Second-order nonlinear optical properties of the four tetranitrotetrapropoxycalix[4]arene conformers

Article abstract of DOI:10.1021/ja980791t

This paper reports a systematic experimental and theoretical study of the second-order nonlinear optical properties of multichromophoric molecules that range from dipolar symmetry to three-dimensional octupolar symmetry. The four possible conformers of te

Full text of DOI:10.1021/ja980791t

J. Am. Chem. Soc. 1998, 120, 7875-7883
7875
Second-Order Nonlinear Optical Properties of the Four
Tetranitrotetrapropoxycalix[4]arene Conformers
⊥
§
‡
#
Paul J. A. Kenis, Oscar F. J. Noordman, Stephan Houbrechts, Gerrit J. van Hummel,
#
⊥
‡
⊥
Sybolt Harkema, Frank C. J. M. van Veggel, Koen Clays, Johan F. J. Engbersen,
‡
,§
,⊥
Andre Persoons, Niek F. van Hulst,* and David N. Reinhoudt*
Contribution from the Laboratory of Supramolecular Chemistry and Technology and Applied Optics Group
(
both MESA Research Institute) and Laboratory of Chemical Physics, UniVersity of Twente, P.O. Box 217,
NL-7500 AE Enschede, The Netherlands, and Laboratory of Chemical and Biological Dynamics,
UniVersity of LeuVen, Celestijnenlaan 200 D, B-3001 LeuVen-HeVerlee, Belgium
ReceiVed March 9, 1998
Abstract: This paper reports a systematic experimental and theoretical study of the second-order nonlinear
optical properties of multichromophoric molecules that range from dipolar symmetry to three-dimensional
octupolar symmetry. The four possible conformers of tetranitrotetrapropoxycalix[4]arene (cone, paco, 1,2-
alt, 1,3-alt) were studied by nanosecond hyper-Rayleigh scattering and a newly developed time-resolved
femtosecond hyper-Rayleigh scattering technique. The latter enables to correct for long-lived fluorescence
contributions to the second harmonic scattering intensity. The depolarization ratios Dx/z prove the (partial)
octupolar symmetry of the 1,2-alt and 1,3-alt conformers, and thus explain why their hyperpolarizabilities
âFHRS are of the same order of magnitude as those of the dipolar cone and paco conformers. The corresponding
theoretical second-order nonlinear optical properties (both âFHRS and Dx/z) were calculated using the
conformations obtained from single-crystal X-ray diffraction, molecular mechanics (MM), and molecular
dynamics (MD) calculations. In contrast with sum-over-state calculations presented in the literature, our
theoretical method takes also into account octupolar contributions by linearly adding the NLO-properties of
the separate chromophoric groups and using Bersohn’s theory. The agreement between experimental and
theoretical results is good both for the conformers having dipolar symmetry and for the conformers having
(
[
partly) three-dimensional octupolar symmetry. The 1,2-alt and 1,3-alt conformers of the tetranitrotetrapropoxycalix-
4]arene represent the first examples of multichromophoric molecules that have high hyperpolarizabilities â
due to 3D octupolar symmetry.
Introduction
Scheme 1
Organic molecules with second-order nonlinear optical (NLO)
properties have various potential in the development of materials
for applications, e.g., in frequency doubling and optical switch-
1
ing. Molecules with high second-order NLO activities are
related with high asymmetric polarizability, expressed in the
hyperpolarizability â, which is a third-rank tensor consisting
of 27 components. Typical examples of organic NLO-active
molecules are p-nitroaniline, PNA (1), and dimethylaminoni-
trostilbene, DANS (2), as depicted in Scheme 1. In these
molecules an electron-donating group (D) is connected to an
electron-accepting group (A) Via a π-conjugated system. These
so-called D-π-A units meet thereby the requirement of asym-
metric polarizability. The combination of several D-π-A units
within one single molecule has the advantages that a high dipole
moment is combined with a high hyperpolarizability â if the
D-π-A units are organized in a dipolar configuration. Moreover,
the possibility to enlarge â without the usually observed and
dipolar multichromophoric systems potentially suitable as
3
,4
materials for frequency doubling.
The triphenylcarbinol
5
6
derivatives 4, the calix[4]arene derivatives 5 (cone conforma-
tion, Vide infra), and the bis-dipolar 6,6′-disubstituted binaphthol
7
,8
derivatives 6, as depicted in Scheme 2, are typical examples
of such multichromophoric dipolar molecules.
The combination of several D-π-A units that are not perfectly
aligned in a single molecule leads to more nonzero tensor
(2) Zyss, J.; Ledoux, I.; Bertault, M.; Toupet, E. Chem. Phys. 1991, 150,
2
125.
undesired red shift of the charge transfer band makes such
(3) See, for example: (a) Wolf, J. J.; L a¨ ngle, D.; Hillenbrand, D.;
⊥
Laboratory of Supramolecular Chemistry and Technology.
Applied Optics Group.
Laboratory of Chemical and Biological Dynamics.
Laboratory of Chemical Physics.
Wortman, R.; Matschiner, R.; Glania, C.; Kr a¨ mer, P. AdV. Mater. 1997, 9,
138-143. (b) Verbiest, T.; Clays, K.; Samyn, C.; Wolff, J. J.; Reinhoudt,
D. N.; Persoons, A. J. Am. Chem. Soc. 1994, 116, 9320. (c) Stadler, S.;
Feiner, F.; Br a¨ uchle, C.; Brandl, S.; Gompper, R. Chem. Phys. Lett. 1995,
245, 292.
§
‡
#
(1) (a) Zyss, J.; Chemla, D. S. Nonlinear Optical Properties of Organic
Molecules and Crystals; Academic Press: Orlando, 1987; Vol. 1. (b) Prasad,
P.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules
and Polymers’, John Wiley & Sons: New York, 1991.
(4) Kelderman, E.; Derhaeg, L.; Heesink, G. J. T.; Verboom, W.;
Engbersen, J. F. J.; Van Hulst, N. F.; Clays, K.; Persoons, A.; Reinhoudt,
D. N. AdV. Mater. 1993, 5, 925.
S0002-7863(98)00791-4 CCC: $15.00 © 1998 American Chemical Society
Published on Web 07/23/1998

7876 J. Am. Chem. Soc., Vol. 120, No. 31, 1998
Kenis et al.
Scheme 2
Scheme 3
components than only the â333 and â311 which dominate the â
tensor in simple planar dipolar systems like PNA (Scheme 1).
For most of the multichromophoric systems the contribution of
the individual D-π-A units to the overall â tensor has not been
analyzed in the literature. However, if such a multichro-
mophoric system still has a considerable dipolar character, the
different contributions to the overall â tensor can be obtained
by analysis of the results of both electric-field-induced second-
harmonic generation (EFISH) and hyper-Rayleigh scattering
(HRS) because these techniques assess different combinations
of the first hyperpolarizability tensor. This was shown previ-
ously by Deussen et al.7 and Hendrickx et al.8 in their
investigation of the nonlinear optical properties of the bis-dipolar
certain conformers of calix[4]arenes, molecules containing three-
1
1,12
dimensional octupolar symmetry.
