The Image and Van der Waals Forces at a Metallic Surface

Calculations based on a model which takes the structure of the metal into account indicate that the force on an electron outside the surface of a metal is just the classical image force, but that the van der Waals force on a neutral molecule may be smaller than that given by a semi-classical calculation based on the method of images. An approximate value for the van der Waals energy between two systems A and B is obtained by calculating the energy of B in the field of A, supposing that the electrons of A are in fixed positions. The result is then averaged over the coordinates of the electrons of A, giving an energy WA. Systems A and B may be reversed in the above calculation, and an energy WB be found. The true van der Waals energy is given roughly by WAWB(WA+WB). This method gives a new approximate formula for the van der Waals interaction between two molecules, which reduces to a well-known result when further approximations are made. If system A is the molecule and system B a metallic surface, the energy WA is that found by the image method. The energy WB is also evaluated, and is shown to be of the same order of magnitude as WA for ordinary electron densities in the metal. Thus the true energy of interaction may be considerably smaller than that given by the image method.