In this work, the properties of the synthesized high-nitrogen compounds 4,4',6,6'-tetra(azido)azo-1,3,5-triazine (TAAT) and 4,4',6,6'-tetra(azido)hydrazo-1,3,5-triazine (TART), and a set of designed bridged triazines with similar bridges were studied theoretically to facilitate further developments for the molecules of interests. The gas-phase heats of formation were predicted based on the isodesmic reactions by using the DFT-B3LYP/AUG-cc-PVDZ method. The estimates of the condensed-phase heats of formation and heats of sublimation were estimated in the framework of the Politzer approach. Calculation results show that the method gives a good estimation for enthalpies, in comparison with available experimental data for TAAT and TART. The crystal density has been computed using molecular packing calculations. The calculated detonation velocities and detonation pressures indicate that -NF(2), -NO(2), -N=N-, and -N=N(O)- groups are effective structural units for improving the detonation performance of the bridged triazines. The synthesized TAAT and TART are not preferred energetic materials due to their inferior detonation performance. The p ->pi conjugation effect between the triazine rings and bridges makes the molecule stable as,a whole. The electrostatic behavior of the bridged triazines is characterized by an anomalous surface potential imbalance when incorporating the strongly electron withdrawing -NF(2) and -NO(2) groups into the molecule. An analysis of the bond dissociation energies shows that all these derivatives have good thermal stability over RDX and HMX, and the -NH-NH- bridge is more helpful for improving the stability than -N=N(O) and -N=N- bridges. Considering the detonation performance and thermal stability, three bridged triazines may be considered as the potential candidates of high-energy density materials (HEDMs).