A. S. RODQERS, M. C. R. Wu, AND L. I~UITU
918 Langmuir equation assuming an evaporation coefficient near unity.
Acknowledgment. This work was performed under the auspices of .the U. S. Atomic Energy Commission.
A Comparison of Stabilization Energy and Resonance Energy as a
Measure of the Delocalization Energy in Free Radicals'. by A. S. Rodgers,* M. C. R. Wu,lb and L. Kuitu Thermodynamics Research Center, Department of Chemistry, Texas A & M University, College Station, Texas 77840 (Received August $0,2971) Publication costs assisted by the Robert A . Welch Foundation
There are, in the literature, two measures of the Ir-delocalization energy for free radicals: the resonance energy, RE", introduced by Szwarc2and defined as REO = AHb" - AH,", and the stabilization energy, SE",introduced by Benson6 and defined as SE" = AH," - AH,".
R,H
+H e~~+ H
4
CH, --t
R,
+H
R,H +Rs
(4 (b) (c)
In reactions a and c, Rr represents a Ir-delocalized radical and R, represents the analogous, hydrogen-saturated radical. It is evident that these two definitions will yield different values for the delocalization energy of the same radical as they use different models for the localized radical. It is reasonable to expect that the delocalization energy should be a property of the radical and not depend on the particular bond that is broken. As a result, both definitions have been generalized to include dissociation reactions of the R-X bond where X is any atom or group and have been tested for consistency. It was found that only the stabilization energy of Benson was properly invariant to changes in the bond being broken. On this basis it was concluded that the stabilization energy is the preferred measure of the delocalization energy in free radicals.
I n 1948, Szwarc2studied the pyrolysis of toluene and deduced a value of 77.5 kcal mol-' for the bond dissociation energy of the primary C-H bond. He noted that this was 24.5 kcal mol-' less than the then accepted value for the C-H bond dissociation energy (BDE) in methane and attributed this difference to the resonance energy of the benzyl radical. While these numbers have changed with time, t h e definition of resonance energy for delocalized radicals introduced by him has persisted.8 If one considers the example of a delocalized radical obtained from the scission of a primary C-H bond, as in benzyl and allyl radicals, then the resonance energy, RE", is given as (298.15 K is implied unless otherwise stated) RE"(R,eH2) = A H ~ O- AH,"
-
R,CH, +R&H2
CH~
+H
C H ~+ H
(1)
(4 (b)
I n 1965, Benson6 suggested an alternative definition. Rather than comparing the C-H BDE of the unsatThe Journal of Physical Chemistry, Vol. 78, No. 6,1978
urated compound with that of methane, he suggested that it be compared with the analogous C-H BDE in the corresponding fully hydrogenated compound (R,CHa). He recognized that such a definition would yield numerical results different from those of Szwarc2 so that he suggested the term "stabilization energy" be applied.6 Thus, the stabilization energy, SE", is given bys
SEO(R,~H~ =) AH," - AH,"
(2)
(1) (a) This work was supported by the Robert A. Welch Foundation. (b) Robert A. Welch Foundation Predoctoral Fellow 19691971. (2) M. Szwarc, J . Chem. Phys., 16,128 (1948). (3) See, for example, R. T. Morrison and R. N. Boyd, "Organic Chemistry," 2nd ed, Allyn and Bacon Inc., Boston, Mass., 1966, p 390. (4) While we shall consider this particular example, the results are readdy generalized to radicals derived from the scission of secondary and tertiary bonds. (5) 8.W.Benson, J . Chem. Educ., 42,510 (1965). ( 6 ) Corrections to eq 2 for changes in strain and resonance energies may be necessary in particular cases.
919
DELOCALIZATION ENERGY IN FREERADICALS Table I: Dissociation Enthalpies for the C-X Bond at 298 K in kcal mol-' CeHsCHzX
X
CHFCHCHZX
CHa CzHs (CHa)zCH' BP
I'
CHsX
CeHsX
85.2c
104. Ob,'" 91.4eJ 88.2d 84.7d 84.3d 69. Besf 56.2'
98.ob,'"
88.6~ 82.3' 75.44 72. Id 71. 2d@' 57.2' 43.gh
85.0"'" 78.2'*' 71. Bd 68. 7d 68.1' 54.7' 40.08
Ha
OH.
trans-CHaCH=CHCHzX
*..
72. Od 68. 7d
... ... ...
91.1" 84. 5d 81.5d 80. 7dJ 67.6"' 53. 24ff
* Reference 7; these data and AHf" (RH, g, 298 K ) from ref 13 determine AHfo(R,g, 298 K). Refa AHro(X, g, 298 K), ref 12. AHf"(RX, g, 298 K), ref 13. e AHr"(RX, erence 8 ; these da,ta and AHf"(RH, g, 298 K ) from ref 13 determine AHro(R, g, 298 K). AHf"(RX,g, 298K), ref 15. ' AHf"(R, g, 298K), ref 8. AHf"(RX, g, 298K), ref 16. g, 298K), ref 14.
