published articles-Navamani

This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 17947--17961 17947
Cite this: Phys.Chem.Chem.Phys.,2013,
15, 17947
Effect of structural fluctuations on charge carrier
mobility in thiophene, thiazole and thiazolothiazole
based oligomers†
K. Navamani, G. Saranya, P. Kolandaivel and K. Senthilkumar*
Charge transport properties of thiophene, thiazole and thiazolothiazole based oligomers have been
studied using electronic structure calculations. The charge transport parameters such as charge transfer
integral and site energy are calculated through matrix elements of Kohn–Sham Hamiltonian. The
reorganization energy for the presence of excess positive and negative charges and rate of charge
transfer calculated from Marcus theory are used to find the mobility of charge carriers. The effect of
structural fluctuations on charge transport was studied through the polaron hopping model. Theoretical
results show that for the studied oligomers, the charge transfer kinetics follows the static non-Condon
effect and the charge transfer decay at particular site is exponential, non-dispersive and the rate coefficient
is time independent. It has been observed that the thiazole derivatives have good hole and electron
mobility.
1. Introduction
Organic semiconducting materials are widely studied for use in
organic light-emitting diodes (OLEDs),1,2
organic field effect
transistors (OFETs)3–5
and organic photovoltaic cells (OPVs)6,7
because of their potential advantages such as mechanical
flexibility, low cost and easy fabrication. During the past several
years, much research has been carried out on organic semi-
conductor materials both at experimental and theoretical
levels.8–13
In particular, oligothiophenes14–17
and oligoacenes18–20
have been extensively investigated due to their high charge carrier
mobilities. The development of n-type organic semiconductor
lags behind the p-type materials due to their instability in air
conditions and lower charge carrier mobility.21–23
Therefore, the
design and fabrication of high-performance and ambient-stable
n-channel materials is crucial for the development of organic
electronic devices such as organic p–n junctions, bipolar transistors
and integrated circuits.
Oligothiophenes are good p-type semiconductors and exhibit
high hole mobility in thin-film OFETs. These molecules have
relatively high HOMO energy levels, which lead to poor air-stability
and low current on/off ratios.24
This problem can be overcome by
introducing planar electron-accepting heterocycles in the oligomer
which could reduce the air oxidation, improve the electron
transport property and down shift the HOMO energy level.25,26
In an earlier study, Facchetti et al.27,28
have shown that
the substitution of perfluoroalkyl groups induces the n-type
semiconducting behavior in thiophene oligomers. Previously,
Gundlach et al.29
and Meng et al.30
reported that planar
molecules have a high charge transfer integral and less reorganiza-
tion energy which are the essential criteria for high performance
OFETs. Current interest in the multi-cyclic rigid like fused
p-conjugated aromatic molecules has grown, because of their
improved stability and planarity which reduce the band gap and
improve charge transport ability.31
Introduction of electron-
withdrawing moieties into p-conjugated molecules lower the
LUMO energy.26
The earlier studies showed that the presence
of electron-deficient nitrogen containing azine and azole fragments
in thiophene based oligomers improve the electron transporting
ability and reduce the threshold voltage in FET devices.25,26
Thiazole is a well-known molecule in the azole family and
has electron-deficient properties due to the presence of the
electron-withdrawing nitrogen replacing the carbon atom at the
3rd position of thiophene.32
Replacement of thiophene with
thiazole in p-conjugated system tends to lower both HOMO and
LUMO energy levels.26
The presence of thiazole rings in thio-
phene based oligomers can reduce steric interactions leading to
the planar structure.33
The electron affinity increases with the
increase of thiazole rings34
and the fused thiazole rings have a
rigid planar structure that lead to strong p–p interactions, less
structural relaxation following the introduction of extra charge
and a small HOMO–LUMO energy gap.34,35
Thiazole–thiophene
and thiazolothiazole–thiophene copolymers act as donor–acceptor
Department of Physics, Bharathiar University, Coimbatore-641 046, India.
E-mail: ksenthil@buc.edu.in
† Electronic supplementary information (ESI) available. See DOI: 10.1039/
c3cp53099j
Received 23rd July 2013,
Accepted 3rd September 2013
DOI: 10.1039/c3cp53099j
www.rsc.org/pccp
PCCP
PAPER
Publishedon04September2013.DownloadedbyBharathiarUniversityon26/05/201512:59:53.
View Article Online
View Journal | View Issue

17948 Phys. Chem. Chem. Phys., 2013, 15, 17947--17961 This journal is c the Owner Societies 2013
compounds due to the presence of the CQN bond which converts
p-type into n-type semi-conducting characteristics.25,26,36–39
Previous studies show that the introduction of a thiazole ring
in oligothiophenes with trifluromethylphenyl as the substitution
group improves the electron transporting ability.25,26,40
McCullough
et al.41–43
have achieved good FET performance by combining
thiophene and thiazolothiazole (fused thiazole units) molecules.
Ando et al.33–35,44
synthesized a set of thiophene (T1, T2), thiazole
(TZ1–TZ5) and thiazolothiazole (TZTZ1–TZTZ3) oligomers and
studied the opto-electronic properties. In the above study the
trifluoromethylphenyl substitution group is used to improve
the n-type semiconducting property of the studied oligomers.
The experimental studies reveal that the studied oligomers
(T1 and T2, TZ1–TZ5 and TZTZ1–TZTZ3) have a p-stacking
structure with columnar motif which favors the transport of
charge carriers.33–35
The X-ray crystallographic studies show
that these oligomers are having sufficient planarity that is
inherently favorable for large charge transfer integral and less
reorganization energy.34,35
The inter-molecular distance
through p-stacking in TZTZ1, TZTZ2 and T1 oligomers is
3.53 Å,35
and in TZTZ3 oligomer the inter-molecular distance
is 3.59 Å.33
The thiazole oligomers TZ1–TZ5 and thiophene
oligomer T2 are having inter-molecular p-stacking distance of
3.37 Å.34
The LUMO energy of these oligomers is nearer to the
work function of metals such as magnesium and aluminum
that support the fabrication of high performance n-type semi-
conducting devices.34,45,46
The chemical structure of these
p-conjugated oligomers T1, T2, TZ1–TZ5, TZTZ1, TZTZ2 and
TZTZ3 is shown in Fig. 1.
It has been shown that the FET mobility depends on the
substrate used and temperature of the deposition. For thiophene
oligomer T1, the mobility increases from 0.07 to 0.18 cm2
VÀ1
sÀ1
as the temperature increases from 25 1C to 50 1C on the SiO2
substrate. At room temperature, thiazole oligomer TZ1 has FET
mobility of 0.21, 0.52 and 1.83 cm2
VÀ1
sÀ1
with the substrates
SiO2, HMDS and OTS, respectively. It has been found that the
oligomer TZ1 has good mobility but no FET characteristics are
reported for its structural isomer, TZ2. The position of S and N
atoms in the isomers determines the planarity of the molecule
and FET performance. Also, the isomers TZ4 and TZ5
have diﬀerent mobility values. The FET mobility in TZ4 is
0.085 cm2
VÀ1
sÀ1
, whereas the mobility of charge carrier in
TZ5 is 0.018 cm2
VÀ1
sÀ1
at room temperature in the SiO2
substrate. The position of thiophene and thiazole rings in the
isomers TZ4 and TZ5 is responsible for their FET performance.
Among the thiazolothiazole oligomers, TZTZ2 has the maximum
charge carrier mobility of 0.12, 0.30 and 0.26 cm2
VÀ1
sÀ1
at the
temperatures 25, 50 and 100 1C, respectively, on the SiO2
substrate. The FET mobility is not observed in TZTZ1. Therefore,
to understand the charge transport properties of these mole-
cules, one of the most important tasks is studying the electronic
properties of these molecules at a molecular level through the
key parameters of charge transport such as site energy, charge
transfer integral, reorganization energy and the eﬀect of struc-
tural fluctuations on these parameters which determine the rate
of charge transfer and mobility.
In the present study, a method proposed by Siebbeles and
co-workers47
based on the fragment molecular orbital (FMO)
Fig. 1 The chemical structure of thiophene, thiazole and thiazolothiazole based
oligomers.
Paper PCCP
View Article Online

approach has been used to calculate the charge transfer integral
(also called electronic coupling or hopping matrix element) and
site energy for hole and electron transport in these molecules.
Further, these values are used to calculate the rate of charge
transfer and carrier mobility. The molecular dynamics (MD)
simulations were performed to study the structural fluctuations
in the form of stacking angle in the studied oligomers. In order
to study the polaronic effect on the charge carrier mobility,
Monte-Carlo (MC) simulations were performed.
2. Theoretical methodology
By using tight binding Hamiltonian approach the presence of
excess charge in a p-stacked molecular system is expressed as48,49
^H ¼
X
i
eiðyÞai
þ
ai þ
X
j 4 i
Ji;jðyÞai
þ
aj (1)
where, ai
+
and ai are creation and annihilation operators, ei(y) is
the site energy, energy of the charge when it is localized at ith
molecular site and is calculated as diagonal element of the
Kohn–Sham Hamiltonian, ei = hji|HˆKS|jii, the second term of
eqn (1), Ji, j is the off-diagonal matrix element of Hamiltonian,
Ji, j = hji|HˆKS|jji known as charge transfer integral or electronic
coupling, which measures the strength of the overlap between
ji and jj (HOMO or LUMO of nearby molecules i and j ).
Within the semi-classical Marcus theory, the rate of charge
transfer (KCT) is determined using the reorganization energy (l)
and effective charge transfer integral ( Jeff)50–52
KCT ¼
Jeff
2
ðyÞ
h
p
lkBT
1=2
exp À
l
4kBT

(2)
where kB is the Boltzmann constant and T is the temperature
(here T = 298 K). Here, Jeff is dependent on the stacking angle (y)
between the adjacent molecules. The stacking angle is the
mutual angle between two p-stacked molecules, where the
center of mass is the center of rotation. The generalized or
effective charge transfer integral is defined in terms of charge
transfer integral (J), spatial overlap integral (S) and site energy
(e) as,53
Jeffð Þi;j¼ Ji;j À Si;j
ei þ ej
2

(3)
where, ei and ej are the energy of a charge when it is localized at
ith and jth molecules, respectively. The site energy, charge
transfer integral and spatial overlap integral were computed
using the fragment molecular orbital (FMO) approach as
implemented in the Amsterdam Density Functional (ADF)
theory program.47,54,55
In ADF calculation, we have used the
Becke–Perdew (BP)56,57
exchange correlation functional with
triple-z plus double polarization (TZ2P) basis sets. For comparison
purposes, for a few oligomers, the ADF calculations were per-
formed with correct asymptotic behavior type exchange correlation
functional statistical average of orbital potentials (SAOP).58,59
In
these methods, the charge transfer integral and site energy are
calculated directly from the Kohn–Sham Hamiltonian.47,48
Here
the charge transfer integral and site energy are calculated without
invoking the assumption of zero spatial overlap integral, and it
is not necessary to apply an electric field to bring the site energy
of the molecules into resonance.55
In the present work, the
calculations were carried out for different stacking angles.
The reorganization energy measures the change in energy of the
molecule due to the presence of excess charge and the surrounding
medium. The reorganization energy for the presence of excess
hole (positive charge, l+) and electron (negative charge, lÀ) is
calculated as,60,61
lÆ = [EÆ
( g0
) À EÆ
( gÆ
)] + [E0
( gÆ
) À E0
( g0
)] (4)
where, EÆ
( g0
) is total energy of an ion in neutral geometry,
EÆ
( gÆ
) is the energy of an ion in ionic geometry, E0
( gÆ
) is the
energy of the neutral molecule in ionic geometry and E0
( g0
) is
the optimized ground state energy of the neutral molecule. The
geometry of the studied oligomers T1, T2, TZ1–TZ5 and TZTZ1–
TZTZ3 in neutral and ionic states are optimized using density
functional theory method (DFT), B3LYP62–64
in conjunction with
the 6-311G(2d,2p) basis set, as implemented in the Q-Chem
software package.65
In a regular static p-stacked system, the site energy disorder
is minimum and the charge transfer rate (KCT) is constant. The
mobility (m) can be calculated from the Einstein relation,
m ¼
eR2
kBT

KCT (5)
where R is the inter-molecular distance. As reported in previous
studies,55,66,67
the structural fluctuations in the form of change
in p-stacking angle strongly influence the rate of charge transfer.
In the disordered geometry, the migration of charge from one
site to another site can be explained through the incoherent
hopping charge transport mechanism. In the present study, we
have performed Monte-Carlo (MC) simulations to calculate the
charge carrier mobility in a disordered system, in which charge
is propagated on the basis of the rate of charge transfer
calculated from semi classical Marcus theory (eqn (2)).48,55
In this model, we assume that the charge transport takes
place along the sequence of p-stacked molecules and the charge
does not reach the end of molecular chain within the time scale
of simulation. In each step of Monte-Carlo simulation, the
most probable hopping pathway is found from the simulated
trajectories based on the charge transfer rate at a particular
conformation. In the case of normal Gaussian diffusion of the
charge carrier in one dimension, the diffusion constant D is
calculated from mean square displacement, hX2
(t)i which
increases linearly with time, t
D ¼ lim
t!1
X2
tð Þ

2t
(6)
The charge carrier mobility is calculated from diffusion con-
stant D by the Einstein relation,68
m ¼
e
kBT

D (7)
To get the quantitative insight on charge transport properties
in these molecules, the information about stacking angle and its
PCCP Paper
View Article Online

fluctuation from equilibrium is required. To get this information
the molecular dynamics simulation for stacked dimer was
performed using TINKER 4.2 molecular modeling package69,70
with standard molecular mechanics force field, MM3.71,72
The
simulations were performed up to 10 ns with time step of 1 fs
and the atomic coordinates in trajectories were saved in intervals
of 0.1 ps. The energy and occurrence of a particular conformation
were analyzed in all the saved 100 000 frames to find the stacking
angle and its fluctuation from equilibrium value.
3. Results and discussion
The monomer geometry of the ten oligomers was optimized
using DFT calculations at B3LYP/6-311G(2d,2p) level of theory
and are shown in Fig. S1 (ESI†). As a reasonable approximation,
the positive charge (hole) will migrate through the highest
occupied molecular orbital (HOMO) and the negative charge
(electron) will migrate through the lowest unoccupied molecular
orbital (LUMO) of the stacked oligomers. The charge transfer
integrals, spatial overlap integrals and site energies corres-
ponding to positive and negative charges were calculated based
on coefficients and energies of HOMO and LUMO. The density
plot of HOMO and LUMO of the studied oligomers calculated at
B3LYP/6-311G(2d,2p) level of theory is shown in Fig. 2 and 3,
respectively. As shown in Fig. 2 and 3, the HOMO and LUMO are
p orbitals and are delocalized mainly on the thiazolothiazole,
thiazole and thiophene rings and possess less density on the end
substituted trifluoromethylphenyl groups. It has been observed
that the introduction of a thiazole group enhances the electron
density delocalization on the LUMO.
3.1. Effective charge transfer integral
The effective charge transfer integral ( Jeff) for hole and electron
transport in thiophene, thiazole and thiazolothiazole derivatives
are calculated using eqn (3) and are summarized in Tables 1 and 2
and Tables S1 and S2 (ESI†). In agreement with an earlier study,47
the calculated results show that both Becke–Perdew (BP) and
statistical average of orbital potentials (SAOP) exchange correla-
tion functionals provide similar results. The variation of Jeff with
respect to stacking angle for hole and electron transport in the
studied oligomers is shown in Fig. 4 and 5, respectively. It has
been observed that the effective charge transfer integral ( Jeff) for
hole and electron transport is maximum at 01 of stacking angle.
The percentage of monomer orbital contribution for electronic
coupling in a dimer system is calculated using a fragment orbital
approach and is summarized in Tables S3 and S4 (ESI†). At 01 of
stacking angle, the HOMO of the dimer consists of 50% of
HOMO of each monomer, and the LUMO of the stacked dimer
consists of LUMO of each monomer with equal contribution
which leads to orbital overlapping in same phase.
For hole transport, among the thiophene derivatives, T2 has
maximum Jeff value of 0.34 eV at 01 of stacking angle because of
better planarity of T2 than T1. At larger stacking angles, T1 has
slightly higher Jeff than T2 for both hole and electron transport.
This is due to the fact that at the larger stacking angles, the
overlap between frontier orbitals (HOMO or LUMO) of the
studied T1 monomer is larger than that of T2, which is
Fig. 2 Highest Occupied Molecular Orbitals (HOMO) of the studied thiophene, thiazole and thiazolothiazole based oligomers.
Paper PCCP
View Article Online

associated with the relatively strong delocalized nature of
HOMO (or LUMO) at the middle thiophene rings of T1 oligo-
mer [see Fig. 2 and 3]. Thiazole (TZ) derivatives, TZ1–TZ5 are
having almost similar Jeff value of 0.34 eV at 01 of stacking
angle. The presence of the thiazole unit and the position of the
thiazole and thiophene units do not significantly affect the
Fig. 3 Lowest Unoccupied Molecular Orbitals (LUMO) of the studied thiophene, thiazole and thiazolothiazole based oligomers.
Table 2 Effective charge transfer integral, Jeff (in eV) at different stacking angle y (in degree) for electron transport
Stacking angle (y) in degree
Effective charge transfer integral ( Jeff) in eV
Thiophene derivatives Thiazole derivatives Thiazolothiazole derivatives
T1 T2 TZ1 TZ2 TZ3 TZ4 TZ5 TZTZ1 TZTZ2 TZTZ3
0 0.248 0.333 0.392 0.268 0.401 0.383 0.364 0.282 0.268 0.301
15 0.151 0.167 0.227 0.157 0.194 0.157 0.227 0.174 0.132 0.155
30 0.031 0.037 0.092 0.084 0.103 0.143 0.120 0.041 0.047 0.041
45 0.051 0.075 0.048 0.079 0.059 0.077 0.052 0.044 0.003 0.004
60 0.156 0.134 0.087 0.135 0.080 0.042 0.082 0.110 0.061 0.064
75 0.169 0.160 0.149 0.179 0.127 0.102 0.135 0.064 0.033 0.039
90 0.161 0.147 0.173 0.180 0.148 0.134 0.157 0.001 0.005 0.000
Table 1 Effective charge transfer integral, Jeff (in eV) at different stacking angle, y (in degree) for hole transport
Stacking angle (y) in degree
Effective charge transfer integral ( Jeff) in eV
Thiophene derivatives Thiazole derivatives Thiazolothiazole derivatives
T1 T2 TZ1 TZ2 TZ3 TZ4 TZ5 TZTZ1 TZTZ2 TZTZ3
0 0.275 0.343 0.336 0.347 0.336 0.347 0.344 0.254 0.261 0.270
15 0.199 0.243 0.267 0.255 0.217 0.241 0.219 0.214 0.178 0.166
30 0.110 0.100 0.167 0.130 0.087 0.134 0.080 0.152 0.097 0.073
45 0.051 0.042 0.088 0.031 0.012 0.051 0.014 0.106 0.064 0.047
60 0.040 0.020 0.039 0.008 0.014 0.008 0.012 0.093 0.058 0.045
75 0.027 0.017 0.015 0.007 0.012 0.010 0.011 0.048 0.033 0.026
90 0.027 0.015 0.0003 0.003 0.000 0.016 0.0005 0.041 0.030 0.025
PCCP Paper
View Article Online

Jeff value. Among the thiazolothiazole derivatives, TZTZ3 has
maximum Jeff value of 0.27 eV. From Fig. 4, it has been observed
that the Jeff is exponentially decreasing with increase in the
stacking angle for all the studied oligomers. This is due to an
unequal contribution of HOMO of each monomer on the
HOMO of the dimer. For instance, at 301 of stacking angle,
the HOMO of the T1 dimer consists of HOMO of the
first monomer by 74% and HOMO of the second monomer
by 25%. Notably, at the stacking angle of 901, thiophene and
thiazolothiazole derivatives have a significant Jeff value. For
example, Jeff calculated for TZTZ1 dimer with 901 of stacking
angle is 0.04 eV, because, at this stacking angle the HOMO of
the dimer consists of HOMO of the first monomer by 50% and
the second monomer by 49%. But, the thiazole derivatives have
negligible Jeff value at 901 of stacking angle. This is due to the
fact that the HOMO of thiazole dimer consists of the first
monomer HOMO by 97% and the contribution of second
monomer HOMO is negligible.
Fig. 4 Effective charge transfer integral (Jeff, in eV) for hole transport in (a) thiophene, (b) thiazole and (c) thiazolothiazole derivatives at different stacking angles
(y, in degree).
Paper PCCP
View Article Online

In thiophene derivatives, for electron transport, T2 has a
maximum effective charge transfer integral of 0.33 eV at 01 of
stacking angle. Among the studied thiazole derivatives, TZ3 has
a maximum Jeff value of 0.4 eV for electron transport which
shows that the presence of more thiazole rings favors electron
transport. At 01 of stacking angle, the isomers TZ1 and TZ2 have
a different Jeff value of 0.39 and 0.27 eV, respectively which is
due to the position of the CQN bonds in the thiazole rings. In
the thiazolothiazole derivatives, TZTZ3 has a maximum Jeff
value of 0.3 eV at 01 of stacking angle. While increasing the
stacking angle from 01 to 301, the Jeff for electron transport is
decreased. Note that except for the TZ4 oligomer, further
increase in the stacking angle from 451 leads to an increase
in the Jeff value. At the stacking angle of 751, the calculated Jeff
value for the TZ2 dimer is found to be 0.18 eV. At 751 of stacking
angle, the LUMO of TZ2 dimer consists of LUMO of the first
monomer by 47% and LUMO of the second monomer by 52%.
From Table 2, it has been observed that thiophene and thiazole
Fig. 5 Effective charge transfer integral (Jeff, in eV) for electron transport in (a) thiophene, (b) thiazole and (c) thiazolothiazole derivatives at different stacking angles
(y, in degree).
PCCP Paper
View Article Online

derivatives have significant effective charge transfer integrals at
the stacking angle of 901. Thiazolothiazole (TZTZ) derivatives
have a negligible Jeff value at the stacking angle of 901. Because
at this stacking angle the LUMO of TZTZ derivatives dimer
consist of 85–90% of LUMO of the first monomer and 10–15%
of LUMO of the second monomer. The above results show that
even at a larger stacking angle, thiophene derivatives have both
hole and electron transport ability. Whereas, the thiazole
derivatives have electron transport ability and thiazolothiazole
derivatives have hole transport ability at larger stacking angles
(see Fig. 4 and 5). These results confirm the results of earlier
studies,47,73
that the charge transfer integral corresponding to
hole and electron transport in organic molecules strongly
depends on the stacking angle and the presence of different
hetero atoms and their positions in the aromatic rings.
3.2. Reorganization energy
The presence of excess charge on a molecule will alter its
geometry. The energy change due to this structural reorganiza-
tion will act as a barrier for charge transport. The optimization
of neutral, anionic and cationic geometries of all the studied
oligomers is carried out at B3LYP/6-311G(2d,2p) level of theory
and the reorganization energies calculated using eqn (4) are
summarized in Table 3.
In thiophene derivatives, T2 has a minimum reorganization
energy of 0.31 and 0.38 eV for the presence of excess positive
and negative charge, respectively. This is because T2 oligomer
has more thiophene rings and more of a planar structure than
T1 which leads to a symmetrical charge distribution in T2
(see Fig. 2). Among the studied thiazole derivatives, TZ2 has a
maximum reorganization energy of 0.39 and 0.48 eV in the
presence of excess positive and negative charges, respectively.
By analyzing the optimized geometries of TZ2, it has been
observed that the presence of excess charge (positive or negative)
alters the C4–C3 bond length upto 0.04 Å and dihedral angles, C8–
C7–C5–C6 and S1–C2–C18–C16 up to 271 (for the numbering of
atoms see Fig. 1). For TZ3, TZ4 and TZ5 the calculated reorganiza-
tion energy value for the presence of excess positive charge is
similar (0.3 eV). Notably, TZ3 has a minimum reorganization
energy of 0.24 eV in the presence of excess negative charge. Because
the presence of more thiazole rings enhances the planarity and core
rigidity which reduces the structural relaxation due to the presence
of excess negative charge. The thiazolothiazole derivatives have a
similar reorganization energy value of 0.33 eV for the presence
of excess positive charge and TZTZ3 derivative has a minimum
reorganization energy value of 0.24 eV for the presence of excess
negative charge. The above results show that the presence of
thiazole and thiophene rings in the studied thiazole and
thiazolothiazole oligomers does not significantly alter the
reorganization energy for the presence of excess positive
charge, whereas TZ3 and TZTZ3 oligomers have a comparatively
smaller reorganization energy of 0.24 eV in the presence of
excess electrons which show the symmetrical negative charge
distribution in these oligomers and favor electron transport.
3.3. Charge carrier mobility
For a regular static sequence of stacked oligomers, the effective
charge transfer integral along the stack is equal to the Jeff values
are summarized in Tables 1 and 2. In this case, the mobility of
charge carrier can be calculated from eqn (5). The calculated
static mobility of positive and negative charges at different
stacking angle is summarized in Tables S6 and S7 (ESI†),
respectively. It is observed that a change in mobility with
respect to stacking angle is in accordance with the change in
Jeff value. The oligomer with a small reorganization energy has a
large mobility value. The static and dynamic structural disorder
in the p-conjugated system strongly affects the charge transfer
process via electronic coupling. As observed in earlier studies,55,66,74
the calculated Jeff value for hole and electron transport show that
the structural fluctuation in the form of stacking angle would
strongly affect the charge transport in studied oligomers. In the
present investigation, stacking angle fluctuation in thiophene,
thiazole and thiazolothiazole derivatives has been studied using
molecular dynamic (MD) simulations. The MD results provide the
information about stacking angle and its fluctuation from
equilibrium value. In the present study, the MD simulations
were carried out for stacked dimers with fixed intermolecular
distance of 3.53 Å for TZTZ1, TZTZ2 and T1 oligomers35
and
3.59 Å for TZTZ3 oligomer33
and 3.37 Å for TZ1–TZ5 and T2
oligomers34
using NVT ensembles at temperature 298.15 K and
pressure 10À5
Pa, as described in Section 2. The stacking angle
and potential energy of the stacked molecules in all the saved
100 000 frames were calculated and analyzed.
The graph has been plotted between the stacking angle and
number of occurrences of particular conformation with that
stacking angle. The plot for the thiazole oligomer, TZ1 is shown
in Fig. 6. Similar plots were obtained for the other studied
oligomers. It has been observed that the most probable con-
formation with particular stacking angle is to have a maximum
number of occurrences and minimum energy. The calculated
equilibrium stacking angle and corresponding effective charge
transfer integral of hole and electron transport for all the
studied oligomers are summarized in Table 4. It has been
observed that for thiophene oligomers, the most favorable
conformation occurs at the stacking angle of B181. The most
favorable conformation of TZ1 and TZ2 is around 301 and for TZ3–
TZ5 the stacking angle is around 151. The equilibrium stacking
Table 3 Reorganization energy, l (in eV) of thiophene (T1, T2), thiazole
(TZ1–TZ5) and thiazolothiazole (TZTZ1–TZTZ3) based oligomers
Oligomer
Reorganization energy (l) in eV
Hole Electron
T1 0.37 0.50
T2 0.31 0.38
TZ1 0.34 0.32
TZ2 0.39 0.48
TZ3 0.31 0.24
TZ4 0.30 0.27
TZ5 0.30 0.35
TZTZ1 0.32 0.36
TZTZ2 0.33 0.32
TZTZ3 0.33 0.24
Paper PCCP
View Article Online

angle for TZTZ1, TZTZ2 and TZTZ3 is 271, 211 and 261, respectively.
The force constant corresponding to stacking angle fluctuation has
been calculated by fitting the relative potential energy curve with
the classical harmonic oscillator equation. From the stacking angle
distribution (Fig. 6) it has been found that for all the studied
oligomers the stacking angle fluctuation of up to 101 is expected
from their equilibrium stacking angle value. As shown in Fig. 4
and 5, the Jeff will differ from place to place based on stacking
angle fluctuations. For this case, as described in Section 2, the
mobility of charge carrier has been calculated numerically using
Monte-Carlo simulations of polaron hopping transport.
During the Monte-Carlo simulations, the mean-square
displacement, hX2
(t)i of the charge has been monitored as a
function of time (t). The variation in hX2
(t)i with respect to time for
the TZ1 oligomer is shown in Fig. 7, and for other oligomers, the
results are shown in Fig. S2 (ESI†). For both hole and electron
transport, the hX2
(t)i increases linearly with respect to time. As
described in Section 2, the diffusion constant D for the charge
carrier is obtained as half of the slope of the line and based on the
Einstein relation (eqn (7)), the charge carrier mobility is directly
calculated from D. The calculated mobility of hole and electron in
the studied oligomers is summarized in Table 5. For all the studied
oligomers, the calculated mobility values from the Monte-Carlo
simulation is slightly larger than the mobility values calculated
for a static situation at the equilibrium stacking angle (see
Tables S6 and S7, ESI† and Table 5). The previous studies75,76
show that the non-Condon effect due to the structural fluctuation
influences the carrier mobility. That is the distortion in p-stack is
almost static in nature and fluctuation around the equilibrium
stacking angle favors charge transport.
To get further insight on charge transfer kinetics, the survival
probability P(t) is calculated. The P(t) is a measure of probability
for a charge carrier to be localized at particular site at a particular
time. The calculated survival probability for a charge carrier in
the thiazole oligomer, TZ1 is shown in Fig. 8, similar results were
obtained for the other oligomers and are shown in Fig. S2 (ESI†).
It has been observed that the survival probability decreases
exponentially with time and obeys the exponential law, P(t) =
exp(Àkt), here k is the charge transfer rate coefficient.77,78
At high temperatures (here, T = 298 K), the structural fluctuation
is fast and the corresponding disorder becomes dynamic rather
than static.79
The dynamic fluctuation effect on CT kinetics is
characterized using the rate coefficient which is defined as79
kðtÞ ¼ À
d ln PðtÞ
dt
(8)
The time evolution on CT kinetics in the tunneling regime is
studied using eqn (8). Based on this analysis, the type of
fluctuation (slow or fast) and the corresponding non-Condon
(NC) effect (kinetic or static) on CT kinetics is studied. To analyze
the NC effect, we plotted the charge transfer rate as a function of
time (see Fig. 9 and Fig. S2, ESI†, for TZ1 and other studied
oligomers) and fitted the line using the power law79
k(t) = ka
taÀ1
, 0 o a r 1 (9)
where, the rate coefficient, k was obtained from the survival
probability curve. It has been observed that the charge transfer
rate, k(t) varies slowly with respect to time. The dispersive
parameter ‘a’ is calculated by fitting the line with the above
eqn (9). The calculated dispersive parameter corresponding to
hole and electron transport in the studied oligomers are
summarized in Table 5. For all the studied oligomers the
dispersive parameter, a is nearer to 1 which revealed that the
Table 4 Equilibrium stacking angle (in degrees) calculated from molecular
dynamics simulations and the corresponding effective charge transfer integral
(in eV) of thiophene (T1, T2), thiazole (TZ1–TZ5) and thiazolothiazole (TZTZ1–
TZTZ3) based oligomers
Oligomers
Equilibrium stacking
angle (in degree)
Effective charge transfer
integral ( Jeff) in eV
Hole Electron
T1 19 0.170 0.110
T2 18 0.204 0.140
TZ1 30 0.167 0.092
TZ2 32 0.130 0.106
TZ3 19 0.180 0.186
TZ4 14 0.238 0.206
TZ5 18 0.187 0.204
TZTZ1 27 0.166 0.075
TZTZ2 21 0.152 0.100
TZTZ3 26 0.115 0.078
Fig. 6 The plot between the number of occurrence, relative potential energy with respect to stacking angle for TZ1 oligomer.
PCCP Paper
View Article Online

