Much recent attention has been given to molecules containing only nitrogen atoms. Such molecules N-x can undergo the reaction N-x --> (x/2)N-2, which is very exothermic. These molecules are potential candidates for high energy density materials (HEDM). However, many all-nitrogen molecules dissociate too easily to be stable, practical energy sources. It is important to know which nitrogen molecules will be stable and which will not. In the current study, a variety of N-12 cages with all single bonds are examined by theoretical calculations to determine which ones are the most thermodynamically stable. Calculations are carried out using Hartree-Fock (HF) theory, gradient-corrected density functional theory (DFT), and Moller-Plesset perturbation theory (MP2 and MP4). Relative energies among the various isomers are calculated and trends are examined in order to determine which structural features lead to the most energetically favorable molecules.