  A systematic first-principle study is performed to calculate the lattice
parameters, electronic structure, and thermodynamic properties of UN using the
local-density approximation (LDA)+\emph{U} and the generalized gradient
approximation (GGA)+\emph{U} formalisms. To properly describe the strong
correlation in the U $5f$ electrons, we optimized the \emph{U} parameter in
calculating the total energy, lattice parameters, and bulk modulus at the
nonmagnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM)
configurations. Our results show that by choosing the Hubbard \emph{U} around 2
eV within the GGA+\emph{U} approach, it is promising to correctly and
consistently describe the above mentioned properties of UN. The localization
behavior of 5$f$ electrons is found to be stronger than that of UC and our
electronic analysis indicates that the effective charge of UN can be
represented as U$^{1.71+}$N$^{1.71-}$. As for the thermodynamic study, the
phonon dispersion illustrates the stability of UN and we further predict the
lattice vibration energy, thermal expansion, and specific heat by utilizing the
quasiharmonic approximation. Our calculated specific heat is well consistent
with experiments.
