Spectroscopic characterization and modeling of quadrupolar charge-transfer dyes with bulky substituents

Article abstract of DOI:10.1021/jp3005508

Joint experimental and theoretical work is presented on two quadrupolar D-π-A-π-D chromophores characterized by the same bulky donor (D) group and two different central cores. The first chromophore, a newly synthesized species with a malononitrile-based acceptor (A) group, has a V-shaped structure that makes its absorption spectrum very broad, covering most of the visible region. The second chromophore has a squaraine-based core and therefore a linear structure, as also evinced from its absorption spectra. Both chromophores show an anomalous red shift of the absorption band upon increasing solvent polarity, a feature that is ascribed to the large, bulky structure of the molecules. For these molecules, the basic description of polar solvation in terms of a uniform reaction field fails. Indeed, a simple extension of the model to account for two independent reaction fields associated with the two molecular arms quantitatively reproduces the observed linear absorption and fluorescence as well as fluorescence anisotropy spectra, fully rationalizing their nontrivial dependence on solvent polarity. The model derived from the analysis of linear spectra is adopted to predict nonlinear spectra and specifically hyper-Rayleigh scattering and two-photon absorption spectra. In polar solvents, the V-shaped chromophore is predicted to have a large HRS response in a wide spectral region (approximately 600-1300 nm). Anomalously large and largely solvent-dependent HRS responses for the linear chromophores are ascribed to symmetry lowering induced by polar solvation and amplified in this bulky system by the presence of two reaction fields.

Full text of DOI:10.1021/jp3005508

Article
pubs.acs.org/JPCB
Spectroscopic Characterization and Modeling of Quadrupolar
Charge-Transfer Dyes with Bulky Substituents
Cristina Sissa,† Francesca Terenziani,† Anna Painelli,*,† Raja Bhaskar Kanth Siram,‡ and Satish Patil‡
†Dipartimento di Chimica GIAF and INSTM-UdR Parma, Universita
̀
di Parma, Parco Area delle Scienze 17/a, 43124 Parma, Italy
‡Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
S
* Supporting Information
ABSTRACT: Joint experimental and theoretical work is presented on two
quadrupolar D-π-A-π-D chromophores characterized by the same bulky donor
(D) group and two different central cores. The first chromophore, a newly
synthesized species with a malononitrile-based acceptor (A) group, has a V-
shaped structure that makes its absorption spectrum very broad, covering most
of the visible region. The second chromophore has a squaraine-based core and
therefore a linear structure, as also evinced from its absorption spectra. Both
chromophores show an anomalous red shift of the absorption band upon
increasing solvent polarity, a feature that is ascribed to the large, bulky structure of the molecules. For these molecules, the basic
description of polar solvation in terms of a uniform reaction field fails. Indeed, a simple extension of the model to account for two
independent reaction fields associated with the two molecular arms quantitatively reproduces the observed linear absorption and
fluorescence as well as fluorescence anisotropy spectra, fully rationalizing their nontrivial dependence on solvent polarity. The
model derived from the analysis of linear spectra is adopted to predict nonlinear spectra and specifically hyper-Rayleigh scattering
and two-photon absorption spectra. In polar solvents, the V-shaped chromophore is predicted to have a large HRS response in a
wide spectral region (approximately 600−1300 nm). Anomalously large and largely solvent-dependent HRS responses for the
linear chromophores are ascribed to symmetry lowering induced by polar solvation and amplified in this bulky system by the
presence of two reaction fields.
fluorescence spectrum is marginally affected by solvent polarity.
Several examples are known for class I dyes,19,28−30 while class
II dyes are comprised of the very interesting family of
squaraine-based dyes.23−25,28 Class III behavior has been only
recently recognized in cyanine dyes undergoing symmetry
breaking in polar solvents.31 The three-state model that
describes the spectroscopic behavior of quadrupolar chromo-
phores has been recently extended to account for bent
quadrupolar structures.32
In this paper, we present an extensive study of optical spectra
of the two quadrupolar dyes shown in Scheme 1. The two dyes
include a newly synthesized malononitrile derivative, 1, and a
squaraine-based dye, 2.33 In both cases, the D groups attached
to the central acceptor consist of the bulky 1,4-diethyl-2,3-
diphenyl-1,2,3,4-tetrahydroquinoxaline-6-carbaldehyde group.
