Six stereoisomers of 5,5'-bis(amino)-1,1'-azobis (tetrazoles) and 30 other structures, including all possible bis(amino)-azobis(azoles) with an N−N0N−N unit, were designed. The molecular geometries were fully optimized at the DFT-B3LYP level with the 6-31++g (d, p) basis set. From the absence of any imaginary frequency in the infrared vibration frequency spectrum, it is predicted that all these studied structures may exist in stable forms. The results of the total energies of the stereoisomers of 5,5'-bis(amino)-1,1'-azobis(tetrazoles) indicate that the two symmetric trans-form structures are more likely to exist than the other four. The pyrolysis process, chemical stability and molecular electrostatic potential were studied via the investigation of their electronic structure. Heats of formation (HOFs) were calculated using the atomization energy method based on the results of the harmonic vibration frequencies, and a linear relationship was found between the HOF and nitrogen chain or nitrogen content. Densities of the title compounds were predicted with the Monte Carlo method. Finally, according to the results of the calculated HOFs and densities, the explosive parameters of these compounds were calculated using the Kamlet−Jacobs formula. 5,5'-Bis(amino)-1,1'-azobis(tetrazoles) and its isomer 5,5'-bis (amino)-2,2'-azobis(tetrazoles) may have potential for use as energetic compounds.