Quantifying the Effect of Intermonomer Improper Angles on Electron Delocalization in Conjugated Polymers

Electron delocalization between monomers in conjugated polymers influences both the charge transport and the mechanical properties of this class of materials. While this delocalization is generally understood to be maximized by coplanar monomer arrangements that enable π-orbital overlap, the precise geometric factors controlling delocalization remain incompletely characterized. Current molecular mechanics (MM) models of conjugated polymers primarily focus on intermonomer dihedral torsion, neglecting the potential effects of out-of-plane ("improper") torsion between monomers. Here, we develop a method to isolate and quantify improper dihedral torsion effects on the electronic structure of dimer or donor-acceptor unit structures for three representative polymers: P3HT, PTB7, and PNDI-T. Quantum mechanical calculations reveal that improper torsion generally disrupts electronic delocalization, though PNDI-T maintains significant conjugation even at improper angles up to 30°─likely due to its extended π-system. While coupling between improper and dihedral torsion is observed, the energetic effects appear to be minimal (<1 kcal/mol) under typical conditions. These findings suggest that existing MM models may safely omit improper torsion parameters for simulations of local structures and motivates future studies aimed at quantifying its effect on larger-scale polymer films. Finally, to aid interpretation of these results, we have developed an interactive visualization tool that simultaneously displays delocalization energy profiles and 3D electron density isosurfaces.