Anisotropic Interface Continuum Solvation Model and the Finite-Element Anisotropic Poisson Solver

We propose an anisotropic interfacial continuum solvation (AICS) model to simulate the distinct in-plane and out-of-plane dielectric constants of liquids near solid-liquid interfaces and their spatial variations along the surface normal direction. In low-electron-density regions, each dielectric function in the diagonal components of a dielectric tensor varies monotonically with distance from the solid surface along the surface normal direction; in high-electron-density regions near the surface, each dielectric function adopts the electron-density-based formulation proposed by Andreussi et al. (J. Chem. Phys. 2012, 136, 064102). The resulting dielectric tensor is continuously differentiable with respect to both electron density and spatial coordinates. We derived analytical expressions for electrostatic contributions to the Kohn-Sham potential and atomic forces and implemented the AICS model, including these analytical derivatives, into the CP2K software package. To solve the anisotropic Poisson equations, we developed a parallel finite-element anisotropic Poisson solver (FEAPS) based on the FEniCSx platform and its interface with CP2K. Analytical forces were validated against finite-difference calculations, while electrostatic potentials computed under vacuum and isotropic solvent conditions using AICS and FEAPS were benchmarked against standard vacuum DFT and SCCS results, respectively. In the anisotropic interfacial solvent environment characterized by the enhanced in-plane and reduced out-of-plane dielectric functions near the Ag(111) surface, we calculated the resulting work functions and electrostatic potentials and optimized the adsorption geometry for OH*. Compared to the isotropic case, we observed more pronounced work function shifts and spatially modulated electrostatic profiles across different charge states. Our results also showed that OH* tilted more toward the plane parallel to the surface under the anisotropic dielectric conditions.