Energy Gap between the Poly-p-phenylene Bridge and Donor Groups Controls the Hole Delocalization in Donor-Bridge-Donor Wires

Article abstract of DOI:10.1021/jacs.6b09209

Poly-p-phenylene wires are critically important as charge-transfer materials in photovoltaics. A comparative analysis of a series of poly-p-phenylene (^RPP_n) wires, capped with isoalkyl (^iAPP_n), alkoxy (^ROPP_n), and dialkylamino (^R2NPP_n) groups, shows unexpected evolution of oxidation potentials, i.e., decrease (-260 mV) for ^iAPP_n, while increase for ^ROPP_n (+100 mV) and ^R2NPP_n (+350 mV) with increasing number of p-phenylenes. Moreover, redox/optical properties and DFT calculations of ^R2NPP_n/^R2NPP_n^+? further show that the symmetric bell-shaped hole distribution distorts and shifts toward one end of the molecule with only 4 p-phenylenes in ^R2NPP_n^+?, while shifting of the hole occurs with 6 and 8 p-phenylenes in ^ROPP_n^+? and ^iAPP_n^+?, respectively. Availability of accurate experimental data on highly electron-rich dialkylamino-capped ^R2NPP_n together with ^ROPP_n and ^iAPP_n allowed us to demonstrate, using our recently developed Marcus-based multistate model (MSM), that an increase of oxidation potentials in ^R2NPP_n arises due to an interplay between the electronic coupling (H_ab) and energy difference between the end-capped groups and bridging phenylenes (Δ?). A comparison of the three series of ^RPP_n with varied Δ? further demonstrates that decrease/increase/no change in oxidation energies of ^RPP_n can be predicted based on the energy gap Δ? and coupling H_ab, i.e., decrease if Δ? < H_ab (i.e., ^iAPP_n), increase if Δ? > H_ab (i.e., ^R2NPP_n), and minimal change if Δ? ≈ H_ab (i.e., ^ROPP_n). MSM also reproduces the switching of the nature of electronic transition in higher homologues of ^R2NPP_n^+? (n ≥ 4). These findings will aid in the development of improved models for charge-transfer dynamics in donor-bridge-acceptor systems.

Full text of DOI:10.1021/jacs.6b09209

Subscriber access provided by UNIV TORONTO
Article
Energy Gap between the Poly-p-phenylene Bridge and Donor Groups
Controls the Hole Delocalization in Donor–Bridge–Donor Wires
Denan Wang, Marat R. Talipov, Maxim V. Ivanov, and Rajendra Rathore
J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 23 Nov 2016
Downloaded from http://pubs.acs.org on November 23, 2016
Just Accepted
“Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted
online prior to technical editing, formatting for publication and author proofing. The American Chemical
Society provides “Just Accepted” as a free service to the research community to expedite the
dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts
appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been
fully peer reviewed, but should not be considered the official version of record. They are accessible to all
readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered
to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published
in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just
Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor
changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers
and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors
or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Journal of the American Chemical Society is published by the American Chemical
Society. 1155 Sixteenth Street N.W., Washington, DC 20036
Published by American Chemical Society. Copyright © American Chemical Society.
However, no copyright claim is made to original U.S. Government works, or works
produced by employees of any Commonwealth realm Crown government in the course
of their duties.

Page 1 of 10
Journal of the American Chemical Society
1
2
3
4
5
6
7
8
9
Energy Gap between the Poly-p-phenylene Bridge and
Donor Groups Controls the Hole Delocalization in
Donor–Bridge–Donor Wires
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Denan Wang, Marat R. Talipov, Maxim V. Ivanov, and Rajendra Rathore*
Department of Chemistry, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881
Charge transfer, poly-p-phenylene wires, Marcus theory
ABSTRACT: Poly-p-phenylene wires are critically important as charge-transfer materials in photovoltaics. A comparative analysis
of a series of poly-p-phenylene (RPPn) wires, capped with isoalkyl (iAPPn), alkoxy (ROPPn), and dialkylamino (R2NPPn) groups, shows
unexpected evolution of oxidation potentials, i.e. decrease (-260 mV) for iAPPn, while increase for ROPPn (+100 mV) and R2NPPn
(+350 mV) with increasing number of p-phenylenes. Moreover, redox/optical properties and DFT calculations of R2NPPn/R2NPPn
+•
further show that the symmetric bell-shaped hole distribution distorts and shifts toward one end of the molecule with only 4 p-
phenylenes in R2NPPn+•, while shifting of the hole occurs with 6 and 8 p-phenylenes in ROPPn+• and iAPPn+•, respectively. Availability
of accurate experimental data on highly electron-rich dialkylamino-capped R2NPPn together with ROPPn and iAPPn allowed us to
demonstrate using our recently-developed Marcus-based multi-state model (MSM) that an increase of oxidation potentials in
R2NPPn arises due to an interplay between the electronic coupling (Hab) and energy difference between the end-capped groups and
bridging phenylenes (∆ε). A comparison of the three series of RPPn with varied ∆ε further demonstrate that decrease/increase/no
R
change in oxidation energies of PPn can be predicted based on the energy gap ∆ε and coupling Hab, i.e. decrease if ∆ε < Hab (i.e.
iAPPn), increase if ∆ε > Hab (i.e. R2NPPn), and minimal change if ∆ε ≈ Hab (i.e. ROPPn). MSM also reproduces the switching of the na-
ture of electronic transition in higher homologues of R2NPPn+• (n≥4). These findings will aid in development of improved models for
charge-transfer dynamics in donor-bridge-acceptor systems.
