The potential energy function for a ligand substitution reaction of square-planar platinum (II) complex in water: The important role of three-body effect

Abstract

The analytical potential energy function for interaction of [Pt(NH3)3]2+, Cl−, and H2O has been determined to describe the ligand substitution reaction: [Pt(NH3)3(H2O)]2+ +Cl−→[Pt(NH3)3Cl]++H2O in solution. The Honda–Kitaura potential function is used as the two-body potential function. Although the Honda–Kitaura potential reproduces the ab initio two-body interaction energy very well, the potential function that assumes pairwise additivity cannot reproduce the potential energy of the entire three-body complex because of a large repulsive three-body interaction in the strongly interacting region. We analyzed the origin of three-body energies, derived the physically meaningful potential functional forms from a perturbation theory, and fitted the ab initio three-body energies into an analytical form. The full potential function, the sum of pairwise two-body potential functions and the three-body terms, can reproduce very well the ab initio interaction energies in the entire geometrical space as well as the structures of the reaction intermediates and transition states. The results of the preliminary reaction coordinate and Monte Carlo calculation for the reaction in a cluster of water molecules are also presented.