A new approximate method is developed for the calculation of the adiabatic potential energy surface for a molecule outside a metal surface. It is computationally fast enough to be useful in simulations of the dynamics of adsorbing and desorbing molecules. The method is characterized by the fact that the functional form of the total energy expression is derived from density functional theory, that each of the terms entering can be given a precise physical interpretation, and that most of the parameters entering can be calculated, within the local density approximation. The method is explicitly derived for H2 outside metal surfaces and the applicability is illustrated for H2 adsorbing on various Cu and Ni surfaces. Although very approximate, the calculated potentials seem to include a number of features observed experimentally: Ni is more active in dissociating H2 than Cu, and open surfaces are more active than close-packed ones. Moreover, the method is simple enough that one can contemplate studying variations in dissociation pathways over the surface unit cell. For the Cu surfaces these variations are substantial accounting for at least part of the variation of the sticking coefficient with the kinetic energy of the incoming molecule. Because of the transparent nature of the energy expression, all these trends can be given a simple physical interpretation. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.