INTRODUCTION
Development of efficient π-conjugated molecular wires for
long-range charge transfer remains a highly sought goal for
photovoltaics and molecular electronics applications.1-5 To
this end, the identification of the parameters influencing
charge delocalization in para-phenylene-based molecular
wires is critically important for the guided design of efficient
charge-transfer materials for modern applications. Recently,
we showed that a single positive charge (i.e. hole) in long (n >
7) poly-p-phenylene wires (PPn) delocalizes only onto seven p-
phenylene units, and lies in the center of the π-conjugated
chain (Figure 1) owing to the interplay between the energetic
gain from charge delocalization and concomitant energetic
penalty from the structural/solvent reorganization.6 Further-
more, in end-capped poly-p-phenylene wires (RPPn) with elec-
tron-donating substituents (i.e. R = iA or RO), the hole is ob-
served to gravitate toward one end of the molecule to make
use of the electron-donating terminal units for hole stabiliza-
tion (Figure 1). The observed displacement of the hole toward
one end in RPPn and its consequences to the redox and optical
properties were reproduced by a versatile Marcus-based mul-
Figure. 1. Per-unit hole distribution in various poly-p-phenylene
wires (as indicated) [B1LYP-40/6-31G(d)+PCM(CH2Cl2)], and the
corresponding hole distribution bar plots reproduced by the mul-
tistate model (bottom panel).6
tistate parabolic model (MPM), where energies of the substi-
tuted terminal units with respect to bridging p-phenylenes
were lowered (by ∆ε) while the coupling (Hab) and the reor-
ganization parameter λ were kept constant for all RPPn, where
R = H, iA, RO (Figure 1, bottom).6
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 2 of 10
A curious finding of this work was that, while the oxidation however its solubility was decreased rather sharply
potentials of isoalkyl-capped iAPPn showed an expected de-
crease with increasing number of p-phenylene units (n), the
alkoxy-capped ROPPn showed a modest increase with n. In
order to examine this further, in this study we investigate
redox and optoelectronic properties of poly-p-phenylene
wires capped with highly electron-rich N,N-diisopropylamino
substituents (i.e. R2NPPn). A cursory examination of R2NPPn
using our MPM with identical parameter Hab/λ and the one
variable parameter ∆ε, which was significantly larger for
(<1 mg/10 mL in CH2Cl2), in line with our previous observation
with higher homologues of other RPPn.6,22 The model com-
pounds tBu/R2NPPn were similarly obtained as summarized in
Scheme 1C. The structures of various R2NPPn and model
tBu/R2NPPn were established by 1H/13C NMR spectroscopy, mass
spectrometry, and were further confirmed by X-ray crystal-
lography of representative molecules (see Section S6, S7 in
the Supporting Information).
1
2
3
4
5
6
7
8
9
Electrochemistry. The oxidation potentials of R2NPPn and
model tBu/R2NPPn were measured by electrochemical oxidation
at a platinum electrode of 2 mM solutions in anhydrous
CH2Cl2 containing 0.1 M tetra-n-butylammonium hexafluoro-
phosphate (n-Bu4NPF6), and were referenced to added 1,4-
dimethoxy-2,5-dimethylbenzene (Eox = 0.66 V vs. Fc/Fc+) as an
internal standard.23,24 The voltammograms of R2NPPn and
model compounds, which are all reversible, are compiled in
Figure 3. Interestingly, a comparison of the Eox1 values of
R2NPPn, referenced to Fc/Fc+, showed an increase of ~350 mV
moving from n = 2 (Eox1 = -0.08 V) to 3 (Eox1 = 0.15 V) to 4 (Eox1
= 0.27 V), remaining constant for n = 5 and 6 (Figure 3, Table
1).25 In contrast, the oxidation potentials of model tBu/R2NPPn
were invariant with increasing number of p-phenylenes, and
R
R2NPPn (Figure 2) in comparison to other PPn, indicated that
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
the hole is shifted toward one end of the wire with just two
bridging p-phenylene units (i.e. R2NPP4+•).
their Eox1 values (0.27 ± 0.02 V) were close to that of R2NPP4-6
,
Figure 2. Graphical depiction of multistate model applied to dial-
kylamino-capped poly-p-phenylenes and comparison with other
RPPn cation radicals.
+•
which suggests that the extent of hole stabilization in R2NPPn
(n ≥ 4) and model tBu/R2NPPn+• is similar.
Scheme 1. Synthetic schemes for the preparation of R2NPPn
and model tBu/R2NPPn
In order to provide a detailed picture of the critical role of
energy gap between the terminal and bridging p-phenylene
units on the extent of hole distribution and evolution of oxi-
dation energies,7-11 we undertook the syntheses of a series of
R2NPPn (n = 2–6) and model compounds tBu/R2NPPn (n = 2–4)
containing N,N-diisopropylamino and tert-butyl groups at the
opposite ends.5 The availability of this new series of poly-p-
phenylene wires and the precise redox and optical data of
their cation radicals and X-ray structures allow us to probe
the extent of hole delocalization and evolution of their redox
and optical properties in comparison with other RPPn wires. A
DFT and MPM analysis of these experimental findings reveals
that the energy gap between the terminal and bridging p-
R
phenylene units in various PPn controls the evolution of re-
dox and optical properties. The details of these findings are
discussed herein.
