SIMPLIFICATIONS IN THE THEORETICAL TREATMENT OF SOLVATION EFFECTS BASED ON THE QUADRATIC EXPANSION OF THE ENERGY

An analysis of the electrostatic free energies of a set of neutral test molecules in water is presented, as calculated within the polarizable continuum model (PCM). The analysis is based on the formalism of the quadratic expansions of the energy. A general expression is derived for the solvation energy and a sequence of approximations to it, ranging from the rigorous linear response, to the linear regime, to an approximate linear response, to the zeroth-order response. It is shown that the linear response of the solvated molecule to the solvent reaction field potential is of sufficient accuracy for most purposes, whereas the zeroth-order response may not be. The merits of each approximate expression are also compared, showing that the use of an approximate linear response allows one to drastically reduce the computational effort associated with the treatment of solvation effects to a negligible portion of a standard quantum chemical calculation, without degrading the overall accuracy.