c r2.6 yo COO'O - 72.8 - 6.72 2-24 0.78 - I - - 1-40 % 3'8 % - I - - 100'0 79.6 7-91 2.84 1.07 191.43 2580 Weighed statistical deviation . Pure statistical deviation . 0'3 % 8.0 Yo TABLE I1 CH3D CHzDa Ions Ion Currents Ions Ion Currents Mass 18 I7 16 I5 I4 I3 I2 CH,D$ CH,C++ CD,+ CHD+ CD+ + CH,+ CHf C+ CHD,+ 1-000 M,, ~ 5 0 0 ~ M15 0-5oob M1,+o*167a2 M,, o.667ab MX4 o.500a2b M1,+o.r67b2 M,, o.500ab2 M13 a2b2 M,, - CH,D+ CH,D+ CH,+ +CHD+ CH,++CD+ CH+ C+ CHD, CD, CD4+ CD,+ CD,+ CD+ C+ - - - - 20 19 18 I7 16 I5 14 13 I2 - CHD3+ CD,+ CHD,+ CD$ CHD+ CD+ CH+ C+SCHISSLER, THOMPSON AND TURKEVICH 49 taking the square root of the sum of the squares of the deviations and dividing it by the total’number of ions produced.The figuxe of merit so obtained for the pure statistical calculation is given in Table I. While This approach reveals the qualitative features of the experimental spectra of the various deutef-omethanes, it is not satisfactory from the quantitative point of view. The second approximation consists in weighing the rupture of a C-H bond in a deutero compound by a factox a and the rupture of a C-D bond by a factor b.49 The resulting iormulae are listed in Table 11.Using these formulae, the con- stants a and b are so chosen as to give a minimum value for the figure of merit. The values of a and b that give the best fit t o the experimental data, the corresponding cal- culated spectra, and the figure of merit are given in Table I. It is seen that the calculated spectra are in good agreement with those obtained experi- mentally. Furthermore, the values of a and b chosen t o give the best fit vary linearly with the deuterium content of the deuteromethane (Fig. I). Application of this method t o the data of Dibeler and Mohler on deuteromethanes 6 gives a good approximation t o the ex- perimental values except that all deviations are positive when the values of a and b herein reported are used.The mass spectra of the deuteromethanes were also measured a t an electron bom- bardment potential of 15-2 V. At this electron energy, the methane molecule suffers the rupture of only one carbon hydrogen bond and the positive ions produced are those of the parent mass and the parent mass less one or two depending on whether a hydrogen atom or a deuterium atom is lost. Thus, rhe isotopic factors a and b can be measured directly under these conditions. Thk I FIG. I.-Relationship of isotopic factors to deuterium content of methanes. values found are 1.12 and 0.5G for CH,D, 1-14 and 0.59 for CH2D2 and 1-58 and 0-79 for CHD,. It is evident that these factors differ from those used in the calculation of the spectra characteristic of 75-V electrons, although they do show the same tendency to increase with increasing deuterium content of the deutero- methane.Ethane .-The mass spectra of ethane, monodeuteromethane, dideutero- ethane I-d2, trideuteroethane I-d,, and hexadeuteroethane are presented in Table I11 with the spectra for monodeuteroethane and dideuteroethane I -d, calculated by a method similar to that used for methane and based on the formulae given in Table IV. The agreement between the calculated and ob- served spectra is satisfactory. The greatest discrepancies occur in masses 29 and 30 in dideuteroethane and, as we shall see later, this discrepancy may be associ- ated with the process of removal of two hydrogen atoms from the ethane mole- cule.The paxtern for trideuteroethane I-d, calculated in the same fashion is very different from the observed one. This difference may arise from a re- arrangement of the deuterium atoms in the preparation of trideuteroethane 1-d3, giving rise t o some trideuteroethane 1-d2, 2-d or may be due to a selectivity in the process of dissociation of ethane on electron bombardment. The dissociation of ethane leads to the production of a very large ethylene ion current (320 units) which is caused either by a e + C2H, -+ C2H4+ + H2 + 26,50 MASS SPECTRA or by a e + C2H, 3 C,H,+ + 2H + 28 process. The fact that the appearance potential for the ethylene ion is lower than that for the ethyl ion and is equal to that for the production of the C2H,+ ion suggests that the process of formation of the C,H,+ involves the removal of a H, molecule rather tban two H atoms.This H, molecule may be formed by the removal of two hydrogen atoms from the same carbon atom or from adjacent carbon atoms. The latter process appears favourable on chemical grounds be- cause i t leads to the formation of CH,=CH,f, while the other process would lead t o a CHs-CH+ species. TABLE I11 Mass C2H6D expt. 36 34 33 32 31 30 29 28 27 26 25 24 - - - - - 100'0 70.76 320.0 95'6 63'7 9-50 2'00 - - - - 100'0 62-4 133.0 63.0 33'7 6.1 1-54 256.7 Weighed statistical deviation Pure statistical deviation 18 I7 16 15'5 I5 14'5 I4 13'5 I3 I2 Sens. div. / mm. -- - - 0-28 10.44 3'43 0.17 1-19 0.56 - 8-49 I 240 . . - - 5'87 9-17 4'67 3'40 1-13 0.71 - 0'12 1005 CHaCHD, expt. - - - 100'0 55'9 181.7 196.5 77'6 52-1 28.3 5'1 1.50 - - - 4-14 2-30 2.68 5-69 2.85 2.61 0'10 0.95 0.78 I010 CHsCHD1 calc.a = 1.15 b = 0.80 - - - 100'0 54'3 187.9 186.0 81.8 55'6 25'9 6.1 2'22 2'0 yo 4'8 % - - - - - - - - - - - CH3CDs expt . - - 100'0 43'9 59'6 285'9 131-8 82.7 61.2 2 6.5 5.20 2.40 - - 2-50 4'77 3'14 6.19 1-62 3'42 1-20 0'10 1-20 1-19 830 C2H6 100'0 61-4 - 343'8 - 78.2 - 53'8 - 6.26 1.07 - 10'1 10'2 2'00 0.07 0.32 1-98 - - - 0.75 I 250 -- We must consider, then, three different processes for the removal of two bydrogen atoms : (I) the removal of two hydrogens from the same carbon atom, (2) the removal of two hydrogens from adjacent carbon atoms, and (3) a random process involving a statistical combination of the two.It emerges that there is no difference in the statistics of these three processes for the case of monodeuteroethane. For dideuteroethane I-d, and trideuteroethane I-d%, 2-d, the differences are very small. However, for trideuteroethane I-dg, the removal of two hydrogens from the same carbon gives the ratio of 0.5 : 0.0 : 0.5 for H, : HD : D,, from adjacent carbon atoms the ratio is 0-0 : 1-0 : 0-0, and random removal gives 0.2 : 0.6 : 0-2. The experimental value obtained from the observed spectrum is 0.06 : 0.71 : 0.23.* *These values were obtained by subtracting from the current of mass 31 the statistical value of the current due to the loss of one deuterium atom ; from mass 30, the very small contribution from the loss of three hydrogen atoms and, from mass 29, the statistical value of a (2H + D) process.SCHISSLER, THOMPSON AND TURKEVICH 51 In an attempt to gain further insight into the process of hydrogen removal from ethane, a study was made of the ions produced by electrons of 13'0V energy.At this potential, one obtains only the ions of the parent mass and the ions resulting from the loss of two hydrogen atoms. There are observed, there- fore, mass 29, 30 and 31 resulting from the loss of D,, HD and H, uncomplicated by contributions from one atom or 3 atom processes. With trideuteroethane I-d3, the following ion currents were measured : 5-1 for mass 31 ; 87.0 for mass 30 ; and 31.0 for mass 29. Thus, the ratio of removal of H, : HD : D, is 0.04 : 0-71 : 0.25 in agreement with the value calculated from the 75 V data.It is curious to note that the removal of D, is favoured over H, in this compound. If one uses this ratio of two hydrogen removal obtained at low potential to calculate the two atom removal process for the CH3CH, spectrum and the statistical approach with u and b equal to one for the production of all the other ions, one obtains a calculated spectrum that is very similar to the one observed experimentally. This is, however, not entirely satisfactory and addi- tional deuteroethanes must be synthesized in order to obtain a complete under- standing of the dissociation process of ethane in the mass spectrometer. 112-0 for mass 33 ; TABLE IV CH3CH,D Mass 32 31 30 29 28 27 26 25 24 Ions C,H,D + C,H,D + C,H,+ + C2H3D+ C,H,+ + C,H,D+ C,H,+ + C,D+ C,H + C2H3+ + CgHD+ c2 + 32 31 30 29 28 27 26 25 34 Ion Current - M30 0 .8 8 3 ~ M29 o-167b MBY + 0 . 6 6 7 ~ ~ M,, o~500a2b M,, + 0 . 3 3 3 ~ ~ M,, o.667a3b M,, + 0 . 1 6 7 ~ ~ M,, o.833a4b M,, 0'333Ub M28 + 0*500U3 M27 afb M24 CH ,CHD, C2H4D2+ C,H,D + +C,H,Ds + C2H3D2+ C,H3D+ +C,HD, + C,H,++C,H,D++C,I C,H +C2HD + C,H + C,H, + C,D + c2 + '2 + %I 0 . 6 6 7 ~ M29 0.533Ub M28+O*ZOOU3 M27 o.067b2 M,,+o.600u2b M,, +0.067a4 M,, 0.400ab2 M,,+o-533u3b M2, o.400a2b zM26+o-333u*b M,, o.667a3b2 M,, a4b2 M,, 0'333b M,g+o'400a2 fif,, The ion currents corresponding to the C, fragments as shown by the mass spectrum taken at 75 V electron bombardment are determined by the molecular structure of the isotopic species, but are complicated by the occurrence of doubly charged ions of the C, group and possible rearrangements of the hydrogens during the fission of the carbon-carbon bond.The following may be stated about the doubly charged ions. The number of doubly charged ions is not proportional to the corresponding singly charged ions. The parent ion is not capable of carrying a double charge as shown by the absence of the 15-5 peak in C2H,D and 16.5 peak in C,H3D If one lowers the bombarding potential t o 17.5 V the doubly charged ions $sappear and so also does the fragmentation of the methyl ion into methylene and methyne ions. A pure methyl ion spectrum is obtained under these conditions. If the compound preserved the methyl group structure on electron bombard- ment one would obtain for CH,CD3 only masses 18 and 15 in equal amounts, and for CH,CHD2 masses 17 and 15.The occurrence of masses 17 and 16 in the methyl ion spectrum of the CH,CD, compound and mass 16 in the methyl The results are presented in Table V.52 MASS SPECTRA ion spectrum of the CH3CHD2 compound signify either that there is a reshuffle of the hydrogen atoms when the caxbon-carbon bond is broken or that the com- pounds prepared, while containing the expected number of deuterium atoms, did not have the deuterium atoms in the desired positions due to rearrangement in the synthesis. It is hoped that infra-red examination of the compounds will clear up this point. TABLE V Mass CHaCDs 18 7'2 17 2'5 16 2'1 1.5 7'1 CHaCHDz - 9'2 3'0 9'5 - - - 11'0 10'2 21'2 Propane .-The mass spectra of propane, monodeuteropropane zdl and dideuteropropane 2d2 are given in Table VI.The mass spectra of monodeutero- propane 2dl and monodeuteropropane 2dz were previously discussed.* No attempt shall be made a t this time to develop a scheme ot calculating the spectra. Some observations will be made extending those given in the previous communication. The removal of the first hydrogen from C,H, must come predominantly from the secondary hydrogen in the molecule because the value of the ion current of mass I lower in C,H,D2-2d2 is very low, 14.8 compared to 83-4 for C3H, and 76.6 for C,H,D-2dl. The value of 221-1 for the mass 31 in the spectrum of C3H,D2-2d, indicates that the two deuterium atoms are on the central carbon atom. The equal values for mass 30 in C2H,D, and 28 in C,H, signifies that when methane is formed from a propane molecule the methyl group picks up a hydrogen not from the central carbon atom but from the end carbon atom.An examination This must wait the synthesis of more deuteropropanes. TABLE V1.-PROPANE Mass 46 45 44 43 42 4= 40 39 38 37 36 31 30 29 28 27 26 25 24 16 15 I4 I3 12 - I 100'0 12'0 38.1 10.6 83'4 4'32 7-8 I 36-5 1'0 - - 244'8 151-2 82-3 14.5 1-26 0'20 0.26 5.86 2-27 0.81 0'45 CsH,D-zdl - 100'0 76.6 18.5 27'9 15'9 19'5 25'5 9'0 1.14 5-48 - 267.0 172.4 77'0 45'9 8-88 1-06 0.39 2-54 6'47 1.93 0.71 0.59 100'0 14.8 27.2 15.6 I 6.6 18.1 14'4 9-81 5'59 3-52 0.84 221'1 157.4 70'7 61-5 23'7 4'32 0.46 2-64 4-09 1-54 0.53 0.32 0'10SCHISSLER, THOMPSON AND TURKEVICH 53 of the appearance potential of the mass 28 in C,H, disclosed that i t had approxim- ately the same value as the appearance potential of the parent ion and a lower potential than that necessary for the removal of a methyl group (mass 29). This would seem to indicate that when the parent ion can form an olefin ion and a molecule, e.g. ethylene and methane, this will take place very readily. It should be noted that the formation of propylene and hydrogen is not a favoured process as is the formation of ethylene and hydrogen from ethane. We wish to thank Dr. Oliver A. Schaeffer and Mr. Adolph P. Irsa for assistance in the mass spectrographic work. The work presented has been carried out in part under the auspices of the U.S. Atomic Energy Com- mission. Chemistry Department, Chemistry Department, Princeton University, Brookhaven National Laboratory, Princeton, New Jersey, Ufiton, Long Island, U.S.A . New York, U.S.A.