RESULTS AND DISCUSSION
Synthesis of R2NPPn and model tBu/R2NPPn. Synthesis and
study of a series of N,N-diisopropylamino-capped R2NPPn wires
was undertaken instead of more readily-available N,N-
diarylamino-capped wires because of the complications from
significant hole delocalization on the additional aryl groups
linked to nitrogens.9-18 The diisopropylamino group was cho-
sen as capping groups because the resulting R2NPPn wires un-
derwent reversible electrochemical oxidation unlike dimethyl-
or diethylamino-capped wires.19 An oxidative coupling of N,N-
diisopropylaniline readily afforded R2NPP2 (see the Supporting
Information for details). The synthesis of higher homologues
(n = 3–5) was accomplished via efficient Suzuki coupling20,21
between 1-bromo-4-N,N-diisopropylaminobenzene and bis-
boronic esters of benzene, biphenyl, and terphenyl, see
Scheme 1A. The synthesis of R2NPP6 is depicted in Scheme 1B,
ACS Paragon Plus Environment

Page 3 of 10
Journal of the American Chemical Society
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Figure. 3. Cyclic (blue lines) and square-wave (red lines) voltam-
mograms of 2 mM R2NPPn (left) and tBu/R2NPPn (right) in CH2Cl2 (0.1
M n-Bu4NPF6) at a scan rate of 200 mV s-1 and 22 ºC. The scale for
measure of current (in μA) for each cyclic voltammogram is
shown in blue color.
Generation and electronic spectroscopy of the cation radi-
cals. The relatively low oxidation potentials of R2NPPn and the
model compounds allowed for ready generation of their cati-
on radicals in solution by quantitative redox titration using a
–
well-characterized aromatic cation radical THE+•SbCl6 (THE =
1,2,3,4,5,6,7,8-octahydro-9,10-dimethoxy-1,4:5,8-dimethano-
anthracene) as an oxidant (Ered1 = 0.67 V vs Fc/Fc+, λmax = 518
nm, εmax = 7300 cm-1 M-1).26 For example, Figure 4A compiles
the electronic spectra obtained by an incremental (sub-
stoichiometric) addition of a CH2Cl2 solution of tBu/R2NPP2 to a
–
solution of THE+•SbCl6 , which showed a complete consump-
tion of the oxidant and formation of tBu/R2NPP2 after the ad-
+•
dition of 1 equivalent of tBu/R2NPP2. A careful quantification at
each titration point by a recently described deconvolution
procedure12,27 further established a 1:1 stoichiometry of the
redox reaction, i.e. tBu/R2NPP2 + THE+•
→
tBu/R2NPP2+• + THE. The
cation radical spectra of various R2NPPn and the model com-
pounds shown in Figure 4B were generated similarly (Section
S5 in the Supporting Information). Note that the absorption
spectra of R2NPPn+• and tBu/R2NPPn+• in Figure 4B did not change
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 4 of 10
either upon a tenfold increase in their concentration or tem-
graphic characterization. For example, the single crystals of
perature lowering to -50 ºC.28
R2NPP2+• SbCl6 were obtained from a mixture of CH2Cl2 and
hexanes at -10 ºC, see the Supporting Information for details.
Availability of the precise X-ray structures of the neutral (Fig-
ure 5A) and cation radical (Figure 5B) of R2NPP2 established
that a single charge is fully delocalized over both aryl groups
as judged by the oxidation-induced bond length changes (Fig-
ure 5D). Moreover, the oxidation-induced shortening of the
central C-C bond (from 1.482 Å to 1.433 Å) and decrease of
the interplanar dihedral angle between two p-phenylenes
(from 20.7º to 0.3º) further attests to the complete delocali-
zation of the charge (Figure 5C, D).
–
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
It is particularly noteworthy that the elongations of the
bonds in R2NPP2+• were observed at the positions of the bond-
ing lobes of HOMO, whereas the contractions of bonds at the
positions of antibonding lobes of HOMO, and all bond length
changes were in close agreement with those obtained by the
DFT calculations (Figure 5D). Unfortunately, repeated at-
tempts to obtain the single crystals of the higher homologues
of R2NPPn+• were thus far unsuccessful.
Table 1. Compilation of experimental oxidation potentials Eox1
(V vs Fc/Fc+), absorption λmax (nm)/εmax (103 M-1cm-1) and
emission λem(nm) of R2NPPn and tBu/R2NPPn and absorption λmax
+•
(nm)/εmax(103 M-1cm-1) of R2NPPn+• and tBu/R2NPPn
.
+•
RPPn
RPPn
n
Eox1
λmax
εmax
λem
λmax
εmax
39
3
105
5
2
3
4
5
6
2
3
4
-0.084
329
26.6
28.6
35.3
13.5
6.8
41
4
171
8
0.152
0.268
0.268
0.268
0.252
0.284
0.270
342
348
349
347
312
334
343
42.1
37.5
45.0
-b-
44
6
R2NPPn
840
870
820
713
826
880
47
1
47
6
-b-
Figure 4. A: Spectral changes and corresponding evolution of
mole fractions of oxidant and electron donor cation radicals on
the representative titration of tBu/R2NPP2 with 42 μM THE+• in
CH2Cl2 at 22 ºC. B: Compilation of the absorption spectra of
CH2Cl2 solutions of the cation radicals of R2NPPn (solid lines) and
tBu/R2NPPn (dotted lines) plotted against molar absorptivity at
22 ºC.
