Some Relationships between Different Uses of the Electrostatic Potential

Abstract

The electrostatic potential at a point $\vec r$ in the vicinity of an atom or molecule is (in a.u.):

$$v^{ES} \left( {\vec r} \right) = \sum\limits_A {\frac{{Z_A }} {{\left| {\vec r - \vec R_A } \right|}}} - \int {\frac{{\rho \left( {\vec r} \right)}} {{\left| {\vec r - \vec r'} \right|}}} d\vec r'$$

(1)

where Z_A is the charge on nucleus A, located at ${\vec R_A}$ _A, and ρ($\overrightarrow {r'}$ ) is the electronic charge density. As is clear from equation (1), the electrostatic potential represents the net electric potential field at point $\vec r$ caused by the unperturbed, i.e., static, charge distribution of an atom or molecule. As such the electrostatic potential determines the classical coulombic component of the interaction energy of a static target with anything. In this chapter a few relationships and differences between various kinds of uses of the electrostatic potential are discussed.