Polynitrogen molecules have been studied systematically at high levels of ab initio and density functional theory (DFT). Besides N-2, the thermodynamically most stable N-n molecules, located with the help of a newly developed energy increment system, are all based on pentazole units. The geometric, energetic, and magnetic criteria establish pentazole (2) and its anion (3) to be as aromatic as their isoelectronic analogues, e.g., furan, pyrrole, and the cyclopentadienyl anion. The bond lengths in 2 and 3 are equalized; both have large aromatic stabilization energies (ASE) and also substantial magnetic susceptibility exaltations (Lambda). The C-s symmetric azidopentazole (14), a candidate for experimental investigation, is the lowest energy N-8 isomer but is still 196.7 kcal/mol higher in energy than four N-2 molecules. Octaazapentalene (12) with 10 pi electrons also is aromatic. The D-2d symmetric bispentazole (21) is the lowest energy N-10 minimum but is 260 kcal/mol higher in energy than five N-2 molecules. For strain-free molecules, the average deviation is +/-2.6 kcal/mol between the DFT energies and those based on the increment scheme. The inclement scheme also provides estimates of the strain energies of polynitrogen compounds, e.g., tetraazatetrahedrane (8, 48.2 kcal/mol), octaazacubane (11, 192.6 kcal/mol), and N-20 (27, 294.6 kcal/mol), and is useful in searching for new high-energy-high-density materials.