The C₃H₄N₂ isomers comprising of thirteen members were subjected to computational calculations using the Gaussian 4 compound method. Important parameters including dipole moment, bond distance and angle, standard enthalpy of formation, rotational constants and vibrational frequencies were obtained from the optimized geometries of these isomers and compared with experimental results where available. Imidazole was found to be the most stable among the C₃H₄N₂ isomers with the least standard enthalpy of formation of 26.641 kcal/mol. The bond distances and angles for Imidazole and Pyrazole were observed to be in excellent agreement with the measured experimental values. Additionally, the computationally calculated rotational constants; A=9.7740943, B=9.4123152, C=4.7948970 and A=12.4751355, B=3.8580794, C=3.0007692, and dipole moments of 3.8535D and 2.2268D for Imidazole and Pyrazole respectively were accurately determined when compared with experimental results. Thus, the high accuracy obtained from this quantum chemical calculation indicates that other C₃H₄N₂ isomers with no experimental values are well predicted with the Gaussian-4G4 compound model.