Dispersion potential between three-bodies with arbitrary electric multipole polarizabilities: molecular QED theory

Molecular quantum electrodynamics is used to obtain an expression for the retarded dispersion energy shift between three arbitrarily electrically polarizable atoms or molecules. A generalized Craig-Power Hamiltonian that depends quadratically on the electric displacement field is employed together with third-order diagrammatic perturbation theory. This approach simplifies the calculation relative to the use of the usual multipolar coupling Hamiltonian that is linear in the displacement field. Specific higher multipole non-additive contributions are then extracted. These include dipole-dipole-quadrupole, dipole-quadrupole-quadrupole, and dipole-dipole-octupole potentials valid for oriented and isotropic species with arbitrary separation distances between particles, extending recent work in which these energy shifts were given for equilateral triangle and collinear geometries. Near-zone limiting forms are found to agree with earlier works in which static inter-particle couplings were used.