Electronic and vibronic contributions to two-photon absorption in donor-acceptor-donor squaraine chromophores

Article abstract of DOI:10.1002/chem.200801055

Many squaraines have been observed to exhibit two-photon absorption at transition energies close to those of the lowest energy one-photon electronic transitions. Here, the electronic and vibronic contributions to these low-energy two-photon absorptions ar

Full text of DOI:10.1002/chem.200801055

DOI: 10.1002/chem.200801055
Electronic and Vibronic Contributions to Two-Photon Absorption in
Donor–Acceptor–Donor Squaraine ACTHNUGRTENUNGChromophores
Shino Ohira, Indranil Rudra, Karin Schmidt, Stephen Barlow, Sung-Jae Chung,
Qing Zhang, Jon Matichak, Seth R. Marder, and Jean-Luc Brꢀdas*[a]
Abstract: Many squaraines have been
observed to exhibit two-photon absorp-
tion at transition energies close to
those of the lowest energy one-photon
electronic transitions. Here, the elec-
tronic and vibronic contributions to
these low-energy two-photon absorp-
tions are elucidated by performing cor-
related quantum-chemical calculations
on model chromophores that differ in
their terminal donor groups (diarylami-
nothienyl, indolenylidenemethyl, dime-
thylaminopolyenyl, or 4-(dimethylami-
no)phenylpolyenyl). For squaraines
with diarylaminothienyl and dimethyl-
longer examples of 4-(dimethylamino)-
phenylpolyenyl donors, the calculated
energies of the lowest two-photon
active states approach those of the
lowest energy one-photon active (1Bu)
states. This is consistent with the exis-
tence of purely electronic channels for
low-energy two-photon absorption
(TPA) in these types of chromophores.
On the other hand, for all squaraines
donors, the calculations indicate that
there are no low-lying electronic states
of appropriate symmetry for TPA. Ac-
tually, we find that the lowest energy
TPA transitions can be explained
through coupling of the one-photon ab-
sorption (OPA) active 1Bu state with bu
vibrational modes. Through implemen-
tation of Herzberg–Teller theory, we
are able to identify the vibrational
modes responsible for the low-energy
TPA peak and to reproduce, at least
qualitatively, the experimental TPA
spectra of several squaraines of this
type.
containing
indolinylidenemethyl
Keywords: chromophores · nonlin-
ear optics · squaraines · two-photon
absorption · vibronic coupling
ACHTUNGTRENNUNGaminopolyenyl donors and for the
Introduction
with various structural motifs, including donor–acceptor–
donor (D-A-D) conjugated chromophores. Among this class
of chromophores, the linear and nonlinear optical properties
of D-A-D squaraines (also known as squarylium dyes) con-
sisting of two electron-donor terminal groups (D) and a cen-
tral electron-poor 1,3-disubstituted C4O2-unit (A) have been
extensively studied, because of their narrow and intense
one-photon absorption (OPA) bands and large real and
imaginary third-order non-linear optical (NLO) respons-
es.[7–22]
Organic materials with large two-photon absorption (TPA)
cross sections (d) are of interest due to potential optical,
materials fabrication, and biological applications.[1–6] High
TPA cross sections have been observed for chromophores
High TPA cross sections ranging from 750[13] to
33000 GM[16] (1 GM [Goeppert-Mayer]=10ꢀ50 cm4 sꢀ1 per
photon) have been measured at photon energies close to the
OPA edge for a variety of squaraines. Assuming centrosym-
metric conformations,1 this corresponds to excitation to a
[a] S. Ohira, Dr. I. Rudra, Dr. K. Schmidt, Dr. S. Barlow,
Dr. S.-J. Chung, Dr. Q. Zhang, J. Matichak, Prof. S. R. Marder,
Prof. J.-L. Brꢀdas
School of Chemistry and Biochemistry and
Center of Organic Photonics and Electronics
Georgia Institute of Technology, Atlanta
Georgia 30332–0400 (USA)
Fax : (+1)404-894-7452
E-mail: jean-luc.bredas@chemistry.gatech.edu
1
Even though, as discussed in the results and discussion section, squar-
aine compounds can adopt several non-centrosymmetric conformations,
the behavior of their excited states typically remains strongly reminis-
cent of the properties of strictly ungerade and gerade states found in
the centrosymmetric conformers; this is particularly true for extended
molecules. We have, therefore, referred to all excited states assuming
inversion symmetry, that is, as (one-photon active) Bu or (two-photon
active) Ag states, even if the structure of a particular conformer devi-
ates from centrosymmetry.
Supporting information for this article is available on the WWW
under http://dx.doi.org/10.1002/chem.200801055. It contains the com-
plete synthetic procedures and characterization data for the new
squaraine compounds 2, 7, and 8, the details of the TPA measure-
ments, and the details of the quantum-chemical calculations
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FULL PAPER
singlet Ag state referred to here as peak 3 (see Figure 1 for
general peak labeling). Some of these cross sections are re-
markably large, even when normalized for the number of p
at energy similar to the lowest OPA active state in an exam-
ple of a squaraine in which the donors are substituted pyr-
roles with extended conjugation, with cross sections of 800
and 1600 GM at photon wavelengths of 1.3 and 1.5 mm, re-
spectively.[16] Despite the cross section of peak 2 typically
being considerably lower than that of the near-resonant
state (peak 3), peak 2 can be of importance for optoelec-
tronic applications, since, depending on the molecular struc-
ture, this absorption is located close to or within the tele-
communications band of the near-infrared (1.30–1.55 mm).
