Dielectric properties of solids in the regular and split-charge equilibration formalisms

We investigate the generic dielectric properties of solids in the split-charge equilibration (SQE) formalism, which contains the regular charge equilibration (QE) method as a limiting case, but augments it with a bond hardness term. It is shown that QE always mimics ideal conductors, while any positive bond hardness used in SQE turns the solid into a dielectric. Crystals with simple cubic and rocksalt structure are considered explicitly. For these symmetries, we solve the continuum limit of the SQE formalism analytically. As a result, we provide simple analytical expressions for how dielectric constant and penetration depth of the electrostatic field depend on atomic hardness, bond hardness, and lattice constant. This mapping may prove useful not only for force field parametrization but also for solving dielectric responses on coarse-grained scales. Successful comparison of numerical data to analytical solutions is made, including those containing discretization corrections.