Influence of disorder on electronic excited states: An experimental and numerical study of alkylthiotriphenylene columnar phases

Article abstract of DOI:10.1021/jp980623n

The spectroscopic properties of discotic hexa-alkylthiotriphenylenes are studied in solution and thin films and compared to those of hexa-alkyloxytriphenylenes. The solution properties are analyzed in the light of CS-INDO-CIPSI quantum chemistry calculations. The absorption maximum is assigned to the degenerate S₀ → S₄ transition. The fluorescence of the neat phases is attributed to weakly bound excimers. The phase transition leading from ordered to disordered columnar stacks induces an increase in the oscillator strength of the S₀ → S₁ transition and favors excimer formation. The influence of structural disorder on the properties of the delocalized states is rationalized by using various approximations within the frame of the exciton theory; three models for the calculation of the exciton coupling (point dipole, extended dipole, atomic transition charge distribution) are tested, short and long range interactions are considered, and the introduction of a dielectric constant is discussed. The best agreement between experimental and calculated absorption maxima is obtained using the atomic charge transition model. Off-diagonal disorder is correlated to structural disorder by changing the orientation and the position of the molecules within the aggregate. The case of degenerate molecular states is compared to that of nondegenerate ones. Orientational disorder has a dramatic effect on the energy and the localization of the upper eigenstate when molecular states are nondegenerate. Conversely, the properties of degenerate eigenstates are quite insensitive to orientational disorder. The magnitude of the off-diagonal disorder induced by positional disorder largely depends on the model used in the calculation of the exciton coupling. The results of the numerical calculations are in agreement with the small change observed in the neat phases absorption maxima upon a quasi one-dimensional melting of columnar stacks.

Full text of DOI:10.1021/jp980623n

J. Phys. Chem. B 1998, 102, 4697-4710
4697
ARTICLES
Influence of Disorder on Electronic Excited States: An Experimental and Numerical Study
of Alkylthiotriphenylene Columnar Phases
†
,†
‡
†
Sylvie Marguet, Dimitra Markovitsi,* Philippe Milli e´ , and Herv e´ Sigal
CEA/Saclay, DRECAM, 91191 Gif-sur-YVette, France
Sandeep Kumar
Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore, 560013, India
ReceiVed: January 5, 1998; In Final Form: March 16, 1998
The spectroscopic properties of discotic hexa-alkylthiotriphenylenes are studied in solution and thin films
and compared to those of hexa-alkyloxytriphenylenes. The solution properties are analyzed in the light of
CS-INDO-CIPSI quantum chemistry calculations. The absorption maximum is assigned to the degenerate S
f S transition. The fluorescence of the neat phases is attributed to weakly bound excimers. The phase
transition leading from ordered to disordered columnar stacks induces an increase in the oscillator strength
of the S f S transition and favors excimer formation. The influence of structural disorder on the properties
0
4
0
1
of the delocalized states is rationalized by using various approximations within the frame of the exciton
theory; three models for the calculation of the exciton coupling (point dipole, extended dipole, atomic transition
charge distribution) are tested, short and long range interactions are considered, and the introduction of a
dielectric constant is discussed. The best agreement between experimental and calculated absorption maxima
is obtained using the atomic charge transition model. Off-diagonal disorder is correlated to structural disorder
by changing the orientation and the position of the molecules within the aggregate. The case of degenerate
molecular states is compared to that of nondegenerate ones. Orientational disorder has a dramatic effect on
the energy and the localization of the upper eigenstate when molecular states are nondegenerate. Conversely,
the properties of degenerate eigenstates are quite insensitive to orientational disorder. The magnitude of the
off-diagonal disorder induced by positional disorder largely depends on the model used in the calculation of
the exciton coupling. The results of the numerical calculations are in agreement with the small change observed
in the neat phases absorption maxima upon a quasi one-dimensional melting of columnar stacks.
1
. Introduction
exciton theory, describing the excited states of the examined
systems as linear combinations of the excited states localized
The influence of disorder on the electronic excited states of
2,3
on each molecule. The disorder in the molecular arrangement
is depicted by a disorder in the diagonal or off-diagonal terms
molecular assemblies as well as on charge and energy transport
in these systems is the subject of numerous studies. This
research topic is important for molecular electronics because
structural disorder is an intrinsic characteristic of molecular
materials. The extent to which disorder in the molecular
arrangement will influence a given macroscopic property is
related to the electronic properties of molecules. Therefore, it
is important to be able to predict molecular properties required
to make the material behavior less sensitive to disorder. This
prediction depends on the level of approximation of the
theoretical models used to correlate the macrosopic properties
to the molecular ones. For example, an investigation of the
excitation hopping in columnar liquid crystals, showing that the
hopping times derived from experimental data, highly depend
on the model used for their analysis.1
4
-8
in the Hamiltonian matrix,
respectively representing the
excitation energy of the states localized on each chromophore
and the coupling between transition moments. In these studies,
the molecules are considered as points. Knowing that the point
dipole model is a poor approximation when the interchro-
mophore separation is small compared to their planar dimen-
9,10
sions, one can ask if the quantitative conclusions of the above-
mentioned studies remain valid when the level of approximation
for the exciton coupling is improved.
A model based on the exciton theory and on semiempirical
11
quantum chemistry methods allowing the representation of
molecules no longer as points but atom-by-atom was proposed
a few years ago. The diagonal and off-diagonal terms in the
Hamiltonian matrix can be calculated by taking into account
both the electronic structure of the molecules and their
coordinates within the aggregate. This methodology was applied
to calculate the eigenstate properties of columnar aggregates
Most studies dealing with the influence of disorder on
electronic excited states are carried out within the frame of the
†
SCM (Division of CEA/Saclay) CNRS-URA 331.
SPAM (Division of CEA/Saclay).
‡
S1089-5647(98)00623-3 CCC: $15.00 © 1998 American Chemical Society
Published on Web 05/23/1998

4698 J. Phys. Chem. B, Vol. 102, No. 24, 1998
Marguet et al.
eigenstates built on degenerate molecular states to that of
eigenstates built on nondegenerate ones, commonly studied in
the literature.
The experimental properties obtained for the sulfur derivative
H6TT are compared to those found for the oxygen derivative
H5OT (Figure 1). This enables us to make a connection with
previous photophysical studies of hexa-alkyloxytriphenylenes.1
The paper is organized as follows. The experimental details
are given in section 2. In section 3, the procedure followed
both in the quantum chemistry calculations (section 3.1) and in
the calculation of the exciton matrix are described (section 3.2).
Section 4 deals with “isolated” chromophores. The properties
of the electronic excited states obtained by quantum chemistry
calculations and the photophysical properties of solutions are
discussed. The photophysical properties of the organized phases
are described in section 5, and the exciton states are studied
numerically in section 6. In section 7, a quantitative comparison
of the experimental and calculated exciton shift values is made.
Finally, in section 8, the main results are summarized and
conclusions are drawn.
Figure 1. The studied hexa-alkylthiotriphenylenes (HnTT: X ) S, R
2n+1) and hexaalkyloxytriphenylenes (HnOT: X ) O, R )
)
n
C H
C H2n+1).
n
formed by triarylpyrylium salts11 and hexa-alkyloxytriphen-
ylenes.1 More recently, similar calculations were carried out
for conjugated oligomers.12
The question arises whether it is possible to obtain a
quantitative description of the influence of disorder on the
excited states of molecular assemblies. For this purpose, the
calculated properties must be compared with observables
obtained for a physical system whose degree of order can be
experimentally controlled. The hexa-hexylthiotriphenylene
(
H6TT) shown in Figure 1 is particularly attractive from this
1
3-17
point of view, because it presents a rich polymorphism.
2. Experimental Details
At room temperature it forms a K crystalline phase having a
monoclinic structure. Upon heating to 62 °C, a solid columnar
phase H appears which is transformed to a columnar liquid
crystal (Dh) at 70 °C. The latter is stable up to 93 °C,
temperature at which an isotropic liquid (I) is obtained.
2
.1. Synthesis of the Compounds. 2,3,6,7,10,11-hexa-n-
hexylthiotriphenylene was prepared following a modification
of previously reported methods.
16,20
Potassium-t-butoxide (4.17
g, 34 mmol) was added to a solution of hexanethiol (4.04 g, 34
mmol) in 1-methyl-2-pyrrolidinone (25 mL). After the solution
was heated at 100 °C for 5 min and then cooled to 70 °C,
hexabromotriphenylene (2.0 g, 2.85 mmol) was added. The
reaction mixture was stirred at 70 °C, and 1-bromohexane was
added (2.8 g, 17 mmol). It was left to react overnight. After
addition of water, the compound was extracted using diethyl
ether. The crude product was purified by column chromatog-
raphy over silica gel eluting with 2.5% ethyl acetate in n-hexane.
The powder compound was dissolved in diethyl ether and passed
through 0.2 mm filter paper. Finally, it was recrystallized in
an ethyl ether/acetone mixture. Yield was 83%.
2,3,6,7,10,11-Hexa-n-pentyloxytriphenylene was prepared
following a modification of the method described in ref 21.
Anhydrous ferric chloride (4.8, 0.03 mol) was added to a
solution of 1,2-dipentyloxy benzene (2.5 g, 0.01 mol) in 15 mL
of dry dichloromethane containing 1% concentrated H2SO4. The
reaction mixture was stirred at room temperature for 20 min
under anhydrous conditions and was poured over cold methanol
(50 mL). The white precipitate was filtered out, washed with
methanol, and purified over neutral alumina eluting with 2%
ethyl acetate in n-hexane. The powder compound was dissolved
in diethyl ether and passed through 0.2 mm filter paper. Finally,
it was recrystallized in an ethyl ether/methanol mixture. Yield
was 50%.
6
2 °C
70 °C
93 °C
K 7
8 H 7
8 Dh 7
8 I
The H f Dh transition is a unique example of quasi-one-
dimensional melting of molecular stacks. In both the H and
Dh phases, the column axes form a hexagonal lattice. Within
the columns of the H phase, adjacent molecules are rotated by
4
5° giving rise to a helical stucture. Upon the H f Dh
transition, the intercolumnar distance and the average stacking
distance remain practically the same, while the helical structure
is destroyed, (i.e., the molecular orientation around the column
axis becomes random). Furthermore, the amplitude of the
molecular motion around the average position of the aromatic
cores in the stacks increases and the correlation between columns
is lost.
We have undertaken an investigation of H6TT in solution18
and its various organized phases. Our aim was 2-fold. On one
hand, we wanted to characterize the excited states associated
to photon absorption and emission. To that end, we used, jointly
to the experiments, quantum chemistry calculations based on
the CS-INDO-CIPSI (Conformation spectra-intermediate ne-
glect of differential overlap-configuration interaction by per-
turbative selected iterations) method. We also wanted to see
how changes in the molecular arrangement induced by phase
transitions affect some basic photophysical properties. On the
other hand, we intended to rationalize the influence of the
structural disorder on the properties of the exciton states. In
particular, we focused on the off-diagonal disorder induced by
rotational and positional structural disorder. For this purpose,
it was important to compare the experimental results to the
results of numerical calculations obtained by various ap-
proximations of the exciton model. These approximations refer
to the calculation of the exciton coupling (point dipole, extended
dipole, atomic transition charge distribution), the consideration
of short or long range interactions and the use of a dielectric
constant. The strong electronic transition of triphenylenes being
degenerate, it seemed important to compare the behavior of
Remark: Filtration improved the purity of the compound by
eliminating alumina particles. Thus, the maximum molar
5
-1
-1
extinction coefficient found in this work (1.2 × 10 M cm ,
5
Figure 2) is more accurate than that reported in ref 1 (10
-
1
-1
M cm ).
2.2. Apparatus and Experimental Procedure. In order
to record absorption spectra of thin film in the region of the
absorption maximum without saturation of the detector, it was
necessary to use spectroscopic cells whose thickness was smaller
than 0.2 µm. These cells were prepared by pressing together
two quartz slides and filled by capillary effect upon heating
the powder compound to its isotropic phase. The planeity of
these quartz slides was better than 0.1 µm. An appropriate
cleaning procedure of the quartz slides was required; they were

