Quantal Density Functional Theory of Degenerate States

TL;DR

This paper extends quantal density functional theory (Q-DFT) to accurately describe degenerate states in Kohn-Sham DFT, providing a rigorous physical interpretation and practical examples for ground and excited states.

Contribution

It introduces a Q-DFT framework for degenerate states, unifying ground and excited, pure and ensemble densities within a consistent physical model.

Findings

Provides a mapping for degenerate states within Q-DFT

Offers a physical interpretation of density and energy functionals

Includes examples demonstrating the Q-DFT mappings

Abstract

The treatment of degenerate states within Kohn-Sham density functional theory (KS-DFT) is a problem of longstanding interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory (Q-DFT). We describe the Q-DFT of \textit{both} ground and excited degenerate states, and for the cases of \textit{both} pure state and ensemble v-representable densities. This then further provides a rigorous physical interpretation of the density and bidensity energy functionals, and of their functional derivatives, of the corresponding KS-DFT. We conclude with examples of the mappings within Q-DFT.