ISSN:0366-9033    

DOI:10.1039/DF9511000046

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

SCHISSLER, THOMPSON AND TURKEVICH 53 THE IONIZATION AND DISSOCIATION OF MOLECULES BY ELECTRON IMPACT BY C. A. MCDOWELL AND J. W. WARREN Received 19th February, I 95 I Part I describes the results of a study of the dissociation of methane by electron impact in a mass spectrometer. The appearance potentials of the ions have been measured and a method is given which shows qualitatively whether or not an ion is formed with initial kinetic energy. Various possible dissociation processes are discussed and from the more probable of these we have derived values for the dissociation energies D(CH,-H) , D(CH,-H), D(CH-H) and D(C-H). Of these the only one about which there can be much uncertainty is the value for D(CH-H). Some independent experimental determination of this dissociation energy is highly desirable.Part I1 gives the results cf appearance potential measurements on the ions CH,+, CH+, and C+ produced from methyl cyanide by electron impact. Various possible dissociation processes leading to the formation of these ions are dis- cussed. From the experimental data given in this section of the paper we have deduced values for D(CH-H) which are in good agreement with that obtained in Part I. PART 1.-METHANE Electron impact studies yield information concerning the ionization potentials of molecules and also knowledge of the amount of energy required to cause certain dissociation processes to occur. From this latter information one can in a number of cases derive values for the dissociation energies of various chemical bonds. This electron impact method is a very general one and can in principle be applied to any volatile compound.Furthermore, it has the advantage over most of the other methods in that it can yield values for the dissociation energies of several of the bonds in a particular molecule. There are two ways in which electron impact data can be used to determine dissociation energies ; these have been called the indirect and the direct methods by Hipple and Stevens0n.l The indirect method involves taking differences between the appearance potentials V(X+) of ions formed by similar dissociation processes ; whereas, the direct Hipple and Stevenson, Physic. Rev., 1943, 63, 621.54 IONIZATION AND DISSOCIATION ELECTRON method involves the determination of the appearance potential of a particular ion, and a knowledge of the ionization potential of its parent free radical. It should be mentioned that the direct method gives an upper limit for the dissociation energy of a bond and in several cases it has been found that the direct and indirect methods are in excellent agreement.The pioneer research on the dissociation of methane by electron impact using modern mass spectrometric technique was carried out by Smith Smith measured the appearance potentials of all the positive and negative ions formed, using the method of initial upward breaks to determine the appearance potentials. Though Smith gave a fairly full discussion of the possible dissociation processes, some of these may require modification for the precision of his instrument was much below that which is now possible.The appearance potentials of the positive ions CH,+, CH,+, CH2+ and CH+ were more recently determined by Koffel and Lad 3 who used the method of extrapolated straight line intercepts. These authors claim a somewhat higher precision than Smith,2 but it must be pointed out that the straight line intercept method of determining appearance potentials is not nowadays regarded as being entirely satisfactory. There is one remarkable discrepancy between the results of these authors and those of Smith; namely, Koffel and Lad failed to detect the second upward break in the CH,+ ionization efficiency curve reported by Smith, and only quote one appearance potential for this ion, giving a value which is intermediate between the two values given by Smith (see Table 11).We have confirmed the occurrence of this second process and very recently Geerk and Neuert have also ob- served this second ionization process producing the CH2+ ion. These authors record values for the appearance potentials of all the positive ions. Mitchell and Coleman 5 have also studied the dissociation of methane by electron impact but only report results for the CH,+ and CH,+ ions. These authors used a variation of the method of initial upward breaks to determine the appearance potentials and obtained a high degree of consistency in their results. Their method of calibration is, however, not entirely free from objection and their procedure might well have introduced systematic errors. Nevertheless, their result for V(CH,+) of 13-04 & 0.02 eV is supported by the work of Honig who used a very different technique.in 1937. Experimental Apparatus.-The dissociation processes produced by electron bombard- ment were studied in a Metropolitan-Vickers mass spectrometer ; the ion abundances being measured in the normal manner. For measurement of ap- pearance potentials the normal filament emission control unit was replaced by one dcsigned in this laboratory to enable the energy of the electrons to be varied over a range from o to IOO V. Determination of Appearance Potentials .-Though modern opinion is strongly in favour of the method of initial upward breaks for determining ap- pearance potentials7 from the ionization efficiency curves, i t is often far from clear how this method is applied by different authors.In most cases i t seems that the tails of the ionization efficiency curves are extrapolated to the voltage axis, on the tacit assumption that they intercept the latter a t a finite angle ; whereas they are actually asymptotic to this axis. By this method quite reproducible results are obtained in a given apparatus and under accurately reproducible conditions of sensitivity, but discrepancies are to be expected between the results of different workers. Smith, Physic. Rev., 1937, 51, 653. Koffel and Lad, J . Chem. Physacs, 1948, 16, 420. Geerk and Neuert, 2. Naturforsch.., 1950, 5 ~ , 502. Mitchell and Coleman, J . Ch.em. Physics, 1949, 17, 44. 6 Honig, J . Ckem. Physics, 1948, 16, 105. 7 Hagstrum, J . Chew?. Physics, 1948, 16, 848.C.A. McDOWELL AND J. W. WARREN 55 In the present work an attempt has been made to place the technique on a sounder foundation by the following procedure.8 The ionization efficiency curves ior the ion under investigation and for the calibrating ion are plotted so as to make parallel the approximately linear portions a few volts above the " initial break ". Differences of voltage between the two curves SV, for various ion currents I are then determined, and a graph of SV against I is then drawn. This graph is then extrapolated to zero current and the extrapolated value of SV taken to be the difference between the appearance potentials of the two ions. This method has been found to give very consistent results when applied to ions of high or moderate relative abundance, and in the present case has been applied to the more abundant ions from methane, namely, CH4+, CH,+, and CH,+.For ions of low relative abundance, such as CH+ and C+ from methane, considerable difficulty arises in the application of this method. Any technique requiring measurements of the " tail " in the ionization efficiency curve of such small beams of ions must be inaccurate. This is especi- ally the case when there is present a very small amount of an impurity giving the same ion a t a lower appearance potential, and such impurities are likely to arise, e.g. from thermal dissociation even when the gas sample is of the highest purity. So far we have been unable to solve the problem of accurate measurement in such cases. A definite and reproducible result can be obtained by the method of extrapolated straight line intercepts even for quite small beams.We find that, in general, this method gives rather high results com- pared with those obtained from observations on the tail of the ionization efficiency curve, when the standard is an inert gas. We consider, therefore, that our results obtained by this method in general give upper limits to the appearance potentials of those ions for which i t is used. Determination of the Initial Kinetic Energy of the Ions.-If an ion is produced with appreciable kinetic energy i t is to be expected that there will be some effect upon the distribution of the intensity in the focused beams of ions reaching the collector slit. Such effects have been observed in apparatus of very different design from ours and have been used to measure the initial kinetic energies of the ions.* The only effect that is observable with our apparatus is a very small increase in the width of the beam a t the collector slit, that is, i t is slightly defocused.On sweeping the beam across the collector slit by varying the ion accelerating potential P we can find the voltage change SP corresponding to the half-width of the beam. Then i t can easily be shown that the half-width is proportional to SP/P. This ratio is found to be roughly constant for all ions formed without kinetic energy, but it is higher when there is initial energy. The effect is illustrated in Fig. I for the ions from air. The magnetic field is kept constant and the different ions detected by varying P.The value of SP/P is seen to be the same for the molecular ions 02+, N,+ and H,O+ which must have very small initial kinetic energy in order to conserve momentum, whilst the beams for Of and N+ are wider. These ions are known to be formed with kinetic energy, that for O+ varying@ from o t o 1-1 V. It has not proved possible to obtain quantitative results by this method, which is nevertheless of value in providing evidence for or against the existence of initial kinetic energy in many cases. Fig. z shows the results obtained with methane together with a small amount of nitrogen. It appears that the ions CH,+, CH,+, CH+ and C+ are formed without kinetic energy. However, it must be noted that these ions will in this case receive only a very small part of the total kinetic energy evolved in their formation as a iesult of the conservation of momentum. Hence we cannot definitely exclude the possibility that there may be kinetic energy released in the formation of these ions.Results The relative abundances of the five heavy positive ions produced from methane by bombardment with 50-V electrons are shown in Table I, together with those found by Smith,a Diebler and Mohler,lo and Geerk and N e ~ e r t . ~ In Fig. 3 the early portions of the ionization efficiency curves €or CH,+, CH,+ and CH,+ are shown. These curves are typical for ions of fairly high relative abundance and so require no special comment. For CH2+, however, Warren, Nature, 1950. 165, 810. Hagstum and Tate, Physic. Rev., 1941, 59, 354 ; Berry, Physic. Rev., 1950, 7% 597.l o Diebler and Mohler, J . Bes. Nut. Bur. Stand., 1948, 40, 25.56 IONIZATION AND DISSOCIATION ELECTRON ~~ ~~~ FIG. 1.-1on beam half-widths for ions from air. FIG. 2.-Ion beam half-widths €or ions from methane. FIG. 3.-Ionization efficiency curves for CH4+, CH3+, and CH2+ from methane.C. A. McDOWELL AND J. W. WARREN 57 TABLE I.-RELATIVE ABUNDANCES OF THE HEAVIER POSITIVE IONS FROM METHANE PRODUCED BY 50-V ELECTRONS CH, + CH,+ CH,+ CH + C+ Ion 1 Smith I00 77'9 8.3 3'4 1'2 Diebler and Mohler I00 84.6 15'9 7'9 2'4 Geerk and Neuert I00 85 15'7 6.8 2.7 This Work I00 76.4 15-8 6.0 2'1 if the ionization efficiency curve is followed to slightly higher ionizating voltages, certain interesting features are observed. A typical ionization efficiency curve for this ion is shown in Fig.4. This curve is of particular interest in view of the fact that the second break was not observed by Koffel and Lad.3 The second break a t C is quite definite and reproducible. By straight line intercepts FIG. 4.-Ionization efficiency curve for CH,' from methane. TABLE II.-APPEARANCE POTENTIALS IN eV OF THE HEAVY POSITIVE IONS FROM hlETHANE Ion I Smith* CH, + CH3+ CH+ C+ CH,+ Koffel and Lad Mitchell and Coleman Geerk and Neuert 13'3 f o . 