Rigorous formulation of quantum transition state theory and its dynamical corrections

We describe a procedure for computing the thermal rate constants for infrequent events that occur in complicated quantum mechanical systems. Following the ideas of Gillan, the procedure focuses on the equilibrium statistics of the centroids for the imaginary time quantum paths. We argue that the imaginary time statistics can be used to efficiently bias Monte Carlo sampling of the real time reaction dynamics. Consideration of imaginary time paths or equilibrium statistics alone leads to a quantum transition state theory. Analytical versions of this transition state theory are developed with the aid of a variational principle. Numerical applications of the quantum transition state theory are given for the one-dimensional Eckart barrier problem and for the nonseparable two-dimensional collinear H2+H reaction. Remarkably accurate results are obtained. The quantum transition state theory we describe provides a rigorous basis and generalizes algorithms recently employed to treat electron transfer and also ionization in polar media.