Crystal structure and experimental and theoretical studies of the second-order nonlinear optical properties of salts of triphenylguanidine with carboxylic acids

Article abstract of DOI:10.1021/jp909005q

N,N′,N″-triphenylguanidinium carboxylate salts have been prepared by acid-base reactions of triphenylguanidine with formic, benzoic, and m-methoxybenzoic acids, and their single-crystal X-ray structure analysis has been performed. The salts were found to crystallize into noncentrosymmetric structures with an orthorhombic space group P2₁2₁2 ₁ for the formate and m-methoxybenzoate salts and a monoclinic space group Cc for the benzoate salt. The anions and cations are linked by intermolecular hydrogen bonds with the same motifs in the three salts. By using the molecular structures, the molecular first hyperpolarizabilities of several clusters were determined by semiempirical methods, and the components of the second-order susceptibility tensor, d, of triphenylguanidine and those of the reported crystals were evaluated using the oriented gas model with two different local-field corrections. The efficiency of the second-harmonic generation of triphenylguanidine and that of the reported triphenylguanidinium salts were measured using the Kurtz and Perry powder method.

Full text of DOI:10.1021/jp909005q

J. Phys. Chem. A 2010, 114, 2607–2617
2607
Crystal Structure and Experimental and Theoretical Studies of the Second-Order Nonlinear
Optical Properties of Salts of Triphenylguanidine with Carboxylic Acids
Pedro S. Pereira Silva,*,† Cla´udia Cardoso,‡ Manuela Ramos Silva,† Jose´ A. Paixa˜o,†
Ana Matos Beja,† Maria Helena Garcia,¶ and Nelson Lopes§
CEMDRX, Physics Department, UniVersity of Coimbra, P-3004-516 Coimbra, Portugal, CFC, Physics
Department, UniVersity of Coimbra, P-3004-516 Coimbra, Portugal, Faculdade de Cieˆncias da UniVersidade
de Lisboa, Ed. C8 Campo Grande, P-1749-016 Lisbon, Portugal, and GoLP/Centro de F´ısica de Plasmas,
Instituto Superior Te´cnico, P-1049-001 Lisbon, Portugal
ReceiVed: September 17, 2009; ReVised Manuscript ReceiVed: December 23, 2009
N,N′,N′′-triphenylguanidinium carboxylate salts have been prepared by acid-base reactions of triphenylguani-
dine with formic, benzoic, and m-methoxybenzoic acids, and their single-crystal X-ray structure analysis has
been performed. The salts were found to crystallize into noncentrosymmetric structures with an orthorhombic
space group P212121 for the formate and m-methoxybenzoate salts and a monoclinic space group Cc for the
benzoate salt. The anions and cations are linked by intermolecular hydrogen bonds with the same motifs in
the three salts. By using the molecular structures, the molecular first hyperpolarizabilities of several clusters
were determined by semiempirical methods, and the components of the second-order susceptibility tensor, d,
of triphenylguanidine and those of the reported crystals were evaluated using the oriented gas model with
two different local-field corrections. The efficiency of the second-harmonic generation of triphenylguanidine
and that of the reported triphenylguanidinium salts were measured using the Kurtz and Perry powder method.
1. Introduction
methyl-stilbazolium tosylate) crystal3,5 and the NPP (N-(4-
nitrophenyl)-(L)-prolinol) crystal,6 which led to the first dem-
onstration of a near-IR optical parametric oscillation in a organic
crystal.7 One should also cite the role of chirality (the use of
natural amino acid derivatives) to prevent centrosymmetry with
certainty; see, for example, the case of MAP (methyl-(2,4-
dinitrophenyl)aminopropanoate) crystal.8
For the past three decades, organic materials that show
quadratic nonlinear optical (NLO) properties have received
considerable attention due to their promising potential applica-
tions in optical signal processing.1,2 In particular, measurements
of the second-order NLO effect, second-harmonic generation
(SHG), on certain organic NLO compounds have produced
results that by far exceed those obtained from inorganic NLO
alternatives such as lithium niobate (LiNbO3) or potassium
dihydrogen phosphate (KDP).3,4 Organic materials offer other
advantages over conventional inorganic NLO materials, includ-
ing fast response times, high optical damage thresholds, and
much greater versatility in molecular design compared with their
inorganic counterparts, thereby providing many more opportuni-
ties for improving the SHG response.
However, purely organic compounds in which van der Waals
interactions dominate lack sufficient mechanical strength and
thermal stability for practical uses. That is why we have used
recently a crystal engineering strategy based essentially on the
crystallization of ionic salts to get more cohesive crystalline
structures. One aspect of particular interest with organic salts
is the use of counterion variations to tailor crystal packing,
potentially producing noncentrosymmetric bulk structures which
are essential for quadratic NLO effects. Furthermore, crystalline
salts possess inherently greater stabilities and higher chro-
mophore number densities than potential alternatives for NLO
device applications such as poled polymer materials. Within
this crystal engineering strategy, several success cases have been
reported, for instance, the DAST (4-N,N-dimethylamino-4′-N′-
A second-order NLO chromophore typically contains a
conjugated π-electron system, asymmetrically substituted by
electron donor and acceptor groups, through which a charge
transfer occurs. In such systems, the dominant first hyperpo-
larizability component is along the direction of charge transfer.
The antiparallel alignment of the dipole moments of one-
dimensional chromophores leads the majority of π-conjugated
organic molecules to crystallize in centrosymmetric space
groups, having therefore null second-order bulk susceptibility.
One of the solutions to achieve dipole minimization without
losing the molecular hyperpolarizability is the use of octupolar
systems since their symmetry ensures cancellation of the
molecular dipole moment.9,10 Furthermore, a noncentrosym-
metric octupolar structure facilitates an optimal transfer of the
molecular hyperpolarizability components to the macroscopic
level,11,12 as exemplified in the TTB (1,3,5-tricyano-2,4,6-tris(p-
diethylaminostyryl)benzene) crystal.13
Guanidine derivatives can be regarded as potentially interest-
ing for quadratic NLO applications, as was demonstrated in 1993
by Zyss et al. with the encapsulation of guanidinium cations
between hydrogen L-tartrate anions.14
Triphenylguanidine (TPG) is easily protonated, and its
cationic form is capable of forming ionic crystals with a large
variety of acids.15-21 Although the previously reported structures
are centrosymmetric, we succeeded to crystallize the three
noncentrosymmetric structures of triphenylguanidine salts with
carboxylic acids, reported here.
* To whom correspondence should be addressed. E-mail: psidonio@
pollux.fis.uc.pt.
† CEMDRX, Physics Department, University of Coimbra.
‡ CFC, Physics Department, University of Coimbra.
¶ Faculdade de Cieˆncias da Universidade de Lisboa.
§ Instituto Superior Te´cnico.
10.1021/jp909005q  2010 American Chemical Society
Published on Web 02/01/2010

2608 J. Phys. Chem. A, Vol. 114, No. 7, 2010
Silva et al.
TABLE 1: Crystal Data and Structure Refinement of the
Although the triphenylguanidinium cation (TPG+) is not
octupolar since it loses the three-fold rotational symmetry in
the crystal,22 it would be expected that the magnitude of the
octupolar irreducible component would be appreciable because
of the presence of the guanidinium central fragment.
When the crystal structure of a compound is known, its
nonlinear optical properties can be estimated assuming the
additivity of the molecular hyperpolarizabilities according to
the oriented gas model first employed by Chemla et al.23 In
this model, the macroscopic crystal susceptibilities are obtained
by performing a tensor sum of the microscopic hyperpolariz-
abilities of the unit cell, and the effects of the surroundings are
described by local field factors.
To the best of our knowledge, the oriented gas calculations
reported in the literature are usually limited to the case of one-
or two-dimensional molecular units, and they use the relations
between microscopic and macroscopic lowest-order nonlineari-
ties derived in the theoretical study by Zyss and Oudar.24 In
the case of chromophores with three-dimensional charge transfer
or when the actual chromophore is a pair of ions, these relations
cannot be used at all or may lead to severe errors. In these cases,
the oriented gas calculations must be performed with the general
expression. Also, most of the studies use the oriented gas
approximation with the Lorenz-Lorentz local field correction.
In this study, we used a combination of the oriented gas model
with the supermolecule approach, with the microscopic linear
and nonlinear properties calculated by semiempirical methods.
Several calculations using composite molecular species with
different shapes and sizes are compared. We compare also the
use of two different local field corrections, the anisotropic
Lorenz-Lorentz spherical cavity local field factors and another
approach by Wortmann and Bishop (W-B)25 where an exten-
sion of the Onsager’s reaction field model is used. The
performance of the semiempirical methods PM3 and PM6 for
the determination of polarizabilities and hyperpolarizabilities
is also tested, by comparison with the experimental results.
