Efficient treatment of long-range electrostatics in charge equilibration approaches

A charge equilibration method based on real-space Gaussians as charge densities is presented. The implementation is part of the Electrode package available in the Large-scale Atomic/Molecular Massively Parallel Simulator and benefits from its efficient particle-mesh Ewald approach. A simple strategy required to switch from the previously used Slater-type orbital (STO) shielding to Gaussians is provided by fitting the Coulomb energy of two Gaussian charge distributions to the repulsion between two STOs. Their widths were optimized for O, Si, and Ti species, obtaining results consistent with previous studies using STOs in the case of SiO2 polymorphs. In the limit of sufficiently narrow Gaussians, it is shown that the implementation converges to electronegativity equalization method results for the case of Ti/TiOx interfaces. The method presented is implemented in a way that is potentially beneficial for the application of modern machine-learning force fields that include long-range electrostatic interactions.