## 1 Introduction  
Uranium tri-iodide, UJ\({}_{3}\), is a rare anti-ferromagnetic inorganic compound that forms in the PuBr\({}_{3}\)-type, _Cmcm_, orthorhombic structure [1, 2]. This structure has the same space group number (#63) as the ground-state phase of uranium metal (\(\alpha\)-uranium). From an applications standpoint, it has been used as a starting material for organometallic uranium chemistry [3, 4, 5] and for separation of uranium metal [6]. Aside from its crystal structure and magnetic configuration, UJ\({}_{3}\)'s physical properties have not received a lot of attention compared to those of other uranium compounds. As with most uranium compounds, UJ\({}_{3}\) has substantial magnetic moments that have been reported in the range 1.97-3.65 \(\upmu_{\text{B}}\) on the uranium atoms [2, 3]. These moments are reported [2] to order in a complex non-intuitive anti-ferromagnetic fashion. In addition to its structure and magnetic properties, the energy of formation (or formation enthalpy) has been measured (\(-\)98.8 [7] and \(-\)111.6 kcal/mol [8]). From a fundamental science perspective, first-principles approaches have not yet been applied for the study of UJ\({}_{3}\) as a bulk material that we are aware of, but in the form of a two-dimensional monolayer [9]. In that investigation, the magnetic properties were the primary interest and the fact that this 2-D material may be a possible candidate for spintronic applications. The research [9] involved conventional density-functional theory with a pseudopotential approach that neglected spin-orbit coupling. In contrast to the bulk, the monolayer was predicted to favor ferromagnetism over anti-ferromagnetism and the spin moment was reported to be 3.0 \(\upmu_{\text{B}}\). It is expected that the bulk spin moment is quenched somewhat relative to that of the monolayer and should therefore be less than 3.0 \(\upmu_{\text{B}}\). The spin-orbit interaction was also ignored [9] and there was no consideration of an orbital moment. In reality, however, uranium compounds typically have rather large orbital moments with a magnitude comparable to that of the spin moment but aligned anti-parallel (uranium atom has less than half filled 5f shell). The total magnetic moment (sum of spin and orbital contributions) is thus significantly reduced when full relativity and orbital moments are addressed. The primary focus of the present work on UI\({}_{3}\) is not magnetism but the fundamental thermodynamic properties at elevated temperatures. In general, the high-temperature thermodynamic information often provides useful guidance for controlling thermally induced phase evolution and/or reaction kinetics of the chemical compounds (e.g., thermal decomposition at high temperatures) [10]. In addition, the temperature-dependent thermodynamics is the important basis for modeling phase transformations and associated microstructure evolution upon temperature variation since it determines the driving force for the kinetic processes [11; 12; 13]. To this end, accurate computational approaches for investigating the thermodynamics at elevated temperatures can play a critical role in establishing essential thermodynamic databases of chemical compounds. As mentioned above, the fundamental bulk properties of uranium tri-iodide have not been investigated with any ab initio method so far. Therefore, we apply our well-established density-functional theory (DFT) method to the bulk UI\({}_{3}\) compound to compute fundamental thermodynamic properties in this study. Contrary to the previous study [9] of the UI\({}_{3}\) monolayer, we do not limit ourselves to the pseudopotential approximation. Furthermore, we go beyond that approach [9] and address all relativistic effects including spin-orbit coupling with an extension to allow for orbital polarization (orbital-orbital coupling).