Structural designs and property characterizations for second-harmonic generation materials

Article abstract of DOI:10.1007/430_2011_64

Second-harmonic generation (SHG) materials only exist in solids that have no inversion center space groups, and they are constructed by the building blocks or chromophores of noncentrosymmetricity (NCS). In this chapter, we employed one or multiple chromophores that result from the coordination structure distortions of a d⁰ cation, polar displacement of d ¹⁰ cation center, a stereochemically active lone pair (SCALP) of cations, and asymmetrical delocalization π-charge systems, as building blocks to obtain some new compounds with NCS space group. The single-crystal structures were characterized, and physical properties, in particular SHG responses, were measured for these compounds. The electronic structures and density of states were calculated by DFT method, and the SHG properties are simulated to gain an insight into the relations between structure and NLO properties for the materials. The electronic origination of large SHG responses was assigned in terms of the calculated results.

Full text of DOI:10.1007/430_2011_64

Struct Bond (2012) 144: 1–42
DOI: 10.1007/430_2011_64
#
Springer-Verlag Berlin Heidelberg 2012
Published online: 31 January 2012
Structural Designs and Property
Characterizations for Second-Harmonic
Generation Materials
Wen-Dan Cheng, Chen-Sheng Lin, Wei-Long Zhang, and Hao Zhang
Abstract Second-harmonic generation (SHG) materials only exist in solids that
have no inversion center space groups, and they are constructed by the building
blocks or chromophores of noncentrosymmetricity (NCS). In this chapter,
we employed one or multiple chromophores that result from the coordination
0
10
structure distortions of a d cation, polar displacement of d cation center, a
stereochemically active lone pair (SCALP) of cations, and asymmetrical delocali-
zation p-charge systems, as building blocks to obtain some new compounds with
NCS space group. The single-crystal structures were characterized, and physical
properties, in particular SHG responses, were measured for these compounds. The
electronic structures and density of states were calculated by DFT method, and the
SHG properties are simulated to gain an insight into the relations between structure
and NLO properties for the materials. The electronic origination of large SHG
responses was assigned in terms of the calculated results.
Keywords Density functional theory calculations ꢀ Photophysical characterization ꢀ
Second-order harmonic generation ꢀ Structural design
Contents
1
2
Introduction ..................................................................................
POA Crystal by Packing of Chromophores with p-Charge Asymmetrical Distributions .
2
3
3
8
2
.1 Syntheses of POA and Descriptions of the Crystal Structure ........................
.2 Electronic Spectra and Second-Harmonic Generations of POA .....................
2
3
Effect of Lone Pair on SHG Responses in Eulytite-Type Compounds of Pb
and Ba Bi (PO ............................................................................. 14
.1 Preparation Processes and Structural Descriptions ................................... 14
.2 Electronic Structures and SHG Properties ............................................ 17
3 4 3
Bi (PO )
3
4 3
)
3
3
W.-D. Cheng (*), C.-S. Lin, W.-L. Zhang, and H. Zhang
State Key Laboratory of Structural Chemistry Fujian Institute of Research on the Structure
of Matter, Chinese Academy of Sciences, Fuzhou 350002, People’s Republic of China
e-mail: cwd@fjirsm.ac.cn
1

2
4
W.-D. Cheng et al.
ZnO-Based SHG Materials of KZn
4
SbO
7
and KZn
4 3
Sb O
12 ............................... 20
4
4
.1 Simple Descriptions of Synthesis and Structures of KZn
.2 Second-Harmonic Generation Investigations ......................................... 23
BiO(BO with 3-Chromophore Asymmetric Building Units 28
.1 Preparation and Structure of Single Crystal of CBOB ............................... 29
4
SbO
7
and KZn
4
(SbO
4
)
3
.
20
5
A Strong SHG Material Cd
4
3 3
)
5
5
5
.2 Electronic Structural Calculations of CBOB ......................................... 32
.3 Investigations of Nonlinear Optical Response of CBOB ............................. 34
6 Conclusions .................................................................................. 38
References ........................................................................................ 39
1
Introduction
The development of NLO can be essentially traced to the improvement of the
performances of the NLO materials [1–8]. At the first demonstration of SHG, a
weak output signal was recorded on photographic paper when a quartz crystal was
used as NLO media and a ruby laser was used as incident light resource [9]. It has
became the most popular for visible and UV applications since beta-barium borate
(b-BBO) crystal was discovered [10, 11]; the applications of lithium triborate
(LBO) [12] mainly concentrated around SHG of near IR radiation and OPO (optical
parametric oscillator) in visible and near IR ranges. Lithium niobate (LN) has very
high value of effective second-order nonlinear coefficient along optical axis, and
the periodically poled LN has become one of the most popular nonlinear materials
since the 1990s [13, 16]. Potassium titanyl phosphate (KTP) is a basic NLO crystal
for the construction of compact visible solid-state laser systems applied to diode-
pumped Nd:laser [15]. We believe that it will be higher demands for the nature and
performance of NLO materials with the developments of laser technology and
scientific experiments. In short, large frequency-doubling coefficients and figure
of merit (FOM) are essentials for NLO material applications. They depend on the
inherent nature of the material, in which the FOM value is proportional to the
square of the SHG effective coefficient and inversely proportional to about cube of
2
eff
2
the refractive index ðFOM ¼ d =n n Þ [16]. Now, the understanding of the
o
2o
material structure characteristics relating with the NLO mechanisms has been
considerably improved. The new development of the fabrication techniques and
growth of artificial materials has dramatically contributed to this evolution.
It is known that SHG response requires noncentrosymmetricity (NCS), and so it
only exists in solids that have no inversion center space groups. Crystallographi-
cally, the 230 space groups can be classified into 32 classes or point groups, in
which 20 are not a center of symmetry except of point group 432 (or O). Accord-
ingly, NLO behavior is achieved by off-centering of ions in polyhedra or NCS
chromophores cooperatively effect in solid-state materials. Here, the chromophore
0
can result from the coordination structure distortion of a d cation with a second-
1
0
order Jahn–Tellere effect [17–19], polar displacement of d cation centers [20],
distortion from a stereochemically active lone pair (SCALP) of cations [21, 22], or
borate p-orbital systems [23–25]. Sometimes, two NCS chromophores occur natu-
rally in the same material [17, 26–28]. For example, PbTiO has a SCALP on the Pb
3

Structural Designs and Property Characterizations
3
ion, as well as SOJT off-centering of the Ti [27]. However, only one example of
three-chromophore asymmetrical building units existing in the same SHG material
has been reported until now [29].
In this chapter, we will describe some new NLO materials with a large SHG
response by the controlling cooperativity of NCS chromophore and the choices of
the chromophore that will lead to asymmetrical distortion, and we will calculate the
electronic structures and simulate NLO properties to gain an insight into the
relations between structure and NLO properties for the materials. We will introduce
that the NLO crystal material of 2-carboxylic acid-4-nitropyridine-1-oxide (POA)
was synthesized to use POA chromophore with p-charge asymmetrical distortion,
and charge transfers among the chromophores make great contribution to SHG
response of POA crystal [30]. We will discuss lone-pair enhancement of
SHG responses in inorganic solid-state compound of Pb Bi(PO ) , and three off-
3
4 3
centering chromophores cooperative effect led to a strong SHG material of Cd BiO
4
(
BO ) [29, 31].
3 3
2
POA Crystal by Packing of Chromophores with p-Charge
Asymmetrical Distributions
In this respect, we develop two new crystals as candidates of second-order nonlinear
optical (NLO) materials with the choice of chromophore and crystal engineering
method [32–34]. First, we design a new chromophore of 2-carboxylic acid-
4
-nitropyridine-1-oxide (POA) with large hyperpolarizability, then we control
growing conditions to obtain two POA crystals with two different crystallizing
forms but with the same space group [30].
2
.1 Syntheses of POA and Descriptions of the Crystal Structure
A mixture of glacial acetic acid and pyridine-2-carboxylic acid contained in a
ꢁ
round-bottomed flask was shaken, with cold (0–5 C) 30% hydrogen peroxide
added, and the mixture was heated in an oil bath for 24 h. After the excess acetic
acid and water were removed under reduced pressure, the residue was cooled to
ꢁ
ꢁ
0
–5 C in an ice–salt bath, and cold (0–5 C) 40% aqueous sodium hydroxide
solution was added slowly with shaking and neutralized with shaking. The solution
was extracted with chloroform, and the extracts were filtered and concentrated by
distillation under reduced pressure. The residue was cooled, and the white crystal-
ꢁ
line powder of POA was obtained. This white powder is of mp. 172 ꢂ 0.5 C.
ꢁ
The white powder of this middle product was added to cold (0–5 C) sulfuric acid
(sp. gr. 1.84) contained in a round-bottomed flask immersed in an ice–salt bath.
ꢁ
The resulting mixture was cooled to about 10 C, and fuming yellow nitric acid was

