Solvation energies and electronic spectra in polar, polarizable media: Simulation tests of dielectric continuum theory

Abstract

A dielectric continuum theory for the solvation of a polar molecule in a polar, polarizable solvent is tested using computer simulations of formaldehyde in water. Many classes of experiments, for example those which measure solvent-shifted vertical transition energies or electron transfer rates, require an explicit consideration of the solvent electronic polarization. Due to the computational cost of simulating a polarizable solvent, many simulation models employ non-polarizable solute and solvent molecules and use dielectric continuum theory to relate the properties of the non-polarizable system to the properties of a more realistic polarizable system. We have performed simulations of ground and excited state formaldehyde in both polarizable and non-polarizable water, and the solvation energies and solvent-shifted electronic spectra we obtained are used to test dielectric continuum, linear response predictions. Dielectric continuum theory correctly predicts that free energy differences are the same in polarizable and non-polarizable water. The theory wrongly predicts that the reorganization energy in a polarizable solvent is 30% smaller than the reorganization energy in a polar, non-polarizable solvent; in the simulations, the reorganization energies differ by only 6%. We suggest that the dielectric continuum theory fails because it assumes that both solute electronic states exist in the same size cavity in the solvent, whereas in the simulation the cavity radius increases by 20% after the electronic transition. We account for the change in the cavity size by adding a non-linear solute–solvent coupling to the dielectric continuum theory, and find that the resulting predictions are just outside the error bounds from the simulation. The cavity size corrections have the undesired and incorrect side-effect of predicting fluctuations far smaller than seen in the simulations. This reveals the inherent difficulty in devising a simple, fully self-consistent dielectric continuum theory for solvation.