N,N′,N′′-Triphenylguanidinium Saltsa
salt
1
2
3
emp. formula
C20H19N3O2
333.38
293(2)
0.71073
orthorh.
P212121
7.4214(2)
11.3585(4)
21.3888(7)
90
C26H23N3O2
409.47
293(2)
0.71073
monoc.
Cc
11.4369(15)
15.8900(18)
13.525(3)
90
113.170(11)
90
2259.6(6)
4
1.204
0.077
C27H25N3O2
439.50
293(2)
0.71073
orthorh.
P212121
7.2482(2)
10.9828(3)
29.0436(9)
90
formula weight
temperature (K)
wavelength (Å)
crystal system
space group
a (Å)
b (Å)
c (Å)
R(°)
ꢀ(°)
90
90
90
90
γ(°)
volume (Å3)
Z
1802.99(10)
4
1.228
0.081
0.059(5)
704
2312.03(11)
4
1.263
0.083
0.052(4)
928
calc. dens. (g/ cm3)
abs. coef. (mm-1
extinction coef.
F(000)
)
-
864
crystal size (mm)
0. 37 × 0.12
0.30 × 0.14
0. 38 × 0.11
× 0.09
× 0.08
× 0.03
data collec. range
index ranges: h
k
l
1.90-27. 88° 2.32-27. 53° 1.98-26. 66°
-8, 9
-13, 14
-28, 28
-14, 14
0, 20
-17, 6
-8, 9
-13, 13
-35, 34
Reflections:
collected
unique
57924
2381
3951
2601
61472
2523
R (int)
completeness
(θ ) 25.00°)
0.0508
100%
0.0154
100%
0.0624
99.2%
refin. method
full-matrix least-squares on F2
data/restraints/parameters 2381/0/227
2601/2/280
1.030
2523/0/300
1.190
F2 goodness-of-fit
1.140
R indices:
final [I > 2σ(I)]
wR2
all data
wR2
0.0470
0.1036
0.0912
0.1374
0.482
0.0370
0.0936
0.0622
0.1070
0.123
0.0453
0.0974
0.0847
0.1278
0.409
Largest diff. peak
and hole (eÅ-3
)
-0.497
-0.152
-0.360
a 1: N, N′, N′′-triphenylguanidinium formate; 2: N,N′,N′′-triphenyl-
guanidinium benzoate; 3 N,N′,N′′-triphenylguanidinium m-methoxy-
benzoate.
2. Experimental and Computational Methods
2.1. Synthesis. Compound 1 (N,N′,N′′-triphenylguanidinium
formate): 0.0102 g (0.0344 mmol) of N,N′,N′′-triphenylguanidine
(TCI, 97%) was dissolved in 20 mL of ethanol, and 1 mL of
formic acid (Sigma-Aldrich, g95%) was added to this solution.
Additionally, 20 mL of water was added to the solution. The
solution was stirred for 30 min at 40 °C and left to evaporate
under ambient conditions. After 15 days, small prism-like
yellowish single crystals with appropriate quality for X-ray
measurements were deposited.
Compound 2 (N,N′,N′′-triphenylguanidinium benzoate): 0.0174
g (0.142 mmol) of benzoic acid (Sigma-Aldrich, g 99.5%)
was dissolved in 50 mL of boiling water, and 0.0421 (0.141
mmol) of N,N′,N′′-triphenylguanidine (TCI, 97%) was dissolved
in 50 mL of boiling ethanol. The acid solution was slowly added
to the basic solution. The resultant solution was then left to
evaporate at room temperature and pressure. After 3 weeks,
small single crystals, transparent and colorless, were obtained.
Compound 3 (N,N′,N′′-triphenylguanidinium m-methoxyben-
zoate: 0.0128 g (0.0833 mmol) of m-methoxybenzoic acid
(Sigma-Aldrich, g 99%) and 0.0247 (0.0834 mmol) of
N,N′,N′′-triphenylguanidine (TCI, 97%) were dissolved in 100
mL of ethanol. After approximately 1 month, transparent single
crystals with a thin plate habit appeared in the solution.
The crystals of TPG used in the Kurtz and Perry powder
experiments were grown from an ethanolic solution of TPG
(97%) purchased from TCI.
2.2. X-ray Diffraction Studies. The diffraction measure-
ments for N,N′,N′′-triphenylguanidinium benzoate were carried
out on a single crystal using Mo KR radiation on a CAD-4
diffractometer. Data reduction was performed with HELENA.
26 Lorenz and polarization corrections were applied. For the other
two salts, the diffraction measurements were carried out on
single crystals using Mo KR radiation on a Bruker APEX II
diffractometer. 27 Data reduction was performed with SMART
and SAINT software.27 Lorenz and polarization corrections were
applied. Absorption correction was applied using SADABS. The
structures were solved by direct methods using SHELXS-97
program28 and refined on F2s by full-matrix least-squares with
SHELXL-97 program.28 The anisotropic displacement param-
eters for non-hydrogen atoms were applied. The hydrogen atoms
were placed at calculated positions and refined with isotropic
parameters as riding atoms. An extinction correction was applied
during the refinements of the N,N′,N′′-triphenylguanidinium
formate and N,N′,N′′-triphenylguanidinium m-methoxybenzoate
structures.28 The crystal data and details concerning data
collection and structure refinement are given in Table 1.
Because of the weak anomalous scattering at the Mo
wavelength, the absolute structures could not be determined from
the X-ray data.

Triphenylguanidine with Carboxylic Acids
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2609
2.3. Kurtz and Perry Powder Method. The efficiency on
SHG of the orthorhombic polymorph of TPG and of the reported
TPG salts was measured using the Kurtz and Perry powder
method.29 The measurements were performed at the fundamental
wavelength of 1064 nm originated directly by a Nd:YAG laser
at low power (50 mJ per pulse), producing 40 ns pulses with a
repetition rate of 10 Hz. The experimental setup is described in
detail in ref 30. The second-harmonic light produced on the
sample was collected by a spherical mirror and sent to the
detector through two interference filters (for the second har-
monic) in order to eliminate the fundamental laser light as well
as any other light present in the sample. The detector used in
the measurements of the efficiencies was a photomultiplier. The
voltage from the photomultiplier was measured by the oscil-
loscope, which was triggered by the signal itself. The photo-
multiplier voltage and the neutral density filter area were
optimized to obtain a good signal-to-noise relation and prevent
the saturation of the photomultiplier. The oscilloscope measured
the time integral of the photomultiplier voltage automatically,
which was proportional to the SHG efficiency. The oscilloscope
also performed, automatically, the average over several laser
shots. In order to investigate the existence of phase matching,
the intensity dependence on the particle size of TPG powder
samples was studied. For these measurements, the detector used
was a silicon photodiode (Thorlabs model DET100A/M) con-
nected to an oscilloscope. The measurements taken in the
oscilloscope were the pulse peak amplitude and the time integral
of the pulse amplitude (pulse area). The oscilloscope was
triggered by the signal itself. The measurements where taken
from a single shot to an average of a few hundred shots
depending on the compound resistance to intense laser light.
Even at the single shot, an average of at least five shots was
taken to reduce the error caused by laser power variation or
thermal fluctuations. The SHG efficiency measurement of the
urea reference sample was performed under the same experi-
mental conditions as those of each test sample.
diffraction studies as the structure optimization performed in
vacuum did not take into consideration all of the interactions
of the crystalline environment).
2.4.2. Calculation of Macroscopic Optical Properties. In
most organic molecular crystals, the energy of van der Waals
or hydrogen bonds responsible for the intermolecular cohesion
is much weaker, by 1 or 2 orders of magnitude, than that of
intramolecular chemical bonds. Molecules remain therefore
distinguishable entities, and the macroscopic nonlinear response
of the materials may be described using a simple summation
scheme following the oriented gas model, whereby the macro-
scopic second-order susceptibility tensor dIJK originates es-
sentially from the molecular quadratic hyperpolarizability tensor
ꢀ
ijk expressed in molecular coordinates i, j, k.24 The susceptibility
coefficients depend on the crystal symmetry, the precise
orientation of the molecule with respect to the crystal axes, and
the conformation of the molecule. The relationship between
microscopic and macroscopic parameters is given by
N
V
dIJK(-ω;ω1, ω2) ) fI(ω)fJ(ω1)fK(ω2)bIJK
1
Ng
bIJK
)
cos θ(s) cos θ(s) cos θ(s) × ꢀ(s)(-ω;ω1, ω2) (1)
Ii Jj Kk ijk
∑ ∑
s
ijk
where I, J, K are the crystal axes, Ng is the number of equivalent
positions in the unit cell of volume V that has N molecules,
fI(ω) are local field factors appropriate for the crystal axis I,
and the cosine product terms represent the rotation from the
molecular reference frame onto the crystal frame. The equivalent
positions are labeled by the index s. The local field factors are
essentially a correction for the difference between an applied
field that would be felt by the molecule in free space and the
local field detected in a material, and according to Hamada,37
the oriented gas approximation may be meaningless if it is used
without this correction. Beyond the crudest approximation that
consists of neglecting these local field factors altogether (fI )
1), several expressions have been used to account for the
anisotropy of the medium. The simplest is the anisotropic
Lorenz-Lorentz spherical cavity expression
The samples preparation procedure was the following: the
materials were mulled to a fine powder and compacted in a
mount and then installed in the sample holder. Sample grain
sizes were not standardized. For this reason, signals between
individual measurements were seen to vary in some cases by
as much as (20%. For a proper comparison with the urea
reference material, the measurements were averaged over several
laser thermal cycles.