Absorption spectra of both dyes show an anomalous
solvatochromism that cannot be reconciled with the standard
models for quadrupolar dyes,28,32 calling for the definition of a
new model. Specifically, we will extend the standard model for
quadrupolar dyes to account for two solvent cavities, in line
with the presence of bulky groups. The model quantitatively
describes optical spectra of the two dyes and suggests large and
nontrivial solvent effects in their nonlinear optical responses.
1. INTRODUCTION
Charge-transfer chromophores represent a wide class of π-
conjugated molecules where the presence of electron-donor
(D) and -acceptor (A) groups ensures the occurrence of low-
energy excited states with large transition dipole moments.
Polar (D-π-A) chromophores are good polarity sensors1−5 and
may show large nonlinear optical response,6−12 and some of
them behave as molecular rectifiers.13−17 Quadrupolar (D-π-A-
π-D or A-π-D-π-A) dyes were specifically developed as two-
photon absorbers,18−22 and some of them proved particularly
interesting for two-photon-induced photodynamic ther-
apy.22−24 The important fluorescence solvatochromism shown
by some quadrupolar dyes makes them also interesting for
polarity- and voltage-sensing applications,25,26 while quadrupo-
lar structures were recently considered as light-harvesting
species in solar cells.27
An extensive joint experimental and theoretical study28 led to
the definition of three different classes of quadrupolar
chromophores, according to their spectroscopic behavior.
Class I dyes show nonsolvatochromic absorption, as expected
for nonpolar dyes, but due to the occurrence of symmetry
breaking in the first excited state, they show a strongly
solvatochromic fluorescence. Class II chromophores do not
undergo symmetry breaking, and their spectra are marginally
affected by solvent polarity. Finally, class III dyes undergo
symmetry breaking in the ground state and show an important
inverse solvatochromism of the absorption band, while their
Received: January 17, 2012
Revised: April 1, 2012
Published: April 2, 2012
© 2012 American Chemical Society
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Scheme 1. Molecular Structures of the Investigated Compounds
Scheme 2. Synthesis of D-π-A-π-D Chromophore 1
emission and excitation spectra were measured on solutions
with a concentration of ∼10−6 M. Fluorscein in NaOH 0.1 M
was used as the standard for fluorescence quantum yield
measurements (ϕ = 90%).
Fluorescence excitation anisotropy spectra were collected on
a Fluoromax-3 Horiba Jobin-Yvon spectrofluorometer equip-
ped with excitation and emission Glan-Thompson automatic
polarizers for anisotropy measurements (single-channel L-
format). Fluorescence anisotropy is defined as
2. EXPERIMENTAL PROCEDURES
Materials. Analytical-grade solvents were used in the
synthetic procedures. The squaraine dye 2 shown in Scheme
1 and 2,3-diphenylquinoxaline, 1,4-diethyl-2,3-diphenyl-1,2,3,4-
tetrahydroquinoxaline, and 2-(2,6-dimethyl-4H-pyran-4-
ylidene)malononitrile were synthesized according to literature
procedures.34−36 1H NMR and 13C NMR spectra were
recorded on a Bruker 400 MHz spectrophotometer in
CDCl3. Chemical shifts are given in parts per million (ppm)
and coupling constants (J) in Hertz.
Synthesis of 2-(2,6-Bis((E)-2-(1,4-diethyl-2,3-diphenyl-
1,2,3,4-tetrahydroquinoxalin-6-yl)vinyl)-4H-pyran-4-
ylidene)malononitrile (1). Piperidine (0.2 mL) was added
under an argon atmosphere to a mixture of 2-(2,6-dimethyl-4H-
pyran-4-ylidene)malononitrile (0.162 g, 0.94 mmol) and 1,4-
diethyl-2,3-diphenyl-1,2,3,4-tetrahydroquinoxaline-6-carbalde-
hyde (0.7 g, 1.88 mmol) in dry acetonitrile. The reaction
mixture was refluxed for about 24 h. It was concentrated, and
the compound was purified by using column chromatography.
