Equilibrium Solvation, Electron-Transfer Reactions, and Stokes-Shift Dynamics in Ionic Liquids

A microscopic theory of solvent response by room-temperature ionic liquids is formulated based on the dynamic longitudinal susceptibility of liquid's charge density. The susceptibility function combines the structural information in terms of reciprocal-space structure factors with the memory function responsible for solvation dynamics. The charge-density structure factors and corresponding intermediate scattering functions are analyzed here by molecular dynamics simulations. They show the existence of two drastically different time scales of charge-density fluctuations. Faster, stretched-exponential dynamics are consistent with dielectric measurements. It contributes to the Stokes-shift dynamics of coumarin-153 optical dye calculated with the new theory and compared to experimental reports. The second, much slower and exponential, relaxation shows the phenomenology of de Gennes narrowing: the relaxation time passes through a strong maximum at the wave vector representing the first peak of the structure factor. This peak, which is particularly sharp for the charge density, contributes significantly to the equilibrium free energy of solvation, thus invalidating dielectric theories of solvation for ionic liquids. Dynamics of charge density fluctuations at the length scale consistent with the sharp peak require long observation times. Electron-transfer reactions occurring on faster time-scales are not affected by these slow dynamics. Nonergodic reorganization energy of electron transfer, accounting for the observation window established by the reaction time, drops sharply when the reaction rate crosses the main peak in the Stokes-shift loss spectrum. The dependence of the reorganization energy on the reaction rate strongly affects the energy-gap law of electron transfer, with a tendency for a shallow or entirely disappearing inverted region.