Context: Energy-containing materials such as explosives have attracted considerable interest recently. In the field of high-energy materials, tetrazine and its derivatives can largely meet the requirements of high nitrogen content and oxygen balance. Nitrogen-rich energetic salts are important research subjects. Nitrogen-rich salt of 3,6-dinitramino-1,2,4,5-tetrazine is a high-energy nitrogen-rich material, but there are few related studies. This paper systematically studies the crystal structure and electronic, vibrational, and thermodynamic properties of (NH4)2(DNAT). The lattice parameters of (NH4)2(DNAT) are observed to align well with the experimental values. The properties of electrons are analyzed by band structure and density of states (DOS). The phonon dispersion curves indicate that the compound is dynamically stable. The vibrational modes of bonds and chemical groups are described in detail, and the peaks in the Raman and infrared spectra are assigned to different vibration modes. Based on the vibration characteristics, thermodynamic properties such as enthalpy (H), Helmholtz free energy (F), entropy (S), Gibbs free energy (G), constant volume heat capacity (CV), and Debye temperature (Θ) are analyzed. This article can pave the way for subsequent work or provide data support to other researchers, promoting further research. Methods: In this study, we utilized the density functional theory (DFT) for our calculations. The exchange–correlation potential and van der Waals interactions were characterized based on the GGA-PBE + G function calculation. We obtained Brillouin zone integrals using Monkhorst–Pack k-point grids, with the k-point of the Brillouin zone set to a 2 × 2 × 2 grid. During the self-consistent field operation, we set the total energy convergence tolerance to 5 × 10−6 eV per atom. The cut-off energy for the calculation was established at 830 eV. Additionally, the states of H (1s1), C (2s2 2p2), N (2s2 2p3), and O (2s2 2p4) were treated as valence electrons in our study. [ABSTRACT FROM AUTHOR]