The orthorhombic molybdenum trioxide is comprehensively investigated using the density function theory based on all-electron full potential linear augmented plane wave ( ) method as implemented in code within four types of exchange correlation potentials, namely the local density approximation ( ), generalized gradient approximation ( ), Engel-Vosko generalized gradient approximation ( ) and the modified Becke-Johnson potential ( ). The conduction band minimum ( ) is situated at point of Brillouin zone ( ), whereas the valence band maximum ( ) is located at point of . Calculation demonstrated that is an indirect band gap insulator. The calculated electronic band structure and the total density of states confirm that brings the calculated energy band gap (2.81 eV) closer to the experimental one (3.03, 3.10 eV). The electronic space charge density distribution of is explored in two crystallographic planes (0 0 1) and (1 0 1) to scrutinize the origin of chemical bonds. It is found that majority of charges are accumulated on O site and the distribution of electronic charge is spherical. The optical properties are calculated for three tensor components along the polarization directions [1 0 0], [0 1 0] and [0 0 1] with respect to the crystalline axes. It is found that the regions confined between 6.5 - 8.0 eV and 10.0 -13.5 eV are considered as a lossless regions. The calculated optical properties support our observation from the calculated electronic band structure and the density of states which shows that , and underestimate the energy band gap, while succeed by large amount in bringing the calculated energy band gap closer to the experimental one.