1
3
The calix[4]arene cyclophanes consist of four phenol
6
,6′-disubstituted binaphthol derivatives 6 (Scheme 2).
1
4
moieties connected by methylene bridges. The calix[4]arene
structure can adopt four extreme conformations: the cone, the
partial cone, the 1,2-alternate, and the 1,3-alternate (Scheme
Upon reducing the dipolar arrangement of D-π-A units in
such multichromophoric system, the dipolar component of the
â tensor will decrease, eventually to zero. However, Zyss et
15
3
). Upon alkylation of the phenolic hydroxyl groups with four
9,10
al. have shown that the third rank â tensor contains also an
octupolar component, which starts to play an important role in
nondipolar multichromophoric systems. Based on the math-
ematical properties of tensors they deduced that the hyperpo-
larizability â, which is a fully symmetric third-rank tensor under
propyl groups, interconversion between these conformations is
16
blocked resulting in four different conformers. By subsequent
introduction of four nitro groups at the para position of the
phenoxy groups, four D-π-A units are combined within each
4
,6
calix[4]arene (Scheme 3).
11
Kleinmann symmetry, will have two irreducible components:
The relative orientation of the four D-π-A units in the four
conformers is highly different, and the character of the conform-
ers varies from strongly dipolar for the cone and partial cone
a dipolar part of weight J ) 1 and an octupolar part (J ) 3, eq
1
), each having 2J + 1 independent coefficients.10
â ) âJ)1 + âJ)3
(paco) conformers to an essentially nondipolar symmetry for
(1)
the 1,2-alt(ernate) and 1,3-alt(ernate) conformers (Scheme 3).
The 1,2-alt and the 1,3-alt conformers represent examples of
three-dimensional nondipolar NLO molecules, in which the
dipolar vectors of the four chromophoric units are oppositely
oriented. Whereas the dipolar contribution will be significantly
lower than those of the cone and paco conformers, the 1,2-alt
and 1,3-alt conformers may exhibit interesting higher order
Due to the octupolar contribution, high hyperpolarizabilities â
can also be obtained for nondipolar multichromophoric systems.
Zyss9b has also shown that for molecules strictly belonging to
a multipolar symmetry group of weight J, all irreducible
tensorial components of weight lower than J cancel due to
symmetry requirements. Thus, for molecules with octupolar
symmetry (J ) 3) all dipolar (J ) 1) contributions vanish. The
main difference between the equivalent dipolar system and these
octupolar systems lies in the strongly different off-diagonal â311
values, while the diagonal â333 values are comparable. A typical
example, triisopropylaminotrinitrobenzene (3, TIATB), is de-
picted in Scheme 1. A difficulty of studying nondipolar
molecules is the lack of a dipole moment, thereby excluding
the possibility of the use of the EFISH technique. Until now,
mainly the nonlinear optical properties of molecules with highly
dipolar or two-dimensional (planar) octupolar symmetry have
been studied. Here we present a systematic investigation on
(octupolar) contributions to the hyperpolarizability of these
molecules.
In this paper we describe a systematic study of the nonlinear
optical properties of molecules which range from a dipolar
symmetry to a (partly) three-dimensional octupolar symmetry.
(11) Kleinman, D. A. Phys. ReV. 1962, 126, 1977.
(12) Recently, indications for three-dimensional octupolar symmetry in
bacteriorhodopsin trimers have been reported: Hendrickx, E.; Vinckier, A.;
Clays, K.; Persoons, A. J. Phys. Chem. 1996, 100, 19672-80.
(
13) The official IUPAC name for the unsubstituted [1.1.1.1]metacy-
clophane without the hydroxyl groups: pentacyclo[19.3.1.13,7.19,13.115,19]-
octacosa-1(25),3,5,7(28),9,11,13(27),15,17,19(26),21,23-dodecaene.
(14) (a) B o¨ hmer, V. Angew. Chem., Int. Ed. Engl. 1995, 34, 713-745.
(
5) Kelderman, E.; Starmans, W. A. J.; Van Duynhoven, J. P. M.;
Verboom, W.; Engbersen, J. F. J.; Reinhoudt, D. N. Chem. Mater. 1994, 6,
12-417.
6) Kelderman, E.; Heesink, G. J. T.; Derhaeg, L.; Verbiest, T.; Klaase,
(b) Gutsche, C. D. Calixarenes; Royal Society of Chemistry: Cambridge,
1989. (c) Calixarenes. A Versatile Class of Macrocylcic Compounds; Vicens,
J., B o¨ hmer, V., Eds.; Kluwer Academic Publishers: Dordrecht, 1991. (d)
Ikeda, A.; Shinkai, S. Chem. ReV. 1997, 97, 1713-1734. (e) Pochini, A.;
Ungaro, R In ComprehensiVe Supramolecular Chemistry; V o¨ gtle, F.; Ed.;
Pergamon Press: Oxford, 1996; Vol. 2, pp 103-144.
4
(
P. T. A.; Verboom, W.; Engbersen, J. F. J.; Van Hulst, N. F.; Persoons, A.;
Reinhoudt, D. N. Angew. Chem., Int. Ed. Engl. 1992, 31, 1074.
(
7) Deussen, H.-J.; Hendrickx, E.; Boutton, C.; Krog, D.; Clays, K.;
Bechgaard, K.; Persoons, A.; Bjornholm, T. J. Am. Chem. Soc. 1996, 118,
841-6852.
8) Hendrickx, E.; Boutton, C.; Clays, K.; Persoons, A.; Van Es, S.;
Biemans, T.; Meijer, B. Chem. Phys. Lett. 1997, 270, 241-244.
9) (a) Ledoux, I.; Zyss, J.; Siegel, J. S.; Brienne, J.; Lehn, J.-M. Chem.
Phys. Lett. 1990, 172, 440-444. (b) Zyss, J. J. Phys. Chem. 1993, 99, 6583-
599.
10) Zyss, J. Nonlinear Opt. 1991, 1, 1.
(15) (a) Van Loon, J.-D.; Arduini, A.; Coppi, L.; Verboom, W.; Pochini,
A.; Ungaro, R.; Harkema, S.; Reinhoudt, D. N. J. Org. Chem. 1990, 55,
5639. (b) Groenen, L. C.; Van Loon, J.-D.; Verboom, W.; Harkema, S.;
Casnati, A.; Ungaro, R.; Pochini, A.; Ugozzoli, F.; Reinhoudt, D. N. J.
Am. Chem. Soc. 1991, 113, 2385. (c) Groenen, L. C.; Ru e¨ l, B. H. M.;
Casnati, A.; Timmerman, P.; Verboom, W.; Harkema, S.; Pochini, A.;
Ungaro, R.; Reinhoudt, D. N. Tetrahedron Lett. 1991, 32, 2675.
(16) Iwamoto, K.; Araki, K.; Shinkai, S. J. Org. Chem. 1991, 56, 4955-
4962.
