Atomic Charges and the Electrostatic Potential Are Ill-Defined in Degenerate Ground States

A system in a spatially degenerate ground state responds in a qualitatively different way to positive and negative point charges. This means that the molecular electrostatic potential is ill-defined for degenerate ground states due to the ill-defined nature of the electron density. It also means that it is impossible, in practice, to define fixed atomic charges for molecular mechanics simulations of molecules with (quasi-)degenerate ground states. Atomic-polarizability-based models and electronegativity-equalization-type models for molecular polarization also fail to capture this effect. We demonstrate the ambiguity in the electrostatic potential using several molecules of different degree of degeneracy, quasi-degeneracy, and symmetry.