4. Inclusion of Higher Multipole Moments

In this chapter, contributions to the retarded two-body dispersion potential arising from higher multipole moments, are computed. First, a general formula is obtained for the energy shift between two species with pure electric multipole polarisability of arbitrary order. Interaction energies between an electric dipole polarisable molecule and a second that is electric quadrupole or octupole polarisable, as well as between two electric quadrupole polarisable molecules, are then extracted. Useful insight is gained by decomposing the octupole moment into irreducible components of weights-1 and -3. Magnetic effects are accounted for by including magnetic dipole and lowest-order diamagnetic coupling terms in the interaction Hamiltonian in addition to the electric dipole contribution. Remarkably, the energy shift between an electrically polarisable atom and a paramagnetically susceptible one is repulsive, unlike earlier examples, which are always attractive when both species are in the ground electronic state. Another interesting case arises when both molecules are chiral, and characterised by mixed electric-magnetic dipole polarisability. The energy shift is found to be discriminatory, dependent upon the handedness of each species. Asymptotic forms for \(\Delta E\) are obtained for each of the examples considered. In all of the cases involving electric coupling, retardation effects weaken the potentials relative to their semi-classically derived counterparts.