Rate constants in quantum mechanical systems: A rigorous and practical path-integral formulation for computer simulations

In this letter we present rigorous equations, amenable to computer simulations, for using Feynman path integrals to calculate thermal rate constants. The quantum mechanical expression for the thermal rate constant in terms of the derivative of a side–side correlation function developed by Miller, Schwartz and Tromp (J. Chem. Phys. 79 (1983) 4889) is used. We calculate the side–side correlation function with a discretized Feynman path integral. The derivative of the side–side correlation function is calculated using statistical mechanical free energy perturbation calculation methods after computing the trace. The theory is illustrated with the Monte Carlo simulation of a free particle.