Tight-binding parametrization for the chromium nitride: A NMTO study

We investigate the band structure of chromium nitride using the $N$th-order muffin-tin orbitals (NMTO) based downfolding technique. We obtain downfolded Cr $d$ bands including both $e_{g}$ and $t_{2g}$ states and the hopping integrals of the tight-binding Cr $d$ bands for both cubic and orthorhombic lattice. We further analyze the chemical bonding and tight-binding parameters from the NMTO produced tight-binding Hamiltonian. The effect of lattice distortion is also discussed according to the downfolded tight-binding parameters.