4
W.-D. Cheng et al.
added with shaking. An efficient spiral condenser was attached to the flask, and
ꢁ
latter was placed in an oil bath. The temperature was slowly raised to 95–100 C,
ꢁ
and the heating was continued at 100–105 C for 4 h. The reaction mixture was
ꢁ
cooled to 10 C and poured onto crushed ice contained in a beaker. Addition of
sodium carbonate monohydrate in small portions with stirring caused the separation
of the yellow crystalline product along with sodium sulfate. The mixture was then
allowed to stand for 3 h to expel nitrogen oxides. The yellow solid was collected by
suction filtration, thoroughly washed with water, and rendered as dry as possible on
the filter. The filtrates were transferred to separator funnel. The collected solid was
extracted with portions of boiling chloroform, the combined extracts were used to
extract the aqueous filtrates contained in the separator funnel, and the extraction
was repeated with several fresh portions of chloroform. The combined chloroform
extracts were given preliminary drying over anhydrous sodium sulfate and
evaporated to dryness by distillation under reduced pressure. The pale-yellow-
colored product of POA was filtered by suction, the filtrates were removed and
saved, and the collected solid was washed with ether and dried. The pale yellow
ꢁ
powder of POA is of mp. 146 ꢂ 1 C. The synthetic route of POA is outlined in
Scheme 1.
The pale yellow powder of POA was dissolved in boiling mixture of methanol
and dichloromethane to obtain POA crystals. The solution was cooled to about
ꢁ
3
0 C and carefully filtered. The filtered solution was maintained at few degrees
above the saturation temperature for homogenization, and the microcrystals were
formed in the mother liquid. It was placed in the constant temperature bath whose
ꢁ
temperature was controlled to the accuracy of 35 ꢂ 0.05 C to ensure microcrystal
to be dissolved sufficiently. Growth commenced at this temperature. Solvent
evaporation was controlled by tight covering at the top of the beakers using
polyethene sheets. Transparent pale-yellow-colored crystal (POA-I crystal) was
ꢁ
harvested after a period of 20 days, mp. 148 ꢂ 0.5 C. The grown crystal was
3
prism in shape and had the dimensions of 4.0 ꢃ 3.0 ꢃ 3.0 mm . A mixture of
dichloromethane and pale yellow powder of POA was added to a mixture of
methanol and potassium hydroxide. After 48 h, a mixture of water and glacial
acetic acid that serves as a pH control was added to the abovementioned mixture
NO2
HAc,H O
HNO ,H SO
3 2 4
2
2
ii
i
N
COOH
N
COOH
N
COOH
O
O
Scheme 1 Preparation of POA. (i) Pyridine-2-carboxylic acid, glacial acetic acid, 30% hydrogen
ꢁ
peroxide, 80 C oil bath for 24 h; (ii) sulfuric acid (sp. gr. 1.84), fuming yellow nitric acid,
1
ꢁ
00–105 C oil bath for 4 h

Structural Designs and Property Characterizations
5
Fig. 1 ORTEP diagram of POA
and carefully filtered. Transparent pale-yellow-colored crystal (POA-II crystal) was
ꢁ
harvested after a period of 7 days, mp. 156 ꢂ 0.5 C. The grown crystal was needle
3
in shape and had the dimensions of 0.80 ꢃ 0.18 ꢃ 0.14 mm .
POA-I and POA-II crystal structures were determined by single-crystal X-ray
diffraction at room temperature and solved by direct methods [30]. The molecular
configuration parenthesis atomic symbol of POA is presented in Fig. 1, and selected
interatomic distances and angles are presented in Table 1.
Single-crystal X-ray analysis showed that the atoms of crystal POA-I are all in a
plane. Its least-square equation is 6.389(5) X + 2.944 (1) Y ꢄ 6.565(3) Z ꢄ 2.064
˚
˚
(
(
(
4) A ¼ 0 with 0.0704 A of r.m.s. deviation. The length of O(1)–N(1) bond (1.323
˚ ˚
2) A) is longer than the corresponding bond (1.285(3) A) in 2-POM and the bond
˚
1.288(2) A) in POM [35, 36]. The length of C(3)–N(2) bond (1.469(3) A) is longer
˚
˚
than the corresponding bond (1.450(3) A) in 2-POM and is in an agreement with the
˚
corresponding bond (1.460(3) A) in POM. The lengths of O(4)–N(2) and O(5)–N(2)
˚
˚
bonds (1.218(3) A and 1.221(3) A) are in agreement with the corresponding bonds
˚ ˚ ˚ ˚
1.223(3) A and 1.238(3) A) in 2-POM and bonds (1.224(3) A and 1.226(3) A) in
POM. The environments of oxygen atoms in carbonic acid are not the same. One
(
˚
oxygen (O(2)) is linked by a hydrogen (the length of O(2)–H(02) is 1.0701 A), and
˚
another (O(3)) is not. The length of O(3)–C(6) bond (1.203(3) A) is shorter than that
˚
of O(2)–C(6) (1.305(3) A). There are intramolecular hydrogen bonds in the crystal
.
POA-I. The hydrogen bond length of O(2)–H O(1) is 2.460(2) A. The angle of
. .
˚
.
O(2)–H O(1) hydrogen bond is 159.6 . There are four molecules in one unit cell.
. .
ꢁ

6
W.-D. Cheng et al.
Crystal II
Table 1 Selected bond
lengths (A) and angles ( )
of POA crystals
˚
Bond (A)
Crystal I
˚
ꢁ
C(1)–N(1)
C(1)–C(2)
C(1)–C(6)
C(2)–C(3)
C(2)–H(2A)
C(3)–C(4)
C(3)–N(2)
C(4)–C(5)
C(4)–H(4A)
C(5)–N(1)
C(5)–H(5A)
C(6)–O(3)
C(6)–O(2)
N(1)–O(1)
N(2)–O(4)
N(2)–O(5)
O(2)–H(02)
1.368(2)
1.377(3)
1.511(3)
1.369(3)
0.9300
1.363(4)
1.360(4)
1.505(4)
1.371(4)
0.9300
1.376(3)
1.469(3)
1.367(3)
0.9300
1.371(5)
1.472(4)
1.361(5)
0.9300
1.353(2)
0.9300
1.352(4)
0.9300
1.203(3)
1.305(3)
1.323(2)
1.218(3)
1.221(3)
1.0701
1.206(4)
1.306(4)
1.318(4)
1.216(4)
1.220(4)
0.8925
ꢁ
Angle ( )
Crystal I
118.9(2)
120.7(2)
120.3(2)
119.2(2)
121.6(2)
119.2(2)
119.1(2)
118.2(2)
120.7(2)
123.9(2)
119.5(2)
116.6(2)
118.0(2)
120.7(2)
121.4(2)
124.2(2)
118.0(2)
117.8(2)
Crystal II
118.9(3)
120.4(3)
120.6(3)
120.3(3)
120.5(3)
119.6(3)
119.9(3)
118.4(3)
121.1(3)
123.0(3)
119.7(3)
117.3(3)
118.3(3)
120.9(3)
120.8(3)
124.4(4)
117.8(3)
117.7(4)
N(1)–C(1)–C(2)
N(1)–C(1)–C(6)
C(2)–C(1)–C(6)
C(3)–C(2)–C(1)
C(2)–C(3)–C(4)
C(2)–C(3)–N(2)
C(4)–C(3)–N(2)
C(5)–C(4)–C(3)
N(1)–C(5)–C(4)
O(3)–C(6)–O(2)
O(3)–C(6)–C(1)
O(2)–C(6)–C(1)
O(1)–N(1)–C(5)
O(1)–N(1)–C(1)
C(5)–N(1)–C(1)
O(4)–N(2)–O(5)
O(4)–N(2)–C(3)
O(5)–N(2)–C(3)
The molecules are not parallel with each other in unit cell. The dihedral angles
ꢁ
ꢁ
ꢁ
between neighbored molecules are 88.46(3) , 59.13(3) , and 59.08(3) , respec-
tively (shown in Fig. 2a). It can be seen from the one-dimensional chain structure
.
. .
that there exist C(5)–H O(3a) (symmetry code: a, ꢄ1/2 + x, 1/2 ꢄ y, 1 ꢄ z)
intermolecular hydrogen bonds in the crystal POA-I (shown in Fig. 3a). The
C(5)–H groups act as proton donor in the hydrogen-bonded system [37]. The
.
. .
˚
bond lengths of C(5)–H and H O(3a) are 0.930 and 2.576 A, respectively, and
.
the bond angle of C(5)–H O(3a) is 140.1 . The calculation using B3LYP [38] in
. .
ꢁ

Structural Designs and Property Characterizations
7
a
b
Fig. 2 Packing arrangement in a unit cell for (a) POA-I and (b) POA-II
Fig. 3 Packing arrangement with hydrogen bonds for (a) POA-I and (b) POA-II
conjunction with the 6–311 + G(3df,2p) basis set indicates that the binding energy
.
. .
ꢄ1
of C(5)–H O(3a) hydrogen bond is about 0.64 kJ mol , which is a weak hydrogen
bond.