(nI(ω)2 + 2)
1
fI(ω) )
)
(2)
3
4 N
1 - π aII
3 V
To investigate the existence of phase matching in TPG, one
sample was ground to a fine powder and sieved into different
particle size ranges (<63, 63-90, 90-125, 125-212, and
212-355 µm), compacted in a mount, and then installed in the
sample holder. For a proper comparison with the urea reference
material, the measurements were performed with urea sieved
at the same grain size as the samples, averaged over several
laser thermal cycles. The results of the efficiencies were obtained
by the signal area ratio. Due to lack of sufficient material of
the three salts, the investigation of the existence of phase
matching was not performed for these samples.
where the refractive indices nI(ω) are related, within the principal
dielectric axis reference frame, to a diagonal tensor aII represent-
ing the average linear polarizability of the unit cell per molecule,
which can be related, within the oriented gas model, to the
molecular linear polarizability Rij by
1
aII )
cos θ(s)cos θ(s)R(s)
(3)
∑ ∑
Ii
Jj ij
Ng
s
ij
2.4. Computational Methods. 2.4.1. Calculation of Mi-
croscopic Optical Properties. The static R and ꢀ tensor
components used in the oriented gas model calculations were
computed with the PM331-34 and PM635 Hamiltonians available
in MOPAC2009.36 Several microscopic units ranging from the
single molecule (or pair of ions) to clusters with different sizes
and shapes were considered, with the ions’ relative positions
and geometries as those in the crystals (since the optimized
structures were very different from those obtained with the X-ray
It is important to recall that by using this expression for fI(ω),
one assumes that the nonlinear contribution to the local field is
negligible. This relationship can be improved by considering
an ellipsoidal cavity for which analytical expressions can be
found from solving the Maxwell equations with boundary
conditions.38 However, there is evidence that the Lorenz-Lorentz
(L-L) field factor, commonly used in extracting hyperpolar-
izabilities from experimental susceptibilities, may introduce
errors of 50% or more.39

2610 J. Phys. Chem. A, Vol. 114, No. 7, 2010
Silva et al.
Wortmann and Bishop (W-B)25 addressed the problem of
connecting single-molecule property calculations and actual
measurements deriving local field factors from an extension of
Onsager’s reaction field model. Onsager40 expressed the local
field EL at the location of a solute molecule as the sum of the
cavity field EC and the reaction field ER
a1a2a3
∞
ds
(s + a2r )[(s + a21)(s + a22)(s + a32)]1/2
(12)
κr )
∫
0
2
and they satisfy the relation κ1 + κ2 + κ3 ) 1.
The local field correction of eq 8, originally proposed in the
context of solutions, can be used in eq 1 to relate the
macroscopic second-order susceptibility tensor dIJK to the unit
cell nonlinearity per molecule bIJK. When there are no experi-
mental values of the refractive indices, the components of the
dielectric constant tensor in the dielectric frame can be obtained
from the calculated polarizability using the Onsager-Bo¨ttcher
relation for an ellipsoidal cavity38
EL ) EC + ER
(4)
In the generalization of W-B to nonlinear optics, the local field
is decomposed into Fourier components with amplitudes ELΩ
CΩ, and ERΩ
,
E
ELΩ ) ECΩ + ERΩ
(5)
9κI(1 - κIx)aII
2 + x - 3κIx -
12πεII
a1a2a3
and a local response of the medium to a uniform electric field
is assumed. The cavity field is related to the macroscopic field
in the medium by38
V
N
)
(εII - 1)(2εII + 1)
2aII
(13)
ECΩ ) fCΩ ·EΩ
(6)
where x ) 2(εII - 1)/(2εII + 1). The ellipsoidal cavity is adapted
to the shape and dimensions of the clusters, and its volume obeys
the condition (4π/3)(N/V)a1a2a3 ) 1. It should be noted that
the semiaxes of the ellipsoidal cavity are aligned with the
dielectric principal axes.
where fCΩ is the cavity field tensor at frequency Ω. The reaction
field is related to the total (permanent + induced) dipole moment
pΩ of the solute molecule at frequency Ω according to38
˜ ˜ ˜
Regarding the dielectric reference frame (XYZ) used in the
calculations, it must be pointed out that, for the orthorhombic
space groups, the dielectric axes are parallel to the crystal-
lographic axes, but for the case of the lower-symmetry point
ERΩ ) fRΩ ·pΩ
(7)
where fRΩ is the reaction field tensor.
˜
group m (e.g., compound 2), only the Y axis will coincide with
eff
The effective first-order hyperpolarizability ꢀ (-2ω; ω, ω)
the crystallographic [010] axis that is perpendicular to the glide
planes, while the two other dielectric axes, which lie in the (010)
plane, are free, in general, to rotate about the [010] axis
depending on the light frequency. However, the specific
molecular content of the unit cell can lock the dielectric axes
to the crystallographic axes. The principal dielectric axes can
be defined as the set of eigendirections of the crystalline
polarizability tensor aIJ if it is assumed that local field corrections
will not introduce further rotations.41 The rotation Ψ around b
rst
sol
of the molecule in the cavity (solute molecule) ꢀ (-2ω; ω, ω)
rst
derived by W-B is given by
ꢀeff(-2ω;ω, ω) ) FrRrr2ω(FRωfsCsω)(FRωftCt ω) ×
rst
ss
tt
sol
rst
ꢀ (-2ω;ω, ω) (8)
where they used the argument that, to first order, the cavity
˜
˜
of the principal dielectric axis X (or Z) away from the crystal
axis a (or c, respectively) can be calculated from the diagonal-
ization of the aIJ tensor, which leads to the following expression
field does not contain Fourier components at any harmonic
Rω
frequencies. In eq 8, F is related to the reaction field factor
rr
Rω
f
by
rr
2aXZ
1
Rω
rr
tan(2Ψ) )
(14)
F
)
(9)
aXX - aZZ
1 - frRr ωRrsrol(-ω;ω)
We calculated the unit cell nonlinearity per molecule, bIJK
,
sol
where R (-ω; ω) is one diagonal component of the polariz-
rr
using the PM3- and PM6-calculated values of the microscopic
quadratic polarizability ꢀ tensor components and taking into
account the crystal symmetry of each material. The ꢀijk values,
for all crystals under consideration, were calculated in the
molecular Cartesian coordinate system and then transformed
into the crystal coordinate system with the aid of VMD code
(version 1.8.6, April 7, 2007).42 The macroscopic NLO coef-
ficients, dIJK, were obtained using eq 1 with the L-L or the
W-B local field factors. The local field factors were calculated
using the average linear polarizability of the unit cell per
molecule, a, which is related to the microscopic tensor R by
the same rotation matrix as that obtained with VMD.
ability in the gas phase.
For an ellipsoidal cavity with semiaxes a1, a2, a3 in a medium
with dielectric constant εω at frequency ω, the cavity and
reaction field tensor components are given by38
εω
Cω
f
)
δrs
(10)
(11)
rs
εω - κr(εω - 1)
3κr(1 - κr)(εω - 1)
a1a2a3[εω - κr(εω - 1)]
Rω
rs
f
)
δrs
3. Results and Discussion
The quantities κr depend on the form of the ellipsoid and are
3.1. Crystal Structures. The three TPG salts crystallize in
noncentrossymmetric space groups. Triphenylguanidinium for-
given by38

Triphenylguanidine with Carboxylic Acids
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2611
Figure 3. Molecular structure (thermal ellipsoids at 50% probability)
and the atom numbering scheme for compound 3 (Mercury43).
