Quantum dynamics of H$_2$-H$_2$ collisions*

The H$_2-$H$_2$ system has long been considered as a benchmark candidate for quantum dynamics studies of molecule-molecule collisions. H$_2$ is the most abundant molecular species in the interstellar medium and rotational and vibrational transitions in collisions between H$_2$ molecules have been topics of considerable interest. Here, we present a full quantum mechanical treatment of collisions between ortho-ortho, para-para, and ortho-para H$_2$ molecules as well as the HD-H$_2$ system over a wide range of energies and for different initial rovibrational levels of the molecules. The computed rate constants are compared against available experimental data and previous theoretical results.