Activated rate processes are often described in terms of a generalized Langevin equation. The concept of an optimized planar dividing surface in conjuction with variational transition state theory has been demonstrated to be useful in understanding the effects of nonlinearities on reaction rates. A different approach is based on the Rayleigh quotient method, in which one varies the trial functions. We prove a restricted identity of the two methods. The restrictions are that the variational transition state theory method is limited to planar dividing surfaces. The Rayleigh quotient method is restricted to the class of Kramers functions. These functions are constructed by replacing the true potential with a parabolic barrier and using the known eigenfunction for the parabolic barrier. The parameters of the parabolic barrier are used as variational parameters in the Rayleigh quotient for the true nonlinear potential.

• Received 9 May 1994

DOI:https://doi.org/10.1103/PhysRevE.50.2646