1025
COMMUNICATIONS TO THE EDITOR
Comment on Resonance Stabilization Energies from Cis-Trans Isomerization Studies
Sir: In a recent publication,' Marley and Jeffers reported single pulse shock tube relative rate measurements for the cis-trans isomerization of crotononitrile, 1,3-pentadiene, and 3-methyl-1,3-pentadiene.The results are log k (crotononitrile) = 13.2 - 58.1/0, log k (1,3-pentadiene) = 13.6 - 53.0/0, and log k (3-methyl-l,3-pentadiene) = 14.0 - 55.0/0, where 0 = 2.303RT kcal/mol. On the assumption of a biradical mechanism for cis-trans isomerization the authors compared these findings with their previously established parameters for cis-2-butene,' log k = 14.6 66.2/8, to obtain resonance stabilization energies of 8 kcal/mol for the cyano group, 13 kcal/mol for allyl, and -11 kcal/mol for methyl allyl. These values were concluded to be in good agreement with values of 6 kcal/mol for CN found by Sarner et al.,3 11.6 kcal mol for methyl allyl deduced from the work of Walters and Frey,' and 12.6 kcal/mol for allyl. The latter was quoted as being the "standard" accepted by Benson and O'Neal.' Recent measurements, however, have firmly established that the ~ , ~that for allyl stabilization energy is 10 k c a l / m ~ l ,and methyl allyl should be 13 kcal/m01.~Furthermore, the value for the cyano stabilization energy found by Sarner et al. from the pyrolysis of cyclobutyl cyanide is relative to a hydrogen atom. The definition of stabilization energy'' requires that the comparison be made with respect to the corresponding alkyl substituent. Such a comparison is included in the value derived from cis-trans isomerizations. On this basis, a value of -5 kcal/mol may be obtained from the kinetics of pyrolysis of several cyanosubstituted small ring corn pound^.^^"^'^ This is strongly supported by a substantial body of recent data on the pyrolysis of alkyl cy ani de^.'^"^ Thus the agreement between stabilization energies derived from cis-trans isomerizations and values from other sources appears not to be as good as suggested by Marley and Jeffers. The discrepancies may be due to the shock tube data although it is difficult to find any uncertainties. Nevertheless, it is noteworthy that a very recent study14of the cis-trans isomerization of 2-butene gave results in excellent agreement with early studies and not with the "high" parameters established by the shock tube technique.2 Note also that the shock tube A factor for cis-Zbutene is about a power of ten higher than the transition-state estimate.' Also, the shock tube data yield a surprisingly large difference in A factors s-l) between crotononitrile and 2-butene. The biradical mechanism for cis-trans isomerization proposed by Benson and co-w~rkers'~~'~ may be depicted as follows
-
-
i
--
R
W
H
"
H
Jf
R\C=C/H
/
H
- 2-K L
\
R'
R\.
H-
/H
'R'
Rotation about the sp2-sp2 single bond in the biradical is rate determining. When a substituent can interact with the biradical, the A factor will be lowered because of the stiffening of internal rotations accompanying this interaction'^'','' but this will not be the case with CN because of the cylindrical symmetry of the triple bond. Although increases in the frequencies of C-CEN bends may make some contribution to a decreased A factor13such changes are not likely to lead to a decrease of as much as 101.4 ~ 1 . According to the biradical mechanism the activation energy is the enthalpy of reaction to the biradical (which is equivalent to the n-bond energy in the olefin) plus the