Two regimes of HH interaction outside a metal surface are considered: (i) Beyond the spill-out region of the metal electrons (physisorption) (ii) Embedded protons in the electron spill-out. Using an extension of the Heitier-London model to treat (i), the H 2 binding energy for the molecule parallel to the surface is reduced, whereas for the perpendicular configuration stronger binding obtains. In (ii), the asymptotic form of the screening charge round a single proton is considered, in a linear response framework, and for an infinite barrier model of the surface. If the screened potential has no singularities in k space, then the interaction energy ∆ E( X), X being the distance between the protons, falls off as X-5 times an oscillatory function, for H 2 parallel to the planar metal surface. The effect of self-consistency on this result is then examined and it is concluded that the asymptotic interaction energy is unchanged in form, though the amplitude is altered.