Page 1069 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

do this, structural features that strengthen or weaken the bond in the reactant must 1053
be accounted for. The AIM approach (see Section 1.4.3) provides the basis for one
such scheme. The intrinsic bond energy BE was defined in terms of the AIM energy TOPIC 11.1
i
E r
and charge density r
: Relationships between
i
i
BCP
BCP
Bond and Radical
Stabilization Energies
BE = c 1 AB E r BCP
/ c 2 AB + r BCP
−c 3 AB R (11.6)
i
i
i
where c AB c AB , and c AB are empirical characteristics of bond types and R is the
1 2 3
difference between the length of the AIM bond path and the internuclear distance. 226
This concept of inherent bond energy was extended by Exner and Schleyer to a
wider range of structures. 227 The approach reproduced atomization energies for typical
alkanes and alkenes with a standard deviation of about 4.6 kcal/mol, i.e., within about
1%, although some molecules, e.g., allene and cyclopropene, fell well outside those
limits. The calculated intrinsic bond energies BE were then compared with BDE,
i
the energy required for homolytic dissociation. This analysis suggested that most of
the dependence of BDE on structure can be attributed to the “extra stabilization”
of the radicals, rather than to inherent differences in bond strength. Table 11.10
includes experimental bond energies, computed (G2) bond dissociation energies, the
BE resulting from application of Equation (11.6), and the resulting RSE.
i
The data conform to familiar qualitative trends. We see the methyl < pri <
sec < tert trend for alkyl groups. The strong stabilization of allyl radicals is evident
in the value C(3)−H bond energy for propene, whereas the positive RSE for ethene,
2
ethyne, and benzene reflect the low stability of radicals at sp and sp carbons. Also
apparent in these data is the relative strength of C−H bonds in strained-ring compounds
(cyclopropane). These results are also in accord with the concept of assigning most
of the change in the BDE to radical stabilization or destabilization. The intrinsic bond
energies, BE , show much less variation with substitution than the BDE.
i

Table 11.10. Comparison of Experimental, Computational, and Calculated C−H Bond
Dissociation Energies (kcal/mol) a

Compound BDE (exp) BDE (G2) BE i RSE b
Methane 104 9 105 8 103 9 +1 0
Ethane 101 4 102 6 104 1 −2 7
Propane 98 6 100 3 100 3 −5 7
Isobutane 96 5 98 8 104 4 −7 9
Cyclopropane 106 3 113 0 105 8 +0 5
Cyclobutane 96 5 102 1 104 3 −7 8
Cyclopentane 94 5 103 9 −9 4
Cyclohexane 94 5 103 5 −9 0
Ethene 112 2 112 0 106 0 +5 2
Ethyne 132 8 135 0 110 4 +22 4
Propene 88 2 88 7 103 2 −15 0
Benzene 111 2 106 5 +4 7

a. K. Exner and P. v. R. Schleyer, J. Phys. Chem A., 105, 3407 (2001).
b. Apparent radical stabilization from BDE (exp) – BE i [Equation ( 11.6)]

226 S. Grimme, J. Am. Chem. Soc., 118, 1529 (1996).
227
K. Exner and P. v. R. Schleyer, J. Phys. Chem. A, 105, 3407 (2001)