Alkylthiotriphenylene Columnar Phases
J. Phys. Chem. B, Vol. 102, No. 24, 1998 4699
0
.59).22 Fluorescence decays were obtained by the single photon
counting technique. The excitation source was the second
harmonic (λex ) 300 nm) of a dye laser synchronously pumped
by a mode-locked Nd:Yag laser. A Glan-Thomson prism,
forming an angle of 54.7° with the polarization direction of the
exciting beam, was positioned in front of the monochromator.
The detector was a microchannel plate (R1564 U Hamamatsu)
providing an instrumental response function of 60 ps (fwhm).
3
. Methods of Calculation
.1. CS-INDO-CIPSI Calculations. The calculation of
3
excited electronic states of large aromatic compounds, using
semiempirical methods of quantum chemistry, is confronted with
several obstacles that are the large number of bielectronic
integrals and the size of the configuration interaction (CI) matrix.
In general, reliable methods have to take into account both, the
correlation energy and the reorganization of the whole σ system
in the excited states. A new CS-INDO-CIPSI-type method
allowing the resolution of these difficulties was recently
2
3
developped by Germain and Milli e´ . This new method, in
which the π and σ system are distinct and the σ molecular
orbitals (MO) localized, has proved successful in studying the
23,24
electronic states of small-sized, medium-sized,
large chromophores.
and even very
2
5
Since the length of the lateral alkyl chains does not have
1
significant effects on the excited-state properties, we performed
our calculations for H1OT and H1TT bearing six methyloxy
and six methylthio groups, respectively (Figure 1). Geometry
optimization of the two compounds H1OT and H1TT was
2
6
performed with the MOPAC package using AM1 force field.
Both ground-state geometries obtained from this optimization
have a D3h symmetry and greatly resemble that of the conformer
“a” of ref 1. The two X-CH3 bonds of each phenyl ring are
in the plane of the aromatic core and point to opposite directions.
The calculation of the electronic states of H1OT and H1TT
were performed by the previously cited CS-INDO-CIPSI method
in the whole MO basis set (78 occupied orbitals and 66 virtual
orbitals). No d orbitals were considered in the case of sulfur
derivative H1TT because the sulfur atoms are divalent. Within
this method, a preliminary singly-CI calculation is required
before the CIPSI calculations in order to determine the natural
Figure 2. Decomposition of the absorption spectra of (a) H6TT and
(
b) H5OT in n-heptane into Gaussian bands according to a vibronic
progression model. Attribution of these Gaussians to the electronic
transitions: bands 1,2 (S f S ), band 3 (S f S ), bands 4-6 (S
), bands 6-10 (S f S ).
0
1
0
2
0
f
S
3
0
4
sonicated successively in dichloromethane, detergent solution,
distilled water and ethanol (20 min each time), and then
pyrolyzed at 300 °C. The determination of the molar absorption
coefficient corresponding to the S0fS1 transition for the various
phases (K, H, Dh) was achieved by means of calibrated
Shinshikyu silica spacers (Dodwell marketing services, Japan)
of various sizes 1.3, 5, or 10 µm. We verified that the
absorption spectra obtained for different cell thicknesses overlap
after normalization by taking the optical path-length into
account. The sample alignment was checked by using a LEITZ
polarizing microscope equipped with a METTLER temperature
controller. For spectroscopic measurements, the temperature
of thin films was regulated using either an Oxford Instruments
liquid nitrogen cryostat (DN1704) equipped with a PID tem-
perature controller unit (ITC-4) or a LINKAM heating stage
2
3,25
orbitals.
From such a preliminary S-CI treatment, the six
highest occupied MOs and the six lowest virtual MOs (all in
the π system) were found to be involved in the initial variational
S subspace of CIPSI. In the localization procedure of the σ
system, the topological criterion called “2” in ref 23 was used.
This approximation allowed us to reduce the number of two-
6
6
electron integrals from 54.5 × 10 to 1.6 × 10 . CIPSI
calculations were performed using the two-classes version of
2
7,28
the CIPSI algorithm.
A Moller-Plesset partition was used
(
LTS 350) equipped with a LINKAM TP 92 temperature
in the perturbation treatment and the threshold η, used in the
iterative construction of the S variational space, was equal to
0.07. Following the CIPSI procedure, a final CI calculation
was performed in order to obtain the dipole moments and the
transition dipole moments. This was done by including in the
CI matrix all determinants having a coefficient larger than 0.01
in the CIPSI procedure.
controller. A waiting time of 30 min was necessary to reach
thermal equilibrium with the cryostat, whereas a few minutes
were sufficient with the heating stage.
Steady-state absorption spectra were recorded with a PERKIN
ELMER spectrophotometer (Lambda 900). Steady-state fluo-
rescence emission and excitation spectra were recorded with a
SPEX Fluorolog-2 spectrofluorometer; the spectra were cor-
rected for the spectral response of the dispersing elements and
the photomultiplier. For the neat phases, the exciting beam was
perpendicular to the surface of the cell and fluorescence was
collected at an angle of 20° with respect to the incident beam.
Fluorescence quantum yields were determined using dihydrate
3.2. Exciton Theory Calculations. 3.2.1 General Consid-
erations. The Frenkel exciton model, widely used to analyze
the excited states of molecular assemblies, does not consider
intermolecular charge transfer states. Indeed, within this model,
the excited states of the super system are described as a linear
combination of the excited states localized on each chro-
-
3
2,3
quinine sulfate in 0.1 mol dm HClO4 as a reference (Φf )
mophore:

