Spectral dispersion of second molecular hyperpolarizability of diacetylene
derivatives: Correlation with electronic and chemical structure
A. V. V. Nampoothiri, P. N. Puntambekar, Bhanu P. Singh, R. Sachdeva, A. Sarkar et al.
Citation: J. Chem. Phys. 109, 685 (1998); doi: 10.1063/1.476607
View online: http://dx.doi.org/10.1063/1.476607
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 2
8 JULY 1998
Spectral dispersion of second molecular hyperpolarizability of diacetylene
derivatives: Correlation with electronic and chemical structure
A. V. V. Nampoothiri, P. N. Puntambekar, and Bhanu P. Singha)
Department of Physics, Indian Institute of Technology, Powai, Bombay-400 076, India
R. Sachdeva, A. Sarkar, Dipti Saha, A. N. Suresh, and S. S. Talwar
Department of Chemistry, Indian Institute of Technology, Powai, Bombay-400 076, India
~Received 10 December 1997; accepted 2 April 1998!
Dispersion of the second hyperpolarizability g (2 v ; v , v ,2 v ) of a series of conjugated diacetylene
derivatives measured by single beam Z-scan technique, is presented. The spectrum of g is explained
by a three-level model involving a one-photon excited state, a two-photon excited state and the
ground state. The location of one and two-photon states and corresponding transition dipole
moments have been estimated. The influence of various electronic states on the nonlinear optical
properties of these derivatives have been discussed. Broad correlations of the nonlinearity with the
structure have been drawn. © 1998 American Institute of Physics. @S0021-9606~98!51126-9#
I. INTRODUCTION
Recently, a large nonlinear susceptibility (;4.8
31027 esu) has been reported10 for a pyrrole derivative of a
conjugated diacetylene monomer solution in acetone at 514
nm. This is a surprisingly large nonlinearity for such a small
molecule in the transparent region of its absorption spectrum.
However, to the best of our knowledge, no further investigations to understand the origin of such large nonlinearity in
terms of the electronic structure have been reported so far.
This has prompted us to systematically investigate the relationship of the nonlinearity with the electronic and chemical
structure of derivatives of conjugated diacetylenes. Since
x (3) strongly reflects the internal molecular resonances, its
spectral dispersion can provide a wealth of information not
only on the ordering, location and oscillator strengths of
various electronic states but also on their relative influences
on the nonlinear optical response. In this paper we present
the results of dispersion studies on six aryl substituted conjugated diacetylenes. The experimental results have been
analyzed within the framework of three-essential state
model11–17 based on sum-over-states approach and the correlation between nonlinearity and structure has been sought.
Conjugated organic molecules have attracted considerable attention as nonlinear optical ~NLO! materials for photonics due to their large nonresonant third order susceptibility and ultrafast response arising from delocalized p -electron
system.1–3 Especially, the polymers have been investigated
extensively to identify potential materials for nonlinear optical devices. Amongst the variety of polymeric structures,
polydiacetylenes possess one of the largest nonlinear
response.4 Still, the nonlinearity of the polymers so far does
not meet the requirements of practical devices. However,
these do offer scope for further improvement by structural
modifications.
The long chain conjugated polymer approach toward developing practical NLO materials suffers from the following
limitations: First, in the long chain molecules, it is difficult to
extend the p -electron delocalization over the entire molecular chain. It is often interrupted by conformational defects
and only smaller segments of the structure contribute to the
second molecular hyperpolarizability actively. Further, it has
been shown both theoretically and experimentally that with
the increase in number of repeat units, the molecular hyperpolarizability per repeat unit, which determines the bulk nonlinear susceptibility x (3) , levels off beyond few repeat units
(.15).5,6 This sets a limit for improving x (3) by increasing
chain length. It then appears undesirable to expand the molecular structure beyond this limit. Second, the inherent uneven distribution of molecular weights/chain sizes in polymers lead to refractive index inhomogeneities and large
residual absorption tail which results in poor figure of
merit3,7,8 for NLO devices.
