The atomic positions of 3-methyl-1,4-dioxo-1, 4-dohydronaphthalen-2-yl-sulfanyl (3MDS) single crystal taken from XRD data were optimized by minimizing the forces. We make use of the optimized geometry as a starting point of the comprehensive theoretical calculations by employing the all-electron full potential linearized augmented plane wave method to solve the Kohn Sham equations. The calculated electronic band structure and densities of states suggested that this single crystal possesses the energy band gap of about 1.575 eV using the local density approximation, 1.640 eV by generalized gradient approximation, 1.740 eV for the Engel-Vosko generalized gradient approximation and 2.223 eV using modified Becke-Johnson potential (mBJ). From our calculated electron charge density distribution, we obtain an image of the electron clouds that surround the molecules in the average unit cell of the crystal. The chemical bonding features were analyzed and the substantial covalent interactions were observed between O and C, C and S and as well as between C and H atoms. The optical response functions were calculated and discussed using the calculated energy band structures.