EQeq+C: An Empirical Bond-Order-Corrected Extended Charge Equilibration Method

The extended charge equilibration (EQeq) scheme computes atomic partial charges using the experimentally measured ionization potentials and electron affinities of atoms. However, EQeq erroneously predicts constant (environment independent) charges for high-oxidation-state transition metals in amine-templated metal oxide (ATMO) compounds, contrary to the variation observed in iterative Hirshfeld (Hirshfeld-I) charges, bond-valence sum calculations, and formal oxidation state calculations. To fix this problem, we present a simple, noniterative empirical pairwise correction based on the Pauling bond-order/distance relationship, which we denote EQeq+C. We parametrized the corrections to reproduce the Hirshfeld-I charges of ATMO compounds and REPEAT charges of metal organic framework (MOF) compounds. The EQeq+C correction fixes the metal charge problem and significantly improves the partial atomic charges compared to EQeq. We demonstrate the transferability of the parametrization by applying it to a set of unrelated dipeptides. After an initial parametrization, the EQeq+C correction requires minimal computational overhead, making it suitable for treating large unit cell solids and performing large-scale computational materials screening.