QUANTUM ACTIVATED RATE THEORY - VARIATIONAL OPTIMIZATION OF PLANAR DIVIDING SURFACES

A variational procedure is presented for finding the optimal planar di viding 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 cho osing the best coordinate and momentum dependent dividing surfaces tha t was previously presented by the authors [J. Chem. Phys. 98, 8525 (19 93)]. The present approach can also be considered a direct quantum mec hanical generalization of the classical variational method of Berezhko vskii, Pollak, and Zitserman [J. Chem. Phys. 97, 2422 (1992)]. We also relate this method to the analytical approach of Voth [Chem. Phys. Le tt. 170, 289 (1990)] that incorporates a transmission coefficient in t he centroid-density based quantum rate theory. The variational procedu re is also applicable to systems coupled to a continuum of oscillators , and it is shown that this procedure can be efficiently implemented f or an arbitrary number of oscillators in the bath. Numerical results a re presented for an Eckart barrier coupled to a bath of harmonic oscil lators. Numerical results show that a strict variational optimization of the planar dividing surface offers some improvement for the rate co nstants relative to those of the analytic theory of Voth, thus justify ing the extra work needed for the variational search.