Controlling nonpolar solvation time scales: An instantaneous normal mode viewpoint

The effects of temperature, solvent mass, ground-state solute-solvent interaction potential, and difference potential on the time scale for the decay of an electronic transition energy gap correlation function (ECF) are investigated within the context of a linear instantaneous normal mode (INM) model of fluid dynamics. This correlation function is also known as the solvation autocorrelation. The system described here is the B-state transition of methyl iodide in the nonpolar solvents argon and methane. The required ground- and excited state interaction potentials have been determined in previous experimental spectroscopic studies. The solvation time scale is of the order of 100-200 fs for solvent densities ranging from ρ*=0.08 to ρ*=0.8. The molecular properties responsible for determining the solvation time scale of this nonpolar system are delineated here. Via this INM approach, the nonpolar solvation time scale can be approximated by the ratio of a characteristic solute-solvent separation distance scaled by the shape of the difference potential and the inertial velocity of the solvent particles. The time scale of solvation is found to be independent of the magnitude of the difference potential (solute-solvent coupling strength). Thus by changing the coupling strength and leaving the shape of the difference potential constant, the corresponding electronic absorption spectrum passes from the inhomogeneous to the motional narrowing limit. This is due to the change in the decay time of the static dipole correlation function and not to any change in system dynamics. Only very modest changes in this decay time are found for realistic temperature increases and mass changes of the solvent. Similarly, changes in the ground-state solute-solvent potential are found to have only a minimal effect on the ECF decay time. Finally, if the shape of the difference potential is similar for two different observables in a given solvent, the use of the spectral density of one for the description of the (ultrafast) solvent response of the other observable is rationalized.