6
(
(
6
(

Second-Order Nonlinear Optical Properties
J. Am. Chem. Soc., Vol. 120, No. 31, 1998 7877
Scheme 4
Figure 1. Configuration of the space-fixed coordinate system of the
HRS experiments.
into the 1,2-alt conformer of tetranitrotetrapropoxycalix[4]arene
(10) in 83% yield by means of a modified ipso-nitration (Scheme
4
).
I. Hyper-Rayleigh Scattering Experiments
Theory. From harmonic light scattering theory as developed
2
1
For that purpose the four possible conformers of tetranitrotetra-
propoxycalix[4]arene were studied by nanosecond and time-
resolved femtosecond hyper-Rayleigh scattering, NHRS and
FHRS respectively, as described in the first part of this paper.
In the second part of this paper the corresponding theoretical
second-order nonlinear optical properties are calculated starting
from conformations obtained from single-crystal X-ray diffrac-
tion, molecular mechanics (MM), and molecular dynamics (MD)
calculations. In the third part the excellent agreement between
experimental and theoretical results for molecules that range
from dipolar to octupolar symmetries will be shown. This
demonstrates the power of time-resolved femtosecond hyper-
Rayleigh scattering measurements combined with calculations
based on X-ray, MM, or MD structures in the full interpretation
of the nonlinear optical properties of multichromophoric
molecules of different symmetries in general.
by Bersohn et al. in 1966, it is known that in the space-fixed
coordinate system depicted in Figure 1, the intensities of the
detected scattered light polarized in the x- and z-direction, Ix
z
and I , respectively, are proportional to the macroscopic ob-
2
2
servables 〈âzzz 〉 and 〈âxzz 〉 (eq 1). In this configuration, the
fundamental laser beam is propagating in the x-direction and is
linearly polarized in the z-direction. The scattered second
harmonic light is detected in the y-direction.
2
I
∝ 〈âxzz
〉
〉
x
2
Ix ∝ 〈âzzz
(1)
2
The total scattering intensity IHRS ∝ 〈âHRS 〉 is proportional to
the sum of the macroscopic observables (eq 2).
2
2
2
IHRS ∝ 〈âHRS 〉 ) 〈âzzz 〉 + 〈âxzz
〉
(2)
Results and Discussion
The hyperpolarizabilities â in eqs 1 and 2 are defined in a
macroscopic space-fixed coordinate system. Bersohn et al.21
have also derived these macroscopic expressions (eqs 1 and 2)
in terms of microscopic â by averaging of the molecules-fixed
axes relative to the space-fixed axes over all orientations.
Obviously, these expressions depend on the symmetry of the
molecule and become more simple upon increasing symmetry.
For molecules with C2V symmetry having only one nonzero â
component â333, the macroscopic observables are given by eq
3.
Synthesis. The synthesis of the four different conformers
of tetranitrotetrapropoxycalix[4]arene (Scheme 3) proceeds via
alkylation of tetra-tert-butylcalix[4]arenes, using different reac-
tion conditions for the respective conformers. Kelderman et
6,17
al.
have already reported the selective preparation of three
of the four different tetra-tert-butyltetrapropoxycalix[4]arene
conformers, the cone, paco, and 1,3-alt. They showed that
consecutive ipso-nitration afforded the three corresponding
6,18
tetranitrotetrapropoxycalix[4]arene conformers.
The 1,2-alternate conformer of tetra-tert-butyltetrapropoxycalix-
2
3
05
2
〈
〈
âxzz 〉 ∝
â333
[
4]arene could be obtained via a stepwise route as described by
1
1
9,20
Shinkai et al.
(Scheme 4). When the alkylation of tetra-
tert-butyl-1,3-dibenzylcalix[4]arene 7 was performed in a
mixture of DMF and THF, according to Shinkai et al., less than
5% of the desired paco conformer 8 was obtained. However,
2
15
2
âzzz 〉 ∝
â333
105
(3)
1
For molecules with D3h symmetry, with â333 ) -â311 ) -â131
-â113 and the other components being zero (2D octupole),
the macroscopic observables are given by eq 4.
the yield of 8 could be improved considerably (67%) when the
reaction was performed in neat THF. Debenzylation of 8 and
subsequent propylation yielded the 1,2-alt conformer of tetra-
tert-butyltetrapropoxycalix[4]arene (9), which was converted
)
2
16
1
2
〈
〈
âxzz 〉 ∝
â333
05
(17) Kelderman, E.; Heesink, G. J. T.; Derhaeg, L.; Verbiest, T.; Klaase,
P. T. A.; Verboom, W.; Engbersen, J. F. J.; Van Hulst, N. F.; Persoons, A.;
Reinhoudt, D. N. Angew. Chem., Int. Ed. Engl. 1992, 31, 1074.
2
24
2
âzzz 〉 ∝
â333
(4)
(
18) Verboom, W.; Durie, A.; Reinhoudt, D. N. J. Org. Chem. 1992,
7, 1313.
19) The synthesis and analytical data of compounds 7-9 are de-
scribed: Iwamoto, K.; Araki, K.; Shinkai, S. Tetrahedron 1991, 47, 4325-
342.
20) The synthesis of 10 starting from 9 is described: Iwamoto, K.; Araki,
1
05
5
(
The ratio of the macroscopic observables Ix and Iz is defined
as the depolarization ratio Dx/z (eq 5). Respectively, a horizontal
and a vertical analyzer can be introduced in the detection path
4
(
K.; Shinkai, S. J. Chem. Soc., Perkin Trans I. 1991, 1611-1613. The
analytical data of 10 are described: Iwamoto, K.; Araki, K.; Shinkai, S. J.
Org. Chem. 1991, 56, 4955-4962.
(21) Bersohn, R.; Pao, Y-H.; Frisch, H. L. J. Chem. Phys. 1966, 45,
3184.

7878 J. Am. Chem. Soc., Vol. 120, No. 31, 1998
Kenis et al.
Figure 2. Typical time-dependent FHRS signals of the four conformers of tetranitrotetrapropoxycalix[4]arene. Note the different y-scales.
Table 1. Experimental Hyperpolarizabilities â (in ‚10- esu;
30
al.26 Especially, excitation of the NLO chromophores by two
or three photons can give rise to fluorescence emission in the
range of the frequency-doubled light (multiphoton fluorescence).
In the NHRS measurement both the contributions of hyper-
Rayleigh scattering and multiphoton fluorescence are detected,
as HRS and two-photon fluorescence are both incoherent
processes that scale with the square of the fundamental intensity
and occur on the same nanosecond time scale. Therefore, the
NHRS technique will give rise to the higher apparent hyper-
polarizability â if multiphoton fluorescence occurs.
