  Ensemble density functional theory is a promising method for the efficient
and accurate calculation of excitations of quantum systems, at least if useful
functionals can be developed to broaden its domain of practical applicability.
Here, we introduce a guaranteed single-valued 'Hartree-exchange' ensemble
density functional, $E_{Hx}[n]$, in terms of the right derivative of the
universal ensemble density functional with respect to the coupling constant at
vanishing interaction. We show that $E_{Hx}[n]$ is straightforwardly
expressible using block eigenvalues of a simple matrix [equation (14)].
Specialized expressions for $E_{Hx}[n]$ from the literature, including those
involving superpositions of Slater determinants, can now be regarded as
originating from the unifying picture presented here. We thus establish a clear
and practical description for Hartree-exchange in ensemble systems.
