## 3 Results  
Uranium mononitride is a rather stable compound and that is reflected in a strongly negative formation enthalpy; -293.6 kJ/mol (-223.65 mRy/at) [20]. The formation enthalpy can be modeled within the DFT approach because the energy of the constituents of UN (uranium and nitrogen) as well as the compound itself (ignoring the possibility of a non-stochiometric compound) can be calculated. Uranium metal forms in an orthorhombic structure, \(\alpha\) uranium, that was studied within the DFT model a while ago [68]. The structure is defined by axial b/a and c/a ratios as well as an internal parameter, y, that were carefully determined [68] and these parameters were used in the present calculation for \(\alpha\)-uranium. Uranium mononitride, on the other hand, forms in the cubic sodium-chloride structure and has no free parameters due to its symmetry. The calculation of the nitrogen (nitrogen gas, N\({}_{2}\)) is less straightforward in the context of conventional density-functional theory. [PERSON] et al. [69] addressed the problem associated with N\({}_{2}\) gas molecules in their attempts to calculate formation enthalpies of the actinide mononitrides from DFT. They simulated an N\({}_{2}\) dimer by constructing a large tetragonal unit cell and compared its energy with nitrogen atoms placed in a cubic cell and very far apart. From this they deduced a dissociation energy of N\({}_{2}\) = 462.2 kJ/mol (352.08 mRy/at). In the present study we added this amount to the energy of a large cell of the simple cubic \(\alpha\)-N\({}_{2}\)[70] for an estimate of the nitrogen-atom energy. Combining this result and the calculated energies of \(\alpha\)-U andUN, we obtained a formation enthalpy of UN; \(\Delta_{\rm{f}}\)H = \(-\)297.5 kJ/mol (\(-\)226.6 mRy/at), in exceptional agreement with the experimental value of \(-\)293.6 kJ/mol (\(-\)223.6 mRy/at) [20]. In Table 1 we collect formation enthalpy and some other calculated ground-state properties for UN. Overall, our results are in excellent agreement with experiment and depend only very weakly on the magnetic configuration. Even the non-magnetic treatment appears reasonable, suggesting that ignoring magnetism, as is done here for the phonon calculations, is sensible. The calculated magnetic moment agrees with neutron diffraction [3] only when orbital polarization is considered. Without orbital-orbital coupling the orbital moment is severely underestimated and the total moment too large (the spin and orbital moments couple anti-parallel). In addition to thermodynamical stability, mechanical stability is important for a relevant material. The elastic constants provide information on mechanical properties and they have been measured [18] and computed [39; 71] for UN and we compare our results to those in Table 2. In general, DFT elastic constants have larger errors than either the atomic volume or the bulk modulus and with that in mind, the calculated zero-temperature elastic constants compare very favorably with the measured room-temperature data. Reviewing the performance of the DFT (GGA+OP) model for UN in Tables 1 and 2, we realize that there is no compelling argument for going beyond this level of theory. In a recent DFT+U study [38] the atomic volume and bulk modulus were calculated as functions of the Hubbard U parameter for the purpose of finding the U value that best reproduces the data (U = 2 eV). However, for the optimized value of U, the agreement with experiment was still worse than our GGA+OP approach presented in Table 1. The reason the DFT+U result was less accurate is likely that the electronic structure was not obtained from an all-electron treatment and that neither spin-orbit coupling, nor orbital polarization was accounted for [38]. As discussed above, being a potential fuel, the thermodynamical properties of uranium mononitride at rather high temperatures are of interest.