Decoupling Planarizing and Steric Energetics to Accurately Model the Rigidity of π-Conjugated Polymers

The π-conjugated backbone of semiconducting polymers gives rise to both their electronic properties and structural rigidity. However, current computational methods for understanding the rigidity of polymer chains fail in one crucial way. Namely, standard torsional scan (TS) methods do not satisfactorily capture the behavior of polymers exhibiting a high degree of steric hindrance. This deficiency in part stems from the method by which torsional scans decouple energy related to electron delocalization from that related to nonbonded interactions. These methods do so by applying classical corrections of the nonbonded energy to the quantum mechanical (QM) torsional profile for polymers that are highly sterically hindered. These large corrections to the energy from nonbonded interactions can substantially skew the calculated QM energies related to torsion, resulting in an inaccurate or imprecise estimation of the rigidity of a polymer. As a consequence, simulations of the morphology of a highly sterically hindered polymer using the TS method can be highly inaccurate. Here, we describe an alternative, generalizable method by which the delocalization energy can be decoupled from the energy associated with nonbonded interactions─the "isolation of delocalization energy" (DE) method. From torsional energy calculations, we find that the relative accuracy of the DE method is similar to the TS method (within 1 kJ/mol) for two model polymers (P3HT, PTB7) when compared to quantum mechanical calculations. However, the DE method significantly increased the relative accuracy for simulations of PNDI-T, a highly sterically hindered polymer (8.16 kJ/mol). Likewise, we show that comparison of the planarization energy (i.e., backbone rigidity) from torsional parameters is significantly more precise for both PTB7 and PNDI-T when using the DE method as opposed to the TS method. These differences affect the simulated morphology, with the DE method predicting a significantly more planar configuration of PNDI-T.