The total yield was 0.54 g (65%). NMR (400 MHz, CDCl3): δ
7.47 (d, J = 16 Hz, 2H), 7.12 (m, 4H), 7.03 (t, J = 8 Hz, 10H),
6.96 (br, 2H), 6.71 (m, 10H), 6.55 (s, 2H), 6.52 (d, J = 16 Hz,
2H), 4.55 (d, J = 4 Hz, 4H), 3.44 (m, 4H), 3.12 (m,4H), 1.03
(t, J = 8 Hz, 6H), 1.00 (t, J = 8 Hz, 6H). 13C NMR (100 MHz,
CDCl3): δ 139.09, 138.68, 138.35, 138.23, 135.24, 129.39,
129.28, 127.57, 124.04, 121.03, 116.53, 113.55, 113.04, 110.76,
109.94, 105.29, 65.68, 64.20, 43.71, 42.60, 11.16, 10.42. FTIR
(KBr): 2925, 2854, 2202, 1634, 1518, 1489, 1412, 1351, 1261,
1170 cm−1. HRMS [found: m/z 877.4601 [M + H]+; calcd for
C60H56N6O [M + H]+: 877.4594].
I − I⊥
r =
I + 2I⊥
(1)
where I∥ is the emission intensity measured when the excitation
and emission polarizers are parallel, while I⊥ is the emission
intensity when the two polarizers are mutually perpendicular.
Further information on fluorescence anisotropy measurements
can be found in ref 37.
3. RESULTS
Knoevenagel condensation of 2-(2,6-dimethyl-4H-pyran-4-
ylidene)malononitrile (A) with 1,4-diethyl-2,3-diphenyl-
1,2,3,4-tetrahydroquinoxaline-6-carbaldehyde (B) in the pres-
ence of piperidine gives the D-A-D chromophore 1 (see
Scheme 2). Chromophore 2 was synthesized by the earlier
reported procedure.36 All of these dyes were characterized by
1H NMR, 13C NMR, HRMS, and IR spectroscopy.
Absorption and emission spectra of 1 and 2 collected in
solvents of different polarity are shown in Figure 1. The main
spectroscopic data are summarized in Table 1. The broad
absorption spectrum of 1 spans a large portion of the visible
spectral region, from red−orange to UV, with a very intense
peak (hereafter, the main peak) in the green region and a
weaker peak (the secondary peak) in the blue−violet region.
Both peaks are weakly solvatochromic (shifts of 1230 and 780
cm−1 from cyclohexane to dichloromethane for the main and
the secondary peaks, respectively), an unusual result for
quadrupolar chromophores.28 Fluorescence spectra show a
more important solvatochromism, as expected for largely
neutral (class I) quadrupolar dyes with a broken-symmetry
fluorescent state;28 the emission band shifts to the red by about
3600 cm−1 from cyclohexane to dichloromethane, and the
Stokes shift increases with solvent polarity up to ∼5000 cm−1 in
Spectroscopic Measurements. Solvents used for spectro-
scopic measurements: cyclohexane (Sigma-Aldrich, HPLC);
toluene (Sigma-Aldrich, ≥99.9%); 2-MeTHF (Sigma-Aldrich,
anhydrous, ≥99.5%); dichloromethane (Sigma-Aldrich,
≥99.9%); dimethylsulfoxide (Riedel-de Haen, 99.5%); and
̈
glycerol (Sigma-Aldrich, anhydrous, ≥99.0%). 2-MeTHF was
used after overnight storage on molecular sieves (0.3 nm);
other solvents were used as received.
Absorption spectra were collected on a Lambda 650 UV/vis
Perkin-Elmer spectrophotometer. The Beer−Lambert law was
verified in measurements of the molar extinction coefficients.
Emission spectra were recorded on a Fluoromax-3 Horiba
Jobin-Yvon spectrofluorometer. To minimize self-absorption,
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be compared below with the emission calculated from a
thermalized excited state. This is in line with the thermalization
process, driven by solvent relaxation (typically in the
picosecond regime38), being faster than fluorescence lifetimes
(typically in the nanosecond regime).39
To gain more insight into the nature of the excited states, we
measured fluorescence anisotropy spectra, as reported in Figure
2, at 77 K in 2-MeTHF for 1 and at room temperature in
Figure 1. Experimental absorption and emission spectra of 1 (top
panel) and 2 (bottom panel) in solvents of different polarity.
