High-pressure ${\mathrm{Na}}_3{\left({\mathrm{N}}_2\right)}_4,$ ${\mathrm{Ca}}_3{\left({\mathrm{N}}_2\right)}_4,$ ${\mathrm{Sr}}_3{\left({\mathrm{N}}_2\right)}_4,$ and $\mathrm{Ba}{\left({\mathrm{N}}_2\right)}_3$ featuring nitrogen dimers with noninteger charges and anion-driven metallicity

Charged molecular species, such as ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$, ${{\left[{\mathrm{O}}_2\right]}^x}^{\text{–}}$, ${{\left[{\mathrm{C}}_2\right]}^x}^{\text{–}}$, and ${{\left[{\mathrm{S}}_2\right]}^x}^{\text{–}}$, follow the paradigm of carrying integer values of electrons. Here, the ${\mathrm{Na}}_3{\left({\mathrm{N}}_2\right)}_4$, ${\mathrm{Ca}}_3{\left({\mathrm{N}}_2\right)}_4$, ${\mathrm{Sr}}_3{\left({\mathrm{N}}_2\right)}_4$, and $\mathrm{Ba}{\left({\mathrm{N}}_2\right)}_3$ compounds were produced and characterized <70 GPa and evidenced to be composed of paradigm-breaking ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ dimers with noninteger charges of −0.75, −1.5, −1.5, and −0.67, respectively. The anion-driven metallicity of the compounds is proposed as the physical mechanism enabling the noninteger electron count of the ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ dimers. The properties of these dimers and the compounds bearing them are demonstrated to depend on their noninteger charge, paving the way to materials with electron-tunable features.

Figure 1

Crystal structure of tI44 and cI112 compounds. (a) tI44 ${\mathrm{Sr}}_3{\left({\mathrm{N}}_2\right)}_4$ at 51 GPa, (b) tI44 as viewed along the $c$ axis, (c) Sr1 atom coordinated by nine $\left[{\mathrm{N}}_2\right]$ dimers, and (d) Sr2 atom coordinated by eight dimers. Color code for spheres representing different atoms: green (Sr1), pink (Sr2), blue (N1), and orange (N2). The tI44 ${\mathrm{Sr}}_3{\left({\mathrm{N}}_2\right)}_4$, ${\mathrm{Ca}}_3{\left({\mathrm{N}}_2\right)}_4$, ${\mathrm{Na}}_3{\left({\mathrm{N}}_2\right)}_4$, and ${\mathrm{K}}_3{\left({\mathrm{N}}_2\right)}_4$ are isostructural. (e) cI112 $\mathrm{Ba}{\left({\mathrm{N}}_2\right)}_3$ at 65 GPa, (f) cI112 as viewed along its threefold axis, (g) Ba coordinated by 12 dimers—six side-on and six head-on, and (h) the N1-N2 dimer coordinated by four Ba atoms. The color code for spheres representing different atoms: cyan (Ba1), blue (N1), and orange (N2).

Figure 2

Calculated (average) d(N-N) distances with respect to the formal charge (FC) x− of nitrogen dimers ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$, for 19 simple binary compounds containing ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ species [13, 14, 22, 23, 24, 25, 26, 27, 28]. All distances were computed at 1 bar. The more complex binary compounds that contain ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ species along with another anionic nitrogen species were not included (e.g., ${\mathrm{Sr}}_4{\mathrm{N}}_3$ [32], ${\mathrm{ReN}}_2$ [37]). For the ${\mathrm{FeN}}_2$ [20], ${\mathrm{CrN}}_2$ [35], and ${\mathrm{RhN}}_2$ [80] compounds, the assessment of the FC of the nitrogen dimer was based on their reported Raman modes and bulk moduli. Compounds featuring ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ species but with missing calculated data on their intramolecular bond lengths (BLs) have been omitted. Since the charge on the ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ dimer in ${\mathrm{CuN}}_2$ is not known [13], it was not included in the plot. The linear correlation between the N-N BLs and FC of the ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ dimers is expressed as $\mathrm{BL}=0.074\left(1\right)\AA$, $\mathrm{FC}+1.104\AA$ and is drawn as a dashed line. The $y$ axis intercept at $x=0$ was fixed at $1.104\AA$, which is the ${\mathrm{N}}_2$ molecule BL at 1 bar. Inset: Molecular orbital diagram of the pernitride ${\left[{\mathrm{N}}_2\right]}^{4\text{–}}$.

Figure 3

Visualization of the electron localization function (ELF) analysis at 1 bar. The blue and red colors represent, respectively, no to little electron localization and a significant electron localization. The lack of pronounced electron localization in ${\mathrm{Sr}}_3{\left({\mathrm{N}}_2\right)}_4$ between (a) $\mathrm{Sr}-\mathrm{Sr}$ and $\mathrm{Sr}\text{−}\left[{\mathrm{N}}_2\right]$ units [(200) slice] and (b) between $\left[{\mathrm{N}}_2\right]-\left[{\mathrm{N}}_2\right]$ [(002) slice] is visible. Likewise, as shown in (c), no notable electron localization is seen in $\mathrm{Ba}{\left({\mathrm{N}}_2\right)}_3$ [(001) slice] between any species aside from the ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ intramolecular bond. In both compounds, electron localization is never found away from an atomic site, as it would be the case for an electride.

Figure 4

Calculated electronic density of states (DOS) for the $\mathrm{Ba}{\left({\mathrm{N}}_2\right)}_3$ compound at 1 bar. (a) The total DOS with contributions from all atoms. The compound is metallic, as seen by the nonzero DOS at the Fermi energy (set at 0 eV). (b) Partial DOS calculations, where only the electronic states belonging to nitrogen atoms were considered. The electrons constituting the partially filled band are lying on the π* antibonding orbitals of the ${{\left[{\mathrm{N}}_2\right]}^x}^{\text{–}}$ species. (c) Partial DOS calculations, this time only showing the electronic states formed by the barium atoms. The equivalent graphs can be found for the ${\mathrm{Na}}_3{\left({\mathrm{N}}_2\right)}_4$, ${\mathrm{K}}_3{\left({\mathrm{N}}_2\right)}_4$, and ${\mathrm{Sr}}_3{\left({\mathrm{N}}_2\right)}_4$ in Figs. S10–S13 in the Supplemental Material [55].