The Levy-Perdew-Sahni equation for the density: accurate effective potential and self-consistent solution for two-electron atomic systems

TL;DR

This paper explicitly calculates the Levy-Perdew-Sahni effective potential for two-electron systems using accurate wavefunctions, solving the LPS equation self-consistently to obtain precise densities and chemical potentials.

Contribution

It provides an explicit calculation of the LPS effective potential and demonstrates a self-consistent solution for two-electron systems, improving density and chemical potential accuracy.

Findings

Accurate densities for two-electron systems

Precise chemical potentials obtained

Validation of the LPS equation approach

Abstract

Levy-Perdew-Sahni (LPS) provided a proof of the connection between the density and ionization potential of a many-electron system using the equation for the density directly. This equation employs an effective potential which is derived by LPS from the many-electron wavefunction of the system. In this paper, we calculate this potential explicitly by employing an accurate wavefunction for two-electron systems. With this wavefunction connection the LPS equation is then solved self- consistently employing this potential and shown to lead to accurate densities and chemical potentials for these systems.