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We have combined ab initio molecular dynamics with the intrinsic reactioncoordinate in order to investigate the mechanisms of stability and pyrolysis ofN$_{4}$-- N$_{120}$ fullerene-like nitrogen cages. The stability of the cageswas evaluated in terms of the activation barriers and the activation Gibbsenergies of their thermal-induced breaking. We found that binding energies,bond lengths, and quantum-mechanical descriptors failed to predict thestability of the cages. However, we derived a simple topological rule thatadjacent hexagons on the cage surface resulted in its instability. For thisreason, the number of stable nitrogen cages is significantly restricted incomparison with their carbon counterparts. As a rule, smaller clusters are morestable, whereas earlier proposed rather large cages collapse at roomtemperature. The most stable all-nitrogen cages are N$_{4}$ and N$_{6}$clusters, which can form the van-der-Waals crystals with the densities of 1.23and 1.36 g/cm$^{3}$, respectively. Examination of their band structures anddensities of electronic states shows that they are both insulators. Their powerand sensitivity are not inferior to the modern advanced high-energynanosystems.

All-nitrogen cages and molecular crystals: Topological rules, stability, and pyrolysis paths