## 1 Introduction  
Uranium mononitride (UN) is an actinide compound that forms in the cubic sodium-chloride structure (B1), similar to other actinide nitrides and carbides. The location of the uranium and nitrogen atoms are interchangeable in this phase that is a face-centered cubic, with one atom in the origin and the other in the cube center. The B1 actinide-nitride and actinide-carbon systems are characterized by high melting temperatures and substantial electrical and thermal conductivities. Sometimes these compounds are magnetic. In the case of UN, the U-U distance is greater (\(\sim\)3.5 A) than that of \(\alpha\)-uranium (\(\sim\)2.8 A) and consequently, a magnetic moment forms on the uranium atom in UN but not in \(\alpha\)-uranium. Uranium mononitride has received a lot of attention from both experimental [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29] and computational angles [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43] due to its potential as a nuclear fuel for fast-breeder reactors [44]. It has superior thermophysical properties, including high melting temperature, uranium loading (content), thermal conductivity, and resistance to corrosion in air and water. It further exhibits good thermal and irradiation behavior, and is compatible with numerous candidate space reactor coolants, e.g., sodium, and other structure materials. Experimentally, several fundamental properties of UN have been characterized: (i) structural, (ii) mechanical, (iii) thermodynamical, and (iv) magnetic properties. For the structural properties (lattice parameter, density, and thermal expansion) a number of studies involving X-ray diffraction (XRD) have been reported [1; 7; 11; 16; 17; 21; 22; 25; 26; 29]. For the mechanical properties (bulk modulus, shear modulus, Poisson's ratio, elastic constants, lattice dynamics), ultrasonic pulse-echo (velocity and frequency) techniques and inelastic neutron scattering have been extensively used and the results from these experiments are presented in [2; 6; 7; 14; 18; 21; 22; 23; 26; 27]. For thermodynamical properties (specific heat, enthalpy, entropy, Gibbs free energy, melting point, heat of formation, and the resulting phase-diagram), most of the relevant experiments have relied on specific-heat measurements by different calorimeter capabilities [4; 5; 9; 10; 13; 15; 19; 20; 22], although the laser flash method is used in [12]. Determinations of the heat of formation for uranium mononitride are reported in References [10; 19; 20; 24]. Recently, [PERSON] et al. [29] developed an advanced technique to study uranium mononitride fuel thermochemical stability based on XRD, scanning electron microscopy (SEM), and mass-spectrometry. Finally, magnetic properties obtained from neutron scattering have been reported [3]. Accurate modeling of ground-state and particularly thermodynamical properties of uranium mononitride can play an important role in interpreting existing materials data and establishing a better understanding of its thermodynamical stability and fuel performance. Theoretical studies of uranium mononitrides can be divided into one of three categories; phenomenological models, first-principles electronic-structure calculations, and thermodynamical modeling. In this report we focus on the two latter approaches. We present details of our electronic-structure method in Section 2.1 and its application to investigate phonons in Section 2.2. In the literature, there are numerous papers focused on ab-initio-theory studies of uranium mononitride [30; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43]. The heat capacity of uranium mononitride has been estimated by molecular-dynamics simulations by [PERSON] et al. [32] utilizing the phonon spectrum data by [PERSON] et al. [40]. [PERSON] and [PERSON] [33] calculated the equilibrium lattice parameter, bulk modulus, and cohesive energy. [PERSON] et al.