Tetraazatetrahedrane, N-4 (2), is 11.3 kJ mol(-1) lower in energy than tetrazete (1) at the G2 level, in contrast to its hydrocarbon analogue, tetrahedrane (4), which has 108.9 kJ mol(-1) higher energy than that of cyclobutadiene (3). The open-chain C-s structure of tetranitrogen (5) having the triplet ground state is the most stable isomer of N-4, and its energy is 62.0 kJ mol(-1) lower than that of tetrazete. At the G2 level, the enthalpies of formation, Delta H-f298, of tetraazatetrahedrane, tetrazete, and the open-chain tetranitrogen are 732.5 +/- 8.0, 746.5 +/- 7.6, and 686.6 +/- 7.6 kJ mol(-1), respectively. The high thermodynamical instability of tetraazatetrahedrane and tetrazete toward their dissociations into molecular nitrogen may be attributed to the comparative weakness of the single N-N and double N=N bonds, the strengths of which are only 29.0 and 54.2% of the strength of the N=N bond. For the C-C and C=C bonds, the corresponding ratios are 38.0 and 74.8%, respectively, and consequently, cyclobutadiene is stable with respect to dissociation into two acetylene molecules. After correction for the strain energy of the four-membered nitrogen ring, the antiaromatic destabilization of tetrazete is 54.1 kJ mol(-1); this is considerably less than the antiaromatic destabilization of cyclobutadiene (170 +/- 7 kJ mol(-1) at the G2 level). At the G2 level the strain energies of tetraazatetrahedrane N-4, tetrazetine, N4H2, and tetrazetidine, (NH)4, are 205.5, 156.9, and 131.4 kJ mol(-1), respectively. Azasubstituted cyclobutadienes have planar structures with bond-length alternation and, with the exception of tetrazete, are lower in energy than the corresponding azasubstituted tetrahedranes. The energy difference decreases with increasing number of the nitrogen atoms, and therefore, tetraazatetrahedrane is eventually more stable than tetrazete. 1,3-Diazete is 42.2 kJ mol(-1) lower in energy than 1,2-diazete. The homodesmotic stabilization energies for the azetes show that the azasubstitution results in decreasing destabilization effects in these molecules. However, the more nitrogen atoms in an azete, the greater its tendency to dissociate into triple-bond species, HC=CH, HC=N, or N=N.