Accurate and scalable electronic structure calculation of crystalline conjugated polymers

We have developed a methodology for efficient electronic coarse-graining of molecular semiconductors, enabling the calculation of electronic structure of systems with unit cells too large for conventional density functional theory methods. This includes crystalline conjugated polymers, which require nonlocal density functionals for accurate electronic property calculations. The strong wave-function delocalization along the polymer chain hinders the application of fragmentation approaches designed for non-conjugated polymers or small-molecule solids. The developed methodology is illustrated for archetypal thiophene-based polymers---polythiophene, PEDOT, and P3HT---to investigate how their molecular structure influences their electronic properties. The method requires 2-3 coarse-grained basis functions per monomer to accurately describe the top 2-3 eV of the valence band of these systems. The maximum interchain coupling of 200~meV is observed for well-aligned π-stacks. Sliding and tilting motions introduce a large thermal disorder to intermolecular couplings. Depending on the amplitude of this disorder and on the equilibrium interchain alignment, we observe two opposite cases: PEDOT and polythiophene. The π-stacked form of PEDOT has optimal alignment at average geometry and moderate thermal disorder, whereas polythiophene has moderate orbital overlap due to the herringbone geometry and large disorder reverting the sign of the couplings upon thermal fluctuations.