37
3
18.5
17.0
21.0
18.9
17.2
14.6
42
1
tBu/R2NPPn
45
6
+•
A comparison of the absorption spectra of R2NPPn showed
a The UV/vis absorption and emission spectra of neutral compounds were
recorded in CH2Cl2 at 22 ºC; see Figures S1 and S2 in the Supporting In-
formation. bOwing to the poor solubility of R2NPP6, its quantitative data
could not be obtained (also see Figures S3, S4 and S8 in the Supporting
Information).
that the low-energy band with prominent vibronic structure
in R2NPP2 (1055 nm) is red shifted in R2NPP3 (1718 nm)
+•
+•
whereas in higher homologues R2NPP4 and R2NPP5 it shifted
+•
+•
back to higher energy (840 and 870 nm, respectively). Inter-
estingly, the absorption spectra of R2NPP4 and R2NPP5 and
the positions of the low-energy bands were strikingly similar
to the cation radical spectrum of model tBu/R2NPP4+•, see Figure
4B and Table 1. Consistent with the electrochemical analysis
presented above, electronic spectroscopy of the cation radi-
+•
+•
+•
+•
cal of R2NPPn and model tBu/R2NPPn indicates that the hole
delocalization/stabilization in R2NPPn (n ≥ 4) must be very
+•
similar to that in the model compounds.
+•
X-ray crystallography. The high stability of various R2NPPn
prompted us to grow single crystals for their X-ray crystallo-
ACS Paragon Plus Environment

Page 5 of 10
Journal of the American Chemical Society
31G(d)+PCM(CH2Cl2)]. Also see Figures S13 and S14 in the Sup-
1
porting Information.
2
3
4
5
6
7
8
9
The spin/charge distribution plots presented in Figure 6
clearly show that in R2NPPn+• with n ≥ 4 and model compounds
+•
+•
tBu/R2NPP3 and tBu/R2NPP4 the hole is stabilized by the termi-
nal electron-rich unit, in accord with the electrochemical and
spectroscopic analysis (Figures 3 and 4). (TD-)DFT calculations
also reproduced the experimentally observed evolution of
oxidation energies of R2NPPn and model tBu/R2NPPn as well as
the excitation energies of their cation radicals (Figure 7). Note
that the observed lowest-energy transition of R2NPPn+• switch-
es from D0 → D1 in n = 2 and 3 to D0 → D2 in higher homo-
logues (i.e. n ≥ 4), where hole (in the ground state) shifts to-
ward one end (see Figures S13, S14 and Table S2 in the Sup-
porting Information).
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Figure 7. Comparison of the oxidation energies of R2NPPn (A) and
+•
excitation energies of R2NPPn (B, n = 2, 3: D0 → D1, filled red
circle and n = 4-6: D0 → D2, empty red circles) vs cos π/(n+1),37
where n is the number of p-phenylene units. Black filled circles
(connected by black solid lines) denote experimental data points,
and red circles (connected by red lines) denote data points from
the (TD-)DFT calculations [B1LYP-40/6-31G(d)+PCM(CH2Cl2)].
Figure 5. The ORTEP diagrams (50% probability) of R2NPP2 (A) and
its cation radical salt (B) as well as the juxtaposition of neutral
(yellow) and cation radical (grey) structures (C). Comparison of
the oxidation-induced bond length changes obtained by X-ray
crystallography and DFT calculations (D).29
R
Application of the 2- and 3-state Marcus-based model to PP2
DFT calculations. DFT calculations at the B1LYP-40/6-
31G(d)+PCM(CH2Cl2) level of theory (see Section S8 in the
Supporting Information for the computational details)6,12,30-34
reproduced the electronic structure of R2NPPn+• as obtained by
the X-ray crystallography (Figure 5). The DFT calculations
and RPP3. The evolution of the oxidation energies with increasing
n of R2NPPn series was somewhat surprising, as the increase in
oxidation potentials by 0.24 and 0.35 V by inserting one and two
bridging p-phenylenes in R2NPP2 and saturation at n = 4 were in
sharp contrast with the observed decrease in the Eox1 values in
the isoalkyl-substituted iAPPn with increasing n, which showed
saturation at n > 7 (Figure 8). A comparison of the oxidation en-
ergies of R2NPPn series with our recently published ROPPn series,
having weaker electron-donating alkoxy-capping groups, showed
a modest increase in Eox1 values (~0.10 V) with increasing n,
which saturated at n = 5-6 (Figure 8).
showed that spin/charge (hole) was symmetrically distributed
+• 35
in R2NPP2+•, somewhat skewed in R2NPP3
,
and in higher
homologues with n ≥ 4, was shifted toward one end of the
molecule and closely resembled the hole distribution in mod-
el tBu/R2NPP3+• and tBu/R2NPP4+• (Figure 6).36
Figure 6. Spin density distribution plots (+0.001 au) in the ground
(D0) electronic states of R2NPPn+• (n = 2, 3) (left), R2NPPn+• (n = 4-6)
+•
(middle) and tBu/R2NPPn
(n = 2-4) (right) [B1LYP-40/6-
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 6 of 10
ꢄ/4 ꢅ ∆ꢆ
ꢀꢁ ꢂ ꢃ
ꢇꢈꢉ
ꢄ/4 ꢅ ∆ꢆ
ꢊ
(eq 1)
(eq 2)
1
2
3
4
5
6
7
8
ꢇꢈꢉ
ꢄ ꢅ ∆ꢆ ꢇꢈꢉ
0
ꢇꢈꢉ
0
0
ꢇꢈꢉ
ꢀꢋ ꢂ ꢌ
ꢍ
ꢇꢈꢉ ꢄ ꢅ ∆ꢆ
The Hamiltonian matrices in eqs. 1 and 2 for different end-
capping groups, represented in Figure 10, can be analytically
diagonalized, and the resulting eigenvalues (eqs. S1 and S2 in
the Supporting Information) provide adiabatic ground state
9
energies, which relate directly to Eox1 of PP2 and RPP3. For
R
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
example, a comparison of the lowest eigenvalues of H2 and
H3 with different values of ∆ε and constant Hab and λ (see
Section S9 in the Supporting Information for details) shows
R
R
Figure 8. Showing the evolution of Eox1 of various RPPn, where R =
iA, RO, and R2N, vs cos π/(n+1),37 where n is the number of p-
phenylene units.
that Eox1 of PP3 would be similar to Eox1 of PP2 [i.e. ∆Eox
Eox1(RPP3)–Eox1(RPP2) = 0] if the energy difference between the
capped terminal and bridging p-phenylene unit (∆ ) was
comparable to the coupling (Hab), i.e. ∆ ≈ H (i.e. R = RO). In
contrast, the oxidation potential is predicted to decrease (i.e.