CT kinetics evolves dominantly in the static type of non-
Condon effect (fast fluctuation). In this type of CT process,
the survival probability of charge evolves as an exponential
decrease and CT is non-dispersive and the rate coefficient is
time-independent. In this case, the self-averaging of effective
charge transfer integral is responsible for the time independent
rate coefficient and therefore the mean squared displacement
of charge carrier always increases linearly with time along the
full simulation time. The above results show that the mobility is
independent of frequency and the use of Einstein relation
(eqn (7)) to calculate the mobility of charge carriers in the
studied oligomers is valid.
By using the survival probability, P(t), the disorder drift80
can be studied through thermodynamical relation for entropy,
X
t
SðtÞ ¼ ÀkB
X
t
PðtÞ log PðtÞ (10)
X
t
SðtÞ ¼ kB
X
t
ðktÞ expðÀktÞ (11)
Fig. 7 The mean square displacement of (a) positive and (b) negative charge in TZ1 oligomer with respect to time.
Table 5 Mobility (m), disorder drift time (St), rate coefficient (k) and dispersive parameter (a) for hole and electron transport in thiophene (T1, T2), thiazole (TZ1–TZ5)
and thiazolothiazole (TZTZ1–TZTZ3) based oligomers
Oligomer
Mobility (m) in cm2
VÀ1
sÀ1
Disorder drift time (St) in fs Rate coefficient (k)a
in Â1014
sÀ1
Dispersive parameter (a)
Hole Electron Hole Electron Hole Electron Hole Electron
T1 1.10 0.13 17.89 160.91 0.515 0.066 0.92 0.75
T2 2.88 0.62 6.38 32.59 1.421 0.310 0.91 0.81
TZ1 1.36 0.61 15.22 34.82 3.195 0.338 0.92 0.80
TZ2 0.37 0.08 59.76 257.27 0.245 0.033 0.74 0.90
TZ3 2.28 4.51 8.53 4.16 1.304 2.541 0.70 0.79
TZ4 4.05 3.32 4.23 5.70 2.097 1.645 0.94 0.86
TZ5 2.63 4.51 6.26 10.30 1.291 0.857 0.92 0.90
TZTZ1 1.72 0.25 12.30 99.79 0.751 0.155 0.87 0.70
TZTZ2 1.22 0.52 15.40 38.00 0.570 0.325 0.82 0.73
TZTZ3 0.55 0.81 40.76 34.75 0.277 0.439 0.87 0.81
a
Rate coefficient also referred as charge decay rate.
Paper PCCP
View Article Online

where, kB is Boltzmann constant. The plot for disorder drift in
thiazole oligomer, TZ1 is shown in Fig. 10 and for other
oligomers, the results are shown in Fig. S2 (ESI†). The disorder
drift causes a time delay for the transient charge along the
tunneling regime. The disorder drift time, St is the time at
which the disorder drift is at a maximum and is calculated from
the graph. The high disorder drift time means the system is in
its equilibrium stacking angle for a longer time which
decreases the charge transfer rate and the mobility of the
charge carrier is almost equal to the static case mobility
calculated at the equilibrium stacking angle. Along with charge
carrier mobility and dispersive parameter (a), the disorder
drift time corresponding to hole and electron transport are
summarized in Table 5 and based on these values the charge
transfer in studied oligomers is discussed below.
As expected, in thiophene derivatives the mobility of the
positive charge is higher than the mobility of the electron and
T2 has a higher hole mobility of 2.88 cm2
VÀ1
sÀ1
with small
disorder drift time of 6.38 fs. By comparing the mobility values
calculated for thiazole isomers TZ1 and TZ2, it has been
observed that TZ2 has a lower hole and electron mobility of
0.37 and 0.08 cm2
VÀ1
sÀ1
. The small eﬀective charge transfer
integral at the equilibrium stacking angle (321) and high
reorganization energy leads to a maximum disorder drift time
corresponding to hole and electron transport in the TZ2 oligomer.
In this case both the carriers strand a longer time on a particular
molecule instead of migrating due to less coupling between the
HOMO (or LUMO) states of nearby molecules. These results are in
agreement with the experimental results of Ando et al.34
It has
been shown in their studies that the FET mobility of TZ2 is
smaller than that of TZ1 by two orders of magnitude. While
comparing the mobility of charge carriers in thiazole isomers TZ3
and TZ4, it has been found that the hole mobility is maximum in
TZ4 and electron mobility is maximum in TZ3. Oligomer TZ4 has
a minimum disorder drift time of 4.23 fs for hole transport
(minimal dispersion and purely static NC eﬀect) and has hole
mobility of 4.05 cm2
VÀ1
sÀ1
. This is because, the hole transport in
oligomer TZ4 evolves with fast fluctuation around the equilibrium
stacking angle of 141 and this angle is comparatively smaller than
that of the other studied oligomers. The electron mobility in TZ3
and TZ5 is 4.51 cm2
VÀ1
sÀ1
. The above results clearly show that
the charge carrier mobility strongly depends on the arrangement
of atoms and structural alignment of nearby oligomers. It has
been observed that increasing the number of thiophene rings
enhances the hole transport significantly. The introduction of
thiazole rings in oligothiophene promotes n-type characteristics
and introduces the ambipolar transporting ability. It has been
observed that the mobility of charge carriers in thiazolothiazole
oligomers is relatively smaller than that in thiazole oligomers.
Among the studied thiazolothiazole oligomers, TZTZ1 and TZTZ2
Fig. 8 The survival probability of (a) positive and (b) negative charge in TZ1 oligomer with respect to time.
PCCP Paper
View Article Online

have hole mobility of 1.72 and 1.22 cm2
VÀ1
sÀ1
, respectively and a
corresponding disorder drift time of 12.3 and 15.4 fs.
One of the important factors that influence the charge
transport in a p-stacked system is the difference between the
site energy of nearby molecules. In the present work, the site
energy of p-stacked oligomers (e1 and e2) is calculated as the
diagonal matrix elements of the Kohn–Sham Hamiltonian and
the site-energy difference of p-stacked dimers is summarized in
Tables S8 and S9 (ESI†) at different stacking angles for positive
and negative charges. For all the studied p-stacked oligomers,
the significant difference between e1 and e2 is noted around the
equilibrium stacking angle for both hole and electron trans-
port. For thiophene oligomers, the site energy difference up to
0.06 eV was observed for hole and electron transport. Among
the thiazole oligomers, TZ1 and TZ3 have a maximum site
energy difference of B0.06 eV around the equilibrium stacking
angle for both hole and electron transport, and the oligomers
TZ2 and TZ4 have a site energy difference of B0.03 eV. The
thiazolothiazole oligomer, TZTZ2 has a relatively small site
energy difference of 0.01 eV around the equilibrium stacking
angle of 211. The site energy difference would act as a barrier
for charge transport and reduce the rate of charge transfer and
mobility. The above discussed mobility values were obtained
from Marcus rate eqn (6) and the site energy difference was not
included in the Monte-Carlo simulation for charge transport.
Hence, the reported mobility values are an upper limit and
provide qualitative information about charge transport in the
studied oligomers.
4. Conclusion
The parameters involved in the charge transport calculation
such as the charge transfer integral, site energy and reorganiza-
tion energy have been calculated for thiophene, thiazole and
thiazolothiazole based oligomers using quantum chemical
calculations. The effect of structural fluctuation in the form
of stacking angle distribution on the charge transfer rate was
studied using molecular dynamics (MD) and Monte-Carlo (MC)
simulations. It has been observed that the charge transfer
kinetics follows the static non-Condon effect due to the fast
fluctuation. In this regime, the charge transfer decay is expo-
nential, non-dispersive and the rate coefficient is time inde-
pendent due to the self-averaging of the effective charge
transfer integral. The calculated mobility of charge carriers in
TZ1 and TZ2 and also in TZ4 and TZ5 isomers shows that the
structural arrangement and position of thiophene and thiazole
rings are the crucial factors that determine the structural
planarity and efficient charge transport. Among the studied
thiazole oligomers, TZ1, TZ3, TZ4 and TZ5 have hole mobility of
1.36, 2.28, 4.05, 2.63 cm2
VÀ1
sÀ1
, respectively, and electron
mobility of 0.61, 4.51, 3.32 and 4.51 cm2
VÀ1
sÀ1
, respectively. It
has been found that the presence of thiazole rings promotes
Fig. 9 Time evolution of the rate coefficients for (a) positive and (b) negative charge transport in TZ1 oligomer.
Paper PCCP
View Article Online

n-type semiconducting performance. The addition of fused
bithiazole (thiazolothiazole) oligomer does not significantly
enhance the mobility of the charge carriers. The studied
thiazole oligomers TZ1 and TZ3–TZ5 have a good ambipolar
property which is useful for molecular electronics applications.
Acknowledgements
The authors thank the Department of Science and Technology
(DST), India for awarding this research project under the Fast
Track Scheme.
References
1 C. W. Tang and S. A. Vanslyke, Appl. Phys. Lett., 1987, 51,
913–915.
2 J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks,
K. Mackay, R. H. Friend, P. L. Burns and A. B. Holmes,
Nature, 1990, 347, 539–541.
3 H. E. Katz, J. Mater. Chem., 1997, 7, 369–376.
4 H. E. Katz, A. J. Lovinger, J. Johnson, C. Kloc, T. Siegrist,
W. Li, Y. Y. Lin and A. Dodabalapur, Nature, 2000, 404,
478–481.
5 M. Shim, A. Javey, N. W. Shi Kam and H. Dai, J. Am. Chem.
Soc., 2001, 123, 11512–11513.
6 N. S. Sariciftci, L. Smilowitz, A. J. Heeger and F. Wudl,
Science, 1992, 258, 1474–1476.
7 X. Zhan, Z. a. Tan, B. Domercq, Z. An, X. Zhang, S. Barlow,
Y. Li, D. Zhu, B. Kippelen and S. R. Marder, J. Am. Chem.
Soc., 2007, 129, 7246–7247.
8 G. H. Gelinck, T. C. T. Geuns and D. M. D. Leeuw, Appl. Phys.
Lett., 2000, 77, 1487–1489.
9 A. P. Kulkarni, C. J. Tonzla, A. Babel and S. A. Jenekhe,
Chem. Mater., 2004, 16, 4556–4573.
10 A. R. Murphy and J. M. J. Frechet, Chem. Rev., 2007, 107,
1066–1096.
11 Y. Shirota and H. Kageyama, Chem. Rev., 2007, 107, 953–1010.
12 L. Wang, G. Nan, X. Yang, Q. Peng, Q. Li and Z. Shuai, Chem.
Soc. Rev., 2010, 39, 423–434.
13 Y. Geng, S.-X. Xu, H.-B. Li, X.-D. Tang, Y. Wu, Z.-M. Su and
Y. Liao, J. Mater. Chem., 2011, 21, 15558–15566.
14 D. Fichou, Handbook of Oligo and Polythiophenes, Wiley –
VCH, Weinheim, 1999.
15 Handbook of Thiophene based Materials, ed. I. F. Perepichka
and D. F. Perepichka, Wiley – VCH, Weinheim, 2009.
16 J. M. Tour, Chem. Rev., 1996, 96, 537.
17 X. Yang, L. Wang, C. Wang, W. Long and Z. Shuai, Chem.
Mater., 2008, 20, 3205.
18 J. L. Bredas, D. Beljionne, V. Coropceanu and J. Cornil,
Chem. Rev., 2004, 104, 4971.
Fig. 10 Disorder drift time for (a) hole and (b) electron transport in TZ1 oligomer.
PCCP Paper
View Article Online

19 F. J. M. Z. Heringdorf, M. C. Reuter and R. M. Tromp,
Nature, 2001, 412, 517.
20 C. Kim, A. Facchetti and T. J. Marks, Science, 2007, 318,
76.
21 Q. Wu, R. Li, W. Hong, H. Li, X. Gao and D. Zhu, Chem.
Mater., 2011, 3138–3140.
22 Z. Bao, Adv. Mater., 2000, 12, 227–230.
23 Y. Geng, J. Wang, S. Wu, H. Li, F. Yu, G. Yang, H. Gao and
Z. Su, J. Mater. Chem., 2011, 21, 134–143.
24 H. E. Katz, Z. Bao and S. L. Gilat, Acc. Chem. Res., 2001,
34, 359.
25 R. P. Ortiz, H. Yan, A. Facchetti and T. J. Marks, Materials,
2010, 3, 1533.
26 Y. Lin, H. Fan, Y. Li and X. Zhan, Adv. Mater., 2012, 24, 3087.
27 A. Facchetti, M. Mushrush, H. E. Katz and T. J. Marks, Adv.
Mater., 2003, 15, 33.
28 A. Facchetti, J. Letizia, M.-H. Yoon, M. Mushrush, H. E. Katz
and T. J. Marks, Chem. Mater., 2004, 16, 4715.
29 D. J. Gundlach, Y. Y. Lin, T. N. Jackson and S. F. Nelson,
Appl. Phys. Lett., 2002, 80, 2925.
30 H. Meng, M. Bendikov, G. Mitchell, R. Helgeson, F. Wudl,
Z. Bao, T. Siegrist, C. Kloc and C. H. Chen, Adv. Mater., 2003,
15, 1090.
31 D. Pranabesh, P. Hanok, L. Woo-Hyoung, K. In-Nam and
L. Soo-Hyoung, Org. Electron., 2012, 13, 3183.
32 M. Zhang, H. Fan, X. Guo, Y. He, Z. Zhang, J. Min, J. Zhang,
G. Zhao, X. Zhan and Y. Li, Macromolecules, 2010, 43, 5706.
33 S. Ando, J. Nishida, Y. Inoue, S. Tokito and Y. Yamashita,
J. Mater. Chem., 2004, 14, 1787–1790.
34 S. Ando, R. Murakami, J. Nishida, H. Tada, Y. Inoue,
S. Tokito, S. Tokito and Y. Yamashita, J. Am. Chem. Soc.,
2005, 127, 14996–14997.
35 S. Ando, J. Nishida, H. Tada, Y. Inoue, S. Tokito and
Y. Yamashita, J. Am. Chem. Soc., 2005, 127, 5336–5337.
36 G. Xia, F. Haijun, Z. Maojie, H. Yu, T. Songting and
L. Yongfang, J. Appl. Polym. Sci., 2012, 124, 847.
37 B. Balan, C. Vijayakumar, A. Saeki, Y. Koizumi and S. Seki,
Macromolecules, 2012, 45, 2709.
38 S. Van mierloo, S. Chambon, A. E. Boyukbayram,
P. Adriaensens, L. Lutsen, T. J. Cleij and D. Vanderzande,
Magn. Reson. Chem., 2010, 48, 362.
39 T. Kono, D. Kumaki, J.-i. Nishida, S. Tokito and
Y. Yamashita, Chem. Commun., 2010, 46, 3265.
40 M. Mamada, J.-I. Nishida, D. Kumaki, S. Tokito and
Y. Yamashita, Chem. Mater., 2007, 19, 5404.
41 M. Mamada, J.-I. Nishida, S. Tokito and Y. Yamashita,
Chem. Lett., 2008, 766.
42 I. Osaka, G. Sauve, R. Zhang, T. Kowalewski and
R. D. McCullough, Adv. Mater., 2007, 19, 4160.
43 I. Osaka, R. Zhang, G. Sauve, D.-M. Smilgies, T. Kowalewski
and R. D. McCullough, J. Am. Chem. Soc., 2009, 131, 2521.
44 S. N. Ando, J. Nishida, H. Tada, Y. Inoue, S. Tokito and
Y. Yamashita, J. Am. Chem. Soc., 2005, 127, 5336–5337.
45 C. R. Newman, C. D. Frisbie, D. A. da Silva Filho,
J.-L. Bredas, P. C. Ewbank and K. R. Mann, Chem. Mater.,
2004, 16, 4436.
46 M. Stossel, J. Staudigel, F. Steuber, J. Simmerer and
A. Winnacker, Appl. Phys. A: Mater. Sci. Process., 1999,
68, 387.
47 K. Senthilkumar, F. C. Grozema, F. M. Bichelhaupt and
L. D. A. Siebbeles, J. Chem. Phys., 2003, 119, 9809.
48 F. C. Grozema and L. D. A. Siebbles, Int. Rev. Phys. Chem.,
2008, 27, 87–138.
49 E. A. Silinsh, Organic Molecular Crystals, Springer – Verlag,
Berlin, 1980.
50 R. A. Marcus, Annu. Rev. Phys. Chem., 1964, 15, 155.
51 R. A. Marcus, Rev. Mod. Phys., 1993, 65, 599.
52 M. Bixon and J. Jortner, J. Chem. Phys., 2002, 281, 393.
53 M. D. Newton, Chem. Rev., 1991, 91, 767.
54 G. Te Velde, F. M. Bickelhaupt, E. J. Baerends, C. Fonseca
Guerra, S. J. A. Van Gisbergeh, J. G. Snijders and T. Ziegler,
J. Comput. Chem., 2001, 22, 931.
55 P. Prins, K. Senthilkumar, F. C. Grozema, P. Jonkheijm,
A. P. H. J. Schenning, E. W. Meijer and L. D. A. Siebbles,
J. Phys. Chem. B, 2005, 109, 18267–18274.
56 A. D. Becke, Phys. Rev. A, 1988, 38, 3098.
57 J. P. Perdew, Phys. Rev. B: Condens. Matter Mater. Phys., 1986,
33, 8822.
58 P. R. T. Schipper, O. V. Gritsenko, S. J. A. van Gisbergen and
E. J. Baerends, J. Chem. Phys., 2000, 112, 1344.
59 O. V. Gritsenko, P. R. T. Schipper and E. J. Baerends, Chem.
Phys. Lett., 1999, 302, 199.
60 H. L. Tavernier and M. D. Fayer, J. Phys. Chem. B, 2000,
104, 11541.
61 M. M. Torrent, M. Durkut, P. Hadley, X. Ribas and C. Rovira,
J. Am. Chem. Soc., 2004, 126, 984.
62 S. H. Vosko, L. Wilk and M. Nusair, Can. J. Phys., 1980, 58,
1200–1211.
63 A. D. Becke, J. Chem. Phys., 1993, 98, 5648–5652.
64 C. T. Lee, W. T. Yang and R. G. Parr, Phys. Rev. B: Condens.
Matter Mater. Phys., 1988, 37, 785–789.
65 Y. Shao, L. F. Molnar, Y. Jung, J. Kussmann, C. Ochsenfeld,
S. T. Brown, A. T. Gilbert, L. V. Slipchenko, S. V. Levchenko,
D. P. O’Neill, R. A. DiStasio, Jr., R. C. Lochan, T. Wang,
G. J. Beran, N. A. Besley, J. M. Herbert, C. Y. Lin, T. Van
Voorhis, S. H. Chien, A. Sodt, R. P. Steele, V. A. Rassolov,
P. E. Maslen, P. P. Korambath, R. D. Adamson, B. Austin,
J. Baker, E. F. Byrd, H. Dachsel, R. J. Doerksen, A. Dreuw,
B. D. Dunietz, A. D. Dutoi, T. R. Furlani, S. R. Gwaltney,
A. Heyden, S. Hirata, C. P. Hsu, G. Kedziora, R. Z. Khalliulin,
P. Klunzinger, A. M. Lee, M. S. Lee, W. Liang, I. Lotan,
N. Nair, B. Peters, E. I. Proynov, P. A. Pieniazek, Y. M. Rhee,
J. Ritchie, E. Rosta, C. D. Sherrill, A. C. Simmonett,
J. E. Subotnik, H. L. Woodcock, 3rd, W. Zhang, A. T. Bell,
A. K. Chakraborty, D. M. Chipman, F. J. Keil, A. Warshel,
W. J. Hehre, H. F. r. Schaefer, J. Kong, A. I. Krylov, P. M. Gill
and M. Head-Gordon, Phys. Chem. Chem. Phys., 2006, 8,
3172–3191.
66 P. Prins, F. C. Grozema and L. D. A. Siebbeles, J. Phys. Chem.
B, 2006, 110, 14659–14666.
67 Y. A. Berlin, F. C. Grozema, L. D. A. Siebbeles and
M. A. Ratner, J. Phys. Chem. C, 2008, 112, 10988–11000.
Paper PCCP
View Article Online

68 L. B. Schein and A. R. McGhie, Phys. Rev. B: Condens. Matter
Mater. Phys., 1979, 20, 1631.
69 J. W. Ponder, TINKER: 4.2, Software tools for molecular
design, Saint Louis, Washington, 2004.
70 P. Ren and J. W. Ponder, J. Phys. Chem. B, 2003, 107, 5933.
71 J. H. Lii and N. L. Allinger, J. Am. Chem. Soc., 1989,
111, 8576.
72 N. L. Allinger, F. Yan, L. Li and J. C. Tai, J. Comput. Chem.,
1990, 11, 868.
73 G. Saranya, N. Santhanamoorthi, P. Kolandaivel and
K. Senthilkumar, Int. J. Quantum Chem., 2012, 112, 713–723.
74 P. Prins, F. C. Grozema, F. Galbrecht, U. Scherf and L. D. A.
Siebbles, J. Phys. Chem. C, 2007, 111, 11104–11112.
75 W. Zhang, W. Liang and Y. Zhao, J. Chem. Phys., 2010, 133,
1–11.
76 S. S. Skourtis, I. A. Balabin, T. Kawatsu and D. N. Beratan,
Proc. Natl. Acad. Sci. U. S. A., 2005, 102, 3552.
77 F. C. Grozema, Y. A. Berlin and L. D. A. Siebbeles, Int. J.
Quantum Chem., 1999, 75, 1009–1016.
78 F. Reif, Fundamentals of Statistical and Thermal Physics,
McGraw-Hill, 1965, ch. 12, pp. 461–490.
80 S. L. Miller and D. G. Childers, Probability and Random
Processes with Applications to Signal Processing and Commu-
nications, Elsevier Inc., 2004, ch. 9, pp. 323–359.
PCCP Paper
View Article Online

Effect of Structural Fluctuations on Charge Carrier Dynamics in
Triazene Based Octupolar Molecules
K. Navamani and K. Senthilkumar*
Department of Physics, Bharathiar University, Coimbatore 641 046, India
*S Supporting Information
ABSTRACT: The charge transport in 2,4,6-tris(thiophene-2-yl)-1,3,5-triazene based octupolar
molecules is studied. The effect of structural fluctuation on charge transfer integral and site energy is
included while studying the charge transfer kinetics through kinetic Monte Carlo simulation. The charge
transfer kinetic parameters such as rate coefficient, dispersive parameter, disorder drift time, mobility,
and hopping conductivity are studied for both steady state (Δε = 0) and non-steady state (Δε ≠ 0). It
has been found that the hopping conductivity depends on the charge transfer rate and electric
permittivity of the medium. The disorder drift time (St) is acting as the crossover point between
adiabatic band and nonadiabatic hopping charge transfer mechanism. The calculated hole and electron
mobilities in 2,4,6-tris[5-(3,4,6-trioctyloxyphenyl)thiophene-2-yl]-1,3,5-triazene (1b) and 2,4,6-tris[5′-
(3,4,6-tridodecyloxyphenyl)-2,2′-bithiophene-5-yl]-1,3,5-triazene (2) are in good agreement with
experimental results. The theoretical results show that the methoxy-substituted octupolar molecule 1c
is having good hole and electron transporting ability with mobility values of 0.15 and 1.6 cm2
/(V s).
1. INTRODUCTION
For the past three decades the organic electronics is an
emerging field in science and technology due to its applications
in light-emitting diodes,1,2
field effect transistors,3−5
and
photovoltaic cells.6,7
The organic materials have soft condensed
phase property, easily tunable electronic property through the
structural modification and suitable functional group sub-
stitution, and having self-assembling character.8−10
At room
temperature, the molecules possess the structural disorder, and
the charge transfer integral (or coupling strength) between the
electronic states is small due to the presence of electron−
phonon scattering and hence the electronic states are
localized.8,11−15
The localized wave function of the charge
carrier is thermally activated by the incoherent hopping
mechanism.9,16−18
The interaction of charge carrier with the
electronic and nuclear degrees of freedom leads to diffusion-
limited localized charge transport by the dynamic disorder and
breakdown of the Franck−Condon (FC) principle.15,19−23
In
this case, the wave function of the charge carrier will spread
over the tunneling path, and this dynamic localization will
facilitate the charge transfer.11,15,19−21,24,25
In the present work,
we have studied the effect of nuclear and electronic degrees of
freedom on charge transfer (CT) kinetics in triazene based
organic molecules, and an intermediate charge transfer
mechanism between the adiabatic band transport and non-
adiabatic hopping transport is characterized in terms of disorder
drift time.20,21,26
In general, most of the organic molecules have p-type
character because of their intrinsic electronic structure.27
Therefore, the current interest in molecular electronics is to
synthesize ambipolar materials through the substitution of
suitable electron donor and acceptor units.10,28,29
In this work,
the charge transport properties of recently synthesized 2,4,6-
tris(thiophene-2-yl)-1,3,5-triazene based molecules are stud-
ied.29
As shown in Figure 1, in these molecules the peripheral
arms are consisting of electron-rich thiophene and phenyl rings
with alkyl side chains which are acting as an electron donor, and
the central core of triazene unit has large electron affinity which
is serving as an acceptor. This hybrid characteristic of these
octupolar molecules will facilitate the transport of both hole
and electron. These triazene based octupolar molecules were
synthesized in liquid crystalline state and have columnar self-
assembling and π-stacking properties. The columnar self-
assembling character will provide an one-dimensional path for
charge transport. Among the reported 2,4,6-tris(thiophene-2-
yl)-1,3,5-triazene based octupolar molecules, the 2,4,6-tris[5-
(3,4,6-trioctyloxyphenyl)thiophene-2-yl]-1,3,5-triazene (1b),
2,4,6-tris[5-(3,4,6-trimethoxyphenyl)thiophene-2-yl]-1,3,5-tria-
zene (1c), and 2,4,6-tris[5′-(3,4,6-tridodecyloxyphenyl)-2,2′-
bithiophene-5-yl]-1,3,5-triazene (2) molecules have high degree
of coplanarity29
which leads the strong π-stacking property. It
has been shown in earlier study that these molecules possess
well-organized hexagonal columnar phase even at temperature
higher than 100 °C which shows their thermal stability.29
The
intramolecular nonbonded S···N interactions restrict the
rotation of nearby thiophene rings which allow the efficient
columnar π-stacking arrangement. The X-ray crystallographic
analysis on molecules 1b and 1c shows that the intermolecular
distance between the π-stacked molecules in the columnar
arrangement is 3.3 and 3.5 Å, respectively.29
The time-of-flight
measurement shows that the octupolar molecule 1b has the
anisotropic hole and electron mobilities in the order of 10−5
Received: September 18, 2014
Revised: November 7, 2014
Published: November 13, 2014
Article
pubs.acs.org/JPCC
© 2014 American Chemical Society 27754 dx.doi.org/10.1021/jp509450k | J. Phys. Chem. C 2014, 118, 27754−27762

and 10−3
cm2
/(V s), respectively.29
Comparably, the molecule
2 has higher hole mobility than 1b and is in the order of 10−3
cm2
/(V s).29
The hole and electron mobilities of 1c and the
electron mobility of 2 are not reported. Therefore, to
understand the charge transport properties of these molecules,
the electronic structure and charge transport properties such as
charge transfer integral, site energy, reorganization energy, rate
of charge transfer, mobility of charge carriers, and the effects of
nuclear and electronic degrees of freedom on the charge
transfer kinetics are studied.
In the present work, the rate of charge transfer is studied in
two situations: in the first case, the charge transfer between two
identical sites with same site energy, that is, Δεij = 0; in the
second case, the charge transfer between two nonidentical sites,
that is, Δεij ≠ 0.10,17
To get better insight into charge transport
in studied molecules, we have studied the CT kinetic
parameters such as disorder drift time, effect of structural
fluctuation on charge carrier flux, and hopping conductivity.
Here, the disorder drift time is used to identify possible
intermediate regime between band transport and localized
hopping transport. In the present study, we have formulated the
density flux equation which describes the charge diffusion
nature in the localized sites (by thermal disorder), and the time
evolution of density flux provides the relation between the
hopping conductivity and transition rate. The results obtained
from the present investigation and past studies19,20,30
show that
the structural fluctuation in the form of stacking angle change
strongly alters the charge transfer kinetics. Hence, in the
present work, the classical molecular dynamics is used to study
the stacking angle distribution in the studied molecules.
2. THEORETICAL FORMALISM
By using the tight binding Hamiltonian approach, the presence
of excess charge in a π-stacked molecular system is expressed
as31,32
∑ ∑ε θ θ̂ = ++
≠
+
H a a J a a( ) ( )
i
i i i
i j
i j i j,
(1)
where ai
+
and ai are the creation and annihilation operators;
εi(θ) is the site energy, energy of the charge when it is localized
at the ith molecular site and is calculated as diagonal matrix
element of the Kohn−Sham Hamiltonian, εi = ⟨φi|ĤKS|φi⟩. The
second term of eq 1, Ji,j, is the off-diagonal matrix element of
the Hamiltonian, Ji,j = ⟨φi|ĤKS|φj⟩, known as charge transfer
integral or electronic coupling which measures the strength of
the overlap between φi and φj (HOMO or LUMO of nearby
molecules i and j). Based on the semiclassical Marcus theory,
the charge transfer rate (k) is defined as17,23,33
π
ρ=
ℏ
| |k J
2
eff
2
FCT (2)
The effective charge transfer integral Jeff is defined in terms of
charge transfer integral J, spatial overlap integral S, and site
energy ε as34
ε ε
= −
+⎛
⎝
⎜
⎞
⎠
⎟J J S
2i j i j
i j
eff , ,i j,
(3)
where εi and εj are the energy of a charge when it is localized at
ith and jth molecules, respectively. The site energy, charge
transfer integral, and spatial overlap integral were computed
using the fragment molecular orbital (FMO) approach as
implemented in the Amsterdam density functional (ADF)
theory program.30,35,36
In ADF calculation, we have used the
Becke−Perdew (BP)37,38
exchange correlation functional with
triple-ζ plus double polarization (TZ2P) basis set.39
In this
procedure, the charge transfer integral and site energy
corresponding to hole and electron transport are calculated
directly from the Kohn−Sham Hamiltonian.31,35
In eq 2, the Franck−Condon (FC) factor ρFCT measures the
weightage of density of states (DOS) and is calculated from the
reorganization energy (λ) and the site energy difference
between initial and final states, Δεij = εj − εi.
ρ
πλ
ε λ
λ
= −
Δ +⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥k T k T
1
4
exp
( )
4
ij
FCT
B
2
B (4)
The reorganization energy measures the change in energy of
the molecule due to the presence of excess charge and changes
in the surrounding medium. The reorganization energy due to
the presence of excess hole (positive charge, λ+) and electron
(negative charge, λ−) is calculated as40,41
λ = − + −±
± ± ± ±
E g E g E g E g[ ( ) ( )] [ ( ) ( )]0 0 0 0
(5)
Figure 1. Chemical structure of triazene based octupolar molecules 1
(1b: R = OC8H17; 1c: R = OCH3) and 2 (R = OC12H25).
The Journal of Physical Chemistry C Article
dx.doi.org/10.1021/jp509450k | J. Phys. Chem. C 2014, 118, 27754−2776227755

