Self-consistent-field electronic structure ofCu+impurity states in a LiCl crystal

Abstract

The electronic structure of ${\mathrm{Cu}}^{+}$ impurity states in an LiCl crystal has been calculated by the method of linear combinations of atomic orbitals (LCAO). A self-consistent-field (SCF) band structure for the pure LiCl crystal is first determined with the local-density-functional approximation for exchange, and is used, along with an SCF solution for a free ${\mathrm{Cu}}^{+}$ ion, to construct an initial potential for the LiCl:${\mathrm{Cu}}^{+}$ system. The impurity-state wave functions are expanded as linear combinations of localized orbitals centered at atomic sites up to the twelfth nearest neighbors to ${\mathrm{Cu}}^{+}$. An iterative procedure is devised to carry the impurity-state solution to self-consistency. The wave function for the LiCl:${\mathrm{Cu}}^{+}$ $4s$ state is relatively localized, consisting of a distorted ${\mathrm{Cu}}^{+}$ $4s$ state with admixture from the occupied orbitals of the six surrounding Cl atoms. The $4p$ state is much more diffuse penetrating into the third-nearest neighbors, and the "unoccupied states" of the host atoms are important in the LCAO expansion. The calculated $3d\to 4s$ and $3d\to 4p$ transition energies and the $3d\to 4p$ oscillator strength are in good agreement with experiment. The LCAO calculation also shows distortion of the valence band of the host crystal, in particular the formation of a group of states with charge density localized at the six nearest-neighbor Cl atoms splitting off from the bottom of the bulk valence band.