New relations between elastic constants of different orders for structure-independent interactions with application to electrons in metals

Abstract

Isotropy relations more extensive than, but containing, those usually quoted are obtained by considering structure-independent contributions to the energy of a crystal in a formalism involving a first order elastic constant. These lead to relations between Brugger elastic constants of different orders. The results are applied to the kinetic, exchange and correlation energies of free electrons and to the first order perturbation band-structure energy. In all cases the full set of first, second and third order elastic constant contributions follow from a single quantity. Fallacious statements concerning the bulk modulus of the electron gas are exposed.