Dihedral-Angle-Controlled Crossover from Static Hole Delocalization to Dynamic Hopping in Biaryl Cation Radicals

Article abstract of DOI:10.1002/anie.201609695

In cases of coherent charge-transfer mechanism in biaryl compounds the rates follow a squared cosine trend with varying dihedral angle. Herein we demonstrate using a series of biaryl cation radicals with varying dihedral angles that the hole stabilization

Full text of DOI:10.1002/anie.201609695

Angewandte
Communications
Chemie
International Edition: DOI: 10.1002/anie.201609695
German Edition: DOI: 10.1002/ange.201609695
Conducting Materials
Hot Paper
Dihedral Angle-Controlled Crossover from Static Hole Delocalization
to Dynamic Hopping in Biaryl Cation Radicals
Marat R. Talipov, Tushar S. Navale, Mohammad M. Hossain, Ruchi Shukla, Maxim V. Ivanov,
and Rajendra Rathore*
Dedicated to Professor Michael R. Wasielewski
Abstract: In cases of coherent charge-transfer mechanism in
biaryl compounds the rates follow a squared cosine trend with
varying dihedral angle. Herein we demonstrate using a series of
biaryl cation radicals with varying dihedral angles that the hole
stabilization shows two different regimes where the mechanism
of the hole stabilization switches over from (static) delocaliza-
tion over both aryl rings to (dynamic) hopping. The exper-
imental data and DFT calculations of biaryls with different
dihedral angles unequivocally support that a crossover from
delocalization to hopping occurs at a unique dihedral angle
Scheme 1. The structures and naming scheme for biaryls.
where the electronic coupling (Hab) is one half of reorganiza-
tion (l), that is, Hab = l/2. The implication of this finding in
non-coherent charge-transfer rates is being investigated.
a polymethylene chain or tert-butyl groups linked at the 2 and
2’ positions (Scheme 1).
B
iaryl compounds represent the smallest building blocks for
exploration of the fundamental properties of the charge
transfer in p-conjugated molecular wires. For example, the
angular dependence of the charge transfer in biaryls has been
probed by conductance measurements using break-junction
techniques.[1–4] These measurements have shown that under
coherent transport mechanism the charge-transfer rates scale
as the square of the electronic coupling in biaryl compounds,
and since the electronic coupling varies with the interplanar
dihedral angle (f) between the aryl groups, the charge-
transfer rates follow a squared cosine trend with f.[5–8]
Importantly, the residence time for the charge onto biaryls
is expected to be negligible in coherent charge transport using
break-junction techniques.[2,4]
Electrochemistry, generation of cation radicals of 1—7,
and their electronic spectroscopy, X-ray crystallography, and
DFT calculations allow us to demonstrate for the first time
that the stabilization of a cationic charge (hole) in biaryls
follow a linear cosf trend only for small angles (f = 08 ꢀ458)
and breaks down at larger angles (f > 458) due to a crossover
of the hole stabilization mechanism from (static) delocaliza-
tion to (dynamic) hopping. We will demonstrate that the
crossover occurs due to the interplay between electronic
coupling, which varies with f and the structural/solvent
reorganization. Details of these findings are described herein.
Biaryls 1–6 and tBu-7 (7) were synthesized by adopting the
literature procedures,[9–11] and the experimental details includ-
ing X-ray structural data of 1–4 are compiled in the Support-
ing Information. The X-ray structures of 1–4 were accurately
reproduced by DFT calculations [B1LYP-40/6-31G(d) +
PCM(CH2Cl2)][12–16] (Figure S7). However, for higher homo-
logues 4–6, conformational search revealed the presence of
multiple conformers (Tables S10, S11). In order to establish
the true identity of the conformations of 2–7 in solution, we
resorted to 1H NMR spectroscopy.
Unlike the break-junction techniques, the non-coherent
charge transfer through a biaryl linkage would involve a finite
residence time onto the biaryl and would depend on the
interplay between the electronic coupling and the structural
reorganization. In such a charge-transfer scenario, it is unclear
how the f controls the mechanism of charge stabilization.
In order to address this question, we undertake synthesis
and study of a series of biaryls where f was varied with
The 1H NMR chemical shifts of aromatic protons are
highly sensitive to the dihedral angle f in biaryls.[17] The
chemical shieldings of the 2,2’-aryl protons for all possible
conformations of 1–7 were determined using a gauche-
independent atomic orbital (GIAO) approach (see the
Supporting Information for details). The linear relationship
between computed chemical shieldings of 2,2’-protons of the
lowest-energy conformer against the experimental chemical
shifts (Figure 1A) establishes the conformational identity of
1–7 in solution, as depicted in Figure 1B.
