Fourier Space Uncoupled Hartree-Fock Polarizabilities of One-Dimensionally Periodic Systems. Polyethylene and Polysilane Revisited

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 Andre. 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.