Distortion and Polarization near Color Centers

A general method is presented for calculating the static polarization and distortion near a defect. It assumes that the lattice responds to the average, but consistently chosen, charge distribution of the electrons associated with the defect, and uses the shell model to describe the lattice dynamic and dielectric properties of the host. The lattice is discrete, without continuum approximations; there are no artificial restrictions on the range of the distortion, and asymmetric distortions, as from the Jahn-Teller (JT) effect, are included. The variation of the electronic wave function as the lattice distorts may be included consistently even in cases where there is mixing of nearby levels. The method is illustrated by a calculation for the $2p$ excited state of the $F$ center in KBr. It proves necessary to include the ion-size terms in the interaction of the defect electron with the lattice. The results are sensitive to the detailed model chosen for the lattice dynamics. However, certain features, such as the outward motion of the nearest neighbors, the JT distortion, usually tetragonal, and the substantial energy lowering, typically 0.5 eV, are common to these models.