Hellmann-Feynman theorem, elastic moduli, and the Cauchy relations

Abstract

The Hellmann-Feynman theorem is used to derive a formula for the harmonic elastic moduli of crystals in which every atom is at a center of symmetry in terms of the electron density and its distortion due to the crystal deformation. It is shown that these moduli satisfy the Cauchy relations if the electron density distribution deforms according to the same affine transformation which governs the crystal deformation.