TPA in this region can potentially be exploited for applica-
tions such as all-optical beam stabilization and dynamic
range compression, while the presence of a TPA-allowed
state close to this region will affect the telecommunication-
band dispersion of the real part of the third-order polariza-
bility g, which can be exploited for all-optical switching.
To take full advantage of such TPA in the near-IR region,
it is important to better understand the origin of the associ-
ated excited state. However, previous quantum-chemical
studies on such compounds have considered only purely
electronic channels for TPA and have neither addressed the
nature of this state in detail nor been successful in reproduc-
ing the small energetic separations observed between peak 1
(the OPA peak) and peak 2, that is, in general <0.2 eV.[17–20]
Rather than assigning peak 2 to a low-lying electronic state,
Scherer et al. proposed an alternative origin for peak 2,[13]
suggesting the possibility of vibronic coupling between the
first excited electronic 1Bu state and vibrational modes of bu
symmetry. Furthermore, the presence of both centroymmet-
ric and non-centrosymmetric conformational isomers, which
is supported by NMR experiments for certain squar-
aines,[21,23] has also been put forward as an explanation for
the closely spaced peaks 1 and 2;[20,21] in this case, peak 2
would primarily originate from the lowest electronic excited
state, that is, a strongly OPA active state, of the non-centro-
symmetric conformers. In such non-centrosymmetric con-
formers, the OPA active state is not of strict ungerade (i.e.,
Bu) character and can, therefore, in principle, exhibit a non-
zero TPA cross section due to TPA through purely electron-
ic channels. The observed energetic offset between the OPA
peak 1 and TPA peak 2 signals could then potentially be at-
tributed to somewhat different OPA state energies for cen-
trosymmetric and non-centrosymmetric conformers.2
Figure 1. Illustration of the one-photon (light line) and two-photon (bold
line) absorption processes in squaraines. Left: Sketch of the absorption
spectra of squaraines. Middle: peak 2 is purely electronic. Right: peak 2
has the same electronic nature as the 1Bu state.
electrons in the molecules, and originate largely from reso-
nance enhancement, that is, from the appropriate photon
energy closely approaching the one-photon transition
energy.[16] It is worth pointing out that is possible to observe
the effects of resonance enhancement, that is, to probe TPA
with excitation energies very close to the OPA transition,
due to the remarkably sharp OPA absorption edge. Howev-
er, in squaraines with indolinylidenemethyl donor groups, in
addition to the strong high-energy TPA state, there is evi-
dence for another TPA state (referred to here as peak 2) at
state energy similar to that of the lowest energy OPA transi-
tion; this lower energy TPA then occurs with maxima in the
near-infrared spectral region at photon wavelengths of 1.1–
1.4 mm, with cross sections ranging from 45[15] to 500 GM[13]
(this is shown below for the new compound 8 in Figure 2).
Recently, we have also found a low-energy TPA active state
Thus, there can be three possible origins for the lowest-
energy TPA active state in squaraines: 1) peak 2 is primarily
of electronic nature and due to TPA into the lowest OPA
excited states of noncentrosymmetric conformers; 2) peak 2
is primarily electronic in nature and arises from a TPA-al-
lowed 2Ag state close in energy to the OPA-allowed 1Bu; or
3) the state corresponding to peak 2 has the same electronic
nature as the OPA 1Bu state, but acquires cross section due
to vibronic coupling (non-zero coupling of 1Bu state to
higher lying Ag states (Figure 1) through bu modes). In the
Figure 2. OPA spectrum of 8 (solid line) compared with a degenerate
TPA spectrum from Z-scan measurements (open squares, dotted line)
and with nondegenerate TPA spectra acquired using the WLC method
with pump wavelengths of 1180 and 1600 nm (solid circles, dot-dash line
and open triangles, dashed line, respectively). All data were acquired in
CH2Cl2 solution.
2
Moreover, the TPA maximum is typically shifted towards higher ener-
gies with respect to the corresponding OPA maximum, since Franck–
Condon coupling can redistribute TPA cross section from the (0–0)
into the (0–1) vibrational transition.[22]
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J.-L. Brꢀdas et al.
third scenario, the electronic sum-over-states model must be
extended to account for vibronic coupling. In the linear cou-
pling regime, this can be achieved by applying Herzberg–
Teller (HT) theory.[24]
theoretical analysis of the possibility of low-lying electroni-
cally allowed TPA states in the different types of squaraines
under consideration. Finally, we investigate how vibronic
coupling of the lowest OPA state to antisymmetric vibra-
tional modes can give rise to low-energy TPA in squaraines
with indolinylidenemethyl donors.