NHRS, FHRS) and Depolarization Ratios Dx/z (FHRS) of All Four
a
Conformers of Tetranitrotetrapropoxycalix[4]arene
b
c
c
conformation
â
NHRS
â(0)
N
â
FHRS
â(0)
F
D
x/z
cone
paco
21
22
30
8
14
36
19
20
9
19
10
10
5
0.15 ( 0.02
0.18 ( 0.04
0.39 ( 0.06
0.47 ( 0.18
d
d
d
14
19
5
d
1
1
,2-alt
,3-alt
a
All measurements in CHCl at room temperature, error: <20%.
Nanosecond hyper-Rayleigh scattering (NHRS) with Nd:YAG laser
1064 nm). Femtosecond hyper-Rayleigh scattering (FHRS) with Ti-
Sapphire laser (900 nm). Values contain a fluorescence contribution.
3
b
c
(
d
Femtosecond Hyper-Rayleigh Scattering. The recently
developed time-resolved femtosecond hyper-Rayleigh scattering
2
3
(
FHRS) technique was used in order to correct for most of
in order to measure the Ix and Iz separately at a fixed intensity
the long-lived fluorescence contributions to the hyperpolariz-
abilities of the four calixarene conformers. The time-dependent
scattered signals of the conformers at four different concentra-
tions were measured at a fundamental wavelength of 900 nm.
In Figure 2 a typical time-dependent signal of each of the four
calixarene conformers is given. The background signal that is
present in all these measurements is due to dark counts from
the microchannel plate photomultiplier tube as well as due to a
of the fundamental beam.
2
Ix 〈âxzz
Dx/z + Iz
〉
〉
)
(5)
2
〈âzzz
The observables are dependent on the symmetry of the molecule
as shown above. Consequently, the same holds for the
depolarization ratio. For example, in case of C2V symmetry (eq
2
7
constant electronic system response.
2
2
For the cone and the 1,3-alt conformer the time-dependent
signal is very sharp and returns fast to the baseline. However,
the time-dependent signals from the paco and the 1,2-alt
calixarene solutions show a clear contribution of fluorescence
with a lifetime of approximately 2 ns. Although the signals of
the cone and the 1,3-alt are much more intense than the signal
obtained of neat chloroform, they are all equal in shape and
width. As the chloroform solution itself does not give rise to
a substantial fluorescence signal, the signals from both the cone
and the 1,3-alt calix[4]arene solutions must also originate from
instantaneously scattered second harmonic light and can be used
as such to determine the hyperpolarizabilities â. However, for
the paco and 1,2-alt conformers the time-resolved measurements
are essential to correct for the fluorescence contributions in order
to obtain the hyperpolarizabilities â. By using a time-window
of 0.3 ns centered at t ) 0 most of the long-lived fluorescence
contributions are eliminated. Unfortunately, (mathematical)
correction for the fast fluorescent emission within the 0.3 ns
time-window is difficult, as the starting point of this fast
fluorescence is unknown and is overlapping with the actual
3
) the ratio of 〈âzzz 〉 and 〈âxzz 〉 is equal to 0.2, whereas in case
of D3h symmetry (eq 4, 2D octupole) this ratio is 0.67.
Measurements. The hyperpolarizabilities â of the four
conformers were determined by two hyper-Rayleigh Scattering
(
HRS) methods operating in different time-windows. Firstly,
the results with the nanosecond hyper-Rayleigh scattering
NHRS) technique22 and then the results with the faster
(
23
femtosecond hyper-Rayleigh scattering (FHRS) technique are
discussed.
Nanosecond Hyper-Rayleigh Scattering. The hyperpolar-
izabilities â of all four conformers of tetranitrotetrapropoxycalix-
[4]arene were determined by nanosecond hyper-Rayleigh Scat-
tering (NHRS) at a fundamental wavelength of 1064 nm with
chloroform as a reference. The âNHRS data are listed in Table
24
1.
However, we should be careful in the interpretation of these
hyperpolarizabilities obtained by NHRS. The HRS signal can
possibly contain a fluorescence contribution from multiphoton
processes as was described by Flipse et al. and Hendrickx et
25
(
22) (a) Clays, K.; Persoons, A. Phys. ReV. Lett. 1991, 66, 2980; (b)
Clays, K.; Persoons, A. ReV. Sci. Instrum. 1992, 63, 3285.
23) Noordman, O. F. J.; Van Hulst, N. F. Chem. Phys. Lett. 1996, 253,
45-150.
24) For the cone conformer âNHRS values of 27‚10
2
3
(
second-harmonic signal. The resulting hyperpolarizabilities
1
-
30
(
esu have been
(26) Hendrickx, E.; Dehu, C.; Clays, K.; Bredas, J. L.; Persoons, A.
Experimental and Theoretical Investigation of the Second Order Optical
Properties of the Chromophore Retinal and its Derivatives. In Polymers
for Second-Order Nonlinear Optics; Lindsay, G. A. and Singer, K. D., Eds.;
ACS Symposium Series 601, American Chemical Society: Washington,
DC, 1995; Chapter 6.
reported earlier. See ref 4 and Heesink et al. (Heesink, G. J. T.; Van Hulst,
N. F.; B o¨ lger, B.; Kelderman, E.; Engbersen, J. F. J.; Verboom, W.;
Reinhoudt, D. N. Appl. Phys. Lett. 1993, 62, 2015-2017). Since the other
three conformers were not studied by HRS, also the cone conformer was
synthesized and measured to allow for a good comparison.
(
25) Flipse, M. C.; de Jonge, R.; Woudenberg, R. H.; Marsman, A. W.;
(27) Since these counts are not correlated with the laser pulses, they can
easily be subtracted.
Walree, C. A.; Jenneskens, L. W. Chem. Phys. Lett. 1995, 245, 297.

Second-Order Nonlinear Optical Properties
J. Am. Chem. Soc., Vol. 120, No. 31, 1998 7879
064 nm, respectively. According to the two-level model,29
1
2
a
4% higher resonance enhancement is expected at 900 nm (1.93
vs 1.55 at 1064 nm with λmax ) 291 nm) for the four
3
0
conformers.
Obviously, resonance corrections can only
explain relative differences between the two sets of HRS data
measured at different wavelengths. Furthermore, the experi-
mental error in HRS data can be as high as 20%. Good
agreement between NHRS and FHRS data is obtained by taking
into account the fluorescence contributions and the two factors
just mentioned (Table 1). As the FHRS data are corrected for
long-lived fluorescence, these data will be used in the further
discussion of this paper.
Depolarization Ratios. In order to obtain information about
the symmetry of the four conformers, FHRS depolarization
2
3
ratios Dx/z were determined (Table 1). These measurements
were also performed with a 0.3 ns time-window to eliminate
long-lived fluorescence.
Figure 3. Schematic representation of fluorescence enhancement of
the scattered signal.
âFHRS of the four tetranitrotetrapropoxycalix[4]arene conformers
are listed in Table 1. Comparison with the results of the NHRS
measurements confirms that for a realistic comparison of the
hyperpolarizabilities of the conformers, these time-resolved
measurements are crucial. Nevertheless, still contributions from
fast fluorescence to the âFHRS values are possible.
