Method of Functional Derivatives in the Theory of Point Defects in Crystals: I. General Theory. Representations of the Self‐Energy

A novel method is suggested for the calculation of point defect electronic structure in arbitrary crystals using a non‐orthogonal localized atomic orbital basis set. The method is based on the concept of a cluster Green's function and uses a special truncating procedure for the Green's function chain, such that only the defective region of the crystal is considered precisely, while the rest of the crystal as well as its interaction with the defective region are considered in Hartree‐Fock approximation. It is shown, that the correct incorporation of an electronic correlation in the defective region is connected with a relevant choice of a cluster self‐energy operator. Decompositions of this operator into a series either over screened or unscreened interaction are investigated. An approximation analogous to the simplest Hedin's GW‐approximation is considered. Qualitatively this approach is equivalent to that which uses the generalized Anderson Hamiltonian.