Exact results for the polarization energy of clusters of polarizable particles containing one or two ions

We present exact analytical expressions for the polarization, or full dipolar induction, energy of clusters of polarizable particles in the form of regular polyhedra with a charge at the centre and for an octahedral arrangement of polarizable particles with two ions symmetrically placed about the centre of the structure. Each particle is considered to have an isotropic polarizability, α. The many-body expansion of the polarization energy is performed for an equilateral triangle and for a tetrahedron. The polarizability tensor is obtained for an equilateral triangle and for a tetrahedron of polarizable particles with isotropic polarizability, α.