Electrostatic potential–electronic density relationships in atoms. II

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Abstract
An exact equation has been derived that relates the derivative of the electrostatic potential at any radial distance from the nucleus of a neutral atom to the amount of electronic charge that is located beyond that radial distance. This equation assumes a particularly simple form at distances corresponding to minima in the radial density function, and can be used to show that at such a distance, rm, the electrostatic potential due to the electronic charge beyond rm is exactly half (but with opposite sign) of that produced by the nucleus and the electronic charge within the radial distance rm. When applied at the outermost radial density minimum, which has been proposed as the boundary between the core and valence regions of a ground‐state neutral atom, the new equation can be used to significantly improve a previously derived atomic energy formula.