Enhancing charge mobilities in selectively fluorinated oligophenyl organic semiconductors: a design approach based on experimental and computational perspectives

Article abstract of DOI:10.1039/c8tc06517a

Fluorination can be used to tune optoelectronic properties at the molecular level. A series of oligophenyls with various difluorinations of the phenyl rings has been synthesized, crystalized, structurally resolved and computationally analyzed for charge m

Full text of DOI:10.1039/c8tc06517a

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Materials Chemistry C
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Enhancing charge mobilities in selectively
fluorinated oligophenyl organic semiconductors:
a design approach based on experimental and
computational perspectives†
Cite this:DOI: 10.1039/c8tc06517a
Buddhadev Maiti, ‡ Kunlun Wang, ‡ Srijana Bhandari, ‡ Scott D. Bunge,
Robert J. Twieg * and Barry D. Dunietz
*
*
Fluorination can be used to tune optoelectronic properties at the molecular level. A series of oligophenyls
with various difluorinations of the phenyl rings has been synthesized, crystalized, structurally resolved and
computationally analyzed for charge mobility. We find that difluorination of the phenyl rings at para positions
leads to oligophenyls that are stacked in symmetrical overlap with significantly enhanced hole mobility as
well as the highest electron mobility of the molecules considered. Other difluorinations lead to relatively
shifted molecular units in the p-stacked crystal and therefore to lower mobilities. The selectively fluorinated
oligophenyls were synthesized using the Suzuki–Miyaura cross coupling reaction. The structures of the
1
13
19
Received 24th December 2018,
Accepted 26th February 2019
products were characterized by X-ray diffraction (XRD), H, C, F NMR spectroscopy and gas
chromatography (GC)/mass spectroscopy (MS) measurements. Computational analysis of the materials
based on state-of-the-art tools are used to predict their charge transport properties in the crystal phase.
In short, we establish a molecular design approach based on fluorination of oligophenyls to achieve
enhanced hole mobilities and relatively high electron mobilities.
DOI: 10.1039/c8tc06517a
rsc.li/materials-c
11,12
negative dielectric anisotropy essential for display applications.
Such fluorinated oligophenyls forming liquid crystalline phases
Charge mobility plays a crucial role in establishing the performances include systems with difluoro-substitution of the phenyl
1
. Introduction
1,2
13
of devices based on organic semiconducting materials. Here we precursors.
consider an approach to increase charge mobility in crystal films of Systematic introduction of polar C–F bonds in organic semi-
oligophenyl (OP) derivatives by tuning their properties at the mole- conducting materials establishes a chemical means to tune the
3
14,15
cular level. Specifically, we study a series of fluorinated oligophenyls optoelectronic properties of organic semiconducting materials.
that vary in the number of rings and the sites of fluorination. Fluorinated organic molecules have been used as electron
OPs are widely utilized as molecular building blocks of organic transporting materials. Selective fluorination is known to enhance
16
17
semiconductors and liquid crystals. These materials can be intermolecular attractive interactions resulting in molecules
readily synthesized presenting thermal stability and a wide range arranged in the solid-state with p stacked arrangements. More
4
of electronic and optical properties. For example, p-quaterphenyl recently we showed that symmetrical fluorination where the intro-
derivatives have been used as a liquid crystal semiconductor duced bond polarities mutually cancel resulting with vanishing
5,6
electrode material. OPs can be tuned through chemical substitu- dipole enhances charge mobilities in the crystal phase since charge
7–10
18
tion, and by varying the number of rings.
Fluorinated liquid trapping is minimized. In this work, we implement a similar
crystal materials exhibit rotational viscosity, a broad range of phase design approach based on a series of fluorinated OPs, which are
transition temperatures and in particular the potential for highly synthesized, characterized structurally and analyzed computationally
to predict their transport properties.
Department of Chemistry and Biochemistry, Kent State University, Kent, Ohio
4
4242-0001, USA. E-mail: bdunietz@kent.edu, bunge@kent.edu, twieg@kent.edu
†
Electronic supplementary information (ESI) available: Reorganization energies,
2
. Molecular classes
molecular orbital-based coupling energies, HRFs, normal modes, transport rates,
mobilities and atomic coordinates (see in Section 2.4). CCDC 1864595–1864597.
For ESI and crystallographic data in CIF or other electronic format see DOI:
We study a family of OPs with rings bearing two fluorine atoms.
Three isomers of di-fluorinated phenyls (DFPs), illustrated in the
upper panel of Fig. 1, are used as the building blocks of the OPs.
1
0.1039/c8tc06517a
‡
These authors contributed equally to this work.
