CENTROID-DENSITY QUANTUM RATE THEORY - VARIATIONAL OPTIMIZATION OF THE DIVIDING SURFACE

A generalization of Feynman path integral quantum activated rate theor y is presented that has classical variational transition state theory as its foundation. This approach is achieved by recasting the expressi on for the rate constant in a form that mimics the phase-space integra tion over a dividing surface that is found in the classical theory. Ce ntroid constrained partition functions are evaluated in terms of phase -space imaginary time path integrals that have the coordinate and mome nta centroids tied to the dividing surface. The present treatment exte nds the formalism developed by Voth, Chandler, and Miller [J. Chem. Ph ys. 91, 7749 (1989)] to arbitrary nonplanar and/or momentum dependent dividing surfaces. The resulting expression for the rate constant redu ces to a strict variational upper bound to the rate constant in both t he harmonic and classical limits. In the case of an activated system l inearly coupled to a harmonic bath, the dividing surface may contain e xplicit solvent coordinate dependence so that one can take advantage o f previously developed influence functionals associated with the harmo nic bath even with nonplanar or momentum dependent dividing surfaces. The theory is tested on the model two-dimensional system consisting of an Eckart barrier linearly coupled to a single, harmonic oscillator b ath. The resulting rate constants calculated from our approximate theo ry are in excellent agreement with previous accurate results obtained from accurate quantum mechanical calculations [McRae et al., J. Chem. Phys. 97, 7392 (1992)].