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Hyperconjugative Stabilization in Alkyl Carbocations:  Direct Estimate of the β-Effect of Group-14 Elements

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journal contribution
posted on 16.08.2007, 00:00 by Israel Fernández, Gernot Frenking
DFT calculations at the BP86/TZ2P level have been carried out for the primary, secondary, and tertiary carbenium ions [H2C−CH(EH3)2]+ (1ae), [HC{CH(EH3)2}2]+, (2ae), and [C{CH(EH3)2}3]+ (3ae) for E = C, Si, Ge, Sn, Pb. The nature of the interaction between the carbenium center H2-nC+ and the substituents {CH(EH3)2}m has been investigated with an energy decomposition analysis (EDA) aiming at estimating the strength of the π hyperconjugation which electronically stabilizes the carbenium ions. The results of the EDA show that the calculated ΔEπ values can be used as a measure for the strength of hyperconjugation in carbenium ions arising from the interactions of saturated groups possessing π orbitals. The theoretical data suggest that the ability of σ 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 13 and the hyperconjugation estimated by the ΔEπ values.