On the transition from microscopic to macroscopic electrodynamics

Implicit in the change from microscopic electrodynamics to a macroscopic, multipole theory is a set of molecule-fixed coordinate systems – and hence an arbitrary set of molecular origins {O n } – relative to which the positions of molecular constituents are specified. We examine the extent to which this theory satisfies a Van Vleck–Buckingham-type translational invariance with respect to the choice of {O n } in a linear, homogeneous, anisotropic medium. For contributions above electric dipole order, the theory is only partially invariant, and therefore incomplete: the corresponding macroscopic Maxwell equations yield unphysical results for certain phenomena. We propose a fully invariant formulation, based on the use of invariant molecular polarizability tensors in the quantum-mechanical expressions for expectation values of molecular multipole moments induced by harmonic, plane electromagnetic waves. We show that expressions for the invariant polarizabilities can be discerned from the partially invariant theory, and we discuss the uniqueness of our procedure.