Exact Conditions for Ensemble Density Functional Theory

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.