In order to proof the occurrence of fluorescence during the
NHRS measurements in the area of the second-harmonic
wavelength, additional NHRS measurements were performed
using different interference filters. Such filters allow only a
certain range of wavelengths to pass through. This would
explain the discrepancies between the hyperpolarizabilities from
the nanosecond (âNHRS) and femtosecond (âFHRS) hyper-Ray-
leigh scattering measurements. Moreover, this should give also
information about the relative contribution of fluorescence to
the signal in the NHRS experiments for the different calixarene
conformers at different wavelengths. Since no fluorescence
could be detected in static fluorescence experiments using a
common fluorospectrophotometer,28 the measurements were
performed with the same intense Nd:YAG laser as used in the
NHRS experiments operating at a fundamental wavelength of
Discussion. Based on the idealized symmetric structures of
the four conformers, a very small or zero value of â is expected
for the 1,2-alt and 1,3-alt conformers compared to the cone and
paco conformers, which have a strongly dipolar character.
Experimentally, however, the 1,2-alt and 1,3-alt conformers
exhibit âHRS values of the same order of magnitude as the cone
conformer. One possible explanation is that the 1,2-alt and 1,3-
alt conformers do not adopt solely the ideal symmetric structure
in solution at the time-scale of the HRS measurement, but by
thermal motions of the four chromophoric units in the molecule,
considerable deviations occur. However, this cannot explain
why the cone conformer in which the four dipoles of the D-π-A
systems have a relatively high degree of alignment exhibits an
even lower â than the 1,2-alt conformer. Since all four
conformers have the same absorption maximum of 291 nm (part
of) the observed differences in hyperpolarizabilities cannot
originate from differences in electronic structure or from
differences in resonance enhancement either.
The depolarization ratios obtained for the four conformers
(Table 1) explain the small difference between the âHRS values
of the dipolar cone and paco conformers (Dx/z close to theoretical
value of 0.2) compared to the nondipolar 1,3-alt conformer (Dx/z
enhanced closer to the theoretical value of 0.67 for D3h
symmetry). In fact, the 1,3-alt conformer is a 3D representative
of a nondipolar, noncentrosymmetric molecule, in which the
strong dipolar vectors of the individual NLO-phores in the
molecule cancel. From such molecules considerable higher
order (octupolar) contributions to the â tensor can be expected
as explained above. The depolarization ratio of the 1,2-alt
conformer of 0.39 points to an intermediate, lower symmetry.
In view of these results, we have investigated the second-
order nonlinear optical properties of the four conformers also
at a theoretical level in order to obtain further evidence for the
interpretation of the experimental results. This is the subject
of the second part of this paper.
1
064 nm. Chloroform solutions of 1,3-alt and cone conformers
showed only weak background fluorescence from the solvent
if a 480 nm interference filter was positioned in the detection
path. Solutions of the paco and the 1,2-alt conformers exhibited
a fluorescence intensity that was 6 and 3 times larger than the
value for the solvent, respectively. The same experiment with
a 600 nm interference filter showed a fluorescence enhancement
of 33 and 25 times for the paco and 1,2-alt conformer,
respectively. For the cone conformer no and for the 1,3-alt
conformer only a slight fluorescence enhancement was observed
at this wavelength. These results indicate that in the NHRS
experiments of the paco and the 1,2-alt conformers a substantial
part of the signal intensity at 532 nm (the second harmonic
wavelength is between the two wavelengths of the interference
filters) is caused by fluorescence. This is schematically
explained in Figure 3. Consequently, the real âNHRS values for
the paco and the 1,2-alt conformers are lower as confirmed by
FHRS. It is however impossible to correct the âNHRS values
quantitatively for the fluorescence contribution.
II. Theoretical Hyperpolarizabilities and Depolarization
Ratios
In order to calculate the second-order nonlinear optical
properties of a molecule, knowledge of the energetically
favorable molecular conformations is required. Although in
principle these conformations could be obtained by ab initio
calculations, this would be a tremendous mathematical task for
the multichromophoric calix[4]arene conformers studied in this
Most of the discrepancies between the observed FHRS and
NHRS hyperpolarizabilities can be explained by taking the
fluorescence contribution in the NHRS experiments into account.
However, some other factors can play a role. The FHRS and
NHRS experiments were performed at wavelengths of 900 and
(
28) These fluorescence spectra were recorded on a SPEX fluorolog 1691
(29) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664.
(30) For the same reason, an enhancement of 16% for the â of chloroform
was observed experimentally in accordance with the two-level model.
spectrofluorometer (SPEX Industries, Edison, NJ) equipped with a 450 W
SPEX 1907 Xenon light source.

7880 J. Am. Chem. Soc., Vol. 120, No. 31, 1998
Kenis et al.
work. Alternatively, information about possible favorable
conformations could be derived from single-crystal X-ray
structures, if available. A second alternative is to calculate the
conformations employing semiempirical force fields of molec-
ular mechanics or dynamics packages. An advantage of
molecular dynamics calculations is that also conformational
dynamics in solution can be taken into account. The latter
allows for a better comparison of the calculated, and the
experimental results as the actual NLO properties are measured
in solution.
Theory. Brouyere et al.31 have calculated by using sum-
oVer-state calculations hyperpolarizabilities of 24, 14, 1, and 1
-
30
(‚10
esu), respectively, for the cone, paco, 1,2-alt, and 1,3-
alt conformers of tetranitrotetramethoxycalix[4]arene. In these
calculations an averaged, symmetrical conformation for each
conformer, obtained from single crystal X-ray structures of
similar calix[4]arene conformers, is used. Although this method
takes into account electronic transitions between the ground state
and many excited states, as well as transitions between excited
states it does not account for the conformational dynamics that
can play an important role in a multichromophoric system in
solution. Moreover, possible octupolar contributions to the
second-order nonlinear optical properties have also not been
taken into account.
Figure 4. X-ray structures of all four tetranitrotetrapropoxycalix[4]-
arene conformers.
In this work the hyperpolarizabilities were calculated in a
more qualitative way, but our method also takes possible
octupolar contributions into account. The four D-π-A units in
the molecule are considered to contribute independently to the
molecular â. The latter implies that possible changes in the
electronic structure due to interactions between the D-π-A
systems are neglected. This seems a valid assumption as from
the theoretical work by Di Bella et al.32 it can be deduced that
the four chromophoric units in the calix[4]arene structure have
an effect of less than 10% on the mutual NLO properties. This
effect is within the experimental error, being up to 20%.
Furthermore, in the calculations it is assumed that the four
separate D-π-A units in the calix[4]arene have two major
components that contribute to the â tensor: the first in the
direction of the dipole moment of the single D-π-A system
(
â333)3 and the second perpendicular to the direction of the first,
3
Figure 5. Energy minimized structures (MM) of all four tetranitro-
tetrapropoxycalix[4]arene conformers.
