Ab initio calculation of the lattice distortions induced by substitutional ${\mathrm{Ag}}^{-}$ and ${\mathrm{Cu}}^{-}$ impurities in alkali halide crystals

An ab initio study of the doping of alkali halide crystals $(AX:$ $A=\mathrm{Li},$ Na, K, Rb; X = F, Cl, Br, I) by ${\mathrm{ns}}^2$ anions $({\mathrm{Ag}}^{-}$ and ${\mathrm{Cu}}^{-})$ is presented. Large active clusters with 179 ions embedded in the surrounding crystalline lattice are considered in order to describe properly the lattice relaxation induced by the introduction of substitutional impurities. In all the cases considered, the lattice distortions imply the concerted movement of several shells of neighbors. The shell displacements are smaller for the smaller anion ${\mathrm{Cu}}^{-},$ as expected. The study of the family of rock-salt alkali halides (excepting CsF) allows us to extract trends that might be useful at a predictive level in the study of other impurity systems. Those trends are presented and discussed in terms of simple geometric arguments.