704 (5) F. D. Chattaway and G. Hoyle, J. Chem. SOC.,123, 654 (1923). (6) J. C. Evans and G. Y . 4 . Lo, J. Chem. Phys.,44, 3638 (1966). (7) C. Hall, D. W. Kydon, R. E. Richards. and F. R. S. Sharp, Proc. Roy. Soc.,Ser. A, 318, 119 (1970). (8) T. Migchelsen and A. Vas, Acta Crysta//ogr.,22, 812 (1967). (9) (a) C. H. Townes and B. P. Dailey, J. Chem. Phys., 17, 782 (1949); (b) B.
(10) ( 1 1) (12) (13) (14)
P. Dailey and C. H. Townes, ibid., 23, 118 (1955). W. Gabes and M. A. N. Nyrnan-Meester, Inorg. Chem., 12, 589 (1973). E. F. Riedel and R. D. Willett, Theoret. Chim. Acta, in press. R. Ikeda. D. Nakarnura, and M. Kubo, J. Phys. Chem., 69, 2101 (1965). H. Fleming and M. W. Hanna, J. Amer. Chem. Soc., 93, 5030 (1971). D. E. Scaife, Aust. J. Chem., 24, 1993 (1971).
Electrostatics and the Chemical Bond. I. Saturated Hydrocarbons Sidney W. Benson* and Menachem Luria2 Contribution from the Department of Thermochemistry and Chemical Kinetics, Stanford Research Institute, Menlo Park. California 94025. Received April 18. I974
Abstract: A model of the C-H bond is proposed in which each H atom in an alkane bears a formal charge of +0.278 X esu (0.0581 electronic charge) and each C atom a neutralizing negative formal charge. Summing u p all of the electrostatic interactions in a n alkane due to these formal charges gives rise to a net stabilizing electrostatic energy for each alkane E,I(C,H~,+~)which depends only on the geometrical structure. This is then shown to lead to a surprisingly simple formula for the standard enthalpies of formation for alkanes given by: AHro298(CnH2,,+~gas) = -2.0(n 1) - 0.5 E,I(C,H2n+2). This fits the observed values of AHf029#for all the n-alkanes to n-C7H 1 6 and for the branched alkanes up to C5H12 to f 0 . 2 kcal/mol. I t is also shown that the observed dipole moments of propane and I‘-CdHIOagree well with the formal charge distribution if proper account is taken of mutual group polarization. I t is furthcr shown that the barrier to rotation about single bonds and the unfavorable gauche conformations in hydrocarbons cannot be quantitatively accounted for by electrostatic interactions. The rotation barrier, the gauche interaction. and the anomalously large C-C--C and C=C-C angles in alkanes and olefins are discussed instead in terms of a purely van der Waals He. .H interaction, predominantly repulsive.
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The standard heats of formation of compounds from their elements ( A H f o ) have been shown to follow more or less accurately simple additivity laws.3 T h e law of group additivity is capable of reproducing known values of AHfO for most species to within the experimental uncertainty when small (i.e., 51.0 kcal) corrections are made for recognizable steric effects. A few compounds of very high polarity, such as CH3CF3, CH2CC12, and the cyanocarbons, deviate from group additivity by amounts which may be as large as 8-9 kcal/mol, but such examples are so far relatively rare. I n all such cases, it has been proposed that the deviations arise from polar interaction^^-^ and relatively simple electrostatic models have been used to rationalize these deviations.’ The law of group additivity is based on the decomposition of molecular properties into contributions from groups, a group being defined as a polyvalent atom together with all of its atomically bound neighbors (e.g., C2Hh is composed of two identical groups, C-(C)(H)3, carbon bound to three H atoms, and one C atom). The fact that group additivity works so well, particularly for the not-too-polar compounds and radicals,3c can be rationalized by the deduction that interactions between next-next-nearest neighbors is very small. The group, by definition, includes all interactions between nearest neighbors (bonded atoms) and next-nearest neighbors (1,3-nonbonded interactions). The law of bond additivity, which is the next simpler stage in the hierarchy of additivity laws, uses a decomposition of molecular properties into sums of contributions from bonds. Average deviations of observed and calculated A H f o with this law are about f 3 kcal for nonpolar compounds, f 6 kcal for polar compounds, and up to f 1 2 kcal in extreme cases. It is the purpose of the present paper to examine the theoretical basis for these differences i n accuracy between the laws of bond and group additivity and to present a very simple electrostatic model which can account quantitatively for the interactions responsible for the deviations observed. Journal of the American Chemical Society
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97:4