It transpires from the above discussion that the oligomers and smaller organic molecules with large enough nonlinearity and well characterized structures may also prove
useful for practical applications.5,9
II. EXPERIMENT
The six aryl substituted conjugated diacetylenes used for
this study were synthesized in our laboratory. Their chemical
structures are shown in Fig. 1. 1,4-bis(3 8 - thienyl!-1,3butadiyne ~3DTDA!,18 1,4-bis~1 8 - naphthyl!-1,3- butadiyne
~1DNDA!,19
1,4-bis~3 8 quinolyl!-1,3butadiyne
~3DQDA!20 are reported in literature and were prepared by
Hay’s coupling21 of the corresponding aryl acetylenes. 1,4Bis~3 8 -thianaphthyl!-1,3-butadiyne ~3TNDA!22 was also
synthesized using Hay’s procedure for coupling of corresponding aryl acetylene. 1-~3 8 quinolyl!-1,3-butadiyne
~3QDA! was prepared by Cadiot-Chodkiewicz coupling23,24
of 2-~3 8 -quinolyl!-1-bromoacetylene and 2-methyl-3-butyn2-ol and acetonolysis of the product. The unsymmetrical
substituted
1-~2 8 -thienyl!-4-~3 9 -quinolyl!-1,3-butadiyne
~2TQDA! was prepared by Cadiot-Chodkiewicz coupling of
a!
Electronic mail: [email protected]
0021-9606/98/109(2)/685/6/$15.00
685
© 1998 American Institute of Physics
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686
Nampoothiri et al.
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
FIG. 2. Z-scan experimental setup. D1 ,D2 —photodetectors, L1 ,L2 —
Lock-in amplifiers, PC—Microcomputer, BS—Beam-splitter, and L—
Focusing lens.
FIG. 1. Chemical structure of the various diacetylenes.
2-~3 8 -quinolyl!-1-bromoacetylene and 2-thienylacetylene.
Details of the synthesis will be published elsewhere. The
compounds were purified by column chromatography before
use.
The third order nonlinear susceptibilities x (3) were measured using the Z-scan technique.25,26 In this technique, a
Gaussian beam is focused using a lens and the sample is
scanned across the focal region along the beam propagation
direction, Z. The intensity dependent phase front distortions
of the beam are measured in terms of the transmittance variation of an aperture placed in the far field of the outgoing
beam as a function of Z. The intensity dependent transmission of the sample measured without an aperture ~‘‘open
scan’’! gives information on purely absorptive nonlinearity
whereas the apertured scan ~‘‘closed scan’’! contains the information of both absorptive and refractive nonlinearity. The
real and imaginary parts of the nonlinear susceptibility x (3)
can be obtained from these scans using the theoretical formalism given in Ref. 25. The prefocal maximum followed by
a post focal minimum in the closed aperture Z-scan is the
signature of negative ~self defocusing! and vice versa for the
positive ~self focusing! nonlinearity. Thus this method provides a direct measurement of the real and imaginary parts of
the nonlinearity along with its sign. The sign of the nonlinearity is not only an important parameter for practical realization of optical signal processing devices but also is an
important input often for quantum chemical calculations.
This information cannot be obtained by other commonly
used techniques such as degenerate four wave mixing and
third harmonic generation.
The typical Z-scan experimental setup is shown in Fig.
2. Transform limited, 80 fs pulses ~spectral width50.0163
eV! from a self mode-locked Ti:sapphire laser were used for
the Z-scan experiments. Z-scan measurements at different
wavelengths were done using a 1022 M solution of the diacetylenes in a 1.0 mm path length quartz cell. The solvent
for 3QDA and 3DQDA was chloroform and for the other
diacetylenes the solvent used was tetrahydrofuran. The
Gaussian beam of the laser was focused with an 8cm focal
length lens to a spotsize of 40m m. The sample was scanned
across the focal region of the lens by a motorized translation
stage. The exit beam from the sample was split into two arms
for the simultaneous measurement of closed and open aperture scans. The transmitted energy was measured using a
calibrated photodiode and a lock-in amplifier interfaced with
a computer. Care was taken to keep the maximum nonlinear
phase change much less than p radians, by adjusting the
input pulse energy to the sample. The Rayleigh range of the
beam was found to be larger than sample thickness at all
wavelengths, thus allowing the use of thin sample approximation for Z-scan analysis.25 The Z-scan experimental setup
was standardized by toluene. Its measured x (3) value (4.55
310213 esu! is in excellent agreement with the earlier reported value of 4.77310213 esu.27
The x (3) dispersion for solution and solvent was studied
from 730 nm to 810 nm and the second molecular hyperpolarizability g was evaluated using28
g5
3!