[*] Dr. M. R. Talipov, Dr. T. S. Navale, M. M. Hossain, Dr. R. Shukla,
Dr. M. V. Ivanov, Prof. R. Rathore
Department of Chemistry, Marquette University
Milwaukee, WI 53201-1881 (USA)
E-mail: rajendra.rathore@marquette.edu
Supporting information for this article, including synthesis and
characterization of biaryls 1–7, X-ray crystallography details, cyclic
voltammetry, and the generation and quantitative spectroscopic
analysis of the cation radicals of 1–7, can be found under:
http://dx.doi.org/10.1002/anie.201609695.
Angew. Chem. Int. Ed. 2016, 55, 1 – 5
ꢀ 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1
These are not the final page numbers!

Angewandte
Communications
Chemie
arenes, that is, 3,4-dimethoxytoluene (Eox1 = 0.87 V)[9] and
3,4-dimethoxy-1-tert-butylbenzene (Eox1 = 0.90 V).[18]
The cation radicals of 1–7 were generated by quan-
titative redox titrations using THE+CSbCl6
(THE =
ꢀ
1,2,3,4,5,6,7,8-octa-hydro-9,10-dimethoxy-1,4:5,8-dimethano-
anthracene,
E
red = 0.67 V,
and NAP+CSbCl6 (NAP = 1,2,3,4,7,8,9,10-
Ered
lmax = 518 nm,
emax =
[19]
ꢀ
7300 cmꢀ1mꢀ1
)
octahydro-1,1,4,4,7,7,10,10-octamethylnaphtacene,
=
0.94 V, lmax = 672 nm, emax = 9300 cmꢀ1mꢀ1) as aromatic oxi-
dants.[20,21] The redox titrations were performed by an
incremental addition of a neutral biaryl to a solution of
THE+C (or NAP+C) in CH2Cl2 at 228C, and the resulting
absorption spectra were quantitatively analyzed (section S4
in the Supporting Information) to obtain the absorption
spectra of 1+C–7+C (Figure 2B). The spectra of 1+C–4+C showed
a red shift of the low-energy band from 1098 to 1850 nm
while 5+C–7+C showed little variance in the position of the low-
energy band, but rather a dramatically reduced molar
absorptivity for the near-infrared band decreasing from 4+C
to 7+C (Figure 2B).
Figure 1. A) 1H NMR chemical shift of 2,2’-protons of 1–7 plotted
against the calculated/scaled (top/bottom axis) chemical shifts. The
lowest-/highest-energy conformers of 4–6 are shown by empty trian-
gles/filled circles. B) Superposition of the structures of 2–6 showing
the variation in dihedral angles with increasing number of methylenes.
Methoxy groups on one of aryl rings are omitted for clarity.
Reversible cyclic voltammograms of 1–7 provide the
oxidation potentials (Figure 2A), which show an increase of
about 0.5 V going from a planarized (i.e. 1, f = 08) to
perpendicularly oriented biaryls (i.e. 6 and 7, f ca. 908).
Interestingly, the Eox1 of biaryls with f ’ 90ꢁ (6: 0.83 V, 7:
0.87 V) were similar to Eox1 of the corresponding model
The X-ray crystallography of representative cation radi-
cals (1+CSbCl6 and 3+CSbCl6 ) shows considerable oxidation-
ꢀ
ꢀ
induced bond-length changes in the biaryls, especially in the
ꢀ
central aryl–aryl C C bond (by 0.036 ꢀ and 0.022 ꢀ, respec-
tively). See the Supporting Information for detailed analysis
of the X-ray structures and ORTEP diagrams. The dihedral
angle between the aryl moieties in 3+C (fCR; 258) showed an
oxidation-induced decrease of ca. 108.
The DFT calculations [B1LYP-40/6-31G(d) + PCM-
(CH2Cl2)] accurately reproduced the available X-ray struc-
tures and dihedral angles for neutral (i.e. f) and cation
radicals (i.e. fCR) of biaryls (Tables S7, S8 and Figures S8, S9).
The (TD-)DFT calculations of the structures of neutral and
cation radicals of 1–7 reproduced the experimental Eox1 and
the excitation energies for the lowest-energy transition in 1+C–
7+C (Figure S11). The calculated dihedral angles in the biaryl
cation radicals show an oxidation-induced decrease of 4–198
(Table S11), and the most pronounced changes in the dihedral
angle were observed with 4+C–6+C owing to the flexibility of the
polymethylene linker (Figure 1).