4700 J. Phys. Chem. B, Vol. 102, No. 24, 1998
Marguet et al.
N
I
interaction energy between the molecule n in its ith excited state
i
i
n
0
,0
|
k〉 )
C
|Ψ 〉
(1)
(Si) and the molecule m in its ground state (S0), and E
∑
∑
k,n
n,m*n
n)1 i)1
denotes the interaction energy when both molecules are in their
ground state. The calculation of these electrostatic interactions
requires a representation of the electronic densities of the S0
and Si states.
N denotes the number of chromophores of the aggregate and I
the number of singlet electronic states that has to be considered
i
on each chromophore. Ψ is the wave function of the super
i
n
i
n
n
The off-diagonal terms 〈Ψ |H|Ψ 〉 of the exciton matrix can
system when the molecule n is in its ith singlet excited state
φ wave function) whereas all the other molecules m are in
their ground state (φ wave functions):
i,j
n,m
i
n
0
m
0
n
j
m
i,j
n,m
be written as V
) 〈φ φ |V|φ φ 〉 where V
is the
i
n
(
so-called exciton coupling. The approximation that the inter-
0
m
molecular electron exchange terms are negligible, the exciton
i,j
n,m
coupling V represents the electrostatic interaction between
i
n
i
n
0
m
Ψ ) φ
φ
(2)
∏
the two transition electronic densities, corresponding to S0 f
Si and S0 f Sj. Here again, a representation of the transition
electronic density based on a multipolar multicenter development
is required in order to obtain accurate results. We have shown1
that this development can be limited to one charge and one
elementary dipole on each atom of the molecule. When the
electronic transition is mainly described by π f π* configura-
tions, this development can be restricted to one charge on each
atom. Indeed, in the INDO approximation, the elementary
atomic dipoles arise from the monocentric 〈s|r|p〉 integrals
between a s-type AO and a p-type AO. These monocentric
monoelectronic integrals are only involved when the σ system
is involved (i.e., when the electronic transition is described with
σ f π* (e.g., n f π*), π f σ* or σ f σ* configurations).
This representation of the transition electronic density as a
multicentric monopole expansion is called in the following, the
atomic transition charge distribution.
m*n
Inherent to the exciton model is the assumption that the
coupling between two configurations localized on two different
molecules (e.g., πm f π*m and πn f π*n) is much smaller
than the coupling between two configurations localized on the
same molecule (e.g., π m f π *m and π m f π *m). In other
words, intermolecular interactions are assumed to be weak with
respect to intramolecular interactions in such a way that it is
possible to decompose the total Hamiltonian (H) of the super
system as the sum of the N Hamiltonians of the isolated
molecules (H0) plus an interaction operator V:
1
2
3
4
N
H )
+ V ) H + V
(3)
∑
0
n)1
In the NDO-type (neglect of differential overlap) semi-
It is worth-stressing that the usefulness of the exciton model
is restricted to the case where the exciton coupling is larger
than the static and dynamic fluctuations of the diagonal terms
including the Boltzmann factor (kT). Indeed, when the total
exciton coupling (coulomb + exchange + orbital penetration)
is much smaller than variations of the diagonal terms, the
eigenstates are localized and the eigenvalues correspond to the
excitation energies of noninteracting chromophores. For this
reason, within the formalism used in this study, the exciton
model is of no use for the symmetry-forbidden S0 f S1
transition of H1TT and H10T.
i
empirical methods, the Ψ wave functions are orthogonal
n
because of the orthogonality of the molecular orbitals (MO)
which are totally localized on a single chromophore. The orbital
overlap between any MO of the chromophore m and any MO
of the chromophore n, (n * m) is equal to zero and hence the
intermolecular interactions arising from orbital penetration are
neglected. Ab initio calculations, have shown that these
interactions can become significant at short distance, especially
2
9,30
in the case of weak transitions.
i
The Ψ eigenfunctions of H0 form the basis of the total
n
Hamiltonian matrix, the so-called exciton matrix. A full
3.2.2. Approximations in the Calculation of the Exciton
Matrix. In this section, we comment on four approximations
which are often made in the exciton model. The first is related
to the number of the electronic states of the molecule that has
to be taken into consideration. The second is related to the
diagonal terms of the exciton matrix, the third concerns the
structure of the matrix and the fourth is related to the calculation
of the exciton coupling.
(i) The study of the exciton states arising from an electronic
Si state has to involve all the Sj electronic states which are
“close” to Si. This means all the Sj states whose exciton band
may interfere with the exciton band of the Si state. Therefore,
the two important parameters are the energy difference between
the Si and Sj states and the intensities of the transition dipole
moments S0 f Si and S0 f Sj. In the numerical calculations
presented in section 6 the exciton states are built on the
degenerate S4 state of H1TT. In this particular case, it is
diagonalization of the exciton matrix provides the eigenvectors
i
(
C ) and the eigenvalues (Ek) corresponding to the NI eigen-
k,n
states |k〉 of the super system.
i
n
i
n
The diagonal term 〈Ψ |H|Ψ 〉 of the exciton matrix repre-
sents the S0 f Si excitation energy of the molecule n “solvated”
within the aggregate in the manner of solvent molecules. This
diagonal terms can be calculated combining quantum chemistry
calculations and molecular interaction calculations based, for
example, on the semiempirical Claverie’s method.31 Intermo-
lecular interactions are rationalized as the sum of electrostatic,
polarization, dispersion, and repulsion terms. In the case of
ionic compounds and for compounds whose transition induces
an important variation in the atomic charge distribution, the
electrostatic term is predominant, and thus, the solvation energy
can be calculated with a good accuracy.11 Conversely, for the
triphenylene derivatives examined here, both the net atomic
charges and the photoinduced variation of the atomic charges
reasonable to neglect both the S3 and S5 states. Since only one
1
i,j
n,m
are very weak. In this case, the predominant term in the
transition is considered in the exciton matrix, V is simplified
interaction energy is no more the electrostatic but the dispersion
term which cannot be calculated with acceptable accuracy for
the excited states. Therefore, the solvation energy cannot be
correctly calculated for such chromophores. The electrostatic
energies involved in the calculation of the diagonal term n are
to Vn,m in the following. Since the transition is degenerate, there
are four coupling terms between two distinct chromophores m
and n. The off-diagonal term localized on the chromophore n
I,II
n,n
(V where I and II represent the two components of the
degenerate transition) is taken equal to zero because this term
is equal to zero for the isolated chromophore.
i,0
0,0
i,0
of two kinds, either E
or E
, where E
denotes the
n,m*n
n,m*n
n,m*n

Alkylthiotriphenylene Columnar Phases
ii) A current approximation is the assumption that all
J. Phys. Chem. B, Vol. 102, No. 24, 1998 4701
(
Vn,m )
diagonal terms are equal. This approximation is very reasonable
when the molecular transitions do not present any intramolecular
charge transfer character or when the permanent dipole moments
are zero for symmetry reasons. As an illustration of the
accuracy of this approximation, it is worth remembering that,
for a columnar aggregate of H1OT, the differences between the
excitation energies of the molecules within the aggregate due
to intermolecular electrostatic interactions, were found to be
2
2
R
q
1
1
-
2
2
l
l
1
+
2(1 - cos θn,m
)
1 +
2(1 + cos θn,m
)
[
]
x
2
R
x
2R
(
5)
(c) In the atomic transition charge distribution model, already
-
1
-1
smaller than 70 cm for S0 f S1 and equal to about 130 cm
mentioned in section 3.2.1, the coupling is expressed as the sum
of charge-charge interaction terms between all the atoms of
the chromophore m and all the atoms of the chromophore n.
1
for S0 f S4. These energy differences are mainly observed at
the two ends of the aggregate whereas the excitation energies
are roughly constant within the aggregate. This is the so-called
edge effect. On the other hand, large variations of the diagonal
n
m
j
Nat Nat q q
i
terms are expected in the case of ionic compounds or in the
case of the intramolecular charge transfer states.11
V
n,m
)
∑ ∑ r
(6)
i)1 j)1
i,j
(iii) In the nearest neighbor approximation, only the short-
range interactions (i.e., only Vn,n(1 terms) are taken into
consideration, whereas all the other off-diagonal terms are taken
equal to zero. When all diagonal terms are equal, the structure
of the excitonic matrix is that of a H u¨ ckel matrix for a polyene
chain and whatever the values of these off-diagonal terms Vn,n(1,
the eigenstate energies are always symmetrically distributed
around the energy of the isolated chromophores. This distribu-
tion of the energies of the eigenstates around the energy of the
isolated chromophore is used as a parameter allowing us to
estimate the error made when the long-range interactions are
neglected (section 6).
ri,j is the interatomic distance between the atoms i and j and
n
q is the charge of the atome i. This atomic transition charge
i
distribution results from our quantum chemistry calculations and
represents the transition electronic density:
Nat
Nat
n
i
n
i
n
i
q ) 0 and q r ) bµ
b
(7)
∑
∑
i)1
i)1
where bµ denotes the transition dipole moment. The detail of
the calculation of these atomic charges in the INDO formalism
1
(iv) The fourth approximation is related to the model used
is described in a previous paper. Two charge distributions
n,I
n,II
in the calculation of the exciton coupling. Three models are
presented below by increasing order of accuracy.
(
q ) and (q ) are used to represent the electronic density
i
i
associated to a degenerate transition where I and II represent
the two components of the transition. In the case of the S0 f
S4 transition of H1TT, the contribution of the atomic transition
charges to the total CS-INDO-CIPSI transition dipole moment
is equal to 93%, and consequently, the approximation of a
multicentric monopole expansion is reasonable.
The common aim of these three models is to provide a
convenient way to calculate the exciton coupling whose direct
expression is a sum of two-electron integrals. A recent review
of the various models used in the calculation of the exciton
coupling is given in ref 32.
(a) In the point dipole model, the exciton coupling is
simplified to the interaction between two transition dipole
moments. This model is still widely used in the literature,
although it was pointed out already in 1964 that it is not valid
when the separation of the chromophores is small compared to
their planar dimensions.9 In the case of the columnar ag-
gregates, the calculation of the exciton coupling in the point
dipole approximation is given by
µµ cosθn,m
Vn,m
)
(4)
A property of the matrix diagonalization is largely used in
this study: when all the matrix elements are divided by the same
3
R
constant, then all the eigenvalues (Ek) are divided by this same
where θn,m denotes the rotation angle between the two molecules
n and m and µ is the transition dipole moment.
i
constant but each eigenvector (C ) remains unchanged. One
k,n
can notice that when the transition moment is multiplied by a
(b) In the extended dipole model, the transition dipole moment
2
factor f , the exciton coupling is mutiplied by f whatever the
µ is replaced by two opposite charges +q and -q at a distance
model used (eqs 4-6). In section 6, for the degenerate S f
0
10
l; q and l are two unknown parameters with no other condition
than ql ) µ. Although this approximation is better than that of
the point dipole model, it is used only by few authors. The
coupling calculated according to this model is the sum of four
charge-charge electrostatic interactions. At long distance, the
extended dipole is equivalent to the point dipole. At short
distance, this model is a rather good approximation for strongly
allowed transitions whereas it is a very crude approximation
for weak transitions.1 A dipole length of the order of the size
of the chromophore is generally chosen. However, a good way
to choose the dipole length consists of adjusting the value of l
from the calculation of the electrostatic interactions as presented
in section 6. In the case of columnar aggregates, the general
formula for the calculation of the exciton coupling in the
extended dipole approximation is given by eq 5 where q,l,R,µ
and Vn,m are in atomic units:
S4 transition, we have multiplied each transition atomic charge
resulting from the CS-INDO CIPSI calculation by a factor f in
order to adjust the CS-INDO-CIPSI value of the transition dipole
moment (µ ) 10.89 D) to the value found from the fit of the
absorption spectrum (µ ) 9.2D).
3.2.3. Degree of Localization of the Eigenstates. According
to the linear expression of the wave functions (eq 1), the relative
contribution of each chromophore n in the description of the
total wave function |k〉, can be calculated from the square of
2
the coefficient (C ) . This is a very common way to identify
k,n
the nature of the wave functions in quantum chemistry. By
sorting the localized configurations whose contribution is larger
than a certain threshold, one can determine the number of
chromophores Lk involved in the excitation of the eigenstate k.
This resulting Lk number depends on the threshold value: the
larger the threshold, the lower the Lk values.

