Density functional theory of solvation in a polar solvent: Extracting the functional from homogeneous solvent simulations

Abstract

In the density functional theory formulation of molecular solvents, the solvation free energy of a solute can be obtained directly by minimization of a functional, instead of the thermodynamic integration scheme necessary when using atomistic simulations. In the homogeneous reference fluid approximation, the expression of the free-energy functional relies on the direct correlation function of the pure solvent. To obtain that function as exactly as possible for a given atomistic solvent model, we propose the following approach: first to perform molecular simulations of the homogeneous solvent and compute the position and angle-dependent two-body distribution functions, and then to invert the Ornstein-Zernike relation using a finite rotational invariant basis set to get the corresponding direct correlation function. This rather natural scheme is proved, for the first time to our knowledge, to be valuable for a dipolar solvent involving long range interactions. The resulting solvent free-energy functional can then be minimized on a three-dimensional grid around a solute to get the solvent particle and polarization density profiles and solvation free energies. The viability of this approach is proven in a comparison with "exact" molecular dynamics calculations for the simple test case of spherical ions in a dipolar solvent.

Molecular Density Functional Theory of Water

“…In the so-called homogeneous reference fluid (HRF) approximation, the (unknown) excess free energy can be inferred from the angular-dependent direct correlation function of the bulk solvent, that can be predetermined from molecular simulations of the pure solvent. Compared to reference molecular dynamics calculations, such approximation was shown to be accurate for polar, non-hydrogen bonded fluids [35,[38][39][40][41], but to require some corrections for water [39,[42][43][44].…”

“…In the so-called homogeneous reference fluid (HRF) approximation, the (unknown) excess free energy can be inferred from the angular-dependent direct correlation function of the bulk solvent, that can be predetermined from molecular simulations of the pure solvent. Compared to reference molecular dynamics calculations, such approximation was shown to be accurate for polar, non-hydrogen bonded fluids [35,[38][39][40][41], but to require some corrections for water [39,[42][43][44].In this paper we introduce a simplified version of MDFT that can be derived rigorously for SPC-or TIPnP-like representations of water, involving a single LennardJones interaction site and distributed partial charges. In that case we will seek a simpler functional form expressed in terms of the particle density n(r) and site-distributed polarisation density P(r), and requiring as input simpler physical quantities than the full position and orientation-dependent direct correlation function.…”

“…This functional may be considered as a multipolar generalization of the generic dipolar fluid free-energy functional F[n(r), P(r)] introduced in Refs. [35,37].A functional of n(r) and P(r). We start from SPC-or TIPnP-like representation 1 of water, constituted by a single Lennard-Jones center, located on the oxygen, and m charges distributed on various sites.…”

“…Recently, a molecular density functional theory (MDFT) approach to solvation has been introduced. [35][36][37][38][39][40] It relies on the definition of a free-energy functional depending on the full six-dimensional position and orientation solvent density. In the so-called homogeneous reference fluid (HRF) approximation, the (unknown) excess free energy can be inferred from the angular-dependent direct correlation function of the bulk solvent, that can be predetermined from molecular simulations of the pure solvent.…”

A molecularly based theory for electron transfer reorganization energy

“…17,18,[21][22][23][24][25][26][27][28][29][30] However, multiple long trajectories are required to perform umbrella sampling, making it impractical to perform calculations for general solvents. Integral-equation theories [31][32][33][34][35][36][37][38] are a more convenient alternative to the laborious nonequilibrium sampling schemes in MD simulations, but nanosecond MD simulations are still required to compute the solvent correlation functions in these approaches. Also, it is cumbersome to include the induced dipoles of the solvent in simulations and integral-equation theories; as such, these methods often treat solvent molecules as nonpolarizable, with the effects of solvent electronic response approximated or ignored.…”