Real-space approach to calculation of electric polarization and dielectric constants

We describe a real-space approach to the calculation of the properties of an insulating crystal in an applied electric field, based on the iterative determination of the Wannier functions (WF's) of the occupied bands. It has been recently shown that a knowledge of the occupied WF's allows the calculation of the spontaneous (zero-field) electronic polarization. Building on these ideas, we describe a method for calculating the electronic polarization and dielectric constants of a material in non-zero field. The method is demonstrated for a one-dimensional tight-binding Hamiltonian.