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Quantum reaction rates and sampling of quantum equilibrium structure.

The time dependent quantum reaction rate may be expressed in terms of the Kubo-transformed reactive flux correlation function involving the Kubo-transformed quantum spectral density function W¯A(X,0). The rate constant, which is obtained from the long time limit of this correlation function, can also be expressed in terms of a simple quantum canonical correlation function. In this context, two useful alternative expressions, WA(X,iℏβ/2) and ReWA(X,0), to the difficult-to-compute W¯A(X,0) function are compared. The spectral density WA(X,iℏβ/2) is a real and symmetric approximation to W¯A(X,0) while ReWA(X,0) is a much simpler form obtained from the quantum canonical correlation function. Computations on a simple parabolic barrier crossing problem and a two-level system reactive system confirm that the long time reaction rate constant is the same for all spectral density expressions. Our results show that the density function WA(X,iℏβ/2) may be more suitable for simple model systems while ReWA(X,0) may be m...