where E±
(g0
) is the total energy of an ion in neutral geometry,
E±
(g±
(g±
) is the
energy of the neutral molecule in ionic geometry, and E0
(g0
) is
geometries of the studied molecules 1b, 1c, and 2 in neutral
and ionic states are optimized using the density functional
theory method B3LYP42−44
in conjunction with the 6-31G(d,
p) basis set, as implemented in the GAUSSIAN 09 package.45
As reported in previous studies,19,20,30,46
the structural
fluctuations in the form of periodic fluctuation in π-stacking
angle strongly influence the rate of charge transfer. In the
disordered geometry, the migration of charge from one site to
another site can be modeled through incoherent hopping
charge transport mechanism. In the present study, we have
performed the kinetic Monte Carlo (KMC) simulation to
calculate the charge carrier mobility in which charge is
propagated on the basis of rate of charge transfer calculated
from eq 2. In this model, we assume that the charge transport
takes place along the sequence of π-stacked molecules, and the
charge does not reach the end of molecular chain within the
time scale of simulation. In each step of KMC simulation, the
most probable hopping pathway is found out from the
simulated trajectories based on the charge transfer rate at
particular conformation. In the case of normal Gaussian
diffusion of the charge carrier in one dimension, the diffusion
constant D is calculated from mean-squared displacement
⟨X2
(t)⟩ which increases linearly with time t
=
⟨ ⟩
→∞
D
X t
t
lim
( )
2t
2
(6)
The charge carrier mobility is calculated from diffusion
coefficient D by using the Einstein relation47
μ =
⎛
⎝
⎜
⎞
⎠
⎟
e
k T
D
B (7)
The charge transfer kinetics on the studied molecules is
analyzed based on the key parameters of charge transport, rate
coefficient, mobility, hopping conductivity, disorder drift time,
dispersive parameter, and density flux along the charge transfer
path. At room temperature (T = 298 K), the structural
fluctuation is fast, and the corresponding disorder becomes
dynamic rather than static.19
The dynamic fluctuation effect on
CT kinetics is characterized by using the rate coefficient which
is defined as19
= −k t
P t
t
( )
d ln ( )
d (8)
where P(t) is the survival probability of charge at particular
electronic state. Based on this analysis, the type of fluctuation
(slow or fast) and corresponding non-Condon (NC) effect
(kinetic or static) on CT kinetics are studied. The time
dependency character of rate coefficient is analyzed by using
the power law19,20
= ≤−
k t k t a( ) , 0 1a a 1
(9)
In this case, the timely varying rate coefficient k(t) is calculated
by using eq 8. Here, the dispersive parameter a is calculated by
fitting the plotted curve of rate coefficient versus time on eq 9.
In addition to this, the dynamic disorder effect is studied by
using survival probability through the entropy relation:20,48
∑ ∑= −S t k P t P t( ) ( ) log ( )
t t
B
(10)
As observed in the previous studies,19−21,25
the dynamic
disorder kinetically drifts the charge carrier along the charge
transfer path. The variation of disorder drift (S(t)/kB) during
CT is numerically calculated on the basis of eq 10. In adiabatic
regime, the drift for CT takes finite time to get the energy from
the environment to overcome the trapping potential due to
structural disorder.11
The disorder drift time St is the time at
which the disorder drift is maximum and is calculated from the
graph (see Figures 8 and 9). That is, the timely varying drift
curve provides the information about charge diffusion process.
It has been shown in earlier studies15,19,21,24
that the presence
of dynamic disorder is kinetically favorable for CT because the
dynamic fluctuation relaxes the barrier and promotes the carrier
motion between the stacked molecules. The timely varying
density flux at particular site can be calculated by using S(t) and
is described as
ρ ρ= −
⎛
⎝
⎜
⎞
⎠
⎟
S t
k
exp
3 ( )
5S S
B
0
(11)
where ρS0
is the density flux in the absence of dynamic disorder.
By taking the time evolution of density flux (eq 11), the
hopping conductivity is described as
σ ε=
∂
∂
P
t
3
5
Hop
(12)
That is, the hopping conductivity purely depends on the rate of
transition probability (or charge transfer rate which is equal to
∂P/∂t) and electric permittivity (ε) of the medium. In
agreement with the previous Hall effect measurement
studies,15,49
eq 12 shows that the hopping conductivity depends
only on the electric component of the medium. The calculated
rate coefficient from survival probability graph (see Figures 4
and 5) is used in eq 12 to calculate the hopping conductivity.
To find the time-dependent density flux in charge transfer path,
the ratio of charge density (ρ/ρ0) is studied through the
disorder drift and density flux equations (10) and (11). The
change in density flux during the simulation period is calculated
and plotted.
To get the quantitative insight into charge transport
properties in these molecules, the information about stacking
angle and its fluctuation around the equilibrium is required. As
reported in previous study,20
the equilibrium stacking angle and
its fluctuation were investigated by using classical molecular
dynamics (CMD) simulations. The molecular dynamics
simulation was performed for stacked dimers with fixed
intermolecular distance of 3.3 Å for 1b and 3.5 Å for molecules
1c and 2 using NVT ensemble at temperature 298.15 K and
pressure 10−5
Pa, using the TINKER 4.2 molecular modeling
package50,51
with the standard molecular mechanics force field
MM3.52,53
The simulations were performed up to 10 ns with
time step of 1 fs, and the atomic coordinates in trajectories were
saved in the interval of 0.1 ps. The energy and occurrence of
particular conformation were analyzed in all the saved 100 000
frames to find the stacking angle and its fluctuation around the
equilibrium value.20
3. RESULTS AND DISCUSSION
The geometry of the triazene based octupolar molecules 1 and
2 was optimized using the DFT method at the B3LYP/6-

31G(d, p) level of theory and is shown in Figure S1. Note that
the molecules 1b and 1c are differed by the substitution of alkyl
groups on the end phenyl rings. For molecule 1b the side chain
is OC8H17, and in molecule 1c, the substitution group is
OCH3.29
It has been shown in earlier studies24,54
that the effect
of side chains on the electronic states of individual molecules is
small. Hence, the electronic structure calculations were
performed only for OCH3-substituted molecule 1c; the results
were used in the CT calculations for molecule 1b, and also for
molecule 2 the electronic structure calculations were performed
with OCH3 substitution. As a good approximation, the positive
charge (hole) will migrate through the highest occupied
molecular orbital (HOMO), and the negative charge (electron)
will migrate through the lowest unoccupied molecular orbital
(LUMO) of the stacked molecules; the charge transfer integral,
spatial overlap integral, and site energy corresponding to
positive and negative charges were calculated based on
coefficients and energies of HOMO and LUMO. The density
plots of HOMO and LUMO of the studied molecules
calculated at the B3LYP/6-31G(d, p) level of theory are
shown in Figures S2 and S3, respectively. As shown in Figures
S2 and S3, the HOMO and LUMO are π orbital and HOMO is
delocalized mainly on the three peripheral arms and no density
on the central triazene core. The LUMO is delocalized on the
triazene core and on the thiophene rings of two peripheral arms
and less density on the phenyl rings. That is, the overlap of
peripheral arms of the stacked molecules favors the hole
transport, and the overlap of triazene cores and thiophene rings
of the nearby molecules favors the electron transport.
3.1. Effective Charge Transfer Integral. The effective
charge transfer integral (Jeff) for hole and electron transport in
the studied molecules is calculated by using eq 3. It has been
shown in earlier studies20,30,35
that the Jeff strongly depends on
stacking distance and stacking angle. Previous experimental
study29
shows that for molecules 1b and 1c the stacking
distance is 3.3 and 3.5 Å, respectively, and for molecule 2, the
CMD simulation was performed to find the stacking distance.
During the MD simulation the alkyl side chains in the
molecules 1b and 2 are included as reported in previous
work.29
As shown in Figure S4, the CMD results show that the
stacking distance for molecule 2 is 3.5 Å, which is closer to that
of many liquid crystalline molecules. The Jeff for hole and
electron transport in 1b, 1c, and 2 is calculated by fixing the
stacking distance as 3.3 Å for 1b and 3.5 Å for 1c and 2, and the
stacking angle is varied from 0 to 180° in the step of 10°. For
both hole and electron transport, the molecule 1b has a larger
Jeff value than 1c due to the small intermolecular distance of 3.3
Å. The variation of Jeff with respect to stacking angle is shown in
Figures S5 and S6. The shape and distribution of the frontier
molecular orbital on each monomer are responsible for overlap
of orbital of nearby molecules. As shown in Figure S2, the
HOMO is delocalized on the peripheral arms of the molecules,
and molecule 2 has larger peripheral arms which favor the
strong overlap of HOMO of nearby molecules at the stacking
angle of 0 and 120°. As shown in Figure S5, for hole transport,
the Jeff is high at the stacking angle range of 100°−130°. At
these angles, the HOMO of each monomer contributes nearly
equally for HOMO of the dimer. For instance, at 120° of
stacking angle the HOMO of the 1c dimer consists of HOMO
of first monomer by 48% and the second monomer by 51%.
It has been observed that the effective charge transfer integral
(Jeff) for electron transport is maximum at 0° of stacking angle.
At this ideal orientation, the delocalization of LUMO on the
triazene core and on two thiophene rings (see Figure S3) favors
the overlap of LUMO of π-stacked molecules. Notably, the
significant Jeff is calculated for electron transport at the stacking
angle range of 70°−130° (see Figure S6). At the stacking angle
of 120°, the Jeff for electron transport in 1c is 0.15 eV. At this
stacking angle the LUMO of the dimer consists of LUMO of
first monomer by 47% and the second monomer by 52%, which
favors the constructive overlap. In agreement with the previous
studies,11,19,30,31,46
the above results clearly show that the
structural fluctuations in the form of stacking angle change
strongly affect the Jeff. Hence, the equilibrium stacking angle
and its fluctuation from equilibrium value are studied for
molecules 1b, 1c, and 2 using classical molecular dynamics
simulations. The CMD result shows that the equilibrium
stacking angle for molecules 1b, 1c, and 2 is 166°, 113°, and
160°, respectively, and the stacking angle fluctuation up to 10°
to 15° from the equilibrium angle is observed (see Figure S7).
Within this stacking angle fluctuation range the Jeff for hole
transport in molecules 1b and 2 is less (∼0.002 and 0.001 eV),
and for molecule 1c the Jeff is around 0.1 eV (see Figure S5). As
shown in Figure S6, for electron transport in molecule 1c the
Jeff value is nearly 0.15 eV around the equilibrium stacking
angle, and the molecules 1b and 2 have the Jeff value of 0.08 and
0.04 eV, respectively. The fluctuation in Jeff around the
equilibrium stacking angle is included in the kinetic Monte
Carlo simulation to calculate the CT kinetic parameters.
3.2. Site Energy Difference. One of the important factors
that influence the charge transport in π-stacked systems is the
difference between site energy (Δεij = εj − εi) of nearby
molecules. The hopping rate exponentially depends on Δεij.
The site energy difference arises due to the conformational
change, electrostatic interactions, and polarization effects.
According to Marcus theory of charge transfer rate equation,
if Δεij is negative, it will serve as the driving force, and if Δεij is
positive, it will act as a barrier for charge transfer between π-
stacked molecules. The variation of site energy difference with
respect to the stacking angle for hole and electron transport in
the studied molecules is shown in Figures S8 and S9,
respectively. It has been observed that the variation of site
energy difference with respect to stacking angle follows the
same trend for both hole and electron transport in the studied
molecules. For both hole and electron transport in 1b and 1c,
the site energy difference is maximum at 90° of stacking angle.
For hole transport in molecule 2, the maximum Δεij of 0.15 eV
is calculated at the stacking angle range of 130°−140°, and for
electron transport the maximum Δεij of 0.08 eV is calculated.
For hole transport, within the equilibrium stacking angle
fluctuation range the molecules 1b, 1c, and 2 have the average
site energy difference of around 0.04, −0.04, and 0.02 eV,
respectively, and for electron transport the average site energy
difference is 0.06, 0.07, and 0.03 eV. That is, the Δεij calculated
for electron transport in molecule 1c will act as a driving force
for charge transfer, and for other cases Δεij is acting as a barrier.
The calculated Δεij values were included while calculating the
mobility and other kinetic parameters through Monte Carlo
simulation.
3.3. Reorganization Energy. The change in energy of the
molecule due to structural reorganization induced by excess
charge will act as a barrier for charge transport. The geometry
of neutral, anionic, and cationic states of the studied molecules
were optimized at the B3LYP/6-31G(d, p) level of theory, and
the reorganization energy is calculated by using eq 5.

Among the studied molecules, the molecule 2 has minimum
reorganization energy of 0.37 and 0.2 eV for excess positive and
negative charges, respectively. The reorganization energy of
molecule 1 is 0.56 and 0.3 eV for excess positive and negative
charges, respectively. By analyzing the optimized geometry of
neutral and ionic states of molecule 1, we found that the
presence of negative charge alters the length of C1−N1, C3
N1, and C1−C4 bonds in the triazene core up to 0.03 Å. As
shown in Table S1, in addition to the above changes, the
presence of excess positive charge significantly alters the
dihedral angle between the thiophene and phenyl rings of
peripheral arms up to 11°, which is the reason for the high hole
reorganization energy of 0.56 eV. For molecule 2, the presence
of positive and negative charges alters the dihedral angle (C−
C−CS) between the phenyl and thiophene rings up to 11°.
Since the molecule 2 has larger size than the molecule 1, the
reorganization energy of molecule 2 is lesser than that of
molecule 1. The calculated reorganization energy values shows
that the negative charge transport is more feasible than the
positive charge transport in the studied octupolar molecules.
3.4. Charge Transfer Kinetics. The calculated effective
charge transfer integral (Jeff), site energy difference (Δεij), and
reorganization energy (λ) are used to calculate the transfer rate
and mobility of the charge carriers in the studied octupolar
molecules. In the present work, the charge transfer kinetics is
studied in two situations: steady state (Δεij = 0) and non-steady
state (Δεij ≠ 0). As shown in Figures 2 and 3, the mean-
squared displacement ⟨X2
(t)⟩ of the charge carrier calculated
from kinetic Monte Carlo simulation is linearly increasing with
time, and the survival probability P(t) of the charge carrier at
particular site exponentially decreases (see Figures 4 and 5) for
hole and electron transport in the studied molecule 1c. Similar
trends were observed for the molecules 1b and 2. As described
in section 2, the diffusion constant D for the charge carrier is
obtained as half of the slope of the line, and based on the
Einstein relation (eq 7) the charge carrier mobility is calculated
from the D. The calculated mobility and rate coefficient for
hole and electron transport in steady and non-steady states are
summarized in Tables 2 and 3.
In the steady state regime (Δεij = 0), for hole transport in 1c
and 2 the dispersive parameter (a) is above 0.75 (see Table 2),
which shows that the CT kinetics follows static non-Condon
effect. As shown in Figure 6, the rate varies slowly with respect
to time, approximately constant for hole transport in the
molecule 1c. In the non-steady state regime (Δεij ≠ 0), the
dispersive parameter calculated for hole transport in molecule
1b is 0.17; that is, the CT follows kinetic non-Condon effect,
and the rate coefficient is time dependent.19
In this non-steady
state regime, the disorder drift time for hole transport in
molecule 1b is larger than that of other studied molecules (see
Tables 2 and 3). Both in steady and non-steady states, the hole
mobility in molecule 1b is nearly 0.0003 cm2
/(V s), which is
due to the small Jeff calculated at equilibrium stacking angle
range of 156°−176°. Molecule 1c has significant hole mobility
of 0.13 and 0.2 cm2
/(V s) at steady and non-steady states, and
the corresponding hopping conductivity is 41.36 and 76.62 S/
m, respectively, which is due to significant Jeff and negative Δεij
Figure 2. Mean-squared displacement of hole in molecule 1c in (a)
steady state (b) non-steady state with respect to time.
Figure 3. Mean-squared displacement of electron in molecule 1c in
(a) steady state (b) non-steady state with respect to time.
Table 1. Equilibrium Stacking Angle θeq, Effective Charge
Transfer Integral Jeff(θeq), and Time Averaging Site Energy
Difference Δε for Hole and Electron Transport in Octupolar
Molecules
Jeff(θeq) (eV) Δε (eV)
molecule θeq (deg) hole electron hole electron
octupolar 1b 166 0.003 0.08 0.04 0.06
octupolar 1c 113 0.08 0.15 −0.04 0.07
octopolar 2 160 0.001 0.04 0.02 0.03

around the equilibrium stacking angle. That is, Δεij is acting as
a driving force for charge transport. In the non-steady state, the
charge carrier takes a small time (St = 100 fs) to drift, and in the
steady state, St = 194.3 fs. Both in steady and non-steady states,
the hole mobility in molecule 2 is 0.001 cm2
/(V s), and the
drift time is 1.95 and 1.43 ps at steady and non-steady states.
This slow drift is resisting the charge flux along the tunneling
path. That is, the drift time is higher than the charge transfer
time, and the dynamic disorder does not favor the hole
transport.
As shown in Table 3, in both steady and non-steady states
the calculated dispersive parameter for electron transport in 1b,
1c, and 2 is nearly 1 (a → 1). That is, the CT process is purely
kinetic and follows the static non-Condon effect. As shown in
Figure 7, in this static non-Condon case, the rate coefficient is
almost constant for molecule 1c. Similar trends were observed
for molecules 1b and 2. Among the studied molecules, the
molecule 1c has high electron mobility of 1.7 cm2
/(V s), and
the corresponding hopping conductivity is 375.5 S/m. For
molecule 1c, the Jeff at the equilibrium stacking angle of 113° is
around 0.14 eV, and the calculated drift time is 12.33 fs. The
plot of disorder drift with respect to time for electron transport
in molecule 1c is shown in Figure 9. The small disorder drift
time shows the absence of disorder which leads the continuum
charge distribution and band-like charge transport. That is, in
molecule 1c, there is a crossover from nonadiabatic hopping to
adiabatic band transport, and the effect of fluctuation in Δεij is
not significant. In this case the dynamic fluctuation limits the
diffusion (hopping mechanism) and promotes the delocaliza-
tion of charge (band) which is commonly known as diffusion
limited by thermal disorder.10,15,21,24
Both in steady and non-
steady states the molecules 1b and 2 are having significant
electron mobility of around 0.35 and 0.26 cm2
/(V s),
respectively.
Table 2. Rate Coefficient (k), Mobility (μ), Hopping Conductivity (σHop), Disorder Drift Time (St), and Dispersive Parameter
(a) for Hole Transport in Octupolar Molecules in the Steady State (Δεij = 0) and in Non-Steady State (Δεij ≠ 0)
k (ps−1
) μ (cm2
/(V s)) σHop (S/m) St (fs) a
molecule Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0
octupolar 1b 0.006 5.1 × 10−4
2.35 × 10−4
2.50 × 10−4
0.03 0.003 1.96 × 105
3.1 × 106
0.62 0.17
octupolar 1c 7.79 14.43 0.13 0.20 41.36 76.62 194.3 100 0.84 0.76
octupolar 2 0.01 0.009 1.47 × 10−3
1.36 × 10−3
0.053 0.048 1.95 × 103
1.43 × 105
0.91 0.99
Table 3. Rate Coefficient (k), Mobility (μ), Hopping Conductivity (σHop), Disorder Drift Time (St), and Dispersive Parameter
(a) for Electron Transport in Octupolar Molecules in the Steady State (Δεij = 0) and in Non-Steady State (Δεij ≠ 0)
k (ps−1
) μ (cm2
/(V s)) σHop (S/m) St (fs) a
molecule Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0 Δεij = 0 Δεij ≠ 0
octupolar 1b 18.77 5.53 0.38 0.35 99.67 29.35 48.51 252.13 0.95 0.94
octupolar 1c 70.71 25.2 1.71 1.62 375.47 133.8 12.33 34.7 0.99 0.99
octupolar 2 13.1 7.84 0.27 0.26 69.56 41.65 83.5 135.34 0.75 0.81
Figure 4. Survival probability of positive charge in molecule 1c in (a)
steady state (b) non-steady state with respect to time. Figure 5. Survival probability of negative charge in molecule 1c in (a)
steady state (b) non-steady state with respect to time.

To get further insight into charge transport in studied
molecules, the charge transfer time (τCT) is calculated as the
inverse of the static charge transfer rate (τCT = 1/kstatic) and
compared with disorder drift time St. In the steady state, the
hole transfer time in molecule 1b is 1.19 ns, which is greater
than the disorder drift time (St) of 0.196 ns. It has been
observed that the calculated dynamic rate (0.006 × 1012
/s) is
greater than the static rate (0.0008 × 1012
/s). That is, the
structural fluctuation promotes the charge transport. Notably,
in the non-steady state regime, the τCT for hole transport in
molecule 1b is 0.45 ns, which is lesser than the drift time of 3.1
ns, and the dynamic rate (0.51 × 109
/s) is lesser than the static
rate (2.2 × 109
/s). Note that, in this case, the site energy
difference Δεij is acting as a barrier for hole transport. It has
been observed that for electron transport in molecule 1c the
Figure 6. Time evolution of the rate coefficient for hole transport in
molecule 1c in (a) steady state (b) non-steady state.
Figure 7. Time evolution of the rate coefficient for electron transport
in molecule 1c in (a) steady state (b) non-steady state.
Figure 8. Disorder drift with respect to time for hole transport in
Figure 9. Disorder drift with respect to time for electron transport in

τCT and St are comparable in both steady and non-steady states,
which shows that both the static and dynamic rates are nearly
comparable and the effect of Δεij is not significant. That is, as
described before, the electron transport in molecule 1c follows
band-like transport rather than the hopping. That is, the charge
is delocalized on more number of electronic states, and the
charge density is minimum due to the large bandwidth (see
Figures 10 and 11). The calculated results show that if St is less
than the charge transfer time (τCT), the charge transfer process
is kinetically favorable and the dynamic rate is higher than the
static rate. If St ∼ τCT, both the static and dynamic rates are
comparable; i.e., the fluctuation does not have significant effect
on carrier transport. When St τCT, the static rate is larger than
the dynamic rate and the carrier may potentially trap at the
localized sites due to the presence of disorder. Based on eq 11,
the charge density ratio (ρ/ρ0) is calculated, and the plot of (ρ/
ρ0) with respect to time is shown in Figures 10 and 11 for hole
and electron transport in the molecule 1c. A similar trend is
observed for molecules 1b and 2 in steady and non-steady
states. As expected, (ρ/ρ0) is minimum at time t = St. This
crossover behavior of charge carrier dynamics due to the
dynamic disorder is in agreement with the previous
studies.15,21,24,26
4. CONCLUSIONS
The calculated charge transfer integral, site energy, reorganiza-
tion energy, and the information about the structural
fluctuations in the form of stacking distance and the stacking
angle obtained from molecular dynamics simulations were used
in the kinetic Monte Carlo simulations to study the charge
transport in a few 2,4,6-tris(thiophene-2-yl)-1,3,5-triazene
based octupolar molecules. The charge transfer kinetic
parameters such as rate coefficient, disorder drift time, mobility,
and hopping conductivity were studied at both steady state (Δε
= 0) and non-steady state (Δε ≠ 0). It has been found that the
structural fluctuation promotes the density flux in the tunneling
regime. Calculated mobility values are in agreement with the
available experimental values and show that the methoxy-
substituted octupolar molecule (1c) is having good hole and
electron transporting ability with mobility values of 0.15 and 1.6
cm2
/(V s). The disorder drift time (St) is acting as the
crossover point between the band and hopping transports. The
expression for hopping conductivity obtained from density flux
equation clearly shows that the hopping conductivity depends
on charge transfer rate and electric permittivity of the medium.
By comparing the charge transfer time and disorder drift time,
the dynamics of the charge carrier is studied.
■ ASSOCIATED CONTENT
*S Supporting Information
Optimized structure of triazene based octupolar molecules 1
and 2 (Figure S1); highest occupied molecular orbitals
(HOMO) and the lowest unoccupied molecular orbitals
(LUMO) of the studied molecules 1 and 2 (Figures S2 and
S3, respectively); plot of number of occurrence, relative
potential energy with respect to the intermolecular distance
calculated from CMD for the molecule 2 (Figure S4);
calculated effective charge transfer integral (Jeff, in eV) for
hole and electron transport in (a) molecule 1b, (b) molecule
1c, and (c) molecule 2 at different stacking angles (θ, in
degree) (Figures S5 and S6, respectively); plot of number of
occurrence, relative potential energy with respect to stacking
angle calculation from CMD for the molecules (a) 1c and (b) 2
(Figure S7); site energy difference (Δε, in eV) for hole and
electron transport in the studied molecules (a) 1b, (b) 1c, and
(c) 2 at different stacking angles (θ, in degree) (Figures S8 and
S9); calculated geometrical parameters (a) bond length, (b)
bond angle, and (c) dihedral angle of the studied molecules 1
Figure 10. Time evolution of the density flux for hole transport in
Figure 11. Time evolution of the density flux for electron transport in

and 2 in neutral and ionic states (Table S1). This material is
available free of charge via the Internet at http://pubs.acs.org.
■ AUTHOR INFORMATION
Corresponding Author
*E-mail ksenthil@buc.edu.in; Tel 0091-422-2428445 (K.S.).
Notes
The authors declare no competing ﬁnancial interest.
■ ACKNOWLEDGMENTS
(DST), India, for awarding research project under Fast Track
Scheme.
■ REFERENCES
(1) Burroughes, J. H.; Bradley, D. D. C.; Brown, A. R.; Marks, R. N.;
Mackay, K.; Friend, R. H.; Burns, P. L.; Holmes, A. B. Nature 1990,
347, 539−541.
(2) Tang, C. W.; Vanslyke, S. A. Appl. Phys. Lett. 1987, 51, 913−915.
(3) Katz, H. E. J. Mater. Chem. 1997, 7, 369−376.
(4) Katz, H. E.; Lovinger, A. J.; Johnson, J.; Kloc, C.; Siegrist, T.; Li,
W.; Lin, Y. Y.; Dodabalapur, A. Nature 2000, 404, 478−481.
(5) Shim, M.; Javey, A.; Shi Kam, N. W.; Dai, H. J. Am. Chem. Soc.
2001, 123, 11512−11513.
(6) Sariciftci, N. S.; Smilowitz, L.; Heeger, A. J.; Wudl, F. Science
1992, 258, 1474−1476.
(7) Zhan, X.; Tan, Z.; Domercq, B.; An, Z.; Zhang, X.; Barlow, S.; Li,
Y.; Zhu, D.; Kippelen, B.; Marder, S. R. J. Am. Chem. Soc. 2007, 129,
7246−7247.
(8) Andrienko, D.; Kirkpatrick, J.; Marcon, V.; Nelson, J.; Kremer, K.
Phys. Status Solidi B 2008, 245, 830−834.
(9) Baumeier, B.; Kirkpatrick, J.; Andrienko, D. Phys. Chem. Chem.
Phys. 2010, 12, 11103−11113.
(10) Ruhle, V.; Lukyanov, A.; May, F.; Schrader, M.; Vehoff, T.;
Kirkpatrick, J.; Baumeier, B.; Andrienko, D. J. Chem. Theory Comput.
2011, 7, 3335−3345.
(11) Bohlin, J.; Linares, M.; Stafstrom, S. Phys. Rev. B 2011, 83,
085209.
(12) Bredas, J. L.; Calbert, J. P.; Filho, D. A. d. S.; Cornil, J. Proc.
Natl. Acad. Sci. U. S. A. 2002, 99, 5804−5809.
(13) Deng, W. Q.; Goddard, W. A. J. Phys. Chem. B 2004, 108,
8614−8621.
(14) Pensack, R. D.; Asbury, J. B. J. Phys. Chem. Lett. 2010, 1, 2255−
2263.
(15) Troisi, A. Chem. Soc. Rev. 2011, 40, 2347−2358.
(16) Kirkpatrick, J.; Marcon, V.; Kremer, K.; Nelson, J.; Andrienko,
D. J. Chem. Phys. 2008, 129, 094506.
(17) Kocherzhenko, A. A.; Grozema, F. C.; Vyrko, S. A.; Poklonski,
N. A.; Siebbeles, L. D. A. J. Phys. Chem. C 2010, 114, 20424−20430.
(18) Yang, X.; Wang, L.; Wang, C.; Long, W.; Shuai, Z. Chem. Mater.
2008, 20, 3205−3211.
(19) Berlin, Y. A.; Grozema, F. C.; Siebbeles, L. D. A.; Ratner, M. A.
J. Phys. Chem. C 2008, 112, 10988−11000.
(20) Navamani, K.; Saranya, G.; Kolandaivel, P.; Senthilkumar, K.
Phys. Chem. Chem. Phys. 2013, 15, 17947−17961.
(21) Troisi, A.; Cheung, D. L. J. Chem. Phys. 2009, 131, 014703.
(22) Troisi, A.; Orlandi, G. Phys. Rev. Lett. 2006, 96, 086601.
(23) Troisi, A.; Nitzan, A.; Ratner, M. A. J. Chem. Phys. 2003, 119,
5782−5788.
(24) Cheung, D. L.; Troisi, A. Phys. Chem. Chem. Phys. 2008, 10,
5941−5952.
(25) Skourtis, S. S.; Balabin, I. A.; Kawatsu, T.; Beratan, D. N. Proc.
Natl. Acad. Sci. U. S. A. 2005, 102, 3552−3557.
(26) Wang, L.; Beljonne, D. J. Phys. Chem. Lett. 2013, 4, 1888−1894.
(27) Marcon, V.; Kirkpatrick, J.; Pisula, W.; Andrienko, D. Phys.
Status Solidi B 2008, 245, 820−824.
(28) Schrader, M.; Fitzner, R.; Hein, M.; Elschner, C.; Baumeier, B.;
Leo, K.; Riede, M.; Bauerle, P.; Andrienko, D. J. Am. Chem. Soc. 2012,
134, 6052−6056.
(29) Yasuda, T.; Shimizu, T.; Liu, F.; Ungar, G.; Kato, T. J. Am.
Chem. Soc. 2011, 133, 13437−13444.
(30) Prins, P.; Senthilkumar, K.; Grozema, F. C.; Jonkheijm, P.;
Schenning, A. P. H. J.; Meijer, E. W.; Siebbles, L. D. A. J. Phys. Chem. B
2005, 109, 18267−18274.
(31) Grozema, F. C.; Siebbles, L. D. A. Int. Rev. Phys. Chem. 2008, 27,
87−138.
(32) Silinsh, E. A. Organic Molecular Crystals; Springer-Verlag: Berlin,
1980.
(33) McMahon, D. P.; Troisi, A. Phys. Chem. Chem. Phys. 2011, 13,
10241−10248.
(34) Newton, M. D. Chem. Rev. 1991, 91, 767−792.
(35) Senthilkumar, K.; Grozema, F. C.; Bichelhaupt, F. M.; Siebbeles,
L. D. A. J. Chem. Phys. 2003, 119, 9809−9817.
(36) Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca
Guerra, C.; Van Gisbergeh, S. J. A.; Snijders, J. G.; Ziegler, T. J.
Comput. Chem. 2001, 22, 931−967.
(37) Becke, A. D. Phys. Rev. A 1988, 38, 3098−3100.
(38) Perdew, J. P. Phys. Rev. B 1986, 33, 8822−8824.
(39) Snijders, J. G.; Vernooijs, P.; Baerends, E. J. At. Data Nucl. Data
Tables 1981, 26.
(40) Tavernier, H. L.; Fayer, M. D. J. Phys. Chem. B 2000, 104,
11541−11550.
(41) Torrent, M. M.; Durkut, M.; Hadley, P.; Ribas, X.; Rovira, C. J.
Am. Chem. Soc. 2004, 126, 984−985.
(42) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200−
1211.
(43) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652.
(44) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785−
789.
(45) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci,
B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H.
P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.;
Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima,
T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.;
Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin,
K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.;
Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega,
N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.;
Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.;
Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.;
Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.;
Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09,
Revision B.01; Gaussian, Inc.: Wallingford, CT, 2009.
(46) Prins, P.; Grozema, F. C.; Siebbeles, L. D. A. J. Phys. Chem. B
2006, 110, 14659−14666.
(47) Schein, L. B.; McGhie, A. R. Phys. Rev. B: Condens. Matter Mater.
Phys. 1979, 20, 1631−1639.
(48) Miller, S. L.; Childers, D. G. Probability and Random Process;
Elsevier Inc.: Amsterdam, 2004; Chapter 9, pp 323−359.
(49) Takeya, J.; Tsukkagoshi, K.; Aoyagi, Y.; Takenobu, T.; Iwasa, Y.
Jpn. J. Appl. Phys. 2005, 44, L1393.
(50) Ponder, J. W. TINKER: 4.2, Software tools for molecular design,
St. Louis, Washington, 2004.
(51) Ren, P.; Ponder, J. W. J. Phys. Chem. B 2003, 107, 5933−5947.
(52) Allinger, N. L.; Yan, F.; Li, L.; Tai, J. C. J. Comput. Chem. 1990,
11, 868−895.
(53) Lii, J. H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8576−
8582.
(54) Garcia, G.; Moral, M.; Granadino-Roldan, J. M.; Garzon, A.;
Navarro, A.; Fernandez-Gomez, M. J. Phys. Chem. C 2013, 117, 15−22.

