Transfer of atoms, ions and molecular groups in solution. Part 4.—Methods for Metropolis/Monte Carlo simulations

Abstract

Metropolis/Monte Carlo importance sampling has been applied to the evaluation of rate constants for the transition-state theory of atom-, ion- and group-transfer reactions. This paper continues the calculation of the simple inversion of a solvated, bent A—B—A molecule which was initiated in Part 3. The rate constant is a weighted sum of contributions, each of which satisfies either the adiabatic or diabatic limit for the individual transfers in the ensemble. The result is a general expression for the rate constant, which is automatically valid for any limit of the reaction, adiabatic to diabatic. In this Part, techniques are developed which are needed in particular to evaluate the environmental contributions to the pre-exponential factor in the expression for the rate constant. Emphasis is placed on the development of methods to handle the construction of average values of the determinants of force constants which are found in the expressions of the rate constants.