Including charge penetration effects into the ESP derived partial charge operator

Electrostatic potential (ESP) derived partial charge provides a useful tool for describing intermolecular electrostatic (ES) interactions. One can also devise a corresponding charge “operator” that generates partial charge upon taking the expectation value over molecular wavefunctions. While the ESP charge operator has been utilized in various QM/MM(-type) calculations, it has the drawback that short-range ES interactions are overestimated due to the neglect of charge penetration effects. Here, we develop a screened version of the ESP charge operator that includes penetration effects at short range and thereby improve its accuracy. Numerical tests are performed for typical ions in aqueous solution.