Effect of dynamic disorder on charge carrier
dynamics in Ph4DP and Ph4DTP molecules†
Electronic structure calculations were used to study the charge transport and optical properties of 2,20
,6,60
-
tetraphenyldipyranylidene (Ph4DP) and its sulfur analogue 2,20
,6,60
-tetraphenyldithiopyranylidene
(Ph4DTP) based molecules. The dynamic disorder effect is included while calculating the charge transfer
kinetic parameters such as rate coefficient, disorder drift time, hopping conductivity and mobility of
charge carriers through the kinetic Monte Carlo simulations. The existence of degeneracy levels
promotes the delocalization of charge carrier and charge transfer. Theoretical results show that if the
orbital splitting rate is larger than the static charge transfer rate (OR kstatic), the charge transfer is
kinetically favored. If OR kstatic, the charge carrier is potentially trapped in the localized site. In the case
of OR $ kstatic, the charge carrier motion is not affected by the dynamic disorder. The calculated hole
mobility in Ph4DP and Ph4DTP molecules is 0.04 and 0.03 cm2
VÀ1
sÀ1
and is in agreement with the
experimental results. It has been found that fluorine and chlorine substituted Ph4DP molecules have
good ambipolar transporting character. The absorption and emission spectra were calculated using
the time dependent density functional theory (TDDFT) method at the CAM-B3LYP/6-31G(d,p) and
M062X/6-31G(d,p) levels of theory. The calculated absorption spectra are in agreement with the
experimental results.
1. Introduction
Studying charge transport behavior of organic materials is of
great interest because of its relevance in the development of
optoelectronic devices such as organic light emitting diodes,1–4
thin lm transistors,5–8
organic photovoltaic cells and eld
effect transistors.9–12
The advantage of organic materials rather
than inorganic semiconductors is their relatively low cost, lower
molecular weight and tunable electronic structure.12,13
The
optoelectronic properties of organic semiconductors are
improved by the structural modication, substitution of suit-
able electron donating (ED), electron withdrawing (EW) groups,
and active heterocyclic compounds.14
The substitution of
different EW and ED groups alters the delocalization of electron
density on the frontier molecular orbitals of the molecule. The
substitution of heterocyclic groups inuences the structure and
optoelectronic properties such as molecular packing,
conjugation length, bandwidth and ionic state properties.15
The
self-aggregation and phase properties are controlled by the
addition of appropriate side chains.16–18
At high temperature (T 150 K), the charge carrier mean free
path is shorter than the intermolecular spacing, and the wave
function of the charge carrier is localized on particular molecule
due to weak coupling between the electronic states.12,19,20
Therefore, the charge transport in these materials is due to
thermally activated hopping mechanism rather than band like
transport.12,17,21,22
Understanding the charge carrier dynamics
along the localized sites is difficult due to the interaction
between nuclear and electronic degrees of freedom. It has been
shown in earlier studies that the dynamic disorder along the
charge transfer path decreases the effect of electron-phonon
scattering on the charge carrier motion and provides the
dynamic localization of charge carrier rather than the static
localization.19,23–25
Here, the dynamic disorder, such as nuclear
degrees of freedom, perturbs the localized charge carrier and so
the coefficients of charge carrier wave function are no longer
zero at its boundaries.25
The perturbed localization is called as
dynamic localization which is responsible for charge ux which
facilitates the charge transfer (CT) kinetics, and unperturbed
localization is named as static localization (or Anderson local-
ization).25–27
In this dynamic uctuation regime, the charge
transport behaviour is termed as diffusion limited crossover
from non-adiabatic localization to adiabatic delocaliza-
tion.12,19,20,28,29
The structural uctuations leads to breakdown of
Department of Physics, Bharathiar University, Coimbatore-641 046, India. E-mail:
ksenthil@buc.edu.in
† Electronic supplementary information (ESI) available: The optimized structure
of Ph4DP and Ph4DTP molecules are given in Fig. S1. Mean squared
displacement, survival probability, time dependence of rate coefficient, disorder
dri with in time scale of simulation and time evolution of dispersal energy
difference ratio for hole and electron transport in studied molecules is given in
Fig. S2. The calculated geometrical parameters of the studied molecules are
summarized in Table S1. Calculated effective charge transfer integral (Jeff, in eV)
for hole and electron transport in Ph4DP and Ph4DTP molecules is summarized
in Table S3. See DOI: 10.1039/c4ra15779f
Cite this: RSC Adv., 2015, 5, 38722
Received 4th December 2014
Accepted 22nd April 2015
DOI: 10.1039/c4ra15779f
www.rsc.org/advances
38722 | RSC Adv., 2015, 5, 38722–38732 This journal is © The Royal Society of Chemistry 2015
RSC Advances
PAPER

the Franck–Condon (FC) principle and makes signicant
impact on charge carrier motion.30,31
Even in crystal packing, at
room temperature, the molecules are uctuating from their
equilibrium position.32
Hence, for better understanding of
charge transfer phenomena in organic crystals, the charge
transport properties should be studied at molecular level.
Altan Bolag et al.33
have synthesized 2,20
,6,60
-tetraphenyldi-
pyranylidene (Ph4DP), its sulfur analogue 2,20
,6,60
-tetraphe-
nyldithiopyranylidene (Ph4DTP) crystals and their derivatives.
These molecules have quinoid structure and core is attached
with tetrathiafulvalene (TTF), a well-known family of p-electron
donor groups. The Ph4DTP possesses quasi-planar conforma-
tion with phenyl rings tilted by 12
relative to the core.33
The
Ph4DP and Ph4DTP are reported as new p-type semiconductors
due to their hole mobility and on/off ratios, and they have the
following advantages, rst, they have an isoelectronic structure
with TTF, their cation and dication states are stable. Second,
they have the extended p-conjugated structure which is favor-
able for strong intermolecular interaction leading to high
charge carrier mobility. Third, the preparation method is
simple and substituents can easily be introduced. Finally, due
to the presence of sulfur atom in Ph4DTP, the molecule exhibits
with high polarizability nature which provides strong p–p
interaction,34
and the presence of oxygen atom in Ph4DP
reduces the steric repulsion which is responsible for the planar
structure and p-stacking aggregation in crystal packing. The
chemical structure of Ph4DP and Ph4DTP molecules is shown
in Fig. 1. The experimental results on these molecules moti-
vated us to study the charge transport and optical properties of
Ph4DP, Ph4DTP and their substituted analogues. The time-
dependent density functional theory (TD-DFT) method is used
to calculate the absorption and emission spectra of Ph4DP and
Ph4DTP molecules. This study will provide information to tune
the optoelectronic properties of organic semiconductors.
2. Theoretical formalism
Based on tight binding Hamiltonian approach, the presence of
excess charge in a p-stacked molecular system is expressed
as13,35
^H ¼
X
i
3iðqÞai
þ
ai þ
X
j . i
Ji;jðqÞai
þ
aj (1)
where, ai
+
and ai are creation and annihilation operators, 3i(q) is
molecular site and Ji,j is the charge transfer integral or elec-
tronic coupling. By considering a two state model, the energy
eigenvalue equation can be written as,
HC À ESC ¼ 0 (2)
where, H, C and S are the Hamiltonian, orbital coefficient and
spatial overlap matrix element of a two state system for which
the Hamiltonian is written as,
H ¼

311 J12
J21 322

(3)
and the spatial overlap matrix,
S ¼

1 S12
S21 1

(4)
here, site energy 31 ¼ hj1|ˆH|j1i and J12 ¼ hj1|ˆH|j2i are diagonal
and off-diagonal matrix elements of the Hamiltonian.
The charge transfer rate between the localized sites is
described by semi-classical theory of Marcus–Hush model,
which coupled the density of states (DOS) and square of the
effective charge transfer integral (Jeff),22,36,37
ki/f ¼
2p
ħ

Jeff

2
rFCT (5)
Fig. 1 The chemical structure of tetraphenyldipyranylidene derivatives.
This journal is © The Royal Society of Chemistry 2015 RSC Adv., 2015, 5, 38722–38732 | 38723
Paper RSC Advances

The density of states (DOS) are weighted by the Franck–
Condon factor, rFCT and is calculated by using reorganization
energy (l),22
rFCT ¼
1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4plkBT
p exp

À
l
4kBT

(6)
where, kB is Boltzmann constant and T is the temperature. Here,
the two key parameters, the effective charge transfer integral
(Jeff) and reorganization energy (l) determines the charge
transfer rate.
The effective charge transfer integral (Jeff) is calculated from
charge transfer integral, spatial overlap integral and site energy
as,38,39
Jeff ¼ Jij À
S
À
3i þ 3j
Á
2
(7)
As described above the site energies, 3i and 3j are the energy
of a charge when it is localized at ith
and jth
molecules,
respectively, and Jij represents the electronic coupling between
HOMO (or LUMO for electron) of nearby molecules i and j. As
described in previous studies,13,31,39
the J, S and 3 are calculated
by using the fragment molecular orbital approach39
as imple-
mented in the Amsterdam density functional (ADF)
program.40,41
In ADF calculation, we have used the Becke–Per-
dew (BP) exchange correlation functional42,43
with triple-zeta
plus double polarization (TZ2P) basis set.
The reorganization energy (l) is the energy change associ-
ated with relaxation of molecular geometry due to the presence
of excess charge on a molecule. The reorganization energy is
evaluated directly from the adiabatic potential energy surfaces
of neutral, cation and anion geometries.44,45
Within this
approximation, the reorganization energy is dened as,
lÆ
¼ [EÆ
(go
) À EÆ
(gÆ
)] + [ Eo
(gÆ
) À Eo
(go
)] (8)
where, EÆ
(go
) is the total energy of a molecule with an excess
(positive or negative) charge in the optimized neutral geometry,
EÆ
(gÆ
) is the total energy of optimized ionic geometry, Eo
(gÆ
) is
the total energy of neutral molecule in ionic geometry and Eo
(go
)
is the total energy of optimized neutral molecule. The neutral,
cationic and anionic geometries were optimized using density
functional theory method, B3LYP46–48
in conjunction with the 6-
31G(d,p)32
basis set using GAUSSIAN 09 program package49
and
these energy values are used to nd the reorganization energy
for hole (l+
) and electron (lÀ
) transport.
It has been shown in earlier studies that the structural
uctuation in the form of stacking angle change have signi-
cant impact on charge carrier mobility.31,41,50
Thus, the effective
charge transfer integral (Jeff) calculated at different stacking
angle is used to study the rate of charge transfer between the
localized sites. Based on the charge transfer rate calculated
from Marcus eqn (5) kinetic Monte Carlo simulation is per-
formed to calculate the mean squared displacement of the
charge carrier in the p-stacked system. The motion of charge
carrier in the disordered molecular system is described in the
form of thermal diffusion process.13
The diffusion co-efficient
(D) is calculated from the time evolution of mean squared
displacement as,
D ¼

X2
ðtÞ

2t
(9)
Based on the Einstein diffusion model, the dri mobility of
the charge carrier is calculated from the diffusion coefficient, D
as,51
m ¼
eD
kBT
(10)
As described in our previous study the hopping conductivity
is calculated on the basis of density ux model and is described
as,52
sHop ¼
3
5
3
vP
vt
(11)
where, 3 is electric permittivity of the medium and
vP
vt
is the rate
of transition probability (or charge transfer rate). At room
temperature the structural uctuation in the form of stacking
angle change will affect the charge transport.30,31
During the
Monte Carlo simulation the stacking angle uctuation up to 6
from the equilibrium position is allowed41,53
and is assumed
that the stacking angle uctuation from the equilibrium value is
harmonic and molecules are bounded within the unit cell.
In the present work, the charge transport calculations were
performed with experimental crystal structure of uorinated
Ph4DP and unsubstituted Ph4DTP molecules. To nd the
crystal structure of unsubstituted Ph4DP and chlorine
substituted Ph4DP the DFT calculations were performed by
using Vienna Abinitio Simulation Package (VASP)54–56
with
projected augmented wave potential, force convergence of 0.02
eV ˚AÀ1
and energy convergence of 0.001 eV. The optimized
structure of Ph4DP has triclinic structure with P1 space group
and the crystal structure of Ph4DTP has monoclinic structure
with the space group of C2/c. In the unit cell, the uorinated
Ph4DP and unsubstituted Ph4DTP molecules are packed in co-
axial manner along the a-axis and b-axis, respectively, and the
corresponding intermolecular distance is 6.08 and 5.52 ˚A. In the
optimized structure of unsubstituted Ph4DP and chlorine
substituted Ph4DP, the molecules are arranged in parallel along
the a-axis with the intermolecular distances of 4.13 and 5.92 ˚A,
respectively.
To calculate the emission spectra, the excited state geometry
of Ph4DP, F and Cl substituted Ph4DP and Ph4DTP molecules
has been optimized in dichloromethane medium by using time-
dependent density functional theory (TD-DFT) method at
B3LYP/6-31G(d,p) level of theory. Based on the ground and
excited states geometry, the absorption and emission spectra
were calculated using TD-DFT method at CAM-B3LYP/6-
31G(d,p) and M06-2X/6-31G(d,p) level of theories. Tomasi's57
polarized continuum model (PCM) in self-consistent reaction
eld (SCRF) theory is used to include the solvent effect on the
optical properties of the studied molecules. The SWizard
program58,59
was used to plot and analyse the absorption and
RSC Advances Paper

emission spectra of the studied molecules. The spectra were
generated using the following Gaussian function,
3ðuÞ ¼ c2
X
I
fI
D1=2;I
exp À 2:773
ðu À uI Þ2
D1=2;I
2
!
(12)
where, 3(u) is the molar extinction coeﬃcient in MÀ1
cmÀ1
, u is
the energy of the allowed transition in cmÀ1
, fI is the oscillator
strength and D1/2 is the half-bandwidth and is xed as 3000
cmÀ1
.
3.1. Frontier molecular orbitals
In the p-stacked organic molecules the excess positive charge
migrates through the highest occupied molecular orbital
(HOMO) and the excess negative charge migrates through the
lowest unoccupied molecular orbital (LUMO) of nearby mole-
cules. That is, the charge transport, optical absorption and
emission properties of the p-stacked molecules strongly
depends on the delocalization of electron density on the fron-
tier molecular orbitals of the individual molecules. The density
plot of the HOMO and LUMO of Ph4DP, F substituted Ph4DP, Cl
substituted Ph4DP and Ph4DTP molecules are obtained at
B3LYP/6-31G(d,p) level of theory and are shown in Fig. 2 and 3.
It has been observed that HOMO is delocalized on the center of
heptacyclic ring and LUMO is delocalized over the entire
molecule. The distribution of HOMO and LUMO on the studied
molecules exhibits p-orbital character. It has been observed
that the substitution of F or Cl and O or S atoms on the core
does not alter the delocalization of electron density on the
frontier molecular orbitals. The energy of HOMO, LUMO and
energy gap between HOMO and LUMO of the studied Ph4DP
and Ph4DTP molecules are calculated at B3LYP/6-31G(d,p) level
of theory and are summarized in Table 1. It has been observed
that the HOMO and LUMO energies of Ph4DP molecule is À4.03
and À1.48 eV, respectively. The F and Cl substitution decreases
the HOMO level by 0.2 and 0.4 eV and the LUMO level around
0.14 and 0.45 eV which is in agreement with the experimental
results.33
3.2. Reorganization energy and ionic state properties
The reorganization energy due to the presence of excess positive
(l+
) and negative (lÀ
) charges on the studied molecules has
been calculated using eqn (8) and are summarized in Table 1.
The presence of excess charge on the molecules alters the
structural parameters signicantly. The selected geometrical
parameters of the studied molecules in the neutral and ionic
states are summarized in Table S1.†
It has been observed that the l+
calculated for unsubstituted,
and substituted Ph4DP and Ph4DTP molecules are almost same
and is nearly 0.29 eV. As observed from Table S1,† the presence
of excess negative charge on the Ph4DTP signicantly alters the
Fig. 2 Plot of highest occupied molecular orbital (HOMO) of the Ph4DP and Ph4DTP molecules.
Paper RSC Advances

structural parameters, particularly the dihedral angles. As given
in Table 1, the lÀ
calculated for Ph4DP molecules is around 0.3
eV. Notably, the reorganization energy corresponding to pres-
ence of excess negative charge on Ph4DTP is 0.51 eV. In agree-
ment with previous experimental results,33
the above results
show that the migration of positive charge on the studied
molecules is more favorable than the migration of negative
charge.
The ionization potential (IP) and electron affinity (EA) are the
basic properties and determines the stability, injection barrier
and charge polarity of a molecule. The adiabatic ionization
potential (AIP), vertical ionization potential (VIP), adiabatic
electron affinity (AEA) and vertical electron affinity (VEA) are
calculated using total energy of neutral and ionic states and are
summarized in Table 1. Among the studied Ph4DP molecules,
the unsubstituted Ph4DP molecule has minimum ionization
potential of 5.52 and 5.10 eV for vertical and adiabatic excita-
tions. The IP of Ph4DTP is higher than that of Ph4DP by 0.13 eV.
The substitution of F and Cl atoms on Ph4DP molecule
increases the IP and EA by 0.2 to 0.5 eV. That is, the creation of
hole on Ph4DP molecule is easier than on the other studied
molecules. Among the studied molecules, the unsubstituted
Ph4DP is having minimum EA of 0.41 and 0.58 eV for vertical
and adiabatic excitations. The substitution of Cl atoms on
Ph4DP increases the EA by 0.5 eV. Tabulated values clearly show
that the AIP is smaller than the VIP, and the AEA is higher than
Fig. 3 Plot of lowest unoccupied molecular orbitals (LUMO) of the Ph4DP and Ph4DTP molecules.
Table 1 Molecular orbital energies (EHOMO, ELUMO), energy gap (DE), ionization potential (IP), electron affinity (EA) and reorganization energy (l)
for Ph4DP, F and Cl substituted Ph4DP and PH4DTP molecules
Molecule EH (in eV) EL (in eV)
Energy gap EH–EL
(in eV)
Ionization potential
(in eV) Electron affinity (in eV)
Reorganization
energy (in eV)
Theory Exp.a
Vertical Adiabatic Vertical Adiabatic Hole Electron
Ph4DP À4.03 À1.48 2.55 2.02 5.25 5.10 0.41 0.58 0.28 0.31
F-Ph4DP À4.23 À1.62 2.60 2.25 5.44 5.28 0.55 0.73 0.31 0.33
Cl-Ph4DP À4.44 À1.93 2.50 2.18 5.59 5.45 0.92 1.08 0.29 0.30
Ph4DTP À4.19 À1.75 2.43 1.98 5.38 5.23 0.67 0.93 0.30 0.51
a
Values taken from ref. 33.
RSC Advances Paper

the VEA. That is, the studied molecules relax more when there is
an excess negative charge. This result is in agreement with the
results obtained from reorganization energy values.
The effective charge transfer integral, Jeff for hole and electron
transport in studied molecules has been calculated by using eqn
(7) and are summarized in Table 2. For F substituted Ph4DP and
Ph4DTP the ADF calculations were performed for the dimer
structure taken from crystal structure data and for other mole-
cules the dimer structure is taken from the optimized structures
as described in Section 2. It has been observed that the struc-
ture, substitution and intermolecular arrangement determines
the Jeff. In the case of Ph4DP molecules, the F substituted
Ph4DP molecule is having maximum Jeff of 0.1 eV for hole
transport. In this molecule, the intermolecular distance is 6.08
˚A and the arrangement of molecules is such that the HOMO of
each molecule is interacting constructively. For electron trans-
port, the Ph4DTP molecule has maximum Jeff of 0.1 eV. The
chlorine substituted Ph4DP molecule has minimum Jeff of 0.03
for hole transport and 0.02 eV for electron transport which is
due to unequal contribution of HOMO (or LUMO) of each
monomer on the dimer HOMO (LUMO for electron transport).
The earlier studies19,28,30,31,52,60
show that the structural uctua-
tion at room temperature provides the signicant effect on
charge transfer integral and mobility. In the present study,
while calculating the charge transfer kinetic parameters the
variation of Jeff due to structural uctuation in the form of
stacking angle is included.
3.4. Charge transfer kinetics
The computed effective charge transfer integral (Jeff) and reor-
ganization energy (l) are used to calculate the charge transfer
rate using eqn (5) and (6). During the kinetic Monte Carlo
(KMC) simulations, the excess charge is propagated based on
the charge transfer rate calculated from semi-classical Marcus
theory. The time evolution of mean squared displacement
hX2
(t)i is used to calculate the carrier mobility by using eqn (9)
and (10). As shown in Fig. 4 and S1,† hX2
(t)i is linearly increasing
with time. The results show that the CT is the normal diffusion
process in which the charge carrier does not reach the end of
hopping site within the simulation time. As shown in Fig. 5, the
survival probability for the charge carrier at particular site is
decreasing exponentially with respect to time. The calculated
rate coefficient from survival probability graph is used in eqn
(11) to calculate the hopping conductivity.52
As described in previous studies,30,31,52
the time evolution of
CT kinetics is studied on the basis of rate coefficient (k),
dispersive parameter (a), survival probability (P(t)), thermal
disorder S(t) and disorder dri time (St). The results are shown
in Fig. 4–7 and S2† for hole and electron transport in the
studied molecules. Here, the disorder dri time St is the
simulation time at which the dynamic disorder is maximum.
On the basis of statistical relation, the disorder dri and the
possible number of electronic states (Z) along the charge
transfer path are related as,61
SðtÞ
kB
¼ ln Z (13)
As described earlier, the dynamic disorder due to structural
uctuation promotes the carrier dynamics from static to
dynamic localization.12,19,24,25,29
As shown in Fig. 7, from the
disorder dri curve the rate of splitting of energy states (OR) can
be calculated as
OR ¼
Zd À Z0
St
(14)
Table 2 The effective charge transfer integral (Jeff) for hole and
electron transport in Ph4DP, F and Cl substituted Ph4DP and Ph4DTP
molecules
Molecules
Intermolecular
distances (˚A)
Effective charge transfer
integral (Jeff in eV)
Hole Electron
Ph4DP 4.13 0.02 0.07
F-Ph4DP 6.08 0.10 0.03
Cl-Ph4DP 5.92 0.03 0.02
Ph4DTP 5.52 0.005 0.10
Fig. 4 Mean squared displacement of electron in Ph4DP molecule
with respect to time.
Fig. 5 Survival probability of negative charge in Ph4DP molecule with
respect to time.
Paper RSC Advances

where, Zd and Z0 are the number of electronic states at time t ¼
St and at time t ¼ 0, respectively. The energy distribution among
the possible electronic states is studied by calculating the
dispersed energy difference due to the dynamic disorder and is
described as
DEdisðSÞ z DES0
exp

