Valence electron densities for LiNiN: (a) (110) plane through Li (upper right), Ni (lower left), N (lower right); (b) (001) plane through Ni atoms. A logarithmic grid of contour lines has been used ( x i ) x 0 2 i /3 , 

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... expected from a structural model which (23) nonbonding states appear in the range between -1.5 and -0.6 eV. Figure 4 shows the valence electron densities for LiNiN in two planes. The density plot for the (110) plane visualizes the covalent bonds between Ni and N while weak interactions within the Ni layers stacked along the c-axis of the hexagonal structure are apparent from the plot in the (001) plane. ...

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... 2/2 ] 2 - chains with formal Ni 1 + ions in a d 9 configuration, such that the chain is one electron short of filling the d - p bands. This configuration might be expected to promote anti-ferromagnetic interactions along the chains and to exhibit spin Peierls instability, leading to superstructure formation. Of the nitrides containing ∞ [NiN 2/2 ] chains, CaNiN is the most studied. Perhaps unexpectedly, CaNiN is metallic, and no anomalies in the resistivity and magnetic susceptibility have been observed. 7 The electronic structure of CaNiN has been studied a number of times since the discovery of the nitridonickelate. 9 - 12 The initial DFT calculations attributed the absence of distortions to 2D and 3D interchain coupling and a low likelihood of Fermi surface-driven charge density wave (CDW) or spin density wave (SDW) instabilities. 9 Subsequent studies acknowledge the more than peripheral significance of Ca interactions with the 1 ∞ [NiN 2/2 ] 2 - chains in suppressing such instabilities. 11,12 There are perhaps two important distinctions between CaNiN and LiNiN which may influence the electronic structure and behavior of the lithium compound. First, formal electron counting suggests the formula- tion LiNi(II)N, although the charge balance may be achieved by the formation of holes in bands dominated by N states as proposed for Li 3 - x Co x N compounds. 13 Second, by contrast to CaNiN, all the 1 ∞ [NiN 2/2 ] n - chains in LiNiN are parallel, and none are spatially separated by a layer of electropositive atoms (ions). The preliminary evidence for fascinating electronic properties combined with fast Li + ion diffusion prompted us to carry out a more detailed investigation. Powder neutron diffraction (PND) has allowed us to make more definitive conclusions about the structure of LiNiN, particularly in terms of nickel substitution levels and the distribution of Li + vacancies. The structural study clarifies the subtle differences between LiNiN and the disordered Li 3 - x - y Ni x N phases and presents us with the starting point for our density functional theory (DFT) calculations of the band structure. These calculations combined with new results from magic angle spinning 7 Li NMR support the postulated 1D metallic behavior of LiNiN. Structure Refinement. Initially, a structural model in space group P h m 2 was considered in which the Li stoichiometry is set to 1 and the Li atoms are constrained to occupy the 1b (0, 0, 1 / 2 ) site, as determined previously from single-crystal X-ray diffraction. 3 Refinements employing this model, according to the procedure described in the Experimental Section, produced very good fits to the data ( R wp ≈ 1%) at each collection temperature, and no additional reflections were observed across the range of measured temperatures. Final crystallographic parameters are shown in Table 1, refined structural parameters in Table 2, and selected interatomic distances in Table 3. The structure from PND data is shown in Figure 1, and representative examples of profile fits are shown in Figure 2. Additional models in the same space group were considered and tested, but these produced higher residuals and goodness of fit values and/or physically unrealistic refined parameters. For example, relaxing the constraint on Li stoichiometry, resulted in 1b site occupancies greater than unity at each of the measured temperatures. Similarly, relaxing the stiochiometry constraint and allowing Li occupancy for both the 1b and the 1d ( 1 / 3 , 2 / 3 , 1 / 2 ) sites in the [LiN] plane to vary freely led to either negative site occupancies or negative thermal parameters. A model in which the Li stoichiometry was constrained to 1 and the fractional occupancies of both the above Li sites were allowed to vary, led to instabilities, lack of convergence and occupancies for the 1b and 1d sites greater and less than unity and zero, respectively. Figure 3 shows the band structure for LiNiN obtained using the FLAPW method as described in the Experimental Section, as well as the total DOS and the most important local partial DOS components. As expected from a structural model which might not suggest significant interchain interactions, the bands are rather flat, except in directions parallel to the z -axis of the Brillouin zone where they cross the Fermi level. This indicates that LiNiN exhibits a very anisotropic electronic conductivity. The band between about - 14 and - 12.8 eV is dominated by N 2s states with a Li 2s and 2p admixture. In the energy range from about - 6.2 eV to the Fermi level there is a complex of bands which can be approximately