A finite-temperature exact-exchange (EXX) formalism derived within the framework of finite-temperature density-functional theory for grand canonical ensembles is introduced. Based on this formalism a finite temperature EXX method for solids using plane-wave basis sets is presented. The method is generally applicable, i.e., applicable to insulators, semiconductors, or metals and enables the investigation of temperature effects. For simple test systems, .e.g., aluminum, the EXX method is compared to conventional density- functional method using the local density approximation. The presented EXX method belongs to a new generation of density-functional methods employing orbital-dependent functionals. This new generation of density-functional methods not only enables an exact treatment of exchange interactions but offers new possibilites for approximating electron correlation. To that end a new approach to treat the correlation energies of electronic systems within the exact-exchange random phase approximation based on the adiabatic- connection fluctuation-dissipation theorem is presented and promising results for molecule test cases are shown.
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