TABLE 2: Selected Structural Parameters (Å, °) of the
Three Salts
1
2
3
Figure 1. Molecular structure (thermal ellipsoids at 50% probability)
and the atom numbering scheme for compound 1 (Mercury43).
C1-N1
1.323(3)
1.332(3)
1.349(3)
1.420(3)
1.433(3)
1.421(3)
1.236(3)
1.237(3)
1.317(3)
1.338(3)
1.342(3)
1.428(3)
1.418(3)
1.421(3)
1.247(3)
1.258(3)
1.321(4)
1.333(4)
1.350(4)
1.421(4)
1.434(4)
1.423(4)
1.247(4)
1.267(4)
C1-N2
C1-N3
N1-C2
N2-C8
N3-C14
C20-O1
C20-O2
N1-C1-N2
N1-C1-N3
N2-C1-N3
C1-N1-C2
C1-N2-C8
C1-N3-C14
O1-C20-O2
C2-N1-C1-N2
C2-N1-C1-N3
C8-N2-C1-N1
C8-N2-C1-N3
C14-N3-C1-N1
C14-N3-C1-N2
C3-C2-N1-C1
C1-N2-C8-C13
C1-N3-C14-C19
117.6(2)
117.0(2)
118.5(3)
121.8(2)
120.6(2)
127.3(2)
123.6(2)
122.7(2)
127.7(2)
163.4(2)
-16.7(4)
155.4(2)
-24.5(4)
144.8(2)
-35.3(4)
146.9(3)
128.5(3)
-44.3(3)
121.6(2)
121.4(2)
126.9(2)
124.9(2)
124.1(2)
124.6(2)
168.5(3)
-12.8(4)
144.0(3)
-34.7(4)
157.7(2)
-23.7(4)
-51.1(4)
150.9(3)
-43.7(4)
120.8(3)
120.7(2)
125.8(3)
123.5(3)
123.6(3)
124.9(3)
164.2(3)
-16.6(4)
152.5(3)
-26.7(4)
148.3(3)
-32.5(4)
136.5(3)
-57.3(4)
131.5(3)
m-methoxybenzoate is the first crystal structure of a m-
methoxybenzoic acid salt to be reported.
The CN3 fragment of the guanidinium group of the N,N′,N′′-
triphenylguanidinium cation has a planar geometry in the three
salts, as expected for sp2 hybridization of the central C atom,
since the sum of the valence angles around C1 is 360.0(3)°,
but the N-C-N angles differ considerably from the mean value
of 120°. The largest deviation is that of N1-C1-N2 in
triphenylguanidinium benzoate [117.0(2)°]. The bond lengths
C1-N are within the range expected for a delocalized C-N
bond (see Table 2).
The lengths of the N-C(Ph) bonds (see Table 2) reveal more
delocalization of the nitrogen lone pair electron density out onto
the attached phenyl rings than that in neutral TPG.44 In the three
crystals, the Caryl atoms are not coplanar with the guanidinium
group, and inspection of the torsion angles shows that the twist
angles around the C1-N bonds differ for each ring (see Table
2). Also, the individual rotation angles of the phenyl rings
around the Caryl-N bonds are different for each ring in the three
structures. The angles between the least-squares planes of the
Figure 2. Molecular structure (thermal ellipsoids at 50% probability)
and the atom numbering scheme for compound 2 (Mercury43).
mate (Figure 1) and triphenylguanidinium m-methoxybenzoate
(Figure 3) are orthorhombic with the chiral space group P212121,
while triphenylguanidinium benzoate (Figure 2) crystallizes in
the monoclinic polar space group Cc. In all of these structures,
the ions are assembled in chains by moderate to strong
N-H· · ·O hydrogen bonds.
Supplementary data have been deposited at the Cambridge
Crystallographic Data Centre (CCDC No. 746265, No. 746266,
and No. 746267). These data can be obtained free of charge
from The Cambridge Crystallographic Data Centre via www.
ccdc.cam.ac.uk/data_request/cif.
According to a search of the Cambridge Structural Database
(CSD version 5.30, November 2008), triphenylguanidinium

2612 J. Phys. Chem. A, Vol. 114, No. 7, 2010
Silva et al.
TABLE 3: Angles between the Least-Squares Planes of the
Guanidinium Central Fragment and the Phenyl Rings (°)
ring
1
2
3
C2-C7
C8-C13
C14-C19
46.3(1)
67.2(1)
67.7(1)
57.7(1)
59.9(1)
57.7(1)
55.4(1)
73.5(1)
70.6(1)
guanidinium central fragment and the phenyl rings vary from
46.3(1) to 73.5(1)° (see Table 3), revealing the flexibility of
the triphenylguanidinium cation.
Regarding the anions of the three structures, the O-C-O
angles of the carboxylate groups are greater than 120° because
of the steric effect of lone pair electrons on both O atoms. The
bond lengths in the deprotonated carboxyl groups are intermedi-
2
ate between normal single Csp -O (1.308-1.320 Å) and double
45
2
Csp dO bond lengths (1.214-1.224 Å), indicating delocal-
ization of the charge over both O atoms of the COO- group.
In triphenylguanidinium benzoate, the carboxylate group of
the anion is rotated 14.9(3)° out of the benzenic ring.
Figure 5. Projection of the packing diagram of 2 along the b axis,
with the hydrogen bonds depicted as dashed lines. The benzenic rings
have been omitted for clarity.
The carboxylate group of m-methoxybenzoate is bent out of
the plane of the benzene ring by 4.7° and is also twisted
approximately 14° around the C20-C21 bond. In the methoxy
substituent, the O atom and the methyl C are almost exactly in
the plane of the benzenic ring, with deviations of 0.011(4) and
0.028(6) Å, respectively.
Anions and cations are linked by intermolecular hydrogen
bonds. Full hydrogen bond capability of the triphenylguani-
dinium cations is achieved in the three structures, every H atom
being donated to an O atom of the carboxylate group of the
respective anion. In each anion, the O1 atom accepts one H
atom, while the O2 atom is an acceptor of two H atoms (Figures
4-6, Table 4). In the two salts with orthorhombic structures,
the cations are linked in infinite chains running parallel to the
a axis. The hydrogen-bonding functionality of the monoclinic
structure is identical, but the infinite chains run along the c axis.
Graph-set analysis46 shows that the hydrogen-bonding motifs
are similar in the three salts (see Table 5). The main feature is
the formation of rings of descriptor R22(8), according to Etter’s
graph-set theory.46 Another salt of TPG with a carboxylic acid,
namely, trifluoroacetic acid, has the same type of hydrogen bond
topology.17 These conserved hydrogen-bonding motifs may serve
as robust synthons in crystal engineering and design.47 It could
be expected that salts of TPG with other carboxylic acids will
Figure 6. Projection of the packing diagram of 3 along the b axis,
with the hydrogen bonds depicted as dashed lines. Molecular fragments
not involved in the hydrogen bonds have been omitted for clarity.
TABLE 4: Hydrogen-Bonding Geometry (Å, °) of the
Reported Salts
D-H
H· · ·A
D· · ·A
D-H· · ·A
1
a N1-H1· · ·O1
b N2-H2· · ·O2
c N3-H3· · ·O2a
0.86
0.86
0.86
1.83
2.04
2.00
2.687(3)
2.868(3)
2.831(3)
174.8
160.5
163.0
2
a N1-H1· · ·O1b
b N2-H2· · ·O2b
c N3-H3· · ·O2
0.86
0.86
0.86
1.85
1.95
1.97
2.682(3)
2.764(3)
2.813(3)
162.6
157.4
164.7
3
a N1-H1· · ·O1
b N2-H2· · ·O2
c N3-H3· · ·O2c
0.86
0.86
0.86
1.82
2.05
2.07
2.667(3)
2.794(3)
2.920(3)
168.8
144.5
168.5
a Symmetry code: x - 1, y, z. b Symmetry code: x, -y, z - 1/2.
c Symmetry code: x + 1, y, z.
crystallize with the same hydrogen bond pattern, unless the acids
have other hydrogen acceptors that compete with the carboxylate
group.
3.2. Kurtz and Perry Powder Method Results. The powder
SHG technique of Kurtz and Perry29 still plays an important role
as a method for fast initial screening of noncentrosymmetric
structures, although more elaborate methods are being developed.48-50
The Kurtz and Perry method can give some qualitative measure
of the second-harmonic efficiency to assess whether a material may
be useful for the purpose of nonlinear optics.51 The results of the
Kurtz and Perry powder tests are presented in Table 6.
The interpretation of the powder SHG data is not simple,
and the results must be taken with caution. It is clear that for
Figure 4. Projection of the packing diagram of 1 along the c axis,
with the hydrogen bonds depicted as dashed lines. The phenyl rings
have been omitted for clarity.

