  To understand the non-exponential 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 1/f
dependence in a wide frequency range over 2 to 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 1/f behavior
in its power spectra shows fast relaxation of the memory function and
single-exponential decay of solvation dynamics in the long-time regime.
