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tokens: considered (see Table 1 ). Most of the population of H 2 will be in these ( v , j ) states under the conditions of ISM where radiative cooling of H 2 can dominate. When a bulk system of hydrogen molecules is thermally equilibrated, over 99% of the population is in these states at 1000 K and over 50% of the population is in these states at 5000 K. Table 1 Energy Levels of Selected ( v , j ) States in eV Note. a Energy relative to potential energy minimum of H 2 . For comparison, the energy at the dissociation limit is 4.74825 eV. The collision systems He + H 2 , H + H 2 , and H 2 + H 2 are among the most widely studied systems in reaction dynamics. For the electronic ground states of these systems, the interaction potentials are known to chemical accuracy (within 0.04 eV) and, in some cases, to spectroscopic accuracy (within 0.001 eV). This means that it is possible to simulate, to a high degree of precision, collisions within each of these collision systems. Exact quantum calculations are restricted to reduced dimensionality or to the lower energy states. For full-dimensional calculations involving dissociation, quantum calculations are not always feasible and quasiclassical trajectory (QCT) methods may be used. The development of ab initio potentials for the computational study of H 2 + H 2 paralleled the availability of computational resources. Schwenke ( 1988 ) developed a H 2 + H 2 potential to study the recombination of H atoms in the presence of H 2 using QCTs. The global H 2 + H 2 potential of Boothroyd et al. ( 1991 ) was developed with the intention of permitting full-dimensional calculations of energy transfer and dissociation to be carried out. The functional forms have derivatives that are evaluated analytically. The van der Waals well was fitted empirically. This is in contrast to earlier calculations which had been focused on those parts of the potential relevant to van der Waals interactions of H 2 molecules with low internal energy. Aguado et al. ( 1994 ) fitted the points of Boothroyd et al. ( 1991 ) to a functional form that was particularly convenient for quantum calculations. Although not spectroscopically accurate, these global potentials were deemed to be close to chemically accurate (Aguado et al. 1994 ). Diep Johnson ( 2000a , 2000b ) developed a potential for H 2 + H 2 which was focused on the (H 2 ) 2 dimer where each H 2 was treated as a rigid rotor in the ground vibrational state. Boothroyd et al. ( 2002a ) refined their earlier H 2 + H 2 potential with over 40,000 additional ab initio points. Like the earlier potential from this group, this BMKP2 potential also had analytical derivatives and an empirically fitted van der Waals region. The potential of Hinde ( 2008 ) was determined to spectroscopic accuracy for the (H 2 ) 2 dimer. Particular attention was paid to the van der Waals well for atomic separations within H 2 corresponding to low ( v , j ) states. The availability of these potentials permitted detailed