A b i n i t i o Hartree–Fock perturbed-cluster treatment of local defects in crystals

Abstract

An ab initio Hartree–Fock self-consistent-field embedding scheme is presented for the treatment of local defects in crystals. It is a ‘‘perturbed-cluster’’ (PC) scheme in the sense that the density matrix in the defect region is obtained by taking as a reference the solution for a molecular cluster that describes that region. Corrective terms are then added in order to realize the coupling between the cluster and the surrounding medium, which are expressed in terms of the density of states of the perfect host crystal. The approximations adopted are much less severe than in previous formulations; essentially, it is assumed that the density of states projected onto the indented crystal surrounding the defect region is only marginally affected by the presence of the defect. New PC equations are derived and their features are discussed with reference to previous formulations. The algorithms needed to implement the new theory and to calculate the defect formation energy are described in some detail. The main difficulty encountered with the present approach appears to be an adequate treatment of polarization of the medium and the charge transfer between the local and the nonlocal region. Perfect and defective hexagonal boron nitride is used as a simple test system to check the adequacy of the underlying assumptions and to exemplify the computational problems that are encountered.