All-nitrogen materials, as a unique branch of energetic materials, have gained huge attentions, of which cyclo-N5− derivatives are the representative synthetically reported materials. However, the energetic performance of cyclo-N5− compounds has certain limitations and cannot go beyond that of CL-20. In order to reach the higher energy, in this work, we presented two kinds of polynitrogen species, N4 and N8. Two isomers of N4 and four isomers of N8 were fully calculated by using density functional theory (DFT). Theoretical results show that all these polynitrogen materials exhibit excellent heats of formation (7.92–16.60 kJ g−1), desirable detonation performance (D: 9766–11620 m s−1; p: 36.8–61.1 GPa), as well as the remarkable specific impulses (330.1–436.2 s), which are much superior to CL-20. Among them, N4-2 (tetraazahedrane) (D: 10037 m s−1; p: 40.1 GPa; Isp: 409.7 s) and cube N8-4 (D: 11620 m s−1; p: 61.1 GPa; Isp: 436.2 s) have the highest energetic properties, which are expected to become promising high-energy-density-materials. Moreover, electrostatic surface potentials, Frontier molecular orbitals, infrared spectra, natural bond orbital charges, and weak interactions were also investigated to further understand their relationship between structure and performance.