Van der Waals interaction and magnetic dipole dipole interaction
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).