A simple approach for the direct calculation of electron density bypassing the Schrodinger equation

Abstract

In this paper, we review two of our recent works dealing with a quadratic equation for the direct calculation of the electronic density and properties of atoms and ions. The equation incorporates a first-gradient kinetic energy correction, Dirac exchange and Wigner-type correlation contributions. Its results for various atomic and ionic systems are surprisingly good, considering the simplicity of the equation. The equation also yields a universal density criterion which unifies and correlates various empirical radii (covalent, ionic, Van der Waals and Wigner-Seitz radii) as well as other properties of atoms and ions.