Density-functional calculation of the parameters in the Anderson model: Application to Mn in CdTe

We discuss methods for ab initio calculations of the parameters in the Anderson model. First, we present a very simple method for calculating the appropriate combination of hopping matrix elements needed in the impurity Anderson model. For a substitutional impurity, we show that to a good approximation it is sufficient to know the potential of the impurity atom and the local density of states of the unperturbed host. Calculations are performed for Mn substituting Cd in CdTe. As expected, the Mn 3d orbitals have a strong coupling to the Te 5p--derived valence band, but there is also a strong coupling to the conduction band. The dependence of the hopping matrix elements on the Mn configuration is studied. While there is a strong dependence on the Mn net charge, we find that the creation of, e.g., a core hole has a fairly small effect on the matrix elements, provided that the 3d occupancy is allowed to relax. Second, the Coulomb integrals between two Mn 3d orbitals and between a 3d orbital and a core orbital are calculated. The renormalization of these quantities due to the radial relaxation of the Mn 3d, 4s, and 4p orbitals, and due to charge-transfer effects, are analyzed in detail. Because of the nonmetallic character of CdTe, a change in the number of Mn 3d electrons is only partly screened by a charge transfer to the Mn 4s and 4p orbitals. Because of the moderate size of the band gap, this screening is, nevertheless, important. The radial relaxation of the Mn 3d, 4s, and 4p wave functions is also important. The relaxation of the neighboring atoms plays a rather small role. Results for the photoemission spectra are calculated including multiplet effects. The results are found to be in rather good agreement with experiment.