8
W.-D. Cheng et al.
The atoms of crystal POA-II are all in a plane too. Its least-square equation is
˚
˚
3
deviation, excelled deviation of crystal POA-I. The lengths of O(1)–N(1) bond
.015(3) X ꢄ 8.226 (4) Y + 0.633(8) Z ꢄ 4.285 (5) A ¼ 0 with 0.0332 A of r.m.s.
˚ ˚ ˚
(
(
(
1.318(4) A), C(3)–N(2) bond (1.472(4) A), O(4)–N(2) bond (1.216(4) A), O
˚
5)–N(2) bond (1.220(4) A), O(3)–C(6) bond (1.206(4) A), and O(2)–C(6) bond
˚
˚
1.306(4) A) are in agreement with those of crystal POA-I, respectively. The
environments of oxygen atoms in carbonic acid are not the same as POA-I. The
˚
˚
length of O(2)–H(02) bond (0.8925 A) is shorter than that (1.0701 A) of crystal
POA-I. There are intramolecular hydrogen bonds in the crystal POA-II too. The
.
hydrogen bond length of O(2)–H O(1) is 2.461(2) A. The angle of O(2)–H O(1)
. .
. . .
˚
ꢁ
hydrogen bond is 151.5 . The stacking of crystal POA-II is not the same as that of
crystal POA-I. The dihedral angles between neighbor molecules in crystal POA-II
ꢁ
ꢁ
ꢁ
are 66.09(4) , 65.81(4) , and 5.47(8) , respectively (shown in Fig. 2b). It can be seen
.
. .
from the one-dimensional chain structure that there exist C(4)–H O(5a) (symmetry
code: a, ꢄ1/2 + x, 1/2 ꢄ y, 1 ꢄ z) intermolecular hydrogen bonds in the crystal
.
POA-II (shown in Fig. 3b). The bond lengths of C(4)–H and H O(5a) are 0.930 and
. .
.
.381 A, respectively, and the bond angle of C(4)–H O(5a) is 154.0 . The two
. .
ꢁ
˚
2
.
. .
molecules in the POA crystals are held together by weak hydrogen bond of C–H O,
and one of molecules donates one hydrogen bond to the other. The one-dimensional
chains are formed, and the POA crystals are stabilized by these weak hydrogen
bonds. In effect, weak hydrogen bonds are employed collectively to work as
effectively as their stronger counterparts [39].
Here, we describe the distinguishing of syntheses and crystal structures between
the POA-I and POA-II crystals. The preparing measure and conditions are different
between the POA-I and POA-II crystals. The POA-I crystal is formed through the
filtrating and recrystal processes; however, the POA-II crystal is only through the
filtrating process. The molecular arrangements are different between the POA-I and
POA-II crystals. The dihedral angles between neighbor molecules in a unit cell are
ꢁ ꢁ ꢁ ꢁ ꢁ ꢁ
8
8.46 , 59.08 , 59.13 , 59.13 , 59.08 , and 88.46 , respectively, for POA-I crystals
ꢁ
ꢁ
ꢁ
ꢁ
ꢁ
ꢁ
and are 66.09 , 5.47 , 65.81 , 65.81 , 5.47 , and 66.09 , respectively for POA-II
crystals.
2
.2 Electronic Spectra and Second-Harmonic
Generations of POA
The absorption spectra were recorded by UV-3101PC spectrometer at 300 K from
00 to 800 nm. Figure 4 shows the absorption spectra of POA-I and POA-II powder
determined from reflection measurements. The strongest absorption peaks locate at
74 and 278 nm, and the second ones are localized at 373 and 353 nm for the POA-I
2
2
and POA–II powder, respectively. In order to assign the electronic absorption
peaks, we made the quantum chemical calculations. Density functional theory
(
DFT) calculations were performed with Gaussian 03 package. The properties of

Structural Designs and Property Characterizations
9
2
1
1
0
5
0
5
0
a
b 14
1
1
2
0
8
6
4
2
0
2
POA-I
POA-II
-
1
00 200 300 400 500 600 700 800 900 10001100
Wavelength (nm)
100 200 300 400 500 600 700 800 900 10001100
Wavelength (nm)
Fig. 4 Electronic absorption spectra of POA powder: (a) POA-I and (b) POA-II
a 0
.35
b 0.30
one-molecule of POA-I
one-molecule of POA-II
0
.30
.25
.20
.15
.10
.05
.00
0
0
0
0
.25
.20
.15
.10
0
0
0
0
0
0
0.05
0.00
200
300
400
500
200
250
300
350
400
450
Wavelength (nm)
Wavelength (nm)
Fig. 5 The calculated absorption spectra of one molecule: (a) POA-I and (b) POA-II
excited states were calculated by using time-dependent density functional theory
TD-DFT) with BP86 functional [40, 41] and 3-21G* basis set. The calculated
(
absorption spectra of one molecule of POA at TD-BP86/3-21G* level are plotted in
Fig. 5. The measurement absorption bands from 180 to 340 nm and from 340 to
4
40 nm correspond to calculated ones from 180 to 310 nm and from 310 to 350 nm
for POA-I and correspond to calculated ones from 180 to 300 nm and 300 to 380 nm
for POA-II, individually. Here, we noted that absorption spectrum of crystal is
different from that of single molecule and intermolecular excitonic interactions
result in the red shift of absorption spectra from molecule to crystal. These results
were discussed in detail in the published paper by M. Pierre et al. [42]. We make
systemic comparisons between the single molecule and corresponding crystal in
order to give an assignment of crystal absorption spectrum. Our calculations
indicate that the maximum absorption band observed in the experiment corresponds
to the S11 state that has larger oscillator strength. The analysis of TDDFT wave
function indicates that the S11 state has the p–p* transition characteristics. This
shows that the largest absorption band of POA crystals mainly originates from p–p
charge transfer transitions.

1
0
W.-D. Cheng et al.
1
0
8
6
4
2
0
a
b 14
βtot
β
τοτ
12
1
0
8
6
4
2
0
β
β
β
1
23 β231
β
123
231
312
β
312
0
20
40
60
80
100
120
0
20
40
60
80
100
120
Number of States
Number of States
Fig. 6 Convergent behavior of b values with number of states for 4-molecule cluster: (a) POA-I
and (b) POA-II
We choose the 4-molecular cluster from one unit cell as basic model to calculate
the second-order polarizabilities b(ꢄ2o; o, o) of SHG process to include the
supramolecular interactions in the POA-I and POA-II crystal materials. The x, y, z
directions in the Cartesian coordination correspond to the unit cell a, b, c axes of
orthorhombic system, respectively. With the calculated dipole moments and transi-
tion moments of excited states of 4-molecule cluster in a POA crystal, the sum over
states (SOS) formalism [43, 44] was employed to evaluate the NLO responses of 4-
molecular cluster and the optical physical property superposition of 4-molecular
cluster is applied to obtain optical susceptibility of POA crystal. For the calculations
of b, we first consider how to truncate the infinite SOS expansion to a finite one.
Figure 6 shows the plots of the calculated second-order polarizabilities bxyz, byzx, bzxy
and b (ꢄ2o; o, o) at the TDBP86/3-21G* level vs the number of states for POA-I
tot
and POA-II at input photon energy of hꢀ o ¼ 1.165 eV.
The curve of b (ꢄ2o; o, o) of POA-I shows good convergence after state 32
tot
and convince that the truncation with 120 states is reasonable. The 13th state makes
a large contribution to the btot value, and the calculated btot value including the first
1
3 states is about 63% of the btot value including 120 states. While the
b (ꢄ2o;o,o) of POA-II is considered, the curve has oscillation and the conver-
tot
gence is not as good as that of POA-I. But it can be found that all the values after six
ꢄ30
5
cm esu , which is acceptable for the
ꢄ1
states fall in the range of 9–15 ꢃ 10
deviations. The fourth state of 4-molecule cluster in POA-II crystal makes the
largest contribution to the btot value. Both the 13th state of POA-I and 4th state
of POA-II have the significant configurations of HOMO-3!LUMO, where HOMO-
3
is the p-bonding orbital mainly located at one monomer but with a small mixing
from neighboring monomer, and LUMO is p*-antibonding orbital located on
another monomer in the 4-molecule cluster (shown in Fig. 7). From the analysis of
the molecular orbitals and configuration contributions, it can be found that charge
transfers between the monomers make mainly contributions to the hyperpolar-
izability of POA-I and POA-II 4-molecule clusters. Furthermore, structure–property
relations at molecular level are discussed in details for POA molecules.

