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

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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 expresssed 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.

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