3!
x ~solution
2 x ~solvent
L 4 N solute
~1!
based on a pairwise additive model for noninteracting molecules. Here N solute is the number density of solute, L5(n 2
12)/3 is the local field factor and n is the refractive index of
the medium.
III. RESULTS AND DISCUSSIONS
A typical Z-scan of a diacetylene 3QDA in chloroform is
shown in Fig. 3. It shows a prefocal maximum followed by a
post focal minimum indicating a negative nonlinearity for
the solution. No transmittance variation was observed in the
open aperture scan. This implies that the observed nonlinearity is predominantly refractive and the imaginary part of the
nonlinearity, if any, is below our detection limit ~Imaginary
x (3) ;6310213 esu!. Above observations are common to all
the samples throughout the spectral range used for the dis-
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Nampoothiri et al.
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
687
FIG. 3. A typical Z-scan signature of 3QDA. Solid curve is the theoretical
to the experimental data, using the theoretical formalism given in Ref. 25.
FIG. 4. Dispersion of g (2 v ; v , v ,2 v ) for 3DTDA and 3QDA. Solid
curve represents the best fit to the three-level model as described in the text.
persion studies here. The second molecular hyperpolarizability ( g ) from the Z-scan data were calculated at each wavelength using equation ~1!. The g values for all the derivatives
are found to be negative ~self defocusing! at all the wavelengths.
The measured g values of diacetylene derivatives at the
two end wavelengths ~740 nm and 810 nm! of the spectral
range investigated are given in Table I. These g values are
larger than those reported for other small conjugated
molecules.28,29 It may be noted that the g value at 810 nm
increases nearly 17 times simply by replacing the thiophene
end group of the diacetylene by a quinoline end group. The
observed dispersions of g for various diacetylenes are shown
in Figs. 4, 5 and 6. The g value increases steadily for most
diacetylenes as one tunes the wavelength from 810 nm to
740 nm. In case of 2T3QDA and 3TNDA, the g value
switches from a near constant low value branch to a high
value branch ~;1.6 times that of low branch!. For 3DTDA,
3DQDA and 3QDA the enhancement in g values are 3.3, 2.7
and 2.8 respectively. Evidently, these enhancements are due
to the frequency of the incident radiation approaching that of
optical transitions between the electronic states of the
material.
For one dimensional conjugated chains having C 2h symmetry, the p -electron states can be classified as even (A g )
and odd (B u ) parity states.30 One-photon transition dipole
moment vanishes between states of same parity whilst a twophoton transition is allowed. For chains possessing C 2 v symmetry, the transition from the ground state 1 1 A 1 to 2 1 A 1 is
one-photon allowed for light polarized perpendicular to the
chain and to 1 B 2 for light polarized parallel to the chain.
Since for quasi 1-D chains, the component of transition dipole moment perpendicular to the chain is vanishingly small,
these states can be treated analogous to 1 A g and 1 B u states of
the C 2h group. The electronic nonlinearity of a molecule
arises from the mixing of its ground and the excited states
and can be calculated within the framework of perturbation
theory by summing over the response from all the states of
the system. However, it has been shown that in organic molecules, nonlinear optical response could be adequately explained by considering only the low lying three or four
states.14,31 In the three-level model, these have been identified as the ground state u 0 & and the lowest one and twophoton allowed states u 1 & and u 2 & respectively. According to
TABLE I. Fit parameters ~locations of excited states and transition dipole moments between them! used in the three-level model. The error in g values
estimated from repetitive measurements is 617%.
a
u g u (10232esu)
E 10~meas.!
