Many-electron theory of distorted lattices

Abstract

In previous papers an account has been given of a new perturbation approach to the many-electron theory of insulators with regular lattices. The discussion was based on Wannier functions. To discuss distorted lattices the analogues of Wannier functions for distorted lattices are required. It is suggested that they be obtained by a unitary transformation of the Wannier functions. A possible form is suggested for the transformation, and an account of how the perturbation theory is affected is then given. By means of a simple example, NaCl it is shown that the elastic but also by the consequences that follow from the requirement that as the nuclei move the electrons must follow, and that the basic wavefunctions must therefore change, to preserve orthogonality. The analogues of the Wannier functions for a distorted lattice are thereby given physical significance. Criteria for the equilibrium conditions of a periodic lattice are also discussed.