4702 J. Phys. Chem. B, Vol. 102, No. 24, 1998
Marguet et al.
TABLE 1: Excited State Properties Calculated by the
CS-INDO-CIPSI Method
TABLE 2: Decomposition of the Absorption Spectra of
H6TT and H5OT in n-Heptane into Gaussian Bands
d
According to a Model of Vibronic Progression (Figure 2)
H1TT
H1OT
W
cm
i
/
νj (0-0)
/
∆ νj /
transition symmetry energy/cm-
1
µ/D energy/cm-1 µ/D
1
-1
-1
compound transition
N
i
cm
cm
µ/D
S
S
S
S
S
0
0
0
0
0
f S
f S
f S
f S
f S
1
2
3
4
5
A′
A′
E′
E′
E′
1
2
27 700
0
0
28 800
33 600
34 600
39 100
41 400
0
0
a
b
b
a
a
b
b
a
S
S
S
S
S
S
S
S
0
0
0
0
0
0
0
0
f S
f S
f S
f S
f S
f S
f S
f S
1
2
3
4
1
2
3
4
2
1
3
4
2
1
3
4
900 25400 1280
1360 28100c
1.4
2.1
6.2
32 400
32 900
36 800
39 300
5.77
10.89
0.92
5.60
10.45
1.19
H6TT
1280 29100c 1180, 970
1400 32400 1320, 1310, 1310 9.6
700 27900 1050
1.0
1.1
5.7
840 30100c
Another way to define the number of chromophores partici-
H5OT
1640 31300c 1460, 1660
pating in a given eigenstate k is to use the empirical parameter
Lk defined as the inverse ratio of the sum of the fourth power
of the coefficients.
1200 36000 1330, 1280, 1280 9.2
a
Estimated error: 10%. Estimated error: 50%. c Estimated error:
1000 cm ; the errors are due to the fact that somewhat different N
i
b
6-8
-
1
(
d
values give acceptable fits.
i i
N : number of gaussian bands. W :
N
4
Gaussian bandwidth (fwhm). νj (0-0): energy of the first Gaussian band.
Lk ) 1/ (C )
(8)
∑
k,n
∆ νj : energy separation between two succesive gaussian bands. The
n)1
transition dipole moment (µ) is determined from the sum of the areas
2
∫
ꢀ( νj )d νj beneath the N
10 ∫ꢀ( νj )d νj / νj .
i
Gaussian according to the equation µ ) 9.166
Lk is equal to N for a totally delocalized eigenstate (all the
-3
×
-
1/2
coefficients equal to N ), and it is equal to 1 for a single-site
localized eigenstate. When the molecular electronic states are
degenerate it is easy to show that eq 8 becomes
spectra are decomposed according to a vibronic progression
model. The position of the peaks corresponding to S0 f S1
lowest in energy peak) and S0 f S4 (most intense peak) are
(
N
easily determined on the spectra whereas the energies of the
other transitions are derived through a fitting procedure based
on the results of the quantum chemistry calculations. For this
purpose, a commercial software (Peak-Fit 4.0) is used. Each
transition S0 f Si is simulated by the sum of Ni Gaussian bands
with the same bandwidth Wi. Ni is fixed, whereas Wi, the energy
at the maximum νj (0-0), and the amplitude of each Gaussian band
are considered as fitting parameters. The minimum number of
Gaussians giving a good fit is used. The H5OT spectrum is
fitted first, because the vibronic progressions are more easily
assigned on it. Then, the H6TT spectrum is fitted using the
same number of gaussians as that found for H5OT. This is
reasonable since electronic excitations are mainly localized on
the aromatic core. Therefore, the active vibronic progressions
are not expected to be related to peripheral groups (alkylthio
or alkyloxy). The results of the fits are presented in Table 2.
The transition moments corresponding to S0 f S1 and S0 f
S2 are higher for H6TT than for H5OT (Table 2). The oscillator
strength of symmetry forbidden transitions is due to vibronic
coupling with allowed transitions. The smaller the energy
difference between the allowed and the forbidden transition,
I
k,n
2
II 2 2
k,n
Lk ) 1/ [(C ) + (C ) ]
(9)
∑
n)1
I
k,n
II
k,n
where C and C denote the two coefficients corresponding
to the chromophore n in the description of the electronic
transition.
From a comparative study of these two methods, in the case
of H1TT columnar aggregates, the following conclusions were
drawn, using either the square of an coefficients with a certain
threshold or eqs 8 and 9. First, when the eigenstate is localized
on a moderate number of chromophores (less than 20% of the
total number), the two methods are equivalent and eqs 8 and 9
give a good estimation of the number of chromophores involved
in the excitation. On the other hand, for largely delocalized
eigenstates, with both methods it becomes difficult to precisely
estimate the number of participating chromophores, since all
the coefficients are very small. The Lk value corresponding to
the eigenstate bearing the oscillator strength (noted Lk,abs) found
from eqs 8 and 9 for an aggregate of 60 molecules is 43. This
value can be compared to the theoretical value (Lk ) N ) 60)
corresponding to an “equally” delocalized eigenstate. Actually,
the ratio Lk,abs/N decreases when N increases. As an example,
Lk,abs/N is respectively equal to 1, 0.78, 0.71, and 0.70 when N
is equal to 2, 15, 60, and 200.
33
the higher the oscillator strength acquired by the latter. The
energy difference between the peaks corresponding to S0 f S1
-1
and S0 f S4 is bigger for H5OT (8100 cm ) than for H6TT
-1
(
7000 cm ). This could explain why the S0 f S1 and S0 f
S2 transitions moments are larger for the thio derivative than
for the oxygen derivative. Another origin for the oscillator
strength of the studied hexasubstituted triphenylenes is a
symmetry break because of a nonsymmetric arrangement of the
4
. Properties of “Isolated” Chromophores
Table 1 shows the properties of the lowest energy singlet-
singlet transitions calculated by the CS-INDO-CIPSI method
for H1OT and H1TT. For both compounds, the transitions S0
f S1 and S0 f S2 are symmetry forbidden whereas S0 f S3,
S0 f S4, and S0 f S5 are symmetry allowed and degenerate.
The two components of a degenerate transition are orthogonal
and their vectorial sum, given in Table 1, corresponds to the
experimental transition moment. S0 f S4 is the most intense
transition (Table 1). The transition energies calculated for H1TT
are lower than those calculated for H1OT. This difference is
1
side groups.
The absorption spectra of H6TT show very weak solvato-
1
chromism, as reported for H5OT. For both compounds, the
largest shift is found between the absorption spectra recorded
for n-heptane and dichloromethane solutions. It is about 3 times
-
1
-1
larger for S0 f S4 (200 cm ) than that for S0 f S1 (70 cm ).
Larger variations of the S0 f S4 excitation energy compared to
the S0 f S1 one, within columnar aggregates of H1OT, were
also shown from a calculation of the electrostatic interaction
energy (Figure 9 in ref 9). This remark will be used in section
7.
-
1
ca. 1100 cm for the three lowest in energy transitions and ca.
2
-
1
200 cm for the highest ones (Table 1).
The electronic absorption spectrum of H6TT in n-heptane
-
6
(
(
10 M) is red-shifted and less structured than the H5OT one
Figure 2). In light of our theoretical calculations, the absorption
Similarly to the absorption spectra, the H6TT fluorescence
spectra are also red-shifted and less structured than those of

