Improved theoretical methods for studies of defects in insulators: Application to theFcenter in LiF

An F center in the lithium fluoride (LiF) crystal is investigated with use of the muffin-tin Green’s-function formalism and a linear combination of atomic orbitals (LCAO) cluster method. Both of these methods properly embed the defect into the host crystal. With the latter method, we are able to include the defect-induced charge relaxation on many shells of nearest-neighbor atoms. We have employed several variants of the density-functional approximation which allow a more accurate description of the ground-state single-electron properties. These methods include an empirical adjustment of the perfect-crystal band gap [the ‘‘LDA scissor operator’’ (where LDA denotes local-density approximation)] as well as the inclusion of electronic self-interaction corrections. Since the validity of the density-functional formalism is questionable for obtaining excited-state properties, we have introduced a single particle-hole excited-state theory, which is based on many-electron arguments, in order to gain insight about the behavior of the excited-state effective potentials. We demonstrate that, in contrast to LDA, for localized excitations the long-range behavior of the effective excited-state potential should exhibit a -1/r tail in neutral systems. While the qualitative behavior of the LDA potential differs from the effective excited-state potential, the self-interaction-corrected LDA potential of the highest occupied defect level exhibits the correct qualitative behavior. By allowing the excited state electron to move in the latter potential, an accurate excitation energy for the $a_{1g}$-$t_{1u}$ absorption in LiF is obtained. Further, in contrast to the density-functional results, the self-interaction-corrected version of the theory correctly places the $t_{1u}$ state below the conduction-band edge.