DFT-PCM studies of solvent effects on the cross-interaction constants in benzhydryl cation and anion formation

The Hammett rho+ and rho- values have been determined by varying substituent Y' for a given Y in the benzhydryl cation and anion formation (YH4C6-CH-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 rho+ and rho- with electron-donating and -withdrawing substituents, Y, respectively, than the corresponding DFT values. The effects of solvent (benzene, dichloroethane, and acetonitrile) on the rho values were calculated by applying the conductor polarizable continuum model method to the DFT results. Finally, the cross-interaction constants (rho(YY)') and their variation with solvent were determined. As the polarity (dielectric constant, epsilon) of the solvent is increased, the magnitude of rho+ and rho- decreased, whereas that of rho(YY)' increased. Satisfactory correlations were obtained between rho values (rho+, rho- and rho(YY)') and the Kirkwood function f(k) (= epsilon - 1/2epsilon + 1). The rho(YY)' values are negative with a magnitude greater for the anionic (rho(YY)'-) than the cationic (rho(YY)'+) system.