∆Eox < 0) when ∆ < H (i.e. R = iA), and increase (i.e. ∆Eox > 0)
when ∆
> H (i.e. R = R2N), Figure 10.38
=
ε
ε
In order to account for this unusual evolution of the redox
potentials of poly-p-phenylenes (RPPn) with end-capping sub-
stituents (i.e. R = iA, RO, or R2N) of increasing electron-donor
ε
R
+•
R
+•
ε
strength, we analysed the PP2 and PP3 series using our
recently developed Marcus-based multi-state parabolic mod-
el (MPM),6,34 as follows.
Comparison of the hole stabilization as elucidated with the
MPM for various RPPn is depicted graphically in Figure 10.
Here we see that a smaller ∆ε in case of isoalkyl-capped poly-
Based on the two-state Marcus model, the model Hamilto-
R
+•
p-phenylenes leads to effective stabilization of hole and
nian H2 for PP2 (Figure 9) can be simplified, as in eq 1, by
thereby lowering of the oxidation potentials in iAPP3+• in com-
R
noting that the hole is symmetrically distributed in PP2+•, i.e.
parison with iAPP2+•. In contrast, the larger ∆ values for ROPPn
ε
the position of the hole corresponding to the minimum of the
adiabatic ground state energy xmin(RPP2+•) = ½. A similar as-
sumption of symmetrical (but not necessarily even) hole dis-
tribution in RPP3+• [i.e. xmin(RPP3+•) = 1] also simplifies the Ham-
iltonian H3 (i.e. eq. 2) for the three-state parabolic model
applicable to RPP3+• (Figure 9).
and R2NPPn, which arise from the large energy difference be-
tween the terminal and bridging p-phenylene units, impede
interchromophoric interaction between the terminal units
and thereby leading to destabilization of the hole (Figure 10).
Note that modest destabilization of ROPP3 (∆Eox = 0.05 V) as
+•
+•
compared to R2NPP3 (∆Eox = 0.24 V) is directly related to the
increased ∆ε
value (Figure 10).39
The MPM analysis further demonstrates that the amount
of hole on the central p-phenylene in RPP3+•, obtained directly
from analytical expression for eigenvectors (eq. S4 in the
Supporting Information) of model Hamiltonian matrix in eq 2,
depletes upon increasing the ∆
terminal and bridging units (Figure 10). In the case of
R2NPP3+•, where ∆
is largest, the hole tends to concentrate
ε between the end-capped
ε
onto the electron-rich terminal units, which leads to destabili-
zation of the hole as verified by increased oxidation potentials
+•
by ~0.24 V. In contrast, for ROPP3 the hole is concentrated
more or less equally on terminal and bridging units, owing to
Figure 9. Graphical representation of the two- and three-state
parabolic models, and the corresponding model Hamiltonians H2
and H3, where Hab—electronic coupling between the interacting
units, λ—reorganization energy, ∆ε—energy difference between
the capped terminal unit and bridging p-phenylene unit, and x—
structural/solvent reorganization coordinate.
the relatively modest increase in ∆
ε
. Finally, the hole distri-
bution in ROPP3 represents a case of ∆
≈ Hab, as attested by
a minimal destabilization of the hole by ~0.05 V, as compared
+•
ε
to ROPP2
.
+• 40
ACS Paragon Plus Environment

Page 7 of 10
Journal of the American Chemical Society
1
2
3
4
5
6
7
8
9
10
Figure 10. Comparison of the hole stabilization and distribution in RPP2+• and RPP3+• calculated using two- and three-state parabolic mod-
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
R
R
els defined in Figure 9. Thick blue/red arrows show increase/decrease in hole stabilization in PP3+• with respect to PP2+•. Parameters
used in the multiparabolic model: Hab = 9.0, λ = 1.0, ∆ε(H) = 0, ∆ε(iA) = 3.7, ∆ε(RO) = 8.5. The value of the ∆ε(R2N) = 19.0 was obtained
based on the linear correlation between the values of ∆ε vs the ionization potentials of model compounds, i.e. benzene (9.24 eV), tolu-
ene (8.83 eV), anisole (8.25 eV), and dimethylaminobenzene (7.15 eV), see Section S9 and Figure S19 in the Supporting Information.
Application of multi-state model to R2NPPn+•. The two- and
three-state parabolic models in presented in Figure 9 and 10
clearly account for the observed trend in the evolution of the
oxidation energies. We have recently shown that more pre-
cise description of the hole distribution in the ground and
especially in the excited states of poly-p-phenylene wires and
the resulting redox and optical properties are better de-
scribed using the a bell-shaped function rather than a parabo-
la.41 Accordingly, herein we employ the multi-state model
+•
(MSM) with bell-shaped function to R2NPPn as follows (also
see Section S10 in the Supporting Information).