Alkylthiotriphenylene Columnar Phases
J. Phys. Chem. B, Vol. 102, No. 24, 1998 4703
Figure 3. Fluorescence spectra of H6TT in n-heptane (‚‚‚), diethyl
ether (- -), ethanol (-‚-) and dichloromethane (s); νj ex ) 29000
Figure 4. Absorption spectra recorded for thin films (<0.2 µm) of
H6TT. Crystalline phase K at 40 °C (‚‚‚), hexagonal phase H at 70 °C
-
1
cm
.
(- -), columnar liquid crystalline phase D
phase I at 120 °C (s).
h
at 90 °C (-‚-), isotropic
TABLE 3: Comparison of the Properties of H6TT and
H5OT in Dichloromethane
compound
τ
f
/nsa
Φ
τ
rad/ns
k
rad/s-1
k
nrad/s-1
b
c
7
6
9
8
H6TT
H5OT
0.64
7.9
0.019
0.060
34
120
2.9 × 10
8.3 × 10
1.5 × 10
1.2 × 10
a
νj ex: 33300 cm-1. b νj ex: 29000 cm-1. c νj ex: 25000 cm-1
.
H5OT. Their profile varies with the solvent (Figure 3), as
reported for other aromatic chromophores.34 The fluorescence
properties of H6TT and H5OT in dichloromethane are compared
in Table 3. The fluorescence lifetime (τf ) 0.64 ns) and the
fluorescence quantum yield (Φ ) 0.019) of H6TT are both
smaller than those of H5OT (τf ) 7.9 ns, Φ ) 0.06). The
radiative lifetime, determined as τrad ) τf/Φ, is much shorter
Figure 5. Temperature dependence of the absorption maximum
determined for thin films (<0.2 µm) of H6TT. The scale on the right
represents the energy difference (∆E) with respect to the absorption
maximum of H6TT in n-heptane.
(34 ns) for H6TT than that for H5OT (120 ns), in agreement
with the values of the transition moments derived from the
absorption spectra. Moreover, the nonradiative rate constant,
knrad ) krad(1 - Φ)/Φ, of H6TT is 12 times higher than that of
H5OT.
absorption maximum corresponding to the strong S0 f S4
electronic transition (µ ) 9.6 D, Table 2), by the existence of
strong exciton interactions leading to collective excited states.
We note ∆E the difference in energy between the absorption
maxima of thin films and n-heptane solutions. Within the
temperature domain of each phase, ∆E decreases slowly with
increasing temperature (T) and the largest ∆E/T slope is found
for Dh (Figure 5). At each phase transition, a jump in ∆E is
The radiative lifetime determined from the fluorescence
lifetime and quantum yield measurements (τrad ) τf/Φ) can be
35
compared to the τrad determined via the Strickler Berg formula.
In the latter case, τrad depends on the number of Gaussian bands
attributed to S0 f S1 in the decomposition of the absorption
spectra. If N1 is equal to 2, τrad is found to be 110 and 50 ns
for H5OT and H6TT, respectively, in good agreement with the
values reported in the previous paragraph. In contrast, when
N1 is equal to 1, much higher τrad values are found (495 ns for
H5OT and 147 ns for H6TT). Consequently, the attribution of
two Gaussians to S0 f S1 is correct and is in agreement with
the observation of a vibrational progression in fluorescence.
Finally, we remark by comparing the values in Tables 1 and
-1
-1
found: 320 cm at the K f H, 160 cm at the H f Dh, and
4
-1
60 cm at the Dh f I. The ∆E values of the four neat phases
of the thio derivative H6TT are smaller than that of the Dh phase
-1
of the oxygen derivative H5OT (2000 cm ). Unlikely to what
is found for H6TT (Figure 5), the ∆E value observed for the
Dh phase of H5OT remains constant over its whole temperature
domain (342-395 K). The temperature dependence of ∆E will
be discussed in section 7.
2
that quantum chemistry calculations provide a good description
of the properties of “isolated” chromophores. Therefore, it is
reasonable to use the atomic transition charge distribution
calculated according to the same method in order to determine
the exciton coupling (section 6).
Figure 6 shows the red edge of the absorption spectra obtained
for the K, H, and Dh phases of H6TT. Using nonoriented films
(macroscopically random orientation of microdomaines) of
known thickness (section 2.2), we found that the Beer-Lambert
law is obeyed. Thus, the molar absorption coefficient can be
determined provided that the chromophore concentration is
known. The molar concentration is calculated from the
structural data provided by X-ray diffraction measurements
taking into account the number of molecules per unit cell (4
for K, 3 for H and Dh) and the dimensions of the unit cell which
5
. Thin Film Properties
The absorption profile of thin films (Figure 4) depends on
the phase. The crystalline phase spectra exhibit two shoulders,
-
1
at ca. 31000 and 36000 cm . The absorption maxima of the
four H6TT neat phases are blue-shifted with respect to the
solution spectra. We explain the observed blue shift of the

4704 J. Phys. Chem. B, Vol. 102, No. 24, 1998
Marguet et al.
Figure 6. Molar extinction coefficient in the red edge of the absorption
spectra of H6TT thin films. Crystalline phase K (s), hexagonal phase
Figure 7. Fluorescence spectra of H6TT thin films; νj ) 29 000 cm-1
.
ex
Crystalline phase K at 40 °C (- -), hexagonal phase H at 70 °C (s),
H (- -), columnar liquid crystalline phase D
h
(‚‚‚).
columnar liquid crystalline phase D at 90 °C (‚‚‚), isotropic phase I at
h
1
20 °C (-‚-).
3
3
is temperature dependent (1399 Å for K at 40 °C, 1483 Å for
3
15,16
H at 70 °C, and 1509 Å for Dh at 120 °C).
The absorption bands shown in Figure 6, mainly correspond
to the S0 f S1 transition and can be decomposed in two
Gaussians, as in the case of n-heptane solutions. Within the
temperature domain of each phase, the positions of these bands
are temperature independent. Going from K to H, the position
-
1
of the νj (0-0) band changes from 25650 to 25100 cm and it
-
1
is shifted to 25050 cm upon the H f Dh transition. For S0
f S1, being a symmetry forbidden electronic transition, mo-
lecular aggregation is not expected to lead to spectral shift
associated to strong dipolar coupling (section 3.2.1). Therefore,
we attribute the difference in the νj (0-0) energy observed
-
1
between the neat phases and the n-heptane solutions (250 cm
blue shift for K, 300 and 350 cm-1 red shift for H and Dh) to
different strength of intermolecular forces. As explained in
section 3.2.1, the predominant forces acting among triphenylene
chromophores are the dispersion ones, which are always
attractive. They are larger for the excited state than for the
ground state leading to a red shift of the absorption of condensed
phases with respect to isolated chromophores. Since they vary
6
as 1/R, the closer the interatomic distances between neighboring
molecules, the strongest the interaction. This explains the
hypsochromic shift of S0 f S1 observed in Figure 6 for the
monoclinic K phase (average stacking distance: 3.9 Å) com-
pared to the columnar hexagonal H phase (stacking distance:
3
.6 Å).
The value of the S0 f S1 transition moment is the same (1.3
(
0.1 D) for the two solid phases, K and H, of H6TT and close
to that determined for solutions (1.4 ( 0.1 D). Going from the
solid H phase to the liquid crystalline Dh phase, the transition
moment increases from 1.3 ( 0.1 D to 2.0 ( 0.4 D. This
behavior characterizes only the thio derivative, since no notice-
able change in the value of the S0 f S1 transition moment is
observed upon the K f Dh phase transition of H5OT. We are
tempted to assign it to a symmetry break due to deformation of
the C-S bonds, which are weaker than the C-O bonds. Such
a deformation could be induced by structural fluctuations typical
of columnar liquid crystals: column bending, lattice dilatation,
Figure 8. Temperature dependence of (a) the fluorescence maximum
-
1
(νex ) 29000 cm ) and (b) the fluorescence lifetime ( νj ex ) 33300
-
1
cm ) of H6TT thin films.
emisssion maximum (23700, 23470, and 23240 cm- respec-
1
tively, for K, H, and Dh) with the exception of the isotropic
-1
phase spectra whose maxima appear at 100 cm higher energy
than those of the Dh spectra. The spectrum width (fwhm)
-
1
-1
increases when going from K (1900 cm ) to H (2500 cm )
-1
and then to Dh (2900 cm ). The spectra of the Dh and I phases
are practically identical. The Stokes shift found for the neat
3
6
or compression.
-
1
The fluorescence spectra of thin films are all red shifted with
respect to the solution spectra (Figure 7). The emission
maximum is constant within the temperature domain of each
phase but it changes abruptly upon the phase transitions (Figure
phases (1900, 1600, 1800, and 1700 cm for K, H, Dh, and I,
respectively) is about 3 times larger than that determined for
-
1
spectra of n-heptane solutions (600 cm ). Such a behavior
could be explained by an interaction between the localized S1
state and a higher in energy intermolecular charge transfer
8a). The higher the temperature, the lower the energy of the