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Table 1 Dipole moment (unit: Debye) along the oligomer main axis (m
perpendicular molecular axis (m ), the axis which is perpendicular to the
molecular plan (m ) and the quadrupole moments (unit: Debye Å) [see in Fig. 1]
X
), the
Y
Z
Class Molecule
m
X
m
Y
m
Z
Q
xx
Q
yy
Q
zz
oB97X-D/6-31G(d)
I
2,3-TFBP 0.00 3.88 0.00
2
2
ꢀ77.46
,3-HFTP 0.00 5.68 0.35 ꢀ112.38 ꢀ125.46 ꢀ132.14
,3-OFQP 0.00 7.35 0.01 ꢀ149.20 ꢀ166.67 ꢀ174.99
ꢀ84.45
ꢀ87.65
II
III
2,5-TFBP 0.00 0.30 0.00
ꢀ76.75 ꢀ89.34 ꢀ88.16
2
,5-HFTP 0.00 0.00 0.00 ꢀ112.49 ꢀ132.38 ꢀ131.86
2,5-OFQP 0.00 0.31 0.00 ꢀ147.46 ꢀ176.11 ꢀ175.16
2,6-TFBP 2.73 0.00 0.00
ꢀ74.29 ꢀ89.02 ꢀ88.81
2
,6-HFTP 4.20 0.00 0.00 ꢀ109.28 ꢀ132.29 ꢀ132.07
2,6-OFQP 5.68 0.00 0.00 ꢀ143.69 ꢀ175.50 ꢀ175.33
oB97X-D/cc-pVTZ
III 2,6-TFBP 2.72 0.01 0.00
ꢀ75.86
ꢀ90.94
ꢀ90.22
the reagents is provided in ESI,† Section 1.1, with a summary of
the approach provided next.
The synthesis of the 2,3-DFP based OPs is shown in Fig. 2.
The 2,3-difluorophenylboronic acid and 2,3-difluoroiodobenzene
were obtained commercially or prepared by the lithiation of
Fig. 1 Three classes of oligomers based on DFP are investigated. The
upper panel introduces the different DFP designating the classes. The lower
panel shows the conformations of the various OP involving two to four units
1
,2-difluorobenzene at the 3-position followed by the addition of
20
each. We also provide to the left side of each panel XY axis that represent the the appropriate electrophile (borate ester or iodine respectively).
dipole moment strength of each class. Class I consists of molecules with
sizable dipole moments along the molecular width axis (labeled by Y; blue):
Class II consists of molecules with symmetrical fluorination that leads to
vanishing dipole moments. Class III consists of molecules with a large
moment along the oligomer main axis (labeled as X; green).
0
0
The 2,3,2 ,3 -tetrafluorobiphenyl 1 (2,3-TFBP) was then obtained
in 60% yield under standard Suzuki–Miyaura cross coupling
conditions. In order to further extend the oligophenyl, the
0
4
-position next to the fluorine in 1 could also be lithiated just
as 2,3-difluorobenzene and the desired monoiodide 2 was
obtained in modest yield together with the formation of the
diiodide 3. While the separation of these two iodides (mono : di =
Each of the OP series corresponds to one of the considered DFP with
up to four rings included. Namely, each series involves tetrafluoro-
biphenyl (TFBP; two rings), hexafluoroterphenyl (HFTP; three rings),
and an octafluoroquaterphenyl (OFQP; four rings); a total of nine
materials. The resulting OPs bearing two to four rings are illustrated
in the lower panels of Fig. 1, where also shown are the associated
trends with regard to the dipole moments of the OPs as follows:
The 2,3-DFP-based ones are with a molecular dipole that is
aligned perpendicularly to the oligomer main axis. The dipole
moment increases along the OP width (Y axis) with the number
of rings in spite of the torsional angle between the rings.
The 2,5-DFP-based ones are with a symmetry that leads to a
vanishing dipole moment along either of the oligomer axis.
The 2,6-DFP-based ones are with a molecular dipole that is
aligned along the oligomer main axis (X axis), which increases with
the addition of rings and vanishing along the perpendicular axis.
The calculated dipoles along the three axis are listed in
Table 1. The quadrupole moment increases with the addition of
fluorine atoms and phenyl rings.
1
: 2 by GC-MS) was not successful, the mixture could be used
directly for the subsequent coupling with excess 2,3-difluoro-
0
0
00 00
phenylboronic acid. The 2,3,2 ,3 ,2 ,3 -hexafluoro-p-terphenyl 4
2,3-HFTP) was isolated from the resulting mixture by extraction
(
with dichloromethane and ethyl acetate in acceptable yield while
the quaterphenyl derivative 5 remained in the residue due to its
3
. Experimental approach
Fig. 2 Synthesis of 2,3-difluorinated oligophenyls and intermediates 1–5.
