Density Functional Theory of Coulombic Excited States Based on Nodal Variational Principle

Ágnes Nagy

doi:10.3390/computation9080093

Abstract

The density functional theory developed earlier for Coulombic excited states is reconsidered using the nodal variational principle. It is much easier to solve the Kohn–Sham equations, because only the correct number of nodes of the orbitals should be insured instead of the orthogonality.

Highlights

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
Zahariev, Gordon, and Levy [33] have presented a nodal variational principle for excited states. They have proved that the minimum of the energy expectation value of trial wave functions that are analytically well behaved and have nodes of the exact wave function is the exact eigenvalue
||n1Coul −n01 ||≤δ where the search is over the wave functions Φ having the excited state density n and orthogonal to the first l − 1 eigen functions of the non-interacting system

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Zahariev, Gordon, and Levy [33] have presented a nodal variational principle for excited states. They have proved that the minimum of the energy expectation value of trial wave functions that are analytically well behaved and have nodes of the exact wave function is the exact eigenvalue. The Coulombic excited state theory is reconsidered utilizing the nodal variational principle. The functionals are the same as in the original theory, but it is much easier to solve the Kohn–Sham equations, because only the correct number of nodes of the orbitals should be insured instead of the orthogonality It is especially important in case of highly excited orbitals.

Coulombic Excited State Theory Using Nodal Variation Principle

Discussion