Introduction: The Role of the Electrostatic Potential in Chemistry

Abstract

The electrostatic potential at a point $\vec r$ in the vicinity of an atomic or molecular system having an electronic density function ρ($\vec r$ ) is given, in atomic units,* by

${V^{ES}}\left( {\overrightarrow r } \right) = \sum\limits_A {\frac{{{Z_A}}}{{\left| {{{\overrightarrow R }_A} - \overrightarrow r } \right|}}} - \int {\frac{{\rho \left( {\overrightarrow {r'} } \right)\overrightarrow {dr'} }}{{\left| {\overrightarrow {r'} - \overrightarrow r } \right|}}}$

(1)

where Z_A is the charge on nucleus A, located at ${\vec R_A}$ _A. The two terms on the right side of equation (1) correspond, respectively, to the nuclear and electronic contributions to the potential. As can be seen, they have opposite signs and accordingly opposite effects; V^ES ($\vec r$) represents the net result at any point $\vec r$. The electrostatic potential is a real physical property, which is rigorously defined by equation (1). It is exactly equal in magnitude to the electrostatic (coulombic) interaction energy between the static (i.e., unperturbed) charge distribution of the system and a positive unit point charge located at $\vec r$.