Density-Functional Theory for Excited States in a Quasi-Local-Density Approximation

The local-density approximation has been very useful for ground-state calculations. Here an analogous approximation is developed for the ensemble of M lowest states, recently discussed by Theophilou. Algorithms are provided for the exchange-correlation energy, ExcM, and potential, νxcM, of ensembles of slowly varying density, $n(r)$. These quantities are highly nonlocal functionals of $n(r)$ but calculable in terms of properties of uniform, thermal ensembles. Excited-state energies and densities can be obtained.