Ab initio study of ladder-type polymers polythiophene and polypyrrole
  This article presents an \textit{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. 
Simon Pesant, Paul Boulanger, Michel C\^ot\'e and Matthias Ernzerhof