Correlation function formulation for the state selected total reaction probability

A correlation function formulation for the state-selected total reaction probability, N-alpha(E), is Suggested. A wave packet, correlating with a specific set of internal reactant quantum numbers, alpha, is propagated forward in time until bifurcation is complete at which time the nonreactive portion of the amplitude is discarded. The autocorrelation function of the remaining amplitude is then computed and Fourier transformed to obtain a reactivity spectrum. Dividing by the corresponding spectrum of the original,unfiltered, wave packet normalizes the reactivity spectrum, yielding the fetal reaction probability from the internal state, alpha. The procedure requires negligible storage and just one time-energy Fourier transform for each initial reactant state; independent of the number of open channels of products. The method is illustrated numerically for the one-dimensional Eckart barrier, using both quantum-mechanical and semiclassical propagation methods. Summing over internal states of reactants gives the cumulative reaction probability, N(E). The relation to the trace formula [W. H. Miller, S. D. Schwartz, J.W. Tromp, J. Chem. Phys. 79, 4889 (1983)], N(E) = 1/2(2 pi (h) over bar)(2) tr((F) over bar delta(H-E)(F) over bar-delta(H-E)), is established, and a new variant of the trace formula is presented. (C) 1998 American Institute of Physics. [S0021-9606(98)01127-1].