Potential Energy Due to the van der Waals-London Force

An attractive force between neutral molecules can be explained to some extent by a dipole-dipole interaction when the particles carry a dipole moment. Such an attractive force even exists between nonpolar molecules as a result of the influence of electron motion in one atom on the motion in the other atom. This force was elucidated by London on the basis of wave mechanics. The charge fluctuations in one atom or molecule induce a fluctuating electric dipole in the other atom or molecule. A dipole-induced dipole interaction is thus set up, which in turn leads to an attractive interaction between the atoms or molecules. The attractive potential due to this force is expressed as 

The expression evaluated by integration will be given below for two cases one involving two large parallel plates and the other involving two spheres of equal radius. The total attractive force per unit area (1 cm ) of the plate is finally given as  

For two spheres of equal radius, the following equation was derived by Hamaker  

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