The gas phase molecular structures and crystal structures of 3, 6-diamino-1, 2, 4, 5-tetrazine (DATz), 3, 6-dihydrazino-1, 2, 4, 5-tetrazine (DHT) and 3, 6-diazido-1, 2, 4, 5-tetrazine(DIAT) were full optimized at the GGA-PW91/DNP level with Materials Studio Program. The energy band, density of state (DOS) and part density of state (PDOS) were calculated. The change rule of the thermodynamic functions with temperature were discussed. The results show that the stability of three tetrazine derivatives obtained by the energy band increases in the order DHT < DATz < DIAT. The active site in main reaction of DATz, DHT and DIAT obtained by analysis of DOS, PDOS and Wiberg bond is N atom on tetrazine ring. The crystal vibration analyses infer that their thermodynamic functions(S_m^θ、C_p,m ^θ、H_m^θ and G_m^θ)display a nearly linear correlation with temperature. With the temperature increasing, S_m^θ、C_{p, m}^θ and H_m^θ gradually increase, whereas G_m^θ gradually decrease.