The most important task for specialists in the field of energy-intensive compounds is the search for new high-energy density materials and the study of their properties. This paper continues the study of series of tetrazines condensed with different types of azoles and presents the results of study of molecule structure of high-energy 5/6/5 tricyclic 1,2,3,4-and 1,2,4,5-tetrazines annelated with nitro-substituted imidazoles. The enthalpies of formation of the given molecules in the gaseous phase have been determined by high-performance quantum-chemical calculations by various calculation methods within the Gaussian 09 program package: G4, G4MP2, ωB97XD/aug-cc-pVTZ, CBS-4M, B3LYP/6-311+G(2d,p), M062X/6-311+G(2d,p). Different calculation methods and approaches have been compared in terms of their accuracy and time consumption. In addition, vibrational IR spectra have been calculated for the given compounds, and the correspondence of characteristic absorption frequencies to key fragments and functional groups of the structures has been determined. Enthalpy of formation of one of the studied substances (4220 kJ/kg) is the highest one among entalpies of formation of energy-intensive bis(nitroazolo)tetrazines calculated up to date.