The electronic structure of a substitutional V2+ impurity ion with a charge-compensating Li+ vacancy at a nearest cation site in a lithium fluoride crystal has been calculated by the method of linear combinations of atomic orbitals. The charge density for the pure LiF crystal and that for the free V2+ ion are used to generate an initial potential for the LiF:V2+ system. The impurity-state wave functions are expanded as linear combinations of localized orbitals at V2+ and at the atomic sites around it through the tenth-nearest neighbors, and the electronic-energy calculation is carried out to self-consistency by an iterative scheme. For the V2+ 3d ground state the calculated t2-e crystal-field splitting (cubic field) agrees well with the experimental value. The 4s state has most of its charge density (83%) associated with the V2+ ion and its six nearest-neighbor anions, but the 4p state is much more diffuse. Both the 4s and 4p states exhibit asymmetric charge distribution about the impurity center. The calculated 3d4s and 3d4p excitation energies are in good agreement with the ultraviolet absorption data, but the calculated oscillator strengths are much larger than the measured values. The distortion of the valence band of the host crystal has been studied. Host-crystal states localized at the F atoms around the impurity sites are found to split off from both edges of the valence band. © 1981 The American Physical Society.