Theory of vibrational relaxation in isolated molecules

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Abstract
A quantum mechanical theory of intramolecular energy transfer is presented which treats the approach to statistical equilibrium of the vibrations in isolated molecules. The theory is appropriate for nonreactive molecules which have at least 6–9 atoms and which are so highly excited that the vibrational interaction couples together many degrees of freedom at a time and causes the simultaneous exchange of a large number of quanta. A generalized master equation of the Van Hove type and a weak‐coupling master equation of the Pauli type are obtained for functions related to occupation probabilities of zero‐order states. The asymptotic behavior of the coarse‐grained occupation probabilities is examined and molecular ergodicity is proved. Convergent infinite expansions for the probabilities are also derived. These analytical expressions make it possible to study the intramolecular dynamics for all relevant times.