The eigenvectors obtained from diagonalization of the n-
state Hamiltonian matrices in MSM provided hole distribu-
RO, or R2N), obtained from MSM, against cos π/(n+1) trend.37 A
tions with uncanny similarity with the spin/charge distribu-
R
Figure 11. A: Oxidation energies G1(xmin) of PPn (n = 2-7, R = iA,
simulated plot of the oxidation energies G1(xmin) obtained using
MSM for a range of energy gaps between the end-capped termi-
tion obtained by the DFT calculations, i.e. the hole shifts to-
ward one end of the R2NPPn+• chain for n ≥ 4 (Figure S26 in the
R
nal and bridging internal units (∆
ε
= 0-70) in hypothetical PPn
wires is shown in grey color. B: Plot of vertical excitation ener-
Supporting Information). Moreover, the eigenvalues provided
oxidation energies of R2NPPn, which increase with increasing
number of p-phenylene units and saturate for n ≥ 4 (compare
Figures 11A and 7). Interestingly, a simulated plot (Figure 11,
gies42 ꢀG(xmin) of PPn (n = 2-7, R = iA, RO, or R2N), obtained
from MSM, against cos π/(n+1) trend.37 Filled circles correspond
to the D0→D1 transition (i.e. ꢀG(xmin) = G2(xmin) - G1 (xmin)), open
circles correspond to the D0→D2 transition (i.e. ꢀG(xmin) =
G3(xmin) - G1(xmin)). The oxidation and excitation energies ob-
tained from MSM were scaled to experimental data.
R
+•
R
grey) of oxidation energies of hypothetical PPn wires with a
wide range of energy gaps between the end-capped terminal
and bridging internal units (∆ε = 0-70) further demonstrate
three different regimes in the evolution of the oxidation en-
R
ergies, amongst which PPn wires with R = iA, RO, R2N repre-
CONCLUSIONS
sent limiting cases, i.e. ∆
ε < H (i.e. R = iA), ∆ε ≈ H (i.e. R =
In this study, we undertook a detailed examination of the
strikingly different trends of evolution of experimental Eox1
and effective conjugation length (ECL) of end-capped poly-p-
phenylenes (RPPn) with electron-rich substituents. For exam-
ple, we have earlier shown that alkyl-capped poly-p-
phenylenes (iAPPn) show a decrease (-0.26 V) in Eox1 with in-
creasing number of p-phenylenes (ECL = 7) while alkoxy-
capped poly-p-phenylenes (ROPPn) show an increase (+0.10 V)
in Eox1 with increasing number of p-phenylenes (ECL = 5).6
RO) and ∆ > H (i.e. R = R2N). It is important to note that
ε
the nature of the observed lowest energy transition changes
from D0→D1 in fully delocalized R2NPPn+• (n = 2, 3) to D0→D2 in
longer homologues (n ≥ 4) and was accurately predicted by
MSM (compare Figures 11B and Figure 7).
Thus, MSM successfully reproduced the evolution of oxida-
tion energies and vertical excitation energies as well as the
nature of the lowest-energy transitions across all RPPn+• series
with R = iA, RO, and R2N (Figure 11), obtained by experiment
or DFT calculations, and provided a clear rationale of the dif-
fering trend in the evolution of redox and optical properties
In order to reconcile this divergent behaviour, we synthe-
sized a series of R2NPPn (n = 2–6) with highly electron-rich N,N-
diisopropylamino end-capping groups and the model com-
pounds (tBu/R2NPPn) with only one end-capping group. The
electrochemical analysis of R2NPPn and model compounds
showed a dramatic increase (+0.35 V) in Eox1 with increasing n
with increasing ∆
ε between the end-capped terminal and
bridging internal units.
[
R2NPP2: -0.08 V, R2NPP3: 0.15 V, R2NPPn (n ≥ 4): 0.27 V, tBu/R2NPPn
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 8 of 10
(n = 2–4): 0.27±0.03 V] with ECL = 3. The optical spectra of generation materials for long-range transport of charge.
R2NPPn+•, obtained via quantitative redox titrations with a ro-
bust one-electron aromatic oxidant, showed a red shift in
low-energy absorption band going from R2NPP2+• (1055 nm) to
R2NPP3+• (1718 nm) while the spectra of higher homologues of
Moreover, the findings detailed herein will aid in the devel-
opment of improved models for charge-transfer dynamics in
donor-bridge-acceptor systems.43-46
1
2
3
4
5
6
7
+•
R2NPPn (n ≥ 4) were remarkably similar to the absorption
ASSOCIATED CONTENT
Supporting Information
+•
spectrum of model tBu/R2NPP4 with a considerably blue-
+•
shifted absorption band at ~880 nm. The ECL = 3 for R2NPPn
,
Supporting Information includes details of synthesis and charac-
terization data for various compounds including X-ray crystallog-
raphy, and computational details. The Supporting Information is
available free of charge on the ACS Publications website.
8
9
determined by electrochemical analysis, is further corrobo-
rated by electronic spectroscopy which shows that the hole
+•
+•
must be delocalized in R2NPP2 and R2NPP3 (red-shifted ab-
sorption band) while it lies toward one end of the molecule in
higher homologues R2NPPn+•, n ≥ 4.