Figure 2. Experimental fluorescence excitation anisotropy (dots).
(Top panel) 1 in glassy 2-MeTHF at T = 77 K. (Bottom panel) 2 in
glycerol at room temperature. Dashed lines in both panels show
fluorescence excitation spectra collected under the same experimental
conditions as those adopted for anisotropy measurements.
dichloromethane. Absorption and emission spectra collected in
cyclohexane show a resolved vibronic structure, but the spectra
broaden in polar solvents. The spectral behavior of 2 is
qualitatively different; absorption and emission bands are very
narrow, and the solvatochromic behavior is less pronounced
than that for 1 (shifts of ∼900 and ∼1100 cm−1 for the
absorption and the emission bands, respectively, from toluene
to glycerol). The observed Stokes shifts are small in all of the
solvents. The fluorescence quantum yield of 1 and 2 is high in
nonpolar solvents and drastically decreases in solvents of
medium and high polarity. The decrease of the fluorescence
quantum yield in polar solvents can be ascribed to several
reasons. First, emission is red-shifted in polar solvents, so that
the probability of the process, scaling with the third power of
the transition frequency, decreases. Moreover, the efficiency of
the emission process is strongly environment-dependent and
hardly predictable because several nonradiative processes,
including collisional events, internal conformational conver-
sions, and so forth, compete with radiative emission. In any
case, the very weak fluorescence observed in polar solvents will
glycerol for 2. Glycerol, being highly viscous at ambient
temperature, is a good solvent for fluorescence anisotropy
measurements.40 Unfortunately, the fluorescence signal of 1 in
glycerol is too weak; therefore, anisotropy data for 1 were
obtained in glassy 2-MeTHF matrixes. The fluorescence
anisotropy spectrum of 2 is flat within the excitation band
and very close to the limiting r = 0.4 value, as expected for
linear molecules,39 whose absorption and fluorescence
transition dipole moments are aligned along the main
molecular axis. On the opposite, the anisotropy of 1 smoothly
decreases from ∼0.37 to ∼0.3 within the main excitation band
at 500 nm, then showing a sharp decrease in correspondence of
the secondary band at about 400 nm.
Table 1. Experimental Spectroscopic Data Relevant to Molecules 1 and 2 in Solvents of Different Polarity
a
a
b
c
solvent
λabs(nm)
λem(nm)
Stokes shift (cm−1
)
ε (mol−1 cm−1
)
ϕ (%)
1
cyclohexane
toluene
495/387
515/391
518/395
527/399
703
563
642
672
705
730
761
780
796
2440
3841
4424
4791
516
22
38
51400
2-MeTHF
dichloromethane
toluene
2
187000
43
4
dichloromethane
dimethylsulfoxide
glycerol
718
787
736
766
750
771
a
b
Absorption and emission wavelengths refer to band maxima. For absorption of 1, the two wavelengths refer to the main/secondary peak. Molar
c
extinction coefficient. Fluorescence quantum yields (in polar solvents, the quantum yield is too small, <1%, to be reliably estimated).
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4. ESSENTIAL-STATE MODELING
Article
allowed. This simple scheme must be slightly modified in bent
molecules where the reduced symmetry makes the two
transitions allowed both in linear absorption (OPA) and two-
photon absorption (TPA) spectra.32 These simple consider-
ations rationalize the appearance of the secondary bands in
linear absorption spectra of 1. However, a thorough analysis of
optical spectra accounting for band shapes and solvatochrom-
ism requires a more detailed modeling, including vibrational
and solvation degrees of freedom. We introduce two effective
vibrational coordinates, q1 and q2, with the same frequency ων
and relaxation energy εν, to describe the relaxation of the
molecular geometry upon excitation on each molecular arm.