À
SðtÞ
2kB

(15)
where, DES0
is the difference in energy distribution among the
electronic levels in the absence of dynamic disorder. As shown
in Fig. 8, the ratio of dispersed energy difference,
ðDEdisðSÞ=DES0
Þ is calculated by using the disorder dri, S(t).
It has been observed that, the dispersive parameter for hole
transport in Ph4DP and electron transport in Ph4DTP is nearly 1
which shows that the CT kinetics follows static non-Condon
effect and the charge decay along the charge transfer path is
coherence.31
For other cases, the dispersive parameter is in the
range of 0.6 to 0.75 and the CT kinetics follows the intermediate
regime between static and kinetic non-Condon effect. Here, the
wave function of the charge carrier is slowly decaying with
respect to time and the charge carrier takes the motion along
the sequential hopping sites. In the present study, the existence
of degeneracy levels per unit time is calculated from the timely
varying disorder dri curve (see Fig. 7) and is associated with
the orbital splitting rate, OR. As given in Table 3, for hole
transport in chlorine and uorine substituted Ph4DP mole-
cules, the orbital splitting rate is 5.4 Â 1012
and 2 Â 1012
sÀ1
,
respectively, showing the coupling strength between the HOMO
of each monomer and responsible for good hole mobility of 0.17
and 0.34 cm2
VÀ1
sÀ1
, and rate coefficient of 2.38 and 4.91 psÀ1
,
respectively. In these molecules the hole dri time by the
dynamic uctuation is 156 and 68 fs which is smaller than that
of other studied molecules. Here, the dynamic disorder
enhances the orbital splitting rate (see Table 3) which is
responsible for the large bandwidth and the maximum hopping
conductivity of 0.13 and 0.26 S cmÀ1
, respectively. The hole
mobility in unsubstituted Ph4DP and Ph4DTP molecules is
around 0.04 cm2
VÀ1
sÀ1
which is in agreement with experi-
mental values of 0.02 and 0.05 cm2
VÀ1
sÀ1
, respectively. For
electron transport, unsubstituted Ph4DP, F and Cl substituted
Ph4DP molecules are having hopping conductivity of 0.4, 0.12
and 0.21 S cmÀ1
and their corresponding rate coefficient is 7.54,
2.19 and 4.02 psÀ1
. While comparing unsubstituted Ph4DP and
F substituted Ph4DP, it has been observed that the F substituted
Ph4DP molecule is having slightly higher electron mobility,
which is due to a small difference in intermolecular distance
(see Table 4). As given in Table 4, in comparison with Ph4DTP,
the Ph4DP molecules are having signicant orbital splitting rate
and electron transporting ability. The disorder dri time, St
calculated for Ph4DTP molecule is 8.08 Â 104
fs which is higher
than that of the Ph4DP molecules and clearly shows the poor
electron transport in Ph4DTP molecule.
By comparing the disorder dri time (St) and charge transfer
time (sCT) (inverse of the static CT rate, sCT ¼ 1/kstatic), in the
static case the structural uctuation effect on charge carrier
dynamics is studied. The static CT rate (kstatic) is directly
calculated from the eqn (5) without invoking the effect of
structural uctuations. In chlorine substituted Ph4DP mole-
cule, the disorder dri time, St ($68 fs) is lesser than the hole
transfer time, sCT ($500 fs), and the dynamic hole transfer rate
4.9 Â 1012
sÀ1
is higher than the static CT rate 2 Â 1012
sÀ1
.
Whereas, in the case of uorine substituted Ph4DP molecule,
the St (156 fs) is greater than the sCT (65 fs), and the static CT
rate ($15.4 psÀ1
) is relatively higher than the dynamic rate ($2.4
psÀ1
). As given in Table 3, for unsubstituted PH4DP molecule,
the calculated hole dri time ($1.6 ps) and static hole transfer
time ($1.4 ps) are comparable, and the static and dynamic hole
Fig. 6 Time evolution of the rate coefficient for electron transport in
Ph4DP molecule.
Fig. 7 Disorder drift with respect to time for electron transport in the
Ph4DP molecule.
Fig. 8 Time evolution of dispersal energy difference ratio for electron
transport in the Ph4DP molecule.
RSC Advances Paper

transfer rates are also comparable (0.71 Â 1012
sÀ1
and 0.85 Â
1012
sÀ1
). As observed from Table 4, in Ph4DTP molecule, the
electron transfer time (sCT ¼ 0.68 ps) is lesser than the disorder
dri time (81 ps) and the static rate is higher than the dynamic
rate. The calculated disorder dri time for electron transport in
Ph4DTP molecule shows that the electron survives longer time
on the localized electronic state and may be potentially trapped.
The above results show that when the carrier dri time is lesser
than the static CT time (St sCT), the dynamic rate (inclusion of
uctuation) is higher than the static CT rate (absence of uc-
tuation), and if St sCT, the dynamic CT rate is lesser than the
static CT rate. When St and sCT are comparable, the static and
dynamic CT rates are also comparable. The above observations
are in agreement with the previous studies.30,52
As given in Tables 3 and 4, if the orbital splitting rate is larger
than the static charge transfer rate (OR kstatic), then the charge
transfer is kinetically favorable due to the formation of large
bandwidth, and if OR kstatic, the charge carrier is potentially
trap on the localized site. In the latter case the energy of the
carrier is not enough for dri from the trapped site. Based on
eqn (15), the dispersed energy difference ratio ðDEdisðSÞ=DES0
Þ is
calculated and the plot of ðDEdisðSÞ=DES0
Þ with respect to time is
shown in Fig. 8 and S2.† As expected ðDEdisðSÞ=DES0
Þ is
minimum at time t ¼ St. That is, at t ¼ St the possible dispersed
Table 3 Calculated charge transfer kinetic parameters, rate coefficient (k), hopping conductivity (sHop), mobility (m), disorder drift time (St),
charge transfer time (sCT), dispersive parameter (a) and orbital splitting rate (Zd À Z0)/St for hole transport in Ph4DP and F and Cl substituted
Ph4DP and Ph4DTP molecules
Molecule
Inter-molecular
distance (˚A) k (psÀ1
) sHop (S cmÀ1
)
m
(cm2
VÀ1
sÀ1
) St (fs) sCT (fs) a (Zd À Z0)/St (psÀ1
)
Ph4DP 4.13 0.85 0.04 0.04 1.62 Â 103
1.39 Â 103
0.97 0.20
F-Ph4DP 6.08 2.38 0.13 0.17 156 65 0.56 1.95
Cl-Ph4DP 5.92 4.91 0.26 0.34 68.2 506 0.60 5.41
Ph4DTP 5.52 0.52 0.03 0.03 1.73 Â 103
2.31 Â 104
0.51 0.16
Table 4 Calculated charge transfer kinetic parameters rate coefficient (k), hopping conductivity (sHop), mobility (m), disorder drift time (St), charge
transfer time (sCT), dispersive parameter (a) and orbital splitting rate (Zd À Z0)/St for electron transport in Ph4DP and F and Cl substituted Ph4DP
and Ph4DTP molecules
Molecule
Inter-molecular
distance (˚A) k (psÀ1
) sHop (S cmÀ1
)
m
(cm2
VÀ1
sÀ1
) St (fs) sCT (fs) a (Zd À Z0)/St (psÀ1
)
Ph4DP 4.13 7.54 0.40 0.16 94 133 0.68 2.11
F-Ph4DP 6.08 2.19 0.12 0.21 820 754 0.72 0.46
Cl-Ph4DP 5.92 4.02 0.21 0.32 217 2.69 Â 103
0.62 1.45
Ph4DTP 5.52 0.06 3.19 Â 10À3
0.06 8.08 Â 104
681 0.91 0.01
Table 5 Experimental absorption wavelength (labs), calculated absorption wavelength, energy, orbital transition and oscillator strength (in a.u) of
Ph4DP, F and Cl substituted Ph4DP and Ph4DTP molecules at CAM-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) level of theories in dichloro-
methane medium
Molecule Exp.a
Orbital transitionsb
CAM-B3LYP/6-31G(d,p) M06-2X/6-31G(d,p)
labs
f
labs
f(nm) (eV) (nm) (eV)
Ph4DP 457 H / L+1 452 2.74 0.14 455 2.72 0.14
273 H / L 441 2.81 1.65 441 2.82 1.60
HÀ1 / L 260 4.77 0.84 260 4.78 0.84
F-Ph4DP 447 H / L+1 446 2.78 0.13 449 2.76 0.14
265 H / L 436 2.84 1.67 436 2.85 1.62
HÀ1 / L 261 4.75 0.84 260 4.76 0.83
Cl-Ph4DP 467 H / L+1 461 2.69 0.17 464 2.67 0.17
280 H / L 454 2.73 1.76 454 2.73 1.71
HÀ1 / L 266 4.66 1.08 266 4.66 1.07
Ph4DTP 465 H / L 471 2.63 1.42 472 2.63 1.37
263 H / L+1 424 2.92 0.10 433 2.86 0.09
HÀ1 / L 267 4.65 0.86 267 4.65 0.86
a
Values taken from ref. 28. b
H and L represent HOMO and LUMO, respectively.
Paper RSC Advances

electronic states are closer to each other which enhances the
delocalization of the charge carrier on the nearby molecules and
rate of charge transfer. The above results show that the disorder
dri time St is acting as the crossover point between the delo-
calized band transport and localized hopping transport. At this
crossover point, the probability of the charge carrier is equally
distributed on the nearby molecules and the diﬀusion process
is limited.19,24,28,52
Among the studied molecules, F and Cl
substituted Ph4DP molecules are having good hole and electron
transporting ability (see Table 3).
3.5. Absorption spectra
The absorption spectra of studied molecules are calculated
using TD-DFT method at CAM-B3LYP/6-31G(d,p) and M06-2X/6-
31G(d,p) level of theories in dichloromethane medium. The
calculated absorption spectra, oscillator strength and corre-
sponding orbital transitions are summarized in Table 5. To
study the nature and the energy of the singlet–singlet electronic
transition, the rst three low lying electronic transitions
energies are calculated. The absorption intensity is directly
related with the dimensionless oscillator strength value and the
dominant absorption bands are the transitions with higher
oscillator strength. The experimental absorption wavelength is
available for all the studied molecules and two absorption peaks
around 450–470 nm and around 265–280 nm have been repor-
ted. As observed from Table 5 and Fig. 9, the calculated
absorption spectra at CAM-B3LYP/6-31G(d,p) and M06-2X/6-
31G(d,p) level of theories in dichloromethane medium are
comparable and are in agreement with the experimental
values.33
The absorption spectra of the molecules at CAM-
B3LYP/6-31G(d,p) method is discussed in detail. The calcu-
lated absorption spectra of the studied molecules exhibit two
intense peaks. As shown in Fig. 9 for Ph4DP molecules, the rst
peak is observed around 440 nm and it corresponds to HOMO
to LUMO and HOMO to LUMO+1 transitions. The second
intense peak is observed at 260 nm and is due to HOMOÀ1 to
LUMO transitions. Similarly, Ph4DTP molecule exhibits two
intense peaks. The rst peak observed at 470 nm corresponds to
Fig. 9 The absorption spectra of the Ph4DP and Ph4DTP molecules computed at CAM-B3LYP/6-31G(d,p) level of theory in dicholoromethane
medium.
Fig. 10 The emission spectra of the Ph4DP and Ph4DTP molecules computed at CAM-B3LYP/6-31G(d,p) level of theory in dicholoromethane
medium.
RSC Advances Paper

excitation of electron from HOMO to LUMO with the maximum
oscillator strength value of 1.4. The second band is observed at
265 nm and is associated with the HOMOÀ1 / LUMO transi-
tion. The absorption pattern shows that the unsubstituted
Ph4DP and F substituted Ph4DP have similar spectra. The
chlorine substituted Ph4DP molecule has intense absorption
spectra at 454 nm with the maximum oscillator strength of 1.76
and is agreement with the experimental value.33
It has been
observed that the introduction of Cl in Ph4DP enhances the
charge transporting ability as well as intensity of absorption and
emission spectra (see Fig. 9 and 10).
3.6. Emission spectra
The emission spectra of the studied molecules were calculated
using time-dependent density functional theory method at
CAM-B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) level of theories.
The calculated emission energy and the corresponding oscil-
lator strength of unsubstituted Ph4DP, F and Cl substituted
Ph4DP and Ph4DTP molecules are summarized in Table 6. The
computed emission spectra at CAM-B3LYP/6-31G(d,p) and M06-
2X/6-31G(d,p) level of theories are similar. Using the SWizard
program, the emission spectra calculated at CAM-B3LYP/6-
31G(d,p) level of theory is plotted and is shown in Fig. 10. The
unsubstituted Ph4DP molecule exhibits the intense emission
peak at 527 nm due to HOMO / LUMO transition and the
corresponding oscillator strength is around 1.6. As observed in
Table 6, the substitution of F on Ph4DP molecule does not affect
the emission spectra and the Cl substitution red shis the
emission spectra by 15 nm. Notably, the emission spectra of
Ph4DTP is red-shied by 50 nm with respect to Ph4DP, that is,
the substitution of sulfur atom decreases the HOMO–LUMO
energy gap and the emission energy.
4. Conclusions
The effect of structural uctuation on charge transfer in Ph4DP
and Ph4DTP molecules has been studied by using kinetic
charge transfer parameters such as rate coefficient, disorder
dri time, orbital splitting rate, hopping conductivity and
mobility. The calculated hole mobility of 0.04 and 0.03 cm2
VÀ1
sÀ1
for unsubstituted Ph4DP and Ph4DTP molecules is in
agreement with the experimental values. The F and Cl
substituted Ph4DP molecules have hole mobility of 0.17 and
0.33 cm2
VÀ1
sÀ1
, and their corresponding hopping conductivity
is 0.13 and 0.26 S cmÀ1
, respectively. Relatively larger orbital
splitting rate in substituent Ph4DP enhances the bandwidth
and delocalization of the charge carrier, which facilitate the
charge transfer. It has been observed that the molecules with
high orbital splitting rate and less disorder dri time possess
good charge transport. Theoretical results show that if the
orbital splitting rate is lesser than the static charge transfer rate,
the charge carrier is potentially trapped on the localized site.
The calculated absorption spectra of the studied Ph4DP and
Ph4DTP molecules are in agreement with experimental results.
Acknowledgements
(DST), India for awarding research project under Fast Track
Scheme.
References
1 C. W. Tang, Appl. Phys. Lett., 1986, 48, 183.
2 J. H. Burroughes, D. D. C. Bradely, A. R. Brown, R. N. Marks,
Nature, 2000, 347, 539.
3 J. R. Sheats, H. Antoniadis, M. Hueschen, W. Leonard,
J. Miller, R. Moon and D. Roitman, Science, 1996, 273, 884.
4 Y. Cao, I. D. Parker, G. Yu, C. Zhang and A. J. Heeger, Nature,
1999, 397, 414.
5 J. H. Burroughes, C. A. Jones and R. H. Friend, Nature, 1988,
335, 137.
6 G. Horowitz, D. Fichou, X. Z. Peng, Z. G. Xu and F. Garnier,
Solid State Commun., 1989, 72, 381.
7 C. R. Kagan, D. B. Mitzi and C. D. Dimitrakopoulos, Science,
1999, 286, 945.
8 T. Someya, Y. Kato, T. Sekitani, S. Iba, Y. Noguchi, Y. Murase,
H. Hawaguchi and T. Sakurai, Proc. Natl. Acad. Sci. U. S. A.,
2005, 102, 12321.
9 A. Facchetti, Mater. Today, 2007, 10, 28.
10 Y. Shirota and H. Kageyama, Chem. Rev., 2007, 107, 953.
11 J. Zaumseil and H. Sirringhaus, Chem. Rev., 2007, 107, 1296.
12 D. L. Cheung and A. Troisi, Phys. Chem. Chem. Phys., 2008,
10, 5941–5952.
2008, 27, 87–138.
14 K. Senthilkumar, F. C. Grozema, C. F. Guerra,
F. M. Bickelhaupt, F. D. Lewis, Y. A. Berlin, M. A. Ratner
and L. D. A. Siebbeles, J. Am. Chem. Soc., 2005, 127, 148094.
15 S. Mohakud, A. P. Alex and S. K. Pati, J. Phys. Chem. C, 2010,
114, 20436–20442.
16 D. Andrienko, J. Kirkpatrick, V. Marcon, J. Nelson and
K. Kremer, Phys. Status Solidi B, 2008, 245, 830–834.
17 J. Kirkpatrick, V. Marcon, K. Kremer, J. Nelson and
D. Andrienko, J. Chem. Phys., 2008, 129, 094506.
Table 6 Calculated emission wavelength and energy and oscillator
strengths (in a.u) for Ph4DP, F and Cl substituted Ph4DP and Ph4DTP
molecules corresponding to electronic transition between HOMO and
LUMO energy levels at CAM-B3LYP/6-31G(d,p) and M06-2X/6-
31G(d,p) level of theories in dichloromethane medium
Molecule Orbital transitionsa
CAM-B3LYP/6-
31G(d,p)
M06-2X/6-
31G(d,p)
lemi
f
lemi
f(nm) (eV) (nm) (eV)
Ph4DP H / L 527 2.35 1.57 526 2.36 1.53
F-Ph4DP H / L 521 2.38 1.59 520 2.39 1.55
Cl-Ph4DP H / L 541 2.29 1.68 541 2.29 1.63
Ph4DTP H / L 577 2.15 1.35 575 2.16 1.30
a
H and L represent HOMO and LUMO, respectively.
Paper RSC Advances

18 V. Ruhle, A. Lukyanov, F. May, M. Schrader, T. Vehoﬀ,
J. Kirkpatrick, B. Baumeier and D. Andrienko, J. Chem.
Theory Comput., 2011, 7, 3335–3345.
19 A. Troisi, Chem. Soc. Rev., 2011, 40, 2347.
20 L. Wang, Q. Li, Z. Shuai, L. Chen and Q. Shi, Phys. Chem.
Chem. Phys., 2010, 12, 3309–3314.
21 B. Baumeier, J. Kirkpatrick and D. Andrienko, Phys. Chem.
Chem. Phys., 2010, 12, 11103–11113.
22 D. P. McMahon and A. Troisi, Phys. Chem. Chem. Phys., 2011,
13, 10241–10248.
23 J. Bohlin, M. Linares and S. Stafstrom, Phys. Rev. B: Condens.
Matter Mater. Phys., 2011, 83, 085209.
24 A. Troisi and D. L. Cheung, J. Chem. Phys., 2009, 131, 014703.
25 A. Kocherzhenko, Charge Transport in Disordered
Molecular Systems, Ph.D. Dissertation, Del University
Press, The Netherlands, 2011.
26 P. W. Anderson, Phys. Rev., 1958, 109, 1492–1505.
27 N. W. Ashcro and N. D. Mermin, Solid State Physics,
Harcourt college publishers, 1976.
28 A. Troisi and G. Orlandi, Phys. Rev. Lett., 2006, 96, 086601.
29 L. Wang and D. Beljonne, J. Phys. Chem. Lett., 2013, 4, 1888–
1894.
31 K. Navamani, G. Saranya, P. Kolandaivel and
K. Senthilkumar, Phys. Chem. Chem. Phys., 2013, 15,
17947–17961.
32 R. S. Sanchez-Carrera, S. Atahan, J. Schrier and A. Aspuru-
Guzik, J. Phys. Chem. C, 2010, 114, 2334–2340.
33 A. Bolag, M. Mamada, J.-ichi Nishida and Y. Yamashita,
Chem. Mater., 2009, 21, 4350.
Mater., 2008, 20, 3205–3211.
35 E. A. Silinsh, Organic Molecular Crystals, Springer, Verlag,
Berlin, 1980.
36 A. A. Kocherzhenko, F. C. Grozema, S. A. Vyrko,
N. A. Poklonski and L. D. A. Siebbeles, J. Phys. Chem. C,
2010, 114, 20424.
37 A. Troisi, A. Nitzan and M. A. Ratner, J. Chem. Phys., 2003,
119, 5782–5788.
38 M. D. Newton, Chem. Rev., 1991, 91, 767–792.
L. D. A. Siebbeles, J. Chem. Phys., 2003, 119, 9809–9817.
J. Comput. Chem., 2001, 22, 931–967.
A. P. H. J. Schenning, E. W. Meijer and L. D. A. Siebbles, J.
Phys. Chem. B, 2005, 109, 18267–18274.
42 A. D. Becke, Phys. Rev. A, 1988, 38, 3098–3100.
43 J. P. Perdew, Phys. Rev. B: Condens. Matter Mater. Phys., 1986,
33, 8822–8824.
44 H. L. Tavernier and M. D. Fayer, J. Phys. Chem. B, 2000, 104,
11541–11550.
J. Am. Chem. Soc., 2004, 126, 984–985.
1200–1211.
48 C. T. Lee, W. T. Yang and R. G. Parr, Phys. Rev. B: Condens.
Matter Mater. Phys., 1988, 37, 785–789.
49 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,
M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone,
B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato,
X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng,
J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota,
R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda,
O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr,
J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd,
E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi,
J. Normand, K. Raghavachari, A. Rendell, J. C. Burant,
S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam,
M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo,
J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev,
A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski,
R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth,
P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels,
O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and
D. J. Fox, Gaussian 09, Revision B.01, Gaussian, Inc.,
Wallingford CT, 2009.
Proc. Natl. Acad. Sci. U. S. A., 2005, 94, 3703.
51 L. B. Schein and A. R. McGhie, Phys. Rev. B: Condens. Matter
Mater. Phys., 1979, 20, 1631–1639.
52 K. Navamani and K. Senthilkumar, J. Phys. Chem. C, 2014,
118, 27754–27762.
53 J. L. Bredas, J. P. Calbert, D. A. d. S. Filho and J. Cornil, Proc.
Natl. Acad. Sci. U. S. A., 2002, 99, 5804–5809.
54 G. Kresse and J. Furthmuller, Comput. Mater. Sci., 1996, 6, 15.
55 G. Kresse and J. Furthmuller, Phys. Rev. B: Condens. Matter
Mater. Phys., 1996, 54, 11169.
56 G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter Mater.
Phys., 1993, 47, 558.
57 S. Mierus, E. Scrocco and J. Tomasi, Chem. Phys., 1981, 55,
117–129.
58 S. I. Gorelsky, Revision 5.0, 2013, http://www.sg-chem.net/.
59 S. I. Gorelsky and A. B. P. Lever, Organomet. Chem., 2001, 635,
187.
60 Z. G. Yu, D. L. Smith, A. Saxena, R. L. Martin and
A. R. Bishop, Phys. Rev. Lett., 2000, 84, 721–724.
61 F. Reif, Fundamentals of Statistical and Thermal Physics,
McGraw-Hill, 1965, ch. 12, pp. 461–490.
RSC Advances Paper

This journal is ©the Owner Societies 2015 Phys. Chem. Chem. Phys., 2015, 17, 17729--17738 | 17729
Cite this: Phys.Chem.Chem.Phys.,
2015, 17, 17729
Forth–back oscillated charge carrier motion in
dynamically disordered hexathienocoronene
molecules: a theoretical study†
Electronic structure calculations were performed to investigate the charge transport properties of
hexathienocoronene (HTC) based molecules. The effective displacement of the charge carrier along the
p-orbital of nearby molecules is calculated by monitoring the forth and back oscillations of the charge
carrier through kinetic Monte Carlo simulation. The charge transport parameters such as charge transfer
rate, mobility, hopping conductivity, localized charge density, time average effective mass and degeneracy
pressure are calculated and used to study the charge transport mechanism in the studied molecules. The
existence of degeneracy levels facilitates the charge transfer and is analyzed through degeneracy pressure.
Theoretical results show that the site energy difference in the dynamically disordered system controls
the forth–back oscillation of charge carrier and facilitates the unidirectional charge transport mechanism
along the sequential localized sites. The ethyl substituted HTC has good hole and electron hopping con-
ductivity of 415 and 894 S cmÀ1
, respectively, whereas unsubstituted HTC has the small hole mobility of
0.06 cm2
VÀ1
sÀ1
which is due to large average effective mass of 1.42 Â 10À28
kg.
1. Introduction
For the last three decades organic electronics has been an
emerging field in science and technology1–5
due to its potential
applications in semiconducting devices such as field effect
transistors,6–8
photovoltaics,9,10
light emitting diodes11,12
and
solar cells.13–15
Organic materials and polymers are having soft
degrees of freedom, structural flexibility and self-assembling
property.2,3,16–19
In addition to this, other potential advantages
are low molecular weight, low cost processing, environmental
compatibility and easily tunable electronic properties through
chemical modification, which makes organic materials more
adaptable for optoelectronic applications.2,5,13,20,21
The weak
intermolecular forces, low dielectric permittivity and structural
disorder are responsible for large electron–phonon coupling
and localized electronic states in organic molecules.22–25
In this
case, the charge carrier is energetically relaxed by the surround-
ing nuclei of the thermally distorted molecule and is a small
polaron.13,16,17,25,26
Therefore, the thermally activated hopping
mechanism is used to describe the charge transfer (CT) process
in organic molecules4,24,27–29
and the Marcus theory of charge
transfer is used to study CT along the sequential sites.20,29–31
It
has been shown in earlier studies that the nuclear dynamics is
significant at room temperature which results the breakdown
of Franck–Condon (FC) principle.1,32–34
In the CT calculations,
the nuclear dynamics is modeled in terms of harmonic oscillators
and is coupled with the electronic degrees of freedom. The
collection of harmonic oscillators dissipates the energy and hence
the charge carrier is thermally activated.22,35
Hence, the charge
transfer process in organic materials has an activation-less barrier,
that is, the nuclear dynamics relaxes the energy barrier between
the neighboring molecules.4,26,34
Earlier studies4,25,26,35,36
show
that the dynamic disorder decreases the electron–phonon
coupling and increases the electronic interaction which facil-
itates the dynamic localization and charge transfer. In this case,
the charge transfer kinetics follows the intermediate regime
between the adiabatic band transport and a non-adiabatic
hopping transport and is characterized by an effective disorder
Department of Physics, Bharathiar University, Coimbatore-641 046, India.
E-mail: ksenthil@buc.edu.in
† Electronic supplementary information (ESI) available: Optimized structures of
unsubstituted hexathienocoronene (HTC-a), hexyl substituted hexathienocoro-
nene (HTC-b), ethyl substituted hexathienocoronene (HTC-c) molecules are given
in Fig. S1. Highest occupied molecular orbitals (HOMO) and the lowest unoccu-
pied molecular orbitals (LUMO) of the studied HTC-a, HTC-b and HTC-c
molecules are given in Fig. S2 and S3, respectively. The plot between the number
of occurrence, potential energy with respect to stacking angle calculation from
molecular dynamics simulation for unsubstituted HTC (HTC-a) molecule is given
in Fig. S4. The effective charge transfer integral ( Jeff) at different stacking angle
(y) for hole and electron transport in the studied HTC-a, HTC-b and HTC-c
molecules are summarized in Table S1. The number of forward (Nf) and backward
(Nb) oscillations and their probabilities (Pf and Pb), effective displacement (deff)
and average site energy difference hDeiji corresponding to forward and backward
charge carrier motions calculated from kinetic Monte Carlo simulation for hole
and electron transport are summarized in Table S2. See DOI: 10.1039/c5cp02189h
Received 15th April 2015,
Accepted 26th May 2015
DOI: 10.1039/c5cp02189h
www.rsc.org/pccp
PCCP
PAPER

17730 | Phys. Chem. Chem. Phys., 2015, 17, 17729--17738 This journal is ©the Owner Societies 2015
drift time, and the CT is termed as the ‘‘diffusion limited by
dynamic disorder’’.16,25
Generally, the device performance is strongly dependent on
the charge carrier dynamics which is closely related with the
morphology and the electronic structure of the materials.13,20,37,38
Therefore, there is current interest in organic electronics for
synthesizing and characterizing appropriate functional materials
on the basis of structure–property relationship and the effect of
substitution of heteroatoms and functional groups.2,3,28,37,39,40
In
this work, the charge transport property of recently synthesized
hexathienocoronene (HTC) molecules is studied.41
These mole-
cules have a thiophene annealed coronene core with six double
bonds in the periphery region which provides good thermal
stability. The experimental study41
shows that the HTC molecules
have good self-aggregating property in the solid state and the
phase transformation depends on the length of the alkyl side
chains. As shown in Fig. 1, the HTC core has six thiophene rings
and the presence of alkyl side chains in the HTC molecules
decreases the steric repulsion which provides better planarity.
That is, the presence of alkyl side chains decreases the torsional
disorder between thiophene and phenyl rings in the HTC mole-
cule. X-ray diffraction study reveals that HTC-b molecules are
stacked with one another in a columnar fashion and the inter-
molecular distance is 3.37 Å.41
Grazing-incidence wide-angle
X-ray scattering (GIWAXS) measurements reveal that HTC-b exists
in a crystalline phase and p-stacked arrangements are parallel to
the surface. Experimental study41
shows that the unsubstituted
(HTC-a) and hexyl substituted HTC (HTC-b) show high crystal-
linity. Field effect mobility values in HTC-a and HTC-b are 0.002
and 0.001 cm2
VÀ1
sÀ1
, respectively.41
In the present work, we
have studied the hole and electron transport in these HTC
molecules through the CT kinetic parameters such as rate of
transition probability, hopping conductivity, mobility, average
effective mass and degeneracy pressure, which are obtained from
electronic structure calculations, molecular dynamics and kinetic
Monte Carlo simulations. The previous studies17,28,38
show that
the fluctuation of charge transfer integral and site energy
difference with respect to nuclear degrees of freedom and
orientation of nearby molecules introduces forth and back
oscillations of charge carriers in the tunneling regime. In the
present study, the forth–back oscillations are studied on the
basis of forward and backward rates and number of forward
and backward oscillations.
2. Theoretical formalism
By using the tight-binding Hamiltonian approach the presence of
excess charge in a p-stacked molecular system is expressed as,13,42
^H ¼
X
i
eiðyÞaþ
i ai þ
X
iaj
Ji;jðyÞaþ
i aj (1)
where, a+
i and ai are creation and annihilation operators, ei(y) is
molecular site and is calculated as diagonal element of the
Kohn–Sham Hamiltonian, ei = hji|HˆKS|jii, the second term of
eqn (1), Ji, j is the off-diagonal matrix element of Hamiltonian,
Ji, j = hji|HˆKS|jji known as charge transfer integral or electronic
coupling, which measures the strength of the overlap between
ji and jj (HOMO or LUMO of nearby molecules i and j).
Based on the semi-classical Marcus theory, the CT rate (k) is
defined as29–31
k ¼
2pJeff
2
h
1
4plkBT
1=2
exp À
Deij þ l
À Á2
4lkBT
!
(2)
where, kB is the Boltzmann constant, T is the temperature (here
T = 298 K), Jeff is the effective charge transfer integral, Deij is the
site energy difference between the nearby molecules, and l is
the reorganization energy. The generalized or effective charge
transfer integral ( Jeff) is defined in terms of charge transfer
integral ( J), spatial overlap integral (S) and site energy (e) as,43,44
Jeffi;j ¼ Ji;j À Si;j
ei þ ej
2

(3)
where, ei and ej are the energy of a charge when it is localized at
ith
and jth
molecules, respectively. The site energy, charge
transfer integral and spatial overlap integral are computed using
the fragment molecular orbital (FMO) approach as implemented
in the Amsterdam density functional (ADF) theory program.18,44,45
In ADF calculation, we have used the Becke–Perdew (BP)46,47
exchange correlation functional with triple-z plus double polariza-
tion (TZ2P) basis set.48
In this procedure, the charge transfer
integral and site energy corresponding to hole and electron trans-
port are calculated directly from the Kohn–Sham Hamiltonian.13,44
The reorganization energy measures the change in energy of
the molecule due to the presence of excess charge and changes
in the surrounding medium. The reorganization energy due to
the presence of excess hole (positive charge, l+) and electron
(negative charge, lÀ) is calculated as,13,49,50
lÆ = [EÆ
(g0
) À EÆ
(gÆ
)] + [E0
(gÆ
) À E0
(g0
)] (4)
Fig. 1 The chemical structure of hexathienocoronene (HTC) based mole-
cules (HTC-a: R0
= H, HTC-b: R0
= C6H13, HTC-c: R0
= C2H5).
Paper PCCP

where, EÆ
(g0
) is the total energy of an ion in neutral geometry,
EÆ
(gÆ
(gÆ
) is the
energy of the neutral molecule in ionic geometry and E0
(g0
) is
geometry of the studied molecules, HTC-a, HTC-b and HTC-c in
neutral and ionic states are optimized using density functional
theory method, B3LYP51–53
in conjunction with the 6-31G(d,p)
basis set, as implemented in the GAUSSIAN 09 package.54
The charge carrier mobility is calculated from diffusion
coefficient, D by using the Einstein relation,55
m ¼
q
kBT