Alkylthiotriphenylene Columnar Phases
J. Phys. Chem. B, Vol. 102, No. 24, 1998 4705
Figure 9. Schematic representation of the columnar aggregates
considered in the numerical calculations. The aromatic cores are all
parallel and their centers are located on the same axis. d denotes the
stacking distance. Each molecule is rotated with respect to its neighbor
by an angle θ.
state,29,30 leading to excimer-like emission. However, both the
width of the fluorescence spectra and the Stokes shift, although
much larger than the monomer ones, are smaller than those
found for typical excimers.3
8,39
Consequently, fluorescence
should arise from weakly bound excimers.
The fluoresence decays recorded for the four neat phases of
H6TT can be fitted by a single exponential, and the correspond-
ing lifetime is of the same order of magnitude as that of
solutions. The temperature dependence of the fluorescence
lifetime is shown Figure 8b. For the phases K, Dh, and I, it
decreases with increasing temperature while it remains constant
for H. The lifetimes found for Dh are longer than those found
for all the other phases. The increased fluorescence lifetime
and width of the emission band in the columnar Dh phase,
compared to those observed for the columnar H phase, show
exciton formation is favored by the disorder in the columnar
stacks.
Figure 10. Energy of the upper eigenstate (Emax) as a function of the
aggregation number. Columnar helical aggregates of H1TT (θ ) 45°).
Degenerate molecular electronic transition (µ
1
) µ ) 6.8 D). The
2
exciton coupling is calculated including long-range interactions and
using two different models: the atomic charge distribution model
(closed circles) and the extended dipole model (dotted lines), and l
denotes the length (6, 7.2, and 8 Å) of the extended dipole.
dipole moment determined from the fit of the absorption spectra
(
µ ) 9.6 D) rather than the value obtained from quantum
chemistry calculations (µ ) 10.9 D). The two components of
the degenerate transition are µ1 ) µ2 ) 9.6/ 2 ) 6.8 D.
x
When the properties of eigenstates built on degenerate molecular
states are compared to those built on nondegenerate molecular
states (section 6.3), we consider that the transition moment of
the nondegenerate transition is equal to the total transition
moment of the degenerate one (µ ) 9.6 D). In this way, both
types of transition could correspond to the same experimental
absorption band. For an aggregate of N molecules, the
dimension of the exciton matrix is (2N × 2N) when the transition
is degenerate, instead of (N × N) for a nondegenerate transition.
6.2. Approximations in the Calculation of the Off-
Diagonal Terms. In this subsection, columnar aggregates
having the structural characteristics of the helical H phase are
considered. Whatever the level of approximation, when the
molecular states are degenerate, all eigenstates are degenerate
and the oscillator strength is born by the upper one. Therefore,
we mainly focus on the energy of the highest eigenstate (Emax)
since it can be related to the experimental absorption spectra.
We are also interested in the “symmetry” of the exciton band,
that is the position of the upper (Emax) and lower (Emin)
eigenstates with respect to the excited-state energy of non-
interacting chromophores. To this end, we calculate the ratio
Emax/(Emax - Emin).
6
. Numerical Study of the Exciton States
In this Section we are interested in the exciton states of
triphenylene columnar aggregates built on the S4 state which is
degenerate and corresponds to the maximum of the absorption
spectra (Figures 2 and 4). In our study, we assume a static
distribution of molecular orientations. This hypothesis is quite
reasonable since molecular motions in liquid crystals occur in
the pico- or nanosecond time scale and are therefore much
39
slower than the time of intermolecular excitation transfer. First,
we present some details about the system for which calculations
are performed. Then, we examine how different approximations
used to calculate the off-diagonal terms in the Hamiltonian
matrix affect the eigenstate properties. These approximations,
developed in section 3.2.2, concern the number of interacting
neighbors (nearest neighbor or long-range interactions), the
model used for the calculation of the exciton coupling (point
dipole, extended dipole, atomic transition charge distribution),
and the use of a dielectric constant. Finally, we study the
influence of disorder on the eigenstate properties. To find out
any particular behavior due to the degeneracy of molecular
excited states, we perform our calculations for both degenerate
and nondegenerate excited states.
Figure 10 shows Emax, calculated using the atomic charge
distribution model and including long-range interactions, as a
function of the aggregation number. Emax increases with the
aggregation number and remains practically constant for N
greater than 60. It can be seen in Figure 11, that interactions
involving up to the sixth neighbor must be taken into account
6
.1. Presentation of the System. We consider a columnar
stack consisting of N H1TT molecules (N ) 2, 3, ..., 100). Their
aromatic cores are all parallel and their centers are located on
the same axis (Figure 9). The stacking distance d is either
constant equal to 3.6 Å or takes random values in the interval
-1
in order to have an error smaller than 200 cm . If only nearest
neighbor interactions are taken into account, the position of Emax
is underestimated by ca. 35% for large aggregates. The
“symmetry” of the exciton band also depends on the number
of interacting chromophores. In the nearest neighbor ap-
proximation, Emax and Emin are symmetrically distributed around
the zero level. When all the interactions are considered, the
positions of all the eigenstates are shifted to higher energy but
the density of states in the lower part of the exciton band
increases, whereas it decreases in the upper part. Emax/(Emax -
Emin) becomes 0.66 instead of 0.50. A similar trend is reported
3
.4-3.8 Å (positional disorder). Each molecule is rotated with
respect to its neighbor by an angle θ. The angle θ is either
constant (helical structure), or takes random values in the interval
0
°-360° (orientational disorder). Orientational and positional
disorder are studied separately. When we study the influence
of disorder, we report the results obtained for 20 individual
random configurations but not the average values.
All diagonal terms are set equal to zero (section 3.2.2). To
compare the results of the calculations with the experimental
absorption spectra (section 7), we use the S0 f S4 transition

4706 J. Phys. Chem. B, Vol. 102, No. 24, 1998
Marguet et al.
Some authors using the point dipole or the extended dipole
approximation divide the exciton coupling by the dielectric
constant ꢀ∞ of the medium. As a result, Emax is divided by the
same ꢀ∞ value (section 3.2.2). The dielectric constant is
supposed to account for the quasi-instantaneous polarization of
the electronic clouds in the medium upon light excitation and
is equal to the square of the refractive index. Typical ꢀ∞ values
1
0,40-42
of 2.5-2.7 are used.
The dielectric constant is a
macroscopic property of the medium which has no meaning at
a molecular level. The polarization of the electronic clouds is
in principle taken into account in a complete quantum chemical
description of the overall system. However, a complete
description has not been performed so far for systems consisting
of a big number of large molecules. In order to roughly simulate
the distance dependence of this effect, we consider that ꢀ∞ is
equal to one for nearest neighbor coupling (Vn,n+1) since no
molecules are intercalated in between. For long distance
coupling (Vn,n+i with i > 1), ꢀ∞ is given a constant value, ranging
from 1.1 to 3.0. We are conscious that this is a further
approximation but it seems to us more appropriate than the use
of a uniform value of dielectric constant. The introduction of
a dielectric constant only for long-range interactions leads to a
decrease of Emax (Figure 12) and makes the exciton band more
symmetric (Table 4). When ꢀ∞ tends to very high values, the
structure of the exciton matrix tends to that of a H u¨ ckel matrix
Figure 11. Energy of the upper eigenstate (Emax) as a function of the
number of interacting chromophores. Columnar helical aggregates of
H1TT (N ) 60, θ ) 45°, degenerate molecular electronic transition:
µ
1
) µ ) 6.8 D). The exciton coupling is calculated according to the
2
atomic charge distribution model including long range interactions.
-1
and Emax tends toward the value (2290 cm ) obtained consider-
ing only nearest neighbor interactions (Table 4 and Figure 12).
General conclusions can be drawn from Table 4, where Emax
and the “symmetry” of the exciton band, calculated using
different approximations, are gathered. In the point dipole
approximation, Emax is largely overestimated with respect to the
values calculated according to the atomic transition charge
distribution model. Typically, Emax is 4.2, 3.5, or 3.3 times
bigger, for aggregation numbers equal to 2, 10, or 100,
respectively. Conversely, within the atomic transition charge
ditribution model, Emax is underestimated by 35% in the nearest
neighbor approximation compared to the case where all the
coupling are taken into consideration. This means that the error
made using the point dipole approximation is much bigger than
that made following the nearest neighbor approximation. Table
Figure 12. Energy of the upper eigenstate (Emax) as a function of the
dielectric constant ꢀ
range coupling Vn,n+i with i > 1. For nearest neighbor coupling (Vn,n+1),
is taken equal to 1. Columnar helical aggregates of H1TT (N ) 60,
∞
taken into account in the calculation of the long-
ꢀ
∞
θ ) 45°, degenerate molecular electronic transition: µ
1
) µ ) 6.8
2
D). The exciton coupling is calculated according to the atomic charge
distribution model.
4
shows that Emax may vary by 1 order of magnitude depending
for J aggregates where the oscillator strength is born by the
lowest eigenstate: when all interactions are taken into account,
Emin is shifted to lower energy and the exciton band becomes
on the approximation level. It is worth noticing that the errors
made by different approximations may compensate each other.
For example, the point dipole model with the nearest neighbor
7
-1
less symmetric.
approximation leads to a Emax value of 9926 cm , which can
be reduced to the value found using the atomic transition charge
We tested the extended dipole approximation for various
lengths (l) of the extended dipole. Figure 10 shows that Emax
calculated for l ) 7.2 Å matches that found using the atomic
transition charge distribution model. It is worth mentioning that
-
1
distribution model (3559 cm ) by the introduction of a
dielectric constant equal to 2.8. In that case, although the Emax
value is artificially corrected, the error made in the “symmetry”
of the exciton band remains (Table 4).
3
the curve VR as a function of R obtained according to the
atomic transition charge distribution model can be fitted using
the same length (l ) 7.2 Å) of the extended dipole (Figure 10
in ref 1). We remark that the latter value corresponds to the
diameter of the disk defined by the triphenylene aromatic core
alone and not of the disk including also the six sulfur atoms
6.3. Influence of Disorder: Comparison of Degenerate
and Nondegenerate States. We examine how off-diagonal
disorder affects Emax and the degree of localization of the exciton
states. For this purpose, columnar aggregates consisting of sixty
molecules are studied. We directly correlate off-diagonal
disorder to structural disorder, orientational and positional, by
changing the coordinates of the molecules within the aggregate.
The off-diagonal terms are calculated using the atomic transition
charge distribution model including long range interactions
without taking any dielectric constant into account.
(
10 Å). This value of 7.2 Å is much longer than the distance
between the barycenters of the positive and negative charges
3 Å) associated to the degenerate S0 f S4 transition from
(
quantum chemistry calculations (section 3.2.2). When l de-
creases, the exciton coupling increases (eq 5), and consequently,
Emax increases. Moreover, the exciton band becomes more
symmetric (Table 4) showing that the “symmetry” of the exciton
band depends not only on the number of interacting chro-
mophores but also on their “size”.
The effect of diagonal disorder on Emax is only briefly
discussed because we cannot correlate diagonal disorder to
structural disorder. As explained in section 3.2.1, the interaction
energy among triphenylene chromophores is governed by

