Semiclassical calculation of cumulative reaction probabilities

It is shown how the rigorous quantum mechanical expression for the cumulative reaction probability (CRP) obtained by Seideman and Miller [J. Chem. Phys. 96, 4412; 97, 2499 (1992)], N(E) =4 tr[<(epsilon)over cap>(r) .(G) over cap*(E).<(epsilon)over cap>(p) .(E)], which has been the basis for quantum calculations of the CRP for simple chemical reactions, can also be utilized with a semiclassical approximation for the Green's function, (G) over cap(E) = (E + i<(epsilon)over cap>-(H) over cap)(-1)=(ih)(-1)integral(0)(infinity)dt exp(iEt/h)exp(-i((H) over cap-i<(epsilon)over cap>)t/h). Specifically, a modified Filinov transformation of an initial value representation of the semiclassical propagator has been used to approximate the Green's function. Numerical application of this trajectory-based semiclassical approximation to a simple one-dimensional (barrier transmission) test problem shows the approach to be an accurate description of the reaction probability, even some ways into the tunneling regime. (C) 1996 American Institute of Physics.