On the ‘‘direct’’ calculation of thermal rate constants

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Abstract
We present a new approach for the direct (and correct) calculation of thermal rate constants k(T) (‘‘direct’’ meaning that one avoids having to solve the state-to-state reactive scattering problem, and ‘‘correct’’ meaning that the method contains no inherent approximations). The rate constant is obtained from the long time limit of the flux-position correlation function, Cf,s(t), whose calculation is made efficient by taking advantage of the low rank of the flux operator. Specifically, the trace required to obtain Cf,s(t) is evaluated by a Lanczos iteration procedure which calculates only the nonzero eigenvalues. The propagation in complex time, tc=t−iℏβ/2, is carried out using a Chebychev expansion. This method is seen to be both accurate and efficient by application to the Eckart barrier, the collinear H+H2 reaction, and the three-dimensional D+H2 (J=0) reaction.

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