The molecular Hamiltonian reads28
Quadrupolar chromophores, with D-π-A-π-D or A-π-D-π-A
structure, have been classified in three different families
according to their spectroscopic behavior.28 However, neither
1 nor 2, both having the classical A-π-D-π-A structure of
quadrupolar dyes, conform to the standard picture. Both dyes
in fact show a normally solvatochromic absorption band (i.e.,
the band moves to the red in polar solvents), while in the
standard model, only class III dyes show a solvatochromic
absorption, but in that case, an inverse solvatochromism is
expected (i.e., the absorption band should move to the blue in
polar solvents). For molecule 1, some solvatochromism can be
ascribed to its bent structure, but as shown in Figures S1 and S2
in the Supporting Information, to quantitatively recover the
observed solvatochromism, one should impose an unphysically
small angle between the two molecular arms (about 90°) that
would also lead to an exceedingly large intensity of the
secondary absorption band. On the other hand, dye 2 has a
linear structure, and the standard model fails badly in
reproducing its spectra (cf Figure S3 in the Supporting
Information). Experimental data for 1 and 2 then call for
some new mechanism.
The solvation model is a delicate issue in the description of
quadrupolar chromophores. Specifically, in the standard model
developed in ref 28 and recently extended to cyanine dyes,31
the solute, located in a cavity inside of the solvent, feels a
uniform electric field (the reaction field) generated by the
reorientation of the solvent molecules around the solute. This
highly approximate scheme yields to reasonably accurate results
in most cases but is expected to fail for large molecules with
bulky and flexible substituents, like the ones discussed in this
work. Describing the solvatochromism of quadrupolar dyes
accounting for a single reaction field implies in fact the
assumption of coherent behavior between the two molecular
arms, or, in other terms, it implies assuming that the excitation
hops too fast between the two molecular harms to allow the
solvent to relax. In the case of bulky groups, however, this
implicit assumption of coherence may break down; due to local
relaxation pathways, the excitation can reside on each arm long
enough to allow the solvent to independently relax around each
molecular arm, so that two reaction fields, relevant to the two
arms, must be introduced. In a different perspective, two
independent reaction fields can account for a nonuniform
reaction field in the cavity, as expected for extended molecules.
Extending the standard model to account for two different
reaction fields leads to a new model that, as discussed below,
quantitatively accounts for the spectral behavior of 1 and 2.
As for the electronic structure, both 1 and 2 can be described
in terms of three basis states,28 corresponding to the three main
resonance structures, a neutral state, |N⟩ = DAD, and two
zwitterionic states | Z1⟩ = DA−D+ and | Z2⟩ = D+A−D. The two
degenerate zwitterionic states are separated by an energy gap 2η
from the neutral state. A nonvanishing matrix element,
−(2)1/2t, mixes |N⟩ with |Z1⟩ and |Z2⟩. The diagonalization of
the electronic problem is conveniently done on a symmetrized
basis with |Z ⟩ corresponding to the in-phase and out-of-phase
combination of |Z1⟩ and |Z2⟩. The linear combination of the
two symmetric basis states, |N⟩ and |Z+⟩, leads to two
symmetric eigenstates, |g⟩ and |e⟩, while the antisymmetric
state stays unmixed, |c⟩ = |Z−⟩. For linear centrosymmetric
molecules, the lowest-energy |g⟩ → |c⟩ transition is one-
photon-allowed, while the |g⟩ → |e⟩ transition is two-photon-
̂
̂
̂
̂
̂
HM = 2η(ρ1 + ρ2) − 2 tσ − 2εν ων(q
̂
1ρ1 + q2
̂
ρ2)
1
2
+
(ων2q2 + ων2q2 + p2 + p22
̂
̂
̂
̂
)
1 2
1
(2)
2
̂
̂
where ρi = |Zi⟩⟨Zi| and σ = ∑i=1 |N⟩⟨Zi| + |Zi⟩⟨N|. The third
term in eq 2 accounts for the coupling between electronic and
vibrational degrees of freedom, while the last term describes the
two harmonic oscillators associated with coordinates q1 and q2,
with p1 and p2 representing the conjugated momenta.
Before addressing polar solvation, we must define the
molecular dipole moment. For bent molecules, like 1, two
components of the molecular dipole moment operator must be
introduced
α
2
̂
̂
̂
μ = μ0 sin (ρ1 − ρ2)
x
α
2
̂
̂
̂
μy = μ0 cos (ρ1 + ρ2)
(3)
where, μ0 is the magnitude of the dipole moment relevant to
either |Z1⟩ or |Z2⟩ and α is the angle between the two molecular
arms. The x and y axes are aligned with the long and short
molecular axis, respectively, with only x being relevant for linear
molecules (like 2) with α = 180°.
