WANNIER AND BLOCH ORBITAL COMPUTATION OF THE NONLINEAR SUSCEPTIBILITY

We present a method to compute high-order derivatives of the total ene rgy of a periodic solid with respect to a uniform electric field. We a pply the 2n + 1 theorem to a recently introduced total energy function al which uses a Wannier representation for the electronic orbitals and we find an expression for the static nonlinear susceptibility which i s much simpler than the one obtained by standard perturbative expansio ns. We show that the zero-field expression of the nonlinear susceptibi lity can be rewritten in a Bloch representation. We test numerically t he validity of our approach with a 1D model Hamiltonian.