Based on ab initio calculations within the density functional theory and crystal structure prediction algorithms, the structure and stability of iron−nitrogen compounds in the pressure range of 100−400 GPa and temperatures up to 4000 K were determined. Three new iron nitrides Fe 4 N 3 -Imm2, Fe 2 N-Pnma, and Fe 3 N-C2/m were predicted. Fe 4 N 3 was shown to be stable at pressures up to 266 GPa and then decompose into Fe 2 N + 2FeN. Predicted Fe 2 N-Pnma becomes stable with respect to the decomposition reaction 9Fe 2 N = Fe 4 N 3 + 2Fe 7 N 3 at pressures above 221 GPa. Fe 3 N-C2/m stabilizes with respect to decomposition into 2Fe + Fe 7 N 3 at pressures above 265 GPa. Also, it was shown that β-Fe 7 N 3 synthesized in diamond anvil cell experiments has an orthorhombic Pbca structure, and at pressures above ∼320 GPa decomposes into 2Fe 2 N + Fe 3 N. All predicted Fe-rich iron nitrides, except Fe 4 N 3 -Imm2, have structural analogs among iron carbides. Considering the temperature effect, we observed that FeN-P2 1 3, Fe 2 N-Pnma, and Fe 3 N-C2/m can be stable at the Earth's inner core pressures and temperatures up to 4000 K, whereas Fe 4 N 3 -Imm2 and β-Fe 7 N 3 are thermodynamically unstable in the entire studied temperature range. Although Fe 7 N 3 -Pbca is thermodynamically unstable at inner core pressures, it shows the closest coincidence of the S-and P-wave velocities with seismic observations among the studied Fe-nitrides. Overall, Fe-nitrides cannot be the major compounds in the inner core of the Earth and can only substitute other elements such as carbon in Fe-carbides in minor amounts.