The dimers of [H3N . BH3](2), [H3N . AlH3](2), and [H3N . GaH3](2) are characterized as head-to-tail complexes with intermolecular H-H hydrogen bonding. In the case of [H3N . BH3](2), that hydrogen bonding is bifurcated resulting in four short (N)H-H(B) distances. For both [H3N . AlH3](2) and [H3N . GaH3](2), there are only two short (N)H-H(Al/Ga) distances, although the four-atom linkage remains far from linear. The binding energies that are calculated at the MP2 level of theory using polarized-double-zeta basis sets are -15.1, -11.8, and -10.7 kcal/mol for [H3N . BH3](2), [H3N . AlH3](2), and [H3N . GaH3](2), respectively. These energies appear converged to within 1 kcal/mol with respect to larger basis sets and more complete accounting for electron correlation effects. Binding energies from density functional calculations are within 0.3 kcal/mol of the MP2 results. All-electron and effective-core-potential basis sets for gallium provide similar predictions.