Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields

Abstract

Abstract New derivations are given of equations relating molecular electric multipole moments and polarizabilities of general order to the electrostatic energy. The unabridged moment convention is shown to yield relatively simple relations between derivatives of the energy with respect to field gradients and the multipole moments and polarizabilities. Care is taken to distinguish various forms of these derivatives, and one form leads to a proof of a general symmetry of polarizability tensors with respect to permutations of rank indices. The condition of internal equilibrium is shown to be fundamental to the existence of this symmetry. The transformation of multipole moment and polarizability tensors under translation of the coordinate origin is expressed in relatively simple general form. The traceless multipole and polarizability tensors of Buckingham and McLean and Yoshimine are obtained as linear combinations of the unabridged tensors and their traces.