H$_2$ potential. Since the interaction potential between two H$_2$ molecules is relatively weak the density of CMSs is rather sparse. The number of diabatic channels included in the calculation depends on the energy. For collision energies $E_c < 100 $ K, a cut-off energy is used to restrict the number of channels. This allows one to include all rotational and vibrational levels below the cut-off energy in the scattering calculations. We used cut-off energies of 20142.76 K (14000 cm$^{-1}$) for $J=0-3$, and 15826.45 K (11000 cm$^{-1}$) for $J=4-10$ for ultralow energy calculations. However, this approach may lead to a proliferation in the number of channels at higher energies as the cut-off energy needs to be higher. Thus only a restricted set of rovibrational levels are included in the calculations. In the present work we retained all CMSs with quantum numbers $v=0,j=0-8$, and $v=1,j=0,2$ for calculations at higher energies. The close-coupling equations  were propagated using the log-derivative matrix propagation method of Johnson [@Johnson73] and Manolopoulos [@Manolopoulos86] to an asymptotic matching distance of $R=53 \ a_0$. For all collision energies, the inelastic cross section is converged at this value of the matching distance. However, to get converged elastic cross section for ultralow 