As discussed in ref 32, sizable normal solvatochromism can
be expected in bent quadrupolar chromophores. However the
solvatochromism of 2, a linear molecule, cannot be explained
on this basis. On the other hand, attempts to describe the
solvatochromism of 1 based on the bent molecule model and
accounting for a single reaction field failed. In fact, to recover
the observed solvatochromism, unphysically large deviations
from linearity should be imposed, leading to a largely
overestimated intensity of the secondary absorption band (cf.
Supporting Information Figure S1). Therefore, here we
introduce two independent reaction fields coupled with the
charge distribution on each molecular arm. The total
Hamiltonian, including solvation, reads
μ2F12
4εor
μ2F22
4εor
0
0
̂
̂
2
H = HM − Fμ ρ − F μ ρ +
+
1
2
0
0
1
(4)
where F1 and F2 are the two reaction fields and εor measures the
solvent relaxation energy.
Vibrational motion is treated exactly, in a truly nonadiabatic
approach, while the reaction fields enter the problem as classical
variables.28,41,42 The Hamiltonian in eq 4 defines, for fixed F1
and F2 values, a coupled electron-vibration problem. The
relevant Hamiltonian matrix is written on the basis defined as
the direct product of the three electronic basis states times the
eigenstates of the two harmonic oscillators associated with q1
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and q2. The two vibrational basis are truncated to the lowest M
states, leading to a 3M2 × 3M2 matrix that is numerically
diagonalized to get (numerically) exact results, provided that M
is large enough to ensure convergence (M = 8 was used in this
work). The resulting F1 and F2-dependent energies and
eigenstates are used to calculate linear absorption and
fluorescence spectra, as well as two-photon absorption and
hyper-Rayleigh scattering spectra, according to explicit
expressions given in refs 20, 41, and 42. The calculations are
repeated on a grid of F1 and F2 values. Total spectra are finally
obtained by summing up contributions from all points in the
grid, weighted by the Boltzmann population on the relevant
potential energy surface. Specifically, for one- and two-photon
absorption and for hyper-Rayleigh scattering spectra, the
Boltzmann population accounts for the (F1,F2)-dependent
ground-state energy, while for emission spectra, the Boltzmann
population of the fluorescent state is accounted for.
Table 2. Essential-State Parameters Adopted To Calculate
Optical Spectra Reported in Figure 2
a
1
2
η (eV)
(2)1/2t (eV)
μ0 (D)
α
1.1
0.75
28.6
0.34
1.05
19.2
120°
180°
ων(eV)
εν(eV)
γ (eV)
0.17
0.45
0.07
0.14
0.12
0.04
a
The value of μ0 only enters the definition of the molar extinction
coefficient and is set to reproduce the experimental value in Table 1.
The last parameter, γ, measures the intrinsic bandwidth of vibronic
absorptions (cf. refs 41 and 42).
The same model, with exactly the same parameters, is
adopted to calculate excitation anisotropy spectra following the
procedure described in refs 37 and 43. Calculated anisotropy
spectra of 2 are not shown because for this linear molecule, we
calculate r = 0.4, in good agreement with experimental data in
the lower panel of Figure 2. For 1, the comparison between
calculated anisotropy spectra in Figure 4 and experimental data
Figure 3 shows calculated spectra, to be compared with
experimental spectra in Figure 1. Relevant model parameters
Figure 4. Calculated fluorescence excitation anisotropy spectra of 1.
Model parameters are listed in Table 2.
in the upper panel of Figure 2 is very satisfactory, particularly in
the region from 450 to 580 nm, corresponding to the main
absorption band. In the region of the secondary absorption
band (∼400 nm), the calculated anisotropy shows an abrupt
decrease, approaching the theoretical lower limit r ≈ −0.2.
Experimental data show a less pronounced decrease in this
region, a discrepancy ascribed to the partial overlap of the
relevant band with other transitions located at higher energies,
as confirmed by the absorption spectra (see the discussion
above and Figure S4 in the Supporting Information).
