Semiclassical approximations to golden rule rate constants

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Abstract
Fermi’s golden rule gives an expression for state-to-state rate constants that involves the Fourier transform of a quantum mechanical time correlation function. It is often convenient to evaluate such an expression semiclassically, by calculating the correlation function classically. For an arbitrary quantum subsystem coupled linearly (in the bath coordinates) to a harmonic bath, I show that the semiclassical result must be multiplied by a certain “quantum correction factor” in order to obtain the exact result. This generalizes the recent work of Bader and Berne, which was for the overall vibrational relaxation rate of a harmonic oscillator bilinearly coupled to a harmonic bath.

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