The electronic structure of 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 Cu+ ion, to construct an initial potential for the LiCl: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 Cu+. An iterative procedure is devised to carry the impurity-state solution to self-consistency. The wave function for the LiCl:Cu+ 4s state is relatively localized, consisting of a distorted 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 3d4s and 3d4p transition energies and the 3d4p 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. © 1981 The American Physical Society.