The synthesis of the various fluorinated OPs is based on the
Suzuki–Miyaura reaction with a different DFP precursor for
each series. A detailed description of the synthesis including of Pd(PPh
Reagents and conditions: (a) (i) THF, n-BuLi, (ii) B(OMe)
ii) I , THF; (c) H O/1,4-dioxane, Pd(PPh , K CO
, K CO , 2,3-difluorophenylboronic acid.
3
, THF; (b) (i) THF, n-BuLi,
; (d) H O/1,4-dioxane,
1
9
(
2
2
3
)
4
2
3
2
3
)
4
2
3
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Fig. 3 Synthesis of 2,5-difluorinated oligophenyls and intermediates 7–11.
Fig. 4 Synthesis of 2,6-difluorinated oligophenyls and intermediates
Reagents and conditions: (e) DMF, KOAc, Pd(PPh
f) 2,5-difluorobromobenzene, H O/1,4-dioxane, Pd(PPh
difluoro-1,4-dibromobenzene, H O/1,4-dioxane, Pd(PPh
O/1,4-dioxane, Pd(PPh , K CO
3
)
4
, bis(pinacolato)diboron;
, K CO ; (g) 2,5-
, K CO ; (h) 9,
1
2–19. Reagents and conditions: (b) (i) THF, n-BuLi, (ii) I
Pd(PPh , bis(pinacolato)diboron; (i) aqueous HCl, NaNO
dioxane, Pd(dppf)Cl , K CO ; (k) 4-bromo-2,6-difluoroiodobenzene, H
dioxane, Pd(PPh , K CO ; (l) 2,6-difluoro-1-iodobenzene, H O/1,4-dioxane,
Pd(PPh , K CO ; (m) 14, H O/1,4-dioxane, Pd(PPh , K CO ; (n) potassium
,6-difluorophenyl trifluoroborate 19b, H O/1,4-dioxane, Pd(PPh , K CO
2
, THF; (e) DMF, KOAc,
, KI; (j) H O/1,4-
O/1,4-
(
2
3
)
4
2
3
3
)
4
2
2
2
3
)
4
2
3
2
2
3
2
H
2
)
3 4
2
3
.
3
)
4
2
3
2
3
)
4
2
3
2
3
)
4
2
3
2
2
3
)
4
2
3
.
poor solubility in dichloromethane and ethyl acetate. We then
managed to isolate quaterphenyl 5 by extracting the residue
0
0
with boiling toluene followed by hot filtration of the toluene The 4-bromo-2,3 ,5 ,6-tetrafluorobiphenyl 15 was prepared
solution and the desired product crystallized out upon cooling. from the commercial precursors 2,6-difluorophenylboronic acid
The synthesis of the 2,5-DFP based OPs is shown in Fig. 3. As and 4-bromo-2,6-difluoro-1-iodobenzene by a highly selective
phenylboronic acids bearing multiple fluorine atoms some- Suzuki coupling reaction at the iodine site. The reactivity of
times work poorly in Suzuki coupling due to their electron iodine is higher than bromine and by controlling the stoichio-
poor nature (especially when the fluorine is located on a carbon metry, the reaction temperature (reflux or lower) and time
adjacent to the carbon attached to boron), fluorinated pinacol- (normally 2–12 hours), the desired biphenyl bromide 15 could
0
0
boronic esters were selected for the synthesis of oligophenyls be isolated in modest to good yield (60–80%). Next, 2,6,3 ,5 -
containing the 2,5-difluorophenyl unit. The boronic ester 6 was tetrafluorobiphenyl-4-Bpin 16 was synthesized by a similar
prepared quantitatively from 2,5-difluorobromobenzene and method as applied in the earlier set. Suzuki coupling between
bis(pinacolato)diboron catalyzed by 0.5–1% palladium tetrakis- 16 and relevant iodide proceeded to afford the final terphenyl
2
1
(
triphenylphosphine). The subsequent Suzuki coupling reac- product 17 and accompanied by the quarterphenyl product 18.
