Maximal and minimal characteristics of molecular electrostatic potentials

Existence of strict local maxima within the molecular electrostatic potential (MESP) maps has been rigorously ruled out. The proof to this effect is based solely on the classical electrostatic Poisson equation. It has been further shown that at least one-directional negative-valued minimum in MESP for a negative molecular ion must occur along any arbitrary direction. Under some special circumstances, an equipotential MESP surface could exist for such a species. These results properly reduce to their atomic counterparts proven by Politzer and co-workers [Weinstein et al., Theor. Chim. Acta (Berl.) 38, 59 (1975); Sen and Politzer, J. Chem. Phys. 90, 4370 (1989)].