3 14'5 f0.3 16.5 50.3 21-5f1-0 22.5 f0.5 27.0 f 1.0 21-5 & I 29'5 Z t 1 Present Work 13-12fo-02 14-39 h0.02 15'30f0'5 22.4 50-1 26.2 foe2 upper limit 27'3 20'1 50.1 - Also, V(CH4+) = 13-04 eV, Honig, 1948. *V(CH,+) '14.5 f 0.1 eV, Hipple and Stevenson, 1943 (see ref. (I)). *Corrected for new value of I (argon).58 IONIZATION AND DISSOCIATION ELECTRON the difference between the first and second appearance potentials is 4-83 -J= 0.04 eV.Smith gave a somewhat greater value €or the difference in voltage between these two processes (see Table 11) but Geerk and Neuert found a value of 5 eV which is more nearly in agreement with our results. We can only suggest that Koffel and Lad probably failed to detect these two breaks because of too low a sensitivity. In this connection i t is interesting to note that a straight line intercept based on the portion CD of our ionization efficiency curve cuts the corrected voltage axis a t about 19.5 eV. It is to be noted that Koffel and Lad gave 20.0 f 0.3 eV as the appearance potential of this ion. i -4 -3 Ion Beam Currenl -3 Ion Beam Currenl -I € / e c h n Energy Valts (uncorr-.] FIG.5.--Ionization efficiency curve for CH+ from methane. FIG. 6.-Ionization efficiency curve for C+ from methane. The ionization efficiency curve for the CH+ ion is shown in Fig. 5. This curve is quite reproducible and there are three quite flat portions. Why these linear portions should occur is not clear. The appearance potential recorded is based on a straight line intercept from the portion AB. The linear portion AB is partly due to a background of impurities (mainly CO) and the straight line intercept of portion CD on the voltage axis has been taken as the appear- ance potential. It must be emphasized that this result is not so accurate as tht. appearance potentials recorded for the other ions.The highest possible value for the appearance potential is obviously the intercept of the linear por- tion DE with the volt.agc axis ; this occurs"at 27.3 eV. Fig. 6 shows the ionization efficiency curve for the C+ ion.C. A. McDOWELL AND J. W. WARREN 59 Dissociation Processes CH3+ Ion.-The process givins rise to this ion is undoubtedly For this process the appearance potential of the CH3+ ion is given by where IT(CH,) is the ionization potential of the methyl radical and D(CH,-H) is the dissociation energy of the CH bond in methane. The uncertainty in this relationship is due to the possibility that in the dissociation process the products might be formed with excess kinetic energy. From Fig. 2, however, we see that the CH,+ ion from methane is produced with little or no kinetic energj.This conclusion is further substantiated by the following considerations. The dis- sociation energy of the C-H bond in methane D(CH3-H), is now generally accepted as being equal to 4.43 & 0.05 eV,ll and subtracting this value from our appearance potential of 13.12 & 0 - 0 2 eV for the CH3+ ion, we calculate the ionization potential of the methyl radical I(C€€,), to be Q 9-96 & 0.05 eV. By direct experiment Hipple and Stevenson have obtained a value of I(CH,) of 10.08 f 0.1 eV. Since this result was obtained by an electron impact method in a mass spectrometer it can be compared directly with that deduced above. The agreement between the two values is so good that one can safely conclude that in the dissociation of methane to form CH,+ + H, the fragments are formed with little or no kinetic energy.CH2+ Ion.-There are two probable alternative processes for the formation of CH,+ ions from methane, namely, CH, + e == CH3+ + €I + ze. v(cH3f) + D(CH3-H)1 - (1) CH, + e = CH,+ + H, + ze . - (za) CH, + e -1 CH,+ + zH + ze. . * (2b) The appearance potential for process ( z b ) will be greater than that for process (2a) by an amount which will be of the order of the energy of dissociation 12 of the H , molecule, i.e. 4'48eV. Both of these processes are found as shown by the results in Table 11, and we can with some confidence identify the first appearance potential a t 15-30 eV with process ( z a ) , hence the appearance potential of the CH,+ ion is given by V(CH2+) > I(CH2) + D(CH3-H) + D(CH2-H) - D(H2).- ( 3 ) According to the data in Fig. 4 there is very little kinetic energy associated with this process * but in this type of multiple dissociative process where the ion detected is much heavier than the other fragments produced i t would be possible for these lighter fragments to be produced with some kinetic energy and yet this is not to be detected in the case of the heavy ion. An electron impact value of 11.9 f 0-2 eV has been obtained for the ionization potential I(CH2) of the C H , radi~a1.l~ Hence taking D(CH,-H) as 4-43 f 0.05 eV. and D(H), = 4-48 eV we can assign an upper limit to D(CH,-H), namely, D(CH,-H) Q 3.45 f 0.2 eV CH+ Ion.-This ion may be produced by either, or both, of the following processes : CH, + e = CH+ + 3H 4- ze .- (4a) CH, + e = CH+ + H, + H + ze (4b) . We have not been able to identify with certainty the occurrence of these alter- native processes. This is also a case where i t is difficult to decide whether much kinetic energy is associated with the dissociation process. Fig. 5 indicates that the CH+ ion itself has very little kinetic energy associated with i t but the other fragments produced are light compared with i t and so one cannot make any precise statement with regard to their kinetic energy. If the dissociation proceeds by process (4a) then we may write the following for the appearance potential of the CH+ ion V(Cli+) > I ( C H ) + D(CH3-H) + D(CH2-H) + D(CH-H). . ( 5 ) l1 Kistiakowsky and van Artsdafen, J Chem. Physics, 1944, 12, 462. l2 Herzberg, Molecular Spectra and Molecular Structure.I . Diatomic Mole- cules (Prentice-Hall, N.Y., 1950). Gaydon, Dissociation Energies and Spectra of Diatomic Aloleciiles (Chapman and Hall, London, 1947). * It should be noted that the beam half-width for the CH2+ ion of mass 14 is probably broadened due to the presence of N+ ions. l3 Langer and Hipple, Physic. Rm., 1946, 69, 691.60 IONIZATION AND DISSOCIATION ELECTRON Using the values given above for D(CH3-H), and D(CH,-H) and the value of 11.1 & 0.2 eV for the ionization potential of the CH radical as given by Douglas and Herzberg,14 we get D(CH-H) Q 3-4 0.3 eV. C+ Ion.-Many different possible ionization processes can be written for the production of this ion, namely, CH, + e = C+ + 4H + ze . - ( 6 4 CH, + e = C+ + 2H2 + 2e .* (6b) CH, + e = C+ + H, + 2H + e. . * (64 The ionization efficiency curves for this ion do not allow one t o decide un- ambiguously which of these three processes is occurring. Smith assumed that the C+ ion were produced by process (6a) and we think that this is the most reasonable assumption to make. If the C+ ions are, in fact, produced by process (6a) then we can write Since 15 I ( C ) = 11.267 eV we can deduce a value of D(CH) < 3.6eV on substituting the values calculated above for the various dissociation energies in this equation. V(C+) I(C) + D(CH3-H) + D(CH2-H) + D(CH-H) + D ( 6 - H ) . (7) Discussion Of the above estimated dissociation energies, that for B(CH3-H) is in excellent agreement with the value now generally accepted. The value obtained for D(CH) of < 3-6 eV is in good agreement with the spectroscopic value of 3.5 eV given by Herzberg.12 No similar check is available for the other two dissociation energies, though for D(CH,-H) Kistiakowsky and Rosenberg l6 have recently made an extensive study of the photochemical decomposition of ketene and from their kinetic results they deduce that D(CH,-H) must be of the order of 80 kcal./mole, or even higher.This agreement must be taken as substantiating the view expressed in this paper that the first appearance potential of the CH,+ ion is that for the process and the second appearance potential relates to the process One way of confirming the value of < 3-45 f 0.2 eV which we obtain for D(CH,-H) would be to study the dissociation of methyl radicals in a mass spectrometer.It is difficult to find any satisfactory way of assessing the accuracy of our value of Q 3-4 & 0.3 eV for D(CH-H). No experimental data are available which will allow one to calculate unambiguously a value for this dissociation energy. Recently, however, certain theoretical dis- cussions 11, 2 o have suggested that a value of about So kcal./mole or about 3.5 eV is to be expected. Some independent experimental confirma- tion is highly necessary because of the uncertainty as to whether the dissociation process we have chosen is, in fact, the correct one. Some uncertainty prevails regarding the value which we have deduced for D(C-H), namely, < 3.6 eV, for it will be recalled that there are other possible dissociation processes t o the one which we have chosen.This value, however, is in very good agreement with the spectroscopic value la of 3-5 eV. There can be little doubt that the true value of D(CH) is about 3-5 eV. If we denote by a, b, c and d, the respective dissociation energies D(CH3-H), D(CH,-H), D(CH-H) and D(C-H), then as Long and l4 Douglas and Herzberg, Can. J . Res. A , 1942, 20, 71. l 5 Bacher and Goudsmit, Atomic Energy States (McGraw-Hill, 1932). l6 Kistiakowsky and Rosenberg, J . Amev. Chem. Soc., 1950, 72, 326. l7 Voge, J . Chem. Physics, 1948, 16, 984 ; 1936, 4, 581. CH, + e = CH,+ + H, + 26, . . (2u) CH, + e = CH,+ + 2H + 28. . * (2b)C. A. McDOWELL AND J. W. WARREN 61 Norrish la have shown we obtain the following relation between the latent heat of sublimation of carbon (graphite) into ground state atoms, Li, at 2 5 O c , L, = a + b + c + d - 226.1 kcal.. - (8) As we have indicated above there is little reason to fear that the values which we have calculated for a, b, and d are much in error for they are in good agreement with data obtained from diverse independent sources. If the value which we have derived for D(CH-H) of 3-4 &0-3 eV is correct then from eqn. (5) we obtain a value of L, of 125 kcal./mole. Herzbergls and more recently Long and Norrish,le and Long 2 O have given extensive arguments to substantiate such a value. There have, however, recently been two direct determinations of the latent heat of vaporization of graphite, one by Brewer, Gilles and Jenkins a1 and the other by Marshall and Both of these groups of workers obtain a value of L, N 170 kcal./mole.It should be mentioned, though, that Goldfinger 22 has reported preliminary results which would suggest that the vapour pressure of graphite is higher than that obtained by these workers ; this would mean a value of L, much lower than 170 kcal./mole. If L, N 170 kcal./mole then it is necessary that D(CH-H) N 125 kcal./mole as has been pointed out by Laidler and Ca~ey.~3 If this value were correct then it would mean that the dissociation process which we have chosen is not the correct one. This high value for D(CH-H) can only be made to agree with our appearance potential for the CH+ ion by assuming that this ion is produced by the process rather than the one which we chose earlier. Furthermore, it would be necessary to assume that the fragments in this process are produced with an excess kinetic energy of - 2-44 eV.Because of the complicated dissociation process and the great difference in the mass of the fragments it is difficult to say how this excess kinetic energy would be distributed amongst the products, but one would have thought that the CH+ ion would have shared sufficient of it to enable an increase in the beam half width to be easily detectable. The data in Fig. 2 show that there is little or no increase in the beam half width for this ion. If the dissociation processes which we have chosen for the production of CH+ and C+ ions are correct then the appearance potentials for these ions lead to a value of L, in agreement with the lower estimates rather than the high value of 170 kcal./mole.This is easily seen by the following reasoning. CH, + e = CH+ + H, + H + 28, . * (4b) The appearance of the C+ ion has been associated with the process CH, + e = C+ + 4H + 2e . - ( 6 4 and the energy required has been found to be 26.2 eV. D(H,) = 4-48 eV,12 I ( C ) = 11.267 eV,16 and the heat of formation of methane = 0-74 eV, we get L, N 5.2 eV N IZO kcal./mole. It was pointed out previously that another interpretation of the ioniza- tion efficiency curve for the C+ ion led to the value of 27.3 eV as being a maximum for V(C+). If this were accepted as being the true value for V(C+) then we would obtain L, - 140 kcal./mole. It should be noted that this is an absolute maximum value if the dissociation process which we have written is the correct one.Since la Long and Norrish, Proc. Roy. Sac. A , 1946, 187, 337. l9 Herzberg, Chem. Rev., 1937, 20, 145. 