cross sections show similar energy dependence for $E_c=0.1-1$ eV. In the lower panel of Fig. \[XSIN-THERMAL-1000-FIG\], we compare state-to-state cross sections at $E_c=0.01$ eV for the BMKPE (white) and BMKP (black) PESs with the corresponding results of Pogrebnya et al. (dashed or gray). Our results on both PESs are in good agreement with those of Pogrebnya et al. for the CMSs (0000), (0200), (0202), (0400), (0402) but differ for the CMSs (0404), (0600), (0602), (0604), (0800). We believe that the differences are due to the CSA method employed in the work of Pogrebnya et al. This applies to the results in both panels of Fig. \[XSIN-THERMAL-1000-FIG\]. The maximum value of the total angular momentum projection quantum number, $\Omega$, on the body-fixed axis $\vec{R}$ used in the calculations of Pogrebnya et al. is $|\Omega|_{\text{max}}=4$. In a body-fixed frame, the orbital angular momentum $\vec{l}$ is always perpendicular to the body-fixed axis $\vec{R}$ and the value $m_l$ of its projection on $\vec{R}$ is zero. This implies that the projection of $\vec{J} = \vec{j}_{12} + \vec{l}$ on the body-fixed axis is $\Omega = m_{j_{12}}$. If $|\Omega|_{\text{max}}$ is restricted to 4, so does $|m_{j_{12}}|$. This is equivalent to exclude all projection quantum numbers $|m_{j_{12}}| > 