Triphenylguanidine with Carboxylic Acids
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2613
TABLE 5: Graph-Set Descriptors of the Motifs and
Second-Order Networks Involving the Hydrogen Bonds of
Table 4
TABLE 8: Theoretical Susceptibility Components (pm/V)
for TPG, Calculated from the ꢀijk Components of the
Isolated Molecule, for Chains along the a Axis with 2, 3, 4,
5, and 6 Molecules (here called, 1c2m, 1c3m, 1c4m, 1c5m,
and 1c6m, respectively) and for Clusters with Two
Neighboring Chains of 2, 3, and 4 Molecules (here called
2c2m, 2c3m and 2c4m, respectively): Lorenz-Lorentz Local
Field Factors
a
b
c
a
b
c
D
R22(8)
D
C22(8)
C22(6)
D
PM3
PM6
TABLE 6: SHG Efficiencies Compared to the Urea
Standard
dZXX
dZYY dZZZ 〈d〉
dZXX
dZYY dZZZ 〈d〉
compound
1 molecule -9.8 21.4 12.5 15.1 -7.3 17.8 11.4 12.7
1c2m
1c3m
1c4m
1c5m
1c6m
2c2m
2c3m
2c4m
-11.6 18.1 12.0 13.3 -8.7 14.5 9.8 10.6
-13.3 15.2 10.8 12.0 -9.7 12.3 8.4 9.4
-14.5 13.9 10.0 11.7 -10.5 11.2 7.7 9.0
-15.2 13.1 9.2 11.5 -11.0 10.5 7.1 8.8
-15.9 12.5 8.9 9.7 -11.4 10.1 6.8 8.7
-12.1 17.7 12.0 13.2 -8.8 14.4 10.4 10.7
-13.3 15.5 11.5 12.3 -9.6 12.4 9.6 9.7
-13.9 14.6 10.6 11.9 -10.1 11.5 8.8 9.2
TPG
0.8
1
2
3
SHG efficiency
0.02
0.18
∼0.01
TABLE 7: SHG Efficiencies of TPG for Different Particle
Sizes Compared to the Urea Standard
particle sizes (µm)
SHG intensity
error
<63
0.62
0.60
4.70
0.71
1.34
3%
3%
6%
6%
6%
63-90
90-125
125-212
212-355
TABLE 9: Theoretical Susceptibility Components (pm/V)
for TPG, Calculated from the ꢀijk Components of the
Isolated Molecule, for Chains along the a Axis with 2, 3, 4,
5, and 6 Molecules (here called 1c2m, 1c3m, 1c4m, 1c5m,
and 1c6m, respectively) and for Clusters with Two
Neighboring Chains of 2, 3, and 4 Molecules (here called
2c2m, 2c3m, and 2c4m, respectively): Wortmann-Bishop
Local Field Factors
any quantitative comparison, one should take into account
properties of the particular experimental arrangement like
particle size and index-matching conditions. Nonetheless, it is
possible to conclude that TPG is appreciably more efficient than
the three salts studied.
PM3
PM6
dZXX
dZYY dZZZ 〈d〉
dZXX dZYY dZZZ 〈d〉
Using this technique, it is also possible to determine the
existence of phase matching in new materials. In a nonphase-
matching material, the maximum intensity is achieved when
the particle size approximately matches the average coherence
length and then falls with any increase in particle size. In a
phase-matching material the intensity, in contrast, reaches a
plateau at large particle sizes. An alternative technique would
be the use of a tunable laser source, as proposed by Tang,52
that determines the limits of the spectral range over which phase
matching can be achieved.
1 molecule -10.8 13.4
8.8 10.3 -7.6 11.1 8.0 8.4
1c2m
1c3m
1c4m
1c5m
1c6m
2c2m
2c3m
2c4m
-9.0
-7.9
-7.6
-7.6
-7.6
13.4 10.7 10.3 -6.8 10.8 8.7 8.3
13.8 11.9 10.7 -5.9 11.2 9.0 8.4
14.5 12.8 11.2 -5.7 11.6 9.3 8.7
15.6 13.4 12.0 -5.7 12.3 9.6 9.2
16.3 14.4 12.6 -5.6 12.8 9.9 9.5
-11.8 13.5
7.5 10.4 -8.3 11.0 6.5 8.2
8.7 11.1 -6.9 12.4 7.4 8.8
9.1 11.4 -6.3 12.6 7.6 8.9
-9.4
-8.4
15.7
16.3
In order to investigate the existence of phase matching in
TPG, the intensity dependence on particle size was monitored.
It is clear from the results of Table 7 that TPG is a nonphase-
matchable material. Although the intensity does not diminish
consistently throughout the samples prepared with larger and
larger particles, this is probably due to imperfect filtering
allowing smaller particles to remain in the larger particle
samples. The highest intensity recorded gave an estimated SHG
efficiency of 4.7 times that of urea, giving an estimated average
effective nonlinearity of around 2 times that of urea. However,
nonphase-matchability has a damping down effect in this
technique, and therefore, in such a case, the true value of the
average effective nonlinearity could be significantly larger.
3.3. Calculated Nonlinear Optical Properties. In this
4 molecules (here called 2c2m, 2c3m, and 2c4m, respectively).
This crystal is orthorhombic with space group Pna21 and point
group mm2; therefore, the only nonvanishing independent
components of the second-order polarizability tensor allowed
by this point group and by the Kleinman symmetry are dZXX
,
53,54
dZYY, and dZZZ
.
The results obtained with the L-L and the
W-B local field corrections are presented in Tables 8 and 9,
respectively. Along with the dIJK components we also present
the angular average of the NLO susceptibility, 〈d2ω〉, using the
expression deduced by Kurtz an Perry.29
The calculations for the salts were performed considering the
following clusters: the closest ion pairs in which the carboxylate
group participates in two hydrogen bonds with the guanidinium
group (cluster1), a cluster of two chains of two dimers (cluster2),
and a chain of four dimers (cluster3). The results of these
calculations are presented in Tables 10 and 11.
By the 222-D2 symmetry and the Kleinman symmetry, there
is only one nonvanishing independent component of the second-
order polarizability tensor for the formate and m-methoxyben-
zoate salts, that is, dXYZ. For the benzoate salt (point group
m-C1h), the nonvanishing components of the susceptibility
tensor are indicated in Tables 10 and 11.
Comparing several calculations, we can see that the PM3
Hamiltonian gives systematically higher values for the compo-
nents of the second-order polarizability tensor. The comparison
of the two local field corrections indicates that the calculations
section, we present the macroscopic NLO coefficients, dIJK
,
calculated from the molecular quadratic hyperpolarizability
tensor ꢀijk with the methodology described in section 2.4.2. The
calculations were performed for the three salts and for the free
base. The shapes of the clusters used in the calculations were
chosen in such a way as to take into account the strongest
intermolecular interactions.
Using the crystal structure of TPG taken from ref 44, we
calculated the ꢀijk tensor components for the isolated molecule,
for chains along the a axis with 2, 3, 4, 5, and 6 molecules
(here called 1c2m, 1c3m, 1c4m, 1c5m, and 1c6m, respectively),
and also for clusters with two neighboring chains of 2, 3, and

2614 J. Phys. Chem. A, Vol. 114, No. 7, 2010
Silva et al.
TABLE 10: Theoretical Susceptibility Components (pm/V)
for the TPG Salts Calculated from ꢀijk Components of
Several Clustersa: Wortmann-Bishop Local Field Factors
TABLE 12: Calculated Susceptibility Components (pm/V)
for 2A5NPDP Compared with the Experimental and
Theoretical Values from Kotler et al56,a
PM3
PM6
d15
d24
d33
cluster1 cluster2 cluster3 cluster1 cluster2 cluster3
dimer (PM3)
(PM6)
chain2 (PM3)
(PM6)
2chains2 (PM3)
(PM6)
dimer (PM3)
(PM6)
25.3
3.7
-3.6
2.4
-4.3
17.1
4.3
3.2
-3.2
1.5
56.0
14.0
19.6
10.9
23.2
13.1
19.8
10.4
19.3
10.9
19.2
10.7
28 ( 4
59.1
46.1
47.3
38.5
40.2
38.0
36.2
37.4
37.7
33.0
34.4
87 ( 4
1
2
dXYZ
〈d〉
-3.4
2.9
0.6
0.5
-0.9
0.8
-1.4
1.2
0.9
0.7
-0.5
0.4
L-L
dXXX
dXYY
dXZZ
dZXX
dZYY
dZZZ
〈d〉
-23.6
-11.3
10.7
-27.2
-10.5
6.3
-7.3
-4.9
3.9
-15.3
-7.2
8.4
-21.1
-8.4
4.6
-10.7
-6.7
3.7
-12.7
-8.4
-20.5
20.7
-0.3
0.2
-10.0
-10.2
-0.9
0.2
8.3
-0.4
0.3
-13.1
-5.2
-10.5
14.9
-0.5
0.4
-7.3
-11.6
-0.7
1.9
10.0
-0.3
0.3
0.9
0.8
3.3
3.3
chain2 (PM3)
(PM6)
W-B
15.3
-0.8
0.7
11.8
-0.4
0.4
-2.3
12.1
2.8
3
dXYZ
〈d〉
2chains2 (PM3)
(PM6)
a Cluster1: the closest ion pairs in which the carboxylate group
participates in two hydrogen bonds with the guanidinium group;
cluster2: two chains of two dimers; cluster3: chain of four dimers.
