In this paper, we present results from ab initio, self-consistent, local density approximation (LDA) calculations of electronic and related properties of cubic antifluorite (anti-) lithium sulfide . Our nonrelativistic computations implemented the linear combination of atomic orbital (LCAO) formalism following the Bagayoko, Zhao and Williams method, as enhanced by Ekuma and Franklin (BZW-EF). Consequently, using several self-consistent calculations with increasing basis sets, we searched for the smallest basis set that yields the absolute minima of the occupied energies. The outcomes of the calculation with this basis set, called the optimal basis set, have the full physical content of density functional theory (DFT). Our calculated indirect band gap, from to , is 3.723 eV, for the low temperature experimental lattice constant of 5.689 Å. The predicted indirect band gap of 3.702 eV is obtained for the computationally determined equilibrium lattice constant of 5.651 Å. We have also calculated the total density of states (DOS) and partial densities of states (pDOS), electron and hole effective masses and the bulk modulus of . Due to a lack of experimental results, most of the calculated ones reported here are predictions for this material suspected of exhibiting a high temperature superconductivity similar to that of . [ABSTRACT FROM AUTHOR]