The structures of the cyclic N4O2 molecule are investigated using three levels of nb initio electronic structure methods. Hartree-Fock self-consistent-field (SCF), second-order Moller-Plesset perturbation theory (MP2), and quadratic configuration interaction including single and double substitutions (QCISD) calculations are performed employing two basis sets of double-zeta plus polarization (DZP) and a triple(plus)-zeta double polarization (TZ-2P) quality. Two structures are located. A boat conformation (C-2v structure) is determined to be a minimum equilibrium structure with exothermicity of similar to 80, 140, and 100 kcal/mol relative to dissociation to 2N(2)O, 2N(2) + O-2, and 2NO + N-2, respectively. A planar (D-2h, structure) previously reported to be a minimum [Jones, W. H. J. Phys. Chem. 1992, 96, 5184] is confirmed in this study to be a transition state (saddle point) lying similar to 7-10 kcal/mol above the boat minimum as calculated at all levels of theory. A search for a chair and a twisted conformation has proven unsuccessful. Harmonic vibrational frequencies and infrared intensities are reported for both optimized boat and planar structures at all levels of theory. The consideration of the stable form of this molecule as a high energy density-material is discussed.