The present work made a molecular theoretical study of the structural and electronic properties of the geometric isomers of magnesium diboride (MgB2). The systems have specific characteristics and are very promising for technological applications, such as magnetic resonance imaging devices, motors, and generators. The same is still used in the industries of electronic devices, floating trains (MAGLEV), electricity and Biomagnetism. The results show that the geometric isomer with the lowest energy value is the cyclic species, which is the most stable. The formation enthalpies found were 205.38 Kcal mol-1 and 45.66 Kcal mol-1 for MgB2-cyclic and for B-Mg-B respectively. By means of the analysis Frontier Molecular Orbital it was possible to identify the shape of the HOMO - LUMO orbitals and how they contribute to the ligand and anti-ligand bands and thus to the superconducting properties of the compound. Finally, the NBO analysis confirmed that the most stable geometric isomer is MgB2-cyclic, presenting more interactions between donor or receptor orbitals.