divided into three regions distinguished by their bonding characteristics. Ni - N d z 2 - p z σ -bonds are found in the lowest-energy region up to around - 4.2 eV, with Ni - N (d xz , d yz ) - (p x , p y ) π -interactions between - 4.2 eV and the Fermi level, while additional Ni (d xy , d x 2 - y 2 ) nonbonding states appear in the range between - 1.5 and - 0.6 eV. Figure 4 shows the valence electron densities for LiNiN in two planes. The density plot for the (110) plane visualizes the covalent bonds between Ni and N while weak interactions within the Ni layers stacked along the c -axis of the hexagonal structure are apparent from the plot in the (001) plane. The two types of bonding between the Ni and N atoms can be discerned in Figure 5, where the electron densities for two energy regions are given, i.e., from ∼ - 6.2 eV to - 4.2 eV showing the Ni - N d z 2 - p z σ -bonds and from - 4.2 eV to the onset of the Ni (d xy ,d x 2 - y 2 ) peak at roughly - 2.2 eV showing the Ni - N (d xz ,d yz ) - (p x ,p y ) π -bonds. Crystal orbital Hamiltonian populations (COHP) computed for different contacts in LiNiN obtained using the TB-LMTO- ASA program are shown in Figure 6. Integrated COHP (ICOHP) values of - 0.41 and - 0.03 Ry/cell were obtained for the shortest Ni - N and Li - N contacts, respectively. It should be noted that Ni - Ni interchain ICOHP absolute values lower than 0.01 Ry/cell were calculated. These results corroborate the primarily 1D nature of the electronic structure of LiNiN, suggested by the FLAPW calculations. Assuming a rigid band model, the Ni - N COHP curve suggests that lengthening of the Ni - N contact within the chain is foreseen upon reduction of the chains. This comes from the π Ni - N antibonding character of the band that crosses the Fermi level. The Fermi surface of LiNiN is shown in Figure 7. As already indicated by the band structure, three bands contribute to the Fermi surface, and hence to electrical conductivity. Band 8 contributes the narrow pocket close to the H point, while most of the surface is determined by bands 9 and 10. In the band structure of Figure 3a these bands are cut by the Fermi energy in directions parallel to the c -axis, specifically Γ - A, M - L, and K - H. They are only degenerate along the Γ - A axis, and away from this symmetry line they form parallel sheets perpendicular to the c -axis. The exceptional topology of the Fermi surface of LiNiN suggests anisotropic electrical conductivity. Further information on electronic structure and bonding can be obtained from the electric-field gradient (EFG). For its calculation a proper description of the higher-lying core states (“semicore”) is essential. Calculated EFG values can be split into the contribution of the sphere around the respective atoms (“sphere contribution”) and the remainder of the crystal lattice. The sphere contribution can be further separated into ll ′ -like contributions, of which only sd, pp, and dd are important, if f electrons do not play a role. For LiNiN the EFG tensors for all three atoms have been calculated. Since all the atoms occupy sites with h m 2 ( D 3 h ) symmetry, there is no asymmetry parameter and the EFG tensor is fully defined by just one number ( V zz ). The total values and the sphere and most important ll ′ -like contributions (including the semicore pp contribution for Ni) are given in Table 4. For LiNiN the principal axes corresponding to the V zz components are always oriented in direction of the c -axis, and since negative EFG components indicate strong interactions with neighboring atoms, the results can be interpreted as follows. The strongest Li interactions are within the ab plane and are directed toward the N atoms while for N they are oriented in the c direction toward the Ni atoms. The situation for Ni is more complicated. The large negative pp contribution originates from Ni - N interactions in the c direction and the similarly large positive dd contribution from Ni - Ni interactions in the (001) plane. The semicore pp contribution is not directly influenced by the atomic neighbors, but only indirectly by the polarizing effect of the valence electrons on the semicore states and usually carries the opposite sign of the valence-electron contribution. The fact that the pp component for Ni is about as large as the dd component (although the p contribution to the DOS is much smaller than the d contribution) is due to the slower increase of the 3d wave function near the nucleus compared to the 4p wave function. Solid-State NMR. Variable-temperature wide-line 7 Li spectra of LiNiN were discussed briefly in our previous communication 4 and are shown in Figure 8. Since the quadrupole moment of 7 Li is relatively small, the single Li site expected from the P h m 2 space group should result in a narrow central line, flanked by a single pair of first-order powder-broadened satellite lines. The value of the EFG ( eq ) of 1.5 × 10 20 V m - 2 obtained from the density functional calculations described above, together with a 7 Li quadrupole moment ( Q ) of - 40.1 × 10 - 31 m 2 , 41 suggests that the quadrupolar coupling constant C Q ) e 2 qQ / h should be 145 kHz. An uncertainty in this calculated value of no more than 15% is expected by comparison with the success of similar calculations for the parent Li 3 N. 25 However, at low ...