0
0
tion worked in good yield to give 2,2 ,5,5 -tetrafluorobiphenyl The purification of this molecule was also done by recrystalliza-
7
2
1
(2,5-TFBP). A similar Suzuki reaction was run between tion from hot toluene. In order to see if 18 could be obtained in
,5-difluorophenyl pinacolboronic ester (1.2 equivalents) and better yield, route B also was examined. The terphenylbromide
,4-dibromo-2,5-difluorobenzene. In this case the reaction was 19 was prepared by a selective Suzuki reaction between 15 and
carefully monitored by TLC and quenched when the starting 4-bromo-2,6-difluoro-1-iodobenzene. Here the corresponding
2
3
dibromide was completely consumed and an acceptable amount of 2,6-difluorophenyl potassium trifluoroborate 19b was utilized
0
0
the desired monoadduct, 4-bromo-2,5,2 ,5 -tetrafluoro-biphenyl 9, instead of the boronic acid, due to the poor reactivity of laterally
0
0
00 00
was obtained. The diadduct, 2,5,2 ,5 ,2 ,5 -hexafluoro-p-terphenyl 8 fluorinated boronic acids according to our experience. Potassium
2,5-HFTP) is also a target and was isolated from this same trifluoroborate 19b worked well and the yield of the Suzuki reaction
(
reaction. The bromobiphenyl 9 is a key intermediate for the was improved to 43% (compared to 27% in the first route), which is
synthesis of the target quaterphenyl 11. As before, the bromine quite acceptable considering the complexity of the system.
in 9 is converted to the pinacolboronic ester 10 and then reacted
The chemical structure of the synthesized fluorinated oligomers
with 9 to give the final quaterphenyl compound 11. This large are confirmed by both NMR spectra (see ESI,† Sections 1.2 and 1.3)
molecule was again isolated and purified by hot filtration/ and mass spectra (see ESI,† Section 1.4). The melting points
recrystallization from toluene.
(MP) of the different crystals including the nonfluorinated OPs
The synthesis of 2,6-DFB based OPs is shown in Fig. 4. The are provided in Fig. 5. The melting point increases as the
0 0
,2 ,6,6 -tetrafluorobiphenyl 13 (2,6-TFBP) was easily prepared conjugated system is extended as expected from increased
2
beginning with the commercial precursors 2,6-difluoroaniline intermolecular attractive forces. The 2,3-DFP presents the low-
and 5-bromo-1,3-difluorobenzene in good yield. It turned out est MP for the three and four rings-based series. The 2,5-DFP
0
that the 4 -position between the two fluorine atoms could be is the lowest for the two ring OPs. The 2,6-DFP materials are of
2
2
0
0
efficiently lithiated and after reaction with iodine the 3,5,2 ,6 - the highest MP among the DFP crystals. Lowering of the MP in
tetrafluoro-4-iodobiphenyl 14 was obtained in 91% yield. 2,3-DFP is noted and is explained by noncoplanar arrangement
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Fig. 5 Melting points, from left to right, of non-F TFBP, 2,3-TFBP, 2,5-
TFBP and 2,6-TFBP (1C).
Fig. 6 Scheme of the charge donor (green) and acceptor (red) potential
r a
energy surfaces. The key energetic parameters, E , E and DE are the
in the crystal reflecting weaker intermolecular attractive forces. reorganization energy, activation energy, and energy difference
respectively.
In spite of significant effort we have not been able to grow
crystals of the terphenyl and quaterphenyl materials of sufficient
size and quality to permit determination of their single crystal
structures.
donor and acceptor states each at their optimized geometries
(see Fig. 6), where for charge transport in a perfect crystal it
vanishes.
Charge mobility in organic crystals, Z, is described by the
Einstein–Smoluchowski equation:
4
. Computational approach
3
3
We proceed next to analyze the charge mobility in the various
OPs. We follow our well benchmarked protocol based on a
Fermi’s golden rule (FGR) theory to calculate charge transfer
eD
Z ¼
;
(3)
kBT
1
8,24–27
and transport rate constants.
mechanical FGR rate constants are given by:
The fully quantum where e, and D indicate the electron charge, and the diffusion
2
8
constant. Eqn (3) is widely used in studying charge transport in
In an idealized one-dimensional transport
picture, that is also widely employed for simplicity,
diffusion constant is evaluated from the rate constant of charge
hopping between neighboring molecules:
P
34–37
organic crystals.
2
ꢀ
S ð2n þ1Þ
jGj
a
a
3
4,37
a
kFGR ¼
e
the
2
ꢀh
ð
1
ex
r
ꢁ
ꢁ
dtF ðtÞ
ꢀ
1
2
D = a k.
(4)
(
)
X
ꢀ
ꢁ
i
ioat
ioat
exp ꢀ DEt þ
Sa ðna þ 1Þeꢀ
þ nae
:
Here a is the distance between the donor and acceptor mole-
cules, and k is the charge hopping rate constant calculated
using a dimer model (evaluated as either kM or kFGR). Therefore
the mobilities reported in this study serve as an upper bound to
the transport in the crystal that is formally three dimensional.