'
*
Table 11: Resonance and Stabilization Energies at 298 K for the Benzyl, Allyl, and Methallyl Radicals (Eq 3 and 4a) for Various Groups 7 Benzyl' REO, kcal mol-1 S E o , kcal mol-1
X
H OH CHI CZH6 (CHs)aCH
19.0 13.2 16.4 16.0 16.2 14.1 16.2
Br
I a
7
REO, koa1 mol-1
13.0 12.9 12.7 12.8 12.6 12.9 13.2
15.4 9.1 12.8 12.6 13.1 12.6 12.4
-
Allyl' SEO, kcal mol-1
9.4 8.8 9.1 9.4 9.5 10.4 9.3
7 Methallyl' REO, koa1 mol-' SEO, kcal mol-1
18.8
12.8
.,.
...
16.2 16.0
12.5 12.8
... ... ...
... ... ...
Based on d a t a of Table I.
R,CHs +R&H2
+H
(c)
The evaluation of eq 2 is greatly simplified by the fact that AH," is not significantly affected by changes in the alkyl moiety R,. The data'ss show that AH," = 98 i 1 kcal mol-' for R, equal to methyl, ethyl, n-propyl, 1 kcal isopropyl, and tert-butyl. As AH,," = 104 these two measures of the delocalization enmol-' ergy of a radical differ by 6 kcal mol-'. One naturally asks the question "Is one to be preferred over the other?" The answer to this is "yes," and it is based on considerations of transferability and utility, One can reasonably expect the delocalization energy of a radical to be a property of that radical and, therefore, its value should not depend upon the particular bond that is broken. Both the definitions of Szwarc and of Benson can be generalized to include dissociation reactions involving the C-X bond where X is any atom or group. Thus, eq 1 and 2 become eq 3 and 4. Ss'
- AHd"
(3)
8Eo(R,CH2) = AH!" - AHa"
(4)
RE'"(R,CH2) = AH," R,CH2X -+ R$H2
+X
+X R,CH2X +R&H2 + X CHaX +CHa
(4 (4
(f) Again, the evaluation of eq 4 is facilitated by the fact that AHf" is nominally independent of R, to the extent
that group additivity applies to compound^^^^^ and radicals." Thus, reaction f may be replaced by g and eq 4 becomes eq 4a.
+X
(g)
SE0(R,CH2) = AH," - AHdO
(44
CHaCHzX---f CHlcHz
The resonance and stabilization energies of the benzyl, allyl, and methallyl radicals are calculated according to eq 3 and 4a using the dissociation enthalpies of Table I.12-16 The results are summarized in Table (7) J. A. Kerr, Chem. Rev., 66,494(1966). (8) D.M. Golden and S. W. Benson, {bid., 69, 125 (1969). (9) 8. W.Benson and J. H. Buss, J.Chem. Phys., 29,546 (1958). (10) S.W. Benson, F. R. Cruickshanlc, D. M. Golden, G . R. Haugen, H. E. O'Neal, A. 8. Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69,279 (1969). (11) H. E. O'Neal and S. W. Benson, Int. J. Chem. Kinet., 1, 221 (1969). (12) D. R. Stull, Ed., "JANAF Thermochemical Tables," The Thermal Research Laboratoriea, Dow Chemical Co., Midland, Mich., 1965. (13) Selected Values of Properties of Hydrocarbons and Related Compounds," API Research Project 44,Thermodynamics Research Center, Texas A & M University, College Station, Texas, 1967. (14) D. R. Stull, E. F. Westrum, Jr., and G. C. Sinke, "The Chemical Thermodynamics of Organic Compounds," Wiley, New York, N. Y., 1969. (15) J. D. Cox and G. Pilcher, "Thermochemistry of Organic and Organometallic Compounds," Academic Press, New York, N. Y . , 1970. (16) A. S. Rodgers, D. M. Golden, and S. W. Benson, J . Amer. Chem. SOC., 88,3194 (1966). The Journal of Physical Chemietry, Vol. 76,No. 6, 1978
A. S. RODGERS,M. C. R. Wu, AND L. KUITU
920
11, from which it is seen that only the stabilization energy of Benson is properly invariant to changes in the character of the bond being broken. The transferability of the stabilization energy is further supported by calculations for the benzyl radical with the following additional groups and their corresponding stabilization energies in kilocalories per mole: -COCH3, 14.7;'j -SH, 13.7;" -SCHI, 13.4;" -SCzH5, 13.2;" -CHzCsH5, 11.3;15 and -C&, 10.5.15 The utility of the stabilization energy results from its transferability. Equation 4a may be expanded to
SE" (R,cHz) = AHf"(C2H5. , g, 298 I