theory56
12 ( 1
λfund )1.34 µm
experiment56
theory56
6 ( 1
35 ( 1
12 ( 1
122 ( 4
16 ( 1
1 ( 0.4
TABLE 11: Theoretical susceptibility components (pm/V)
for the TPG salts calculated from the ꢀijk components of
several clusters (a) - Wortmann-Bishop local-field factors
λfund )1.06 µm
experiment56
7 ( 1
a The ꢀijk components were calculated for the following clusters:
a pair of ions (dimer), a chain of two pairs (chain2), and two chains
of two pairs (2chains2).
PM3
PM6
cluster1 cluster2 cluster3 cluster1 cluster2 cluster3
crystal nonlinear coefficients were determined by the Maker
fringe method at the fundamental wavelengths, 1.34 and 1.06
µm,56 and 2-amino-5-nitropyridinium chloride (2A5NPCl), with
coefficients d12, d13, and d14 measured by phase-matched second-
harmonic generation at 1.32 µm57 and coefficient d11 determined
by the Maker fringe method at 1.32 µm.58 For 2A5NPDP, we
used the atomic coordinates determined by Masse and Zyss.59
The crystal is orthorhombic with space group Pna21 (class mm2),
and the unit cell parameters are a ) 25.645(8) Å, b ) 6.228(2)
Å, and c ) 5.675(2) Å. The atomic coordinates used in the
calculations for 2A5NPCl were taken from the study by Pe´caut
et al.60 The crystal structure of 2A5NPCl belongs to the
monoclinic system (space group P21), and the lattice parameters
are a ) 9.956(5) Å, b ) 7.373(2) Å, c ) 4.813(1) Å, and ꢀ )
95.86(6)°.
The results of the calculations for 2A5NPDP are presented
in Table 12 for a pair of ions (dimer), for a chain of two pairs
(chain2), and for two chains of two pairs (2chains2). The clusters
used in the calculations for 2A5NPCl were the following: a pair
of ions (dimer), a chain of two pairs (chain2), a chain of four
pairs (chain4), two chains of two pairs (2chains2), and two
chains of four pairs (2chains4). In the clusters 2chains2 and
2chains4, the zigzag chains belong to consecutive planes (201)
containing the aromatic rings. The results of the calculations
for 2A5NPCl are presented in Table 13. The theoretical values
reported by Horiuchi et al.,58 presented here for comparison,
were calculated from the hyperpolarizabilities of the neutral
2-amino-5-nitropyridine molecule (2A5NP), the cation
(2A5NP+), and the pair of ions (2A5NP+Cl-).
1
2
dXYZ
〈d〉
-2.7
2.3
-20.0
-8.9
8.2
-11.1
-6.7
-16.2
17.0
0.5
0.5
-17.3
-6.2
5.9
-7.2
0.6
3.4
9.8
-1.0
0.8
-7.9
-5.2
2.4
-10.7
-0.9
0.1
-1.1
0.9
-13.0
-5.7
6.4
-11.4
-4.2
-8.3
12.4
0.8
0.7
-13.7
-5.1
4.2
-5.3
0.5
3.4
7.7
-0.6
0.5
-13.1
-8.4
2.0
-12.5
-0.8
0.9
11.6
-0.3
0.3
dXXX
dXYY
dXZZ
dZXX
dZYY
dZZZ
〈d〉
8.6
-0.4
0.3
3
dXYZ
〈d〉
-0.2
0.2
-0.7
0.6
-0.4
0.3
-0.4
0.3
a Cluster1: the closest ion pairs in which the carboxylate group
participates in two hydrogen bonds with the guanidinium group;
cluster2: two chains of two dimers; cluster3: chain of four dimers.
using the Lorenz-Lorentz factors yield generally higher sus-
ceptibility components.
The calculations for TPG, although overestimating the
experimental result, predict the correct order of magnitude of
the SHG response (compare with the susceptibility of urea of
2.3 pm/V; see Appendix I of ref 55). This overestimation can
be partially explained by the nonphase-matchability of the
material. It can be seen, by comparing Tables 10 and 11, that
the differences between the values of the susceptibility com-
ponents calculated with different clusters are smaller using the
W-B local field correction. Overall, the best results are obtained
with PM6 Hamiltonian and W-B local field factors.
For the two orthorhombic salts (1 and 3), the calculations
foresee poor results, and apparently, there is good agreement
with the experimental values, but we cannot draw a definitive
conclusion since the phase matching was not tested for these
two materials. The results obtained with the different methods
are quite similar for these salts, with the exception of PM3
calculations for the cluster1 of 1, which overestimate the results.
The calculations for 2 show, by far, the worst disagreement
with experiment. However, it seems that, once again, the best
result is obtained with the cluster with more intermolecular
interactions with the PM6 method and W-B local field
correction.
Our theoretical results for 2A5NPDP give a reasonable
estimate of the crystalline NLO coefficients, and the best result
corresponds to the calculation with one cluster of two chains,
each chain with two ion pairs, using the PM6 Hamiltonian and
the W-B local field correction. The calculations give systemati-
cally higher values, and the worst disagreement corresponds to
the component d33. This may be related to the fact that the
dipoles of the 2-amino-5-nitropyridinium ions are aligned along
the c axis so that most of the charge transfer will occur in this
direction.
To verify the reliability of our calculations, the same types
of calculations were performed for two salts 2-amino-5-
nitropyridinium dihydrogen phosphate (2A5NPDP), whose
The d components calculated for 2A5NPDP are closer to the
experimental values than the theoretical values obtained by

Triphenylguanidine with Carboxylic Acids
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2615
TABLE 13: Calculated Susceptibility Components (pm/V) for 2A5NPCl Compared with the Experimental and Theoretical
Values from Horiuchi et al58,a
L-L
W-B
d11
d12
d13
d14
d11
d12
d13
d14
7.6
dimer (PM3)
(PM6)
chain2 (PM3)
(PM6)
chain4 (PM3)
(PM6)
2chains2 (PM3)
(PM6)
-22.3
-26.7
-20.2
-28.3
-23.7
-42.6
-13.4
-14.4
-10.9
-19.1
76.6
-22.8
-43.8
-22.0
-33.2
-24.6
-35.4
-19.8
-22.6
-20.4
-23.7
20.8
-2.4
-0.2
-0.1
-0.3
1.0
-0.4
1.7
0.3
2.2
11.1
7.6
-9.0
-9.5
-7.8
-9.2
-7.2
-9.7
-9.1
-7.4
-4.1
-5.8
-9.6
-14.5
-7.9
-9.7
-8.2
-9.4
-9.2
-9.2
-10.6
-10.0
-2.7
-0.2
-0.1
-0.2
1.2
-0.3
1.6
0.2
2.1
-4.1
-4.8
-3.1
-4.0
-3.3
-1.1
-2.5
0.0
-7.3
-6.0
-6.4
-7.0
-1.7
-4.2
0.0
2chains4 (PM3)
(PM6)
0.2
2.6
-5.0
4.6
0.2
-2.9
theory 2A5NP58
theory 2A 5NP+58
theory 2A 5NP+ Cl-58
experiment57,58
λfund )1.32 µm
28.8
109.8
9 ( 4
3.4
46.9
8 ( 3
0.9
4.6
11 ( 4
0.0
13.7
∼0
a The ꢀijk components were calculated for the following clusters: a pair of ions (dimer), a chain of two pairs (chain2), a chain of four pairs
(chain4), two chains of two pairs (2chains2), and two chains of four pairs (2chains4).
