Subnitride chemistry: A first-principles study of the NaBa3N, Na5Ba3N, and Na16Ba6N phases

An ab initio study on the electronic structure of the subnitrides NaBa₃N, Na₅Ba₃N, and Na₁₆Ba₆N is performed for the first time. The NaBa₃N and Na₅Ba₃N phases consist of infinite ¹_∞NBa_6/2] strands composed of face-sharing NBa₆ octahedra surrounded by a “sea” of sodium atoms. The Na₁₆Ba₆N phase consist of discrete NBa₆] octahedra arranged in a body-cubic fashion, surrounded by a “sea” of sodium atoms. Our calculations suggest that the title subnitrides are metals. Analysis of the electronic structure shows partial interaction of N(2s) with Ba(5p) electrons in the lower energy region for NaBa₃N and Na₅Ba₃N. However, no dispersion is observed for the N(2s) and Ba(5p) bands in the cubic phase Na₁₆Ba₆N. The metallic band below the Fermi level shows a strong mixing of N(2p), Ba(6s), Ba(5d), Ba(6p), Na(3s) and Na(3p) orbitals. The metallic character in these nitrides stems from delocalized electrons corresponding to hybridized 5d^l6s^m6pⁿ barium orbitals which interact with hybridized 3sⁿ3p^m sodium orbitals. Analysis of the electron density and electronic structure in these nitrides shows two different regions: a metallic matrix corresponding to the sodium atoms and the regions around them and heteropolar bonding between nitrogen and barium within the infinite ¹_∞NBa_6/2] strands of the NaBa₃N and Na₅Ba₃N phases, and within the isolated NBa₆] octahedra of the Na₁₆Ba₆N phase. The nitrogen atoms inside the strands and octahedra are negatively charged, the anionic character of nitrogens being larger in the isolated octahedra of the cubic phase Na₁₆Ba₆N, due to the lack of electron delocalization along one direction as opposed to the other phases. The sodium and barium atoms appear to be slightly negatively and positively charged, the latter to a larger extent. From the computed Ba-N overlap populations as well as the analysis of the contour maps of differences between total density and superposition of atomic densities, we suggest partial covalent bonding between nitrogen and barium atoms along the infinite ¹_∞NBa_6/2] strands and within isolated NBa₆] octahedra.