Exploring Foundations of Time-Independent Density Functional Theory for Excited-States

TL;DR

This paper extends the foundational principles of density functional theory to excited states, establishing a rigorous mapping between excited-state densities and external potentials, and demonstrating the theory on atomic systems.

Contribution

It introduces a time-independent density functional formalism for excited states, emphasizing the necessity of ground-state density knowledge for accurate potential mapping.

Findings

Excited-state density uniquely determines the external potential when ground-state density is known.

The excited-state Kohn-Sham system is defined by comparing non-interacting and true kinetic energies.

The theory is validated through extensive atomic system studies.

Abstract

Based on the work of Gorling and that of Levy and Nagy, density-functional formalism for many Fermionic excited-states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that the knowledge of the ground-state density is a must to fix the mapping from an excited-state density to the external potential. This is the excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the ground-state density the density of the excited-state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn-Sham system is defined by comparing it's non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.