A comparison of the structures of neutral 1–7 and their
ꢀ
cation radicals shows that the central aryl–aryl C C bond in
1+C–7+C experiences the most notable shortening and variation
with the dihedral angle fCR (i.e. 2+C: 168, 3+C: 368, 4+C: 458, 5+C:
538, 6+C: 748, 7+C: 888) as depicted in Figure 3.
Most importantly, Figure 3 shows that the biaryls with
dihedral angles fCR = 0–458 (i.e. 1+C–4+C) exhibit (almost)
ꢀ
identical oxidation-induced central C C bond contraction
(0.04 ꢂ 0.002 ꢀ) and a complete delocalization of the hole
over both aryl moieties. In contrast, biaryls with a larger
ꢀ
dihedral angle fCR > 458 show a systematic decrease in the C
C bond shortening with increasing fCR, that is, 0.028 ꢀ in 5+C,
0.014 ꢀ in 6+C, and 0.004 ꢀ in 7+C and a concomitant increase
in the localization of the spin/charge on a single aryl moiety
(Figure 3). This surprising observation of two different
regimes based on dihedral angle, that is, complete versus
partial charge delocalization on two aryl moieties in biaryl
cation radicals, suggests that a change occurs in the mecha-
nism of charge delocalization/stabilization.
Figure 2. A) Cyclic voltammograms (CVs) of 2 mm 1–7 in CH2Cl2
(0.1m n-Bu4NPF6) at a scan rate of 200 mVsꢀ1 and 228C. The value of
Eox1 (vs. Fc/Fc+; Fc=ferrocene) is indicated in each CV. B) The
absorption spectra of 1+C–7+C in CH2Cl2 at 228C. The position of
lowest-energy band (in nm) and molar absorptivity (in Mꢀ1 cmꢀ1) are
shown on each spectrum.
2
www.angewandte.org
ꢀ 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2016, 55, 1 – 5
These are not the final page numbers!

Angewandte
Communications
Chemie
ꢀ
Figure 3. Changes in the oxidation-induced central aryl-aryl C C bonds
Figure 5. Typical examples of complete delocalization to partial or full
localization and nature of the accompanying electronic transition, as
shown by isovalue plots (ꢂ0.003 au) of spin-density distributions.
in various biaryls cation radicals against fCR and the corresponding
isovalue (ꢂ0.003 au) plots of spin-density distribution. The fraction of
spin/charge distribution per aryl moiety, obtained by the natural
population analysis,[22,23] is indicated below the structures. A vertical
line at 458 separates biaryls with completely delocalized (1+C–4+C)
versus partially/fully localized charge (5+C–7+C).
Supporting this view, plots of experimental Eox1 and nmax of
1+C–7+C, shown in Figure 4, also reveal two different trends in
the range of 0–458 and 45–908, where the biaryl with fCR
about 458 represents a crossover point (see Figure 4).
Excitation energies for the D0!D1 transition in biaryls 1+C–
4+C in the “0–458 regime” show a linear red shift against
cos(fCR), and the nature of this electronic transition is
consistent with completely delocalized ground and excited
states (Figure 5). The position of the D0!D1 transition in 5+C–
7+C in the “45–908 regime” remains largely unchanged except
reduced molar absorptivity with increasing fCR, and the
corresponding electronic transition was shown to have
a charge-transfer character (Figure 5). The cation radical
tBu-7+C with fCR about 908 shows that the charge is fully
localized onto one unit with extremely weak D0!D1 tran-
sition of charge-transfer character (Figure 5). The observed
angular dependence of redox and optical properties of 1+C–7+C
(Figure 4) and analysis of the nature of the D0!D1 transitions
(Figures 5 and S15) clearly suggests that there is crossover
from delocalization to hopping mechanism that depends on
a dihedral angle.
Figure 6. A plot of nmax against cos(fCR), obtained from the scan on
a model biaryl (structure shown) with the fCR step size of 58 [TD-
B1LYP-40/6-31G(d)+PCM(CH2Cl2)]. The nmax were scaled according to
linear trend with experiment (Figure S11B, Supporting Information).
