Symmetry arguments and abinitio s.c.f. calculations (double-zeta basis set) are used to show that the exchange reaction H2+ D2 → 2HD could proceed in a concerted fashion through a six-center transition state. The computed barrier height of 90 kcal/mol for this process lies below the experimental dissociation energy of H2 (but above the computed dissociation energy) and also below the energy required for exchange through a four-center transition state. Either the termolecular(2 + 2 + 2 ) or bimolecular(4 + 2 ) cycloadditions are thermally allowed. The presence of a transition metal would allow the reaction to proceed through a four-center geometry, leading to the formation of a possibly stable metal-H4 complex.