Extended transition-state theory and constant-energy chemical-reaction molecular-dynamics method for liquid-phase chemical reactions

Abstract

An extension of transition-state theory for liquid-phase chemical reactions is presented. The effect of adding a second solvent water molecule on the proton-transfer reaction in a formamidine–water (FW) cluster was studied. Ab initio molecular-orbital calculations were performed for the formamidine–water–water (FWW) system to obtain the adiabatic potential-energy surface. It was expressed in two coordinate systems: (i) the total normal-coordinate system of the FWW system, and (ii) the composite normal-coordinate system consisting of two normal-coordinate systems of the isolated FW system and the isolated medium-water molecule. In either of these two systems, the solvent effect can be categorized as either (i) an equilibrium solvation effect or (ii) a frictional effect. In this article, the former effect was investigated in detail and, in the total normal-coordinate system, a frequency diagram was obtained by diagonalizing the Hessian matrix at successive geometries along intrinsic reaction coordinate and then, within the Rice–Ramsperger–Kassel–Marcus (RRkM) formalism, the rate constant was evaluated with the vibrational frequencies assigned in this manner. In the composite normal-coordinate system, the off-diagonal elements found in the Hessian matrix are due to the interaction between the FW system and the medium-water molecule at equilibrium separation. The rate constant was evaluated within the diagonal approximation. As a result, both treatments work well and yield similar conclusions about the role of the solvent to those drawn from chemical-reaction molecular-dynamics simulations. The reaction is found to be enhanced considerably by the assistance of an additional medium-water molecule. The second treatment is concluded to be reasonably applicable in the estimation of reaction rates for liquid-phase chemical reactions.