Exact Conditions for Ensemble Density Functional Theory

TL;DR

This paper establishes fundamental exact conditions for ensemble density functional theory (EDFT), demonstrating their importance through the Hubbard dimer model and highlighting violations in existing approximations.

Contribution

It proves several exact conditions in EDFT using coordinate scaling and explores the strong-correlation limit, advancing theoretical understanding.

Findings

Exact conditions for EDFT are derived and proven.

Violations of these conditions are shown in common approximations.

Weight-dependent derivative discontinuities are revealed in the strong-correlation limit.

Abstract

Ensemble density functional theory (EDFT) is a promising alternative to time-dependent density functional theory for computing electronic excitation energies. Using coordinate scaling, we prove several fundamental exact conditions in EDFT and illustrate them on the exact singlet bi-ensemble of the Hubbard dimer. Several approximations violate these conditions, and some ground-state conditions from quantum chemistry do not generalize to EDFT. The strong-correlation limit is derived for the dimer, revealing weight-dependent derivative discontinuities in EDFT.