Charge self-localization in π-conjugated polymers by long range corrected hybrid functionals

We systematically investigate the capability of hybrid functionals for describing charge self-localization in conjugated polymers, using the critical test that the spatial extension of a localized charge should be polymer length independent. We first compare the new long-range corrected (LRC) hybrids with conventional global hybrids and find that the former has a clear and important advantage over the latter in being significantly less spin contaminated. We then focus on LRC hybrids and investigate in detail the dependence of charge localization on the range parameter. We show that this parameter consistently needs to be about 0.2 bohr(-1) or larger to produce self-localized charges across different polymers. We introduce a new measure to determine the charge localization length, and then consider how properties related to localized charges converge with the polymer length and how they depend on the range parameter. These properties include the reorganization energy in the Marcus theory for electron transfer and the lowest excitation energy of a polaron. We discuss parameter tuning to experimental results and also suggest 0.2 bohr(-1) without tuning for exploratory studies based on the preference for least spin contaminations.