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We investigate the torsion potentials in two prototypical pi-conjugated polymers, polyacetylene and polydiacetylene, as a function of chain length using different flavors of density functional theory. Our study provides a quantitative analysis of the delocalization error in standard semilocal and hybrid density functionals and demonstrates how it can influence structural and thermodynamic properties. The delocalization error is quantified by evaluating the many-electron self-interaction error (MESIE) for fractional electron numbers, which allows us to establish a direct connection between the MESIE and the error in the torsion barriers. The use of non-empirically tuned long-range corrected hybrid functionals results in a very significant reduction of the MESIE and leads to an improved description of torsion barrier heights. In addition, we demonstrate how our analysis allows the determination of the effective conjugation length in polyacetylene and polydiacetylene chains.
The electronic coupling between redox sites in mixed-valence systems has attracted the interest of the chemistry community for a long time. Many computational studies have focused on trying to determine its magnitude as a function of the nature of the redox sites and of the bridge(s) between them. However, in most instances, the quantum-chemical methodologies that have been employed suffer from intrinsic errors that lead to either an overlocalized or an overdelocalized character of the electronic structure. These deficiencies prevent an accurate depiction of the degree of charge (de)localization in the system and, as a result, of the extent of electronic coupling. Here we use nonempirically tuned long-range corrected density functional theory and show that it provides a robust, efficient approach to characterize organic mixed-valence systems. We first demonstrate the performance of this approach via a study of representative Robin-Day class-II (localized) and class-III (delocalized) complexes. We then examine a borderline class-II/class-III complex, which had proven difficult to describe accurately with standard density functional theory and Hartree-Fock methods.