This article presents an ab initio study of four polymers, polythiophene, polypyrrole, ladder-type polythiophene, and ladder-type polypyrrole. Upon an analysis of the variation of the band gap when comparing the unconstrained and the ladder-type polymers, a discrepancy was found between the thiophene and the pyrrole polymer families. For polythiophene, the ladder-type polymer has a larger gap than the unconstrained polymer whereas the opposite is found for the pyrrole polymers. The structural properties and the charge densities using the Bader charge analysis of these four compounds are investigated. The different band gap behaviors in thiophene and pyrrole polymers can be explained in terms of the competition between the bond length alternation and the effect of the charge density in the carbon backbone.

This article presents the results of several magnetic phases of doped La 2−x Sr x CuO 4 using density-functional theory with an added Hubbard term (DFT + U ). Doping factors from x = 0 to 0.25 were examined. We found that a bond-centered stripe is the magnetic ground state for x = 1/8 and 1/4. No stable stripe order was found for x = 1/6. Analysis of the electron density revealed that apical oxygen atoms, those located above and below the copper atoms in the CuO 2 planes, hold a non-negligible part of the holes at large doping and present a small spin polarization. Finally, the charge reorganization caused by the magnetic stripe modulation was studied for bond-centered and atom-centered stripes.

Ladder-type polymers, obtained by small modifications of the atomic structure of ladder-type polythiophene, are studied using density-functional theory calculations. Within the local-density and GW approximations, it is found that upon a simple substitution of the sulfur atoms by nitrogen and boron atoms, the band structure of the resulting polymer exhibits band overlap between the occupied and the unoccupied states. However, the three-parameter Becke hybrid functional predicts these polymers to be small band gap semiconductors. Finally, results of time-dependent density-functional theory are reported on increasing length oligomers, indicating that the polymers would have very low excitation energies.