Development and implementation of the exact exchange method for semiconductors using a localized basis set

One of the major deficiencies of density functional theory is presented in the approximation of the exchange energy term. An important advance in solving this problem has been the development of orbital-dependent exchange functionals. The exact exchange method is one of the best defined releases of such functionals. Up to now it has been applied in solid systems only using a plane wave representation basis set. In this paper we present a development and implementation of the exact exchange formalism for solid semiconductors using a basis set of localized numerical functions. The implementation of the exact exchange scheme has been carried out in the SIESTA code, as a new path to get the exchange part in the Kohn–Sham energy and potential. This program is an ab initio periodic fully self-consistent density functional code which uses norm-conserving non-local pseudopotentials. Linear combination of confined numerical pseudoatomic orbitals have been used to represent the Kohn–Sham orbitals. The calculation results of the electronic properties of several semiconductor systems using different qualities of the basis set are compared with experimental results and presented in this paper.