  The lattice constant, bulk modulus and shear constant of TbN are calculated
by means of density functional theory (DFT) in the local density approximation
(LDA) and generalized gradient approximation (GGA), with 4f-states treated as
valence electrons or core electrons. In addition, local Coulomb repulsions U
are treated both statically as in the LDA+U approach and dynamically as in the
dynamical mean-field theory (DMFT) in the Hubbard-I approximation. It is shown
that all methods, except DFT-LDA with 4f electrons treated as either valence
states, produce lattice constants and bulk moduli in good agreement with
experiment. In the LDA+U approach multiple minima are found, and we focus on
the competition between a state with cubic symmetry and a state obtained from
atomic Hund's rules. We find the state with cubic symmetry to be 0.59 eV lower
in energy than the Hund's rules state, while the opposite was obtained in
previous literature. The shear constant is shown to be rather sensitive to the
theoretical method used, and the Hund's rules state obtained in LDA+U is found
to be unstable towards tetragonal shear. As to the magnetism, we find that the
calculation based on the Hubbard-I approximation reproduces observations with
the best accuracy. Finally, the spectral properties of TbN are discussed,
together with the general applicability of the different methods in describing
rare-earth elements and compounds.