The two distinct regions, separated by a blue line, are identified using
Marcus two-state model where Hab is the electronic coupling between
(charge-localized) diabatic states and l is the structural/solvent
reorganization parameter.[25]
a series of constrained optimizations with fixed fCR and
subsequent TD-DFT calculations provided the excitation
energies (nmax) at different dihedral angles f (see Figure 6).[24]
Because the electronic coupling Hab scales linearly with
cos(fCR),[26,27] the computed nmax in the model biaryl also
follow a linear dependence with cos(fCR) in 0–508 range
(Figure 6, red symbols) in accordance with Marcus two-state
model for fully delocalized systems (Figure 6, bottom right).
In contrast, the crossover from the linear nmax/cos(fCR) trend
in model biaryl with f > 508 is surprising considering that the
electronic coupling Hab continues to decrease linearly with
cos(fCR). The invariance of nmax with the increasing fCR
(Figure 6, blue symbols) signifies, based on the Marcus
model (Figure 6, top left), that the charge transfer occurs by
the hole hopping and thereby nmax directly provides the value
of reorganization energy, that is, nmax = l.[25] Thus, the inter-
play between the invariant l and decreasing Hab in model
biaryl with f > 508 represents the cases where 2Hab < l, that
is, hole distribution switches over from complete delocaliza-
tion over both aryl units (i.e. 2Hab ꢃ l) to partial and then full
hole localization onto a single aryl unit. The crossover point in
As the biaryls 1–7 do not probe the entire continuum of
dihedral angles, we carried out a systematic computational
scan on a model biaryl cation radical (Figure 6), where
Figure 4. Plots of Eox1 of 1–7 (A) and nmax of 1+C–7+C (B) against
cos(fCR). A vertical line at 458 separates biaryls with different linear
trends, that is, 1+C–4+C (full circles) versus 5+C–7+C (empty circles).
Angew. Chem. Int. Ed. 2016, 55, 1 – 5
ꢀ 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.angewandte.org
3
These are not the final page numbers!

Angewandte
Communications
Chemie
such a system is thus expected to occur when 2Hab = l
(Figure 4B). Interestingly, the crossover point of 508 obtained
by computational scan of a model biaryl is rather similar to
the experimental crossover point of about 458 observed for
biaryls 1–7 (compare Figure 4B and Figure 6).
In summary, we have demonstrated for the first time using
a well-defined series of biaryl cation radicals with varied
interplanar dihedral angles that a crossover occurs from
a fully delocalized regime to a mixed-valence regime because
of the interplay between the electronic coupling and reor-
ganization energy. The observation of a crossover point
between two regimes is expected because it represents
a unique point where the reorganization energy is exactly
one half of the electronic coupling, that is, Hab = l/2.
Thus, the linear dependence of charge-transfer rates
against cos2f trend[28] over the entire range of dihedral
angles under a coherent tunneling mechanism should be
contrasted with non-coherent mechanism, where the hole
stabilization mechanism changes from (static) delocalization
to (dynamic) hopping at a unique dihedral angle. Note that
such crossover dihedral angle must satisfy the condition of
[1] D. Vonlanthen, A. Mishchenko, M. Elbing, M. Neuburger, T.
Wandlowski, M. Mayor, Angew. Chem. Int. Ed. 2009, 48, 8886;
Angew. Chem. 2009, 121, 9048.
[2] A. Mishchenko, D. Vonlanthen, V. Meded, M. Burkle, C. Li, I. V.
Pobelov, A. Bagrets, J. K. Viljas, F. Pauly, F. Evers, Nano Lett.
2009, 10, 156.
[3] L. Cui, B. Liu, D. Vonlanthen, M. Mayor, Y. Fu, J.-F. Li, T.
Wandlowski, J. Am. Chem. Soc. 2011, 133, 7332.
[4] L. Venkataraman, J. E. Klare, C. Nuckolls, M. S. Hybertsen,
M. L. Steigerwald, Nature 2006, 442, 904.
[5] A. Heckmann, C. Lambert, Angew. Chem. Int. Ed. 2012, 51, 326;
Angew. Chem. 2012, 124, 334.
[6] D. Hanss, O. S. Wenger, Eur. J. Inorg. Chem. 2009, 3778.
[7] K. E. Spettel, N. H. Damrauer, J. Phys. Chem. C 2016, 120,
10815.
[8] A. C. Benniston, A. Harriman, Chem. Soc. Rev. 2006, 35, 169.
[9] L. Zhai, R. Shukla, S. H. Wadumethrige, R. Rathore, J. Org.
Chem. 2010, 75, 4748.
