Computing reaction rates using a Wigner function based on a new effective frequency theory

Abstract

In this paper, we test the ability of a recently proposed effective frequency theory, viz. the generalised Feynman–Kleinert effective frequency theory (GFK), for calculating the Wigner transform of the thermalised flux operator needed in reaction rate computations based on the classical Wigner model. We consider one-dimensional symmetric and asymmetric barriers at both high and low temperatures. The reaction rates obtained from the GFK theory are found to be close to the results obtained using the accurate Wigner function. The reaction rates obtained from the classical Wigner model are approximate since they are based on classical trajectories. We therefore also present a new version of the so-called effective quantum force method, that improves the classical Wigner rates. This new implementation utilises as input matrix elements of the thermalised flux operator obtained from the GFK theory. We find a significant improvement compared to the classical Wigner reaction rates. Possible extensions to multi-dimensional systems are discussed.