energy required to rotate about the single bond to the perpendicular conformation. Thus the use of cis-trans isomerizations to determine stabilization energies assumes that the barrier to rotation in the resonance stabilized biradical is the same as that in the nonstabilized species." This may not be the case. For example, the difference in n-bond energies between cis-2-butene18and cis-crotononitrilelg is -6 kcal/mol whereas the difference in isomerization activation energies is -8 kcal/mol.' This suggests a slightly higher barrier to rotation in the nonstabilized biradical. Note also that the difference in a-bond energies between ethylene18and cis-1,2-dichloroethylenem (2.1 kcal/mol) agrees with the radical stabilization energy of a C1 atom (relative to a H atom)" whereas the difference in isomerization activation energies (8.1 kcal/mo1)2'22does not. It is suggested that the use of cis-trans isomerization measurements for determining reliable resonance interaction energies should be viewed with caution.23
References and Notes W. M. Marley and P. M. Jeffers, J. Phys. Chem., 79, 2085 (1975). P. M. Jeffers. J. Phvs. Chem.. 78. 1469 11974). S. F. Sarner, D. M. &le, H. K. kll,Jr., and A. 6. Richmond, J. Phys. Chem., 76, 2817 (1972). M. Zupan and W. D. Walters, J . Phys. Chem., 67, 1845 (1963). R. J. Ellis and H. M. Frey, Trans. faraday SOC., 59, 2076 (1963). S. W. Benson and H. E. O'Neal. Natl. Stand. Ref. Data Ser.. Natl. Bur. Stand., No. 21 (1970). D. M. Golden and S. W. Benson, Chem. Rev., 69, 125 (1969). D. M. Golden, N. A. Gac, and S. W. Benson, J. Am. Chem. SOC., 91, 2136 (1969). A. S. Rcdgs~sand M. C. R. Wu, J. Am. Chem. Soc.,95,6913 (1973). A. S. Rcdgers, M. C. R. Wu, and L. Kuitu, J. Phys. Chem., 76,3196 (1972). For references and a discussion, see ref 12. K. D. King and R. D. Goddard, J. Phys. Chem., 80, 546 (1976). K. D. King and R. D. Goddard, J. Am. Chem. Soc., 97, 4504 (1975); Int. J. Chem. Kinet., 7, 837 (1975). D. Masson, C. Richard, and R. Martin, Int. J . Chem. Kinet., 8, 37 (1976). S. W. Benson, K. W. Egger, and D. M. Goklen, J . Am. Chem. SOC., 87, 468 (1965). S. W. Benson, "Thermochemical Kinetics", Wiley, New York, N.Y., 1968. Substituents that generate stabilization energies in one or both of the radical centers of the biradical have essentially the same effect on the a-bond energy as on u bonds and monoradicals." K. W. Egger and A. T. Cocks, Helv. Chim. Acta, 56, 1516 (1973). Assumed to be the same as that for cu-methacrylonitrile.12 Estimated according to the procedure outlined In ref 18 using the data tabulated in J. A. Franklin and G. Huybrechts, Int. J. Chem. Kinet., 1, 3 (1969).
1026
Communications to the Editor
(21)E. N. Cain and R. K. Solly, J. Am. Chem. Soc.,94, 3830 (1972); Ausf. J. Chem., 28, 2079 (1975). (22) J. E. Douglas, B. S. Rabinovitch, and F. S. Looney, J. Chem. Phys., 23, 315 (1955). (23) A referee has called attention to a paper by H. M. Frey, A. M. Lamont, and R. Walsh, J. Chern. SOC. A , 2642 (1971), which presents evidence to show that the cis-trans isomerization of 2,3-dimethyl-l,3-pentadiene almost certainly proceeds via the intermediate formation of 1,2,3-trimethyIcyclobutane and not via a biradical mechanism. These workers also studied the cis-trans isomerization of 1,3-pentadiene. The skiation was less clear but again intermediate formation of a cyclobutane seemed more likely than a biradical mechanlsm. A similar pathway for 3-methyl-l,3-pentadiene seems likely. This paper was overlooked by Marley and Jeffers.