34
in the plane of the phenyl ring. With this second vector also
the â311, â131, and â113 tensor components are included. Next,
all 27 components of the â tensor of each calix[4]arene
conformation are calculated from all the â333, â311, â131, and
â113 tensor components of the individual D-π-A systems, taking
into account their orientation with respect to the molecular plane
through the four methylene groups that connect the four
chromophoric units. The contribution of the separate D-π-A
units to the â tensor of the calix[4]arene is calculated by
performing a coordinate transformation of the â of each D-π-A
unit to the coordinate system of the calix[4]arene. The four
contributions are added linearly. Possible octupolar contribu-
tions are inherently taken into account in this way. From the
situation that only the â333 of a single D-π-A system is nonzero.
The resulting âHRS value of the cone conformer was scaled to
-30
the experimental âFHRS value of 36‚10
esu as these calcula-
tions result in relative rather than quantitative values.
Results. In this work the NLO properties of the four
conformers were calculated by using conformations obtained
from single crystal X-ray diffraction (Figure 4) as well as
structures that were calculated by molecular mechanics (MM)
in vacuum (Figure 5) and by molecular dynamics (MD) in
3
5,36
chloroform using the CHARMm force field.
2
X-ray Diffraction and Molecular Mechanics Calculations.
From all four conformers crystals were grown that were suitable
for single-crystal X-ray diffraction, and their structures have
been elucidated (Figure 4). By using molecular mechanics
calculations (MM) the energy minimized molecular structures
resulting molecular â tensor, the macroscopic observables 〈âzzz 〉
2
and 〈âxzz 〉 are derived, and with those, the theoretical values
for âHRS and Dx/z are calculated, all according to the Bersohn’s
theory.21 In these calculations the ratio between the â311 and
â333 tensor components of a single chromophoric unit was varied
from -0.4 to 0.5 with steps of 0.1. A ratio of 0.0 denotes the
(
35) Quanta/CHARMm 4.1 was bought from Molecular Simulations,
(
31) Brouyere, E.; Persoons, A.; Bredas, J. L. J. Phys. Chem. 1997, 101,
142-4148.
32) Di Bella, S.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 1992,
14, 5842.
33) The vector connecting the oxygen of the propoxy group and the
nitrogen of the nitro group.
34) The vector connecting the C-atoms ortho to the nitro group.
Burlington, MA, U.S.A.
4
(36) The CHARMM force field is described: (a) Brooks, B. R.;
Bruccoleri, R. E.; Olafsen, B. D.; States, D. J.; Swaminathan, S.; Karplus,
M. J. Comput. Chem. 1983, 4, 187. (b) Momany, F. A.; Klimkowski, V. J.;
Sch a¨ fer, L. J. Comput. Chem. 1990, 11, 654. (c) Momany, F. A.; Rone, R.;
Kunz, H.; Frey, R. F.; Newton, S. Q.; Sch a¨ fer, L. J. Mol. Structure 1993,
286, 1.
(
1
(
(

Second-Order Nonlinear Optical Properties
J. Am. Chem. Soc., Vol. 120, No. 31, 1998 7881
Table 2. Dihedral Angles of the X-ray Structures and of the
Energy Minimized Structures (MM) of the Four Conformers of
Tetranitrotetrapropoxycalix[4]arene
φ
1
φ
2
φ
3
φ
4
conformer MM X-ray MM X-ray MM X-ray MM X-ray
cone
paco
83.6 97.9
88.3 96.7
45.5 35.9 84.6 98.0 43.1 35.7
39.2 31.5 88.0 98.5 -92.0 -87.4
1,2-alt 46.7 40.2 -46.7 -56.1 -81.8 -84.2 81.8 84.8
,3-alt 90.2 83.8 -90.2 83.8 90.2 83.8 -90.2 83.8
1
Table 3. Calculated Hyperpolarizabilities âHRS and Depolarization
ratios Dx/z
cone
paco
1,2-alt
1,3-alt
â
311a/
333
â
â
HRS
D
x/z
â
HRS
D
x/z
â
HRS
D
x/z
â
HRS
D
x/z
X-ray 36 0.301 22.8 0.382 14.6 0.509 25.0 0.662
-
-
-
-
0.4 MM
MD
36 0.321 21.8 0.379 12.5 0.513 21.5 0.667
36 0.333 20.9 0.383 12.4 0.526 20.7 0.664
Figure 6. Distribution of the calculated âMDs for the four calixarene
conformers.
X-ray 36 0.236 20.9 0.278 13.8 0.456 18.3 0.657
0.3 MM
MD
36 0.252 20.5 0.282 11.8 0.459 15.5 0.667
36 0.262 19.7 0.287 11.7 0.471 15.3 0.661
significant â values that were calculated for the 1,2-alt
conformer. The Dx/z ratios calculated for the 1,3-alt conformer
clearly point to dominant octupolar contributions to the observed
NLO-activity.
X-ray 36 0.191 19.8 0.199 13.1 0.406 12.0 0.640
0.2 MM
MD
36 0.202 19.7 0.208 11.3 0.408 9.8 0.667
36 0.208 19.0 0.213 11.1 0.418 10.0 0.651
X-ray 36 0.162 19.4 0.156 12.5 0.364 6.8 0.58
0.1 MM
MD
36 0.168 19.5 0.167 10.9 0.367 4.6 0.667
36 0.171 18.8 0.170 10.7 0.372 5.4 0.607
Molecular Dynamics Calculations. In the experiment, the
conformers are dissolved in chloroform at a temperature of 300
K. Due to interaction with the solvent and the thermal motions
of the molecule, the orientation of the D-π-A systems with
respect to each other will vary continuously. In order to take
these interactions into account MD calculations were carried
out with the conformers placed in a chloroform box. After
heating to 300 K and an equilibration period, a molecular
dynamics run of 250 ps was performed. Every 0.2 ps a structure
was recorded, resulting in 1250 structures for each conformer.
The âHRS tensors of all 1250 conformations of each conformer
were calculated and averaged. The resulting âMD values are
listed in Table 3. In Figure 6 the distribution of the calculated
âMD’s is given at a â311/â333 ratio of -0.2. The 1,3-alt and
paco conformers have a small distribution indicating that a small
change in conformation does not influence the âMD much. The
cone and 1,2-alt conformers have, in this order, an increasingly
wider distribution of âMDs. A conformational change in the
latter two conformers has thus a more pronounced effect on
X-ray 36 0.146 19.5 0.145 12.1 0.333 3.8 0.407
0
0
0
0
0
0
.0 MM
MD
36 0.146 19.7 0.153 10.6 0.337 0.0 0.667
36 0.147 19.1 0.154 10.3 0.337 2.5 0.408
X-ray 36 0.137 20.0 0.154 11.7 0.313 5.2 0.511
.1 MM
MD
36 0.134 20.1 0.156 10.4 0.318 3.9 0.667
36 0.133 19.6 0.157 10.1 0.314 4.2 0.561
X-ray 36 0.135 20.6 0.173 11.5 0.300 8.0 0.598
.2 MM
MD
36 0.129 20.6 0.170 10.3 0.308 7.2 0.667
36 0.125 20.1 0.169 10.0 0.299 7.1 0.627
X-ray 36 0.135 21.3 0.195 11.4 0.294 10.8 0.628
.3 MM
MD
36 0.127 21.2 0.187 10.3 0.304 10.0 0.667
36 0.122 20.7 0.186 9.9 0.294 9.7 0.645
X-ray 36 0.138 21.9 0.217 11.3 0.292 13.2 0.641
.4 MM
MD
36 0.128 21.8 0.206 10.3 0.304 12.4 0.667
36 0.123 21.3 0.204 9.9 0.293 11.9 0.652
X-ray 36 0.142 22.5 0.238 11.3 0.293 15.2 0.648
.57 MM
MD
36 0.131 22.3 0.224 10.3 0.307 14.4 0.667
36 0.125 21.8 0.221 9.9 0.295 13.9 0.656
a
Ratio assumed for a single D-π-A system.
