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 W₀. Systems A and B may be reversed in the above calculation, and an energy W₁ be found. The true van der Waals energy is given roughly by W₀{W₁} ({W₀+W₁) }. 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 W₀ is that found by the image method. The energy W₁ is also evaluated, and is shown to be of the same order of magnitude as W₀ for ordinary electron densities in the metal. Thus the true energy of interaction may be considerably smaller than that given by the image method.