This research was performed using Becke’s three-parameter hybrid functional approach with non-local correlation provided by Lee, Yang, and Parr and the cc-pVTZ basis set. The geometry, total energy, and heat of formation of the most stable conformers of the nitramines under study were obtained to obtain the density, resistance to shock stimuli, detonation pressure, and velocity of the materials under study. The results obtained allow us to predict new multipurpose energetic materials with a good balance between energy and stability. Our findings show that N-(2-nitroethyl)-N-(2,4,6-trinitrophenyl)nitramine, N-(2,4,6-trinitrophenyl)-N-[(3,4,5-trinitro-1H-pyrazol-1-yl)methyl]nitramine, N-(2,2-dinitroethyl)-N-(2,4,6-trinitrophenyl)nitramine, N-(2,2,2-trinitroethyl)-N-(2,4,6-trinitrophenyl)nitramine, and N-(trinitromethyl)-N-(2,4,6-trinitrophenyl)nitramine possess better explosive properties and a greater stability compared to tetryl, although they remain sensitive to shock stimuli. Referring to the results obtained, we recommend new tetryl analogs containing dinitroethyl, trinitroethyl, and trinitromethyl substituents for practical usage.