Model for vibrational relaxation: pure-dephasing and depopulation

The three dominant mechanisms giving major contributions to vibrational relaxation in molecular systems are (a) pure dephasing, (b) depopulation (or energy relaxation), and (c) resonant transfer. Here (c) is not considered but the effects due to the simultaneous occurrence of (a) and (b) are treated within a stochastic model. In dealing with (a), the vibrational frequency is assumed to undergo random uncorrelated 'jump', due to fluctuations in the environment of the active molecule between a continuous set of values. The ensuing results are somewhat different from those of the commonly used Kubo model of vibrational dephasing, especially at long times and appear to be better suited in interpreting certain experimental data. The model is next extended to include the simultaneous occurrence of (b). The calculation leads to two important conclusions: (i) the lineshape is not just the convolution of those due to (a) and (b), and (ii) the lineshape is asymmetric, if the intermolecular interactions are not isotropic