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

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