Alkylthiotriphenylene Columnar Phases
J. Phys. Chem. B, Vol. 102, No. 24, 1998 4707
TABLE 4: Energy of the Upper Eigenstate Emax and “Symmetry” of the Exciton Band Emax/(Emax - Emin) Calculated Using
Different Levels of Approximationa
max /cm-
1
E
max/(Emax - Emin)
approximation
E
nearest neighbor interactions
long-range interactions
long-range interactions, ꢀn(n+i) ) 2.5 for all i
long-range interactions, ꢀn(n+i) ) 2.5, for i > 1
9926
11896
4758
0.50
0.57
0.57
0.53
point dipole
10713
nearest neighbor interactions
long-range interactions
long-range interactions, ꢀn(n+i) ) 2.5 for all i
long-range interactions, ꢀn(n+i) ) 2.5, for i > 1
2290
3559
1424
2797
0.50
0.66
0.66
0.57
atomic transition
charge distribution
long-range interactions/l ) 3 Å
long-range interactions/l ) 7.2 Å
long-range interactions/l ) 10 Å
8285
3560
2228
0.59
0.68
0.74
extended dipole
a
E
min denotes the energy of the lowest eigenstate. ꢀn(n+i): dielectric constant used in the calculation of the exciton coupling for the chromophores
n and n + i; its value is reported only when it is different than one. Columnar aggregates consist of 60 H1TT molecules and have the geometrical
characteristics of the helical H phase. Degenerate transition (µ ) µ ) 6.8 D).
1
2
transitions, changes in θ have only a weak effect on Emax, lower
-
1
than 250 cm (Table 5). In the case of degenerate transitions,
the variations of Emax are equal to 5%. When the extended
dipole model is used instead of the atomic transition charge
distribution model, the magnitude of these variations depends
on the dipole length. They are 2%, 13%, and 19% when l is
equal to 3, 7.2, and 10 Å, respectively.
For degenerate molecular states, the oscillator strength is
always born by the upper eigenstate whereas, for nondegenerate
ones, absorption toward the five highest eigenstates may be
important. The variation of the localization index Lk (section
3
.2.3) found for the eigenstates of helical aggregates as a
function of θ is presented in Table 5. In the case of degenerate
molecular transitions, we found that, whatever the θ value, the
upper eigenstate is always largely delocalized (Lk,abs ) 43). The
other eigenstates are also extended; their Lk values range
between 37 and 47. In the case of nondegenerate transitions,
high values of Lk,abs (43) are also found for θ ) 0°; the minimum
Lk,abs value (28) is obtained for θ ) 45°. It is worth noticing
that, for θ ) 90,° despite the absence of nearest neighbor
interactions, many of the eigenstates are largely delocalized as
predicted in ref 5.
Figure 13. Energy of the upper eigenstate (Emax) of columnar helical
aggregates of H1TT (N ) 60) as a function of the angle θ. Exciton
coupling is calculated according to the atomic charge distribution model
including long range interactions. Closed circles: degenerate transition
(
D).
µ
1
) µ ) 6.8 D). Open circles: nondegenerate transition (µ ) 9.6
2
dispersion forces which cannot be calculated with acceptable
accuracy for the excited states. Therefore, diagonal disorder is
simulated by setting random numbers directly to the diagonal
terms of the Hamiltonian matrix. The two types of disorder
are studied separately. When off-diagonal disorder is studied,
the diagonal terms are zero, whereas when diagonal disorder is
introduced, we consider aggregates having the geometrical
configuration of the helical H phase.
We tested the effect of orientational disorder by attributing
random values to the angles θ. For degenerate transitions, the
Emax values are located within the range of Emax found for helical
aggregates (Table 5) and the variations are small (3635 ( 20
-1
cm ). For nondegenerate transitions, the position of the upper
-
1
eigenstate varies between 4400 and 6000 cm . For nonde-
generate states, the localization index decreases significantly,
now ranging from 1 to 25. For degenerate states, the eigenstates
located in the upper part of the exciton band remain largely
delocalized (Table 5).
Figure 13 illustrates the dependence of Emax on the θ angle
of a helical stack for degenerate and nondegenerate transitions.
The difference between the two patterns is quite striking. For
nondegenerate transitions, changes in θ may induce variations
-
1
on Emax as large as 5700 cm , whereas for degenerate
The results summarized in Table 5 clearly show that the
TABLE 5: Influence of Orientational Disorder on the Energy (Emax) of the Upper Eigenstate and the Localization Index (L
the Eigenstates
k
) of
type of
molecular transition
chromophore orientation
around the column axis
max/cm-
1
L
k,abs
a
L
k
a
E
helical
random
[3550-3750]
[3615-3655]
43
43
[37-47]
[37-48]
degenerate
helical
[1750-7450]
28 (θ ) 45°)b
43 (θ)0° or 90°)
10
[28-47]
b
nondegenerate
random
[4400-6000]
[2-25]
a
From eqs 8 and 9. b θ: angle between neighboring chromophores ranging from 0° to 360°. In helical aggregates, all angles θ are identical.
c
L
k,abs denotes the localization index of the eigenstate bearing the oscillator strength. Columnar aggregates consisting of 60 H1TT molecules. The
coupling is calculated according to the atomic transition charge distribution model including long-range interactions without considering any dielectric
constant.

