1f spectrum and memory function analysis of solvation dynamics in a room-temperature ionic liquid

To understand the nonexponential relaxation associated with solvation dynamics in the ionic liquid 1-ethyl-3-methylimidazolium hexafluorophosphate, we study power spectra of the fluctuating Franck-Condon energy gap of a diatomic probe solute via molecular dynamics simulations. Results show 1f dependence in a wide frequency range over 2-3 decades, indicating distributed relaxation times. We analyze the memory function and solvation time in the framework of the generalized Langevin equation using a simple model description for the power spectrum. It is found that the crossover frequency toward the white-noise plateau is directly related to the time scale for the memory function and thus the solvation time. Specifically, the low crossover frequency observed in the ionic liquid leads to a slowly decaying tail in its memory function and long solvation time. By contrast, acetonitrile characterized by a high crossover frequency and (near) absence of 1f behavior in its power spectra shows fast relaxation of the memory function and single exponential decay of solvation dynamics in the long-time regime.