A Molecular Density Functional Theory of aqueous electrolytic solution

TL;DR

The paper extends Molecular Density Functional Theory to mixtures to model aqueous electrolytes efficiently. It derives a grand-potential functional split into $F_{ ext{id}}$, $F_{ ext{ext}}$, and $F_{ ext{exc}}$, and applies the HNC closure with angular projections via Generalized Spherical Harmonics, enabling a 3D implementation that treats water as an orientational density. Two electrolyte models are developed: a three-component model with explicit water and a primitive two-component model with dielectric screening; both are validated against 1D IET for Na^+ and Cl^− solvation, with the explicit-water model capturing multi-shell structuring and orientational ordering around complex solutes like NMA. The results demonstrate MDFT’s ability to accurately describe solvation in electrolytes for arbitrarily shaped solutes at reduced computational cost, offering a versatile tool for electrochemical and biological contexts, while acknowledging potential improvements such as bridge-function enhancements and broader experimental validation.

Abstract

We propose a generalisation of molecular density functional theory to describe inhomogeneous solvent mixture, with the objective of modelling electrolytic solutions. Two electrolytic models are presented, both within the HNC approximation. The first one is a two-components mixture representing a primitive-like model of sodium chloride, where the solvent is described as a dielectric continuum. This popular model has the advantage of simplicity, as the ions densities solely depend on spatial coordinates. Additionally, we develop a realistic three-components electrolyte model, in which water solvent is described by a third density field that depends on both spatial and orientational coordinates. The proposed methodology and its tridimensional implementation (3 spatial coordinates and 3 Euler angles) are validated by comparing the solvation properties of a sodium cation with the predictions of integral equation theory solved in 1D (1 intermolecular distance and 5 Euler angles), showing near-perfect agreement. This methodology enables the study of solvation properties of solutes of arbitrary shapes in electrolytic solutions, as demonstrated with the prototypical N-methylacetamide molecule immersed in both electrolytic solution models.

Figures (6)

• Figure 1: Ion-ion direct correlation functions, $c_\text{AB}(k)$, in the SPC/E NaCl (1M) solution.
• Figure 2: Ion-ion direct correlation functions, $c_\text{AB}(k)$, in the NaCl (1M) primitive-like model.
• Figure 3: Radial distributions functions between the test ion and ions of the primitive solution determined by using IET (lines) and by MDFT (symbols).
• Figure 4: Slices of density in the plane of the NMA molecule. The top panels display the sodium density (left) and the chloride density (right). The bottom panels show the charge density (left), defined as the difference between the sodium density and the chloride density. The right panel explains the colour code for the NMA molecule.
• Figure 5: Radial distributions of aqueous NaCl solution around a Na$^{+}$ cation computed using IET (lines) and MDFT (symbols)