Relationships between Carbocation Stabilities and Electrophilic Reactivity Parameters,E: Quantum Mechanical Studies of Benzhydryl Cation Structures and Stabilities

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Abstract
Quantum chemical calculations of the affinities of benzhydryl cations (XC6H4)2CH+ for the methyl anion, hydroxide, and hydride anion have been performed up to the B3LYP/6-311++G(3df,2pd)//B3LYP/6-31G(d,p) level and compared with rate and equilibrium constants in solution. An excellent linear correlation between the empirical electrophilicity parameter E (by log k = s(N + E); Mayr, H.; Bug, T.; Gotta, M. F.; Hering, N.; Irrgang, B.; Janker, B.; Kempf, B.; Loos, R.; Ofial, A. R.; Remennikov, R.; Schimmel, H. J. Am. Chem. Soc.2001, 123, 9500−9512) and the calculated methyl anion affinities ranging over 46.5 kcal mol-1 is found that reproduces the electrophilicity parameters E which range from −10 to +6 with a standard deviation of ±0.26 (11 points). The calculated OH- and H- affinities correlate with the calculated CH3- affinities with a slope of 1.00, indicating that the relative anion affinities of benzhydrylium ions are independent of the nature of the reference base. Linear correlations of the experimental pKR+ values and chloride ion affinities in solution with the calculated anion affinities in the gas phase indicate that solvation attenuates the differences of carbocation stabilization in the gas phase but does not affect the relative differences. Application of Marcus theory shows that only reaction series with α = ∂ΔG⧧/∂ΔrG° = 0.5 corresponding to a slope parameter of s = 0.67 can have constant intrinsic barriers. The slope parameters s found for π-nucleophiles and C−H hydride donors (s ≈ 1) are interpreted by a decrease of the intrinsic barriers with increasing electrophilicities of the carbocations. On the other hand, a value of s ≤ 0.67 as found for many n-nucleophiles as well as for Si−H, Ge−H, or Sn−H hydride donors is indicative of intrinsic barriers which are constant or slightly increase with increasing electrophilicity of the carbocation.