DFT-PCM Studies of Solvent Effects on the Cross-Interaction Constants in Benzhydryl Cation and Anion Formation

The Hammett ρ+ and ρ- values have been determined by varying substituent Y‘ for a given Y in the benzhydryl cation and anion formation (YH4C6−C*H−C6H4Y‘ where C* is a cationic or an anionic center) at the RHF/3-21G*, RHF/6-31G*, RHF/6-31+G*, and B3LYP/6-31+G* levels. The failure of RHF theory in accounting for the stabilization by delocalization leads to the smaller magnitudes of ρ+ and ρ- with electron-donating and -withdrawing substituents, Y, respectively, than the corresponding DFT values. The effects of solvent (benzene, dichloroethane, and acetonitrile) on the ρ values were calculated by applying the conductor polarizable continuum model method to the DFT results. Finally, the cross-interaction constants (ρYY ‘) and their variation with solvent were determined. As the polarity (dielectric constant, ε) of the solvent is increased, the magnitude of ρ+ and ρ- decreased, whereas that of ρYY ‘ increased. Satisfactory correlations were obtained between ρ values (ρ+, ρ- and ρYY ‘) and the Kirkwood function f k (= ε − 1/2ε + 1). The ρYY ‘ values are negative with a magnitude greater for the anionic (ρYY ‘ -) than the cationic (ρYY ‘ +) system.