G 10~meas.!
E 20
G 20
m 01
m 12
Dm
Sample
~eV/nm!
~eV!
~eV!
~eV!
~D!
~D!
~D!
(810nm)
(740nm)
3DTDA a
3QDA b
1DNDA a
2T3QDA a
3TNDA a
3DQDA b
3.78/328.04
3.65/339.72
3.48/356.32
3.39/365.78
3.51/353.27
3.41/353.63
0.173
0.128
0.097
0.112
0.119
0.144
3.31
3.29
3.33
3.17
3.16
3.29
0.084
0.063
0.059
0.025
0.030
0.103
42.37
39.14
46.67
45.26
62.82
72.54
16.16
11.47
17.16
7.14
11.68
26.61
–
1.91
–
2.17
–
–
0.66
0.73
1.77
2.56
8.04
11.20
2.19
2.03
–
4.21
12.32
30.92
Solvent: Tetrahydrofuran.
Solvent: Chloroform.
b
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688
Nampoothiri et al.
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
degeneracies of a given optical process, m lm is the electronic
transition dipole moment between states u l & and u m & , and
D m 5 m 112 m 00 is the dipole difference.
In the above equation T lmn and D mn represent the triple
and double sums, respectively, which include the damped
energy dispersion terms in the denominators as in Eq. ~43c!
of Ref. 32 and are given by
T lmn 5Î v 1 , v 2 , v 3
3 $ @~ V lg 2 v s !~ V mg 2 v 1 2 v 2 !~ V ng 2 v 1 !# 21
21
1 @~ V *
lg 1 v 3 !~ V mg 2 v 1 2 v 2 !~ V ng 2 v 1 !#
* 1 v 1 1 v 2 !~ V ng 2 v 3 !# 21
1 @~ V *
lg 1 v 1 !~ V mg
* 1 v 1 1 v 2 !~ V *ng 1 v s !# 21 %
1 @~ V *
lg 1 v 1 !~ V mg
~3!
FIG. 5. Dispersion of g (2 v ; v , v ,2 v ) for 1DNDA and 2T3QDA. Solid
curve is the best fit to the three-level model as described in the text.
and
D mn 5Î v 1 , v 2 , v 3
the perturbation expansion given by Orr and Ward,32 the
second molecular hyperpolarizability g ( v s ; v 1 , v 2 , v 3 ) in
this case is given by14,32
FS D
S D
G
g ~ v s ; v 1 , v 2 , v 3 ! 5aK ~ \ ! 23 m 401
1
m 12 2
T 121
m 01
Dm 2
T 1112D 11 ,
m 01
3 $ @~ V mg 2 v s !~ V mg 2 v 3 !~ V ng 2 v 1 !# 21
21
1 @~ V mg 2 v 3 !~ V *
ng 1 v 2 !~ V ng 2 v 1 !#
* 1 v s !~ V mg
* 1 v 3 !~ V ng
* 1 v 1 !# 21
1 @~ V mg
* 1 v 3 !~ V ng 2 v 2 !~ V *ng 1 v 1 !# 21 % ,
1 @~ V mg
~2!
where K is a constant that depends on the frequencies and
FIG. 6. Dispersion of g (2 v ; v , v ,2 v ) for 3TNDA and 3DQDA. Solid
curve is the best fit using a three-level model as described in text.
~4!
where v s 5 v 1 1 v 2 1 v 3 , V lg 5 v lg 2i (G lg /2) with G lg being the damping associated with the the excited state u l & and
\ v mg is the energy difference between states u g & and u m & .
Î v 1 , v 2 , v 3 represents the average of all terms obtained by permuting frequencies v 1 , v 2 and v 3 and a indicates the orientational average which is 1/5 for an isotropic liquid. For self
action process v 1 5 v 2 52 v 3 5 v .
