Density-functional methods, as implemented in the Amsterdam Density Functional program, are used to calculate the electron paramagnetic resonance ͑EPR͒ and electron nuclear double resonance ͑ENDOR͒ parameters of the S 2 Ϫ defect in a halide monovacancy in various alkali halides (M Z:M ϭNa, K, Rb and ZϭCl, Br, I͒ lattices. The calculations were performed on cluster in vacuo models for the defect and its lattice surroundings, involving up to 88 atoms in order to limit boundary effects. For all M Z lattices, the calculated g and 33 S hyperfine tensors of the S 2 Ϫ molecular ion are in very good agreement with the available EPR data, explicitly supporting the monovacancy model for the defect. In addition, computational results for the principal superhyperfine and quadrupole values and axes of the nearest shells of M ϩ and Z Ϫ ions are compared with experimental ENDOR data. The merits and shortcomings of the applied cluster in the vacuo method are critically evaluated.