QUANTUM AND SEMICLASSICAL GREENS-FUNCTIONS IN CHEMICAL-REACTION DYNAMICS

A variety of quantities related to chemical reaction dynamics (state-s elected and cumulative probabilities for chemical reactions, photo-dis sociation or -detachment cross-sections, and others) can be expressed compactly (and exactly) in terms of the quantum mechanical Green's fun ction (actually an operator) <(G)over cap (E)> = (E + <i(epsilon)over cap> - (H) over cap)(-1), where (H) over cap is the Hamiltonian for th e molecular system and <(epsilon)over cap> an absorbing potential. It is emphasized that these 'formal' quantum expressions can serve as the basis for practical calculations by utilizing a straightforward L(2) matrix representation of the operator (E + <i(epsilon)over cap> - (H) over cap). It is also shown how the semiclassical initial value repres entation (IVR) can be used to construct approximations for general mat rix elements of the Green's function, so that these same formally exac t quantum expressions can also be used to provide semiclassical approx imations for all of these dynamical quantities. Recent applications of the quantum and semiclassical methodologies are discussed.