In this contribution based on joint theoretical and experi-
mental studies, we seek to provide insight into various struc-
tural aspects of squaraines that can lead to a peak 2 absorp-
tion in their TPA spectra through one of the three different
origins described in the previous paragraph or a combina-
tion thereof. Here, we consider a series of squaraines with
different terminal donor groups. To ease the systematic
study of their TPA spectra, the squaraines we have experi-
mentally studied have been classified into different groups
depending on the nature of their terminal groups:
Results and Discussion
Two-photon spectra: The TPA spectra for 4, 5, and 6 have
previously been acquired by using Z-scan and two-photon-
induced fluorescence methods,[13,15] while the positions of
peaks 2 and 3 in the TPA spectrum of 3 have been obtained
from the spectral dispersion of third-harmonic generation.[18]
The three group II squaraines, 3–5, are all reported to show
OPA (peak 1) at a state energy of 1.95 eV, a low-energy
TPA peak (peak 2) at approximately 2.1 eV, and a strong
TPA peak (peak 3) at higher energy (3.0 eV for 4 and 5 and
3.3 eV in the case of 3, for which the maximum is only im-
precisely determined).3 The previously studied type-III
squaraine 6 shows OPA and TPA spectra qualitatively simi-
lar to the group II examples, but with all excited states ob-
served at slightly lower energy. The new compounds 2, 7,
and 8 were synthesized as described in the Supporting Infor-
mation; degenerate and non-degenerate two-photon spectra
were acquired by the group of Prof. E. W. Stryland at the
University of Central Florida using the open-aperture fs Z-
scan technique[25,26] and the white-light continuum (WLC)
pump-probe method.[27] The TPA spectra for compound 8
are shown in Figure 2, while those for 2 and 7 are given in
the Supporting Information (S2-1 and S2-2). As shown in
Figure 2, the WLC data afford larger cross sections than the
Z-scan data; these cross sections increase as the wavelength
difference between pump and probe is increased, as expect-
ed from pre-resonance enhancement effects.[28] Compound 2
shows no clear maximum in the high-energy TPA feature
(peak 3); however, the data suggest a degenerate TPA peak
cross section of at least 1300 GM at a detuning energy of
less than 0.25 eV (the detuning energy corresponds to the
difference between the OPA energy and the fundamental
photon energy). Compounds 7 and 8 show high-energy TPA
maxima (peak 3) with degenerate cross sections of 3000–
4000 GM at detuning energies of about 0.4–0.5 eV. All three
compounds show low-energy TPA peaks (peak 2) with
maxima at state energies some 0.13–0.14 eV higher in
energy than the OPA maxima (peak 1) with non-degenerate
TPA cross sections of a few hundred GM (degenerate TPA
cross sections would be anticipated to be somewhat small-
er). The OPA and TPA spectra for 7 and 8 closely resemble
those for the other group III squaraine previously reported
by Scherer et al., compound 6, in terms of detuning energies
and TPA cross sections, the main difference being that the
1) Group I consists of squaraines with diarylaminothienyl
donors, new compound 2 and model compound 1.
2) Group II consists of squaraines 3–5 (4 being used as a
model for 5), in which the N-alkylation of indolinylide-
nemethyl donors is varied.
3) Group III consists of 6 and new compounds 7–8, in
which the role of attaching additional p-conjugated
groups to the 5-position of indolinylidenemethyl donors
is investigated.
4) On the theoretical side, we also consider the hypothetical
compounds of group IV, in which the effect of increasing
the p-conjugation length (n=1–4) between the terminal
donor and central acceptor units are studied in the
model dimethylaminopolyenyl and 4-(dimethylamino)-
phenylpolyenyl-substituted squaraine series 9-n and 10-n.
The TPA spectra of compounds 2, 7, and 8 are reported
for the first time, while TPA spectra for 3–6 can be found in
the literature.[13,15,18]
This paper is structured as follows. First, we describe the
TPA spectra available for the compounds investigated here.
We then discuss the results of computational studies on the
effect of molecular conformation on the TPA spectra, focus-
ing on the possibility of TPA into the lowest lying OPA
state of non-centrosymmetric conformers. We turn next to a
3
An additional high-energy TPA peak was observed for 4 at about
3.5 eV.[15] In another example of a group II squaraine (R1 =Me, R2 =H)
only the high-energy range was studied; however, peak 1 and 3 energies
were similar to those reported for 4 and 5.[22]
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Squaraine Chromophores
FULL PAPER
excited-state energies are consistently about 0.1 eV lower in
the present compounds.
Effect of coexistence of different conformers: We first stud-
ied the effect of molecular (centrosymmetric and non-cen-
trosymmetric) conformations on the TPA spectra of squar-
aines, in order to investigate the likelihood that the experi-
mentally observed lowest lying two-photon active peaks,
that is, peak 2, could be attributed to purely electronic TPA
into the lowest lying one-photon state of non-centrosymmet-
ric conformers. Among the investigated squaraines, we
found that, in general, the approximately planar C2h/Ci cen-
trosymmetric (conformers i and iii) and the C2v/C2 non-cen-
donor and acceptor groups increase as the hydrogen atoms
are replaced by alkyl groups. As a result, 4’ is more stable
than 4’’ by 0.22 eV (equivalent to ꢁ2,500 K). On the other
hand, the energy difference between the two isomers of
squaraine 1 was computed to be negligibly small. Although
our calculations indicate that the non-centrosymmetric con-
formation iv and centrosymmetric conformation iii have
slightly higher energies compared to conformations ii and i
for squaraines 3 and 4, respectively, the possibility of isomer-
ic mixtures (i and iii or ii and iv) cannot be completely ruled
out in solution at ambient temperature. Thus, assuming that
solvation does not substantially affect the relative energies
of the conformers, squaraines 1, 3, and 4 are predicted to be
present at ambient temperature as a mixture; that is, 3 pre-
dominantly as the C2v/C2 conformer (mostly ii and probably
iv), 4 overwhelmingly as the C2h/Ci conformer (mostly i and
probably iii), and 1 as a mixture in which no particular con-
former is dominant. We now discuss the electronic structures
and TPA activity for these two conformers in squaraines 1,
3, and 4.
trosymmetric conformers (conformers ii and iv) are more
stable relative to conformations with a twisted p-systems4
and are, thus, likely to predominate at room temperature.
