Page 448 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

gas phase data, in terms of both the stability order and the energy differences between 429
the carbocations. A plot of the ionization enthalpy and gas phase hydride affinity gives
a line of slope 1.63 with a correlation coefficient of 0.973. This result is in agreement SECTION 4.4
with the expectation that the gas phase stability would be more sensitive to structure Structure and Reactions
of Carbocation
than the solution phase stability. The energy gap between tertiary and secondary Intermediates
ions is about 17 kcal/mol in the gas phase and about 9.5 kcal/mole in the SO ClF
2
solution. An independent measurement of the energy difference between secondary
and tertiary cations in solution is available from calorimetric measurement of the H
of isomerization of the sec-butyl cation to the tert-butyl cation. This value has been
∗
found to be 14.5 kcal/mol in SO ClF solution. 73 An MP2/6-31G computation finds
2
a difference of 14.8 kcal. 74 Some representative data are given in Table 4.17. These
data give some basis for comparison of the stability of secondary and tertiary alkyl
carbocations with aryl-substituted ions. Note also that the solution data also show that
cyclopropyl groups are very stabilizing toward carbocations.
The increase in carbocation stability with additional alkyl substitution is one of
the most important and general trends in organic chemistry. This stability relationship
is fundamental to understanding many aspects of reactivity, especially nucleophilic
substitution. Hyperconjugation is the principal mechanism by which alkyl substituents
stabilize carbocations. There is considerable evidence of the importance of hypercon-
jugation on the structure of carbocations, including NMR data, crystallographic data,
and computational studies. The tert-butyl cation has been studied by each method.
The NMR results indicate shortening of the C−C bonds, as would be predicted by
hyperconjugation. 75 The crystal structure gives a value of 1.44 Å. 76 A computational
study at the MP2/6-31G ∗∗ level shows a slight elongation of the C−H bonds aligned
with the p orbital, and the C−C−H bond angles are slightly reduced (Figure 4.8). 77
Levy has performed NPA, Mulliken, AIM, and CHELPG charge analyses on the
∗
iso-propyl, sec-butyl, and tert-butyl cations using MP2/6-31G -level computations. 74
As mentioned briefly in Section 3.4.1, the trivalent carbon atom in tert-butyl cation

Table 4.17. H for Ionization of Chlorides and Alcohols in
SO ClF
2
H (kcal/mol)
Reactant X=Cl X=OH
CH 3 2 CH−X −15
Ph 2 C CH 3 −X −16
CH 3 3 C−X −25 −35
PhC CH 3 2 −X −30 −40
Ph 2 C CH 3 −X −37 5
Ph 3 C−X −49
C – X
3 −59
a. Data from E. M. Arnett and T. C. Hofelich, J. Am. Chem. Soc., 105, 2889 (1983).

73 E. W. Bittner, E. M. Arnett, and M. Saunders, J. Am. Chem. Soc., 98, 3734 (1976).
74
J. B. Levy, Struct. Chem., 10, 121 (1999).
75
C. S. Yannoni, R. D. Kendrick, P. C. Myhre, D. C. Bebout, and B. L. Petersen, J. Am. Chem. Soc., 111,
6440 (1989).
76 S. Hollenstein and T. Laube, J. Am. Chem. Soc., 115, 7240 (1993).
77
S. Sieber, P. Buzek, P. v. R. Schleyer, W. Koch, and J. W. d. M. Carneiro, J. Am. Chem. Soc., 115,
259 (1993).