jp6b12111_si_002.txt (136.46 kB)
Hückel Theory + Reorganization Energy = Marcus–Hush Theory: Breakdown of the 1/n Trend in π‑Conjugated Poly‑p‑phenylene Cation Radicals Is Explained
dataset
posted on 2017-01-03, 00:00 authored by Maxim
V. Ivanov, Marat R. Talipov, Anitha Boddeda, Sameh H. Abdelwahed, Rajendra RathoreAmong
the π-conjugated poly-p-phenylene
wires, fluorene-based poly-p-phenylene (FPPn) 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 FPPn (n = 2–16) wires. We find that, while
their absorption maxima (νabs) follow a linear trend
against cos[π/(n + 1)] up to the polymeric
limit, redox potentials (Eox) 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 FPPn 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 (Hab) 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.