  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.