Among squaraines 1 (used as a model for experimentally
studied compound 2), 3 and 4, it is only in the case of 3 that
the non-centrosymmetric conformation (3’’; conformation ii)
is energetically more favorable than the centrosymmetric
conformer (3’; conformation i); the energy difference be-
tween the 3’ and 3’’ isomers calculated at the B3LYP/SV(P)
level is 0.06 eV (equivalent to ꢁ700 K). These results are in
agreement with those of the theoretical and experimental
work of Dirk et al.,[21] in which the larger stability of 3’’
compared to 3’ had been attributed to the formation of en-
ergetically more stable hydrogen bonds in 3’’ between both
of the indole-ring nitrogen atoms and the same carbonyl
oxygen atom of the central unit.
INDO/MRDCIS calculations (see Tables S3-2, S3-9 and
S3-11 in Supporting Information for details) suggest very
similar OPA and TPA spectra for both centro- and non-cen-
trosymmetric conformers of 1, 3, and 4. This is true irrespec-
tive of which isomers (i–iv) are considered (we present the
theoretical details for squaraine 4 in table S3–19 under Sup-
porting Information). In particular, the TPA cross section of
the lowest OPA active state, S1, remains negligibly small
In the case of squaraines 4’ (centrosymmetric) and 4’’
(non-centrosymmetric), the possibility for strong hydrogen
bonding is removed, while steric hindrance effects between
AHCTUNGTREGNUN(N <4 GM); therefore, purely electronic TPA channels into S1
in the non-centrosymmetric conformers can be ruled out as
a possible origin of peak 2. By taking squaraine conformers
3’ and 3’’ as representative examples, we can distinguish two
reasons for this absence of TPA-activity for the lowest OPA
state, despite the lack of an inversion center. Since 3’’ has a
non-zero static dipole moment, change of this dipole
moment upon excitation to the one-photon state could, in
principle, give rise to a non-zero TPA cross section. How-
4
Roughly planar geometries were observed in NMR experiments by
Dirk et al.[21] as well as in crystal structures obtained by Kobayashi
et al.[29] In the case of conformation i of squaraine 3, semiempirical
INDO/MRDCI calculations on the isolated molecule indicate that the
conformation with a twist of 10o is 0.12 eV higher in energy than the
fully planar conformation, suggesting the existence of mostly planar
structures.
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J.-L. Brꢀdas et al.
ever, the excited state in both squaraine conformers 3’ and
3’’ can be described principally as arising from a HOMO–
LUMO transition. The HOMO and LUMO of the molecule
(Figure 3) indicate rather little change in the spatial extent
squaraine 1 to model new com-
pound 2. The INDO/MRDCI
computed energies of the
lowest OPA and TPA active
states of 1 are 1.76 and 2.02 eV,
respectively, which are in good
agreement with the experimen-
tal peak 1 and peak 2 maxima
of 1.77 and 1.92 eV, respective-
ly, found for 2 (Figure 4). A
second TPA peak between 2.8
and 3.7 eV6 is consistent with
the experimental feature at
higher energy, which apparently
represents the tail of a TPA
feature with a maximum at a
state energy of approximately
3 eV or higher. It is interesting
to note that the lowest TPA
active state is quite close in
energy (calculated to be within
Figure 4. INDO/MRDCIS-cal-
culated state energies for two
conformers of 1. See Support-
ing Information for the experi-
mental spectra of 2.
0.26 eV) to the OPA active 1Bu state. We would like to
point out that a similar energy-level alignment of peak 2
(with TPA cross section less than 100 GM) with respect to
peaks 1 and 3 was calculated for some extended pyrrole-sub-
stituted squaraines[16] (see the Supporting Information of
reference [16], section on Details of Quantum Chemical
Calculations). The similar behavior of the compounds dis-
cussed in reference [16] to that of 1 and 2, in contrast to that
for group II and III squaraines (vide infra), thus suggests
that they can also be classified as group I compounds. Note
that, although the calculations suggest that peak 2 for this
group is principally electronic in origin, some contributions
from vibronic coupling cannot be ruled out. The model
squaraines of group IV also exhibit low-energy TPA active
states (see Figure 5). In general, the lowest TPA state falls
in energy with conjugation length more rapidly than the
OPA state.
Figure 3. Representation of the HOMO (highest occupied molecular or-
bital) and LUMO (lowest unoccupied molecular orbital) wavefunctions
for two conformations of 3, calculated at the DFT-B3LYP/SV(P) level.
of the electron-density distribution and, as a result, the
change in static dipole moment between the two states
(Dm01) is also quite small (ꢁ0.1 D), while the corresponding
transition dipole moment (M01) is large (ꢁ10 D). Consider-
ing the relation between Dm01, M01 and TPA cross section d
according to the two-state model for TPA into the 1Bu
state,[10,30–32] d/(Dm201M021)/
ACHTUNGTRENNUNG
damental photon energy), it can be easily understood why a
small Dm01 would result in a very small TPA cross section for
the first excited state of squaraine 3’’.