Structural Designs and Property Characterizations
11
Fig. 7 Frontier molecular orbitals: (a) HOMO of POA one molecule, (b) LUMO of POA one
molecule, (c) HOMO-3 of POA-I molecular cluster, (d) LUMO of POA-I molecular cluster,
(
e) HOMO-3 of POA-II molecular cluster, (f) LUMO of POA-II molecular cluster
The molecules both in the POA-I and POA-II crystals are planar with 0.0704 and
0
˚
.0332 A of r.m.s. deviation of atoms, and intramolecular hydrogen bonds form
between the hydroxyl group of COOH and oxygen of N-oxide for the molecules as
mentioned above. The COOH is a planar structure and is composed of hydroxyl and
carbonyl groups. The changes in chemical and physical properties result from the
competition interaction between the hydroxyl and carbonyl functions within the
COOH. A hydrogen bond formed with neighbor oxygen of N-oxide donates a proton
and results in reduced ability of charge transfer of N-oxide; however, the excess
charges of carbonyl group withdrawing from oxygen atom of hydroxyl group in the

1
2
W.-D. Cheng et al.
COOH group transfer into 4-nitropyridine-1-oxide while hydrogen bond forms. The
accepting charge effect of nitro group has no substantial changes due to the com-
pensatory effect between the hydroxyl and carbonyl group in the POA molecules.
Hence, the POA chromophore would not interfere destructively with the basic
charge transfer mechanism from the N-oxide group to the nitro group, which results
in the expected optical nonlinearity. Figure 7a, b gives the plots of HOMO and
LUMO of POA single molecule, and they show the evidence of the charge transfers
from the N-oxide and COOH groups to the nitro group while an electron is promoted
from HOMO to LUMO. On the contrary, the atoms in POM (3-methyl-4-
nitropyridine-1-oxide) is not coplanar since the methyl group in 3-position of
POM is not planar structure itself. Accordingly, the methyl induces a rotation of
the nitro group and results in a reduced conjugation between the donor oxygen of the
oxide and the nitro acceptor. This means that a reduced charge transfers from the N-
oxide to the nitro groups will result in weak optical response of POM chromophore.
Additionally, the intermolecular hydrogen bonds formed from the C–H of pyridine
ring and O of C¼O in COOH group also lead to a quasi-optimal molecular orienta-
tion and enhancement of NLO response in the POA crystals. These conclusions have
been also found in N-(4-nitrophenyl)-(L)-prollnol (NPP) and 2-methyl-4-
nitroaniline (MNA) crystals [45].
In fact, molecule or molecular cluster is a building component of bulk materials,
the physical properties of the bulk materials are dependent on their molecular
components and the manners of arrangement and linking of the components in
the crystalline state. The molecular clusters are taken as calculating models in this
study, which are exactly four molecules in a unit cell of POA-I and POA-II,
respectively. The inherent noncovalent force interaction and optimal arrangement
among 4-molecular cluster are included into the extended solid-state architectures.
For the solid state constructed through the noncovalent force interaction among the
molecules, the optical properties of the solid state simply arise from the 4-molecular
structure and the packing manner among the molecules. For this reason, the studies
of optical properties of materials predigest the investigations of molecular cluster
ð2Þ
optical properties. Accordingly, the NLO susceptibility wabc of bulk material can be
estimated from the first-order hyperpolarizability of the 4-molecular cluster babc
corrected by the local field factor along the three crystal axes.
ð2Þ
w
ðꢄ2o; o; oÞ ¼ NLbabcðꢄ2o; o; oÞ:
(1)
abc
Here, N can be evaluated with N ¼ 1/V (Vcell is the volume of the unit cell of
cell
POA crystal). The local field correction factor is calculated from L ¼ f (2o)f (o)
a
b
2
f (o), and the f(o) ¼ [n(o) + 2]/3 ¼ 1/[1ꢄ(4p/3)Na(o)] with the assumption of
c
Lorentz-Lorenz local field, in which n(o) is the refractive index and a(o) is the
first-order microscopic polarizability. With SOS formalism, we can evaluate a(o)
and thus calculate the macroscopic susceptibility. The calculated main values of
(
2)
w
are listed in Table 2 for the SHG optical process at an input wavelength of
064 nm. The Kurtz powder SHG measurement shows that POA-I and POA-II
1

Structural Designs and Property Characterizations
13
Table 2 Parameters for calculating the NLO susceptibilities of POA at 1064 nm for SHG optical
process
a
N
(2)
w (expt)
b
ð2Þ
b
ð2Þ
b
ð2Þ
b
ð2Þ
b
w
w
w
w
tot
1
23
231
312
POA-I
1.390
1.385
0.78
6.69
1.02
7.76
2.46
6.95
11.56
21.80
14.72
31.80
POA-II
21
a
ꢄ3
1
1
0
0
cm
esu
b
ꢄ9
exhibit powder SHG efficiency about 4.6 times and 9.8 times as that of KDP. The
selected value of the KDP d coefficient originating from an averaging data is
3
6
ꢄ9
(2)
.6 ꢃ 10 esu [46], and thus, our measured d coefficient (2d ¼ w ) are about
1
ꢄ9 ꢄ9 ꢄ9 ꢄ9
7
.36 ꢃ 10 (14.72 ꢃ 10 ) esu and 15.68 ꢃ 10 (31.36 ꢃ 10 ) esu, respec-
ð2Þ
tively. Accordingly, the estimated values of w listed in Table 2 are smaller than
tot
those in experiment but are quite satisfactory estimation.
In our cluster model, molecular orientations and interactions in crystalline state
have been considered in 4-molecular cluster calculations. The influence of individual
molecular orientation in crystalline state on optical property has not been analyzed in
details. At the moment, we make some discussions about structure–property relations
in terms of the definition of “b” tensor, which is dimensionless parameter developed
by Zyss and Oudar [47]. The crystal NLO parameter of d varies directly with angular
factors of molecular orientation within crystalline state while the b tensor is taken as a
unit. For the 222 point group, the optimal value of angular factor (sinf ꢃ cosf ꢃ
2
ꢁ
ꢁ
cony ꢃ sin y, f ¼ 45 , y ¼ 54.7 ) is 0.1924 for maximizing crystal nonlinearity in
regular tetrahedral configuration constructed by the four dipole axes of four molecular
plans [47]. Both the POA-I and POA-II crystals belong to the 222 point group, and the
four dipole axes of four molecular plans form a pseudotetrahedral structure, the
ꢁ
ꢁ
ꢁ
angular factor is 0.1622 (about f ¼ 29.5 , y ¼ 59 ) and 0.1550 (about f ¼ 33 ,
ꢁ
y ¼ 66 ), separately for POA-I and POA-II crystals. It is shown that the angular factor
of the POA-II crystal has a larger difference from the ideal optimum value. However,
the POA-II crystals have larger NLO parameters by compared with ones of the POA-I
crystals both in our calculations and measurements. These results indicate that one-
dimensional dipole model is not good treatment on the POA crystals. It is a good
scheme that the POA crystals are treated to employ multipolar (octupolar) molecular
engineering method [48, 49] due to the COOH substituent in 2-position of 4-nitro-
pyridine-1-oxide.
There are different optical properties between the POA-I and POA-II crystals.
The SHG effect is larger for POA-II than POA-I crystals. A large SHG response of
POA-II crystal comes from a large hyperpolarizability of 4-molecule cluster of
POA-II crystal. The large charge transfers between the molecules will make a large
contribution to hyperpolarizability of 4-molecular cluster of POA-II crystal. The
calculated important state contributing mostly to hyperpolarizabilities has small
transition moment and large electronic transition energy of POA-I molecular cluster
and has large transition moment and small transition energy of POA-II molecular
cluster.