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
ACKNOWLEDGMENT
The analysis presented above was further supported by the
DFT calculations [B1LYP-40/6-31G(d)+PCM(CH2Cl2)], which
reproduced the experimental redox and optical properties of
We thank NSF (CHE-1508677) and NIH (R01-HL112639-04) for
financial support, Dr. Sergey V. Lindeman for X-ray crystallog-
raphy, and Professor S. A. Reid for helpful discussions. The calcu-
lations were performed on the high-performance computing
cluster Père at Marquette University funded by NSF awards OCI-
0923037 and CBET-0521602, and the Extreme Science and Engi-
neering Discovery Environment (XSEDE) funded by NSF (TG-
CHE130101).
+•
R2NPPn/R2NPPn and showed that spin/charge distribution in-
deed shifts toward one end of the molecule in higher homo-
+•
logues (R2NPPn+•, n ≥ 4), similar to the model tBu/R2NPP4
Moreover, the hole is fully delocalized in R2NPP3+• and R2NPP2
and the oxidation-induced bond length changes in R2NPP2
.
,
,
+•
+•
obtained by DFT calculations, were in complete agreement
with those obtained by precise X-ray structures of R2NPP2 and
REFERENCES
(1) Facchetti, A. Chem. Mater. 2010, 23, 733.
(2) Li, C.; Liu, M.; Pschirer, N. G.; Baumgarten, M.; Müllen, K. Chem.
Rev. 2010, 110, 6817.
(3) Lin, Y.; Zhan, X. Acc. Chem. Res. 2016, 49, 175.
(4) Roncali, J.; Leriche, P.; Blanchard, P. Adv. Mater. 2014, 26, 3821.
(5) Carroll, R. L.; Gorman, C. B. Angew. Chem. Int. Ed. 2002, 41, 4378.
(6) Talipov, M. R.; Boddeda, A.; Timerghazin, Q. K.; Rathore, R. J.
Phys. Chem. C. 2014, 118, 21400.
(7) Davis, W. B.; Svec, W. A.; Ratner, M. A.; Wasielewski, M. R. Na-
ture. 1998, 396, 60.
(8) Heitzer, H. M.; Marks, T. J.; Ratner, M. A. J. Am. Chem. Soc. 2015,
137, 7189.
(9) Heckmann, A.; Lambert, C. Angew. Chem. Int. Ed. Engl. 2012, 51,
326.
(10) Lambert, C.; Nöll, G.; Schelter, J. Nat. Mater. 2002, 1, 69.
(11) Lambert, C.; Amthor, S.; Schelter, J. J. Phys. Chem. A. 2004, 108,
6474.
(12) Talipov, M. R.; Hossain, M. M.; Boddeda, A.; Thakur, K.; Rathore,
R. Org. Biomol. Chem. 2016, 14, 2961.
(13) Lambert, C.; Nöll, G. J. Am. Chem. Soc. 1999, 121, 8434.
(14) Low, P. J.; Paterson, M. A. J.; Puschmann, H.; Goeta, A. E.; How-
ard, J. A. K.; Lambert, C.; Cherryman, J. C.; Tackley, D. R.; Leeming, S.;
Brown, B. Chemistry. 2004, 10, 83.
(15) Coropceanu, V.; Gruhn, N. E.; Barlow, S.; Lambert, C.; Durivage,
J. C.; Bill, T. G.; Nöll, G.; Marder, S. R.; Brédas, J. -L. J. Am. Chem. Soc.
2004, 126, 2727.
(16) Kaupp, M.; Renz, M.; Parthey, M.; Stolte, M.; Würthner, F.; Lam-
bert, C. Phys. Chem. Chem. Phys. 2011, 13, 16973.
(17) Sreenath, K.; Suneesh, C. V.; Kumar, V. K. R.; Gopidas, K. R. J.
Org. Chem. 2008, 73, 3245.
(18) Venkataraman, L.; Klare, J. E.; Nuckolls, C.; Hybertsen, M. S.;
Steigerwald, M. L. Nature. 2006, 442, 904.
(19) Khan, F. A.; Wang, D.; Pemberton, B.; Talipov, M. R.; Rathore, R.
J. Photochem. Photobiol. A 2016, 331, 153.
+•
R2NPP3
.
In order to ascertain the role of the energy gap (∆ε) be-
tween the end-capped terminal and bridging p-phenylene
units on the effective conjugation length, we applied our re-
cently developed Marcus-based multistate model (MSM).
Hamiltonian matrices of two- and three-state parabolic mod-
R
+•
+•
els applicable to PP2 and RPP3 were simplified by assump-
tion of symmetrical hole distribution and analytically diago-
nalized to produce eigenvalues (directly related to oxidation
energies) and eigenvectors (related to the distribution of the
hole). A comparison of the simplified Hamiltonian matrices
R
+•
R
+•
for PP2 and PP3 provided a direct relationship between
and electronic coupling between adjacent p-phenylenes
Hab, and showed that oxidation energies will decrease with
increasing number of p-phenylenes if ∆
< H (i.e. iAPPn), in-
crease when ∆
> H (i.e. R2NPPn), and show only a minimal
change when ∆
≈ H (i.e. ROPPn). Moreover, a more pro-
∆ε
ε
ε
ε
nounced increase in the oxidation energies going from n = 2
to 3 of R2NPPn (0.24 V) as compared to ROPPn (0.05 V) was con-
sistent with an increase in ∆ε
from ROPPn (8.5) to R2NPPn (19.0).
Also note that the versatility of the MSM was further demon-
strated by an accurate reproduction of the switching of the
nature of the electronic transition in R2NPPn+• due to shifting of
the hole toward one end of the molecule.
