Extension of exact-exchange density functional theory of solids to finite temperatures

Abstract

A general finite-temperature exact-exchange (EXX) formalism derived within the framework of finite-temperature density functional theory for grand canonical ensembles is presented. 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. More important, however, is that the finite-temperature EXX method enables an EXX treatment of metals by introducing a physically motivated Fermi broadening technique. We tested the method by applying it to sodium, magnesium, and aluminum and compare EXX and LDA (local density approximation) band structures as well as the density of states for the three metals. Differences between LDA and EXX band structures are negligible up to the Fermi level. Above the Fermi level, however, differences between LDA and EXX band structures of magnitudes of 1--2 eV start to build up for energetically higher bands. The magnitude of these differences is of the same order as that of the increases in EXX band gaps compared to LDA band gaps as they are reported for semiconductors and insulators.