Hückel Theory + Reorganization Energy = Marcus–Hush Theory: Breakdown of the 1/n Trend in π-Conjugated Poly-p-phenylene Cation Radicals Is Explained

详细信息    查看全文

• 作者：Maxim V. IvanovMarat R. Talipov ; Anitha BoddedaSameh H. Abdelwahed ; Rajendra Rathore
• 刊名：Journal of Physical Chemistry C
• 出版年：2017
• 出版时间：January 26, 2017
• 年：2017
• 卷：121
• 期：3
• 页码：1552-1561
• 全文大小：761K
• ISSN：1932-7455

文摘

Among the π-conjugated poly-p-phenylene wires, fluorene-based poly-p-phenylene (FPP_n) wires have been extensively explored for their potential as charge-transfer materials in functional photovoltaic devices. Herein, we undertake a systematic study of the redox and optical properties of a set of FPP_n (n = 2–16) wires. We find that, while their absorption maxima (ν_abs) follow a linear trend against cos[π/(n + 1)] up to the polymeric limit, redox potentials (E_ox) show an abrupt breakdown from linearity beginning at n ∼ 8. These observations prompted the development of a generalized model to describe the unusual evolution of redox and optical properties of poly-p-phenylene wires. We show that the cos[π/(n + 1)], commonly expressed as 1/n, dependence of the properties of various π-conjugated wires has its origin in Hückel molecular orbital (HMO) theory, which however, fails to predict the evolution of the redox potentials of these wires, as the oxidation-induced structural/solvent reorganization is unaccounted for in the original formulation of HMO theory. Accordingly, aided by DFT calculations, we introduce here a modified HMO theory that incorporates the reorganization energy (Δα) and coupling (β) and show that the modified theory provides an accurate description of the oxidized FPP_n wires, reproducing the breakdown in the linear cos[π/(n + 1)] trend. A comparison with the Marcus-based multistate model (MSM), where reorganization (λ) and coupling (H_ab) are introduced by design with the aid of empirically adjusted parameters, further confirms that the structural/solvent reorganization limits hole delocalization to ∼8 p-phenylene units and leads to the breakdown in the linear evolution of the redox properties against cos[π/(n + 1)]. The predictive power of the modified HMO theory and MSM offer new tools for rational design of the next-generation, long-range charge-transfer materials for photovoltaics and molecular electronics applications.