Dynamics of radiationless transitions in large molecules: 3. Decay of vibration-phonon states

Abstract

The statistical operator of the ensemble of high-frequency intramolecular vibrations associated with the phonon reservoir depends on the phonon occupation numbers under thermal equilibrium conditions. The eigenvalues of energy of statistically averaged vibration-phonon (VP) states are complex quantities. In the case of weak VP coupling, only one- and two-phonon transitions are taken into consideration for calculating the decay rate constant, in which the difference of phonon energies compensates for the difference in energy between the initial and final intramolecular states. Although the fast evolution of amplitudes of VP states is due to intramolecular redistribution of energy and is not reduced to exponential decay of the initial state, the imaginary components of the eigenvalues coincide with those predicted by Fermi’s golden rule. The relative contribution of two-phonon (combination) transitions compared with one-phonon transitions increases with an increase in the density of intramolecular states and temperature, becoming prevalent for large molecules at T ≥ D ≫ Δ₀ (D = 100–200 K (70–140 cm⁻¹) is the Debye temperature and Δ₀∼10 cm⁻¹ is the spacing between neighboring intramolecular vibration levels). When T ≥ D, the decay rate constant is K ∝ T ².