Ensemble-Hartree-Fock scheme for excited states. The optimized effective potential method

We review the ensemble-Hartree-Fock (eHF) scheme for excited states. The single-particle eHF equations contain different potentials for the various orbitals, leading to off-diagonal Lagrange multipliers that cannot be transformed away as in the ground state case. Using the optimized effective potential method we are able to construct a common local potential and the resulting theory is seen to describe accurately atomic excitation energies. A comparison of the eHF theory with the ensemble-Kohn-Sham (eKS) scheme suggests a correction for the ensemble exchange and correlation energy functional, that helps improve greatly the numerical results of the eKS scheme.