Analysis of infrared absorption line shapes in condensed media: Application of a classical limit of Heisenberg’s equations of motion

A microscopic dynamical treatment of chemical systems comprising both light particles that require a quantal description and heavy ones that may be described adequately by classical mechanics is presented. A (partial) classical limit of Heisenberg’s equations yields a self-consistent set of ‘‘hemiquantal’’ equations (HQE) of motion. The adiabatic limit of the HQE, in which energy is not shared between high-frequency modes of the quantal subsystem and relatively low-frequency modes of the classical subsystem, is applied to a one-dimensional model for infrared absorption by matrix-isolated impurites. The predictions of the model are consistent with recent experimental measurements on the ‘‘Q’’ feature of HCl isolated in Ar.