4708 J. Phys. Chem. B, Vol. 102, No. 24, 1998
Marguet et al.
TABLE 6: Comparison between Experiment and Theoryf
properties (Emax and Lk) of eigenstates built on degenerate
molecular states are not very sensitive to off-diagonal disorder
induced by orientational structural disorder. Indeed, when the
molecular transitions are degenerate, there are four exciton
interactions for each molecular pair. When the angle θ changes,
two of them decrease while the two others increase, compensat-
ing each other.
compound
HO5T (D
h
) H6TT (K) H6TT (H) H6TT (D
h
)
H6TT (I)
∆
∆
Ea
2000
1600
1250
1050-800
-1050
2100-1850
350
-900
1250
E
solv
-900
-900
E
E
exc
2900c
2150d
b
max
3300
e
3550
Focusing on helical aggregates (θ ) 45°), we examine the
influence of the stacking distance d (positional disorder) on the
eigenstate properties. When the stacking is regular (d constant
between 3.4 and 3.8 Å), Emax varies quasi linearly with d. A
a
From section 5. b Calculated according to the atomic transition
charge distribution model including long-range interactions without
c
taking any dielectric constant into account (N ) 60). Hhelical
d
aggregates (θ ) 30°), molecular transition moment ) 9.2 D. Helical
-
1
e
0
.1 Å increase of d leads to a decrease of Emax by ca. 150 cm
aggregates (θ ) 45°), molecular transition moment ) 9.6 D. Emax is
for degenerate or nondegenerate transitions. It is worth stressing
that the influence of the stacking distance on Emax greatly
depends on the model used in the calculation of the exciton
coupling. For example, the variation calculated in the point
dipole approximation are 7 times larger than that calculated in
the atomic transition charge distribution approximation; a 0.1
not calculated for K because the structure is not columnar but
monoclinic.15 ∆E is the difference in the absorption maxima of neat
phases and n-heptane solutions. ∆Esolv is the energy difference of the
f
molecular S
exc ) ∆E - ∆Esolv. Emax is the calculated energy of the upper
eigenstate.
0 4
f S transition in neat phases and n-heptane solutions.
E
-
1
In general, ∆Esolv cannot be determined experimentaly and many
authors consider that it is equal to zero.
In the particular case of triphenylene chromophores we can
evaluate ∆Esolv by observing the position of the absorption band
Å increase of d leads to a decrease of Emax by ca. 1000 cm
both for degenerate or nondegenerate transitions. This happens
because, in point dipole approximation, the coupling varies as
3
1
/R , whereas, in the atomic transition charge distribution model,
1
1
corresponding to the localized S state. First, we found that
it varies as 1/R at short distances.
-
1
this band is shifted only 50 cm upon the H f Dh phase
transition of H6TT with no further shift over the whole
temperature domain of the Dh phases (section 5). This means
that orientational and positional disorder do not affect signifi-
cantly the excitation energy. Second, the position of the
localized S0 f S1 transition in the columnar phases is red-shifted
If the stacking is not regular and d varies randomly between
.4 and 3.8 Å, it induces only small variations of Emax, 1.5%
3
with respect to the value found for d ) 3.6 Å. For the same
positional disorder as above, the changes of Emax are much larger
(15%) if the coupling is calculated in the point dipole ap-
proximation. This type of positional disorder does not affect
the localization index.
-1
by ca. 300 cm with respect to its position found for n-heptane
solutions. Third, the maximum solvatochromic shift observed
for S0 f S4 of both H5OT and H6TT is three times larger than
that found for S0 f S1 (section 4). Consequently, we estimate
With regard to diagonal disorder, we limited our study to
only one type of calculation. We varied the diagonal terms by
introducing random numbers ranging between -500 and 500
-
1
0 4
that the ∆Esolv for S f S corresponding to a given columnar
cm . These energy fluctuations correspond to the width of
the absorption band associated to the localized S0 f S1 transition
observed for the columnar H phase of H6TT (Figure 6). We
found that in the presence of such diagonal disorder Emax is
phase is about 3 times the ∆Esolv for S0 f S1. These values,
-
1
around 1000 cm (Table 6), are not negligible compared to
the observed spectral shifts ∆E.
-
1
The values of ∆E, ∆Esolv, and Eexc obtained from the eq 9
slightly blue-shifted. This shift is less than 100 cm for
-1
for the D phase of H5OT and three neat phases of H6TT are
degenerate molecular states and somewhat higher (ca. 200 cm )
for nondegenerate states.
h
gathered in Table 6. The Emax values presented in the same
table were calculated according to the atomic transition charge
distribution model including long-range interactions without
taking any dielectric constant into account. We considered
helical aggregates having the structural characteristics of the
columns in the corresponding phases. In order to check any
possible intercolumnar interaction, we calculated Emax for two
parallel aggregates located at 20-22 Å (intercolumnar distance
in the neat phases) from each other. We obtained the same
Emax value as for a single aggregate. Thus, the systems studied
can be viewed as one-dimensional regarding to the eigenstate
energy. The length of the columns is at least equal to the
correlation length determined by X-ray diffraction measure-
ments. The latter corresponds to 80 molecules for the Dh phase
7
. Comparison between Experiment and Theory
Among the various calculated eigenstate properties, the only
one which can be compared to an experimental observable is
the energy of the upper eigenstate. We showed in section 6.2
that for degenerate molecular states, the oscillator strength is
born by the upper eigenstate. Therefore, Emax is to be related
to the maxima of absorption spectra. We cannot perform correct
line shape analysis because the absorption bands of the neat
phases are artificially broadened due to the nonuniform optical
pathlength in very thin films. This apparent spectral broadening
will be described quantitatively in a forthcoming communica-
tion.43
44
H5OT, to 220 molecules for the H phase of H6TT, but only
In section 5, we denoted by ∆E the difference in the
absorption maxima of neat phases and n-heptane solutions. ∆E
can be decomposed in two terms:
16
to four to eight molecules for the Dh phase of H6TT.
Therefore, the Emax values in Table 6, calculated for large
aggregates, are given only for the Dh phase H5OT and H phase
of H6TT.
∆
E ) Eexc + ∆Esolv
(10)
We remark in Table 6 that the values of Eexc and Emax found
-
1
for the Dh phase H5OT (2900 and 3300 cm , respectively)
are quite close. The 15% difference could be associated with
the evaluation of ∆Esolv and the determination of the molecular
transition moment through the fitting procedure described in
section 4. As a matter of fact, an error of 10% in the
determination of the transition moment from the experimental
where Eexc is the pure exciton shift which has to be compared
to Emax. ∆Esolv is the difference in the energy of the localized
S0 f S4 transition of the studied triphenylene derivatives in
n-heptane solution and in their neat phases, due to different
intermolecular forces in these two different local environments.

Alkylthiotriphenylene Columnar Phases
J. Phys. Chem. B, Vol. 102, No. 24, 1998 4709
absorption spectra (Table 2) induces an error of ca. 20% in Emax
experimentally observed for the Dh phase of the oxygen
derivative, is in good agreement with the value calculated using
the atomic charge transition model without taking any dielectric
constant into account (15% error). The agreement is not as
good for the columnar phases of H6TT (70% error), possibly
because of interactions between Frenkel excitons and charge-
transfer excitons.
(section 3.2.2). In the case of H6TT helical phase, Emax exceeds
Eexc by 70%. The position of Emax may be affected by
interactions between Frenkel excitons and charge-transfer ex-
2
9,30,45
citons,
neglected in our analysis of the exciton states. It
would not be surprising that these interactions are stronger for
H6TT compared to those of H5OT since charge transport in
4
6
columnar phases is more efficient for the sulfur derivative.
The effects of off-diagonal on the energy of the upper
eigenstate and the degree of localization were also examined.
We correlated off-diagonal disorder to structural disorder
(orientational and positional) simulated by changing the coor-
dinates of the molecules within the aggregate. Orientational
disorder was found to have a dramatic effect on the energy and
the localization extent of the upper eigenstate when it is built
on nondegenerate states. In contrast, when the molecular states
are degenerate, the eigenstate properties are practically almost
unaffected by orientational disorder. For both types of molec-
ular states, positional disorder has only a weak influence on
the previously cited properties. The magnitude of the off-
diagonal disorder induced by positional disorder was shown to
depend largely on the model used in the calculation of the
exciton coupling. The results of numerical calculations are in
agreement with the experimental observations since, the absorp-
tion maxima of H6TT columnar phases hardly change upon the
H f Dh phase transition inducing orientational and positional
disorder.
Eexc remains practically the same in both phases of H6TT
Table 6) being insensitive to the rotational and positional
(
disorder. This behavior is in agreement with the results of our
numerical calculations which revealed that this disorder does
not affect the energy of the upper eigenstate, provided that it is
built on degenerate molecular states. The Eexc of the Dh phase
decreases slightly with increasing temperature; it has 90% of
its initial value near the Dh f I transition. The correlation length
of the columns being quite small for the Dh phase, it is possible
that a temperature increase reduces the physical length of the
columns. Figure 10 suggests that a 10% decrease in the Emax
may be due to a reduction of the aggregation number from N
g 100 to 12. Finally, the value of Eexc in the isotropic phase
-1
is still quite large (1250 cm ) indicating that even though long
range order is lost in this phase, aggregates consisting of a few
molecules (N ) 3-4 according to Figure 10) persist. This
finding is corroborated by the fluorescence spectra of the
isotropic phase which resemble those of the Dh phase (Figure
7
) and not of the solutions (Figure 3).
This experimental and theoretical study of discotic triphen-
ylenes allows us to draw general conclusions and foresee future
developments. (i) The prediction of the absorption maxima
corresponding to collective excited states is highly improved
when the exciton coupling is calculated within the atomic charge
distribution model. It would be interesting to extend this method
to other systems which offer a larger number of observables
which can be compared with the results of numerical calcula-
tions. Such observables may be the absorption line shape and
also fluorescence related to exciton band (J-aggregates, phthalo-
cyanine columnar phases, etc.). (ii) Our work showed that the
degeneracy of molecular excited states make collective states
much less sensitive to structural disorder. The question arises
whether the same lack of sensitivity exists for other properties,
like energy and charge transport, when degenerate states are
involved. A study of excitation hopping, using Monte Carlo
simulations, is underway.
8
. Summary and Conclusions
The main findings of the present work, where the properties
of hexaalkylthiotriphenylenes were studied and compared to
those of hexaalkyloxytriphenylenes, can be summarized as
follows.
First, the isolated chromophores were studied. The properties
of the lowest singlet excited states were calculated by the CS-
INDO-CIPSI method. The results of these calculations showed
that the absorption maximum corresponds to the degenerate S0
f S4 transition whereas the lowest energy transition S0 f S1
is symmetry forbidden. The absorption spectra of solutions were
decomposed according to a model of vibronic progressions and
the energy and the transition dipole moments of the four lowest
transitions were determined. This spectral analysis revealed that
the theoretically forbidden transitions of the thio derivative have
larger dipole moments than those of the oxygen derivative. The
fluorescence of the neat phases is attributed to weakly bound
excimers. The most striking result is that the oscillator strength
related to the lowest excited state increases by 40% when the
liquid crystalline Dh phase is formed. This behavior is observed
only for the thio derivative.
Acknowledgment. This work has been performed within
the framework of COST D4 Action (Project D4/0004/93). We
thank Pr. H. Ringsdorf (University of Mainz, Germany) who
initiated the synthesis of the studied compounds.
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