In this way we address below the mobility along the stacking
axis for the different oligomers.
Molecular geometries and dimer models are calculated
using density functional theory (DFT).
hybrid (RSH) functional oB97X-D that involves dispersion
correction is employed. The oB97X-D functional was bench-
ꢀh
a
(1)
Here, G is the electronic coupling, {o } are the normal mode
a
frequencies, {S
a
} are the Huang–Rhys factors (HRFs), and na ¼
ꢄ
ꢂ
ꢃ
ꢅꢀ
1
ꢀh oa
kBT
exp
ꢀ 1
are the normal mode’s thermal occupancies.
3
8,39
A range-separated
ex
r
ex 2
r
2
4
0
F
(t) = exp[ꢀk
B
TE
t / ꢀh ] accounts for outer-shell solvation,
ex
r
4
1
where E is the corresponding reorganization energy.
Following the high temperature and short time limits, the
semiclassical Marcus rate constant can be obtained from the
FGR expression
marked well in calculating charge reorganization energies in
42
molecular organic P-type semiconductors, while addressing well
the fundamental-gap deficiency that is known to burden the
2
9–32
!
43–47
rffiffiffiffiffiffiffiffiffiffiffiffiffi
simpler local-density-approximation (LDA)-based functionals.
2
2
jGj
p
ðDE þ ErÞ
4kBTEr
kM ¼
exp ꢀ
:
(2)
Polarizable continuum model (PCM) is used to represent effects of
the extended electrostatic environment due to the crystal
ꢀ
h
kBTEr
47–49
47
ex
in
matrix.
Clearly transport properties, geometries and reorga-
r r r
The overall reorganization energy is expressed as E = E + E .
nization energies are strongly affected by the extended electrostatic
environment. For example for 2,3-TFBP gas phase reorganization
energies are 0.724 and 1.285 eV for hole and electron transport
The inner-sphere reorganization energy is given by
P
E ri n
¼
ꢀh oaSa, where the normal modes are calculated using
a
the OP monomers. DE is the energy difference between the respectively, whereas with PCM these energies are significantly
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smaller at 0.493 and 0.738 eV. The 6-31G(d) basis set is used, where
the larger cc-pVTZ basis set values are noted for demonstrating
convergence of the calculated properties.
In particular we find:
ꢂ Class I crystals based on 2,3-DFP oligomers present a
53
noncoplanar arrangement. The calculated dimer intermolecular
by distance of 7.43 Å is in agreement with the experimental measured
5
0,51
The HRFs are calculated using the DUSHIN program
comparing the optimized geometries of the neutral and the value of 7.44 Å. (The intermolecular separation a is set to the
charged oligomers. Normal mode frequencies and eigenvectors distance between the molecular centers of mass.)
are obtained using optimized neutral oligomers. Electronic
coupling coefficients are calculated using configuration inter- head-to-tail orientation with a relative longitudinal displace-
ꢂ Class II crystals based on 2,5-DFP oligomers arrange in
1
7,54
action with constrained density functional theory (CDFT- ment forming a partial facial overlap.
The calculated inter-
In the CDFT calculations, oligomers within an ionic molecular distance of 3.35 Å is in agreement with the crystal
dimer are designated as either the donor or the acceptor of structure value of 3.39 Å.
charge to generate the two states used in the CI treatment. For
ꢂ Class III crystals based on 2,6-DFP oligomers are tightly
completeness we also compare the dimer based calculated E to packed in a cofacial arrangement due to substantial attractive
1
8,52
CI).
1
7
r
simpler monomeric based evaluation.
intermolecular stacking interactions. The calculated inter-
molecular distance of 3.64 Å reproduces well the measured
value of 3.75 Å.
5. Crystal structures
Crystal structures of only the TFBP compounds (1, 7 and 13) are
resolved by XRD (see in ESI,† Section 1.5). Dimers of the different
TFBPs associated with the strongest attractive intermolecular
forces between neighboring molecules are represented in Fig. 7.
Our calculated TFBP dimers compare well with intermolecular
distances extracted from the resolved XRD structures with a root
mean square deviation (RMSD) of only up to 0.3 Å. The RMSD
values and key structural features (intramolecular torsional
angles and intermolecular distances) are listed in Table 2.
6
. Results and discussion
The key electronic structure parameters for the oligomers are
listed in Table 3. We confirm correspondence of the energies of
the highest occupied and lowest unoccupied molecular orbitals
(HOMO [H] and LUMO [L]) within 0.1 eV of the calculated ioniza-
47,55
tion potential (IP) and the electron affinity (EA), respectively.