2 o Long, Proc. Roy. SOC. A, 1949, 198, 62. 21 Brewer, Gilles and Jenkins, J. Chem. Physics, 1948, 16, 797. 22 Goldfinger (private communication to C. A. McD.). 23 Laidler and Casey, J. Chem. Physics, 1949, 17, 1087. 24 Marshall and Norton, J . Amer. Chem. Soc., 1950, 72.62 IONIZATION AND DISSOCIATION ELECTRON A second estimate for L, can be obtained from the appearance potential We have chosen to write the dissociation process leading of the CH+ ion. to the production of this ion as The ionization potential of the CH radical l4 is 11-1 eV ; D(CH) = 3-5 eV, we conclude that the process requires 14.8 eV. Since D(H,) = 4-48 eV l2 and the heat of formation of methane is 0-74 eV, we calculate L, N 120 kcal./mole.Thus this electron impact study of the dissociation of methane in so far as the dissociation processes which we have given are correct tends to be consistent with the lower indirect estimates of the latent heat of vaporization of carbon rather than the high direct experimental values. It must be pointed out, however, that in the very crucial dissociation process leading to the production of CH+ ions it is very difficult to be sure which of the two possible processes which we have given is the correct one. Some direct estimation of D(CH-H) is highly desirable and it might be possible to obtain this by studying the dissociation of CH, radicals in a mass spectrometer. We have made an unsuccessful attempt to do this and are hoping soon to return to this problem.Some indirect evidence as to the magnitude of D(CH-H) can be obtained from electron impact data on methyl cyanide for we have found that this molecule under the influence of electron impact dissociates in a similar manner to methane. The results obtained by a study of the dissociation of methyl cyanide by electron impact in a mass spectrometer are discussed in Part 11. CH, + e = CH+ + 3H + ze. . (44 CH4=C+4H . (9) and l4 since PART 11.-METHYL CYANIDE There has been no previous electron impact study of methyl cyanide as far as we are aware. Under the influence of electron bombardment this molecule gives rise to a considerable number of ions and we shall only consider here those ions which are of interest in helping to assess the correctness of our previous estimates of the dissociation energies of the CH bonds in methane.For this purpose the ions in which we shall be interested are CH,+, CH+ and C+. Experimental The methyl cyanide was a B.D.H. product which was dried over anhydrous magnesium perchlorate and then purified by repeated fractional distillation in a high vacuum. The appearance potentials of the ions were determined as described in Part I. Results As stated above we shall here only consider the ions CH,+, CH+, and C+ as these are the only ones which are of interest in helping to understand the energetics of the dissociation of methane by electron impact. These ions are produced from methyl cyanide with only a very small relative abundance and except for the first appearance potential of the CH,+ ion in the " initial break " method of determining appearance potentials is not applicable.The values we quote in Table I have been obtained by the method of straight line intercepts. It will be remembered that in Pa.rt I we point out that this method yields results which are always high ; but even with this limitation we think that the results quoted are of considerable importance and relevance for our discussion. The beam half-widths for the various ions were measured with a view to detecting the presence of kinetic energy as discussed in Part I. This case is much more favourable than methane because most of the dissociation processes lead to the production of ions which are lighter than certain other fragments. For the ions CH,+, CH+ and C+, in which we are a t present interested, this is particularly fortunate for these ions occur in dissociation processes in whichC .A. McDOWELI, AND J. W. WARREN 63 TABLE I.-APPEARANCE POTENTIALS FOR CERTAIN IONS FROM METHYL CYANIDE CH2+ CH + C+ Appearance Potential I 15-62 $: 0.04 - - Ion Extrapolated Voltage Differences I (eV) Straight Line Intercept CN radicals or HCN molecules are produced simultaneously. The beam half- widths should in this case give reliable results. In Fig. 7 we have plotted the beam half-width for various ions from methyl cyanide with those for 02+, N,+ and H20+ which are produced with zero kinetic energy. The beam half-width for O+ from O2 is also shown in this Figure. It will be recalled that in Part I FIG. 7.-Ion beam half-widths for ions from methyl cyanide.we indicated that this ion is produced witb kinetic energy of between o and 1.1 eV. This point should therefore be above the " zero " kinetic energy line as we have, in fact, found i t to be. Examination of this graph shows that the ions CH2+, CH+ and C+ lie on the line indicating zero kinetic energy of formation. We shall refer t o this fact in our discussion as ir is, of course, important to know when an ion is produced without appreciable kinetic energy. Discussion As with methane, CH2+ is found to be produced by two different dis- These two possible dissociation sociation processes in methyl cyanide. processes are CH,CN + e = CH,+ + HCN + ze . - ( 1 4 CH,CN + e = CH,+ + H + CN + 2e . ' ( I b ) It should be pointed out that another possible dissociation process namely, has been shown not to take place.Similarly no such dissociation pro- cesses occur in methyl cyanide which produce positive and negative CH,CN + e = CH,+ + H + CN- + 2e64 IONIZATION AND DISSOCIATION ELECTRON ions at the same time. We have proved this by studying the formation of CN negative ions from methyl cyanide and have found that these negative ions are only produced by a resonance capture process which produces a free CH , radical simultaneously. The CH,+ ion has mass 14 and it is important to point out that N+ ions are only formed with very low relative abundance from cyanides.22 As only two processes are observed for ion of mass 14 and both processes given above are to be expected we can assume that N+ is either not formed or else its appearance potential is practically coincident with that of CH,+ by the second process.For CH,+ ions beam half-width measurements were made for energies a few volts above and below the second appearance potential. At higher energies the beam is wider because of the formation of N+ from N, in the mixture. We have seen from the data in Fig. 7 that the CH,+ ion is formed with little or no kinetic energy hence we may write for the first appearance potential of the CH,+ ion the equation : From the results obtained in Part I we have hence we get Now the difference between the two appearance potentials for the CH,+ ion, i.e. N 4.0 eV, should give approximately the value of D(HCN). From this we get an approximate value for D(CH,-CN), namely, 4-2 eV.Another estimate of D(CH,CN) can be obtained by comparing the appearance potential of the CH+ ion from methyl cyanide and from methane. For methane we attributed the appearance of the CH+ ion at 22.4 eV to the process With methyl cyanide we have found two appearance potentials for the CH+ ion. The second break in the CH+ ionization efficiency curve occurs at 3 eV above the first. The cyanogen radical has as its ground state the elec- tronic configuration X2Z+ and there is an excited state, the B2Z+ con- figuration, at 3-14 eV above the ground state.l2 Thus the second process leading to the production of CH+ ions may be The first appearance potential of the CH+ ion is 22-4 eV, which is the same as that for the CH+ ion from methane.If this ion is produced by the dissociation processes (3) and (4) then we may write (6) and a similar equation for CH+ ions from methane, i.e., (7) Since ~(~H+)cH,cN = V(CH+)ca, we have l1 D(CH,-H) N D(CH,CN) N 4-43 eV. This value for D(CH,CN) is in very good agreement with that estimated from the appearance potential of the CH,+ ion from CH,CN. Eqn. (6) now enables us to obtain an estimate of D(CH-H) for we already know from Part I a value for D(CH2-H). I(CH) = 11.13fo-2 eV,14 hence, substituting D(CH,CN) N 4-3 eV, we get for D(CH-H) the value 3-5 eV which is in good agreement with the value estimated from the electron impact data on methane given in Part I. It will be recalled 25 Kurch, HustruIid and Tate, Physic. Rev., 1937, 52, 843. Tate, Smith and Vaughan, Physic.Rev., 1935, 48, 523. V(CH2+) = D(CH3CN)-D(HCN) + D(CH8-H) + I(CH2). . ( 2 ) D(CH2-H) + I(CH2) = 15-38 f 0.07 eV ; D(CH,-CN) - D(HCN) = 0.24 0.08 eV. CH, + e = CH+ + 3H + ze. . - (3) - (4) The first we attribute to the process CH,CN + e = CH+ + 2H + CN + ze. CH,CN + e = CH+ + ZH + CN(B2Z+) + 28. . ( 5 ) V(CH+)CH,CN = D(CH,CN) + D(CH,-H) + D(CH-H) + I(CH), V(CH+)ca, = D(CH,-H) + D(CH,-H) + D(CH-H) + I(CH).C. A. McDOWELL AND J. W. WARREN 65 that such a low value requires that the latent heat of vaporization of carbon L, to be N 125 kcal./mole. From Table I we see that the C+ ion is produced by two processes, one occurring at 22.6 f 0.2 eV and the other at 27.0 f 0.3 eV. There are several different ways whereby this ion may be produced.Amongst these the following are the most probable : CH,CN + e = C+ + 3H + CN + 2e . * ( 8 4 CH,CH + e = C+ + 2H + HCN + ze . . (8b) CH,CN + e = C+ + H + H, + CN + ze - (84 . Of these three the first would require the most energy and by analogy we may identify the upper appearance potential with this process. If this is the process occurring at 27.0 f 0.3 eV then since from Fig. 7 we see that the C+ ion does not seem to be produced with much kinetic energy, we get the following equation for the appearance potential Comparing this with the corresponding equation for the appearance potential of the C+ ion from methane we get F ' ( ~ + ) c H ~ c N - ~ ( C + ) C B * = D(CH,CN)-D(CH,-H) . (10) Since ~ ( C + ) C H ~ C N - ~(C+)CH, we again obtain the result that V(C+) = D(CH,CN) + D(CH2-H) + D(CH-H) + D(C-H) + I ( C ) (9) D (CH ,CN) N D (CH 3-H) . The first appearance potential for the C f ion is to be associated with We have previously either of the second two dissociation processes. obtained the result that D(CH,CN)-D(HCN) = 0.24 eV Now since D(CH,-H) = 4-43 eV and D(H,) = 4-48 eV, it would be difficult to distinguish between these two dissociation pro- cesses because the energy required for both of them will be approximately the same. As a corollary, therefore, we may choose either and the value which we obtain for D(CH-H) from the equation for the appearance potential will not depend on the choice of the dissociation process. If we assume that the first appearance potential for the C+ ion is associated with either of the dissociation process (8b) or (8c) then we may estimate the magnitude of D(CH-H). Since V(C+) = 22-6 f 0-2 eV and I ( C ) = 11-267 eV on substituting the values given in Part I for D(CH2-H) and D(C-H), and the value for D(CH,CN) given above we obtain D(CH-H) - 4.0 eV, which is in fair agreement with the previously obtained estimates given above of N 3.5 eV, bearing in mind that the linear intercept method tends to give ' high ' results. Thus the work described above leads to values for D(CH-H) of about 3.5 eV and we have seen in Part I that this value is to be associated with a latent heat of vaporization of carbon of about 125 kcal./mole. If one accepts the directly determined latent heat of vaporization of carbon of 170 kcal./mole as being correct it is difficult to reconcile the electron impact dissociation processes in methane and methyl cyanide with the necessary high value for D(CH-H) N 125 kcal./mole. Department of Inorganic and D (CH ,CN) N D (CH 3-H) . and Physical Chemistry, Department of Physics, University of Liverpool. University of Livevpool. C

