We report theoretical calculations based on ab initio total-energy calculations within the density functional theory to determine the structural, elastic, and electronic properties for several MoN phases. Among the five crystallographic structures that have been investigated, the hexagonal phases have been found to be more stable than the cubic ones. The calculated equilibrium structural parameters are in agreement with the available experiment results. It was found that ${\delta }_3\text{−}\mathrm{Mo}\mathrm{N}$ has the highest bulk modulus compared to the other structures studied here. Charge distributions and density of states are reported to understand the bonding in the different phases. Although MoN is a metal, we found that its bonding presents a large ionic component.

The band structure of the diluted magnetic semiconductor (Ga,Mn)N, and the x-ray absorption near-edge structure (XANES) at the K edge of Mn, were calculated using the linearized augmented plane wave method. The calculated K-edge spectra fit well with experimental data obtained on samples of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ with a wide range of Mn content, from $x=0.3\%$ to 5.7%. These samples were grown by molecular beam epitaxy. X-ray diffraction measurements and extended x-ray absorption fine structure studies were used to confirm the wurtzite structure of the samples, the absence of any secondary phase, and the substitutional position of Mn in the gallium sublattice of GaN. The shape of the measured XANES spectra does not depend on the Mn content, implying the same valence state and local atomic structure around the Mn atom in all samples. The comparison between the measured spectra and the results of the ab initio calculation offers a clear interpretation of the preedge structure: It is mainly due to dipolar transitions, with a single peak in the case of ${\mathrm{Mn}}^{2+}$ and an additional peak for ${\mathrm{Mn}}^{3+}$. Such a behavior of the XANES preedge of ${\mathrm{Mn}}^{2+}$ was confirmed experimentally on (Ga,Mn)As and (Zn,Mn)Te. We conclude that the valence state of Mn in wurtzite (Ga,Mn)N is $3+$, a conclusion which is also supported by infrared optical transmission and magnetization data obtained on the same samples.