%0 DATA
%A Maxim
V., Ivanov
%A Marat R., Talipov
%A Anitha, Boddeda
%A Sameh H., Abdelwahed
%A Rajendra, Rathore
%D 2017
%T Hückel Theory + Reorganization Energy = Marcus–Hush
Theory: Breakdown of the 1/*n* Trend in π‑Conjugated
Poly‑*p*‑phenylene Cation Radicals Is
Explained
%U https://acs.figshare.com/articles/Hu_ckel_Theory_Reorganization_Energy_Marcus_Hush_Theory_Breakdown_of_the_1_i_n_i_Trend_in_Conjugated_Poly_i_p_i_phenylene_Cation_Radicals_Is_Explained/4542877
%R 10.1021/acs.jpcc.6b12111.s001
%2 https://ndownloader.figshare.com/files/7356157
%K phenylene wires
%K Marcus-based multistate model
%K evolution
%K breakdown
%K FPP n wires
%K co
%K poly
%K HMO theory
%K DFT
%K charge-transfer materials
%K FPP n
%K MSM
%K redox potentials
%K reorganization
%X 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.