Quantum rate calculations for the H+O-2-->HO+O combustion reaction, as well as for the reverse reaction, are reported. Using the DMBE IV potential energy surface, the cumulative reaction probability N-0(E) has been directly computed for total angular momentum J=0, by means of the Seideman, Manthe and Miller Lanczos-based absorbing boundary condition method [J. Chem. Phys. 96, 4412 (1992); 99, 3411 (1993)]. Special attention has been paid to the definition of the molecular basis set, and to the sensitivity of the results to the absorbing potentials used in the asymptotic regions. The N-0(E) results show very good overall agreement with the coupled channel calculations of Pack et al. [J. Chem. Phys. 102, 5998 (1995)], although the highly oscillatory behavior just above threshold renders such a comparison difficult in that energy range. The behavior of the J not equal 0 cumulative reaction probability has been estimated from calculations using the J(z)-conserving approximation for J values in the range 10-70. This allowed us to define which reference geometry should be used in the J-shifting approximation, in order to compute the cumulative reaction probability N-J(E) for any J value. By imposing conservation of the total energy within this approximation, the rate constants are shown to display better agreement with the experimental results.