The interaction of the primary water dissociation products H, O and OH with various (111) metal surfaces is studied by density functional theory (DFT) calculations using clusters. It is found that H forms an essentially covalent bond with the metal, whereas O and OH form a largely ionic bond. The O and OH adsorbates prefer the high coordination three-fold hollow site on all metals: no such clear trend for H is found, the adsorption energy for on-top and hollow sites being comparable for most metals, especially on transition metals. The O and OH adsorbates are attracted towards, and donate some electronic charge to, the surface when a positive electric field (electrode potential) is applied, whereas the effect of an applied field on H adsorption is much smaller. We also show how the trends in the OH adsorption energies on different metals, as compared with O adsorption, can be explained by a weaker covalent interaction and a stronger Pauli repulsion of the OH with the metal d electrons.