Keith D. Klng
Department of Chemical Engineering University of Adelaide Adelaide, South Australia 500 1 Received JuV 19, 1976
Reply to the Comment on Resonance Stabilization Energies from Cis-Trans Isomerization Studies
Sir: There is little we can challenge in Professor King’s communication, except perhaps its tone. We feel that the differences in derived stabilization energies may well be within the stated experimental error limits, in most cases. A discussion of the 2-butene rate constant was presented in J. Phys. Chem., 78, 1469 (1974). However, since the stabilization energies under criticism are derived from relative rate measurements, the absolute value chosen for 2-butene isomerization seems irrelevant. Most of the cis-trans isomerization results reported in our series of papers were based on about 10-20 shock experiments. Perhaps what is really needed is a more extensive (and perhaps more careful) set of experiments. Our studies appear to be the most complete and generally reliable set of results on the kinetics of systems which from all indications are difficult to study by other techniques. We would urge further experiments before challenging the shock tube relative rate techniques on the basis of existing cis-trans isomerization results. Department of Chemistry State University of New York at Cortland Cortland, New York 73045
Peter M. Jeffers
Received September 15, 1976
Preliminary Report of a Spur Model Including Spur Overlap
Sir: Experimental results from picosecond pulse radiolysis studies’ have prompted Kupperman2 to introduce significant changes in certain parameters of the spur model in aqueous radiation ~hemistry.~-~ Using the stroboscopic method, Wolff et a1.6 found there was very little, if any, decay of the hydrated electron concentration in pure water during the time period from 20 to 350 ps following the delivery of a short, high-energy electron pulse. Jonah et al.7 have suggested the 3% decay in hydrated electron concentration, which they observe in their electron pulsed water from 100 to 350 ps, is probably within the experimental error of the measurements of Wolff et ala6 However, both Wolff et aL6 and Jonah et al.7 state, for different reasons, that their hydrated electron decay (or lack thereof) differs by amounts greater than their estiThe Journal of Physical Chemistry, Vol. 81, No. 10, 1977
mated experimental error from the spur decay calculations based upon parameters used by Schwarz5 and Kupperman,2 respectively. Most quantitative pulse radiolysis studies have concentrated on either one of two time periods following delivery of the pulse, either the period of “isolated spur decay” or a much later time period when all reactive intermediates are homogeneously distributed. We have completed an experimental pulse radiolysis study of the effects of pulse dose on hydrated electron decay rates in pure water using 20-11s pulses of 14-MeV electrons.8 In order to interpret the results of this study, we have postulated spur overlap as being responsible for the relatively abrupt alterations in the kinetics of electron decay observed as functions of pulse dose and of time following the pulse. A simple model’ for the relaxation of the concentration distribution in the spurs suggests that the critical length parameter is proportional to dose’I3 and the critical (diffusional) time parameter should be scaled as time’/2. The data were analyzed to yield an estimate of the time (in nanoseconds) of spur expansion following a 20-11s electron pulse to reach experimentally observable spur overlap (to):
to =
1.2 x 104 [ d ~ s e ( r a d s ) ] * ns ’~
The time to reach observable spur overlap suggested by these relations is earlier than those predicted by Kenney and Walker.’ Furthermore, these data suggest that spur overlap needs to be taken into account in spur modeling studies, especially when using large pulse doses and/or relatively low energy pulsed electrons as radiation sources. As a result of the above experimental results, we have initiated a computer modeling study to attempt to fit a diffusion model incorporating spur overlap features to pulse radiolysis hydrated electron decay data between lo-’’ and lo-’ s. In this relatively crude model we have included a smooth transition through the time regions of predominantly intraspur electron decay, spur overlap (with spherical symmetry), and, finally, homogeneous reactions of the hydrated electron. This model has given surprisingly good qualitative overall fits to these experimental data over this wide time region and especially good fits to very early electron decay data. We wish to report on these preliminary results at this time because the nature of the initial hydrated electron distribution employed differs qualitatively from those used heretofore. Previously published computer modeling ~ t u d i e s have ~-~ employed concentration probability distribution functions for intermediates created by the ionizing radiation centered about the spur origin with a maximum value at the origin for all intermediates contained in the spur. Such functions appeared to us to be inherently in conflict with at least some of the experimental data of picosecond pulse radiolysis experiments showing the lack of or very small amount of decay between and lo-’ s. They also appeared to be in conflict with the basic ideas of Lea” and Platzman,” namely, that ejected electrons would be hydrated or thermalized at some distance from the parent positive ion. The Gaussian distribution for hydrogen atoms was originally chosen by Samuel and Magee3a(a) for mathematical tractability and (b) since the ejected “electron cannot go very far without suffering wide deflections resulting from s~attering”.~‘We believe that electrons formed in the ionization event may very well be able to travel fairly large distances from their positive ion N