1
4
W.-D. Cheng et al.
3
Effect of Lone Pair on SHG Responses in Eulytite-Type
Compounds of Pb Bi (PO ) and Ba Bi (PO )
3
4 3
3
4 3
In this respect, we describe the fabrication, SHG response, and electronic origin of
optical property of eulytite-like orthophosphates Pb Bi (PO ) and Ba Bi (PO )
4 3
3
4 3
3
[
31]. With the design idea that metal ion including lone pairs will result in coordi-
3
+
nated structural distortion, we introduce Bi into lead phosphates of ternary
systems to obtain SHG materials.
3
.1 Preparation Processes and Structural Descriptions
The syntheses of single crystals Pb Bi(PO ) were carried out using Bi O , PbCl ,
3
4 3
2
3
2
and NH H PO in a molar ratio corresponding to Bi/Pb/P ¼ 1:3:5 of a mass of 2 g,
4
2
4
the excess amount of NH H PO to be used in order to promote crystal growth.
4
2
4
During the preparing processes, first, the mixture was ground in an agate mortar, the
resulting mixture was introduced into a platinum crucible and was heated at 673 K
for 10 h in order to decompose NH H PO ; then heated for 1 day at 1,323 K and
4
2
4
cooled down to 1,023 K at a rate of 3 K/h; and finally cooled to 573 K at 5 K/h before
switching off the furnace. Some colorless crystals of Pb Bi(PO4) were selected
3
3
carefully from a sintered product. After boiled in water, some prism-shaped color-
less crystals of Pb Bi(PO4) were selected carefully for X-ray single-crystal diffrac-
tion. Monophase power of Pb Bi(PO ) was prepared from the stoichiometric
3
3
3
4 3
mixture of PbO, Bi O , and NH H PO in a molar ratio of 6:1:6. This mixture was
2
3
4
2
4
ground in an agate mortar and then calcined at 1,153 K in air for 24 h with several
intermediate grindings in an opening Pt crucible. The monophase products of
homologous compounds Ba Bi(PO ) were prepared using NH H PO , BaCO ,
3
4 3
4
2
4
3
and Bi O by high-temperature solid reaction method at 1,273 K for 1 day. The
2
3
final product was analyzed by X-ray powder diffractions [31].
Single crystal of Pb Bi(PO ) was selected and mounted on glass fibers, and data
3
4 3
collection was performed on a Rigaku SCXmini at the temperature of 293 K.
Absorption correction by the multiscan method, Lorentz and polarization corrections,
2
was applied to data. The structure was solved by direct method and then refined on F
by full-matrix least-squares method and performed in the Shelxl/PC programs [50].
Atomic positions of Bi/Pb, P, and O were determined using direct method. The final
refinement of the structure was achieved using a fixed site occupancy ratio 3:1 for Pb
and Bi equal to the ideal values in accordance with the chemical formula Pb Bi(PO ) .
3
4 3
The atomic and thermal parameters of bismuth were fixed to be same as that of lead.
All atoms in Pb Bi(PO ) were refined with anisotropic thermal parameters [31]. The
3
4 3
atomic coordinates, selected important bond lengths, are listed in Tables 3 and 4 ,
respectively. The final refined solutions obtained were checked with the ADDSYM
algorithm in the program PLATON [51], and no higher symmetry was found. Energy-
dispersive X-ray spectrometry (EDS) using a JSM6700F scanning electron

Structural Designs and Property Characterizations
15
4
2
3
Table 3 Atomic coordinates (ꢃ10 ) and displacement parameters (A ꢃ 10 ) for Pb
3 4 3
Bi(PO )
a
Atom
x
y
z
U(eq)
Occupancy factor
Bi1
Pb1
P1
752(1)
752(1)
2,500
752(1)
752(1)
3,750
752(1)
752(1)
0
14(1)
14(1)
9(1)
0.25
0.75
O1
a
1,390(8)
2,912(8)
513(9)
29(2)
U
(eq) is defined as one-third of the trace of the orthogonalized Uij tensor
˚
ꢁ
3 4 3
Table 4 Important bond lengths (A) and angles ( ) for Pb Bi(PO )
Bond distances
Pb1/Bi1-O1
2.347(8)
2.629(8)
2.347(8)
1.537(9)
1.537(9)
Pb1/Bi1-O11
Pb1/Bi1-O14
Pb1/Bi1-O15
P1-O16
2.347(8)
2.629(8)
2.629(8)
1.537(9)
1.537(9)
Pb1/Bi1-O13
Pb1/Bi1-O12
P1-O1
P1-O17
P1-O18
Important angles
O1-Pb1/Bi1-O11
O11-Pb1/Bi1-O12
O12-Pb1/Bi1-O13
O12-Pb1/Bi1-O14
O1-Pb1/Bi1-O15
O13-Pb1/Bi1-O15
O16-P1-O1
82.1(3)
82.1(3)
O1-Pb1/Bi1-O12
O11-Pb1/Bi1-O13
O1-Pb1/Bi1-O14
O13-Pb1/Bi1-O14
O11-Pb1/Bi1-O15
O14-Pb1/Bi1-O15
O16-P1-O17
82.1(3)
74.1(3
81.51(13)
74.1(3)
81.51(13)
114.53(15)
81.51(13)
114.53(15)
108.6(3)
111.2(6)
108.6(3)
74.1(3)
114.53(15)
108.6(3)
111.2(6)
O1-P1-O17
O16-P1-O18
O1-P1-O18
108.6(3)
O17-P1-O18
1
2
3
4
Symmetry code: (z, x, y); (y, z, x); (z + 0, ꢄx + 0, ꢄy + 1/2); (ꢄy + 1/2,z + 0, ꢄx + 0);
5
8
6
7
(
ꢄx + 0, ꢄy + 1/2, z + 0); (z + 1/4, ꢄy + 3/4, ꢄx + 1/4); (ꢄx + 1/2, y + 0, ꢄz + 0);
(
ꢄz + 1/4, ꢄy + 3/4, x ꢄ 1/4)
microscope of the single crystals indicated the presence of Pb, Bi, P, and O elements.
Inductively coupled plasma (ICP) measurement result indicated that the mixture of Pb
and Bi is in a molar ratio of 2.92:1, which was in good agreement with that one
obtained by the refinement of the crystal structure (Pb:Bi ¼ 3:1) [31].
The structure of compound Pb BiP O exhibits a complicated three dimension
3
3 12
network structure, as shown in Fig. 8. This structure composes of asymmetric
Pb/BiO octahedra and PO tetrahedra that are interconnected via corner or edge
sharing. There are three types atomic positions in the asymmetric unit of Pb Bi
6
4
3
(
Pb Bi(PO ) , P1 and O1 atoms are occupying two single positions, atoms Pb1 and
PO ) , which is different from the compound Ba Bi(PO ) [52]. In compound
4 3 3 4 3
3
4 3
Bi1 are occupying the same position and not able to distinguish, and Pb and Bi are
at fixed site occupancy ratio 3:1 equal to the ideal values in accordance with the
chemical formula Pb BiP O . It has been described in [52] that the unit cell of
3
3 12
Ba Bi(PO ) contains two distinguished sites for large cations (Ba1 and Bi1) and
3
4 3
5
+
two other positions for oxygen anions (O1 and O2). The unique P cations are
coordinated by four oxygen atoms to form a regular tetrahedron with the P–O
˚
distance at 1.537 A. The mixed Pb1/Bi1 atoms were bonded to six oxygen atoms

1
6
W.-D. Cheng et al.
II
III
3 4 3
Fig. 8 View of the structure of Pb Bi(PO ) along the [001] direction. (Pb /Bi ), P, and O atoms
are represented by teal, purple, and red circles, respectively
O1
Fig. 9 The coordination
of oxygen atoms around
O1
O1
Pb1/Bi1 showing the
stereoactivity of the lone pair
Pb1/Bi1
O1
O1
O1
3
from six [PO4] tetrahedral to form a strongly distorted octahedral with the
ꢄ
˚
Pb/Bi–O bond distances ranging from 2.348 to 2.629 A, which is schemed in
2
+
3+
Fig. 9. It is well established that Pb and Bi ions generate distorted structures
due to the electrostatic effect of the lone pair of electrons [53, 54]. The structure
of Pb Bi(PO ) can also be viewed as a three-dimensional network formed by
3
4 3
II
III
edge-sharing-mixed (Pb /Bi ) metal–oxygen octahedra, forming corrugated