Intermolecular binding energies Finter of Class I molecules
are the smallest with values only up to 1.97 eV, for Class II these
increase by 0.2 eV up to 2.16 eV and a substantial further
increase for Class III molecules up to 3.08 eV. As expected from
the intermolecular energies, Class III molecules exhibit the
largest electronic coupling of B0.20–0.22 eV for hole transport
and B0.08–0.09 eV for electron transport, the coupling values
are about one order of magnitude smaller for Class II and even
smaller for Class I molecules. The electronic coupling values
are listed in Table 3 and Table S2 (see in ESI,† Section 2.1).
The electronic couplings obtained from orbital energies are
1
8,52,56
in good agreement with the CDFT-CI values.
To under-
stand the trend of lower coupling in Class II than those of in
Class III we illustrate the HFTP (three ring systems) frontier
orbitals in Fig. 8. The lower Class II values appear to result from
3
4,57
relative displacement of the OPs.
The pair of HOMO lobes
are oriented along the long molecular axis whereas the LUMOs
lobes are oriented along the short molecular axis. Lateral shifts
along the long molecular axis result with a larger overlap of the
Table 2 RMSD from crystal structure, ring torsional angle and inter-
molecular separation of molecular dimers (highlighted in Fig. 7). Measured
values are provided in parentheses
Fig. 7 Class I molecules are arranged in noncoplanar structures, whereas
Class II and III molecules are arranged with parallel rings. In Class II the
monomers are aligned in alternating directions and with an in-plane
relative shift. In Class III the molecules show a cofacial arrangement with Cl.
optimal overlap of the stacked molecular planes. Dimers extracted from
Ring torsional
angle [1]
Intermolecular
separation [Å]
Molecule
oB97X-D/6-31G(d)
RMSD [Å]
the crystal are shown for 2,3-TFBP (Class I), 2,5-TFBP (Class II) and
,6-TFBP (Class III). The intermolecular distances are indicated using
I
II
III
2,3-TFBP
2,5-TFBP
2,6-TFBP
0.33
0.23
0.23
54.50 (56.81)
55.10 (53.50)
49.20 (44.95)
7.43 (7.44)
3.35 (3.39)
3.64 (3.75)
2
red-dotted lines (unit: Å): for Class I crystals, the distance between the
centers of mass of the monomers is used. For Class II and Class III crystals
the distance between two stacked (parallel) phenyl rings is used. The oB97X-D/cc-pVTZ
highlighted dimers (yellow b/g) are used below for mobility calculations.
III
2,6-TFBP
0.10
47.60 (44.95)
3.72 (3.75)
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Table 3 Frontier orbital energies, e
H
(HOMO) and e
L
(LUMO), are in good agreement with the ionization potential (IP) and the electron affinity (EA),
respectively. The intermolecular separation (a) for Class I molecules corresponds to the distance between the molecular centers of mass (c.o.m.), and for
Class II and III molecules it is set to the distance between the molecular planes. The intermolecular binding energies (Finter), electronic coupling for hole
h,d e,d
h,m
r
transport (G
h
) and electron transport (G
e
), and hole and electron transport reorganization energy (calculated using dimers, E
r
, E
r
and monomers, (E
),
e,m
(E
r
)) reveal significant differences between the three molecular classes
h,d
r
h,m
r
e,d
r
e,m
r
Cl. Molecule
e
H
[eV]
e
L
[eV] IP [eV] EA [eV] a [Å]
Finter [eV]
G
h
[eV]
G
e
[eV]
E
[eV]
E
[eV]
E
[eV]
E
[eV]
oB97X-D/6-31G(d)
I
2,3-TFBP
ꢀ8.71
ꢀ8.52
0.76
0.41
0.19
8.45
8.16
8.02
ꢀ0.40
ꢀ0.07
ꢀ0.31
7.43 ꢀ1.07
10.02 ꢀ1.49
13.06 ꢀ1.97
0.013
0.0045
0.554
0.493
0.552
0.541
0.741
0.709
0.710
0.738
0.734
0.710
2
2
,3-HFTP
0.00098 0.00041 0.650
0.0022
,3-OFQP ꢀ8.44
0.0012
0.566
II
III
2,5-TFBP
ꢀ8.46
ꢀ8.35
0.65
0.30
0.11
8.31
8.05
7.93
ꢀ0.30
ꢀ0.16
ꢀ0.40
3.35 ꢀ1.31
3.43 ꢀ1.72
3.41 ꢀ2.16
0.054
0.018
0.0035
0.040
0.021
0.010
0.534
0.511
0.561
0.485
0.492
0.500
0.705
0.648
0.672
0.724
0.701
0.642
2
2
,5-HFTP
,5-OFQP ꢀ8.27
2,6-TFBP
ꢀ8.68
ꢀ8.44
0.68
0.27
0.08
8.41
8.05
7.89
ꢀ0.28
ꢀ0.24
ꢀ0.49
3.64 ꢀ1.40
3.67 ꢀ2.28
3.64 ꢀ3.08
0.216
0.204
0.202
0.092
0.083
0.086
0.615
0.638
0.649
0.557
0.552
0.566
0.714
0.708
0.678
0.782
0.766
0.774
2
2
,6-HFTP
,6-OFQP ꢀ8.33
oB97X-D/cc-pVTZ
III 2,6-TFBP
ꢀ8.98
0.44
8.61
ꢀ0.03
3.66 ꢀ0.51
0.198
0.097
0.671
0.641
0.667
0.762
Fig. 8 Frontier orbitals of 2,5-HFTP (left) and 2,6-HFTP (right) dimers.
