Point Defects in Ionic Crystals. II. The F Center in KCl, KBr, KI, and NaCl

Methods described in a previous paper are applied to the calculation of the electronic structure of the $F$ center in KCl, KBr, KI, and NaCl. Structure of the ions is explicitly taken into account in a region close to the defect site, and an effective-mass method is used in the more distant regions. Dielectric polarization effects are included on the basis of the formulation due to Toyozawa, Haken, and Schottky, but results in best agreement with experiment are obtained by a procedure which deviates somewhat from that formulation, as might be expected also on purely theoretical grounds. It does not appear to be possible to obtain agreement with experiment even for absorption energies if polarization effects are neglected. The calculated energy differences of the $1s$, $2p$, $3p$, and $2s$ states in absorption agree very well with presently available experimental data. Agreement with experiment is fairly good for the $1s$, $2s$, and $2p$ energies in emission. The calculated optical transition matrix elements are very sensitive to the details of the model; those obtained from our best model and wave functions are compatible with experimental results. The results for the spin density at the nearest-neighbor ions are reasonably close to the experimental values.