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 LiFePO 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.