A total of 12 distinct terms appear in each of the triple
sum and double sum expressions. The expressions T 121 and
D 11 represent the contributions from the two-photon and
one-photon transition channels, respectively, and are positive
for incident photon energy below the resonance. The remaining part, T 111 is nonzero only for noncentrosymmetric structures. We have found that the two-state model comprising of
only one-photon channel cannot describe the observed dispersion. The three-essential state model, however, describes
the nature of observed dispersion satisfactorily when we consider a more realistic hyperbolic secant line shape instead of
Lorentzian shape. This is because, the theoretical description
for hyperpolarizability should take into account the inhomogeneously broadened absorption line profile of the electronic
transitions of the molecules. We find that sech hyperbolic
function, as suggested in Ref. 33, provides a better description for the linear absorption spectrum than the Lorentzian
and hence the dispersion of the nonlinearity. In this case, a
typical energy ~frequency! dispersion term in Eqs. ~3! and ~4!
transforms into a convoluted term as below33
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Nampoothiri et al.
J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
1
~ v lg 6n v 6iG lg !
⇒6
1
S
v lg 6n v
1
sech
is lg
s lg
689
D
~ 2/p !~ v lg 6n v !
~ v lg 6n v ! 2 1 ~ p s lg /2! 2
,
~5!
where s lg is the width of the hyperbolic secant function.
Considering the sech line shape in the three-state model @cf.
Eq. ~2!#, the theoretical fits to the observed g dispersion in
various samples are shown in Figs. 4, 5 and 6. The location
of one and two-photon states, their linewidths and the corresponding transition dipole moments obtained from this
analysis are listed in Table I. We find that the most dominant
contributions in the triple sum and double sum expressions
arise from the terms involving the denominators:
T 121 ,T 111→ @~ V 102 v ! 2 ~ V 2022 v !# 21
and
D 11→ ~ V 102 v ! 23 .
A close examination of the one-photon and two-photon
channel contributions at various excitation wavelengths and
the fitted parameters for these samples reveal the following
features. A two-photon state is predicted 0.1–0.5 eV below
the one-photon state. As the photon energies of the radiation
field ~1.5–1.7 eV! are far below one-photon resonance ~.3
eV! in these samples, the one-photon channel ~double sum
expression! does not contribute much to the observe spectral
variation and the nonlinearity arising from this channel is
negative throughout for all the samples. On the other hand,
the two-photon channel contribution changes from positive
to negative as the excitation wavelength approaches the twophoton resonance. The observed dispersion of g is then due
to the mutual cancellation of the contributions of the two
channels at some wavelengths and reinforcement at other
wavelengths. The extent of this reinforcement/cancellation is
governed by the factor ( m 12 / m 01) @cf. Eq. ~2!#, the ratio of
the coupling strengths between various states. This interference effect of the two channels is exemplified using theoretical calculations for 2T3QDA in Fig. 7. The differences in
the nonlinearity of various structures at off-resonant wavelength 810 nm arises predominantly from the differences in
their transition dipole moments.
In the light of above analysis, following broad correlations of nonlinearity with chemical structure can be seen. A
comparison of the results for three symmetrically substituted
diacetylenes 3TNDA, 1DNDA and 3DQDA at 810 nm
shows that the aryl substituents containing a heteroatom such
as N and S produce large transition dipole moment m 01 and
hence higher nonlinearity. This is consistent with the recent
observations in oligomers of conjugated rigid-rod polymer
PBO and PBZT34,35 where the sulphur heteroatom substitution enhanced the nonlinearity by a factor of 3. From our
studies, it seems that N heterocyclic substitution is more effective than the S heterocyclic substitution for achieving
higher nonlinearity. Further, N heterocyclic substitution in
3DQDA yields a higher value of m 12 compared to S heterocyclic substitution in the case of 3TNDA. This large cou-
FIG. 7. One- and two-photon channel contributions to g (2 v ; v , v ,2 v ) of
2T3QDA calculated using the parameters from Table I. Filled circles are the
experimental points. Dashed-dotted line is the one-photon channel contribution, dashed line represents contribution from the two-photon channel. Solid
line gives the net effect. Vertical dotted line separates the region of cancellation and reinforcement of the two channels in the spectra.
pling between states u 1 & and u 2 & is responsible for the stronger dispersion observed in case of 3DQDA than 3TNDA.