D (5)
The above classical Einstein relation is valid for disordered
semiconducting materials when the system is under equili-
brium condition. The previous studies show that the above
relation is invalid when the system is in non-equilibrium
condition, such as FET under applied field, because the electric
field dependent diffusivity is larger than the electric field
response mobility.56,57
In the present work, we assume that the charge carrier is
initially localized on the molecule which is located at the center
of the sequence of p-stacked molecules and the charge does not
reach the end of molecular chain within the time scale of
simulation due to the forth–back oscillations. In each step of
Monte-Carlo simulation, the most probable hopping pathway is
found out from the simulated trajectories based on the forward
and backward charge transfer rates at a particular conforma-
tion. In the case of normal Gaussian diffusion of the charge
carrier in one dimension, the diffusion coefficient, D is calcu-
lated from effective displacement, deff and the total hopping
time, tHop
D ¼
deff
2
2tHop
¼
Pf À Pbj jdð Þ2
2tHop
(6)
where, Pf and Pb are the probability for forward and backward
motions of charge carrier and d is the distance between nearby
p-stacked molecules. The hopping time for such oscillated
motion along the CT path is defined as,28
tHop = Nf/kf + Nb/kb.
The forward and backward CT rates, kf and kb, and number of
forward and backward oscillations, Nf and Nb are numerically
calculated by using kinetic Monte Carlo simulation. As reported
in previous studies,17,28,38
the site energy difference and dynamic
disorder causes the forth–back oscillations of charge carrier in
the tunneling regime. To calculate the forward and backward
CT rates, the Marcus equation for CT rate given in eqn (2) is
rewritten as,
k ¼
2pJeff
2
h
1
4plkBT
1=2
exp À
l
4kBT

exp À
Deij
2
4lkBT

Â exp À
Deij
2kBT
(7)
here, if Deij is positive, k - kb; and if Deij is negative, k is kf.
By comparing eqn (2) and (7), the ratio of forward and
backward CT rates is equal to kf/kb = exp(ÀDeij/kBT), as stated
in the previous studies.28,38
Note that the forth–back oscilla-
tions are purely depending on site energy difference and
fluctuations in site energy. The earlier study28
reports that the
ratio of forward and backward CT rates is equal to the ratio of
the number of forward and backward charge carrier oscilla-
tions, that is, kf/kb = Nf/Nb = exp(ÀDeij/kBT). Therefore, the
number of forward and backward oscillations are explicitly
defined as,
N ¼ exp À
Deij
2
4lkBT

exp À
Deij
2kBT

here, N = Nf when Deij is negative and N = Nb when Deij is
positive.
As given in eqn (6), the effective displacement (deff) is
calculated by using probability for forward (Pf) and backward
(Pb) oscillations and is written as Pf = kf/(kf + kb) and Pb =
kb/(kf + kb).
The electronic and nuclear dynamics facilitates the density
flux along the hopping sites and the time evolution of density
flux gives the hopping conductivity (s) as58
s ¼
3
5
e
@P
@t
(8)
That is, the hopping conductivity is purely depending on the
rate of transition probability and electric permittivity (e) of the
medium. The rate of transition probability for dynamically
disordered system is calculated by using the Master equation
method and is written as28,38,59
@Pi
@t
¼
X
i
Pb;ikb;i À Pf;ikf;i
Â Ã
(9)
The intermolecular electrostatic interaction between the
stacked molecules leads to Frenkel excitonic splitting and
facilitates the overlap of orbitals of nearby molecules.14,40,60,61
The dynamic disorder reduces the influences of electron–phonon
scattering on localized charge carriers and hence the interaction
between the electronic states is increased.26
Here, the dynamic
disorder leads to Wannier delocalized excitonic splitting instead
of pure Frenkel localized excitonic splitting.4,22,25,35
The degen-
eracy pressure is directly related with the orbital splitting and CT
efficiency. The degeneracy pressure is calculated by using the
average effective mass and localized charge density on the
p-orbitals of nearby molecules and is written as62
Pd ¼
3p2
À Á2=3
h2
5 meffh i
n5=3
(10)
here, the distributed charge carrier density (n) on the p-orbitals
is calculated as n = s/em, and its corresponding momentum and
velocity are k = (3p2
n)1/3
and n = deff/tHop, respectively.62
From
the above relations, the average effective mass of the charge
carrier is calculated as, hmeffi = h k/n. Here, the average effective
mass is the mass of the polaron in the distorted molecular
geometry and is interacting continuously with the intermole-
cular forces and electronic and nuclear degrees of freedom.
To get quantitative insight on charge transport properties of
these molecules, the information about stacking angle and its
PCCP Paper

fluctuation around the equilibrium is required. As reported in
previous studies,33,58
the equilibrium stacking angle and its
fluctuation were calculated by using molecular dynamics (MD)
simulation. The molecular dynamics simulation was performed
for stacked dimers with fixed intermolecular distance of 3.37 Å
for all HTC based molecules using NVT ensemble at temperature
298.15 K and pressure 10À5
Pa, using TINKER 4.2 molecular
modeling package with the standard molecular mechanics force
field, MM3. The simulations were performed up to 10 ns with
time step of 1 fs, and the atomic coordinates in trajectories were
saved in the interval of 0.1 ps. The energy and occurrence of
particular conformations were analyzed in all the saved 100 000
frames to find the stacking angle and its fluctuation around the
equilibrium value.
The geometry of the hexathienocoronene based molecules,
HTC-a, HTC-b and HTC-c is optimized using the DFT method
at B3LYP/6-31G(d,p) level of theory and is shown in Fig. S1
(ESI†). The molecules HTC-b and HTC-c differ by the substitu-
tion of the alkyl side chains as C6H13 and C2H5 on the end
thiophene rings, and for HTC-a molecule, the alkyl side chains
were replaced by H atoms. In this work, the electronic structure
calculations and MD simulations were performed for the
studied HTC molecules with the different side chains and the
results were used to study the charge carrier dynamics through
the KMC method, as described in Section 2. As the best
approximation, the positive charge (hole) will migrate through
the highest occupied molecular orbital (HOMO), and the nega-
tive charge (electron) will migrate through the lowest unoccu-
pied molecular orbital (LUMO) of the stacked molecules, and
the charge transfer integral, spatial overlap integral and site
energy corresponding to positive and negative charges are
calculated based on orbital coefficients and energies of the
HOMO and LUMO. The density plots of the HOMO and LUMO
of the studied molecules calculated at B3LYP/6-31G(d,p) level of
theory are shown in Fig. S2 and S3 (ESI†), respectively. As
shown in Fig. S2 and S3 (ESI†), the HOMO and LUMO are p
orbitals and are delocalized on the entire HTC core and have
much less density on the alkyl side chains of HTC-b and HTC-c
molecules. The delocalization of HOMO and LUMO on the HTC
core increases the p-stacking property through p–p orbital
interaction. The alkyl side chains substitution on HTC core
does not significantly affect the delocalization of electron
density on HOMO and LUMO, and the effective charge transfer
integral (see Fig. 2 and 3). That is, in the p-stacked molecules,
the overlap of nearby HTC cores will facilitate both hole and
electron transport along the columnar axis, and these mole-
cules may have ambipolar character.
The effective charge transfer integral ( Jeff) for hole and electron
transport in the studied HTC based molecules is calculated by
using eqn (3). The previous studies18,33
show that the Jeff
strongly depends on p-stacking distance and p-stacking angle.
The experimental result41
shows that the intermolecular dis-
tance between two molecules in the stacked dimer is 3.37 Å for
HTC-b molecules. Therefore, the Jeff for hole and electron
transport in the HTC based molecules is calculated with fixed
stacking distance of 3.37 Å and the stacking angle is varied
from 0 to 901 in steps of 101. The variation of Jeff with respect
to stacking angle for hole and electron transport in the
studied HTC molecules is shown in Fig. 2 and 3, respectively.
The shape and distribution of frontier molecular orbitals
on each monomer are responsible for the orbital overlap
between the neighboring p-stacked molecules. As observed
in Fig. S2 and S3 (ESI†), HOMO and LUMO are delocalized on
the entire HTC core which leads to a significant effective
charge transfer integral for both hole and electron transport.
As observed in Fig. 2, for hole transport, the maximum Jeff
of around 0.48 eV is calculated at the stacking angle range of
45–501. At these stacking angles, the distance between the
sulfur atoms of nearby molecules is around 2.9 Å which
facilitate stronger interaction between the p-stacked mole-
cules. At these p-stacking angles, the HOMO of each monomer
contributes nearly equally for HOMO of the dimer. For example,
at 501 stacking angle, the HOMO of the HTC-a dimer consists
of HOMO of first monomer by 49% and the second monomer
of 50% which leads to constructive overlap between the
Fig. 2 The effective charge transfer integral (Jeff, in eV) for hole transport
in HTC-a (—), HTC-b (Á Á Á) and HTC-c (---) molecules at different stacking
angles (y, in degree).
Fig. 3 The effective charge transfer integral (Jeff, in eV) for electron
transport in HTC-a (—), HTC-b (Á Á Á) and HTC-c (---) molecules at different
stacking angles (y, in degree).
Paper PCCP

p-orbitals. A significant Jeff of 0.32 eV is observed at the
stacking angles of 40 and 601 for hole transport (see Fig. 2
and Table S1, ESI†). This is because of the constructive overlap
between HOMO of each monomer while forming the HOMO of
the dimer. It has been found that the introduction of alkyl side
chains does not affect the Jeff significantly. However, the
substitution of alkyl chains on the HTC core enhances the
planarity of the molecule. It has been found that the Jeff for
hole transport is minimum at stacking angles of 20 and 701.
This is because of the unequal contribution of the HOMO of
each monomer on the HOMO of the stacked dimer. For
instance, the Jeff calculated for hole transport at 701 stacking
angle is below 0.01 eV, at this angle the HOMO of HTC dimer
consists of 87% HOMO of first monomer and 12% HOMO of
the second monomer.
It has been observed that the maximum effective charge
transfer integral ( Jeff) for electron transport in the HTC mole-
cule is 0.41 eV at 701 stacking angle. At this angle, the LUMO of
the dimer consists of LUMO of first monomer by 48% and the
second monomer of 51% which leads to constructive overlap.
As shown in Fig. 3 and Table S1 (ESI†), at 20 and 901 stacking
angle the Jeff value for electron transport is nearly equal to zero
which is due to the destructive overlap of the LUMO of each
monomer in the dimer system. Notably, at the stacking angle of
401, the studied molecules have a significant Jeff value in the
range of 0.15–0.25 eV for both hole and electron transport. The
MD results show that the equilibrium stacking angle for
unsubstituted HTC (HTC-a), hexyl substituted HTC (HTC-b)
and ethyl substituted HTC (HTC-c) is 60, 45 and 551, respec-
tively, and stacking angle fluctuation up to 10 to 151 from the
equilibrium stacking angle is observed (see Fig. S4, ESI†). That
is, the substitution of alkyl side chains on the HTC core reduces
the equilibrium stacking angle. The change in Jeff due to the
stacking angle fluctuation is included while calculating the CT
kinetic parameters through kinetic Monte-Carlo simulation.
3.2. Site energy difference
Site energy difference is one of the key parameters that deter-
mines the rate of CT and is equal to the difference in site energy
(Deij = ej À ei) of nearby p-stacked molecules. The site energy
difference arises due to the conformational disorder, electro-
static interactions and polarization effects. The previous stu-
dies28,38,58
show that the site energy difference (Deij) provides a
significant impact on charge carrier dynamics and is acting as
the driving force for forward motion when Deij is negative, and
is acting as a barrier for forward motion when Deij is positive,
that is, the carrier takes the backward drift due to the positive
value of Deij. The change in site energy difference with respect
to the stacking angle for hole and electron transport in the
studied molecules is shown in Fig. 4 and 5. It has been found
that the stacking angle fluctuation has significant effect on Deij,
except for electron transport in C6H13 substituted HTC up to
401 stacking angle. At 01 stacking angle, Deij is zero for both
hole and electron transport. For both hole and electron transport
in unsubstituted HTC and C2H5 substituted HTC molecules, the
maximum value of Deij is nearly 0.05 eV at 801 stacking angle and
the minimum value is nearly À0.05 eV at a stacking angle of 401.
For hole transport, at equilibrium stacking angle the molecules
HTC-a, HTC-b and HTC-c have site energy difference of around
0.01, 0.02 and À0.02 eV, respectively, and for electron transport
the site energy difference is 0.02, 0.06 and 0.05 eV (see Fig. 4
and 5). The calculated Deij values at different stacking angles
were included while calculating the CT rate and other kinetic
parameters through Monte Carlo simulation. In the present
study, the change in Deij due to the stacking angle variation is
responsible for forth–back oscillations along the p-stacked mole-
cules and is analyzed through forward and backward CT rate, as
described in Section 2.
3.3. Reorganization energy
The change in energy of the molecule due to structural reorga-
nization by the presence of excess charge will act as a barrier for
charge transport. The geometry of neutral, anionic and cationic
states of the studied HTC based molecules were optimized at
B3LYP/6-31G(d,p) level of theory and the reorganization energy
was calculated by using eqn (4).
It has been observed that the unsubstituted HTC (HTC-a)
molecule has maximum reorganization energy value of 0.23 eV
for the presence of excess positive charge. By analyzing the
optimized geometry of neutral and cationic states of the HTC
Fig. 4 The site energy difference (Deij, in eV) for hole transport in HTC-a
(—), HTC-b (Á Á Á) and HTC-c (---) molecules at different stacking angles
(y, in degree).
Fig. 5 The site energy difference (Deij, in eV) for electron transport in
HTC-a (—), HTC-b (Á Á Á) and HTC-c (---) molecules at different stacking
angles (y, in degree).
PCCP Paper

molecule, we found that the presence of positive charge alters
the torsional angle between the thiophene and phenyl rings of
HTC core up to 31 which is the reason for the high hole
reorganization energy. The substitution of alkyl side chains
on the HTC molecule decreases the reorganization energy up to
0.1 eV for hole transport and hence HTC-b and HTC-c mole-
cules have minimum hole reorganization energy of around
0.13 eV. It has been found that the HTC-a, HTC-b and HTC-c
molecules have similar reorganization energy of around 0.14 eV
for the presence of an excess negative charge. Notably, the HTC
core consists of circularly fused phenyl rings attached with six
thiophene rings which lead to the planarity and core rigidity and
is responsible for small structural relaxation due to the presence
of excess negative charge and hence the electron reorganization
energy is minimum for the studied HTC molecules.
3.4. Charge carrier dynamics
The calculated charge transport key parameters such as effec-
tive charge transfer integral, site energy difference, reorganiza-
tion energy and structural fluctuation in the form of stacking
angle distribution are used to study the charge carrier dynamics
through kinetic Monte Carlo simulations. In the present model,
forth–back oscillations of a charge carrier effect on charge
carrier motion in the tunneling regime are studied. The struc-
tural fluctuation and its effect on site energy difference are
responsible for the forward and backward CT. In this paper the
survival probability of a charge carrier corresponding to for-
ward and backward transports has been calculated from kinetic
Monte Carlo simulations, and is shown in Fig. 6 and 7. As
mentioned in the previous section, the forward and backward
CT rates, number of forward and backward oscillations, prob-
ability for forward and backward oscillations, effective displace-
ment, total hopping time, rate of transition probability, average
effective mass and degeneracy pressure are calculated and are
used to study the charge carrier dynamics in the studied HTC
molecules. As shown in Fig. 6, the forward and backward hole
transfer rates in HTC-a are comparable, whereas in HTC-c the
forward CT rate is significantly higher than the backward rate.
As given in Table 1, the effective rate of hole transfer and
hopping conductivity in HTC-a, HTC-b and HTC-c molecules
are 1.3 Â 1014
, 1.17 Â 1015
and 7.82 Â 1015
sÀ1
and 6.9, 62.1 and
415 S cmÀ1
, respectively. The presence of side chains in the
HTC molecule decreases the hole reorganization energy by
0.1 eV which enhances the CT rate and hopping conductivity
(see Table 1). The Jeff for hole transport in the studied HTC-c
molecule is nearly 0.45 eV at the equilibrium stacking angle of
551 (see Fig. 2) which is also responsible for good hole trans-
porting ability. The fluctuation in stacking angle is around
40–701, for the HTC-c molecule, and the variation in effective
electron transfer integral is in the range of 0.15–0.42 eV and the
calculated electron reorganization energy is 0.14 eV, which
enhances the effective electron transfer rate and hopping
conductivity to 1.68 Â 1016
sÀ1
and 894 S cmÀ1
, respectively
(see Table 2). It has been found that the calculated average
effective mass of the polaron for both hole and electron transport
is much heavier than the free electron mass (see Tables 1 and 2),
which is in agreement with the previous study.25
That is, the
effective mass of the polaron is infinite when it is localized in
the distorted molecules, due to lower electronic coupling and
larger electron–phonon coupling.25
Bo¨hlin et al.26
noticed that
in the presence of dynamical disorder, the localized charge
carrier is less influenced by the electron–phonon coupling
(reorganization energy) as compared to the ideal system. The
effect of static and dynamic fluctuation on charge transport in
donor–bridge–acceptor systems has been studied by Berlin
et al.32
and they concluded that the dynamic fluctuation facil-
itates the band-like transport due to the self-averaging effect of
electronic coupling or effective charge transfer integral. There-
fore, the dynamic disorder reduces the effective mass of the
polaron, which enhances the charge transfer. For instance, the
Fig. 6 The survival probability of a positive charge at particular site
corresponding to forward and backward transports with respect to time
in (a) HTC-a (b) HTC-b and (c) HTC-c molecules.
Paper PCCP

average effective mass of the polaron for electron transport in
the HTC-c molecules is less than the other studied HTC mole-
cules (see Table 2), due to lower electron–phonon coupling
(B0.14 eV) and larger values of fluctuated electronic coupling
(0.15–0.42 eV). The number of forward and backward oscillations,
probability for forward and backward oscillations of a charge
carrier and average site energy difference while including the
structural fluctuations in kinetic Monte Carlo simulations are
summarized in Table S2 (ESI†). It has been observed that number
of forward oscillations is higher than the backward oscillations for
hole and electron transport in ethyl substituted HTC (HTC-c)
molecule and their probability for forward charge carrier motion
is 0.76 and 0.91, respectively. That is, the probability for forward
motion of a charge carrier is comparably higher than that of
backward motion which increases the forward transport along the
p-stacked molecules, and hence the ethyl substituted HTC mole-
cule (HTC-c) has good ambipolar charge transport character (see
Tables 1 and 2). Here, the significant effective charge transfer
integral and small reorganization energy reduces the charge loca-
lization time on the frontier molecular orbital (HOMO or LUMO)
and the calculated average effective mass of holes and electrons
at HTC-c is comparably small (2.67 Â 10À30
and 2.26 Â 10À30
kg).
In this case, the calculated average site energy difference corre-
sponding to forward and backward oscillations for hole transport is
À0.054, 0.054 eV and for electron transport is À0.13, 0.13 eV,
respectively. As given in Table S2 (ESI†), the number of forward
oscillations corresponding to hole and electron transport in HTC-c
is relatively higher than the number of backward oscillations, and
the effective displacement (deff) of a charge carrier in the forward
direction is higher in HTC-c molecules.
The hexyl substituted HTC (HTC-b) has stacking angle
fluctuation in the range of 30–601 around the equilibrium
angle of 451 and the variation in Jeff is in the range of 0.1–
0.45 eV which leads to significant charge transporting ability. It
has been found that HTC-b has significant hole and electron
mobility of 1 and 1.63 cm2
VÀ1
sÀ1
and the calculated average
effective mass of hole and electron in HTC-b is 1.51 Â 10À29
and 1.21 Â 10À29
kg, respectively. The number of forward and
backward oscillations corresponding to hole transport in HTC-b
is 1.14 and 0.84 and for electron transport is 1.37 and 0.87,
respectively. The calculated total time for the hopping process
in HTC-b and HTC-c for hole transport is 0.51, 0.42 fs and for
electron transport is 0.65 and 0.53 fs, respectively. The number
of forward and backward oscillations corresponding to hole
and electron transport in unsubstituted HTC (HTC-a) are nearly
equal and hence the charge carrier oscillates for a longer time
before hopping to the next molecule (see Tables 1 and 2). In
this case, the calculated average site energy difference corre-
sponding to forward and backward oscillations for hole trans-
port is À0.005, 0.005 eV and for electron transport is À0.007,
0.007 eV, respectively. As observed in Table S2 (ESI†), the
probability for forward and backward oscillations of a charge
carrier in HTC-a is nearly equal, which increases the average
Fig. 7 The survival probability of a negative charge at particular site
corresponding to forward and backward transports with respect to time
in (a) HTC-a (b) HTC-b and (c) HTC-c molecules.
Table 1 Rate of transition probability (qP/qt), hopping conductivity (s), total hopping time (tHop), mobility (m), p-electron density (n), time average
effective mass (hmeff(t)i) and degeneracy pressure (Pd) for hole transport in hexathienocoronene molecules, HTC-a, HTC-b and HTC-c
Molecule qP/qt (fsÀ1
) s (S cmÀ1
) tHop (fs) m (cm2
VÀ1
sÀ1
) n (Â1026
mÀ3
) hmeff(t)i (Â10À30
kg) Pd (Â105
Pa)
HTC-a (R = H) 0.13 6.9 2.16 0.06 6.53 142.4 0.73
HTC-b (R = C6H13) 1.17 62.1 0.51 1 3.88 15.1 2.92
HTC-c (R = C2H5) 7.82 415 0.42 14.86 1.74 2.67 4.34
PCCP Paper

effective mass and decreases the effective displacement (deff)
and charge transporting ability. The calculated hole mobility is
0.06 cm2
VÀ1
sÀ1
which is higher than the experimental field
effect mobility of 0.002 cm2
VÀ1
sÀ1
. The previous studies show
that the experimentally measured mobility depends on sub-
strate and substrate temperature63–65
and FET mobility is field
dependent and shows non-equilibrium diffusion. However,
theoretically calculated mobility by the Einstein relation is field
independent and is based on an equilibrium thermal diffusion
process. Here the carrier is strongly localized on the molecular
site and the calculated localized charge density is 6.53 Â
1026
mÀ3
. The above results clearly show that the site energy
difference in the geometrically fluctuated molecules controls
the forth–back oscillation of charge carrier and facilitate the
unidirectional charge transfer process (see Tables 1, 2 and
Table S2, ESI†). It has been found that the site energy difference
in the dynamically disordered systems is acting as the driving
force for unidirectional charge transport mechanism. That is,
the forward and backward charge carrier hopping network is
controlled or tuned by the site energy difference, which is in
agreement with the previous studies.28,38
To get further insight on charge transport in the studied mole-
cules, the degeneracy pressure is calculated by using eqn (10).
The existence of degeneracy levels promotes the delocalization
of charge carriers and is calculated as degeneracy pressure.
The previous studies26,32
show that the localized charge carrier
on the dynamically disordered system is less influenced by the
electron–phonon scattering and the CT mechanism follows the
static non-Condon effect. The weak electron–phonon scattering in
the dynamically disordered system increases the coupling strength
between the electronic states which leads to an intermediate
CT mechanism between the localized hopping transport and
delocalized band transport. The calculated degeneracy pressures
are summarized in Tables 1 and 2. It has been found that the high
degeneracy pressure drifts the carrier from one localized site to
another localized site. Among the studied molecules, HTC-c has
comparably maximum degeneracy pressure of 4.34 Â 105
and
6.24 Â 105
Pa for hole and electron transport which favors the
charge transport. Here, the orbital splitting follows the Wannier
type and the carrier is delocalized on the frontier molecular
orbitals. In the case of HTC-a molecule, the degeneracy pressure
for hole dynamics is relatively small (7.35 Â 104
Pa) and the charge
transporting ability of HTC-a is low. In this case, the splitting of
energy levels follows the Frenkel type and charge carrier follows a
large number of forth–back oscillations. The degeneracy pressure
for hole and electron transport in the HTC-b molecule is signifi-
cant and the values are 2.9 Â 105
and 2.37 Â 105
Pa, respectively,
which facilitate the CT process.
4. Conclusion
The charge transport properties of hexathienocoronene (HTC)
based molecules are investigated by using electronic structure
calculations. The structural fluctuation effect on the effective
charge transfer integral and site energy difference is included
while studying the charge carrier dynamics through the kinetic
Monte Carlo simulations. The number of forward and back-
ward oscillations and probability for forward and backward
oscillations are calculated from the kinetic Monte Carlo simu-
lation and are used to study the dynamics of the charge carrier
along the p-stacked molecules. The charge transfer parameters
such as effective charge transfer rate, hopping conductivity,
mobility, localized charge density, average effective mass and
degeneracy pressure were calculated, and the dynamic disorder
effect on charge transport in the HTC molecules was studied. It
has been found that the site energy difference in the dynami-
cally disordered system is acting as the driving force for
unidirectional charge carrier propagation. The ethyl and hexyl
substituted HTC (HTC-c and HTC-b) molecules have good
ambipolar transporting ability. The unsubstituted HTC mole-
cule (HTC-a) has a small hole mobility of 0.06 cm2
VÀ1
sÀ1
which is due to the strong localization of positive charge on the
molecular site and large effective mass, and is in agreement
with the previous experimental results.
Acknowledgements
(DST), India for awarding the research project under Fast Track
Scheme.
References
1 W. Zhang, W. Liang and Y. Zhao, J. Chem. Phys., 2010,
133, 024501.
2 D. Andrienko, J. Kirkpatrick, V. Marcon, J. Nelson and
K. Kremer, Phys. Status Solidi B, 2008, 245, 830–834.
3 V. Marcon, J. Kirkpatrick, W. Pisula and D. Andrienko, Phys.
Status Solidi B, 2008, 245, 820–824.
4 D. L. Cheung and A. Troisi, Phys. Chem. Chem. Phys., 2008,
10, 5941–5952.
5 S. E. Koh, B. Delley, J. E. Medvedeva, A. Facchetti,
A. J. Freeman, T. J. Marks and M. A. Ratner, J. Phys. Chem.
B, 2006, 110, 24361–24370.
6 H. E. Katz, J. Mater. Chem., 1997, 7, 369–376.
Table 2 Rate of transition probability (qP/qt), hopping conductivity (s), total hopping time (tHop), mobility (m), p-electron density (n), time average
effective mass (hmeff(t)i) and degeneracy pressure (Pd) for electron transport in hexathienocoronene molecules, HTC-a, HTC-b and HTC-c
Molecule qP/qt (fsÀ1
) s (S cmÀ1
) tHop (fs) m (cm2
VÀ1
sÀ1
) n (Â1026
mÀ3
) hmeff(t)i (Â10À30
kg) Pd (Â105
Pa)
HTC-a (R = H) 0.49 26 1.04 0.54 3.1 26.46 1.08
HTC-b (R = C6H13) 1.51 80.2 0.65 1.63 2.8 12.1 2.37
HTC-c (R = C2H5) 16.8 894 0.53 28.54 1.96 2.26 6.24
Paper PCCP

7 H. E. Katz, A. J. Lovinger, J. Johnson, C. Kloc, T. Siegrist,
W. Li, Y. Y. Lin and A. Dodabalapur, Nature, 2000, 404,
478–481.
8 M. Shim, A. Javey, N. W. Shi Kam and H. Dai, J. Am. Chem.
Soc., 2001, 123, 11512–11513.
9 N. S. Sariciftci, L. Smilowitz, A. J. Heeger and F. Wudl,
Science, 1992, 258, 1474–1476.
10 X. Zhan, Z. Tan, B. Domercq, Z. An, X. Zhang, S. Barlow,
Y. Li, D. Zhu, B. Kippelen and S. R. Marder, J. Am. Chem.
Soc., 2007, 129, 7246–7247.
11 J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks,
Nature, 1990, 347, 539–541.
12 C. W. Tang and S. A. Vanslyke, Appl. Phys. Lett., 1987, 51,
913–915.
2008, 27, 87–138.
14 S. Mohakud and S. K. Pati, J. Mater. Chem., 2009, 19, 4356–4361.
Mater., 2008, 20, 3205–3211.
16 L. Wang and D. Beljonne, J. Phys. Chem. Lett., 2013, 4,
1888–1894.
17 L. Wang, Q. Li, Z. Shuai, L. Chen and Q. Shi, Phys. Chem.
Chem. Phys., 2010, 12, 3309–3314.
A. P. H. J. Schenning, E. W. Meijer and L. D. A. Siebbles,
J. Phys. Chem. B, 2005, 109, 18267–18274.
19 X. Feng, V. Marcon, W. Pisula, R. Hansen, J. Kirkpatrick,
F. Grozema, D. Andrienko, K. Kremer and K. Mullen, Nat.
Mater., 2009, 8, 421.
20 J. L. Bredas, D. Beljionne, V. Coropceanu and J. Cornil,
Chem. Rev., 2004, 104, 4971.
21 Y.-A. Duan, Y. Geng, H.-B. Li, X.-D. Tang, J.-L. Jin and
Su. Zhong-Min, Org. Electron., 2012, 13, 1213–1222.
22 R. D. Pensack and J. B. Asbury, J. Phys. Chem. Lett., 2010, 1,
2255–2263.
23 W. Q. Deng and W. A. Goddard, J. Phys. Chem. B, 2004, 108,
8614–8621.
24 J. L. Bredas, J. P. Calbert, D. A. d. S. Filho and J. Cornil, Proc.
Natl. Acad. Sci. U. S. A., 2002, 99, 5804–5809.
25 A. Troisi, Chem. Soc. Rev., 2011, 40, 2347–2358.
26 J. Bo¨hlin, M. Linares and S. Stafstrom, Phys. Rev. B, 2011,
83, 085209.
27 B. Baumeier, J. Kirkpatrick and D. Andrienko, Phys. Chem.
Chem. Phys., 2010, 12, 11103–11113.
28 J. Kirkpatrick, V. Marcon, K. Kremer, J. Nelson and
D. Andrienko, J. Chem. Phys., 2008, 129, 094506.
29 A. A. Kocherzhenko, F. C. Grozema, S. A. Vyrko,
N. A. Poklonski and L. D. A. Siebbeles, J. Phys. Chem. C,
2010, 114, 20424–20430.
30 A. Troisi, A. Nitzan and M. A. Ratner, J. Chem. Phys., 2003,
119, 5782–5788.
31 D. P. McMahon and A. Troisi, Phys. Chem. Chem. Phys.,
2011, 13, 10241–10248.
33 K. Navamani, G. Saranya, P. Kolandaivel and
K. Senthilkumar, Phys. Chem. Chem. Phys., 2013, 15,
17947–17961.
Proc. Natl. Acad. Sci. U. S. A., 2005, 102, 3552–3557.
35 A. Troisi and D. L. Cheung, J. Chem. Phys., 2009,
131, 014703.
36 A. Troisi and G. Orlandi, Phys. Rev. Lett., 2006, 96, 086601.
37 M. Jaiswal and R. Menon, Polym. Int., 2006, 55, 1371–1384.
38 V. Ruhle, A. Lukyanov, F. May, M. Schrader, T. Vehoﬀ,
J. Kirkpatrick, B. Baumeier and D. Andrienko, J. Chem.
Theory Comput., 2011, 7, 3335–3345.
39 L. Lin, H. Geng, Z. Shuai and Y. Luo, Org. Electron., 2012, 13,
2763–2772.
40 S. Mohakud, A. P. Alex and S. K. Pati, J. Phys. Chem. C, 2010,
114, 20436–20442.
41 L. Chen, S. R. Puniredd, Y. Z. Tan, M. Baumgarten,
U. Zschieschang, V. Engelmann, W. Pisula, X. Feng,
H. Klauk and K. Mullen, J. Am. Chem. Soc., 2012, 134,
17869–17872.
42 E. A. Silinsh, Organic Molecular Crystals, Springer Verlag,
Berlin, 1980.
43 M. D. Newton, Chem. Rev., 1991, 91, 767–792.
L. D. A. Siebbeles, J. Chem. Phys., 2003, 119, 9809–9817.
J. Comput. Chem., 2001, 22, 931–967.
46 A. D. Becke, Phys. Rev. A: At., Mol., Opt. Phys., 1988, 38,
3098–3100.
47 J. P. Perdew, Phys. Rev. B, 1986, 33, 8822–8824.
48 J. G. Snijders, P. Vernooijs and E. J. Baerends, At. Data Nucl.
Data Tables, 1981, 26, 483.
49 H. L. Tavernier and M. D. Fayer, J. Phys. Chem. B, 2000, 104,
11541–11550.
J. Am. Chem. Soc., 2004, 126, 984–985.
1200–1211.
53 C. T. Lee, W. T. Yang and R. G. Parr, Phys. Rev. B, 1988, 37,
785–789.
54 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria,
M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone,
B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato,
X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng,
J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda,
J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao,
H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta,
F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin,
V. N. Staroverov, R. Kobayashi, J. Normand,
K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar,
J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene,
J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo,
R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin,
R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin,
PCCP Paper