In contrast to groups I and IV, a TPA active electronic
state was not calculated to appear in the vicinity of experi-
mental peak 2 (i.e., close to peak 1) in the bis(indolinylide-
nemethyl) species of groups II and III. Instead, the calculat-
ed OPA state energies and the lowest electronic TPA active
state energies of the molecules were consistent with the ex-
perimental values for peaks 1 and 3, with two TPA states ap-
pearing in the vicinity of the experimentally observed
peak 3 (Figure 6). The energies of both transitions are
rather insensitive to alkylation on the indole nitrogen atoms
(4 vs. 3) and also to extension of conjugation at the 4-posi-
tion of the indole ring system in series III. The insensitivity
to extended conjugation reflects the lack of a direct conjuga-
tion pathway from the six-membered ring of the indole to
the squarylium acceptor; this can be seen from the localiza-
Possible electronic origin of lowest TPA state (peak 2): In
the previous section, we demonstrated that non-centrosym-
metric conformers do not exhibit significant TPA cross sec-
tions into S1, the lowest energy OPA state, through purely
electronic channels. Considering the close similarity of the
OPA and TPA spectra calculated for centro- and non-cen-
trosymmetric conformers, we will henceforth restrict our dis-
cussion to the centrosymmetric conformers.5
To find out whether structural modifications of the termi-
nal donor group can result in a TPA active electronic state
at the position of peak 2, we now turn to a systematic study
of the OPA and TPA spectra of squaraines belonging to
groups I, II, III, and IV. As in the previous section, we use
5
In the context of having multiple species (such as conformers) possibly
6
simultaneously present, it is worth noting that the existence of broken-
symmetry structures (in either ground or first excited states), analogous
to those seen in a few cyanines, can be ruled out due to the absence of
substantial solvatochromism in absorption or fluorescence spectra.[22]
Exact assignment of the TPA peak is made ambiguous due to the pres-
ence of multiple calculated TPA active electronic states in the higher
energy region of interest (see Tables S3–16, S3–17, and S3–18 in Sup-
porting Information for details).
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Squaraine Chromophores
FULL PAPER
tension of the molecules
beyond the primary donor
group cannot participate effec-
tively in the conjugation with
the core moiety and, thus, is not
able to sufficiently stabilize the
lowest TPA state to explain the
origin of peak 2.
Even though indole groups
block through-conjugation into
the thienyl and aminostyryl
substituents of the group III
chromophores, the actual structure of the terminal groups
nonetheless plays an important role in quantitatively deter-
mining the overall nonlinear optical properties. To get a
better quantitative understanding of the d values calculated
with the correction-vector method (CVM), see Table 1, we
Figure 5. INDO/MRDCIS-calculated state energies of 9 (left) and 10
(right) as a function of size of the polyenic segment.
Table 1. TPA cross-section values into the 3Ag state in 4 (top) and 8
(bottom) calculated with the correction vector method (CVM), dCVM, and
a three-state model, d3-state, with the corresponding three-state parameters
from MR-DCI calculations with singles.
E [eV]
m01 [D]
m12 [D]
d3-state [GM]
dCVM [GM]
1Bu
3Ag
1.76
2.86
13
5.6
4.0ꢂ105
2.8ꢂ103
E [eV]
m01 [D]
m12 [D]
d3-state [GM]
dCVM [GM]
1Bu
3Ag
1.74
2.89
15
7.1
1.1ꢂ106
7.7ꢂ103
also used the three-state model [Eq. (1)], which includes the
transition dipole moments between the initial and inter-
mediate states, m01, and between the intermediate and final
states, m12, and the transition energies E01 and E02 between
the relevant excited states and the ground state.
Figure 6. INDO/MRDCIS-calculated OPA and TPA state energies for
compounds 3–8 and experimental values for 3,[18] 4 and 6,[13] 5,[15] and 7
and 8 (see Supporting Information). For 3 and 4, the theoretical data are
obtained for two conformations while the same experimental data (which
refer to an equilibrium mixture of conformations) are plotted twice.
ꢀ
ꢁ
2
E02
E01ꢀE02=2
d3-state ꢂ m201 ꢃ m122
ꢃ
ð1Þ
From Table 1, it can be seen that both the simple three-
state model and CVM approach predict an increase in TPA
cross section into the 3Ag state (peak 3) with conjugation
length, that is, in going from 4 to 8. From the parameters en-
tering Equation (1), is it clear that this increase in d upon
extending the conjugated bridge is caused by an increase in
the transition dipole moments m01 and m12 and, to a much
lesser extent, by a slighly enlarged resonance enhancement
factor, E02/(E01ꢀE02/2). This calculated trend is in agreement
with experiment[15] as the cross section associated with the
second TPA peak (peak 3) is measured to be higher for 8
than for 5 (d=4000 and ꢁ750 GM,[15] respectively). It is im-
portant to note that the number of p-electrons has direct
impact on the nAg states (n>2), but relatively little effect
on the strength of peak 2, that is, transitions to the 2Ag
state. However, the significantly higher computational cost
associated with modeling the NLO properties of complexes
tion of the HOMO and LUMO (which are the key orbitals
involved in the lowest OPA and TPA transitions) in the cen-
tral unit between the two indole nitrogen atoms (Figure 3).
