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.