Kohn-Sham methods with orbital-dependent exchange-correlation functionals, in particular exact-exchange methods, are discussed. The numerical stability of optimized-effective-potential methods to construct the exchange-correlation potential in the case of orbital-dependent energy functionals is considered. A numerically stable exact-exchange Kohn-Sham method is briefly presented. A new ansatz for time-dependent density-functional methods in the response regime is considered and an exact-exchange time-dependent density-functional method based on it is discussed and it is demonstrated that this methods is able to treat qualitatively correctly charge-transfer excitations.
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