ISSN:0366-9033    

DOI:10.1039/DF9511000053

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

POTENTIAL ENERGIES FOR ROTATION ABOUT SINGLE BONDS BY KENNETH S . PITZER’ Received 18th January, 1951 The theoretical relationships between the potential energy function for internal rotation and the energy levels and thermodynamic properties are summarized briefly. The height and shape of the potential barrier in ethane are re-examined in relation to all pertinent data. It is concluded that the barrier is very close to the cosine function in shape and from 2750 to 3000 cal./mole in height. The barrier heights for a number of other hydrocarbons are sum- marized and a few comments are made concerning the cause of these barriers. In the last fifteen years a great deal has been learned about the quanti- tative changes in potential energy associated with rotation about single covalent bonds within a molecule.Probably a majority of the examples investigated are hydrocarbons, and conversely all but the simplest hydro- carbon molecules allow internal rotations. Consequently a discussion of this phenomenon is appropriate to a symposium on hydrocarbons. The present contribution will attempt to review principally the theoretical aspects of restricted internal rotation but will also summarize some present best values for potential barriers. The theoretical problems are of two general sox ts. First are the phenomenological inter-relation- ships-the quantum energy levels and the statistical thermodynamic properties in terms of the potential energy function for internal rotation, the pertinent moments of inertia, etc. Second are theories as to the cause of potential barriers in terms of the behaviour of the valence electrons of the molecule.The principal problem involved in relating other properties to potential barriers associated with internal rotation is the calculation of the quantum energy levels for the system. It is more convenient to assume a form of potential function and then calculate energy levels than the reverse. A simple and very useful form is where V,, is the height of the potential peaks above the valleys, 4 is the rotation angle and n is the number of peaks and valleys, all identical, per revolution. Thus, if one or both of the rotating groups are sym- metrical, such as a methyl group, the appropriate value of n is given by symmetry. Nielson 1 first solved the Schrodinger equation with the potential of eqn.(I) and obtained the energy levels for certain cases. The chief complication is the interaction of the internal rotation with the rotation of the entire molecule. Koehler and Dennison treated this matter in further detail and gave solutions for any molecule which can be described as a pair of coaxial symmetrical tops. Actually Koehler and Dennison were particularly interested in methyl alcohol for which their solution is only an approximation. The Schrodinger equation is transformed by the separation of the over-all rotation co-ordinates and yields for a single internal rotation : V = &V,(I - cos n4), * (1) M”(x) + (a + ze cos ~x)M(x) = 0, . * (2) * On temporary leave from Department of Chemistry, University of Cali- fornia, Berkeley.Nielsen, Physic. Rev., 1932, 40, 44.5. Koehler and Dennison, Physic. Rev., 1940, 57, 1006. :Pitzer and Gwinn, J . Chem. Physics, 1942, 10, 428. 66KENNETH S. PITZER 67 with wherein W is the energy of a quantum state (above the zero of the potential curve), I,. is the reduced moment of inertia for the internal rotation and the other symbols are conventional or defined in connection with eqn. ( I ) . This is a relatively well-investigated differential equation, commonly known as the Mathieu equation. The boundary conditions for accept- able solutions depend on the relative moments of inertia of the two parts of the molecule and upon the quantum numbers of over-all rotation. Although these relationships can be fairly simple in special cases, they are so complex in the general case as to preclude presentation here.How- ever, it is important to give the relationship for the reduced moment of inertia for the most general case of eqn. ( z ) , namely, a symmetrical top attached to any rigid frame 3 r, = A ( I - 2 A & ~ / I ~ ) , . * (3) i=l where A is the moment of inertia (about the axis of internal rotation) of the symmetrical top, is the direction cosine between the axis of internal rotation and the ith principal axis of the whole molecule about which the overall moment of inertia is Id. In the special case of two coaxial tops of moment of inertia A , and A s this reduces to the familiar expression I, = A , A , / ( A , + A2). * (4) The general character of the energy levels as a func- tion of potential barrier height is shown in Fig.I. The energy levels lie within the shaded regions, one within each region. The dashed line indicates the potential barrier height. Well below the barrier the levels are simply defined and essentially vibrational. Above the barrier the regions are wide, indicating large interaction with over- all rotation, and the general spacing follou~s the pattern for rotation. Fig. I is strictly a plot of (a + 28) against 13. From eqn. (2) one then notes that the unit of energy on the figure vo FIG. 1 .-Energy levels for restricted internal rotation. The dashed line shows the top of the potential barrier. is proportional to ( ~ 2 / j , ) . The statistical mechanical formulae for thermodynamic properties involve sums over all the energy levels which, at sufficiently high tem- peratures, are not sensitive to small shifts in individual energy levels.Thus it is commonly sufficient to know that the energy levels for a given molecule are located one within each band shown in Fig. r . The Tables prepared by Gwinn and the writers for the thermodynamic functions are based on this assumption and are limited to the range of temperature,68 ROTATION ABOUT SINGLE BONDS moment of inertia, etc., for which the assumption is valid. While this covers almost all molecules a few exceptions such as methyl alcohol have been found. Halford 4 has given an interesting method for these excep- tional cases wherein a few low energy levels are calculated exactly by the method of Koehler and Dennison 2 and the higher levels are obtained by the much easier but approximate method of Halford6 based on old quantum theory.Treatments have also been given for less symmetrical6 or more com- plex classes of molecules than that of the rigid frame with attached symmetrical top. Although the classical mechanics can be carried out quite rigorously even for rotating groups attached to other rotating groups all unsymmetrical, etc., the quantum mechanics becomes very involved and has been handled only to a low approximation. However, actual molecules in these categories frequently approach classical be- haviour so that the thermodynamic properties can be calculated relatively accurately. Shape of Potential Barrier.-While most of the treatments of restricted internal rotation have been based on the simple cosine formula for poten- tial energy, eqn.(I), it has been realized that this was an assumption, and occasional calculations for other shapes have been made.s Recently Halford 6 s and Blade and Kimball 9 have discussed general methods by which the energy levels can be calculated conveniently for other shapes of potential curves. Halford has considered primarily examples quali- tatively different whereas Blade and Kimball attempted to examine whether eqn. (I) was accurate in simple cases such as ethane. Since some of the conclusions of Blade and Kimball seem to the present author to be misleading, an analysis of the situation for ethane is included here. Blade and Kimball constructed a potential curve from two parabolas fitted smoothly together. The parabola forming the lower part of the potential curve is defined in terms of a cosine barrier with the same curva- ture at the minimum.Specializing our problem to a three-fold sym- metrical barrier as appropriate to ethane, one has for the true cosine barrier equivalent to eqn. (I), v = Q vr (I - cos 34). - ( 5 ) It is important to distinguish between this true cosine barrier height Vgm and the constant for the lower parabola in the two parabola system because the two will be found to have different values for the same set of energy levels. Therefore we write V f z for the quantity defined by Blade and Kimball and their lower parabola becomes The upper parabola is defined in terms of the total potential barrier height as follows, Halford, J. Chem. Physics, 19.50, 18, 444.5Halford, J. Chem. Physics, 1947, 15, 645, and 1948, 16, 410. Pitzer, J. Ckem. Physics, 1946, 14, 239. 7 Kilpatrick and Pitzer, J. Chem. Physics, 1949, 17, 1064. 8 Halford, J. Chem. Physics, 1948, 16, 560. 6 Blade and Kimball, J. Chem. Physzcs, 1950, IS, 630.CORRIGENDUM To replace Plate I-facing page 82 '' Spcctroscopy and Molecular Structure ", etc., Discumion of the Farady Society, No. g, 1950.KENNETH S. PITZER 69 Blade and Kimball derived the energy levels approximately by the phase integral or W.K.B. method and give graphs from which they may be calculated. In treating ethane, however, they considered only one set of heat capacity data on the gas from gz to 134~ K, ignoring other data in this region, all heat capacity data at higher temperatures, the value of the entropy, and the spectroscopic value for the separation of the first two energy levels.Thus their conclusion that barriers over the range 1550 to 2700 cal./mole were correct for ethane cannot be accepted without further examination. In attempting to obtain the maximum information about the potential barrier in ethane, one should first consider the spectroscopic value recently obtained by Smith lo for the separation between the lowest pair of energy levels. His value is based on two combination bands and in each case the rotational fine structure is verified as correct for the assignment given. Thus there can be little doubt but that his value of 290 cm.-l is essentially correct. Unfortunately this value is not as precise as might be desired. The two bands yielded 287-1 and 294.8 cm.-l and it is even conceivable that the band centres were incorrectly identified l1 by 10 or zocm -l.Thus this energy level separation could be as low as the 275 cm.-l value derived by Kistiakowsky, Lacher and Stitt 1 2 from specific heat data. The entropy of ethane was obtained by Witt and Kemp lS from low temperature heat capacity measurements and is compared in Table I with calculated values using Smith's moments of inertia and vibration frequencies. One should first note that the entropy comparison at 184.1' K concerns primarily the lowest energy level separation. This is indicated by the fact that the value for a 3050 cal./mole cosine barrier, which corresponds to a zgo cm.-l separation of the lowest levels, is only 0.04 cal./deg.mole higher than the value for a zgo cm.-l harmonic oscillator, and similarly for the 2750 cal./mole barrier which has a 275 cm.-l separation of the lowest levels. Consequently it would be fruitless to compare a further variety of barrier shapes at this point. TABLE I.-ENTROPY OF ETHANE AT 184.1" I< (Ideal gas a t I atm. in cal./deg. mole) Experimental . - 49'54fO.I5 Harmonic osc. v = 290 cm.-l. . 0.74 Harmonic osc. 275 cm.-l. . 0.81 Calc. for trans., rot., and vibr. . . 48.69 Expl. for internal rotation . 