On the theory of rate processes: The role of coherent mechanical vibrations

Abstract

The influence of the nonequilibrium degrees of freedom of the electron–nuclear system on the rate of relaxation processes is investigated. The electron–nuclear system is modeled by two potential energy hypersurfaces—electronic terms, plus the perturbation causing transitions between these terms. A harmonic approximation with displaced equilibrium positions and with identical frequencies is assumed for a description of the terms. The equations describing rate processes in such a system are derived. These equations determine the change in time not only of mean occupation numbers of electronic levels but of the amplitudes of nuclear vibrations as well. The dependence of the rate constants on the amplitudes of nonequilibrium excited vibrations is investigated under various assumptions about nonequilibrium of the system. The possibility of excitation of coherent nuclear vibrations in the course of nonradiative transition and in the presence of a constant input on the upper electronic level is investigated as well. The conditions under which such coherent vibrations may arise are obtained, and the stationary amplitude of these vibrations is derived. Attempts are made to apply the theory for a description of enzyme catalysis.