By means of first-principles calculations, the structural stability, mechanical properties and electronic structure of the newly synthesized incompressible Re2C, Re2N, Re3N and an analogous compound Re3C have been investigated. Our results agree well with the available experimental and theoretical data. The proposed Re3C is shown to be energetically, mechanically and dynamically stable and also incompressible. Furthermore, it is suggested that the incompressibility of these compounds is originated from the strong covalent bonding character with the hybridization of 5d orbital of Re and the 2p orbital of C or N, and a zigzag topology of interconnected bonds, e.g., Re-Re, Re-C or Re-N bonding.
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