0.85 Cosine barrier Vo = 3050 cal./mole . 0.78 Cosine barrier 2750 cal./mole . 0.87 One can conclude that the separation of the lowest pair of energy levels is probably in the 275-290 cm.-l range, where the upper limit arises from the entropy value and the lower limit from the spectroscopic data.The principal basis for discussion of the shape of the potential barrier is the heat capacity curve for the gas. Fig. 2 shows the experimental data l4 over the range 90-305' K, together with several calculated curves. The contributions of translation, rotation and vibration have been sub- tracted so that only the contribution of internal rotation is shown in Fig. 2 . The two solid curves are for cosine barriers of the heights indicated, while l o Smith, J. Chem. Physics, 1949, 17, 139. l1 Dr. L. Smith mentioned this possibility in private communication. l2 Kistiakowsky, Lacher and Stitt, J . Chem. Physics, 1939, 7, 289. l3 Witt and Kemp, J . Amer. Chem. SOC., 1937, 59, 273. l4 Hunsmann, 2. 9hysiR. Chem. B, 1938, 39, 23 ; Eucken and Parts, 2.physik. Chem., B 1933,20,184 ; Heuse, Ann. Physik, 1g1g,59,86 ; Kistiakowsky and Nazmi, J. Chem. Physics, 1938, 6, 18 ; Kistiakowsky and Rice, J . Chem. Physics, 1939, 7, 281 ; also ref. (12).70 ROTATION ABOUT SINGLE BONDS the dashed curves are for a series of two parabola barriers of various heights. Each of the latter series has the lowest pair of energy levels spaced at 290cm.-l which corresponds to VEG = 2570 cal./mole. One can see from the upper dashed curve, for V F = 2050 cal./mole, how Blade and Kimball were led to false conclusions by considering only the data of Kistiakowsky, Lacher and Stitt. This curve fits this particular set of data fairly well but is totally unacceptable at higher temperatures. Also the difference between the quantities J$- and Vt: is indicated by their respective values 3050 and 2570, each corresponding to the 290 cm.-l separation of lowest energy levels.I FIG. 2.-The heat capacity for internal rotation in ethane for various assumed potential barriers. The 275-290 cm.-l range for the lowest energy level separation, which was found probable above, receives further support from the data near IOOO K in Fig. 2. The cosine barriers fit the somewhat scattered data in the range around 150O K as well as is possible but yield slightly low values near 300° K. However, the difference at the higher temperatures is within the limit of the various errors involved. The best of the two parabola curves, that for VEK = 2830, is no net improvement being too low in the 150-2ooo K range while yielding slightly better fit near 300' K.Thus one can conclude that the potential barrier for ethane probably has a height in the range 2750-3000 cal./mole and is very close to the cosine function in shape. The deviation indicated is that of a slight lowering and flattening of the potential peaks as compared to the re- mainder of the curve. Only recently has the work of Smith l o provided strong evidence from data on ethane itself that the stable or minimum energy configuration is the staggered one (point group DM). However, the general pattern of evidence from substituted ethanes had long indicated this result. Potential Barriers for Various Hydrocarbons .-There are assembled in Table I1 most of the available values for potential barriers to internal rotation in hydrocarbons.The cosine shape of barrier is ordinarily as- sumed. In cases of several equivalent rotations, the barriers are assumed independent and equal. Where this assumption seems doubtful theKENNETH S. PITZER resulting value is indicated as an average, (av.). Ranges of uncertainty are given where the completeness of the data justified it-in other cases somewhat larger uncertainties must be allowed. Most of the barriers in Table I1 are for methyl group rotations under circumstances in which the three-fold symmetry of the methyl group applies also to the potential function. In toluene and approximately in m- and p-xylene the combination of two-fold symmetry of the phenyl group with the three-fold symmetry of the methyl yields a six-fold sym- metry for the potential barrier.Styrene has a two-fold symmetry for the vinyl against phenyl rotation while I : 3-butadiene has two equal potential peaks but the cis and trans minima are different. TABLE 11.-VALUES FOR POTENTIAL BARRIERS TO INTERNAL ROTATION IN VARIOUS HYDROCARBONS Substance Ethane Propane . isoButane . neoPentane . Propylene . isuButene . trans-2-Butene . cis-2-Butene Toluene . m and p-Xylene . o-Xylene . I : 3-Butadiene . Styrene. . Dimethylacetylene Vo, cal./mole I950 450 bV.1 500 & 500 500 f 500 2000 (av.) 5000 trans to peak { 2575 cis to peak } 2200 0 Source Present paper Pitzer,ls also Kemp and Egan 16 Pitzer and Kilpatrick,17 also Aston et a1.18 Pitzer and Kilpatrick,l7 also Aston and Messerly 19 Kilpatrick and Pitzer 20 Kilpatrick and Pitzer,20 also Kilpatrick and Pitzer 2O Kilpatrick and Pitzer,20 also Aston, et aLZ1 Pitzer and Scott 2a Pitzer and Scott 22 Pitzer and Scott 22 Aston, Szasz, Wooley and Brickwedde 21 Pitzer, Guttman and Westrum 2a Kistiakowsky and Osborne et ~ 1 .2 ~ Aston et aL21 Internal rotation about the middle bond in n-butane is related to the r : 3-butadiene case but somewhat more complex. Of the three potential minima for the n-butane, one is in the trans position while the other two are enantiomorphs called gauche or skew forms. The full details of this potential curve for n-butane are not known yet. Assuming that the potential barriers €or the end methyl group rotations are similar to those in propane, one finds the general magnitude of the height of a potential peak above adjoining valleys to be in the 3000-4000 cal.range.26 Also l6 Pitzer, J . Chem. Physics, 1944, 12, 310. 16 Kemp and Egan, J . Amer. Chem. SOC., 1938, 60, 1521. 17 Pitzer and Kilpatrick, Chem. Rev.. 1946, 39, 435. 18 Aston, Kennedy and Schumann, J . Amer. Chem. SOC., 1940, 62, 2059. 19 Aston and Messerly, J . Amer. Chem. SOC., 1936, 58, 2354. 2 0 Kilpatrick and Pitzer, J . Res., Nat. Bur. Stand., 1946, 37, 163 ; also 21 Aston, Szasz, Woolley and Brickwedde, J . Chern. Physics, 1946, 14, 67. 22 Pitzer and Scott, J . Amer. Chem. SOC., 1943, 65, 803. 23 Pitzer, Guttman and Westrum, Jr., J . Amer. Chem. Soc., 1946, 68, 2209. 21 Kistiakowsky and Rice, J . Chem. Physics, 1940, 8, 618. 26 Osborne, Garner and Yost, J . Amer. Chem. Soc., 1941, 63, 3492. 26Pitzer, J .Chem. Physics, 1940, 8, 711 ; Ind. Eng. Chem., 1944, 36, 829. 1947, 38, 191.72 ROTATION ABOUT SINGLE BONDS the gauche or skew minima are known to be about 750-1000 cal./mole above the trans minimum. This latter value came first from the writer’s statistical-thermodynamic treatment of a series of n-paraffins,2s but has recently been measured by Szasz, Sheppard and Rank2’ from the shift of the relative intensity of Raman spectral lines for skew and trans forms with change of temperature. This spectroscopic method has been applied as yet only to the liquid state for n-butane, which leaves the uncertainty of the difference in heat of vaporization of the trans and skew forms. However, data in the gas phase have been obtained for some halogen derivatives using the infra-red instead of the Raman spectrum.Assum- ing that the necessary intensities can be had, gas phase data should be obtainable for hydrocarbons also. The skew-trans energy difference in n-butane has found interesting application in the methyl substituted cyclohexanes where similar geo- metrical situations arise.28 These results also tend to verify the value given above. More complex hydrocarbons have, of course, additional possibilities of internal rotational minima corresponding to non-equivalent configura- tions with different energies. The writer has preferred the term tautonzers (rather than isomers) in describing these configurations since they are in rapid reversible equilibrium with one another. Cause of Potential Barriers.-There have been a number of investiga- tions directed to the explanation of these potential barriers in terms of electron or valence theory.In the present degree of advance of quantum mechanical calculations an exact solution is impossible and attempts at approximation have as often as not yielded the wrong sign or a totally wrong order of magnitude. However, one can say that there is every reason to believe that the actual single bond itself, i.e. the pair of electrons and the orbital describing their motion, does not resist rotation appreciably. The writer has made perturbation calculations for the ethane case and has found that the maximum potential energy differences associated with the carbon-carbon bond itself are several orders of magnitude smaller than the observed barrier.Thus the observed phenomena must be associated with the electron pairs attaching other groups, i.e. the C-H bond electrons in ethane. Of course, where the attached groups are large enough there may also be other interactions between them. stated in 1938 that the potentials were due to “ a n interaction of electron pairs forming single bonds on adjacent polyvalent atoms ”. Today we can add with certainty that the interaction is repulsive, i.e. the staggered configuration is the stable one, and that there is doubt as to the limitation to single bonds on the adjacent atoms. Otherwise this statement summarizes the current position on this question. Of the more detailed calculations that of Lassettre and Dean 5 0 is probably the most interesting and plausible.They attempt to account for the barriers by an electrostatic model recognizing quadrupole as well as dipole moments for the bonds. In hydrocarbons the dipole moments are small but, if the bonding electrons are largely concentrated between the nuclei, the quadrupole moments could be large enough to account for the observed barriers. In extending their work to more complex molecules, Lassettre and Dean found peculiar unsymmetrical configur- ations to have minimum energy in isobutane and neopentane. Thus these molecules would appear to deserve further study. Kistiakowsky, Lacher and Ransom 27 Szasz, Sheppard and Rank, J . Chem. Physics, 1948, 16, 704; see also 28 Beckett, Pitzer and Spitzer, J . Amer. Chem. Soc., 1947, 69, 2488. 29 Kistiakowsky, Lacher and Ransom, J . Chem. Physzcs, 1938, 6, goo. 80 Lassettre and Dean Jr., J . Chew. Physics, 1949, 17, 317. J . Chem. Physics, 1949, 17, 86.KENNETH S. PITZER 73 It seems likely to the writer that the true explanation of these potential barriers may be more complex than any of the treatments offered as yet in that more than one effect is of importance. The same sort of “ van der Waals ” repulsive forces arise between pairs of electrons in different atoms or bonds within a molecule as between different molecules. It has been shown that this effect is too small to account for the full barrier in ethane if only the regions describable as the hydrogen atoms are con- sidered. However, an additional contribution will arise from these same C-H bond electron pairs in the regions near the carbon nuclei and this term is very difficult to calculate. However, these effects can be shown to be of the right order of magnitude. Thus this “van der Waals” type of repulsive forces and the quadrupole electrostatic effects probably each contribute substantially to the net barrier. U.S. Atomic Energy Commission, Washington DC.

