Quantifying Planarity in the Design of Organic Electronic Materials

Planarity is essential for many organic electronic materials as it maximizes the intramolecular π-orbital overlap and enables efficient intermolecular interactions through π-stacking. We propose a statistical way of quantifying the planarity of a wide range of conjugated systems. The quantification takes into account all torsional conformations and their relative contribution to the overall structural disorder, through a planarity index ⟨cos² ϕ⟩. The propensity for planarization and the effect of rotational disorder were examined for a series of commonly used building blocks. The application of the analysis to extended conjugated systems and the correlations between the gas-phase ⟨cos² ϕ⟩ and crystallographically observed planarity in the solid state were explored. Our calculations also reveal a previously unrecognized effect of increasing band gap upon planarization for conjugated systems coupling strong electron donor and acceptor units.