MASTER EQUATION ANALYSIS OF INTERMOLECULAR ENERGY-TRANSFER IN MULTIPLE-WELL, MULTIPLE-CHANNEL UNIMOLECULAR REACTIONS .1. BASIC THEORY

We present a full theoretical analysis of the master-equation formulat ion of the problem of intermolecular energy transfer in multiple-well, multiple-channel systems. It is shown that the master equation for ch emical or thermal activation possesses a unique steady state, that cor responding to the trivial solution, Rate equations local in time and t herefore time-independent rate coefficients for the dissociating proce sses may be obtained only if a state of secular equilibrium exists. Fo r chemically-activated systems, a general state of secular equilibrium may exist which may contain within it a regime wherein there is a wel l-separated, nontrivial, least negative eigenvalue of the master equat ion kernel. The dynamics of thermally activated systems are similarly deduced by treating them as chemically activated systems with appropri ate modifications to the inhomogeneous source term of the master equat ion. A degenerate and nondegenerate perturbation theory analysis of th e case of rapid thermalization in the vicinity of the thermodynamic eq uilibrium state is also enunciated, The special case of negligible the rmalization is analyzed, A classification of the ordering of the time scales of thermalization, isomerization, and dissociation is then give n. (C) 1997 American Institute of Physics.