Berry phase approach to longitudinal dipole moments of infinite chains in electronic-structure methods with local basis sets

The authors provide a reformulation of the modern theory of polarization for one-dimensional stereoregular polymers, at the level of the single determinant Hartree-Fock and Kohn-Sham methods within a basis set of local orbitals. By starting with localization of one-electron orbitals, their approach naturally arrives to the Berry phases of Bloch orbitals. Then they describe a novel numerical algorithm for evaluation of longitudinal dipole moments, computationally more convenient than those presently implemented within the local basis periodic codes. This method is based on the straightforward evaluation of the usual direct space dipole matrix elements between local orbitals, as well as overlap matrices between wave functions at two neighboring k points of the reciprocal space mesh. The practical behavior of the algorithm and its convergence properties with respect to the k -point mesh density are illustrated in benchmark calculations for water chains and fluorinated trans-polyacetylene.