The excitation function of the H + O2 (nu = 0) --> OH + O reaction has been determined from trajectory calculations using the HO2 DMBE IV potential energy surface. Reactive cross sections for thirteen translational energies, corresponding to a total of a quarter of a million trajectories, have been computed covering the range 65 less-than-or-equal-to E(tr)/kJ mol-1 less-than-or-equal-to 550. Various schemes for analyzing the trajectories, three of which aim to correct approximately for the zero-point energy problem of classical dynamics, have been investigated. One of these schemes aims to correct also for known requirements on rotational distributions, e.g., for the fact that by Hund's rules for the coupling of angular momentum the product OH (2PI) molecule always rotates. It has been found that zero-point energy effects and lowest-J constraints on rotational distributions may have a crucial role, especially close to the threshold energy of reaction. Agreement with recent measurements of absolute reactive cross sections is generally satisfactory but, unlike experiment, no sharp maximum is found on the excitation function in the vicinity of E(tr) = 170 kJ mol-1. Possible reasons for this discrepancy are discussed. There is also good agreement with existing experimental data on the products rotational distribution.