TABLE 14: Calculated Refractive Indices for 2A5NPDP
Compared with the Experimental Values at 1340 nm56 (see
text for details)
TABLE 16: Relation of the Ratio between Septor and
Vector Scalar Invariants (G) with the HOMA Aromaticity
Index and the Dipole Moment (the PM6 calculation referred
to the ion’s center of mass) for the TPG Molecule and TPG+
Ions of the Reported Salts
PM3
PM6
nx
ny
nz
nx
ny
dz
compound
µ (D)
HOMA
F
dimer
1.496 1.482 1.620 1.576 1.657 1.817
1.500 1.451 1.647 1.559 1.686 1.789 L-L
1.442 1.532 1.629 1.555 1.709 1.773
1.498 1.508 1.638 1.580 1.707 1.841
1.549 1.409 1.591 1.621 1.592 1.710 O-B
1.448 1.505 1.607 1.564 1.661 1.743
TPG
3.392
2.541
2.481
2.370
0.891
0.990
0.991
0.995
1.137
2.644
3.032
4.618
chain2
2chains2
dimer
TPG+ (1)
TPG+ (3)
TPG+ (2)
chain2
2chains2
experimental56 1.581 1.613 1.681
components of the dielectric constant tensor in the dielectric
frame, obtained with eq 13, the Onsager-Bo¨ttcher (O-B)
relation for an ellipsoidal cavity, using the calculated linear
polarizability of the unit cell per molecule. All of these
calculations were performed with the clusters indicated above.
Kotler et al.56 measured the refractive indices of 2A5NPDP at
various wavelengths in the range of 468-1340 nm, and Horiuchi
et al.57 measured the refractive indices of 2A5NPCl in the
447-1320 nm range. Since our semiempirical calculations are
static, we compare our results with the experimental refractive
indices measured at the highest wavelengths (1340 nm for
2A5NPDP and 1320 nm for 2A5NPCl) (see Tables 14 and 15).
Once more, the best results are obtained with the larger
clusters and using the O-B relation to extract the components
of the dielectric constant tensor. For 2A5NPCl, only the larger
cluster (2chains4) reproduces the correct order of the refractive
indices (ny > nx > nz), with the agreement with the experimental
values being worse than that for 2A5NP.
TABLE 15: Calculated Refractive Indices for 2A5NPCl
Compared with the Experimental Values at 1320 nm57 (see
text for details)
PM3
PM6
nx
ny
nz
nx
ny
dz
dimer
chain2
chain4
2chains2
2chains4
dimer
chain2
chain4
1.751 1.636 1.516 1.869 1.823 1.308
1.719 1.659 1.514 1.845 1.799 1.298
1.733 1.651 1.519 1.903 1.771 1.297 L-L
1.803 1.726 1.374 1.811 1.799 1.264
1.722 1.705 1.461 1.839 1.762 1.288
1.610 1.522 1.467 1.687 1.613 1.288
1.573 1.508 1.451 1.648 1.585 1.275
1.541 1.497 1.414 1.625 1.563 1.265 O-B
1.772 1.600 1.373 1.717 1.640 1.257
1.571 1.636 1.416 1.630 1.650 1.266
2chains2
2chains4
experimental57 1.645 1.787 1.469
Kotler et al.56 The reasons invoked in ref 56 to account for the
discrepancy between measured and calculated values were the
following: (1) The hyperpolarizability of the neutral molecule
has been used; (2) a one-dimensional model has been consid-
ered; (3) the molecular nonlinearity was corrected with L-L
local field factors; and (4) the contribution of the phosphate
anionic sublattice was neglected. All of these issues are
addressed in our calculations.
3.3.1. Scalar InWariants of the Hyperpolarizability. The first
hyperpolarizability ꢀ, being a fully symmetric third-rank tensor
under Kleinmann symmetry, can be decomposed into two tensorial
components ꢀJ)1 and ꢀJ)3, called, respectively, the dipolar (vector)
and the octupolar (septor) irreducible components10,61
ꢀ ) ꢀJ)1 x ꢀJ)3
(15)
Our calculations of the quadratic coefficients for 2A5NPCl
show also a better performance of the W-B local field
correction and of the larger clusters. However, in this particular
case, it is more difficult to draw a definite conclusion about the
best Hamiltonian.
It was recognized by Jerphagnon61 that it is more useful to compare
proper scalar invariants, related to this decomposition, than to
compare the individual tensor components.
For the compounds studied, a considerable octupolar contri-
bution to the NLO effect due to the guanidine and guanidinium
fragments in TPG and TPG+, respectively, is expected. Using
The refractive indices were calculated from the L-L local
field factors using eq 2 and from the square root of the

2616 J. Phys. Chem. A, Vol. 114, No. 7, 2010
Silva et al.
the calculated values of the ꢀ components, it is possible to
estimate the ratio F of the scalar invariants associated with the
septor and the vector parts10
We plan to apply this methodology (oriented gas model, large
cluster, W-B local field correction, PM6 Hamiltonian) to more
compounds with d components determined in accurate experiments.
Acknowledgment. This work was supported by Fundac¸a˜o
para a Cieˆncia e a Tecnologia (FCT), under the Scholarship
SFRH/BD/38387/2008 and under the Project PTDC/FIS/103587/
2008.
|ꢀJ)3
|ꢀJ)1
|
|
F )
(16)
In the case of molecules with no particular symmetry, the most
general formulas, corresponding to class 1, must be used to
calculate the invariants.62
References and Notes
(1) Nonlinear Optical Properties of Organic Molecules and Crystals;
Chemla, D. S., Zyss, J., Eds.; Academic Press: Orlando, FL, 1987; Vol. 1.
(2) Molecular Nonlinear Optics. Materials, Physics, and DeVices; Zyss,
J., Ed.; Academic Press: Boston, MA, 1994.
(3) Marder, S. R.; Perry, J. W.; Schaefer, W. P. Science 1989, 245,
626.
(4) Lacroix, P. J.; Cle´ment, R.; Nakatani, K.; Zyss, J.; Ledoux, I.
Science 1994, 263, 658.
(5) Pan, F.; Kno¨pfle, G.; Bosshard, C.; Follonier, S.; Spreiter, R.; Wong,
M. S.; Gu¨nter, P. Appl. Phys. Lett. 1996, 69, 13.
We calculated the F values for TPG, TPG+, the chromophoric
units of the salts (ion pairs), and also the unit cells when the
crystalline symmetry allowed the existence of both components.
All tensor components were taken from the PM6 calculations,
and for the unit cell, we used the d components of the calculation
with the largest cluster and W-B local field correction.
The vector part of the ꢀ tensor can be related to the dipole
moment,63 and the octupolar part will be higher for a system
with trigonal symmetry; therefore, it is interesting to relate the
F values of the TPG molecule and the TPG+ ions in the three
salts with the dipole moment and the geometry of the central
CN3 fragments. We applied the geometry-based HOMA (har-
monic oscillator measure of aromaticity) index of aromaticity64,65
(HOMA is defined to give 0 for a model nonaromatic system
and 1 for a system where full π-electron delocalization occurs)
to quantify the so-called Y aromaticity66 of the guanidine and
guanidinium fragments (see Table 16). The cations are more
octupolar than TPG since the guanidinium core is more
symmetric, which is reflected in the higher values of the HOMA
index of the cations.
(6) Zyss, J.; Nicoud, J. F.; Coquillay, M. J. Chem. Phys. 1984, 81,
4160.
(7) Josse, D.; Dou, S. X.; Zyss, J.; Andreazza, P.; Pe´rigaud, A. Appl.
Phys. Lett. 1992, 61, 121.
(8) Oudar, J. L.; Zyss, J. Phys. ReV. A 1982, 26, 2016.
(9) Zyss, J. Nonlinear Opt. 1991, 1, 3.
(10) Zyss, J. J. Chem. Phys. 1993, 98, 6583.
(11) Zyss, J.; Brasselet, S.; Thalladi, V. R.; Desiraju, G. R. J. Chem.
Phys. 1998, 109, 658.
(12) Zyss, J.; Ledoux-Rak, I.; Weiss, H.-C.; Bla¨ser, D.; Boese, R.;
Thallapally, P. K.; Thalladi, V. R.; Desiraju, G. R. Chem. Mater. 2003, 15,
3063.
(13) Le Floc’h, V.; Brasselet, S.; Zyss, J.; Cho, B. R.; Lee, S. H.; Jeon,
S.-J.; Cho, M.; Min, K. S.; Suh, M. P. AdV. Mater. 2005, 17, 196.
(14) Zyss, J.; Pe´caut, J.; Levy, J. P.; Masse, R. Acta Crystallogr., Sect.
B 1993, 49, 334.
(15) Kemme, A.; Rutkis, M.; Eiduss, J. LatV. PSR Zinat. Akad. Vestis
Kim. Ser. 1988, 5, 595.
