The quantum theory of atomic polarization II— The van der Waals energy of two atoms

Abstract

Abstract In a previous paper (p. 94) (which will be referred to as Paper I), the polarizability of an atom in a uniform electric field was calculated by a method of varying parameters. The same method can equally well be applied to find the energy of interaction of two atoms a large distance apart, by treating their interaction as a perturbation of the system in which the atoms are separated by an infinite distance. The mutual energy, other than that arising from the ionic charges, if they exist, of the atoms, is usually called the van der Waals energy. We shall suppose that one atom contains N1 electrons, and is represented in its unperturbed state by a determinantal wave function Ψ1(as in equation (3·1) of Paper I), containing electronic functions of the type Ψ p1p3 where p1 may be any one of the N1 occupied states α1,β1, ..., v1 of this atom, and p denotes that the spatial and spin co-ordinates of the pth electron are inserted in ΨP1P> Similarly the second atom contains N2 electrons, and is represented in its unperturbed state by a determinant Ψ2, containing functions Ψp2r, where p2 may be one of the N2 occupied states α2, β2,...,V2, and r refers to the co-ordinates of the rth electron. Then if we neglect any exchange of electrons between the atoms, the wave function of the unperturbed system of two atoms is Ψ=Ψ1Ψ2fΨ*Ψdr = N1! N2!, where the integration is taken over the co-ordinate-space of all N1 electrons of atom 1 and all N2 electrons of atom 2.