  The transition metal nitride BaHfN$_2$, which consists of weakly bonded
neutral slabs of closed shell ions, has structural and chemical similarities to
other layered nitrides which have impressive superconducting T$_c$ when
electron doped: A$_x$HfNCl, A$_x$ZrNCl, A$_x$TiNCl, with $T_c= 25.5$, $15.2$
and $16.5$ K, respectively for appropriate donor (A) concentrations $x$. These
similarities suggest the possibility of BaHfN$_2$ being another relatively high
T$_c$ nitride upon doping, with effects of structure and the role of specific
transition metal ions yet to be understood. We report first-principles
electronic structure calculations for stoichiometric BaHfN$_2$ using density
functional theory with plane-wave basis sets and separable dual-space Gaussian
pseudopotentials. An indirect band gap of 0.8 eV was obtained and the lowest
conduction band is primarily of Hf 5$d_{xy}$ character, similar to
$\beta$-ZrNCl and $\alpha$-TiNCl. The two N sites, one in the Hf layer and
another one in the Ba layer, were found to have very anisotropic Born effective
charges (BEC):deviations from the formal charge (-3) are opposite for the two
sites, and opposite for the two orientations (in-plane, out of plane). LO-TO
splittings and comparison of BECs and dielectric constant tensors to those of
related compounds are discussed, and the effect of electron doping on the
zone-center phonons is reported.