The insensitivity to extended conjugation in compounds of
group III can be contrasted to that in the group IV model
squaraines in which the terminal donor is in direct conjuga-
tion with the acceptor, as shown in Figure 5. The insensitivi-
ty of both peak 1 and peak 3 states to extension in group III
compounds is fully reproduced in D’-D-p-C4O2-p-D-D’-type
model structures. In a series of compounds constructed in
this way, 9-1, 11, and 12 (see also Figures S3-1 and S3-2 of
the Supporting Information for more details), the evolution
of the first and second TPA active-state energies remained
essentially independent of the length of p conjugation
beyond the primary donor group. Thus, a p-conjugation ex-
Chem. Eur. J. 2008, 14, 11082 – 11091
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11087

J.-L. Brꢀdas et al.
Table 2. Strongly coupled bu modes with their coupling strength between
the 1Bu and 2 Ag (=1Bu ꢂbu) state.
with such large numbers of p-electrons makes a quantitative
comparison between theory and experiment a challenging
task.
Mode No.
Frequency
[cmꢀ1
Adiabatic
G
]
coupling [cmꢀ1
]
The contribution of the donor group to the major molecu-
lar orbitals of the low-lying excited states determines the
electronic properties of the squaraines in groups I, II and
III. From our studies, we conclude that peak 2 in group I
squaraines can be attributed to an electronically TPA-al-
lowed state (2Ag) lying close in energy to the lowest energy
OPA state (although the possibility of additional vibronic
contributions cannot be ruled out). In contrast, the experi-
mentally observed peak 2 in squaraines from groups II and
III with indolinylidenemethyl donor fragments cannot be ex-
plained in terms of an electronic origin. We now turn to an
examination of the role of vibronic coupling.
99
1240
1362
1417
1493
1590
ꢀ566
ꢀ681
1161
510
ꢀ2098
107
113
123
131
Formation of a low-lying TPA active state (peak 2) due to
vibronic coupling: To obtain a physical insight into the
origin of peak 2 in group II and III compounds, we have ex-
plored vibronic coupling within Herzberg–Teller (HT)
theory as a possible mechanism. Note that, given the ap-
proximations related to the implementation of HT theory, it
is not expected that the absolute values of the TPA cross
sections computed by this means be quantitatively accu-
rate;[33] also, the experimental cross sections cannot directly
be compared in all cases to the calculated degenerate TPA
cross sections, since the experimental data for peak 2 in
some of the compounds are based on non-degenerate TPA
measurements. Nevertheless, a qualitative description of vi-
brational coupling can be achieved, in particular, since our
implementation of HT theory allows us to investigate the
relevance of the various vibrational modes and electronic
states in enabling TPA activity.
Due to the C2h symmetry of squaraine 3, only vibrational
modes of bu symmetry can mix with the OPA active 1Bu
state to result in a TPA active 2Ag state. Theoretically, vi-
brational modes of both bu and au symmetries can lead to
TPA transitions: Ag!Ag and Ag!Bg, respectively. Howev-
er, as pointed out by Scherer et al.,[13] one can rule out the
possibility that peak 2 is due to an Ag!Bg transition in cen-
trosymmetric squaraine molecules such as 4 from an analy-
sis of the polarization ratio (ratio of TPA cross sections in
circularly and linearly polarized light) obtained with the
two-photon fluorescence technique. Therefore, only bu vi-
brational modes are considered here in our study of the vi-
bronically allowed TPA process. From an examination of
the adiabatic vibronic coupling constants, we found that in
squaraine 3 very few (only 5 out of 48) bu normal modes
strongly couple the one-photon active 1Bu state with the
TPA active 3Ag state. We note that, although additional bu
modes could, in principle, strongly couple the 1Bu state with
higher lying nAg states, their contributions to the two-
photon cross section will be relatively small due to the
larger energy differences from the 1Bu state. Table 2 pro-
vides the adiabatic vibronic coupling constant values be-
tween the 1Bu and 3Ag states. We identified that mode 131
(illustrated in Figure 7) gives rise to a significantly higher
Figure 7. Schematic representation of the bu stretching mode 131 in 3
(top) and mode 159 in 4 (bottom); elongated [compressed] bonds are
shown with bold [dotted] line.
TPA cross section for the 1Ag!2Ag (=1Bu ꢂnbu) transition
than all the other bu modes. Table 3 demonstrates the effect
of vibronic coupling: the TPA transition 1Ag!2 Ag around
2.05 eV (dꢁ8 GM) is due to mode 131. According to our
calculations, the separation between 1Bu and 2Ag is 0.18 eV;
this is in very good agreement with the experimental differ-
ence in state energy between peak 1 and peak 2, especially
considering the approximations involved in our vibronic cal-
culation. It is interesting to note that mode 131 is also
strongly IR active.
Table 3. Electronic and vibronic contributions to TPA cross section
values in 3 (top) and 4 (bottom) computed at the B3LYP/SV(P)//INDO/
MR-DCI singles level, using the HT vibronic coupling model.
Peak
E [eV]
d
[a] [GM]
d[b] [GM]
1
2
3
1Bu
2Ag =1Bu ꢁbu
3Ag
1.87
2.05
2.89
–
–
122
–
7.61
N/A
Peak
E
d[a] [GM]
d[b] [GM]
[eV]
1
2
3
1Bu
2Ag =1Bu ꢁbu
3Ag
2.08
2.27
3.16
–
–
244
–
33.9
N/A
[a] Without HT coupling. [b] With HT coupling.