Significant overlap between HOMOs (lower panels) and smaller overlap for
LUMOs (upper panels) is indicated. Class III molecules (lower right panel)
maintain a substantial cofacial arrangement to increase overlap within the
pair of monomer HOMOs (lower left panel).
HOMOs compared to that of the LUMOs. Additional listings of
frontier orbital energies and illustrations are provided in the
ESI,† Section 2.1.
r
The reorganization energies E tabulated in Table 3 are
within the range of 0.4–0.7 eV. Reorganization energies calcu- (b) Out-of-plane mode 39.86 cm that is associated with the relief of
Fig. 9 (a) Huang–Rhys factors (HRFs) for hole transport in 2,6-HFTP.
ꢀ1
the planar distortion. (c) The monomeric HOMO.
lated using CDFT dimers are reproduced rather well by simpler
ionic monomer calculations, within 0.1 eV in all cases. We
therefore proceed to obtain displacement geometries and HRFs
based on monomer calculations. Corroborating the harmonic HOMO leading to elongation and contraction of bonds in the
approximation the reorganization energies calculated using the bay regions. The HOMO is illustrated in panel (c). Further HRF
HRFs are in good agreement with their direct evaluation, see and frequency distributions are presented in ESI,† Section 2.2.
ESI,† Section 2.2. In ESI,† Section 2.3 we also provide analysis of
Hole and electron transport FGR rate constants and
58,59
the rate constants sensitivity with respect to the external mobilities
at 300 K are listed in Table 4. Importantly, Class I
r
, confirming only marginal influence molecules show the lowest charge mobilities with up to
ex
reorganization energy, E
as expected in a crystal phase.
ꢀ
2
2
ꢀ1 ꢀ1
9.1 ꢁ 10 cm V
s
for hole transport in 2,3-TFBP, reflecting
The modes involved in hole transport are highlighted by weak coupling due to the loose packing. Class II molecules
following the HRF spectral distribution, see panel (a) of Fig. 9 exhibit larger mobilities resulting from the tighter stacking and
for 2,6-HFTP. The key low frequency modes are presented in the larger coupling for both hole and electron transport. Here the
ꢀ1
ꢀ1
2
ꢀ1 ꢀ1
insets of panel (a) with the mode of 39.86 cm illustrated in mobility rises up to 3.1 ꢁ 10 cm V
s
for hole transport in
panel (b) of the figure. This mode appears to result from the 2,5-TFBP. However, it appears that the lateral shift in Class II
relief of steric stress upon depopulation of the monomeric materials between adjacent units dampens the coupling and
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Journal of Materials Chemistry C
Table 4 Marcus rate constants, k , and charge mobilities, Z
Paper
M
M
, are up to one order of magnitude smaller than the FGR values kFGR and ZFGR. Selective