[10] L. Zhai, R. Shukla, R. Rathore, Org. Lett. 2009, 11, 3474.
[11] R. Shukla, R. Rathore, Synthesis 2008, 3769.
[12] M. R. Talipov, A. Boddeda, S. V. Lindeman, R. Rathore, J. Phys.
Chem. Lett. 2015, 6, 3373.
[13] M. R. Talipov, T. S. Navale, R. Rathore, Angew. Chem. Int. Ed.
2015, 54, 14468 – 14472; Angew. Chem. 2015, 127, 14676 – 14680.
[14] M. R. Talipov, R. Jasti, R. Rathore, J. Am. Chem. Soc. 2015, 137,
14999.
Hab = l/2 and therefore the crossover angles will be different
for different molecules owing to the varied reorganization
energies and electronic couplings. The studies of non-
coherent charge-transfer rates will be undertaken using
donor-biaryl-acceptor triads with varied dihedral angles in
order to demonstrate the implication of the crossover of the
hole stabilization mechanism from delocalization to hopping.
[15] M. R. Talipov, A. Boddeda, Q. K. Timerghazin, R. Rathore, J.
Phys. Chem. C 2014, 118, 21400.
[16] M. R. Talipov, M. V. Ivanov, R. Rathore, J. Phys. Chem. C 2016,
120, 6402.
[17] R. B. Bates, F. A. Camou, V. Kane, P. K. Mishra, K. Suvanna-
chut, J. J. White, J. Org. Chem. 1989, 54, 311.
[18] See CVs in the Supporting Information.
[19] R. Rathore, C. L. Burns, M. I. Deselnicu, Org. Synth. 2005, 1.
[20] R. Rathore, J. K. Kochi, Acta Chem. Scand. 1998, 52, 114.
[21] R. Rathore, C. L. Burns, M. I. Deselnicu, Org. Lett. 2001, 3, 2887.
[22] A. E. Reed, L. A. Curtiss, F. Weinhold, Chem. Rev. 1988, 88, 899.
[23] F. Weinhold, C. R. Landis in Valency and bonding: a natural
bond orbital donor-acceptor perspective, Cambridge University
Press, Cambridge, 2005.
[24] Compare the plot of calculated nmax of different conformers of
1+C–7+C against the cos(fCR) in Figure S12 in Supporting Infor-
mation with Figure 6.
Acknowledgements
We thank NSF (CHE-1508677) and NIH (R01-HL112639-04)
for financial support, Dr. Sergey V. Lindeman for X-ray
crystallography, and Professors James Gardinier and Scott
Reid for helpful discussions. The calculations were performed
on the Pꢁre cluster (Marquette University) and XSEDE
(NSF, TG-CHE130101).
[25] B. S. Brunschwig, C. Creutz, N. Sutin, Chem. Soc. Rev. 2002, 31,
168.
[26] R. S. Mulliken, J. Chim. Phys. Phys.-Chim. Biol. 1949, 46, 497.
[27] G. D. Scholes, R. D. Harcourt, K. P. Ghiggino, J. Chem. Phys.
1995, 102, 9574.
[28] In case of coherent tunneling charge-transfer mechanism, the
rate of the charge transfer in biaryls is proportional to square of
the coupling and, therefore, varies linearly with cos2f, see
Refs. [2,4,25].
Conflict of interest
The authors declare no conflict of interest.
Keywords: charge transfer · delocalization · electronic coupling ·
incoherent hopping · radical cations
Manuscript received: October 3, 2016
Final Article published: && &&, &&&&
4
www.angewandte.org
ꢀ 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2016, 55, 1 – 5
These are not the final page numbers!

Angewandte
Communications
Chemie
Communications
Conducting Materials
Charge transport in biaryls: A dihedral
angle-dependent crossover of mecha-
nisms from static delocalization to
dynamic hopping in biaryl cation radicals
was observed (see picture). The exper-
imental data and DFT calculations
unequivocally support that a crossover
from delocalization to hopping occurs at
a unique dihedral angle where the elec-
tronic coupling is exactly one half of the
reorganization energy.
M. R. Talipov, T. S. Navale,
M. M. Hossain, R. Shukla, M. V. Ivanov,
R. Rathore*
&&&& — &&&&
Dihedral Angle-Controlled Crossover
from Static Hole Delocalization to
Dynamic Hopping in Biaryl Cation
Radicals
Angew. Chem. Int. Ed. 2016, 55, 1 – 5
ꢀ 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.angewandte.org
5
These are not the final page numbers!