First principles molecular orbital and plane-wave ab initio calculations have been used to investigate the structural and vibrational properties of the highly efficient low sensitive explosive 1,1-diamino-2,2 dinitroethylene (FOX-7) in both the gas and solid phases. The ab initio molecular orbital calculations performed at second-order (MP2) and fourth-order (MP4) Moller-Plesset levels and using density-functional theory (DFT) methods with B3LYP functional indicate that in the gas phase FOX-7 is the most stable conformer relative to its cis-1,2 and trans-1,2 isomers. The calculated MP2 and DFT structures for the FOX-7 molecule agree well with the experimental X-ray configuration but with twists of the nitro and amino groups much larger than in the solid phase. The calculated fundamental vibrational frequencies at the DFT level generally compare well. with the MP2 results. The IR spectra were computed for the three isomers. The structural properties of the FOX-7 crystal have been studied by a plane-wave DFT method. These calculations were done with periodic boundary conditions in all three directions. The optimization of the crystal structure has been done with full relaxation of the atomic positions and of the lattice parameters under P2(1)/n symmetry. The predicted crystal structure is in good agreement with X-ray data. We have developed an intermolecular potential to describe the structure of the FOX-7 crystal in the approximation of rigid molecules. This potential is composed of pairwise exp-6 Buckingham terms and Coulombic interactions. Crystal-packing calculations without symmetry constraints performed with the proposed potential accurately reproduce the main crystallographic features and yield very good agreement with the estimated lattice energy. This intermolecular potential was further tested in isothermal-isobaric molecular dynamics simulations at atmospheric pressure and in the temperature range of 4.2-450 K. It is found that the increase of temperature does not significantly change the orientations of the molecules inside the unit cell. The thermal expansion coefficients calculated for the model indicate anisotropic behavior with the largest expansion along the b crystallographic direction.