Learning Classical Density Functionals for Ionic Fluids

Accurate and efficient theoretical techniques for describing ionic fluids are highly desirable for many applications across the physical, biological, and materials sciences. With a rigorous statistical mechanical foundation, classical density functional theory (cDFT) is an appealing approach, but the competition between strong Coulombic interactions and steric repulsion limits the accuracy of current approximate functionals. Here, we extend a recently presented machine learning (ML) approach Sammüller et al., Proc. Natl. Acad. Sci. U.S.A., 120, e2312484120 (2023)PNASA60027-842410.1073/pnas.2312484120 designed for systems with short-ranged interactions to ionic fluids. By adopting ideas from local molecular field theory, the framework we present amounts to using neural networks to learn the local relationship between the one-body direct correlation functions and inhomogeneous density profiles for a "mimic" short-ranged system, with effects of long-ranged interactions accounted for in a mean-field, yet well-controlled, manner. By comparing to results from molecular simulations, we show that our approach accurately describes the structure and thermodynamics of prototypical models for electrolyte solutions and ionic liquids, including size-asymmetric and multivalent systems. The framework we present acts as an important step toward extending ML approaches for cDFT to systems with accurate interatomic potentials.