of the four conformers under vacuum conditions at a temperature
of 0 K were obtained (Figure 5). The MM structures of the
different conformers closely resemble their respective X-ray
structures. The dihedral angles (φ1, φ2, φ3, and φ4 between the
planes of the different p-nitropropoxyphenyl units and the
molecular plane through the four methylene groups that connect
the four chromophoric units of each conformation are listed in
Table 2. The dihedral angles of the energy-minimized structures
differ less than 15° from the angles found in the X-ray structures.
Some differences between the structures obtained can be
expected, as polarization within a π-conjugated system is not
taken into account by the CHARMm force field module used
in the MM calculations. Furthermore, the calculations are
carried out in vacuum at 0 K, which means that no solvent
interactions or thermal movements are taken into account.
the calculated âMD.
Discussion. Our calculated hyperpolarizabilities (Table 3)
31
differ significantly from those calculated by Brouyere et al.
(Vide supra) especially for the 1,2-alt and 1,3-alt conformers.
This can be explained by the fact that in their sum-over-state
calculations possible octupolar contributions and conformational
dynamics were not included. Closer examination of the data
given in Table 3 shows that the fact that including also the off
diagonal â311, â131, and â113 tensor components (varying the
â311/â333 ratio) in the calculations has a pronounced effect on
the âHRS values of especially the 1,3-alt conformer and to a
lesser extent on the results of the other conformers. Comparing
the MM and MD results shows that inclusion of conformational
dynamics in the calculations is not essential for the rather rigid
calix[4]arene conformers as long as the off diagonal â311, â131,
and â113 tensor components are taken into account (â311/â333 )
The theoretical âHRS values of each of these conformations
âMM and âX-ray) have been calculated as described above and
(
0
). However, for less rigid multichromophoric systems such
are listed in Table 3. From both the MM and the X-ray structure
of the 1,2-alt conformer (Figures 4 and 5) it is evident that this
molecule might not adopt a pure centrosymmetric conformation
in solution, although this conformer is in principle centrosym-
metric.37 This noncentrosymmetry is indeed reflected in the
(37) A similar conformation was found in the single crystal structure of
the 1,2-alt conformer of tetra-tert-butyltetraethoxycalix[4]arene: Groenen,
L. C.; Van Loon, J.-D.; Verboom, W.; Harkema, S.; Casnati, A.; Ungaro,
R.; Pochini, A.; Ugozzoli, F.; Reinhoudt, D. N. J. Am. Chem. Soc. 1991,
113, 2385-2392.

7882 J. Am. Chem. Soc., Vol. 120, No. 31, 1998
Kenis et al.
Table 4. Experimental Data for the X-ray Diffraction Studies on the Four Conformers
compound
cone
paco
1,2-alt
1,3-alt
colorless prism
C H N O
40 44 4 12
morphology
formula
colorless prism
colorless prism
colorless prism
C
40
H
44
N
772.82
4
O
12
C
40
H
44
N
4
O
12
C
40
44 4
H N O
12
F
w
(g‚mol-1)
772.82
monoclinic
P2 /c
12.910(2)
16.997(2)
17.226(2)
91.73(3)
3773(4)
4
772.82
monoclinic
P2 /n
12.300(5)
12.699(5)
25.236(7)
101.21(2)
3866(4)
4
772.82
tetragonal
P-42
crystal system
space group
a (Å)
orthorhombic
Fddd
23.936(2)
33.007(2)
20.590(2)
1
1
1
m
18.234(3)
18.234(3)
12.544(2)
b (Å)
c (Å)
â (deg)
3
V (Å )
16267(1)
16
4141(3)
4
1.24
0.086
8.6
Z
D
3
calc (g/cm )
1.26
1.36
1.33
0.090
-
1
µ (cm
R (%)
)
0.879
10.6
0.095
3.9
5.7
R
w
(%)
13.4
3.90
4.3
1.38
8.2
3.33
9.9
2.46
S (GOF)
a
With the intensity variations within statistical fluctuations. b Zachariasen, W. H. Acta Crystallogr. 1963, 16, 1139.
5
as the triphenylcarbinoles (Vide supra) these thermal move-
ments will probably play an important role in the overall NLO
activity.
orientation of the D-π-A systems (Figure 6). Thus small
differences of the conformations used in the calculations from
those actually present in solution can result in considerable
deviations in the calculated hyperpolarizabilities. A second
reason for the discrepancy between experimental and theoretical
results for the 1,2-alt conformer can be the enhancement of the
âFHRS value by fast fluorescent emission within the 0.3 ns time-
window used in the FHRS measurements. The third and
probably most important factor is the orientation and mobility
of the electron donating propoxy groups in the different
Morley et al.38 have shown by sum-over-state calculations
that for our tetranitrotetrapropoxycalix[4]arene in the cone
conformer the propoxy donor groups are forced into unfavorable
orientations, which substantially reduce the conjugation between
the lone pair electrons and the π-electron system of the
respective aromatic rings.39 (This aspect is not included in our
or in Brouyere’s calculations.) This gives rise to a lower
hyperpolarizability per D-π-A system in the calix[4]arene cone
conformer than expected on the basis of a similar D-π-A
reference compound. Especially in the 1,2-alt conformer,
however, the rotations of the propoxy groups are not signifi-
cantly hindered. This leads to the expectation that relative to
the cone conformer higher â values are expected for the
individual chromophoric groups and thus also for the 1,2-alt
conformer. Recently, a critical dependence of âHRS on the
3
8
conformers as shown by Morley et al. The high mobility of
the propoxy groups in the 1,2-alt conformer can lead to higher
âHRS values.
Conclusion
The second-order nonlinear optical hyperpolarizabilities âHRS
of the four possible conformers of tetranitrotetrapropoxycalix-
[4]arene have been measured by nanosecond as well as by time-
conformation of the alkoxy donor group was also shown for
,6′-disubstituted binaphtol derivatives (Vide supra).
In the final section the calculated hyperpolarizabilities and
depolarization values of part II are compared with the experi-
mental results as reported in the first part of this paper.
resolved femtosecond hyper-Rayleigh scattering at different
wavelengths. In this way the âHRS values could be corrected
for fluorescence contributions.
