Solid-Liquid Interfacial Free Energies from Atomistic Mean-Field Quantum Mechanical Calculations

Solid-liquid interfacial free energies (IFEs) play a crucial role in nucleation, wetting, and solvent-dependent crystal morphology. However, the quantitative facet-resolved prediction at first-principles accuracy is still a significant challenge. In this study, we introduce a fully atomistic mean-field quantum mechanical framework that integrates a first-principles solid surface to a classical liquid. This integration uses particle-mesh-based electrostatic interactions and charge-density exchange in combination with the mean-field approximation, facilitating extensive and stable sampling of liquid configurations for arbitrary facets. The method is combined with a robust two-stage thermodynamic integration protocol that utilizes attractive and repulsive auxiliary potentials to mitigate end point instabilities. Additionally, we present a practical long-range correction scheme for solid-liquid dispersion interactions, which substantially reduces sensitivity to cutoff distances and allows for the quantitative inclusion of dispersion tails in IFEs. The methodology is validated for the NaCl-water interface by agreement with the Einstein crystal method, and for PbS-water by reproducing facet trends in interfacial stabilization consistent with the dielectric model benchmarks. The method is then applied to nine LiFePO₄ facets in water and ethylene glycol to predict solvent-dependent Wulff morphologies, showing enhanced stabilization of the (010) facet. A molecular-level interpretation of this stabilization is provided, focusing on facet-specific hydroxyl OH coordination that is modulated by the steric accessibility of solvent molecules.