ISSN:0366-9033    

DOI:10.1039/DF9511000066

出版商:RSC    

年代:1951

数据来源: RSC

摘要:

KENNETH S. PITZER 73 THE PRESENT STATUS OF THE PROBLEM OF HINDERED ROTATION IN HYDROCARBONS AND RELATED COMPOUNDS BY JOHN G. ASTON Received 13th February, 1951 A review of the facts and theories related to barriers hindering internal The thermodynamic functions for hindered rotation in hydrocarbons is given. rotations are discussed. It is proposed to review briefly the history and present status of our knowledge about the potential barriers hindering rotation about a single bond with particular reference to hydrocarbons. Historical.-In 1935 Teller and Topleyl made a calculation of the equilibrium constant for the hydrogenation of ethylene using the heat of hydrogenation and the spectroscopic and molecular data. They found a discrepancy which would disappear if the barrier hindering interna 1 rotation were actually 3000 cal.mole-' instead of a value of 360 cal. mole-1 previously calculated by Eyring. In the meantime measurements of the third law entropy of tetramethylmethane by Messerly and Aston 3 and of ethane by Witt and Kemp l4 had given values which did not agree with values calculated from spectroscopic and molecular data. These considerations led Kemp and Pitzer l4 to suggest that a barrier of about 3000 cal. mole-1 hindering internal rotation was responsible in all cases and that this was the rule rather than the exception. Following this, the brilliant paper of Pitzer * appeared in which a number of hydrocarbons were treated and typical barriers evaluated. A general approximate treatment of the problem of the thermodynamic functions for a hindered rotor was given, accompanied by tables for the thermodynamic functions.For the potential function hindering internal rotation the expression is used, where V,, is the barrier height and n is the number of equivalent minima. v = *v,(I - cos we), . - (1) I Tellyr and Topley, J. Chem. SOC., 1935, 876. Eyring, J . Amer. Chem. Soc., 1932, $4, 3191. Aston and Messerly, J. Chem. Physzcs, 1936, 4, 391 ; J. prner. Chem. SOC., 1936, 58, 2354. Pitzer, J . Chem. Physzcs, 1937, 5, 473.74 HINDERED ROTATION The energy and heat capacity are tabulated directly. Instead of recording the entropy value the quantity tabulated is the difference between the entropy S,, and that, S f , calculated using the free rotational partition function. The tabulated values are thus the quantities Srr- S f , with Sj = R(-0.775 +Q In T + Q In I r e d x 1040 - In n) .(2) Instead of the free energy, (Ff - F J / T is tabulated, where F,, is the value for restricted rotation and - F’/T = R(-1-275 + 8 In T + Q In I r e d x 1040 - In n) . ( 3 ) All values are tabulated as a function of Vo/RT and n 2 / I r e d V , with V , expressed in cal. mole-l and I r e d the reduced moment of inertia in c.g.s. units per molecule. The thermodynamic functions for the restricted rotation are added to the usual ones €or translation and for the three degrees of freedom of external rotation. Pitzer computed barrier heights to get the best fit with the experi- mental data. Some of the potential barriers assigned to internal rotations selected by Oosterhoff from a paper of French and Rasmussen6 are given in Table I.In most instances these have been computed by the methods discussed below. TABLE I.--METHYL GROUP BARRIERS FOR TYPICAL COMPOUNDS Compound Potential Barrier (cal./mole) Ethane . Propane isoButane . neoPentane . Me thylamine . Dimethylamine Trime thy lamine Me thylalcohol Dimethylether . Acetone . Me th ylme rcap t an Dime thylsulphide Tetrame thylsiIane 2750 3300 3870 4800 1520 3460 4270 I350 2700 5 60- I 240 1460 1100-1500 2000 Methods of Calculation.-In Pitzer’s paper, discussed in the last section, it was assumed that the rotating groups were sufficiently light so that cross product terms in the rotational kinetic energy could be neglected.7 More recently Pitzer and Gwinn 8 have extended their treat- ment for the case where the rotating groups are symmetrical, so that such cross product terms are taken into account, and have given tables for making the computation, In addition to tabulating the quantities in the last section they have tabulated the restricted rotational entropy and the corresponding FIT values.In this case the tabulation is made in terms of V,/RT and I/QT, where QT is related to the reduced moment of inertia I by the relation QT = 2-815 (1088 IT)llz/n - (4) For a symmetrical group such as methyl attached to a heavy rigid frame I , is approximately equal to the moment of a methyl group. If the group has a small moment of inertia and is not symmetrical (e.g. 5 Oosterhoff, Diss. (University of Leiden, 1949). 8 French and Rasmussen, J .Chew. Physics, 1946, 14, 389. 7 Eidinoff and Aston, J . Chew. Physics, 1935, 3, 379. 8 Pitzer and Gwinn, J . Chem. Physics, 1942, 10, 428.JOHN G. ASTON 75 OH and NH,) and the rigid frame is sufficiently heavy, I is approximately the moment of inertia about the bond; otherwise I can be obtained by the method given by Pitzer.* At this point it is appropriate to discuss the entry of n into eqn. ( 2 ) and ( 3 ) . For a symmetrical group it enters essentially as a symmetry number which is equal to the number of equivalent minima. It now remains to discuss the case where the minima are not equivalent. I f the minima are not equivalent, the simplest procedure is to consider that isomers exist, differentiated by the fact that their low energy states are oscillations about each of the positions of different minimum energy.The energy levels are calculated from a potential function of the form of eqn. (I), with n usually the fraction of a revolution existing between the two adjacent maxima. The thermodynamic functions for each isomer are calculated by the usual methods, but since the partition function of each is restricted to ~ / n of a revolution, n in eqn. (2) and (3) is retained to allow for this fact, even though the symmetry number be unity. To calculate the entropy or free energy, one must add the entropy of mixing of these isomers and for this, one must know their mole fractions. The mole fraction can be calculated by combining the total free energy functions of each isomer with the value of AEoo, the difference between the energy zeros of the two isomers, to obtain the free energy difference between the isomers and hence the equilibrium constant for their con- version.Thus for the isomerization of isomer i into isomer j , where Xi and X j are the mole fractions of the isomers i and j and the symbols represent differences in the molal properties between the isomers. It must be emphasized that Fjo and Fi0 include translational, external rotational and vibrational contributions as well as that due to restricted rotation, and have been brought to a common energy zero. The total heat content is given by ( H O - Eoo) = EXi(Ho - Eoo)i, . - (6) where the sum is to be taken over all isomers and (HO - Eoo)i is the total heat content of each isomer (i.e. 4RT has been added for translation and external rotation and the vibrational contributions also included as well as that for the restricted rotation).Thus the total heat capacity is given by or dXi Cpo = XiCii + ( H O - Eoo)i-;i7: . The first term on the left-hand side is the sum of the contributions of the individual isomers to the heat capacity, while the second can be obtained from the individual heat contents and the change in mole fraction of the isomers with temperature.IO An example of such a calculation is that for butadiene-1 : 3 which consists of a mixture of trans and cis forms The potential energy function of the trans form which best fitted the third law entropy and gaseous heat capacities was while that for the cis was Vets = 2,425 + 1,288 [I - cos ( 6 - n)/0.594] cal. mole-1 .(10) As can be seen from these equations the minima of the cis and trans are lo hston, Szasz, Wooley and Brickwedde, J . Chem. Physics, 1946, 14, 67. Vt,,,, = 2,500 [I - cos 6/0.406] cal. mole-' . ' (9) Pitzer, J . Chem. Physics, 1946, 14, 239.76 HINDERED ROTAT ION separated by 180' but the maxima are so located that the cis form occupies only 0-594 of a revolution the rest being occupied by the trans. The constant term in the expression for the cis form indicates that its energy zero is 2-425 kcal. higher than that of the trans. The solid curve in Fig. I represents these equations while the dotted curve is for the case where each isomer occupied half a revolution. In the first case n in eqn. (2) and (3) is taken as 1/0*5g4 €or the cis form and 1/0.406 for the trans while in the second case it is z for both isomers.Both curves fit the data equally well. Parr and Mulliken l1 have recently concluded from a wave mechanical calculation including n levels and repulsive terms that such a difference in energy should exist between the isomers. By making a slight ap- proximation this method of computation reduces to the method originally given by Pitzer.12 Calculation of Barriers.