Shortcomings of present density-functional methods are considered. Kohn–Sham and time-dependent density-functional methods using orbital- and state-dependent functionals for exchange-correlation energies, potentials, and kernels are discussed as possible remedy for some of these shortcomings. A view on the Kohn–Sham formalism is presented which differs somewhat from the one conventionally taken. The crucial step of constructing local multiplicative exchange-correlation potentials in Kohn–Sham methods based on orbital- and state-dependent functionals is discussed. The description of open-shell systems via a symmetrized Kohn–Sham formalism employing state-dependent exchange-correlation functionals is elucidated. The generalized adiabatic connection Kohn–Sham approach for the self-consistent treatment of excited states within a density-functional framework is considered. In the latter approach orbital- and state-dependent exchange-correlation functionals occur in a density-functional framework which is no longer based on the Hohenberg–Kohn theorem but on a more general relation between electron densities and local multiplicative potentials.
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