Depurated Inversion Method for Orbital-Specific Exchange Potentials

TL;DR

This paper introduces a Depurated Inversion Method to accurately derive orbital-specific exchange potentials from Hartree-Fock wavefunctions, applicable to all atom types and capable of reproducing energies and wavefunctions precisely.

Contribution

The paper presents a novel Depurated Inversion Method for obtaining orbital-specific exchange potentials by inverting Hartree-Fock wavefunctions, ensuring boundary conditions and eliminating poles.

Findings

Accurately reproduces input energies and wavefunctions.

Applicable to all atom types, including noble gases and nitrogen.

Eliminates poles and satisfies boundary conditions in potentials.

Abstract

This work presents exchange potentials for specific orbitals calculated by inverting Hartree-Fock wavefunctions. This was achieved by using a Depurated Inversion Method. The basic idea of the method relies upon the substitution of Hartree-Fock orbitals and eigenvalues into the Kohn-Sham equation. Through inversion, the corresponding effective potentials were obtained. Further treatment of the inverted potential should be carried on. The depuration is a careful optimization which eliminates the poles and also ensures the fullfilment of the appropriate boundary conditions. The procedure developed here is not restricted to the ground state or to a nodeless orbital and is applicable to all kinds of atoms. As an example, exchange potentials for noble gases and term-dependent orbitals of the lower configuration of Nitrogen are calculated. The method allows to reproduce the input energies and wavefunctions with a remarkable degree of accuracy.