-It is rare that the energy levels of the hindered rotor give rise to lines in the Raman or infra-red. When they do, these lines may be used to calculate the barrier hindering internal r ~ t a t i o n . ~ ~ l3 In the case where there are no rotationa.1 isomers possible it is obvious from the foregoing that the third law entropy, compared with that cal- culated from spectroscopic data, is a precise method of calculating the barrier.The chief objection to this method is that it assumes that there is no random orientation at the absolute zero. The likelihood of such a situation will be discussed presently. This was the first method used to determine the barrier in ethane by Kemp and Pitzer l4 but it was soon followed by a determination of the barrier from a careful measurement of the gaseous heat capacities of ethane over a wide temperature range beginning at 143' K.161 16 Where there are rotational isomers, in order to get the barriers with respect to the bond in question as well as the energy differences between the isomers, both the third law entropy' data and gaseous heat capacities over a wide temperature range are necessary for comparison with values from the spectroscopic and molecular data.In the example previously cited this was the way by which Fig. I was obtained. Before leaving the subject of barrier determination it is appropriate to discuss the effect of zero point entropy in the crystal. Any undeter- mined entropy in the crystal at the absolute zero makes the barrier appear higher. For example, the barrier hindering internal rotation in methyl alcohol, obtained from the rotational energy levels determined from microwave data,l' is only 932 cal. mole-l, whereas the value cal- culated by comparing the third law entropy with that calculated from spectroscopic and molecular data l* is 1600 f 700 cal. mole-I. Among other explanations, Halford has attributed the difference to possible zero point entropy at the absolute zero due to hydrogen bonding but has pointed out that uncertainty in the gas imperfection correction and, less likely, in heat of vaporization and vapour pressures, could be re- sponsible.The possible occurrence of zero point entropy in crystalline hydrocarbons will be discussed later. At the present there is no reason to believe that the crystalline hydrocarbons used in key barrier deter- minations have entropies at the absolute zero. l1 Parr and Mulliken, J . Chem. Physics, 1950, 18, 1345. p2 Pitzer, J. Chew. Physics, 1941, 8, 711. l3 Aston and Sagenkahn, J . Amer. Chem. Soc., 1944, 66, 1171. l4 Kemp and Pitzer, J . Chem, Physics, 1936, 4, 749 ; J. Amer. Chem. SOL, l5 Kistiakowsky and Nazmi, J .Chem. Physics, 6, 1938, 18. 16 Euken and Parts, 2. physih. Chem. B, 1933, 20, 184 ; Euken and Betram, 1' Koehler and Dennison (private communication). 18Halford, J . Chem. Physics, 1950, 18, 363. 1937, 59, 277 ; see also Witt and Kemp, J . Amer. Chem. SOC., 1937, 59, 273. 2. 9hysik. Chem., B, 1936, 31, 3.63.JOHN G. ASTON 77 Naturally the barrier height, calculated by comparing measured thermodynamic properties with those calculated from spectroscopic and molecular data, depends on the form of the potential function. This dependence has recently been discussed by Blade and Kimball.lD Rotational Isomerism.-The rotational isomers discussed previously, as exemplified by the cis and trans forms of butadiene-I : 3, often have sufficiently different vibrational spectra so that their presence may be detected by examination of the Raman spectrum.The stable form of n-butane is the trans form with symmetry C2&. By rotation of one-third of a revolution on either side of this are obtained two isomers which have the symmetry C, and are optical isomers. Szasz, Sheppard and Rank 2o have taken the ratio of the intensities of the members of a pair of lines in 5 Fig. I. the Raman spectrum over a wide temperature range. The line at 325 cm.-l is due to the trans while the corresponding line for both of the cis isomers is at 432 cm.-l. This latter line disappears in the solid. The change of the ratio of the intensities of these lines gives a value of the AH" of isomerization from which the corresponding value of AEoo was found to be 770 & go cal.mole-1 in excellent agreement with the value found by Pitzer.12 On the other hand an attempt to carry out a similar investigation in the case of 2-methylbutane and z : 3-dimethyl- butane 2 1 did not give results which were as clear cut. To start with all the main lines persisted in the solid phase. The change of intensity with temperature of a line pair for 2-methylbutane was investigated. The change was very small and indicated either a very small energy difference or that each of the chosen pair of lines was due to one isomer which was the only one in appreciable concentration. This alternative interpretation would yield a large energy difference. Recently Scott, McCullough, Williamson and Waddington 22 have determined the third law entropies and vapour heat capacities of both compounds and compared them with values calculated from spectroscopic 22 Scott, McCullough, Williamson and Waddington, J .Amer. Chem. SOC. (in press). 19 Blade and Kimball, J. Chem. Physics, 1950. 18, 1030. 2 O Szasz, Sheppard and Rank, J. Chem. Physics, 1950, 16, 704. 21 Szasz and Sheppard, J. Chem. Physic$, 1949, 17, 93.78 HINDERED ROTATION and molecular data. From these results it is evident that for a-methyl- butane the rotational isomer with C, symmetry is several kilocalories less stable than that with C, sym-metry. For z : 3-dimethylbutane the energy difference between the rotational isomers was very small. According t o their third law results it is not impossible that some residual entropy exists in crystalline a t the absolute zero.The fact that all lines persist in the solid indicates that the isomers form solid solutions with each other. Below the melting point a : 3-dimethylbutane rotates in the solid state and forms solid solution with other branched hydrocarbons that rotate in the solid state. In the case of mixtures of 2 : a-dimethylbutane and cyclopentane a complex is formed in which there is evidence that rotation (or complete random orientation) persists down to very low temperature~.~~ It is thus possible that the solid solution of rotational isomers of z : 3-dimethylbutane per- sists down to sufficiently low temperatures that the transformation would be so slow that it would not occur, thus leaving zero point entropy. Theory of Origin of Barriers.-As has already been pointed out simple theory does not predict the high barriers hindering the rotation of methyl groups and this is true for other simple groups.The energy difference between the rotational isomers discussed in the last section is undoubtedly steric in origin while other rotational isomers, e.g. those of ethylene dichloride owe their origin t o dipole interaction. The barrier hindering internal rotation of simple groups has no such explanation. An em- pirical treatment of the problem z 4 used a repulsive potential in terms of the distance vij between the hydrogen atoms only, k v=- . Yi,6 Because I : I : I-trifluoroethane,26 I : I : I-trichloroethane 86 and per- fluoroethanc 27 show barriers of the same order as ethane, it is obvious that other atoms act in the same way as hydrogen and the empirical treatment just mentioned needs to be revised.The fact that the same forces cause the cyclopentane ring to be non-planar leaves little doubt that the forces are repulsive. French and Rasmussen have made a satis- factory empirical treatment in terms of the distance of nearest approach of the atoms, with all atoms included but not electron pairs. Lassettre and Dean 3 0 n 31 have carried out a theoretical treatment which makes certain simplifying assumptions about the distribution of molecular electrons. An expansion of the electrostatic potential in inverse powers of the distance was carried as far as quadrupole terms. Most of the barriers can then be accounted for. Oosterhoff has also carried out a thcoretical treatment of the problem and does not agree entirely with the conclusion of Lassettre and Dean that interaction between bonds with fixed charge distributions will explain the barrier.At present neither theoretical treatment is sufficiently unique to make a priori conclusions. Values of Methyl Group Barriers in Unsaturated Hydrocarbons .- In view of the uncertainty of the part played by unshared electrons, the values of the barriers in certain unsaturated compounds are listed in Table 11. In all of these, the methyl or ethyl group is attached to a doubly or triply bound carbon atom or one to which a vinyl or acetyleiiic group is attached. 23 Fink, Cines, Frey and Aston, J . Amer. G e m . SOC., 1947, 69, 1501. 24 Aston, Isserow, Szasz and Kennedy, J . Chem. Physics, 1944, 12, 36. 26 Russell, Golding and Yost, J . Amer. Chem. SOC., 1944, 66, 16. 26 Rubin, Levidahl and Yost, J . Amer. Chem. SOC., 1944, 66, 279. 27 Pace and Aston, J . Amer. Ch.em. Soc., 1948, 70, 566. 28 Aston, Schumann, Fink and Doty, J . Amer. Chem. SOC., 1941, 63, 2029. 29 Aston, Fink and Schumann, J . Amev. Chem. SOC., 1943, 65, 341. 3 0 Lassettre and Dean, J . Chem. Physics, 1948, 16, 157. 553. 31 Lassettre and Dean. J . Chew. Physics, 1949, 17, 317.JOHN G. ASTON TABLE 11.-METHYL AND ETHYL GROUP BARRIERS IN UNSATURATED Compound Propylene . cis-Butene . trans-Butene . Butadiene-1 : 2 . Butene-1 . Butyne-2 . Butyne-1 . COMPOUNDS VO (cal . mole-1) Me, 2,000 Me, 700 Me, 1,900 Me, 1,650 Me, 2,700 ; Et, 2,000 Me, 500 Me, 3,000 79 References 33 and 34 35 36 and 10 37 10 and 38 38 40 The School of Chemistry and Physics, The Pennsylvania State College, Pennsylvania, U.S.A. 33 Kistiakowsky and Rice, J . Chem. Physics, 1940, 8, 610. 34 Telfair, J . Chem. Physics, 1942, 10, 167. 35 Scott, Ferguson and Brickwedde, J . Res. Nat. Bur. Stand., 1944, 33, I. 36 Guttman and Pitzei, J . Amer. Chem. SOC., 1945, 67, 324. 37 Aston and Szasz, J . Amer. Chem. Soc., 1947, 69, 3108. Aston, Fink, Bestul, Pace and Szasz, J . Amer. Chem. SOC., 1946, 68, 52. 39 Osborne, Garner, Doescher and Yost, J Amer. Chem. SOC., 1941, 63, 3496. Aston, Mastrangelo and Moessen, J. Amer. Chem. SOC., 1950, 72, 5291.

ISSN:0366-9033    

DOI:10.1039/DF9511000073

出版商:RSC    

年代:1951

数据来源: RSC