Hyperconjugative stabilization in alkyl carbocations: direct estimate of the beta-effect of group-14 elements

DFT calculations at the BP86/TZ2P level have been carried out for the primary, secondary, and tertiary carbenium ions [H2C-CH(EH3)2](+) (1a-e), [HC{CH(EH3)2}2](+), (2a-e), and [C{CH(EH3)2}3](+) (3a-e) for E = C, Si, Ge, Sn, Pb. The nature of the interaction between the carbenium center H(2-n)C(+) and the substituents {CH(EH3)2}m has been investigated with an energy decomposition analysis (EDA) aiming at estimating the strength of the pi hyperconjugation which electronically stabilizes the carbenium ions. The results of the EDA show that the calculated DeltaEpi values can be used as a measure for the strength of hyperconjugation in carbenium ions arising from the interactions of saturated groups possessing pi orbitals. The theoretical data suggest that the ability of sigma C-E bonds to stabilize positive charges by hyperconjugation follow the order C < Si < Ge < Sn < Pb. Hyperconjugation of C-Si bonds is much stronger than hyperconjugation of C-C bonds while the further rising from silicon to lead is smaller and has about the same step size for each element. The strength of the hyperconjugation in primary, secondary, and tertiary alkyl carbenium ions does not increase linearly with the number of hyperconjugating groups; the incremental stabilization becomes smaller from primary to secondary to tertiary cations. The effect of hyperconjugation is reflected in the shortening of the C-C bond distances and in the lengthening of the C-E bonds, which exhibits a highly linear relationship between the calculated C-C and C-E distances in carbocations 1-3 and the hyperconjugation estimated by the DeltaEpi values.