Theoretical Investigations on Carbocations. Structure and Stability of C₃H₅⁺, C₄H₉⁺ (2-Butyl Cation), C₅H₅⁺ C₆H₇⁺ (Protonated Benzene), and C₇H₁₁⁺ (2-Norbornyl Cation)

The title molecules have been investigated by ab initio methods including electron correlation and by the semiempirical MINDO/3 method. Electron correlation energies of the C₃H₅⁺ system have been calculated explicitly by CEPA. In the other cases a complete CEPA calculation is no longer feasible and correlation effects have been estimated on the basis of pair-energy values. Experimental proton affinities of allene and propyne can be reproduced within experimental accuracy. In contrast, the calculated proton affinity of cyclopropene deviates significantly from the experimental value if, as it has been done in the literature, the cyclopropyl cation is assumed to be the protonated species. In order to resolve this discrepancy we have investigated the C₃H₅⁺ energy hypersurface and looked for reasonable alternatives. As a solution of this problem we suggest that protonated cyclopropene has not been formed at all, but that ring opening has occurred yielding the 2-propenyl cation. An unusually large stabilization effect by polarization functions and by electron correlation has been observed for the square pyramidal form of C₅H₅⁺ in relation to the planar cyclopentadienyl cation. This behavior is explained in terms of chemical bonding. In agreement with other theoretical investigations the a complex of protonated benzene is found more stable than the σ complex. The energy difference is estimated to lie between 1 and 6 kcal/mol, significantly less than obtained from double SCF calculations. For the norbornyl cation system the classical structure is found less stable than the nonclassical one by about 8-13 kcal/mol. However, the edge-protonated stucture is nearly as stable as the nonclassical one. For an interpretation of experimental gas-phase data both of these structures should be considered.