The total electronic energy for condensed systems is examined as a function of nuclear displacements from the equilibrium configuration. The expansion is derived to all orders both for the exact solutions to the many-electron Schrödinger equation and for the approximate Hartree-Fock solutions. The results are shown to be translationally invariant to all orders. Expressions are derived for the electronic contributions to the force-constant tensors in real space and it is shown that the effective nuclear potential has a simple two-body form for a Bravais lattice.
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