Electrostatics on particles: Phenomenological and orientational density functional theory approach

Abstract

In order to describe efficiently the solvation of complex solutes in computer simulations, we introduce several simple particle-based models with the requirement that they yield, on average, either an exact or approximate representation of the macroscopic laws of electrostatics. First, in a phenomenological approach, electrostatics of continuous media is formulated in terms of a polarization density free energy functional, which is projected on randomly distributed discrete Lennard-Jones pseudoparticles. The resulting model is that a polarizable fluid, in which the induced dipoles describe both orientational and electronic polarization. The problem of the connection between the macroscopic dielectric constant and the pseudoparticles polarizability is examined and important deviations with respect to the commonly accepted Clausius–Mossotti relation are found. Dipolar saturation effects can also be added to the model to yield a “nonlocal Langevin solvent model” and an approximate, numerically very efficient, “local Langevin solvent model.” The two models are implemented in molecular dynamics simulations and their solvation properties are compared to continuous electrostatics for simple solutes such as spherical ions or ion pairs. Their computational efficiency is also discussed and compared to explicit microscopic solvent models. Then a statistical mechanics approach based on orientational density functional theory ideas is presented. Starting from a microscopic Hamiltonian describing a polar solvent, and for a given position of all the solvent molecules, a preliminary thermodynamic average over all the possible orientations of the molecules is performed. This can done by defining an orientational free-energy functional which, at a formal stage, is perfectly well-defined and exact. Minimization of the functional with respect the angular degrees of freedom yields an effective Hamiltonian acting on the translational degrees of freedom only which can be explored via molecular dynamics simulations. The simplest approximation for the orientational functional yields a version of the nonlocal Langevin solvent model mentioned above. More general approximations are suggested.