A good correspondence between the experimental data (âFHRS
and Dx/z) and the theoretical data as calculated from single crystal
X-ray diffraction, molecular mechanics (MM), and dynamics
8
6
III. General Discussion
(MD) structures is observed for the cone, paco, and 1,3-alt
Comparison of Experimental and Calculated Data. Since
the calculated hyperpolarizabilities âMM, âX-ray, and âMD are
scaled to the âFHRS value of the cone conformer, they can only
be compared with the experimental âFHRS values of the other
three conformers. The calculated hyperpolarizabilities for the
paco conformer (Table 3) correspond well with the experimental
âFHRS value (Table 1), irrespective of the â311/â333 ratio. For
the 1,3-alt conformer the theoretical and experimental data only
agree well at a â311/â333 ratio of 0.3 and -0.2. Generally, for
conformers if a â311/â333 ratio of -0.2 is assumed. The
relatively high experimental âFHRS value for the 1,2-alt confor-
mation is explained by a still substantial contribution of fast
fluorescent emission to the scattered signal and the higher
freedom of rotation of the electron-donating propoxy donor
groups compared with the other conformers.
In contrast to the MM and MD calculations that are presented
here, both polarization of the D-π-A systems as well as mutual
interactions between the D-π-A systems have been taken into
account in the sum-over-state calculations performed by Morley
a monochromophoric molecule this ratio also has a value around
1
+
/-0.3. If both hyperpolarizabilities and depolarization ratios
38
31
et al. and Brouyere et al. Furthermore, the sum-over-state
method gives absolute values for the hyperpolarizabilities,
whereas in our calculations only relatiVe hyperpolarizabilities
are calculated. However, our calculations show that it is of
eminent importance that in calculations of the hyperpolarizability
in multichromophoric systems such as these calix[4]arenes,
octupolar contributions are also taken into account. The latter
of the four conformers are taken into account, best agreement
between the experimental and theoretical results is found for a
â311/â333 ratio of -0.2. Of the eight â and D values only one
dissonant remains. The calculated hyperpolarizabilities of the
-
30
1
,2-alt conformer vary roughly from 10 to 14‚10
esu, while
-
30
a value of 20‚10
esu was observed experimentally. This
discrepancy between experiment and calculation can have a
number of reasons: Variation of the orientations of the D-π-A
systems have a large relative influence on the observed âHRS
value, especially for the 1,2-alt conformer, due to the antiparallel
(
(
38) Morley, J. O.; Naji, M. J. Phys. Chem. 1997, 101, 2681-2685.
39) This was also theoretically studied for p-cyanodimethylaniline:
Leung, P. C.; Stevens, J. In Nonlinear optical properties of Organic
Molecules II. SPIE. 1989, 1147, 48-60.

Second-Order Nonlinear Optical Properties
J. Am. Chem. Soc., Vol. 120, No. 31, 1998 7883
is especially apparent for nondipolar multichromophoric systems
such as the 1,2-alt and 1,3-alt calix[4]arene conformers. This
The time-resolved FHRS experiments were performed with a Ti-
Sapphire laser operating at a wavelength of 900 nm with 80 fs pulses
in combination with an interference filter (λ ) 450 nm) in the detection
path. Time traces were recorded using time correlated single photon
counting as described in ref 23. The fundamental laser beam (900
nm) is propagating in the x-direction through a sample solution and is
linearly polarized in the z-direction. The scattered second harmonic
light is detected in the y-direction.
also explains the poor agreement of the sum-over-state calcula-
tions reported earlier in the literature31 with the experimental
data presented in this paper.
For the first time the second-order nonlinear optical properties
of a series of closely related multichromophoric molecules
ranging from dipolar to octupolar symmetry are described.
Moreover, a good agreement of the experimentally determined
hyperpolarizabilities and depolarization ratios with the calculated
values was found. In general, these results show that time-
resolved HRS measurements combined with calculations give
a clear insight of the symmetry and second-order nonlinear
optical properties of multichromophoric systems such as
tetranitrotetrapropoxycalix[4]arenes.
The depolarization ratios Dx/z were obtained with the FHRS setup
by measuring at a fixed fundamental intensity the horizontal (I
x
) and
vertical (I ) polarized scattered second harmonic signal with a horizontal
z
and a vertical analyzer, respectively. In order to obtain the correct
depolarization values a low numerical aperture (NA) of 0.14 was used.
Earlier research showed that this value is sufficiently low to obtain
correct ratios.40 This low NA results in low levels of the scattered
-
1
signal. Consequently, high concentrations of typically 40 mmol‚L
of the calixarene conformers were necessary. The dependence of the
quadratic coefficient on the concentration at these high concentrations
is linear, and consequently reliable data for the polarized scattered
second harmonic signal could be obtained.41
Experimental Section
Hyper-Rayleigh Scattering Experiments. The hyperpolarizabilities
of the four conformers have been determined with the nanosecond
Acknowledgment. We thank Casper-Jan Mandos for the
synthesis of the 1,2-alternate conformer. T. W. Stevens and A.
M. Montanaro-Christenhusz of the Department of Chemical
Analysis are acknowledged for recording the mass spectra and
performing the elemental analyses, respectively. This investiga-
tion was financially supported by Akzo Nobel Electronic
Products, Arnhem, The Netherlands and by the OSF program
Micro Optics of the University of Twente.
2
2
hyper-Rayleigh Scattering technique (NHRS) and with the recently
developed time-resolved femtosecond hyper-Rayleigh Scattering tech-
nique (FHRS) which enables elimination of fluorescence contributions.23
Since it is hardly possible to determine absolute â values by measuring
the intensity of the fundamental laser beam and scattered second
harmonic intensities, the internal reference method as introduced by
2
2
Clays et al. was used. The organic molecule with unknown â is
dissolved in a solvent with known microscopic â. When plotting the
quadratic coefficient against the concentration, the unknown âFHRS can
be obtained graphically by substituting the intersect and the slope of
the straight line obtained for each compound in eq 6. In this formula
Supporting Information Available: Experimental Section
with MM and MD calculations, synthesis, and X-ray analyses,
including X-ray data for the cone, paco, 1,2-alt, and 1,3-alt
conformers of tetranitrotetrapropoxycalix[4]arene (6 pages, PDF/
print). See any current masthead page for ordering and Web
access instructions.
N
solv is the solvent concentration, and âsolv the value for pure chloroform
-
30
(-0.49‚10
esu), which was used as the internal reference in both
NHRS and FHRS.
2
slope
intersect
2
〈
âFHRS 〉 )
Nsolv)〈âsolv
〉
(6)
JA980791T
(
(40) Tukker, T.; Van Hulst, N. F. Optics. Commun. Submitted for
publication.
The NHRS experiments were performed with a Nd:YAG laser
operating at a fundamental wavelength of 1064 nm with 10 ns pulses,
as described in ref 22.
(41) The dependency of the quadratic coefficient on the concentration
might become nonlinear at high concentrations due to intermolecular effects,
leading to erroneous depolarization values.