Quantum and semiclassical Green's functions in chemical reaction dynamics

Abstract

A variety of quantities related to chemical reaction dynamics (state-selected and cumulative probabilities for chemical reactions, photo-dissociation or -detachment cross-sections, and others) can be expressed compactly (and exactly) in terms of the quantum mechanical Green's function (actually an operator) Ĝ(E) ≡ (E + i[small epsilon, Greek, circumflex] − Ĥ)⁻¹, where Ĥ is the Hamiltonian for the molecular system and [small epsilon, Greek, circumflex] an absorbing potential. It is emphasized that these ‘formal’ quantum expressions can serve as the basis for practical calculations by utilizing a straightforward L² matrix representation of the operator (E + i[small epsilon, Greek, circumflex] − Ĥ). It is also shown how the semiclassical initial value representation (IVR) can be used to construct approximations for general matrix elements of the Green's function, so that these same formally exact quantum expressions can also be used to provide semiclassical approximations for all of these dynamical quantities. Recent applications of the quantum and semiclassical methodologies are discussed.