Comparison of g values of yet another symmetric molecule 3DTDA with 1DNDA shows that its g value is smaller
despite the presence of S-heteroatom unlike in the case of
3TNDA. This is because, 3DTDA and 1DNDA have comparable m 01 values, but 3DTDA has a larger one-photon energy
gap (;3.8 eV) perhaps due to smaller number of conjugated
p -bonds. Comparison of g values of 2T3QDA and 3QDA
suggest that the asymmetric substitution of diacetylenes does
not produce enhancement of m 01 and g values. It appears
that the g value of diacetylenes can be significantly enhanced
by symmetrical substitution with p -conjugated heterocyclic
substituents. Further, the constructive interference of one and
two-photon channels can possibly be exploited for some optical device application favorably.
Before concluding, we would like to mention that the
fitted values of transition dipole moments are large. Similar
large values have been observed by other groups15,33,36–38 in
an attempt to describe the experimental dispersion of g
within this theoretical framework. It was concluded that fitting the dispersion curves is not an accurate method for obtaining the true transition dipole moments.33 This is presumably due to the neglect of contributions from higher lying
states37,38 in essential state model, which will tend to increase transition dipole moments to artificially large values.
The large fitted values of transition dipole moments in
our three-state model predict positive imaginary g ~Im$ g % )
values large enough for detection in some molecules like
3DQDA at wavelengths close to two-photon resonance while
no signatures of Im$ g % are observed in open aperture scan.
This only strengthens the fact that these fitted values of tran-
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690
sition dipole moments are artificially enhanced to compensate for the contributions arising from other channels which
are neglected here. This indeed is the case because the linear
absorption spectrum shows another higher lying one-photon
state at ;5 eV ~line width ;0.1 eV! in all these samples.
This state, say u 3 & , will resonantly couple to two-photon state
u 2 & over the spectral range investigated. This additional onephoton channel ( u 2 & → u 3 & ) would become operative once
state u 2 & has finite population due to resonant u 0 & → u 2 & transition. The channel u 2 & → u 3 & would give rise to negative real
and imaginary g values. Negative nonlinearity from this
channel will reinforce real g ~Re$ g % ) and result in partial
cancellation of Im$ g % predicted in three-state model. The
reinforcement of Re$ g % will also lead to a reduction in fitted
values of dipole moments m 01 and m 12 . These effects due to
additional channel will thus be able to account for absence of
any signatures of Im$ g % in our open-aperture scan. Certainly,
inclusion of this channel will provide more accurate explanation of observed dispersion. However, in this case, one
needs to resort to a model which considers real resonant
interactions taking account of populations and relaxation
rates of various states.39 This will increase the number of
fitting parameters to a level which our limited number of
data points do not permit. Hence the absolute value of the
transition dipole moments should be taken with caution.
Rather they must be interpreted as fitting parameters and not
as true transition dipole moments. Nonetheless, these still
reflect the relative coupling strengths between various states
and facilitate to analyze trends within a family of materials.
In view of this, our study is a modest attempt to understand
the relation of g with electronic and chemical structure of
diacetylene derivatives.
IV. CONCLUSION
We have studied the spectral dispersion of second molecular hyperpolarizability g of a series of conjugated diacetylene derivatives by single beam Z-scan technique.
Large g values are observed for these small molecules. The
observed dispersion of g has been explained in the framework of three-essential state model. The g dispersion is attributed to the constructive and destructive interference of
one and two-photon channels. The energy of the two-photon
state, transition dipole moments and line widths of transitions have been estimated. The nonlinearity-structural correlations suggest that g value can be enhanced significantly by
symmetrically substituting with conjugated heterocyclic end
groups. The reinforcement effects of one and two-photon
channels can possibly be exploited favorably.
ACKNOWLEDGMENTS
We would like to thank Dr. Tapanendu Kundu for many
useful discussions. This research was supported by the Department of Science and Technology, Government of India.
1
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J. Chem. Phys., Vol. 109, No. 2, 8 July 1998
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