Multistate Parabolic Model: A Unified Framework for Understanding Charge Distribution in π-Conjugated Oligomers

π-Conjugated oligomers hold great promise for advancing molecular electronics and photovoltaics due to their distinctive electronic properties. Understanding the charge distribution within these systems is essential for exploring their full potential. This study introduces the application of the multistate parabolic model (MPM) to elucidate the distribution of negative charges, or polarons, in π-conjugated oligomers. Through a comparative analysis of nine p-phenylene-based oligomer series with density functional theory (DFT) calculations, we demonstrate that MPM accurately reproduces polaron distribution across various oligomer configurations, including hydrogen-capped, asymmetric one-side carbonyl-capped, and symmetric two-side carbonyl-capped oligomers. Our findings reveal a consistent charge localization pattern within the central oligomer units for uncapped oligomers and delineate the effects of terminal capping groups on charge distribution. The MPM's robustness in modeling both radical cations and anions underscores its potential as an efficient tool for the rapid evaluation and prediction of electronic properties in new molecular assemblies.