Density functional theory (DFT) methods, as implemented in the Amsterdam Density Functional program, are used to calculate the electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) parameters of S2-, SSe-, and Se2- molecular ions doped into NaZ (Z=Cl,Br,I) and KI lattices. The calculations are performed on cluster in vacuo models, involving 88 atoms for the defect and its lattice surroundings, assuming that the molecular anions replace a single halide ion. In a previous study on the S2- ion, difficulties were encountered in calculating the superhyperfine and quadrupole principal values and axes of the neighbor cation nuclei. The observed discrepancies were partially attributed to the use of the frozen core approximation. In this work, the influence of this approximation on the calculated EPR and ENDOR parameters is evaluated. The DFT results for the S2-, SSe-, and Se2- molecular ions are in good agreement with the available experimental EPR data for all considered lattices, strongly supporting the monovacancy model for these diatomic defects.