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I. The Methane Problem The alkanes are considered the least polar of all organic compounds and, consequently, they should be expected to show the smallest deviations from simple bond additivity laws. In actual fact, they do follow reasonably well simple bond additivity schemes, but the observed deviations are not small. This is illustrated by the data in Table I showing values of AHrO for compounds in the series CH,(CH3)4-,. If these methyl-substituted methanes followed the law of bond additivity, then the change in AHfO on successive CH2 insertion (i.e., CH3 for H substitution), given by the column labeled A , , should be a constant. This constant would be equal to the contribution of one C-C bond plus two C-H bonds gained by the CH2 insertion. I n fact. we observe that A I becomes progressively more negative indicating progressively greater stability with increasing branching. This has been a somewhat unexpected finding, since one might have intuitively expected that the steric crowding of the methyls would lead to decreased stability. A comparison of the AHfO values for i-C4H10 with n-C4Hio and of neopentane with n-CsHl2 shows similarly that the branched compounds are 2.0 and 5.0 kcal/mol more stable respectively than their straight-chain isomers. This paradoxical result can be called “the methane problem.” The stability of the branched compounds might be ascribed to a general van der Waals’ attraction of the C H 3 groups. However, the fact that the more stable form of nbutane occurs with the terminal-CH3 groups trans to each other, rather than gauche, would conflict with such a hypothesis. The methane problem is by no means unique to hydrocarbons, since we find similar behavior in the fluorinated methanes (Table 11). W e note in this case a much more pronounced increase in stability on F / H substitution than for C H 3 / H substitution as seen by comparing the columns labeled A 1 .
/ February 19, 1975
705 Table I. Heats of Formation of Methyl-Substituted
Methanes, CH,(CH,)a.,a - L.I HI
Compd
kcal/mol
-A1
-Az
typical alkane molecule, the C-H bond has a polarity which can be represented by assigning a formal charge, -y, to C , and the opposite charge, +y, to H. W e ignore for the moment the question of the absolute sign of y. This would lead to a CH4 molecule in which each H atom had a charge of +y and the central C atom, -4y. (+Y)
(+Y)
H\c/:4y)
H/
\H
(+y)
Values from J. D. Cox and G. Pilcher, “Thermochemistry of Organic and Organometallic Compounds,” Academic Press, New York, N. Y.,1970. Uncertainties are about Zt0.07 kcal/mol per C atom.
(+Y,
The ethane molecule would have the charge distribution
a
(+Y) H (-3v) ( - 3 Y ) p
\ . ( + y ) H-€------C-H /
(+Y)
Table 11. Heats of Formation of Fluorinated Methanes, CH,F,-p --~Hl0?9*>
Compd
kcal/mol
CH,
17.9
CHsF
56 8 + 2
-A1
-A?
39 12 51
CHiFz
7
108Zt 1
H
\
(+y)
H
1 6 6 4 ~1
-1
Eel
233 =t1
Data from A. S . Rodgers, R. L. Wilhoit, and B. J. Zwolinski, in press. a
A number of purely empirical schemes8-10 have been proposed to account for deviations from simple bond additivity. The simplest correction is to assume a contribution to AHfO from interactions between each pair of 1,3-nonbonded atoms. (In such a scheme, AHfO(CH4) would be composed of contributions from 4(C-H) bonds. 6(H-H) interactions: AHfO(CH3F) has 3(C-H) bonds, l(C-F) bond, 3(H-H) interactions, and 3(H-F) interactions.) Such a scheme would lead to a constant value of &, the difference in successive values of A I . W e see that such behavior is not obeyed in either series. A further contribution from nonbonded atoms, taken three a t a time (we would add to the above, contributions from 4 ( H H H ) interactions to AHfO(CH4) and for AHfO(CH3F) we would include contributions from 1 ( H H H ) and 3 ( H H F ) interactions), would lead to a variable value of the second difference, A2, but a constant value of A3 (not shown in Tables I and II), the difference between two successive values of A2. Although such a relation is not obeyed in either series (Tables I and 11), it requires only very minor adjustments in the AHfO, all within the limits of experimental error, to obtain a constant 113. The final step in such an hierarchy, to include an interaction between atoms taken four a t a time, would have no predictive value, since it would have as many parameters as data. However, the fact that even group additivity requires steric corrections and possibly polar corrections indicates that simple additive corrections to bond additivity can never be adequate.
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11. An Electrostatic Model of Alkanes
Considerations stemming from the virial theorem, which we shall not discuss here, suggest that a profitable way of considering deviations from simple bond additivity schemes might be in terms of formal charge schemes similar to those used by Pauling in describing bond energies in heteronuclear diatomic molecules.’ Such a model suggests that in a
= Cqiqj/ri,j
(1)
i