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Chem. Eur. J. 2008, 14, 11082 – 11091

Squaraine Chromophores
FULL PAPER
Figure 8. TPA cross-section values obtained at the B3LYP/SV(P)//INDO/
MR-DCI singles level using the HT vibronic coupling model (top) and
IR spectrum computed at the B3LYP/SV(P) level (bottom) for 4. Also
shown is the Gaussian convolution of the calculated TPA spectrum using
a FWHM of 5 meV.
Figure 9. Experimental IR spectrum of 4 in KBr (top) and IR spectrum
computed at the B3LYP/SV(P) level (bottom) for 4.
HT vibronic coupling was also investigated in squaraine 4.
Unlike squaraine 3, the centrosymmetric conformer of this
compound (4’) does not have C2h but Ci symmetry due to a
slight twist from planarity; thus, all the normal modes were
taken into account to compute the vibronic coupling. The
top panel in Figure 8 shows the TPA cross-section values
due to HT vibronic coupling in molecule 4. Although strictly
speaking the TPA active vibronic states do not have bu sym-
metry, we can get an indication from the IR spectrum (con-
sidering the correlation between strength of IR activity and
magnitude of vibronic coupling constant in squaraine 3) of
which modes could yield large TPA cross-section values
through HT vibronic coupling. We observe that the effect of
vibronic coupling on TPA cross section is significantly
higher in mode 159 (see Figure 7) compared to other
normal modes. As with squaraine 3, inclusion of vibronic
coupling in squaraine 4 leads to a predicted peak 2 that is
0.19 eV higher in state energy than peak 1; in this case, the
predicted TPA cross section is somewhat larger (34 GM).
Further analysis of mode 131 in squaraine 3 and mode 159
in squaraine 4 indicates that they both correspond to
stretching modes impacting the degree of bond-length alter-
nations; it is expected that the extent of bond-length alter-
nation can affect both IR intensity and vibronic coupling
strength (Figures 7 and 8).
puted frequencies are slightly overestimated relative to the
experimental values, as is typical for the method. There is
also an apparent discrepancy in the relative intensities of
different modes between the experimental and theoretical
spectra; in particular, in contrast to theory, the experimental
peak at 0.19 eV is not the most intense peak. However, it
should be noted that the 0.19 eV band is broader than all
the others in the experimental spectrum, while the theory
includes no broadening; when properly considering integrat-
ed oscillator strengths, the theoretical spectrum is in consid-
erably better agreement with experiment than a cursory in-
spection of peak intensities might suggest. Thus, overall, the
experimental and computational spectra are indeed in good
agreement.
Conclusion
We have shown that the origin of peak 2 in squaraines is de-
pendent on the nature of substituent donor moiety, changing
from predominantly electronic (e.g., in diarylaminothienyl
donors) to vibronic (e.g., in indolinylidenemethyl donors) in
character. For squaraines with diarylaminothienyl donors
(group I), the lowest TPA active electronic state (2Ag,
peak 2) is located close in energy to the 1Bu (peak 1) state,
thus providing a purely electronic channel for TPA into
peak 2 (although one cannot rule out additional contribu-
tions from vibronic coupling), which corresponds to the sce-
To demonstrate that the vibrational characteristics of
these molecules are computationally well-described, the ex-
perimental IR spectrum of 4 is shown in Figure 9. The com-
Chem. Eur. J. 2008, 14, 11082 – 11091
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11089

J.-L. Brꢀdas et al.
levels. Based on comparison of different methods we concluded that the
INDO/MRDCI method with single excitations (MRD-CIS) is both relia-
ble and computationally feasible for handling large CI active space re-
quired for the squaraines in our study. Details of the electronic and opti-
cal properties computed from all the methods discussed here are avail-
able in the Supporting Information.
nario on the middle in Figure 1. On the other hand, the
lowest electronic TPA active state (3Ag) is energetically
well-separated from the 1Bu state for all squaraines contain-
ing indolinylidenemethyl donors (groups II and III), which
corresponds to scenario on the right in Figure 1.
The possibility of a vibronic origin for peak 2 in group II
and III molecules was investigated by using an efficient im-
plementation of HT theory in conjunction with the ZINDO
Hamiltonian. These calculations confirmed the previous sug-
gestion of Scherer and co-workers[13] of a vibronic origin for
peak 2 in this class of chromophores. The experimental TPA
absorption peak 2 in compounds of groups II and III is
rather sharp, which suggests that only a few modes are
strongly coupled with the 1Bu state and dominate contribu-
tions to the TPA cross section. Our calculations confirm that
this is indeed the case for squaraine molecules containing in-
dolinylidenemethyl fragments and provide an explanation
for the energy and lineshape of the experimentally observed
peak 2 in these compounds.
Although using an ab initio TD-DFT based approach to compute the
TPA cross section in quadrupolar molecules like squaraines could be an
attractive alternative to an INDO/MRDCI-based approach, we are un-
aware of any successful attempt in the literature of such applications to
calculating the TPA of quadrupolar molecules. We note that the nonlin-
ear polarizabilities in TD-DFT-based approaches are often overestimat-
ed, which can be attributed to the lack of orbital-dependent terms in the
exchange correlation potential or self-interaction error.[54] Lately, there
have been some successes in the evaluation of the NLO properties of di-
polar molecules by using long-range correction schemes in the exchange-
correlation functional; however, further improvements would be required
to correctly reflect the multiple excitation character of the higher lying
excited states before such approaches can be applied to quadrupolar sys-
tems. Further details of the quantum-chemical calculations are available
in the Supporting Information.
