Ab initio complex band structure of conjugated polymers: Effects of hydrid DFT and GW schemes

The non-resonant 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.