The power law aspect of solvation dynamics, based on the convolutionless generalized Langevin equation

The familiar generalized Langevin equation (GLE₁) of Mori has a variant, the convolutionless generalized Langevin equation (GLE₂) of Tokuyama and Mori, for which we propose a very simple approximation to calculate time correlation functions. This new method, the reference frequency modulation approximation (RFMA), leads quite straightforwardly to known useful formulas. One is the power law of dynamic solvation due to Maroncelli, Kumar, and Papazyan. Another is a decay-time analog of the Powles-Glarum relation between single-particle and collective dielectric correlation times. A third application gives a relation between single-particle rotational time correlation functions of different tensorial rank recently used by Chang and Castner. The GLE ₂-RFMA method may be considered as the counterpart of the reference memory function approximation of GLE₁ theory.