Quantum activated rate theory: Variational optimization of planar dividing surfaces

Abstract

A variational procedure is presented for finding the optimal planar dividing surface within a centroid-density based quantum rate theory for the model of a general reaction coordinate coupled to a harmonic bath. The approach described here is a limiting form of the method for choosing the best coordinate and momentum dependent dividing surfaces that was previously presented by the authors [J. Chem. Phys. 98, 8525 (1993)]. The present approach can also be considered a direct quantum mechanical generalization of the classical variational method of Berezhkovskii, Pollak, and Zitserman [J. Chem. Phys. 97, 2422 (1992)]. We also relate this method to the analytical approach of Voth [Chem. Phys. Lett. 170, 289 (1990)] that incorporates a transmission coefficient in the centroid-density based quantum rate theory. The variational procedure is also applicable to systems coupled to a continuum of oscillators, and it is shown that this procedure can be efficiently implemented for an arbitrary number of oscillators in the bath. Numerical results are presented for an Eckart barrier coupled to a bath of harmonic oscillators. Numerical results show that a strict variational optimization of the planar dividing surface offers some improvement for the rate constants relative to those of the analytic theory of Voth, thus justifying the extra work needed for the variational search.