K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J.
Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B.
Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09,
Revision B.01, Gaussian, Inc., Wallingford CT, 2009.
55 L. B. Schein and A. R. McGhie, Phys. Rev. B, 1979, 20, 1631–1639.
56 Y. Roichman and N. Tessler, Appl. Phys. Lett., 2002, 80,
1948–1950.
57 G. A. H. Wetzelaer, L. J. A. Koster and P. W. M. Blom, Phys.
Rev. Lett., 2011, 107, 066605.
58 K. Navamani and K. Senthilkumar, J. Phys. Chem. C, 2014,
118, 27754–27762.
59 Z. G. Yu, D. L. Smith, A. Saxena, R. L. Martin and
A. R. Bishop, Phys. Rev. Lett., 2000, 84, 721–724.
60 A. Datta, S. Mohakud and S. K. Pati, J. Mater. Chem., 2007,
17, 1933–1938.
61 A. Datta, S. Mohakud and S. K. Pati, J. Chem. Phys., 2007,
126, 144710.
62 D. J. Griﬃths, Introduction to Quantum Mechanics, Pearson
Education, 2005, pp. 230–260.
63 S. Ando, R. Murakami, J. Nishida, H. Tada, Y. Inoue,
S. Tokito, S. Tokito and Y. Yamashita, J. Am. Chem. Soc.,
2005, 127, 14996.
64 S. Ando, J. Nishida, Y. Inoue, S. Tokito and Y. Yamashita,
J. Mater. Chem., 2004, 14, 1787.
65 S. Ando, J. Nishida, H. Tada, Y. Inoue, S. Tokito and
Y. Yamashita, J. Am. Chem. Soc., 2005, 127, 5336.
Paper PCCP

This article appeared in a journal published by Elsevier. The attached
copy is furnished to the author for internal non-commercial research
and education use, including for instruction at the authors institution
and sharing with colleagues.
Other uses, including reproduction and distribution, or selling or
licensing copies, or posting to personal, institutional or third party
websites are prohibited.
In most cases authors are permitted to post their version of the
article (e.g. in Word or Tex form) to their personal website or
institutional repository. Authors requiring further information
regarding Elsevier’s archiving and manuscript policies are
encouraged to visit:
http://www.elsevier.com/authorsrights

Author's personal copy
A theoretical study on optical and charge transport properties of
anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-b000
]tetrathiophene molecules
G. Saranya, K. Navamani, K. Senthilkumar ⇑
Department of Physics, Bharathiar University, Coimbatore 641 046, India
a r t i c l e i n f o
Article history:
Received 2 October 2013
In final form 29 January 2014
Available online 14 February 2014
Keywords:
Absorption and emission spectra
Charge transfer integral
Reorganization energy
Site energy
Charge carrier mobility
a b s t r a c t
The optical and charge transport properties of 1,2,4,5-tetrakis(5-methylthiophen-2yl)benzene (TMTB),
electron donating and withdrawing groups substituted anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-b000
]tetrathiophene
(ATT) molecules have been studied. The ground and excited states geometry was optimized using the
density functional theory (DFT) and time-dependent DFT methods. The absorption and emission spectra
were calculated at TD-B3LYP/6-311G(d,p) level of theory. It has been observed that the effect of solvent
and the substitution of functional groups on the calculated absorption and emission spectra of ATT mol-
ecules is negligible. The charge transfer integral, site energy and reorganization energy for hole and elec-
tron transport in ATT molecules have been calculated. Molecular dynamics simulations were performed
to find the most favorable conformation. The calculated charge transport properties show that the rate of
charge transfer strongly depends on p-stacking angle and the studied molecules can be used as an
organic semiconductor.
Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction
Over the past two decades, the science and engineering of
organic semiconducting materials have improved very rapidly,
leading to the demonstration and optimization of a range of organ-
ic-based solid-state devices, such as organic light-emitting diodes
(LEDs), field-effect transistors (FETs), photodiodes, and photovol-
taic cells [1–11]. Fundamental studies on the optical and electronic
properties of organic molecules such as acenes were first reported
in the 1960s [12]. Acenes have suitable electronic properties that
are desirable for opto-electronic applications [5,13]. Large acene
molecules such as pentacene are having significant charge carrier
mobility; however, they have a drawback of poor air-stability ow-
ing to their high-lying highest occupied molecular orbital (HOMO)
[14–16]. It has been shown in earlier studies that their stabilities
are fairly improved by introducing heteroatoms in the aromatic
ring [17–19]. The p-extended molecules such as oligoacenes, oli-
gothiophenes, and their derivatives are known to be suitable for
organic semiconductors. Recent studies show that thiophene based
molecules are novel class of organic semiconductors for the fabri-
cation of OFETs [19–23]. In thiophene-based materials, a variety of
inter- and intramolecular interactions such as van der Waals,
sulfur–sulfur interactions and p–p stacking interactions are exist-
ing, which are essential to achieve high charge carrier mobility
[24,25].
Liu et al. [26] synthesized anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-
b000
]tetrathiophene (ATT) through Negishi cross-coupling reaction
between 1,4-dibromo-2,5-diiodobenzene and 5-alkyl-2-thienyl-
zinc chloride. Initially 1,2,4,5-tetrakis(5-methylthiophen-2yl)ben-
zene (TMTB) was prepared in situ from the lithiation of
2-alkylthiophene with n-BuLi followed by the addition of anhy-
drous zinc chloride. Then FeCl3 oxidative cyclization protocol was
utilized to prepare the anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-b000
]tetrathi-
ophene (ATT) skeleton via thienyl–thienyl carbon–carbon bond
formation. Fused heteroarene unit, anthra-[1,2-b:4,3-b0
:5,6-
b00
:8,7-b000
]tetrathiophene serves as the basic skeleton of p-ex-
tended planar core which facilitates molecular self-association
through p–p stacking. Previous theoretical and experimental re-
sults [24–26] show that the charge carrier usually migrates along
the direction of p-electron delocalization. Anthra-[1,2-b:4,3-
b0
:5,6-b00
:8,7-b000
]tetrathiophene (ATT) molecule exhibit good ther-
mal and oxidative stability. Liu et al. [26] investigated the charge
transport and optical properties of ATT molecule and reported
the hole mobility of 0.012 cm2
VÀ1
sÀ1
. In addition to the p-type or-
ganic semiconductors, the study on n-type organic semiconductor
is essential for the fabrication of p–n junctions, bipolar transistors
and complementary circuits. Previous studies [27–30] show that
the n-type or ambipolar organic semiconductors can be obtained
either by introducing the electronegative atoms like fluorine,
http://dx.doi.org/10.1016/j.chemphys.2014.01.020
0301-0104/Ó 2014 Elsevier B.V. All rights reserved.
⇑ Corresponding author. Tel.: +91 04222428445; fax: +91 422 2422387.
E-mail address: ksenthil@buc.edu.in (K. Senthilkumar).
Chemical Physics 433 (2014) 48–59
Contents lists available at ScienceDirect
Chemical Physics
journal homepage: www.elsevier.com/locate/chemphys

chlorine, nitrogen and oxygen or by substituting electron with-
drawing groups (EWG) like CN, CF3 and NO2.
To understand the absorption, emission spectra and charge
transport properties of TMTB and ATT molecules, theoretical inves-
tigation on the structural and electronic properties of these mole-
cules is essential. In the present work, charge transport and optical
properties of TMTB and different electron donating groups (EDG)
such as CH3, C2H5, OCH3 and OH and electron withdrawing groups
(EWG) such as CCl3, CF3, CN and NO2 substituted ATT molecule
have been studied using density functional theory methods. The
chemical structure of the studied TMTB and ATT molecule was pre-
sented in Fig. 1. The present theoretical study will provide ioniza-
tion potential, electron affinity, hole extraction potential and
electron extraction potential along with the optical and charge
transport properties such as site energy, charge transfer integral
and reorganization energy of the studied molecules. To get the
information about stacking angle of ATT molecules, the molecular
dynamics (MD) simulations were performed. Monte-Carlo (MC)
simulations were used to calculate diffusion constant and charge
carrier mobility.
2. Theoretical methodology
The ground and excited states geometry optimization of the
1,2,4,5-tetrakis(5-methylthiophen-2yl)benzene (TMTB) and differ-
ent EDG and EWG substituted anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-
b000
]tetrathiophene (ATT) molecules has been performed using den-
sity functional theory (DFT) and time-dependent DFT with B3LYP
functional [31–33]. The optimized structure was characterized as
minima on the potential energy surface without imaginary fre-
quencies. With the optimized ground and excited states geometry,
the absorption and emission spectra of the studied molecules were
calculated using TD-B3LYP method. All DFT calculations were per-
formed with 6-311G(d,p) basis set.
The ground and excited states optimization and spectral
calculations were carried out in gas phase, tetrahydrofuran (THF),
n-hexane and dichloromethane mediums. Tomasi’s [34] polarized
continuum model (PCM) in self-consistent reaction field (SCRF)
theory is used to introduce the solvent effect on the structural
and optical spectra of the studied molecules. In the present study
the dielectric constant of 7.43, 1.88 and 8.93 is used to represent
the THF, n-hexane and dichloromethane, respectively. The ioniza-
tion potential ðIPÞ, electron affinity ðEAÞ, hole extraction potential
ðHEPÞ, electron extraction potential ðEEPÞ and reorganization en-
ergy ðkÆ
Þ are calculated using the following relations,
IPa ¼ Eþ
ðgþ
Þ À E0
ðg0
Þ
IPv ¼ Eþ
ðg0
Þ À E0
ðg0
Þ
EAa ¼ E0
ðg0
Þ À EÀ
ðgÀ
Þ
EAv ¼ E0
ðg0
Þ À EÀ
ðg0
Þ
HEP ¼ Eþ
ðgþ
Þ À E0
ðgþ
Þ
EEP ¼ E0
ðgÀ
Þ À EÀ
ðgÀ
Þ
ð1Þ
kÆ
¼ ½EÆ
ðg0
Þ À EÆ
ðgÆ
ÞŠ þ ½E0
ðgÆ
Þ À E0
ðg0
ÞŠ ð2Þ
where, E0
ðg0
Þ, EÆ
ðgÆ
Þ, EÆ
ðg0
Þ and E0
ðgÆ
Þ represents the energy of the
neutral molecule in neutral geometry, energy of the ion in ionic
geometry, energy of the ion in neutral geometry and energy of
the neutral molecule in ionic geometry, respectively. Here, the sub-
script a and v represents the adiabatic and vertical IP and EA and kþ
and kÀ
represents the reorganization energy for hole and electron
transport. All the electronic structure calculations were performed
using Gaussian 09 program [35]. The rate of charge transport
(KCT ) is calculated by using Marcus equation [36–38],
KCT ¼
J2
eff
h
ffiffiffiffiffiffiffiffiffiffiffi
p
kKBT
r
e
Àð k
4KBT
Þ
ð3Þ
where h is the Planck’s constant, kB is the Boltzmann’s constant and
Jeff is the generalized or effective charge transfer integral. The effec-
tive charge transfer integral is expressed in terms of charge transfer
integral (J), spatial overlap integral (S) and site energy (e) as [39,40],
Jeff ¼ Jij À
Sðei þ ejÞ
2
ð4Þ
Here, ei and ej are the energy of a charge when it is localized at ith
and jth molecules, respectively, called as site energy and Jij repre-
sents the electronic coupling between HOMO (or LUMO) of nearby
molecules i and j, which measures the strength of the overlap be-
tween orbitals of nearby molecules. Both site energy and electronic
coupling depend on inter- and intramolecular degrees of freedom.
As described in the previous studies [40], the site energy ðeÞ,
h/ijHKSj/ii and charge transfer integral (J), h/ijHKSj/ji are directly
calculated as the diagonal and off-diagonal matrix elements of
Kohn–Sham Hamiltonian, HKS as HKS = SCECÀ1
. Here the overlap
matrix (S), the eigenvector matrix (C), and the eigenvalue (E) are
calculated through fragment molecular orbital (FMO) approach as
implemented in the Amsterdam density functional (ADF) theory
program [41]. In this approach, the molecular orbitals of a stacked
dimer are expressed as a linear combination of the molecular orbi-
tals of the individual monomers.
The optimized ground state monomer geometry was used to
construct the stacked dimer with various stacking angles. Here,
the stacking angle is defined as the mutual angle between two
stacked molecules, where the center of mass is the center of rota-
tion. As reported in the previous study [42], the distance between
the stacked molecules was fixed as 3.5 Å. In ADF, single point en-
ergy calculation for each monomer has been performed with the
atomic basis set of Slater-type orbitals (STOs) of triple-zeta quality
including one set of polarization function (TZP) [43]. The above cal-
culations were performed using the generalized gradient approxi-
mation (GGA). This proceeds from the local density approximation
S S
SS
R
R R
R
TMTB
S
S
S
S
R
R R
R
ATT1=R=CH3
ATT2=R=C2H5
ATT3=R=OCH3
ATT4=R=OH
ATT5=R=CF3
ATT6=R=NO2
ATT7=R=CN
ATT8=R=CCl3
ATT
Fig. 1. Chemical structure of 1,2,4,5-tetrakis(5-methylthiophen-2yl)benzene
(TMTB) and anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-b000
]tetrathiophene (ATT) molecules.
G. Saranya et al. / Chemical Physics 433 (2014) 48–59 49

(LDA) for the exchange and correlation function based on the
parameterization of the electron gas data given by Vosko–Wilk–
Nusair (VWN) [33]. The gradient correction proposed by Becke
[44] for exchange is used with the correlation functional of Perdew
[45]. It has been shown in earlier studies that the charge transfer
integrals and site energies calculated through this procedure is
comparable with the other methods and are independent of ex-
change correlation functional used [25,40].
To get the quantitative insight on charge transport in these mol-
ecules, the information about stacking angle and fluctuations in
stacking angle are required. Therefore, to get this information the
molecular dynamics simulation for stacked dimer was performed
using TINKER program [46,47] with standard molecular mechanics
force field, MM3 [48,49]. It has been shown in earlier studies
[48,50] that the MM3 force field parameters adequately describe
the crystals of the normal alkanes and aromatics, including graph-
ite, benzene, and hexa-methylbenzene. The MM3 force field also
works very well for inter- and intra-molecular interactions. The
simulations were performed with time step of 1 fs and the atomic
coordinates in trajectories were saved in the interval of 0.1 ps. The
simulations were done up to 10 ns.
The charge carrier mobility was calculated numerically by per-
forming the Monte-Carlo (MC) simulations in which charge is
propagated with respect to rate of charge transport calculated from
Marcus equation [51,52]. In this model, the charge transport takes
place along the sequence of the stacked molecules and the charge
does not reach the last molecule within the time scale of simula-
tion. For normal Gaussian diffusion, the diffusion constant (D) is
calculated from mean square displacement, hX2
ðtÞi, which in-
creases linearly with time (t),
D ¼ lim
t!1
hX2
ðtÞi
2t
ð5Þ
The charge carrier mobility is calculated from diffusion constant, D,
by the Einstein relation [53,54],
l ¼
e
kBT

D ð6Þ
The ground state geometry of 1,2,4,5-tetrakis(5-methylthio-
phen-2yl)benzene (TMTB) and different EDG and EWG substituted
anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-b000
]tetrathiophene (ATT) molecules
has been optimized at B3LYP/6-311G(d,p) level of theory in gas
phase is shown in Figs. S1 and S2. The calculated bond length
and bond angle of TMTB, ATT1, ATT3 and ATT6 molecules in gas
phase are summarized in Tables S1 and S2 in the Supporting infor-
mation. The structural parameters of excited state geometry of
TMTB, ATT1, ATT3 and ATT6 molecules calculated at TD-B3LYP/6-
311G(d,p) level of theory in gas phase are also summarized in
Tables S1 and S2. By analyzing the ground and excited states geom-
etry of the studied molecules, the maximum difference of 0.05 Å
has been observed for R7(C5–C18) bond length of TMTB molecule.
Notably, in EDG and EWG substituted ATT molecules there is no
significant difference in structural parameters of ground and ex-
cited states geometry.
3.1. Absorption properties of TMTB and ATT molecules
The absorption spectra of TMTB and different EDG and EWG
substituted ATT molecules have been studied using TD-DFT at
B3LYP/6-311G(d,p) level of theory in gas phase, n-hexane, THF
and dichloromethane mediums. The calculated absorption spectra,
oscillator strength and corresponding orbital transitions are sum-
marized in Table 1. To study the nature and the energy of the sin-
glet–singlet electronic transition and to compare with the available
experimental values, the first four low lying electronic transitions
have been calculated. It has been observed that the absorption
spectra of TMTB and EDG and EWG substituted ATT molecules cal-
culated in gas phase, n-hexane, THF and dichloromethane medi-
ums are similar. A recent study on opto-electronic properties of
thieno[3,4-b]pyrazine analogues and benzosiloles [23,55] show
that the effect of solvent medium on the absorption maxima is
within 10 nm only. Further, the orbital transitions corresponding
to dominant absorption bands are similar in all mediums (see
Table 1). That is, the effect of solvent medium on the absorption
spectra is negligible, which is in agreement with the previous
experimental results [26]. The introduction of solvent medium sig-
nificantly increases the oscillator strength value with respect to gas
phase. Previously, Bertolino et al. [56] studied the effect of solvent
on indocyanine dyes using quantum chemical calculations and re-
ported that the solvent medium increases the oscillator strength of
the spectra. Qu et al. [57] used the polarized continuum model
(PCM) to account the solvent effect on the electronic transitions
of Pheophorbide a and Chlorophyllide a and concluded that the sol-
vent increases the oscillator strength of Q and B bands. Recently,
Moaienla et al. [58] show that the oscillator strength of the absorp-
tion spectra of Glycine and l-alanine is found to increase in aceto-
nitrile, CH3CN and dimethylformamide, DMF. In the solvent
medium, solute–solvent interaction enhances the oscillator
strength of the optical spectra. Here, the results obtained in THF
medium are discussed in detail.
The lowest energy transition for TMTB and different EDG and
EWG substituted ATT molecules is due to the excitation of electron
from highest occupied molecular orbital to the lowest unoccupied
molecular orbital, that is HOMO (H) ? LUMO (L) transition. For the
studied molecules, the absorption energies calculated at TD-
B3LYP/6-311G(d,p) level of theory in THF medium are plotted with
respect to integrated amplitude and is shown in Figs. 2 and 3. The
absorption maximum (kmax) of TMTB was observed at 3.41 eV
(363 nm), which is associated with H ? L transition. Additionally,
two intense bands are observed at 3.96 and 4.34 eV and are corre-
sponding to H-2 ? L and H-1 ? L + 1 transitions, respectively. In
comparison with TMTB, the kmax of ATT1 was red-shifted about
53 nm. It has been observed that CH3 and C2H5 substituted ATT
molecules, ATT1 and ATT2 exhibit similar absorption properties
due to their identical core structure. These results show that the ef-
fect of side chains on the absorption spectra is negligible, which is
in agreement with the experimental results of Liu et al. [26]. Hence,
further discussions are based on ATT1 molecule. The absorption
maximum (kmax) of ATT1 molecule was observed at 2.88 eV
(430 nm), which is associated with H ? L transition. The calculated
absorption maxima (kmax), 430 nm of ATT1 molecule is in agree-
ment with the experimental value, 431 nm of Liu et al. [26] Fur-
ther, the absorption spectrum of ATT1 molecule has two more
bands and the dominant absorption band is observed at 3.62 eV,
which is associated with H ? L + 1 transition.
As shown in Fig. 2, the absorption maxima of OCH3 and OH
substituted ATT molecules, ATT3 and ATT4 exhibit a red-shift of
about 18 nm compared with the kmax of ATT1. The absorption spec-
trum of ATT3 exhibits two intense bands, the dominant absorption
band observed at 3.67 eV is associated with H ? L + 1 transition,
and the second band observed at 3.87 eV is due to H-1 ? L + 1
transition. The absorption spectrum of OH substituted ATT mole-
cule exhibits two bands, which are observed at 3.71 and 3.93 eV,
due to the electronic transitions, H ? L + 1 and H-1 ? L + 1,
respectively.
For CF3 and NO2 substituted ATT molecules, ATT5 and ATT6, the
absorption maxima (kmax) was found at 2.79 (444 nm) and 2.61 eV
(475 nm), respectively, which is associated with H ? L transition.
50 G. Saranya et al. / Chemical Physics 433 (2014) 48–59

In comparison with the ATT1 molecule, the kmax of ATT5 and ATT6
was red-shifted about 14 and 45 nm, respectively. As shown in
Fig. 3, the absorption spectrum of ATT5 exhibits two major bands
and the dominant absorption band is observed at 3.40 eV, which
is associated with H ? L + 1 transition. The second band is
observed at 3.67 eV and is associated with H-1 ? L + 1 transition.
The absorption spectrum of ATT6 exhibits single band at 2.98 eV,
which corresponds to H ? L + 1 transition. In comparison with
ATT1, the kmax of ATT7 and ATT8 exhibit a red-shift within 6 nm
only, that is the substitution of CN and CCl3 does not affect the
kmax. The cyano substituted ATT molecule (ATT7) exhibits two
bands at 3.26 and 3.45 eV, which are associated with the
Table 1
Computed absorption energies (k in nm and in eV) and oscillator strengths (f in a.u) of TMTB, EDG and EWG substituted ATT molecules at TD-B3LYP/6-311G(d,p) method in gas
phase, tetrahydrofuran (THF), n-hexane and dichloromethane mediums.a
System Gas THF n-Hexane Dichloromethane Transition
k (nm) k (eV) f k (nm) k (eV) f k (nm) k (eV) f k (nm) k (eV) f
TMTB 357
306
285
3.47
4.05
4.36
0.29
0.80
0.01
363
313
286
3.41
3.96
4.34
0.36
0.89
0.03
362
312
285
3.42
3.98
4.35
0.35
0.83
0.03
363
314
286
3.41
3.95
4.34
0.36
0.89
0.03
H ? L
H-2 ? L
H-1 ? L + 1
ATT1 426
407
332
301
2.91
3.04
3.73
4.12
0.01
0.09
1.37
0.29
430
413
342
315
2.88
3.01
3.62
3.93
0.23
0.19
1.55
0.35
429
410
342
315
2.89
3.02
3.62
3.94
0.21
0.17
1.55
0.37
431
413
342
316
2.88
3.00
3.62
3.93
0.23
0.19
1.56
0.35
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT2 426
407
334
302
2.91
3.05
3.71
4.11
0.01
0.10
1.45
0.28
431
412
343
316
2.88
3.01
3.61
3.93
0.23
0.19
1.56
0.38
429
413
344
317
2.89
3.01
3.60
3.91
0.22
0.20
1.60
0.40
428
410
344
316
2.90
3.02
3.61
3.92
0.23
0.17
1.60
0.41
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT3 442
429
329
315
2.81
2.89
3.77
3.94
0.01
0.21
1.19
0.25
448
440
338
320
2.77
2.82
3.67
3.87
0.37
0.34
0.95
0.39
445
436
335
318
2.78
2.84
3.70
3.89
0.35
0.33
0.28
0.39
448
440
338
320
2.77
2.82
3.67
3.87
0.37
0.34
0.93
0.40
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT4 444
429
323
311
2.79
2.89
3.83
3.99
0.02
0.20
1.25
0.18
449
437
335
315
2.76
2.84
3.71
3.93
0.25
0.32
1.43
0.31
447
435
333
314
2.77
2.85
3.72
3.95
0.22
0.31
1.41
0.31
449
437
335
315
2.76
2.84
3.70
3.93
0.25
0.32
1.43
0.31
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT5 437
421
363
334
2.84
2.94
3.42
3.71
0.01
0.02
1.34
0.23
444
429
365
338
2.79
2.89
3.40
3.67
0.28
0.02
1.58
0.39
444
427
362
337
2.79
2.90
3.42
3.68
0.26
0.03
1.56
0.37
444
429
365
338
2.79
2.89
3.40
3.67
0.28
0.02
1.59
0.39
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT6 462
455
400
397
2.68
2.73
3.10
3.13
0.08
0.03
1.11
0.26
475
464
419
414
2.61
2.67
2.96
2.99
0.27
0.05
1.14
0.38
474
463
418
410
2.62
2.68
2.97
3.03
0.20
0.04
1.20
0.37
475
464
420
415
2.61
2.67
2.95
2.99
0.28
0.05
1.13
0.39
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT7 430
426
365
352
2.88
2.90
3.40
3.52
0.01
0.003
1.54
0.34
433
428
381
360
2.86
2.89
3.26
3.45
0.21
0.01
1.79
0.50
433
427
379
357
2.86
2.90
3.27
3.47
0.20
0.003
1.79
0.49
433
428
381
360
2.86
2.90
3.25
3.44
0.21
0.01
1.80
0.51
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
ATT8 434
420
368
345
2.86
2.95
3.37
3.59
0.01
0.01
1.52
0.39
436
423
383
354
2.84
2.93
3.24
3.52
0.24
0.02
1.72
0.57
436
422
380
350
2.84
2.94
3.26
3.54
0.24
0.01
1.73
0.55
436
423
383
352
2.84
2.93
3.24
3.52
0.24
0.02
1.73
0.57
H ? L
H-1 ? L
H ? L + 1
H-1 ? L + 1
a
The transitions with oscillator strength higher than 0.01 a.u. are given.
Fig. 2. The absorption spectra of TMTB and EDG substituted ATT molecules computed at TD-B3LYP/6-311G(d,p) level of theory in THF medium. (The spectra were simulated
by using a Gaussian distribution centered at the computed absorption energies with an arbitrary width of 0.05 eV and an integrated amplitude equal to the calculated
oscillator strength).