Structural Designs and Property Characterizations
17
Fig. 10 The corrugated
chains formed by edge
II
sharing of (Pb /Bi )
III
octahedral and further linked
by tetrahedral phosphate
groups via corner sharing
chains linked by tetrahedral phosphate groups via corner sharing, as shown in
Fig. 10. By the comparison of structures between Pb Bi(PO ) and Ba Bi(PO )
3
4 3
3
2+
4 3
3+
2
+
[
52], there is a distinct order in the ionic radius of cations: Ba > Pb > Bi .
The main structural feature of almost all eulytite-like compounds is a presence of
different types of disorder in the cation or anion (or both) frameworks. Atomic
positions and the site occupancy appear to be directly related to the nature and size
of the metallic cations involved in the eulytite structure. In the compound Ba Bi
3
(
clearly distinguished within the lattice [52]. The Ba is bonded to twelve oxygen
PO ) , two oxygen positions (O1 and O2) as well as peculiar sites for Ba and Bi are
4 3
2
+
3
+
˚
atoms with the Ba–O bond distances ranging from 2.662 to 2.766 A, and the Bi is
asymmetrically coordinated by six oxygen atoms to form a distorted octahedron
˚
with the Bi–O bond distances ranging from 2.378 to 2.599 A [31]. In the compound
2
Pb Bi(PO ) , the Pb and Bi are not able to distinguish due to the closed ionic
+
3+
3
4 3
radii of them and surrounded by six oxygen atoms with “normal” bond distances
˚
2.348–2.629 A) to form the large distorted octahedral. So we deem that the relative
(
smaller ligand and same coordinational environment give rise to the accordant
2
direction of the 6s lone pairs, which enhance the efficiency of the SHG.
3
.2 Electronic Structures and SHG Properties
To gain further insights into the electronic origination of optical properties, band
structure and density of states (DOS) calculations of Pb Bi(PO ) based on DFT
3
4 3
were performed using the total-energy code CASTEP [55, 56]. The crystallographic
data of Pb Bi(PO ) determined by X-ray single-crystal diffraction was used for the
3
4 3
band structure calculation, no further geometry optimizations was performed in
theoretical study. The calculation of band structure was made by the DFT with the

1
8
W.-D. Cheng et al.
Fig. 11 The calculated band structures of Pb
The Fermi level is set at 0.0 eV
3
Bi(PO
4
)
3
, crystal in the range of ꢄ2.0 and 7.0 eV.
Perdew–Burke–Ernzerh of generalized gradient approximation, which uses a plane
wave basis set for the valence electrons and norm-conserving pseudopotential for
the core states. The number of plane wave included in the basis was determined by a
cutoff energy of 500 eV. Pseudoatomic calculations were performed for Bi-
1
0
2
3
2
3
2
4
10
2
2
5
d 6s 6p , P-3s 3p , O-2s 2p , and Pb-5d 6s 6p . The calculating parameters
and convergent criterions were set by the default values of CASTEP code. Figure 11
gives the plot of band structure at the first Brillouin zone. It is observed that the
valence bands are very flat, and the conduction bands have some oscillating. The
lowest energy of the conduction bands is located at the point between the G and H
k-points and is 3.56 eV, whereas the highest energy (0.0 eV) of the valence bands is
at k-point of H points, as shown in Fig. 12. 8; hence, Pb Bi(PO ) has an indirect
3
4 3
band gap of 3.56 eV. On the other hand, the optical diffuse reflectance absorption
spectrum of Pb Bi (PO ) was measured ranging from 200 to 1200 nm, and it
indicates that the band gap of Pb Bi(PO ) is approximately 3.97 eV [31]. Accord-
3
4 3
3
4 3
ingly, the calculated band gap of 3.56 eV is a little smaller than the experimental
values of 3.97 eV.
The bands can be assigned according to the total and partial densities of states
(
DOS) as plotted in Fig. 12. The regions below the Fermi level can be divided into
three regions. The VBs ranging from ꢄ21.2 eV to ꢄ15.0 eV are mainly formed by
the states of Pb-5d, Bi-5d, and O-2s states. The VBs ranging from ꢄ10.5 eV to
ꢄ4.0 eV are mainly composed of Pb-6s and Bi-6p states mixing with a small
amount of the P-3p and O-2p states. The VBs just below the Fermi level ranging
from ꢄ4.0 eV to the Fermi level (0.0 eV) are mainly from O-2p and Bi-6p states.
The bands just above the Fermi level are derived from Pb-6p and Bi-6p states
ranging from 3.4 eV to 7.0 eV. The states of Bi-6s, Pb-6s, and P-3p dominate the

Structural Designs and Property Characterizations
19
8
4
0
0
Ef
O-2s
O-2p
0
0
Pb-3s
Pb-3p
2
0
1
1
1
00
Bi-6s
Bi-6p
Bi-5d
50
0
00
Pb-6s
Pb-6p
Pb-5d
50
0
00
Total
50
0
–25
–20
–15
–10
–5
0
5
10
Energy(eV)
3 4 3
Fig. 12 Total and partial DOS of Pb Bi(PO ) . The Fermi level is set at 0.0 eV
VB ranging from 7.0 eV to 10.2 eV mixing with a small amount of the Bi-6p.
Analyzing the PDOSs, we note that the Pb–O and Bi–O interactions are dominant at
the bottom part of the conduction band and also contribute considerably below the
Fermi level. It is shown that the highest occupied states should contain the majority
of O-2p states and less mixed Bi/Pb-6s and Bi/Pb-6p states; the lowest unoccupied
states should involve strong unoccupied Bi/Pb-6p states, much less unoccupied
O-2p states, and least unoccupied Bi/Pb-6s states. Such character is intimately
related to the lone-pair distortion resulting from the mixings among the cation 6s,
6
irregular octahedral of Pb/BiO make a significant contribution to NLO response.
p orbitals, and ligand O-2p orbitals [56–58]. Therefore, the charge transfers within
6
II III
Eulytite-like A M (PO ) compounds crystallize in the acentric space group
3
4 3
ꢄ
I4 3d. Hence, it prompts us to study their SHG properties. The Kurtz–Perry method
is a simple and quick experimental technique that requires only the material in
powder form to estimate its NLO effect before the effort is made to grow large
single crystals [59]. SHG measurements on a Q-switched Nd:YAG laser with the
sieved powder sample (80–100 mesh) revealed that the SHG signal of Pb Bi(PO )
3
4 3
is about 3.0 times of that of KDP. The SHG efficiency can be attributed to the
synergistic effect of the polarizations of the multiple Pb/BiO irregular octahedra
6
2
+
3+
due to stereochemical activity of the Pb and Bi multiple lone-pair electrons
Fig. 9). At the same time, in order to search the relationship of SHG response and
lone-pair stereochemical activity, the SHG measurement of Ba Bi(PO ) was also
(
3
4 3
performed. As it is expected, SHG measurement on powder sample reveals that
Ba Bi(PO ) exhibits a weak SHG signal of about 0.5 times that of KDP. Here, the
3
4 3
3
+
former is only one lone-pair electron of Bi ion by the comparison with those of
Pb Bi(PO ) . It is shown that the SHG efficiency is an increasing as the strengthening
3
4 3
II III
3
of stereochemically active lone-pair electrons in eulytite-like A M (PO )
compounds. It speculated on that the compounds of Pb Bi(PO ) and Ba Bi(PO )
4 3
4 3
3
4 3
3

2
0
W.-D. Cheng et al.
were phase matchable from size dependence of SHG signal measurements (see Fig. 5
in [31]). These results are maybe false appearance of saturation obtained from
measurements of few points and mislead to phase matching. As we have known,
the most common procedure to obtain phase matching is to make use of the birefrin-
gence displayed by the crystals. The crystals belonging to the cubic crystal system are
optically isotropic and no birefringence. The compounds of Pb Bi(PO ) and Ba Bi
3
4 3
3
ꢄ
PO ) both crystallize in the space group I4 3d, and they belong to cubic crystal
4 3
(
system. Accordingly, it is impossible for these two compounds to be phase matchable
in normal conditions.
4
ZnO-Based SHG Materials of KZn SbO and KZn Sb O
4 7 4 3 12
ZnO crystal lacking a center of inversion is of piezoelectric property (NLO prop-
erty) [60]. In most cases, ZnO-based compounds are technologically more impor-
tant than its pure phase. The discovery of a polar ZnSnO reveals a new strategy in
3
searching noncenter symmetrical (NCS) materials containing only cations with an
1
0
0
electronic configuration of (n ꢄ 1)d ns [20]. The features of ZnO and its doped
species suggest using ZnO as reaction precursor to synthesize SHG materials of
KZn SbO and KZn (SbO ) [61].
4
7
4
4 3
4
.1 Simple Descriptions of Synthesis and Structures
of KZn SbO and KZn (SbO )
4
7
4
4 3
Single crystals of KZn SbO (1) and KZn (SbO ) (2) were grown by a high-
4
7
4
4 3
temperature solid-state reaction. The reagents were weighted in the molar ratio of
(K CO ):4 (ZnCO ):2 (Sb O ) for 1 and 2 (K CO ):8 (ZnO):1 (Sb O ) for 2.
2
2
3
3
2
3
2
3
2 3
These starting materials were finely ground in an agate mortar to ensure the best
homogeneity and reactivity. For the synthesis processes of 1, the mixture was firstly
preheated in a platinum crucible; secondly, the products were held at high temper-
ature for 10 h, then slowly cooled down and finally quenched to room temperature.
A few of colorless crystals were obtained from the melt of the mixture. For 2, the
mixture was, firstly, heated to 1,173 K and kept on the temperature for 5 h in a
platinum crucible in air; secondly, the mixture was slowly heated to 1,773 K,
and the products were held at this temperature for 24 h, then slowly cooled down
to 1,573 K at a rate of 2 K/h and finally quenched to room temperature. A few of
colorless crystals were obtained from the melt of the mixture. The powders of
compounds 1 and 2 were prepared from the stoichiometric mixture of K CO ,
2
3
ZnCO , and Sb O in the molar ratio of 1:8:1 for 1 and K CO , ZnO, and Sb O in
3
2
3
2
3
2 3
the molar ratio of 1:8:3 for 2. These mixtures were ground in an agate mortars and
then calcined at 1,473 K in air for 15 h for 1 and at 1,373 K in air for 40 h for