For crystals belonging to point group 222 (ex. space group
P212121), the d tensor reduces to a purely octupolar component,
and its vector part is identically 0; therefore, only the octupolar
part of the molecular ꢀ tensor will contribute to the crystalline
d tensor. Since in TPG+ formate (F ) 0.774) and TPG+
m-methoxybenzoate (F ) 0.846), the octupolar part is ap-
preciable but not dominant at the molecular level (with the ion
pair as the chromophoric unit), most of this nonlinear response
will not contribute to the macroscopic response. In TPG+
benzoate (class m), F ) 0.771 at the molecular level and 1.151
for the unit cell. The TPG crystal may have both dipolar and
octupolar contributions to the macroscopic second-order polar-
izability since it is a medium with mm2 point symmetry. The
TPG molecule has a slight predominance of the octupolar
component of ꢀ (F ) 1.137), and this component is also
dominant in tensor d (F ) 1.662).
(16) Pereira Silva, P. S.; Paixa˜o, J. A.; Ramos Silva, M.; Matos Beja,
A. Acta Crystallogr., Sect. E 2006, 62, o3073.
(17) Pereira Silva, P. S.; Cardoso, C.; Ramos Silva, M.; Paixa˜o, J. A.
Acta Crystallogr., Sect. E 2007, 63, o501.
(18) Pereira Silva, P. S.; Ramos Silva, M.; Paixa˜o, J. A.; Matos Beja,
A. Acta Crystallogr., Sect. E 2007, 63, o2243.
(19) Pereira Silva, P. S.; Ramos Silva, M.; Paixa˜o, J. A.; Matos Beja,
A. Acta Crystallogr., Sect. E 2007, 63, o2524.
(20) Dastychova, L.; Prihoda, J.; J., T. Collect. Czech. Chem. Commun.
2007, 72, 297.
(21) Pereira Silva, P. S.; Domingos, S. R.; Ramos Silva, M.; Paixa˜o,
J. A.; Matos Beja, A. Acta Crystallogr., Sect. E 2008, 64, o1082.
(22) Cardoso, C.; Pereira Silva, P. S.; Ramos Silva, M.; Matos Beja,
A.; Paixa˜o, J. A.; Nogueira, F.; Sobral, A. J. F. N. J. Mol. Struct. 2008,
878, 169.
(23) Chemla, D. S.; Oudar, J. L.; Jerphagnon, J. Phys. ReV. B 1975, 12,
4534.
(24) Zyss, J.; Oudar, J. L. Phys. ReV. A 1982, 26, 2028.
(25) Wortmann, R.; Bishop, D. M. J. Chem. Phys. 1998, 108, 1001.
(26) Spek, A. L. HELENA. CAD-4 Data Reduction Program; University
of Utrecht: Utrecht, The Netherlands, 1997.
4. Conclusions
(27) SMART and SAINT; Bruker AXS Inc.: Madison, WI, 2003.
(28) Sheldrick, G. M. Acta Crystallogr., Sect. A 2008, 64, 112.
(29) Kurtz, S. K.; Perry, T. T. J. Appl. Phys. 1968, 39, 3798.
(30) Garcia, M. H.; Rodrigues, J. C.; Dias, A. R.; Piedade, M. F. M.;
Duarte, M. T.; Robalo, M. P.; Lopes, N. J. Organomet. Chem. 2001, 632,
133.
(31) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209.
(32) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 221.
(33) Stewart, J. J. P. J. Comput. Chem. 1991, 12, 320.
(34) Stewart, J. J. P. J. Mol. Model. 2004, 10, 155.
(35) Stewart, J. J. P. J. Mol. Model. 2007, 13, 1173.
(36) Stewart, J. J. P. MOPAC2009, Version 9.045W ed.; Stewart
Computational Chemistry: Colorado Springs, CO, 2009.
(37) Hamada, T. J. Phys. Chem. 1996, 100, 8777.
(38) Bo¨ttcher, C. J. Theory of Electric Polarization; Elsevier: Amster-
dam, The Netherlands, 1973; Vol. 1.
In this paper, we have performed the calculation of the
second-order susceptibility for crystals made of microscopic
units with no special symmetry. The calculations were based
on the oriented gas model in its most general formulation. We
considered several types of microscopic units from the molecule
to clusters of different sizes/shapes. We also used different local
field corrections. For the calculation of the microscopic ꢀ tensor
components, we used the semiempirical PM3 and PM6
Hamiltonians.
Comparison with the experimental data showed that consid-
eration of a large cluster as the microscopic unit yields better
theoretical results. Also, the use of the W-B local field factors
instead of the usual L-L correction further improved the
calculated d components. The PM6 Hamiltonian performed
better in comparison with the older PM3.
(39) van Duijnen, P. T.; de Vries, A. H.; Swart, M.; Grozema, F.
J. Chem. Phys. 2002, 117, 8442.
(40) Onsager, L. J. Am. Chem. Soc. 1936, 58, 1486.
(41) Zyss, J.; Tsoucaris, G. T. In Structure and Properties of Molecular
Crystals; Pierrot, M., Ed.; Elsevier: Amsterdam, The Netherlands, 1990.

Triphenylguanidine with Carboxylic Acids
J. Phys. Chem. A, Vol. 114, No. 7, 2010 2617
(42) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996,
14.1, 33.
(43) Macrae, C. F.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Shields,
G. P.; Taylor, R.; Towler, M.; van de Streek, J. J. Appl. Crystallogr. 2006,
39, 453.
(44) Pereira Silva, P. S.; Cardoso, C.; Ramos Silva, M.; Paixa˜o, J. A.;
Matos Beja, A.; Nogueira, F. J. Mol. Struct. 2008, 888, 92.
(45) Allen, F. H.; Kennard, O.; Watson, D. G.; Brammer, L.; Orpen,
A. G.; Taylor, R. J. Chem. Soc., Perkin Trans. 2 1987, S1–19.
(46) Etter, M. C. Acc. Chem. Res. 1990, 23, 120.
(47) Desiraju, G. R. Nature 2001, 412, 397.
(54) Boyd, R. W. Nonlinear Optics, 3rd ed.; Academic Press: Burlington,
MA, 2008.
(55) Nonlinear Optical Properties of Organic Molecules and Crystals;
Chemla, D. S., Zyss, J., Eds.; Academic Press: Orlando, FL, 1987; Vol. 2.
(56) Kotler, Z.; Hierle, R.; Zyss, J. J. Opt. Soc. Am. B 1992, 9, 534.
(57) Horicuhi, N.; Lefaucheux, F.; Ibanez, A.; Josse, D.; Zyss, J. Opt.
Mater. 1999, 12, 351.
(58) Horicuhi, N.; Lefaucheux, F.; Ibanez, A.; Josse, D.; Zyss, J. J. Opt.
Soc. Am. B 2002, 19, 1830.
(59) Masse, R.; Zyss, J. Mol. Eng. 1991, 1, 141.
(60) Pe´caut, J.; Le´vy, J. P.; Masse, R. J. Mater. Chem. 1993, 3, 999.
(61) Jerphagnon, J. Phys. ReV. B 1970, 2, 1091.
(62) Jerphagnon, J.; Chemla, D.; Bonneville, R. AdV. Phys. 1978, 27, 609.
(63) The dipole moment of an ion is not independent of origin; therefore,
any reported values from a calculation must specify the origin in order to
be meaningful. In this study, the dipole moments are referred to the center
of mass of the ions.
(48) Le Floc’h, V.; Brasselet, S.; Roch, J.-F.; Zyss, J. J. Phys. Chem.
B. 2003, 107, 12403.
(49) Brasselet, S.; Le Floc’h, V.; Treussart, F.; Roch, J.-F.; Zyss, J.;
Botzung-Appert, E.; Ibanez, A. Phys. ReV. Lett. 2004, 92, 207401.
(50) Brasselet, S.; Zyss, J. C. R. Physique 2007, 8, 165.
(51) Nicoud, J. F.; Twieg, R. J. In Nonlinear Optical Properties of
Organic Molecules and Crystals; Chemla, D. S., Zyss, J., Eds.; Academic
Press: Orlando, FL, 1987; Vol. 2, p 251.
(52) Halbout, J. M.; Blit, S.; Tang, C. L. IEEE J. Quantum Electron.
1981, QE-17, 513.
(53) Kleinman, D. A. Phys. ReV. 1962, 126, 1977.
(64) Krygowski, T. M. J. Chem. Inf. Comput. Sci. 1993, 33, 70.
(65) Krygowski, T. M.; Cyran´ski, M. K. Chem. ReV. 2001, 101, 1385.
(66) Gund, P. J. J. Chem. Educ. 1972, 49, 100.
JP909005Q