Van der Waals interaction and magnetic dipole dipole interaction

Question

I have a conceptual question that bothers me.

From what I understand, van der Waals forces are the primary source of inter-molecular interaction. There are three different possible origins for van der Waals forces: permanent dipole-permanent dipole (Keesom/short range) forces, the permanent dipole-induced dipole (Debije/short range) interactions and induced dipole-induced dipole (London/long range) forces. (Here we talk about electric dipole.)

We also have magnetic dipole dipole interaction which is $\propto \frac{m_1m_2}{r^3}(3\cos^3\theta-1)$ and has quantum mechanical origins such as Pauli's exclusion principle and exchange interaction and etc.

My question is: since both magnetic and electric dipole dipole interactions are interpreted based on vector model mathematical formulation and these interactions happen at atomic level and they are of a similar range, in what cases we consider interaction between electric charge or a dipole, and magnetic dipole?

Or in general, can magnetic dipole-dipole interaction happen along with electric dipole-dipole interaction in a systems? When I read text books on inter-molecular forces (Israelaschvili, Cosgrov, etc) non of them talk about magnetic interactions. I wonder why.

Answer 1

Magnetostatic interactions are much smaller than electrostatic interactions. For atomic and molecular systems, the magnitude of the magnetic potential energy is roughly $\alpha^2 \approx 5\times 10^{-5}$ times the magnitude of the electrostatic potential energy. Therefore magnetic dipole (and higher orders) are usually neglected.

The multipole expansions for the magnetostatic long-range potentials are formally equivalent to the usual electrostatic long-range, with $\mu_0/4\pi$ replacing the $1/4\pi\epsilon_0$ prefactor, where $\mu_0$ is the vacuum permeability.

References:

M. Lepers and O. Dulieu, arXiv:1703.02833v2 [quant-ph] https://arxiv.org/abs/1703.02833v2 1 Z.C. Yan, J.F. Babb, A. Dalgarno, and G.W.F. Drake, Phys. Rev. A - At. Mol. Opt. Phys. 54, 2824 (1996).