Structural Designs and Property Characterizations
21
4 7 4 4 3
Fig. 13 Ball-and-stick representation of (a) KZn SbO (left) and (b) KZn (SbO ) (right)
2
with several intermediate grindings in an opening Pt crucibles. The final products
were analyzed, and the monophases were confirmed by X-ray powder diffraction
studies [61].
The unit cells of single-crystal structures of compounds 1 and 2 are plotted in
Fig. 13. Crystallographic analysis reveals that crystal 1 possesses the same space
group of P6 mc as wurtzite-type ZnO crystal, and the cell parameters of a, b, c are
3
equal to the two times of a, b, and c-axis of wurtzite-type ZnO crystal [62],
individually. There are two crystallographically different Zn atoms, and both of
them are tetrahedrally coordinated by four oxygen atoms in crystal 1. Zn3O4
tetrahedra are linked to each other by a sharing corner to form infinite chains
along the a-axis and b-axis, which are similar to the ZnO4 tetrahedra in wurtzite-
˚
type ZnO crystal. Zn3–O distances are 1.903, 1.942 (ꢃ2), and 1.948 A (see Table 5).
Zn2O tetrahedra are interconnected to SbO octahedra by sharing corners and also
4
6
form infinite chains along the a-axis and b-axis. The Zn2–O bond distances are
˚
˚
˚
1
.954 A and 1.982 A (ꢃ3), and all of the Sb–O bond distances are about 2.02 A in
the regular SbO octahedron of crystal 1 (see Table 5). These two types of chains
6
result in a layered structure down the c-axis, and then, K+ cations are located inside
the vacancy between two types of chains (Fig. 13a). The crystal structure of
compound 1 can be regarded as that of the ZnO submatrix of interconnected ZnO
5
+
tetrahedra that is diluted by Sb ions (i.e., replaced by SbO octahedra) relative to
6
the wurtzite-type ZnO itself as crystal structure, as shown in Fig. 14. Crystal
belongs to the space group R , and it is a novel structural type. There are two
3
2
crystallographically different Zn atoms, the Zn2O is tetrahedrally coordinated by
4
˚
four oxygen atoms, and the average distance of Zn2–O is 1.960 A (see Table 5). The
Zn3O is octahedrally coordinated by six oxygen atoms, and Zn3–O lengths are
6
˚
2
.074 (ꢃ3) and 2.158 (ꢃ3) A in crystal 2 (see Table 5). These two coordination
fashions only separately appear at hexagonal type ZnO crystal (P6 mc symmetry)
3

2
2
W.-D. Cheng et al.
˚
Table 5 The selected bond distances (A) for crystals 1 and 2
1
(KZn
4
SbO
7
)
Sb1–O3
Sb1–O3
Sb1–O3
Sb1–O2
Sb1–O2
Sb1–O2
2.017(5)
2.017(5)
2.017(5)
2.018(4)
2.018(4)
2.018(4)
1.954(8)
1.982(4)
1.982(4)
1.982(4)
3.0751(14)
3.0751(14)
3.0751(14)
Zn3–O1
Zn3–O3
Zn3–O3
Zn3–O2
1.903(2)
1.942(3)
1.942(3)
1.948(5)
3.046(5)
3.046(5)
3.046(5)
3.068(5)
3.068(5)
3.068(5)
3.0751(14)
3.0751(14)
3.0751(14)
1
11
2
2
2
12
1
K4–O3
1
K4–O3
2
Zn2–O1
Zn2–O2
Zn2–O2
Zn2–O2
K4–O3
6
16
K4–O3
K4–O3
K4–O3
K4–O2
K4–O2
K4–O2
1
7
7
9
0
1
18
12
22
23
1
K4–O2
2
K4–O2
2
K4–O2
2
(KZn
4
Sb
3
O
12
)
6
Sb1–O4
Sb1–O3
Sb1–O2
Sb1–O2
Sb1–O1
Sb1–O1
1.922(6)
1.949(6)
1.980(5)
2.009(5)
2.010(5)
2.043(5)
2.074(5)
2.158(5)
2.690(6)
2.690(6)
2.690(6)
2.999(6)
2.999(6)
2.690(6)
Zn2–O3
Zn2–O4
Zn2–O1
Zn2–O3
Zn3–O4
Zn3–O4
Zn3–O2
Zn3–O2
1.953(5)
1.953(6)
1.970(5)
1.965(6)
2.074(5)
2.074(5)
2.158(5)
2.158(5)
3.173(6)
3.173(6)
3.173(6)
3.243(6)
3.243(6)
3.243(6)
1
7
2
3
3
10
10
Zn3–O4
Zn3–O2
3
2
3
1
14
K1–O3
K1–O1
K1–O1
K1–O1
K1–O2
K1–O2
K1–O2
1
6
K1–O3
7
15
16
17
18
K1–O3
1
0
K1–O4
3
K1–O4
1
2
K1–O3
Symmetry code
For compound KZn
1
2
3
4
SbO
7
: (ꢄy + 1, x ꢄ y + 1, z) ; (ꢄx + y, ꢄx + 1, z) ; (ꢄx, ꢄy + 1, z ꢄ 1/2) ;
4
5
6
7
(
ꢄx + 1, ꢄy + 2, z ꢄ 1/2) (ꢄx + 1, ꢄy + 1, z ꢄ 1/2) ; (ꢄy, x ꢄ y, z) ; (ꢄx + y,ꢄx, z) ; (ꢄx, ꢄy,
8
9
10
11
12
z ꢄ 1/2) ; (y, ꢄx + y, z ꢄ 1/2) ; (x ꢄ y, x, z ꢄ 1/2) ; (x, y ꢄ 1, z) ; (y, ꢄx + y, z + 1/2) ;
1
3
14
15;
16
(
(
ꢄx + y + 1, ꢄx + 1, z) ; (ꢄy + 1, x ꢄ y, z) ; (ꢄx, ꢄy, z + 1/2) (ꢄx + 1, ꢄy + 2, z + 1/2) ;
1
7
18
19
y ꢄ 1, ꢄx + y, z + 1/2) ; (x ꢄ y + 1, x, z + 1/2) ; (y, ꢄx + y + 1, z + 1/2) ; (ꢄx, ꢄy + 1,
20;
21
22
23
z + 1/2) (x ꢄ y, x, z + 1/2) ; (x ꢄ y + 1, x + 1, z + 1/2) ; (ꢄx + 1, ꢄy + 1, z + 1/2) ; (x,
24
y + 1, z)
For compound KZn
1
2
4
(SbO
3
4
)
3
: (ꢄy + 4/3, x ꢄ y + 2/3, z ꢄ 1/3) ; (x ꢄ 1/3, y ꢄ 2/3, z + 1/3) ;
4
5
(
ꢄy + 2, x ꢄ y + 1, z) ; (ꢄx + y + 2/3, ꢄx + 4/3, z + 1/3) ; (xꢄ2/3, y ꢄ 1/3, z + 2/3) ; (ꢄx +
6
7
y + 1/3, ꢄx + 5/3, z ꢄ 1/3) ; (ꢄy + 5/3, x ꢄ y + 4/3, z ꢄ 2/3) ; (ꢄy + 5/3, x ꢄ y + 4/3, z + 1/
8
9
10
11
3
3
) ; (x ꢄ 1/3, y + 1/3, z + 1/3) ; (ꢄx + y + 1, ꢄx + 2, z) ; (x, y, z + 1) ; (ꢄx + y + 2/3, ꢄx + 4/
12
13
14
, z ꢄ 2/3) ; (x + 2/3, y + 1/3, z ꢄ 2/3) ; (ꢄy + 7/3, x ꢄ y + 5/3, z ꢄ 1/3) ; (x + 1/3, y ꢄ 1/3,
15
16
17
18
z ꢄ 1/3) ; (x, y, z ꢄ 1) ; (ꢄy + 2, x ꢄ y + 1, z ꢄ 1) ; (ꢄx + y + 1, ꢄx + 2, z ꢄ 1) ; (x + 1/3,
19
20
y + 2/3, z ꢄ 1/3) ; (ꢄx + y + 1/3, ꢄx + 5/3, z + 2/3)
at room temperature [62] and cubic type ZnO crystal (Fm-3 m symmetry) at
high-pressure phases [63, 64]. For 2, four Zn atoms are interconnected to the Sb
atoms via O atoms, and they form a cage-like structure with an open end, and K

