The polynitrotetraazabenzimidazoles were optimized to obtain their molecular geometries and electronic structures at DFT–B3LYP/6-31+G(d) level. The theoretical molecular density (ρ), heat of formation (HOF), detonation velocity (D) and detonation pressure (P), estimated using Kamlet–Jacobs equations, showed that the detonation properties of these compounds were excellent. It is found that there are good linear relationships between volume, density, detonation velocity, detonation pressure and the number of nitro group. The simulation results reveal that molecules F and L outperform HMX, which will be novel potential candidates for high energetic density compounds (HEDCs) when it is successfully synthesized. These results provide basic information for molecular design of novel HEDCs.