A time-dependent wave packet method to study four center (4C) reactions in competition with collision-induced dissociation is presented and applied to the H-2 + H-2 system, using the potential of Aguado et al. [J. Chem. Phys. 101 (1994) 4004] and a reduced dimensionality model. The calculated probabilities are better converged than previous time-independent quantum calculations and, in addition, compare quite satisfactorily with quasiclassical trajectory calculations. Tunneling effects near reaction thresholds are, however, important. For the 4C reaction in H-2(v(1) = 10) + H-2(v(2) = 0), it is estimated that such effects are dominant for temperatures below 1200 K, with decreasing values for more excited initial states or for the dissociation process. (C) 2001 Elsevier Science B.V. All rights reserved.