  Our work is concerned with the case of the solar molecule CN which presents
conspicuous profiles of scattering polarization. We start by calculating
accurate PES for the singlet and triplet electronic ground states in order to
characterize the collisions between the CN molecule in its $X \; ^2\Sigma$
state and the hydrogen in its ground state $^2S$. The PES are included in the
Schr\"oodinger equation to obtain the scattering matrix and the probabilities
of collisions. Depolarizing collisional rate coefficients are computed in the
framework of the infinite order sudden approximation for temperatures ranging
from $T= 2000$ K to $T= 15000$ K. Interpretation of the results and comparison
between singlet and triplet collisional rate coefficients are detailed. We show
that, for typical photospheric hydrogen density ($n_{H} = 10^{15}-10^{16}$
cm$^{-3}$), the $X \; ^2\Sigma$ state of CN is partially or completely
depolarized by isotropic collisions.
