A classical/semiclassical theory for the interaction of infrared radiation with molecular systems

Abstract

A classical model for the interaction of molecular systems with infrared radiation is presented. It differs from the usual ’’semiclassical theory of radiation and matter’’ in that the molecular system is treated by classical rather than quantum mechanics, and the radiation field is described, as in Jaynes’ neoclassical theory, as classical (mechanical) harmonic oscillators rather than as a classical field (i.e., via Maxwell’s equations). The classical Hamiltonian for the composite system—molecules, radiation, and their interaction—is thus that of a completely mechanical system, and its classical dynamics is determined by computing the classical trajectories of the system. Quantum mechanical interference and tunneling effects can be built into the description within the framework of the classical S-matrix theory. Even within the strictly classical limit of the model, it is shown that all dynamical effects in the interaction of radiation and matter are obtained; in the perturbative limit, for example, it is shown that absorption and induced emission, and even spontaneous emission, which is often difficult to obtain in other classical or semiclassical models, appear in a completely straightforward manner.