Physical Picture

The second order term becomes important if the first order term is zero, i.e. when the molecules have no static dipole moment. Quantum mechanically, the expectation value of the dipole moment is zero, but there can be quantum fluctuations as with any expectation value. These fluctuations (`fluctuating dipoles') generate fluctuating electric fields that eventually lead to an attractive interaction between the molecules. In quantum chemistry, the resulting forces are called dispersion forces, in physics they are often called van-der-Waals forces. They can be derived from quantum field theory (quantum electrodynamics), which establishes their close relation to the Casimir effect and also accounts for retardation effects due to the finite propagation velocity of interaction (speed of light). If these retardation effects are neglected, we can derive the van-der-Waals forces from our second order perturbation theory, which was based on semi-classical considerations. This is essentially the derivation that was first given by F. London.