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

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, tc5t2i\b/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 H1H2 reaction, and the three-dimensional D1H2 ~J50! reaction. © 1995 American Institute of Physics.