Reactions of a hydrogen molecule with a ZnO surface are studied by an ab initio method. For simulating the ZnO (10 1BAR 0) surface, one ZnO molecule both with and without a Madelung potential is used. Since the electrostatic potential due to the ionic layer decreases exponentially, the effect of the layers deeper than the second one can be neglected. The Madelung potential is, therefore, expressed by the 32 point charges of +/- 0.5 situated on the first and second layers. Several low-lying states of ZnO and the ZnO + H-2 system have been calculated by the symmetry-adapted cluster (SAC) and SAC-CI methods. It is found that the (1)SIGMA+ state of ZnO is the ground state and catalytic active and the other states are inactive. ZnO ((1)SIGMA+) reacts with H-2 and dissociatively adsorbs it with making Zn-H and O-H bonds. This occurs both with and without the Madelung potential. Without the Madelung potential, the heat of reaction is 81.3 kcal/mol and the reaction barrier is 14.0 kcal/mol. With the Madelung potential, the heat of reaction decreases to 73.5 kcal/mol and the barrier decreases to 11.5 kcal/mol. The mechanism of this reaction is the electron donation from the 2p-pi orbital of O to the antibonding sigma(u) MO of H-2 and the back-donation from the bonding sigma(g) MO of H-2 to the LUMO of ZnO. In the intermediate stage of the reaction, the dipole of ZnO works to increase the overlap of the active MOS to make the reaction easier. Throughout the reaction, the in-plane 2p-pi orbital of O and the HOMO of ZnO are inactive and work to keep the ZnO bond stable during the catalytic process.