Inclusion of Asymptotic Dependence of Reorganization Energy in the Modified Marcus-Based Multistate Model Accurately Predicts Hole Distribution in Poly‑p‑phenylene Wires

We recently developed an intuitive multistate parabolic model (MPM), based on the Marcus two-state model, to describe the redox and optical properties and spin/charge distribution in the cation radicals of different poly-p-phenylene wires and showed that MPM predictions closely matched, in most cases, with the experimental and computational findings. Application of MPM to different classes of poly-p-phenylene-based wires led us to recognize that its performance is not optimal in certain cases, especially in describing the hole distribution in second excited states of poly-p-phenylene wires due to the quadratic shape of the reorganization function. In this work we show that a revised multistate model (MSM), where parabolas were replaced with a composite quadratic/reciprocal function, successfully addresses these issues by taking into account the differing energetic requirement for near and distant units by quadratic and reciprocal components of the reorganization function, respectively. Moreover, the necessity of usage of the reciprocal component of the (composite) quadratic/reciprocal function was consistent with the Marcus equations for describing the reorganization energy and further supported by the constrained DFT calculations. The revised model (MSM) accurately describes the spin/charge distribution in the ground and excited states of various poly-p-phenylene wires and is expected to serve as a versatile and powerful predictive tool for the design and synthesis of next-generation charge-transfer materials for photovoltaic applications.