## 3 Results  
The calculated (DFT) electronic density of states for UI\({}_{3}\), shown in in Figure 1, displays several band gaps, including at the highest occupied energy. It is not uncommon that uranium compounds form band gaps and perhaps the uranium oxides are best known for this behavior. DFT typically underestimates or even fails to predict these band gaps, whereas theory that incorporates Mott-Hubbard electron correlations (DFT + \(U\) method) can correct the size and position of the band gap [35] given an appropriately chosen Hubbard \(U\) parameter. However, photoemission or other experiments illuminating the existence of band gaps have not been undertaken for UI\({}_{3}\) and therefore accurately determining the \(U\) parameter is impossible. Without knowledge of this central parameter, the DFT + \(U\) approach becomes less practical. Fortunately, we are not focused on band gaps or spectroscopical properties in this report, but on high-temperature thermodynamical properties that can be derived from energetics that are less sensitive to unoccupied energy levels associated with band gaps. In terms of the crystal structure, our DFT-relaxed (predicted) structure compares reasonably well with experiments, particularly in regard to the \(a\) and \(c\) lattice parameters of the orthorhombic structure. Our calculated \(b\)/\(a\) and \(c\)/\(a\) axial ratios are 3.56 and 2.29, respectively. These values agree fairly with experiments (3.24 and 2.31) [2] but indicate a non-negligible overestimation of \(b\) in the model. The reason for this overestimation of \(b\) is unclear but could be due to thermal softening that our zero-temperature DFT is not accounting for. The formation energy (or formation enthalpy) can be estimated in our model. From the DFT total energy of UI\({}_{3}\), \(\alpha\)-uranium, and the isolated iodine atom we calculate the formation enthalpy of the UI\({}_{3}\) compound, knowing the enthalpy of formation of the iodine molecule. With our computational technique the molecule is not practical to compute so we adopt the experimental value [36]. From these energies we obtain a zero temperature UI\({}_{3}\) formation enthalpy of \(-\)320 mRy/at (\(-\)100 kcal/mol) in good accord with the experimental numbers \(-\)98.8 and \(-\)111.6 kcal/mol [7,8] and the room-temperature CALPHAD data (\(-\)110 kcal/mol). The experimental formation enthalpies were obtained at 370 \({}^{\circ}\)C [7] and room temperature [8], respectively. This level of agreement suggests that the chemical bonding in the DFT model is rather appropriate and we proceed to investigate the single-crystal elastic constants for UI\({}_{3}\). The orthorhombic symmetry of the crystal implies nine independent elastic constants (\(C_{ij}\)) that are obtained from the total-energy response to different strains [37]. Our calculated elastic moduli for UI\({}_{3}\) are summarized in Table 1. It is illuminating to investigate the mechanical stability criteria to establish stability of UI\({}_{3}\) in the model. For an orthorhombic crystal, necessary and sufficient Born criteria for stability have been published [38] and our calculated elastic constants fulfill those (not shown). However, to categorically demonstrate full phase stability one needs to investigate all phonons, and this is beyond the scope of this study. Unfortunately, there are no experimental single-crystal elastic moduli with which we can verify our results. The calculated moduli thus serve as predictions and can be used to constrain semi-empirical models or interatomic potentials. We mentioned that UI\({}_{3}\) is an anti-ferromagnet with substantial magnetic moments on the uranium atoms. Experimentally, there is a rather large spread between the quoted magnetic moments, ranging from 1.97 to 3.65 \(\mu_{\text{B}}\)[2,3]. Our calculations adopt a simplified anti-fer