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.