Figure 3. Calculated absorption and emission spectra of 1 (top panel)
and 2 (bottom panel) in solvents of different polarity. Essential-state
parameters are listed in Table 2.
Essential-state models, parametrized against linear absorption
spectra, offer a computationally affordable approach for the
calculation of nonlinear optical spectra and proved very
successful in several instances.28,31,41−48 Figures 5 and 6 show
HRS and TPA spectra calculated for 1 and 2 with model
parameters in Table 2 for two εor values to mimic low- and
high-polarity solvents. For the bent molecule, 1, the two
electronic excited states responsible for the main (g → c) and
secondary (g → e) absorption bands are expected to give
sizable contributions to the HRS and TPA signals. Calculated
spectra in Figure 5 confirm this prediction. A weak TPA
intensity is in fact observed in the region of the main (g → c)
absorption peak that would be forbidden for linear symmetrical
molecules. Most of the TPA intensity is however found in the
region of the secondary (g → e) absorption, corresponding to
the allowed TPA band for a linear molecule. Instead, the
are listed in Table 2. The agreement between experimental and
calculated data is very good; accounting for two independent
solvation fields, we quantitatively reproduce absorption and
fluorescence solvatochromism as well as the band shape
evolution with solvent polarity. For molecule 1, the calculated
intensity of the secondary peak is somewhat lower compared to
experimental data, and the solvatochromic shifts are slightly
underestimated. These effects can be ascribed to the presence
of slightly solvatochromic bands, assigned to electronic
transitions localized on either the electron-donor or electron-
acceptor groups and partly overlapping the secondary peak.
This hypothesis is confirmed by absorption spectra collected
for two molecules mimicking the donor and acceptor groups, as
described in the Supporting Information (Figure S4).
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minor effects in both HRS and TPA spectra of 1. HRS peaks
indeed broaden in polar solvents, leading to a large HRS
response in a wide spectral region, with βHRS > 300 × 10−30esu
in the 700−1300 nm interval for simulated spectra in
dichloromethane. Inhomogeneous broadening effects are also
recognized in the red shift of HRS features with respect to the
OPA peak.42
TPA spectra of 2 are largely dominated by the very intense
feature typical of squaraine dyes, associated with the highest-
energy (g → e) transition, almost resonant with the linear
absorption peak.28 Due to the linear structure of 2, the g → c
transition is forbidden in TPA, and just a very weak shoulder is
calculated in this spectral region in the TPA spectrum relevant
to the most polar solvent. This weak feature is associated with
the lowering of molecular symmetry in polar solvents. In fact, in
the proposed model for polar solvation, the two reaction fields,
F1 and F2, associated with the two molecular arms, are mutually
independent and, when F1 ≠ F2, the molecular symmetry is
lowered, allowing for a (weak) TPA intensity of the nominally
forbidden g → c transition. More interesting are HRS spectra;
because the molecule is linear (and strictly so in our model),
the calculated HRS intensity can only derive from symmetry
lowering due to polar solvation, as also confirmed by the large
dependence of the HRS intensity on εor. However, while
symmetry lowering has minor effects on TPA spectra, its effects
on HRS spectra are very important. Indeed, the HRS signal
becomes, in the most polar solvent, as large as that for the bent
molecule 1 or that for the octupolar chromophore in ref 42.
Large inhomogeneous broadening effects in HRS spectra have
already been discussed in terms of band shapes and band
positions.42,49 Here, we emphasize that starting from sym-
metrical structures, the symmetry lowering related to polar
solvation can lead to sizable HRS intensities.
Figure 5. Calculated HRS (top panel) and TPA spectra (bottom
panel) for 1, adopting model parameters in Table 2 and setting εor
=
0.15 (black lines) and 0.6 eV (green lines), corresponding to simulated
spectra in cyclohexane and dichloromethane, respectively (cf., the top
panel of Figure 3). Dotted lines in the upper panel show calculated
linear absorption spectra in arbitrary units.
calculated HRS signal is large (of similar magnitude as that
calculated for an octupolar chromophore42), in correspondence
with both the main and secondary bands. Solvent polarity has
The different sensitivity of HRS and TPA spectra of linear
quadrupolar molecules to symmetry-lowering perturbations can
be rationalized based on simple perturbative arguments.
