A fluctuating charge density formulation of the dielectric behavior of liquids—with applications to equilibrium and nonequilibrium solvation

Abstract

The usual molecular formulation of the dielectric properties of fluids is based on the equilibrium spatial and temporal fluctuations of the local density of vector dipole moments. In this work we discuss an alternative statistical mechanical theory of the longitudinal dielectric response of liquids comprising molecules with arbitrary shape and charge distribution. The molecules are represented by models comprising interaction sites carrying fluctuating partial charges; in this way the role of the electronic polarizability of the solvent molecules is taken into account. The emphasis of the theory is on the fluctuations of the microscopic charge density at equilibrium. It leads to a compact molecular formulation of the frequency- and wavevector-dependent longitudinal dielectric function of the solvent. It also leads to charge susceptibilities required for the description of the solvent response to a time-varying external charge distribution. The theory provides a simple unified description of the dielectric properties of dipolar as well as “non-dipolar” solvents. In the latter case the solvent molecules lack a permanent dipole moment; the solvent “polarity” originates from the molecular electrical multipoles of higher order that are a consequence of the finite size of the molecular charge distribution. We show that the molecular formulation of the dielectric response is especially useful for the discussion of the energetics and dynamics of the solvation process relevant to electron transfer reactions in solution. Thus we examine the dependence of the solvent reorganization energy on the distance between the donor and acceptor groups in an intramolecular charge transfer reaction in acetonitrile and in benzene. The dynamical theory is illustrated by calculating the solvation time correlation function for Coumarin-153 in acetonitrile.