Ab initio complex band structure of conjugated polymers: Effects of hydrid density functional theory and GW schemes

The nonresonant tunneling regime for charge transfer across nanojunctions is critically dependent on the so-called beta parameter, governing the exponential decay of the current as the length of the junction increases. For periodic materials, this parameter can be theoretically evaluated by computing the complex band structure (CBS)-or evanescent states-of the material forming the tunneling junction. In this work we present the calculation of the CBS for organic polymers using a variety of computational schemes, including standard local, semilocal, and hybrid-exchange density functionals, and many-body perturbation theory within the GW approximation. We compare the description of localization and beta parameters among the adopted methods and with experimental data. We show that local and semilocal density functionals systematically underestimate the beta parameter, while hybrid-exchange schemes partially correct for this discrepancy, resulting in a much better agreement with GW calculations and experiments. Self-consistency effects and self-energy representation issues of the GW corrections are discussed together with the use of Wannier functions to interpolate the electronic band structure.