Solvent-induced symmetry lowering is driven by Δ = F1 −
F2. A perturbative expansion on Δ of the electronic states
relevant to the symmetric (Δ = 0) structure, |g⟩, |c⟩, and |e⟩
(see the discussion above and ref 28 for more details), leads to
three Δ-dependent electronic eigenstates
μ
|g(Δ)⟩ = |g⟩ − gc Δ|c⟩
ωgc
μ
ωgc
μ
|c(Δ)⟩ = |c⟩ + gc Δ|g⟩ − ce Δ|e⟩
ω
ce
μ
|e(Δ)⟩ = |e⟩ + ce Δ|c⟩
ω
ce
where μgc = ⟨c|μ|g⟩ and μge = ⟨e|μ|g⟩ are the transition dipole
moments of the g → c and g → e transitions of the symmetric
system and ωgc and ωce are the corresponding transition
frequencies. Inserting these expressions into standard equations
for HRS and TPA signals, one easily recognizes that
perturbative corrections to the HRS signal grow linearly with
Δ, while the leading term in the TPA intensity of the g → c
transition is proportional to Δ2, then representing a minor
correction. We emphasize that symmetry-lowering effects in
HRS spectra are particularly important because of the presence
of two independent reaction fields in the model that largely
increase the density of asymmetric states.
Figure 6. Calculated HRS (top panel) and TPA spectra (bottom
panel) for 2, adopting model parameters in Table 2 and setting εor
=
0.20 (red lines) and 0.52 eV (cyan lines), corresponding to simulated
spectra in toluene and glycerol, respectively (cf., the bottom panel of
Figure 3). Dotted lines in the upper panel show calculated linear
absorption spectra in arbitrary units.
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The Journal of Physical Chemistry B
5. DISCUSSION AND CONCLUSION
Article
ASSOCIATED CONTENT
■
S
* Supporting Information
The broad absorption and emission spectra of 1 contrast with
the narrow spectral features of 2. Narrow spectral features are,
in general, characteristic of squaraine dyes and are related to the
relatively small electron-vibration coupling in these systems
(small εν) and to the large mixing between the neutral and
zwitterionic states, typical of class II quadrupolar dyes,28 that
further reduces the effective vibrational coupling. Broad
absorption and fluorescence bands of 1 are instead typical of
largely neutral (class I) chromophores.28 These features hold
true also in the model discussed in this paper, accounting for
two independent reaction fields. The main spectroscopic
consequence of the presence of two reaction fields is
recognized in the sizable normal solvatochromism of linear
absorption spectra that cannot be rationalized in models
accounting for a single reaction field.
Essential-state models for nonlinear V-shaped quadrupolar
chromophores, like 1, have been recently discussed.32 The
appearance of a secondary band in the linear absorption
spectra, to the blue of the main band, marks the reduced
symmetry of bent molecules; the g → e transition, OPA-
forbidden and TPA-allowed in linear molecules, acquires a
sizable OPA intensity in bent molecules. This makes the overall
absorption spectrum of V-shaped quadrupolar chromophores
very broad; 1, a largely neutral chromophore, showing in the
green spectral region the typical broad absorption band of class
I dyes, shows an additional peak in the blue−violet region, due
to its V-shaped structure. The resulting absorption spectrum
then covers most of the solar spectrum, making this
chromophore, and more generally V-shaped quadrupolar
chromophores, promising for solar cell applications.
Figures S1−S3 show spectra calculated for the two compounds
with slightly different models. Figure S4 shows experimental
absorption spectra of chemical species mimicking the isolated
electron-acceptor and electron-donor groups. This material is
available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: anna.painelli@unipr.it. Tel. +39 0521 905461. Fax +39
0521 905556.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was partly supported by the Indo−Italian Executive
Programme of Scientific and Technological Co-operation
2008−2010 and by Fondazione Cariparma through the Project
2010.0329. C.S. thanks the University of Parma and INSTM for
financial support. S.P. thanks the ISRO-IISc Space Technology
Cell for supporting this work through the Project ISTC/CSS/
STP/252, and S.R.B.K. thanks CSIR for a Senior Research
Fellowship.
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