fluorination of Class III results in increased hole and electron mobilities
ꢀ1
2
ꢀ1 ꢀ1
ꢀ1
2
ꢀ1 ꢀ1
ꢀ1
2
ꢀ1 ꢀ1
ꢀ1
2
ꢀ1 ꢀ1
Molecule k
M
(h) [s
]
Z
M
(h) [cm V
s
] kFGR(h) [s ] ZFGR(h) [cm V
s
] k
M
(e) [s
]
Z
M
(e) [cm V
s
] kFGR(e) [s ] ZFGR(e) [cm V
s ]
oB97X-D/6-31G(d)
1
0
ꢀ3
ꢀ5
ꢀ4
11
9
ꢀ2
ꢀ4
ꢀ3
8
ꢀ5
ꢀ6
ꢀ5
9
ꢀ3
ꢀ5
ꢀ4
2
2
2
,3-TFBP 2.12 ꢁ 10 4.53 ꢁ 10
4.25 ꢁ 10
1.27 ꢁ 10
8.42 ꢁ 10
9.08 ꢁ 10
4.93 ꢁ 10
5.56 ꢁ 10
3.17 ꢁ 10 6.80 ꢁ 10
5.18 ꢁ 10 1.11 ꢁ 10
8
6
7
,3-HFTP 1.44 ꢁ 10 5.60 ꢁ 10
2.83 ꢁ 10 1.00 ꢁ 10
3.67 ꢁ 10 1.40 ꢁ 10
8
9
7
8
,3-OFQP 9.61 ꢁ 10 6.34 ꢁ 10
4.91 ꢁ 10 3.20 ꢁ 10
6.21 ꢁ 10 4.10 ꢁ 10
1
1
ꢀ2
ꢀ3
ꢀ4
12
11
10
ꢀ1
ꢀ2
ꢀ3
10
ꢀ3
ꢀ4
ꢀ4
11
ꢀ2
ꢀ2
ꢀ3
2
2
2
,5-TFBP 6.30 ꢁ 10 2.73 ꢁ 10
7.07 ꢁ 10
7.60 ꢁ 10
2.86 ꢁ 10
3.07 ꢁ 10
3.46 ꢁ 10
1.29 ꢁ 10
5.08 ꢁ 10 2.21 ꢁ 10
8.20 ꢁ 10 3.56 ꢁ 10
10
10
11
,5-HFTP 7.39 ꢁ 10 3.36 ꢁ 10
2.00 ꢁ 10 9.10 ꢁ 10
2.72 ꢁ 10 1.24 ꢁ 10
9
9
10
,5-OFQP 3.01 ꢁ 10 1.35 ꢁ 10
5.46 ꢁ 10 2.46 ꢁ 10
6.82 ꢁ 10 3.07 ꢁ 10
1
2
ꢀ1
ꢀ1
ꢀ1
13
14
13
0
0
0
11
ꢀ3
ꢀ3
ꢀ3
12
ꢀ1
ꢀ1
ꢀ1
2
2
2
,6-TFBP 8.23 ꢁ 10 4.22 ꢁ 10
9.59 ꢁ 10
1.07 ꢁ 10
7.81 ꢁ 10
4.92 ꢁ 10
5.57 ꢁ 10
4.00 ꢁ 10
1.23 ꢁ 10 6.30 ꢁ 10
2.09 ꢁ 10 1.07 ꢁ 10
12
11
12
,6-HFTP 9.80 ꢁ 10 5.11 ꢁ 10
1.91 ꢁ 10 9.95 ꢁ 10
2.87 ꢁ 10 1.50 ꢁ 10
12
11
12
,6-OFQP 8.01 ꢁ 10 4.11 ꢁ 10
1.79 ꢁ 10 9.17 ꢁ 10
2.37 ꢁ 10 1.21 ꢁ 10
oB97X-D/cc-pVTZ
2
,6-TFBP 4.72 ꢁ 10 2.44 ꢁ 10ꢀ1
1
2
5.59 ꢁ 10
13
2.72 ꢁ 10
0
1.36 ꢁ 10 7.05 ꢁ 10ꢀ3
11
2.31 ꢁ 10 1.20 ꢁ 10ꢀ1
12
therefore limits the mobility. Class III molecules exhibit the Acknowledgements
highest electronic coupling and charge mobilities with the
2
ꢀ1 ꢀ1
B. D. D. is grateful for support by a NSF-CHE grant CHE-
362504. We are also grateful to generous resource allocations
on the Ohio Supercomputer Center and the Kent State Uni-
versity, College of Arts and Sciences Computing Cluster. We
thank Dr Suvagata Tripathi for synthetic assistance.
largest mobility of 5.6 cm V
s
found for hole transport
1
in 2,6-HFTP. Interestingly, the semi-classical values are about
one-order of magnitude smaller than the more complete FGR
values, demonstrating the importance of the quantum mechanical
perspective afforded by FGR even for evaluating charge transport.
This trend is in agreement with a recent study of charge transport
6
0
18
in related systems.
Notes and references
1
2
M. Muccini, Nat. Mater., 2006, 5, 605–613.
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. Conclusions
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In conclusion, we study three series of oligomers based on
,3-, 2,5- and 2,6-DFP units, with two to four phenyl rings. All
2
molecules were spectroscopically characterized but crystals
only based on two ring compounds were successfully resolved
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