Exchange-correlation potentials in ground- and excited-state Kohn-Sham theory

Using constrained-search approach, we obtain orbitals and the corresponding local potentials of noninteracting systems that lead to a given exact ground-state or excited-state density with a configuration of our choice. Thus on the basis of constrained-search formulation we demonstrate that all densities, irrespective of whether they belong to the ground state or an excited state, can be treated on equal footing. This has direct relevance to the time-independent excited-state density-functional theory, which makes excited-state calculations as easy as they are for the ground states. We make a comparison of the exact potentials generated by us with the approximate ones obtained using the local-density approximation and show the latter to be as good an approximation for the excited states as it is for the ground state.