H ? L + 1, H-1 ? L + 1 transitions, respectively. The absorption
spectrum of ATT8 exhibits two major bands and the dominant
absorption band is observed at 3.24 eV, which is associated with
H ? L + 1 transition. The next dominant band is observed at
3.52 eV due to H-1 ? L + 1 transition. The above results show that
the substitution of EDG and EWG on ATT molecule increases the
absorption wavelength. The maximum red-shift of 45 nm was ob-
served for EWG, NO2 substituted ATT molecule, ATT6.
3.2. Emission properties of TMTB and ATT molecules
The calculated emission wavelength and corresponding oscilla-
tor strength for TMTB and different EDG and EWG substituted ATT
molecules in gas phase, THF, n-hexane and dichloromethane medi-
ums are summarized in Table 2. As observed in absorption spectra,
the effect of solvent on the emission spectra is negligible, which is
in agreement with the experimental results [26], and the introduc-
tion of solvent medium significantly affects the oscillator strength
value. Here, the emission spectra calculated at TD-B3LYP/6-
311G(d,p) level of theory in THF medium is discussed.
From Table 2, it has been observed that the emission maximum
(kemis) of TMTB was observed at 2.68 eV (464 nm). The calculated
kemis of ATT1 and ATT2 molecules is 483 nm, which is in agreement
with the experimental value of 475 nm [26]. For the studied mol-
ecules, the emission energy calculated at TD-B3LYP/6-311G(d,p)
level of theory in THF medium is plotted with respect to integrated
amplitude and is shown in Figs. 4 and 5. The emission spectrum
(kemis) of ATT1 and ATT2 is red-shifted about 20 nm compared with
the kemis of TMTB molecule. In comparison with the kemis of ATT1,
the kemis of ATT3 and ATT4 was red-shifted about 20 and 25 nm,
respectively, due to the substitution of OCH3 and OH. The kmax of
ATT5, ATT7 and ATT8 exhibit a red-shift within 5 nm only com-
pared with the kemis of ATT1 molecule. The effect of substitution
of CF3, CN and CCl3 on the emission spectra is negligible, whereas
NO2 substituted ATT molecule (ATT6) exhibit a red-shift of 52 nm.
This is because, EWG, NO2 substitution significantly alters the
LUMO and the HOMO–LUMO energy gap of ATT molecule.
3.3. Molecular orbital energies
Energies of frontier molecular orbitals HOMO and LUMO as well
as their spatial distributions are crucial parameters for determin-
ing the opto-electronic and charge transport properties. The den-
sity plot of the HOMO and LUMO of TMTB, different EDG and
EWG substituted ATT molecules are calculated in tetrahydrofuran
medium at B3LYP/6-311G(d,p) level of theory and are shown in
Figs. 6 and 7. The orbital diagrams are plotted with the contour va-
lue of 0.025 a.u. The plot of the HOMO and LUMO of the studied
molecules has typical p-orbital characteristics and the lowest lying
singlet–singlet absorption as well as emission are corresponding to
the electronic transition between p and p⁄
orbital. Figs. 6 and 7
illustrate that for the studied molecules the HOMO and LUMO
are delocalized over the core region of the molecule. Notably, as
shown in Fig. 7, NO2 substitution on ATT molecule (ATT6) signifi-
cantly alters the delocalization of electron density on LUMO.
Fig. 3. The absorption spectra of ATT1 and EWG substituted ATT molecules computed at TD-B3LYP/6-311G(d,p) level of theory in THF medium. (The spectra were simulated
by using a Gaussian distribution centered at the computed absorption energies with an arbitrary width of 0.05 eV and an integrated amplitude equal to the calculated
oscillator strength).
Table 2
Computed emission energies (k in nm and in eV) and oscillator strengths (f in a.u) of TMTB, EDG and EWG substituted ATT molecules at TD-B3LYP/6-311G(d,p) method in gas
phase, tetrahydrofuran (THF), n-hexane and dichloromethane mediums.
System Gas THF n-Hexane Dichloromethane
k (nm) k (eV) f k (nm) k (eV) f k (nm) k (eV) f k (nm) k (eV) f
TMTB 457 2.71 0.08 464 2.68 0.17 463 2.68 0.15 464 2.68 0.17
ATT1 475 2.61 0.04 483 2.57 0.11 482 2.57 0.12 483 2.57 0.11
ATT2 475 2.61 0.03 483 2.57 0.12 480 2.59 0.11 483 2.57 0.11
ATT3 501 2.47 0.07 503 2.46 0.12 503 2.46 0.09 503 2.46 0.13
ATT4 503 2.47 0.05 508 2.44 0.10 508 2.44 0.09 508 2.44 0.10
ATT5 483 2.57 0.11 486 2.55 0.18 486 2.55 0.16 486 2.55 0.18
ATT6 520 2.38 0.21 532 2.33 0.25 526 2.36 0.23 532 2.33 0.25
ATT7 479 2.59 0.12 485 2.56 0.17 485 2.56 0.16 485 2.56 0.17
ATT8 482 2.57 0.12 488 2.54 0.18 488 2.54 0.17 488 2.54 0.18

The energies of HOMO (EH), LUMO (EL) and the energy gap (EH–L)
for ground state TMTB, EDG and EWG substituted ATT molecules
calculated at B3LYP/6-311G(d,p) level of theory in gas phase and
in THF medium are summarized in Table 3. From Table 3, it has
been observed that the effect of solvent medium on the energy
gap (EH–L) is negligible. The calculated EH, EL and EH–L for ATT1 is
À5.20, À2.05 and À3.15 eV, respectively, and are in agreement
with the experimental value [26] of À5.57, À2.64 and À2.93 eV,
respectively. The substitution of C2H5 instead of CH3 does not
change the EH, EL and EH–L values. In comparison with TMTB, the
ATT molecules have lower EH–L due to the presence of thienyl–thi-
enyl carbon–carbon bond in the ATT molecules. The molecules
with small HOMO–LUMO energy gap (EH–L) possess larger absorp-
tion and emission wavelength. The EDG substituted ATT molecules,
ATT3 and ATT4 have EH–L around À3.07 eV and their absorption
and emission energies are about 2.77 and 2.45 eV, respectively.
Similarly, among the EWG substituted ATT molecules, ATT6 has
lower EH–L of À2.81 eV and a maximum absorption and emission
wavelength of 2.61 and 2.33 eV, respectively. The substitution of
EDG and EWG reduces the EH–L by 0.1–0.3 eV, particularly, the
EWG, NO2 substitution reduces the EH–L by 0.34 eV with respect
to ATT1. The above results show that the substitution of EDG and
EWG alters the spatial charge distribution and energy of the fron-
tier molecular orbitals and thereby the spectral properties of stud-
ied molecules.
3.4. Charge transfer properties
3.4.1. Ionization potential and electron affinity
The efficient injection of holes and electrons into organic mole-
cule is important for the better performance of opto-electronic de-
vices. The molecular ionization potential (IP) and electron affinity
(EA) are important key parameters pertaining to charge injection.
Ionization potential (IP) is defined as the energy needed by the sys-
tem when an electron is removed. IP must be low enough to allow
an efficient hole injection into the HOMO of the molecule. Hence,
we have studied the ionization potential (IP), electron affinity
(EA), hole extraction potential ðHEPÞ and electron extraction poten-
tial ðEEPÞ for TMTB, EDG and EWG substituted ATT molecules.
These parameters are calculated by using the eqn. 1 and the results
are summarized in Table 3. It has been observed that ATT mole-
cules, ATT1 and ATT2 have similar IP, EA and extraction potentials.
The above results show that like spectral properties the substitu-
tion of CH3 or C2H5 does not affect the ionic properties. ATT1 has
ionization potential value of 6.38 and 6.32 eV for vertical and adi-
abatic excitations, respectively, suggesting that it is easy to create a
hole in this molecule than TMTB molecule, which has IPv and IPa
values of 6.58 and 6.37 eV. The substitution of EDG reduces the
IP, particularly, OCH3 substituted ATT molecule (ATT3) has IP of
6.08 and 5.97 eV for vertical and adiabatic excitations, respectively.
Table 3 show that the EWG substitution on ATT molecule increase
Fig. 4. The emission spectra of TMTB and EDG substituted ATT molecules computed at TD-B3LYP/6-311G(d,p) level of theory in THF medium. (The spectra were simulated by
using a Gaussian distribution centered at the computed absorption energies with an arbitrary width of 0.05 eV and an integrated amplitude equal to the calculated oscillator
strength).
Fig. 5. The emission spectra of ATT1 and EWG substituted ATT molecules computed at TD-B3LYP/6-311G(d,p) level of theory in THF medium. (The spectra were simulated by
using a Gaussian distribution centered at the computed absorption energies with an arbitrary width of 0.05 eV and an integrated amplitude equal to the calculated oscillator
strength).

the IP. Notably, NO2 substituted ATT molecule, ATT6 has maximum
IP of 8.18 and 8.09 eV for vertical and adiabatic excitations, respec-
tively. Electron affinity (EA) is defined as the energy released by the
system when an electron is added. EA must be high enough to al-
low an efficient electron injection into the LUMO of the molecule.
From the Table 3, it has been observed that ATT1 has electron affin-
ity of 0.68 and 0.75 eV for vertical and adiabatic excitations,
respectively. Whereas, TMTB has electron affinity of 0.33 and
0.55 eV for vertical and adiabatic excitations, respectively. In the
EDG substituted ATT molecules, ATT4 has maximum electron affin-
ity of 0.69 and 0.80 eV for vertical and adiabatic excitations,
respectively. Among the EWG substituted ATT molecules, NO2
substituted ATT molecule (ATT6) has maximum electron affinity
of 2.81 and 2.89 eV for vertical and adiabatic excitations, respec-
tively. As observed for IP, ATT3 has minimum HEP of 5.86 eV. These
results show that among the studied molecules, the injection of
hole into ATT3 is easier than in other molecules. The extraction
of electron from the ATT1 and TMTB molecules requires 0.82 and
TMTB
ATT1 ATT2
ATT3 ATT4
ATT5 ATT6
ATT7 ATT8
Fig. 6. The density plot of highest occupied molecular orbital (HOMO) of TMTB, EDG and EWG substituted ATT molecules calculated at B3LYP/6-311G(d,p) level of theory in
THF medium.

0.74 eV, respectively. The EDG and EWG substitutions on ATT mol-
ecules significantly increase the EEP. Among the studied molecules,
ATT6 has maximum EEP of 2.97 eV. The above results show that
the substitution of EDG and EWG significantly affect the elec-
tron-accepting, donating and -transporting properties of ATT
molecules.
3.4.2. Reorganization energy
The charge transfer in organic molecules strongly depends on
the reorganization energy ðkÞ, which is the measure of change in
energy of the molecule upon the relaxation of the molecular struc-
ture due to the presence of excess positive or negative charge. For
efficient charge transfer, the reorganization energy ðkÞ should be
small. In this study, we have calculated the reorganization energy
of TMTB, EDG and EWG substituted ATT molecules for the presence
of excess positive and negative charge by using Eq. (2)and the re-
sults are summarized in Table 3. Table 3 shows that the studied
molecules have higher reorganization energy value for the pres-
ence of excess negative charge than the positive charge. By analyz-
ing the optimized geometries of studied molecules, it has been
TMTB
ATT1 ATT2
ATT3 ATT4
ATT5 ATT6
ATT7 ATT8
Fig. 7. The density plot of lowest unoccupied molecular orbital (LUMO) of TMTB, EDG and EWG substituted ATT molecules calculated at B3LYP/6-311G(d,p) level of theory in
THF medium.

observed that presence of excess negative charge alters the bond
lengths and bond angles significantly than the positive charge.
ATT1 and ATT2 have similar reorganization energy of 0.12 and
0.13 eV for the presence of excess positive charge (kþ
) and negative
charge (kÀ
), respectively, and kþ
and kÀ
for TMTB is 0.39 and
0.41 eV. By analyzing the optimized geometries of TMTB, it has
been observed that in TMTB molecule, the presence of excess
charge alters the bond lengths up to 0.04 Å and there is no signif-
icant change in bond length and bond angles in ATT1 or ATT2 mol-
ecules due to the presence of excess charge. The substitution of
EDG and EWG on ATT molecule significantly increases the reorga-
nization energy for the presence of excess positive and negative
charges. By analyzing the optimized geometry of the neutral and
ionic states of the studied ATT molecules, it has been observed that
the presence of excess positive and negative charges significantly
alters the bond lengths and bond angles in the substituted ATT
molecules. Among the substituted ATT molecules, the maximum
difference of 0.024 Å was observed for R3(C3–C4) and R4(C4–C5)
bond lengths due to the presence of excess positive charge and
0.026 Å was observed for R8(C1–O1) bond length due to the pres-
ence of excess negative charge in ATT3 molecule. Hence, the mol-
ecule ATT3 has maximum reorganization value of 0.22 and 0.35 eV
for the presence of excess positive and negative charges,
respectively.
3.4.3. Site energy
Experimentally, Liu et al. [26] reported that anthra-[1,2-b:4,3-
b0
:5,6-b00
:8,7-b000
]tetrathiophene (ATT) exhibit p-stacking property.
Hence, along with optical properties we have studied the charge
transfer properties of ATT1, ATT3, ATT6 and ATT7 molecules. We
have chosen these molecules based on the calculated reorganiza-
tion energy values. Among the substituted ATT molecules, CH3,
NO2 and CN substituted ATT molecules, ATT5, ATT6 and ATT7 have
minimum reorganization energy value, which favors the charge
transport. For comparison we have studied the charge transport
property of OCH3 substituted ATT molecule, ATT3, which has max-
imum reorganization energy value. As a reasonable approximation,
the positive charge will migrate through the HOMO, and the nega-
tive charge will migrate through the LUMO of the stacked mole-
cules, the charge transfer integrals, spatial overlap integrals and
site energies corresponding to HOMO and LUMO were calculated
for various stacking angles. The optimized geometry of ATT mole-
cules was used to construct a dimer with stacking angle in the
range of 0–90°, increased in steps of 15°. The stacking distance
was kept as 3.5 Å. The site energy for ATT1, ATT3, ATT6 and ATT7
molecules corresponding to hole and electron transport is calcu-
lated as the diagonal matrix elements of the Kohn–Sham Hamilto-
nian and are summarized in Table S3. Here, e1 and e2 represent the
site energy of the stacked molecules 1 and 2, respectively. From the
tabulated values, it has been observed that the e1 and e2 are simi-
lar, that is, the energy barrier in the form of site energy difference
for charge transport in these molecules is very small. Further, we
have calculated the site energy values for stacked trimer to know
the effect of nearby molecules on the site energy. It has been ob-
served that site energy values for ATT molecules in trimer are sim-
ilar to that of molecules in p-stacked dimer. This result is in
agreement with the previous study on charge transport in colum-
nar stacked triphenylenes [40]. The above results show that the
symmetrical structure of the studied molecules is responsible for
small site energy difference between the nearby molecules even
at larger stacking angles and favors charge transport.
3.4.4. Effective charge transfer integral
The effective charge transfer integral for hole and electron
transport in ATT1, ATT3, ATT6 and ATT7 are calculated using eqn.
4 and are summarized in Table 4. It has been observed that for
the studied molecules, the effective charge transfer integral (Jeff)
for hole and electron transport is maximum at 0° of stacking angle.
At 0° of stacking angle, the HOMO of stacked dimer consists of 50%
of HOMO of each monomer. Similarly, the LUMO of stacked dimer
at 0° of stacking angle consists of LUMO of each monomer with
equal contribution of 50%. For hole transport, among the studied
molecules, ATT1 has maximum Jeff value of 0.31 eV at 0° of stacking
angle. The increase in stacking angle from 0° to 30° leads to a de-
crease in Jeff value for all the studied molecules. This is due to an
unequal contribution of HOMO of each monomer on the HOMO
of the dimer. For instance, at 30° of stacking angle, the HOMO of
ATT3 dimer consists of HOMO of first monomer by 38% and the
contribution of second monomer HOMO by 27%. Further increase
in stacking angle slightly increases the Jeff value. Notably, at the
stacking angle of 60°, the calculated Jeff value for ATT3 is 0.08 eV.
At 60° of stacking angle, the HOMO of ATT3 dimer consist of the
first monomer HOMO by 39% and the second monomer HOMO
by 33%.
For electron transport in ATT1, the calculated Jeff value at 0° of
stacking angle is 0.37 eV. While increasing the stacking angle from
0° to 75°, the calculated Jeff value for electron transport is decreased
for all the studied molecules. Interestingly, at 90° of stacking angle,
all the studied molecules have significant Jeff value for electron
transport. Particularly, the Jeff value of ATT3 is 0.15 eV. Because,
at the stacking angle of 90°, the LUMO of ATT3 dimer consists of
LUMO of each monomer by 49%. From the Table 4, it has been ob-
served that ATT molecules have significant Jeff value for electron
transport even at larger stacking angle. These results confirm the
earlier results [25,51,59,4] that the effective charge transfer inte-
gral corresponding to hole and electron transport strongly depends
on the stacking angle in p-stacked organic molecules. The calcu-
lated effective charge transfer integral (Jeff) value for hole and elec-
tron transport show that the core region of the stacked molecules
Table 3
Calculated ground state HOMO and LUMO energies (EH, EL in eV) and energy gap (EH–L in eV) in gas phase and THF medium, ionization potential (IP), electron affinity (EA),
extraction potentials (HEP,EEP) and reorganization energies, k+
, kÀ
(eV) of TMTB, EDG and EWG substituted ATT molecules in gas phase at B3LYP/6-311G(d,p) level of theory.
System Gas (eV) THF (eV) IP (eV) EA (eV) HEP (eV) EEP (eV) k+
(eV) kÀ
(eV)
EH EL EH–L EH EL EH–L Vertical Adiabatic Vertical Adiabatic
TMTB À5.43 À1.90 À3.53 À5.53 À2.02 À3.51 6.58 6.37 0.33 0.55 6.26 0.74 0.39 0.41
ATT1 À5.21 À2.06 À3.15 À5.31 À2.17 À3.14 6.38 6.32 0.68 0.75 6.19 0.82 0.12 0.13
ATT2 À5.18 À2.04 À3.14 À5.28 À2.14 À3.14 6.35 6.31 0.68 0.75 6.19 0.82 0.12 0.13
ATT3 À5.19 À2.10 À3.09 À5.22 À2.15 À3.07 6.08 5.97 0.52 0.73 5.86 0.88 0.22 0.35
ATT4 À5.13 À2.06 À3.07 À5.23 À2.17 À3.06 6.33 6.24 0.69 0.80 6.15 0.90 0.18 0.21
ATT5 À6.32 À3.37 À2.95 À6.42 À3.46 À2.96 7.64 7.64 1.82 1.93 7.44 2.03 0.20 0.21
ATT6 À6.74 À3.90 À2.84 À6.84 À4.03 À2.81 8.18 8.09 2.81 2.89 8.01 2.97 0.17 0.18
ATT7 À6.63 À3.67 À2.96 À6.73 À3.79 À2.94 7.90 7.85 2.35 2.40 8.79 2.46 0.14 0.15
ATT8 À6.20 À3.29 À2.91 À6.30 À3.39 À2.91 7.45 7.36 2.04 2.16 7.26 2.29 0.19 0.25

is purely responsible for Jeff than the substitution of functional
group.
Previous studies [25,51,59] and present results show that the
structural fluctuations in the form of change in p-stacking angle
significantly affect the charge transport property of the organic
molecules. The study on charge transport in columnar stacked tri-
phenylenes shows that the large lateral displacement leads to de-
crease in charge transfer integral [25]. Hence, to study the charge
transport properties of ATT molecules, the knowledge of stacking
angle and its fluctuation is required. Therefore, the molecular
dynamics (MD) simulations were performed for the stacked dimer
to get the information about stacking angle. In molecular dynamics
simulations the side chains are included as reported in Ref. [26].
During the simulation, the distance between the two molecules
was fixed as 3.5 Å. The MD simulations were performed for ATT1,
ATT3, ATT6 and ATT7 with various initial stacking angle values.
The simulations were performed up to 10 ns. The angle between
the stacked molecules in all the saved 1,00,000 frames has been
calculated and the total number of occurrence of each stacking an-
gle and the potential energy of corresponding frame are analyzed.
The result from MD calculations for ATT1 molecule is shown in
Fig. 8. It has been observed that the most favorable conformation
occurs at the stacking angle of 47° for ATT1 molecule. The calcu-
lated potential energy is minimum at this angle. The angle distri-
bution given in Fig. 8 shows that the stacking angle fluctuation
up to ±20° from the equilibrium value is expected for this mole-
cule. The similar results have been observed for ATT3, ATT6 and
ATT7 molecules. The MD results obtained with different initial
stacking angle values gave similar results. From the potential
energy curve, the force constant corresponding to stacking angle
fluctuation was calculated based on Hooke’s law. The calculated
equilibrium stacking angle and force constant values are used to
model stacking angle fluctuations during the Monte-Carlo
simulation for hole and electron transport along one dimensional
p-stacked ATT molecules.
3.4.5. Charge carrier mobility
During the Monte-Carlo simulations, the charge carrier is prop-
agated with respect to rate calculated from Marcus Eq. (3)and the
mean-squared displacement hx2
ðtÞi of the charge was calculated as
a function of time (t) [54]. The time dependence of the mean-
squared displacement for hole and electron in ATT1 is shown in
Fig. 9(a) and (b) and for ATT3, ATT6 and ATT7 the results are in
Figs. S3(a) and S3(b), respectively. From Figs. 9 and S3, it has been
observed that the mean-squared displacement was found to in-
crease linearly with time. Therefore, the diffusion constant (D) of
the charge carrier is obtained as half of the slope of the line. Based
on the Einstein relation (Eq. (6)) the charge carrier mobility is di-
rectly calculated from the diffusion constant (D). The calculated
hole and electron mobility in studied molecules is given in Figs. 9
and S3. Note that in this simulation the effect of stacking angle
fluctuations in the form of change in effective charge transfer inte-
gral is included and the effect of solvent and site energy fluctua-
tions on rate of charge transport is not included. It has been
observed that among the studied molecules, the CH3 substituted
ATT molecule, ATT1 has maximum hole and electron mobility of
1.67 and 2.40 cm2
/V s, respectively and OCH3 substituted ATT
Table 4
The calculated effective charge transfer integral (Jeff in eV) for hole and electron transport in ATT1, ATT3, ATT6 andATT7 dimer.
Angle (in degree) Hole Electron
ATT1 ATT3 ATT6 ATT7 ATT1 ATT3 ATT6 ATT7
0 0.313 0.279 0.289 0.292 0.368 0.336 0.296 0.322
15 0.192 0.182 0.172 0.179 0.216 0.202 0.168 0.211
30 0.026 0.053 0.010 0.022 0.071 0.064 0.09 0.067
45 0.051 0.050 0.039 0.041 0.073 0.063 0.068 0.072
60 0.071 0.084 0.037 0.046 0.069 0.060 0.069 0.073
75 0.041 0.063 0.028 0.040 0.050 0.055 0.021 0.024
90 0.003 0.001 0.001 0.001 0.127 0.147 0.070 0.113
Fig. 8. Results from molecular dynamics calculation for ATT1 dimer: plot by
number of occurrence, N (Left y-axis) (solid line), relative potential energy, E (right
y-axis) (dashed line) with respect to stacking angle.
Fig. 9. Calculated mean-squared displacement of (a) positive and (b) negative
charge in p-stacked ATT1 molecule with respect to time.

molecule, ATT3 has minimum hole and electron mobility of 0.82
and 0.62 cm2
/V s, respectively, because it has maximum reorgani-
zation energy value of 0.22 and 0.35 eV for the presence of excess
hole and electron, respectively. The calculated hole mobility of
EWG, NO2 and CN substituted ATT molecules, ATT6 and ATT7 is
0.31 and 0.78 cm2
/V s, respectively. The ATT6 and ATT7 molecules
are having significant electron mobility value of 1.76 and 2.03 cm2
/
V s respectively. Though the reorganization energy value for the
presence of excess positive charge in ATT6 and ATT7 is smaller
than that of negative charge, the calculated mobility is higher for
electron transport than the hole transport. This is because, ATT6
and ATT7 have significant effective charge transfer integral for
electron transport than for hole transport even at larger stacking
angles (see Table 4). As shown in Fig. 9, the substitution of EDG,
OCH3 does not improve either hole or electron mobility, whereas
the substitution of EWG, NO2 and CN slightly favor the electron
transport. Note that, the substitution groups (both EDG and
EWG) increases the reorganization energy of ATT molecule and
hence the rate of charge transport in these molecules is decreased.
The above results clearly show that the n-type semiconducting
property or ambipolar character can be obtained by substituting
the suitable EWG in the organic molecules, and the studied mole-
cules can be used for opto-electronic applications.
4. Conclusions
The quantum chemical calculations were performed to study
the optical and charge transport properties of 1,2,4,5-tetrakis(5-
methylthiophen-2yl)benzene (TMTB) and EDG and EWG substi-
tuted anthra-[1,2-b:4,3-b0
:5,6-b00
:8,7-b000
]tetrathiophene (ATT)
molecules. The ground and excited states structure has been opti-
mized at B3LYP/6-311G(d,p) level of theory. Based on the ground
and excited states geometry, the absorption and emission spectra
were calculated at TD-B3LYP/6-311G(d,p) level of theory. The cal-
culated absorption and emission spectra are in good agreement
with the experimental results. It has been observed that the effect
of medium and side on the calculated absorption and emission
spectra is negligible. The NO2 substitution red-shifted the absorp-
tion and emission spectra of ATT molecule by 45 and 52 nm,
respectively. The effective charge transfer integral calculated for
hole and electron transport in ATT molecules decreases exponen-
tially with respect to increase of stacking angle, and the effective
charge transfer is purely depends on the core region and indepen-
dent of the substitutions. The calculated stacking angle and force
constant values from molecular dynamics simulations are used to
model the stacking angle fluctuations during the Monte-Carlo sim-
ulation for hole and electron transport in ATT molecules. Among
the studied molecules, ATT1 has maximum charge carrier mobility
value of 1.67 and 2.4 cm2
/V s for hole and electron transport,
respectively. While comparing the CH3 substitution, the other sub-
stitution groups OCH3, OH, CF3, NO2, CN and CCl3 increases the
reorganization energy and hence the rate of charge transport in
these substituted molecules is decreased. The electron withdraw-
ing groups, NO2 and CN substitution slightly favor the electron
transport.
Acknowledgments
G.S is thankful to the Council of Scientific and Industrial Re-
search (CSIR), India for the award of Senior Research Fellowship
(SRF). One of the authors (K.S.) is thankful to the Department of
Science and Technology (DST), India, for granting a research project
under the DST-Fast track scheme.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.chemphys.2014.
01.020.
References
[1] P.E. Burrows, G. Gu, V. Bulovic, Z. Shen, S.R. Forrest, M.E. Thompson, IEEE Trans.
Electron Devices 44 (1997) 1188.
[2] C.D. Dimitrakopoulos, P.R.L. Malenfant, Adv. Mater. 14 (2002) 99.
[3] M. Bendikov, F. Wudl, D.F. Perepichka, Chem. Rev. 104 (2004) 4891.
[4] J.-L. Brédas, D. Beljonne, V. Coropceanu, J. Cornil, Chem. Rev. 104 (2004) 4971.
[5] J.E. Anthony, Chem. Rev. 106 (2006) 5028.
[6] T.J. Marks, MRS Bull. 35 (2010) 1018.
[7] S. Chai, S.H. Wen, K.-L. Han, Org. Electron. 12 (2011) 1806.
[8] H. Klauk, Organic Electronics, Manufacturing and Applications, Wiley-VCH,
Weinheim, 2006.
[9] J.-J. Kim, M.-K. Han, Y.-Y. Noh, Semicond. Sci. Technol. 26 (2011) 030301.
[10] C.K. Chan, F. Amy, Q. Zhang, S. Barlow, S. Marder, A. Kahn, Chem. Phys. Lett.
431 (2006) 67.
[11] S. Wang, A. Kiersnowski, W. Pisula, K. Müllen, J. Am. Chem. Soc. 134 (2012)
4015.
[12] M. Pope, C.E. Swenberg, Electronic Processes in Organic Crystals and Polymers,
Oxford University Press, New York, 1999.
[13] J.L. Brusso, O.D. Hirst, A. Dadvand, S. Ganesan, F. Cicoira, C.M. Robertson, R.T.
Oakley, F. Rosei, D.F. Perepichka, Chem. Mater. 20 (2008) 2484.
[14] M.M. Payne, S.R. Parkin, J.E. Anthony, J. Am. Chem. Soc. 127 (2005) 8028.
[15] R. Mondal, R.M. Adhikari, B.K. Shah, D.C. Neckers, Org. Lett. 9 (2007) 2505.
[16] M.M. Payne, S.A. Odom, S.R. Parkin, J.E. Anthony, Org. Lett. 6 (2004) 3325.
[17] K. Niimi, S. Shinamura, I. Osaka, E. Miyazaki, K. Takimiya, J. Am. Chem. Soc. 133
(2011) 8732.
[18] P.K. De, D.C. Neckers, Org. Lett. 14 (2012) 78.
[19] G. Saranya, P. Kolandaivel, K. Senthilkumar, J. Phys. Chem. A 115 (2011) 14647.
[20] H.E. Katz, J.G. Laquindanum, A. Lovinger, J. Chem. Mater. 10 (1998) 633.
[21] K. Takimiya, H. Ebata, K. Sakamoto, T. Izawa, T. Otsubo, Y. Kunugi, J. Am. Chem.
Soc. 128 (2006) 12604.
[22] A.L. Briseno, Q. Miao, M.-M. Ling, C. Reese, H. Meng, Z. Bao, F. Wudl, J. Am.
Chem. Soc. 128 (2006) 15576.
[23] G. Saranya, P. Kolandaivel, K. Senthilkumar, Mol. Phys. 111 (2013) 3036.
[24] V. Coropceanu, J. Cornil, D.A. da Silva, Chem. Rev. 107 (2007) 926.
[25] V. Lemaur, D.A. da Silva, J. Cornil, J. Am. Chem. Soc. 126 (2004) 3271.
[26] W.J. Liu, Y. Zhou, Y. Ma, Y. Cao, J. Wang, J. Pei, Org. Lett. 9 (2007) 4187.
[27] Y. Sakamoto, T. Suzuki, M. Kobayashi, Y. Gao, Y. Fukai, Y. Inoue, F. Sato, T. Sato,
J. Am. Chem. Soc. 126 (2004) 8138.
[28] S. Anto, J. Nishida, H. Tada, Y. Inoue, S. Tokito, Y. Yamashita, J. Am. Chem. Soc.
127 (2005) 5336.
[29] Q. Ye, J. Chang, K.-W. Huang, G. Dai, J. Zhang, Z.-K. Chen, J. Wu, C. Chi, Org. Lett.
14 (2012) 2786.
[30] Y. Sakamoto, T. Suzuki, M. Kobayashi, Y. Gao, Y. Inoue, F. Sato, Mol. Cryst. Liq.
Cryst. 444 (2006) 225.
[31] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.
[32] C.T. Lee, W.T. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.
[33] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200.
[34] S. Mierus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981) 117.
[35] M.J. Frisch, et al., Gaussian 09, Revision B.01: Gaussian Inc: Wallingford, CT,
2009.
[36] M. Bixon, J. Jortner, Chem. Phys. 281 (2002) 393.
[37] R.A. Marcus, N. Sutin, Biochim. Biophys Acta Rev. Bioenerg. 811 (1985) 265.
[38] K.V. Mikkelsen, M.A. Ratner, Chem. Rev. 87 (1987) 113.
[39] M.D. Newton, Chem. Rev. 91 (1991) 767.
[40] K. Senthilkumar, F.C. Grozema, F.M. Bickelhaupt, L.D.A. Siebbeles, J. Chem.
Phys. 119 (2003) 9809.
[41] G.T. Velde, F.M. Bickelhaupt, E.J. Baerends, C. Fonseca, J. Comput. Chem. 22
(2001) 931.
[42] A. Pietrangelo, M.J. MacLachlan, M.O. Wolf, B.O. Patrick, Org. Lett. 9 (2007)
3571.
[43] J.G. Sniijders, P. Vernooijs, E.J. Baerends, At. Data Nucl. Data Tables 26 (1981)
483.
[44] A.D. Becke, Phys. Rev. A 38 (1988) 3098.
[45] J.P. Perdew, Phys. Rev. B 33 (1986) 8822.
[46] P. Ren, J.W. Ponder, J. Phys. Chem. B 107 (2003) 5933.
[47] J.W. Ponder, TINKER: 4.2, Software tools for molecular design, Saint Louis,
Washington, 2004.
[48] J.H. Lii, N.L. Allinger, J. Am. Chem. Soc. 111 (1989) 8576.
[49] N.L. Allinger, F. Yan, L. Li, J.C. Tai, J. Comput. Chem. 11 (1990) 868.
[50] J.H. Lii, N.L. Allinger, J. Am. Chem. Soc. 111 (1989) 8566.
[51] P. Prins, K. Senthilkumar, F.C. Grozema, P. Jonkheijm, A.P.H.J. Schenning, E.W.
Meijer, L.D.A. Siebbeles, J. Phys. Chem. B 109 (2005) 18267.
[52] F.C. Grozema, L.D.A. Siebbeles, Int. Rev. Phys. Chem. 27 (2008) 87.
[53] L.B. Schein, A.R. McGhie, Phys. Rev. B 20 (1979) 1631.
[54] K. Navamani, G. Saranya, P. Kolandaivel, K. Senthilkumar, Phys. Chem. Chem.
Phys. 15 (2013) 17947.

[55] R.V. Solomon, A.P. Bella, S.A. Vedha, P. Venuvanalingam, Phys. Chem. Chem.
Phys. 14 (2012) 14229.
[56] C.A. Bertolino, A.M. Ferrari, C. Barolo, G. Viscardi, G. Caputo, S. Coluccia, Chem.
Phys. 330 (2006) 52.
[57] Z. Qu, H. Zhu, V. May, J. Phys. Chem. B 113 (2009) 4817.
[58] T. Moaienla, T.D. Singh, N.R. Singh, M.I. Devi, Spectr. Acta Part A 74 (2009) 434.
[59] G. Saranya, P. Kolandaivel, K. Senthilkumar, Int. J. Quant. Chem. 112 (2012)
713.

published articles-Navamani

More Related Content

What's hot (18)

Viewers also liked (18)

Similar to published articles-Navamani (20)

published articles-Navamani