Variational transition state theory for activated rate processes

A variational transition state theory is formulated for the decay rate of a particle trapped in a metastable potential well and coupled to a heat bath. Rigorous upper bounds are derived for the transmission coefficient and the rate constant. The variational theory leads to minimization of the flux of an effective two degree of freedom Hamiltonian whose parameters depend on the system potential and the time dependent friction kernel. An explicit solution for the canonical variational dividing surface in the presence of nonlinearities in the system potential is provided. The Kramers expression for the rate in the spatial diffusion limit and its generalization to memory friction, is shown to give upper bounds provided that the nonlinearity in the system potential is positive definite. However, the variational result can still lead to substantially lower bounds for the rate. An application of VTST to a symmetric cusped double well potential provides a new expression for the rate, valid for arbitrary friction kernels and damping strength.