In summary, we have demonstrated by combined experi-
mental/DFT/theoretical
modelling
study
of
N,N-
diisopropylamino-capped poly-p-phenylene (or donor-bridge-
donor) wires (R2NPPn) and comparison with isoalkyl- and
alkoxy-capped poly-p-phenylene wires that the extent of hole
R
delocalization (or effective conjugation length) in PPn+•, and
the contrasting trends in evolution of oxidation energy are
critically dependent on the energy gap between end-capped
terminal and bridging p-phenylene units. This study also
demonstrates the versatility of our Marcus-based multistate
model as a valuable tool for the guided design of the next-
(20) Suzuki, A. Chem. Commun. (Camb). 2005, 4759.
(21) Hassan, J.; Sévignon, M.; Gozzi, C.; Schulz, E.; Lemaire, M. Chem.
Rev. 2002, 102, 1359.
(22) Banerjee, M.; Shukla, R.; Rathore, R. J. Am. Chem. Soc. 2009,
131, 1780.
(23) Rathore, R.; Kochi, J. K. J. Org. Chem. 1995, 60, 4399.
ACS Paragon Plus Environment

Page 9 of 10
Journal of the American Chemical Society
(24) Dimethoxybenzene was used as a reference because Eox1 values
speaking is not applicable to describe the properties of poly-p-
phenylene wires; see: Torras, J.; Casanovas, J.; Alemán, C. J. Phys.
Chem. A, 2012, 116, 7571−7583.
of number of R2NPPn were close to ferrocene.
1
2
3
4
5
6
7
8
(25) The second oxidation potentials (Eox2) of R2NPPn remained nearly
independent of n (Eox2 ≈ 0.27 V), and starting from n = 4, they merged
with the first oxidation wave.
(26) Rathore, R.; Burns, C. L.; Deselnicu, M. I. Org. Synth. 2005, 1.
(27) Talipov, M. R.; Boddeda, A.; Hossain, M. M.; Rathore, R. J. Phys.
Org. Chem. 2015, 29, 227.
(28) Further temperature lowering was not possible due to the pre-
cipitation of cation radical salts.
(29) The bond length changes (i.e. b1–b5) depicted in Figure 5D were
based on the averages of equivalent bonds.
(30) Renz, M.; Theilacker, K.; Lambert, C.; Kaupp, M. J. Am. Chem.
Soc. 2009, 131, 16292.
(31) Renz, M.; Kess, M.; Diedenhofen, M.; Klamt, A.; Kaupp, M. J.
Chem. Theory. Comput. 2012, 8, 4189.
(32) Talipov, M. R.; Boddeda, A.; Lindeman, S. V.; Rathore, R. J. Phys.
Chem. Lett. 2015, 3373.
(33) Talipov, M. R.; Navale, T. S.; Rathore, R. Angew. Chem. Int. Ed.
2015, .
(38) Note that the relationship between ∆ε and H was derived for
the cases where H >> λ, as has been shown in the cases of a num-
ber of poly-p-phenylene wires,6 see Section S9 in the Supporting
Information.
(39) This finding is not surprising in the context of molecular orbital
theory where an interaction between the orbitals of only identical
energies affords maximal stabilization/destabilization of the resulting
molecular orbitals (Figure S20 in the Supporting Information). See:
Rauk, A. Orbital interaction theory of organic chemistry, Wiley-
Interscience: New York; 2001.
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
(40) From the analytical expression for eigenvectors (eq. S4 in the
Supporting Information) it was shown that the hole would be evenly
R
+•
delocalized on all three units in a given PP3 when ∆
(which approximately corresponds to the case of ROPP3+•). If
then charge will be more concentrated on the central
unit (case of iAPP3+•), while in the cases of ∆
(e.g.
R2NPP3+•) the charge will be more depleted on the central unit.
ε
λ
H
∆ε
λ
H
ε
λ
H
(34) Talipov, M. R.; Jasti, R.; Rathore, R. J. Am. Chem. Soc. 2015, 137,
14999.
(41) Talipov, M. R.; Ivanov, M. V.; Rathore, R. J. Phys. Chem. C. 2016,
120, 6402.
(35) The skewed hole distribution in R2NPP3+•, predicted by the DFT
calculations, arises due to the sensitivity of hole distribution to a
small variation in the amount of exact exchange in the density func-
tional. See Figure S16 in the Supporting Information.
(36) Note that HOMO is symmetrically delocalized over both diiso-
propylamino-capped terminal units in all R2NPPn (Figure S12A in the
Supporting Information) while the spin/charge distribution is shifted
(42) The MSM predicts identical vertical excitation energies for all
RPP2+• because a single value for electronic coupling H was used for
R
+•
all three series of PPn with R = iA, RO, R2N. A detailed investiga-
R
tion of the role of varying electronic coupling H in PPn with differ-
ent end-capping groups will be discussed in a future publication.
(43) Davis, W. B.; Wasielewski, M. R.; Ratner, M. A.; Mujica, V.;
Nitzan, A. J. Phys. Chem. A. 1997, 101, 6158.
(44) Renger, T.; Marcus, R. A. J. Phys. Chem. A. 2003, 107, 8404.
(45) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996,
100, 13148.
+•
toward one end in R2NPPn with n ≥ 4 due to the structural/solvent
reorganization.
(37) The cos[π/(n + 1)] coordinate originates from the tight-binding
Hückel-like model based on the monomeric HOMOs, and it provides
much better agreement with the experimental redox potentials and
excitation energies of neutral and cation radicals than the reciprocal
1/n coordinate, derived from a particle-in-a-box model and strictly
(46) Davis, W. B.; Ratner, M. A.; Wasielewski, M. R. J. Am. Chem. Soc.
2001, 123, 7877.
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 10 of 10
Table of content graphic
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
10
ACS Paragon Plus Environment