We present density functional theory level predictions and analysis of the basic properties of newly synthesized high-nitrogen compounds together with 3,6-bis(2H-tetrazol-5-yl)-1,2,4,5-tetrazine (BTT) and 3,3'-azobis(6-amino-1,2,4,5-tetrazine) (DAAT), for which experimental data are available. The newly synthesized high-nitrogen compounds are based on tricycle fused 1,2,4-triazine and 1,2,4,5-tetrazine heterocycles. In this work, the molecules BTT and DAAT have been studied in order to validate the theoretical approach and to facilitate further progress developments for the molecules of interest. Molecular structural properties are clarified, and IR spectra predictions are provided to help detection of those compounds in the experiment. The energy content of the molecules in the gas phase is evaluated by calculating standard enthalpies of formation, by using a special selection of isodesmic reaction paths. We also include estimates of the condensed-phase heats of formation and heats of sublimation in the framework of the Politzer approach. The obtained properties are consistent with those new high-nitrogen compounds being a promising set of advanced energetic materials.