Adatom dipole moments on metals and their interactions

An expression is derived for the dipole moment μ, associated with an arbitrary adatom on an arbitrary metal surface, in terms of the differential work done in moving the adatom from the interior of the metal to its actual position in the presence and absence, respectively, of small, asymptotically uniform electric field on the exterior of the metal. With the aid of this expression it is shown that the non-oscillatory part of the interaction energy of two dipoles μ_A and μ_B, situated on the surface and separated by a large distance v, is given by U_AB = 2μ_Aμ_Bv^?3. This exceeds by a factor of 2 the interaction energy of two dipoles in the same relative configuration but in a vacuum.