Following an analysis of the vibrational frequencies obtained from DFT
calculations at the B3LYP/SV(P) level, the adiabatic vibronic coupling
constants were computed from a 25ꢂ25 Rumer basis MRD-CIS calcula-
tion using the ground-state HF determinant and two excited configura-
tions (HOMO!LUMO, HOMO!LUMO+1) as references. We incor-
porated the vibronic effect within the HT theory using the floating
atomic orbital (FAO) approach[55] in ZINDO. The FAO approach is
known to give much better convergence than the direct implementation
of HT expansion. The sparse matrix approach was implemented to
ensure efficiency. Details of the implementation in ZINDO and subse-
quent applications will be published elsewhere.[56]
Computational Details
All calculations were performed without consideration of solvent effects,
since centrosymmetric squaraines show only very slight solvatochromism
in both absorption and fluorescence spectra.[22] All squaraine geometries
were optimized at the DFT/B3LYP[34] level of theory using the SV(P)[35]
basis set, (equivalent to 6-31G* basis set) as implemented in the TUR-
BOMOLE package.[36–38]
In general, either the ground or intermediate or final electronic state
could couple with vibrational modes to contribute to the TPA cross sec-
tion. However, the only term relevant for the problem in hand is the per-
turbation of the final state (1Bu), for which the vibronically allowed part
of the tensor can be written as Equation (2):
Based on DFT-optimized geometries, the excited-state energies and
state- and transition-dipole moments were evaluated with the semiempir-
ical intermediate neglect of differential overlap (INDO) Hamiltonian[39,40]
coupled to a multireference determinant single and double configuration
interaction (MRD-CI[41] with singles (S) or singles and doubles (SD))
scheme by using the Mataga–Nishimoto potential to express the Cou-
lomb repulsion term.[42,43] As we use large CI active spaces for computa-
tional accuracy, MRD-CISD is computationally expensive for large sys-
tems. Hence, this method was only used for the smaller squaraines.
MRD-CIS was used to determine state energies of the squaraines 1–12.
In all the MRD-CIS and MRD-CISD calculations, Rumer CI diagrams
were generated from the reference closed-shell Hartree–Fock (HF)
ground-state determinant and four excited determinants: HOMOꢀ1!
LUMO, HOMO!LUMO, HOMO!LUMO+1, and (HOMO,
HOMO)!(LUMO, LUMO). The TPA cross-section values were com-
puted with either the perturbative sum-over-states (SOS) method of Orr
and Ward[44] (including the 300 lowest-lying states) or the correction
vector method (CVM).[45] The truncation to 300 states in the SOS
method can, in some cases, introduce an uncontrolled error.[45] Since this
problem is avoided in CVM, we use this approach to check the validity
of the SOS TPA cross-section values. While with the SOS method one
can take into account only a finite number of excited states due to the
large memory requirement of the calculations, in CVM, the TPA calcula-
tion requires only the lowest eigenvalue and eigenvector. Therefore, a
larger number of configurations compared with the SOS method can be
handled. We implemented Davidsonꢃs diagonalization algorithm[46] to
obtain the low-lying eigenvalues and eigenvectors of large CI matrices
which were then used in CVM for TPA cross-section calculations. The
size of the CI active space was increased until the first excited states con-
verged to their experimental values.
X
Vfjðma,gimb,ij þ ma,ijmb,gi
E0i ꢀE0gꢀꢀhw
Yi ðQÞjð@H=@Q0ÞjYj ðQÞ
Þ
g0,fv
a,b
S
¼ hcg0jQjcfvi
ij
ð2Þ
ꢂ
ꢃ
ꢀ 0
ꢀ 0
Vij
¼
ꢀ0 ꢀ0
Ej ꢀEi
in which the vibrational integral (hcg0 jQjcvf i)is calculated (in zeroth-order
approximation)[57] between the 0th vibrational wavefunction of the
ground state and nth vibrational wavefunction of the final state; ma,ij and
mb,ij are x, y, z components of the transition dipole moment between
¯
states i and j, and Vij is the vibronic coupling between states i and j (Y
¯
and E denote the wavefunction and energy in the FAO basis). The TPA
cross section, d, due to vibronic coupling was computed using the S-
tensor approach[58,59] for squaraines 3 and 4.
Acknowledgements
We are most grateful to Eric Van Stryland, David Hagan, Lazaro Padilha,
and Jie Fu from the University of Central Florida for graciously provid-
ing us with the experimental spectra for compounds 2, 7, and 8. We
thank DARPA for support through the MORPH program (Grant ONR
N00014-04-0095). The work at Georgia Tech has also been supported in
part by the National Science Foundation through the Science and Tech-
nology Center Program, under Award DMR-0120967, and the CRIF Pro-
gram, under Award CHE-0443564.
As it is essential in our study to obtain very accurate energies of low-
lying excited states, we used the ab initio size-consistent CIS(D)[47,48] (as
implemented in Q-Chem 3.0[49]), TD-DFT,[50–52] INDO/CCSD[53] (coupled
cluster singles and doubles) and INDO/CIS methods besides INDO/
MRDCI approach to investigate the nature of the low-lying energy
11090
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Chem. Eur. J. 2008, 14, 11082 – 11091

Squaraine Chromophores
FULL PAPER
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Received: May 30, 2008
Published online: October 29, 2008
Chem. Eur. J. 2008, 14, 11082 – 11091
ꢁ 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
11091