Cumulative reaction probability in terms of reactant-product wave packet correlation functions

We present new expressions for the cumulative reaction probability (N(E)), cast in terms of time-correlation functions of reactant and product wave pa ckets. The derivation begins with a standard trace expression for the cumul ative reaction probability, expressed in terms of the reactive scattering m atrix elements in an asymptotic internal basis. By combining the property o f invariance of the trace with a wave packet correlation function formulati on of reactive scattering, we obtain an expression for N( E) in terms of th e correlation matrices of incoming and outgoing wave packets which are arbi trary in the internal coordinates. This formulation, like other recent form ulations of N(E), allows calculation of the quantum dynamics just in the in teraction region of the potential, and removes the need for knowledge of th e asymptotic eigenstates. However, unlike earlier formulations, the present formulation is fully compatible with both exact and approximate methods of wave packet propagation. We illustrate this by calculating N(E) for the co llinear hydrogen exchange reaction, both quantally and semiclassically. The se results indicate that the use of wave packet cross-correlation functions , as opposed to a coordinate basis and flux operators, regularizes the semi classical calculation, suggesting that the semiclassical implementation des cribed here may be applied fruitfully to systems with more degrees of freed om. (C) 1999 American Institute of Physics. [S0021-9606(99)01706-7].