A method for the computation of electronic energies of stereoregular polymers is reviewed, using a formulation that makes use of Fourier-representation techniques and the Ewald procedure for accelerating the convergence of lattice sums. That method is in the present work extended to include the computation of electric polarization at an “uncoupled” approximation at the level of second-order perturbation theory based on Hartree–Fock wave functions, using the procedure of Blount and of Genkin and Mednis, as applied to polymers by Barbier, Delhalle, and André. The extension requires computation of the derivatives of Fock matrix elements with respect to the Bloch-wave parameter k, and an effficient numerical procedure for evaluating these derivatives is described here. The computational procedures are incorporated in the authors' ft-1d program, and the new features of that program are validated by reexamining the band structures of polyethylene and polysilane. The results are consistent with the older work on these systems, but exhibit more computational efficiency and greater achievable accuracy.
This work would not have been possible without the important contributions of Prof. Joseph Delhalle and Dr. Isabelle Flamant to the development of the method. FEH was supported by U.S. National Science Foundation Grant PHY-0601758. Part of this research has been funded by BELSPO (IAP P7/05 network “Functional Supramolecular Systems”) and by the Francqui Foundation. The calculations were performed on the computing facilities of the Consortium des Équipements de Calcul Intensif (CÉCI), in particular those of the Plateforme Technologique de Calcul Intensif (PTCI) installed in the University of Namur, for which we gratefully acknowledge financial support from the FNRS-FRFC (Conventions No. 2.4.617.07.F and 2.5020.11) and from the University of Namur.
©2016 Walter de Gruyter Berlin/Boston