Understanding the electronic pi-system of 2D covalent organic frameworks with Wannier functions

We investigate a family of hexagonal 2D covalent organic frameworks (COFs) with phenyl and biphenyl spacer units and different chemical linker species. Chemical trends are elucidated and attributed to microscopic properties of the π-electron-system spanned by atomic p_z-orbitals. We systematically investigate the electronic structure, delocalization of electronic states, effects of disorder, bond torsion, and doping, and correlate these with variable π-conjugation and nucleus-independent chemical shift (NICS) aromaticity. Molecular orbitals are obtained from maximally localized Wannier functions that have σ- and π-character, forming distinct σ- and π-bands for all valence states. The Wannier-orbital description goes beyond simple tight-binding models and enables a detailed understanding of the electronic topology, effective electronic coupling and delocalization. It is shown that a meaningful comparison between COFs with different chemical elements can only be made by examining the entire π-electron system, while a comparison of individual bands (e.g., bands near the Fermi energy) can be a insufficient to derive general design rules for linker and spacer monomer selection. We further identify delocalized states that are spread across tens or hundreds of pores of the 2D COFs and analyze their robustness against structural and energetic disorders like out-of-plane rotations of molecular fragments, different strength of energetic disorder and energetic shifts due to chemical doping.