Structural Designs and Property Characterizations
23
4 7 4 4 3
Fig. 14 Coordinate polyhedron representations of (a) ZnO, (b) KZn SbO , and (c) KZn (SbO )
atom is located in the vacancy that nears to the open end of a cage. The Sb–O bond
˚
distances range from 1.922 to 2.043 A in crystal 2. One of the reasons for the crystal
structure transition from high-symmetry P6 mc to low-symmetry R3 arises from the
3
5
+
2+
5+
large contents of Sb diluter, with Zn /Sb ¼ 4/1 and 4/3 for crystals 1 and 2,
respectively.
4
.2 Second-Harmonic Generation Investigations
The crystal structures of both compounds 1 and 2 belong to NCS space groups, and
it is interesting to study their NLO properties.
4
.2.1 SHG Measurements and Results
The measurement of the powder SHG effect was carried out by means of the
method of Kurtz and Perry [59]. The fundamental wavelength is 1064 nm generated
by a Q-switched Nd: YAG laser. The SHG wavelength is 532 nm. All of the
samples were placed in separate capillary tubes. No index-matching fluid was
used in any of the experiments. Under the same particle size and fundamental
wave intensity, the SHG intensity ratio can be calculated by [59]. Figure 15 gives
the plots of relative SHG intensity for four powder samples of KZn SbO ,
4
7
KZn Sb O , ZnO, and KDP. Here, the particle sizes of the samples are smaller
4
3 12
than 30 mm, and the SHG measurements of ZnO and KDP only give comparisons.
We can find three features of SHG intensity from Fig. 15: (1) the SHG intensity of
compound 1 is closed to the intensity of KDP, (2) the SHG intensity of compound 1
is larger than that of compound 2, and (3) the SHG intensities of both 1 and
2
compounds are smaller than that of ZnO. The reasons of the last two features

2
4
W.-D. Cheng et al.
Fig. 15 Oscilloscope traces of the second-harmonic generation signals of KZn
KZn Sb 12, ZnO, and KDP
4 7
SbO ,
4
3
O
are explained in view of the crystal structures (seen in Fig. 14). Some NLO
chromophores of ZnO tetrahedra in ZnO crystal are replaced by the non-NLO
4
active groups of regular SbO octahedra, and it leads to a small macropolarization
6
and SHG intensity in 1 and 2 crystals. Furthermore, the more replacements of NLO
chromophores by non-NLO active groups are in ZnO crystal, the smaller SHG
intensity of ZnO-based compounds. As mentioned above, the compound 2 has
5
+
larger Sb contents relative to the compound 1; accordingly, the compound 2 exists
at a smaller SHG intensity.
4
.2.2 Calculations of SHG Coefficients
The second-order susceptibilities wði j2k Þðꢄo3; o1; o2Þ can be calculated according to
the formula [65]
ð2Þ
ð1Þ
ð1Þ
ð1Þ
kk
ð2Þ
2
d ðꢄo ; o ; o Þ ¼ w ðꢄo o ; o Þ ¼ F
w
ðo Þw ðo Þw ðo Þ: (2)
ijk
3
1
2
ijk
3;
1
2
ii
3
jj
1
2
ð1Þ
Here, the wmmðonÞ is the first-order nonresonant susceptibility at low-frequency
(
1)
region, and it is given by w (o) ¼ [e(o) ꢄ 1]/4p, and the dielectric func-
mm
mm
tion e(o) can be directly obtained from the output of CASTEP code from
(2)
2 3
Materials Studio at low-frequency region [56, 66]. In (2), the F ¼ ma/(N e ),
and it is derived from a classical anharmonic oscillator (AHO) model [65]. The m
and e are respectively the electron mass and charge, and the parameters a,
characterizing the nonlinearity of the response, can be obtained from experimen-
tal or theoretical estimations. It is noted that N is a density number of unit cells in

Structural Designs and Property Characterizations
25
Fig. 16 The frequency-dependent second-order susceptibility components
a crystal instead of density number of atoms in a classical AHO model. The
calculated susceptibility components of KZn SbO and wurtzite-type ZnO
crystals are given, with the same space group of P6 mc. KZn SbO and ZnO
4
7
3
4
7
belong to the crystal class 6 mm. According to Kleinman’s symmetry conditions,
only two independent components zzz and zxx exist. The frequency-dependent
(
dynamic) second-order susceptibilities of d , d calculated by (2) are shown in
3
3
31
ꢄ6
(
2)
ꢄ6
esu for
Fig. 16 (here in (2), F ¼ 13.9975 ꢃ 10
and 6.6511 ꢃ 10
KZn SbO and ZnO, respectively). It finds from Fig. 16 that the KZn SbO
4
4
7
7
bulk susceptibilities are about one third of ZnO ones. For example, the calculated
ð2Þ
ꢄ9
,
ð2Þ
values of d33;d ðd
31
¼
1=2w ; d31 ¼ 1=2wzxxÞ are about 2.88 ꢃ 10
33
zzz
ꢄ9
ꢄ9
ꢄ9
3
.11 ꢃ 10 esu for KZn SbO bulk and 9.79 ꢃ 10 , 10.73 ꢃ 10 esu for
4
7
ZnO bulk at a wavelength of 1064 nm (1.165 eV), respectively. The variation
trends match with our measured ones, as shown in Fig. 16. It was reported that
the ZnO powder SHG intensity with particle size of 75–150 m is about 15 time of
ꢄ9
quartz one [59]. If the quartz susceptibility is 0.96 ꢃ 10 esu [65], the ZnO
ꢄ9
powder susceptibility is estimated about 14.4 ꢃ 10 esu. This value is closed to
ꢄ9
our calculated value of 10.73 ꢃ 10 esu for ZnO. Accordingly, our calculated
susceptibilities are reliable. Our experimental and theoretical results show that the
SHG intensity will be reduced upon diminishing NCS chromophores in inorganic
materials.

2
6
W.-D. Cheng et al.
4
.2.3 Band Structures and Electronic Originations of SHG
To gain an insight into the relation between electronic structure and optical
properties, the band structure and state density were calculated by using hybrid
B3LYP functional and running code CASTEP version 4.4 [55, 56, 66]. The crystal-
lographic data of 1 and 2 [61], and that of ZnO and Sb O provided [62, 67], were
2
5
used for theoretical calculations. The total energy was calculated using exchange–-
correlation parameters of the hybrid B3LYP functional. The interactions between
the ionic cores and the electrons were described by the custom pseudopotential. The
2
6
1
following orbital electrons were treated as valence electrons: K–3s 3p 4s ,
1
0
2
2
3
2
4
Zn–3d 4s , Sb–5s 5p , and O–2s 2p . The basis set accuracy is medium. The
other calculation parameters and convergent criteria were the default values of the
CASTEP code [66].
The calculated band structures of Fig. 17 show that 1 is a direct gap material
with a band gap of 2.083 eV and 2 is an indirect gap material with a band gap of
3
.113 eV. The calculated band structures of ZnO and Sb O are also plotted in
2 5
Fig. 17 to make comparisons. The measured UV–VIS absorption cutoff is about
80 nm (3.263 eV) and 302 nm (4.106 eV) that deduces from optical diffuse
3
reflectance spectrum for compounds 1 and 2, respectively, as shown in Fig. 18.
By comparisons of experimental gaps between 1 or 2 and ZnO, it is evident that
the gap of 1 is close to the band gap of ZnO (3.37, 3.26 eV) [68, 69] and that of
2
is larger than that of ZnO. Here, we noted that the calculated gaps are smaller
than the experiment values due to a general underestimation of band gap by using
the DFT calculations [70–72]. Fortunately, the underestimated gap can be
compensated by scissors operator, and the obtained results will not change band
structures and DOS distributions. The calculated densities of states plotted in
Fig. 19 indicate that the highest valence bands (H-VB) most contribute from O-2p
states and the lowest conduction bands have some contributions from the unoc-
5
+
cupied states of Sb ions, respectively, for 1 and 2. It finds from Fig. 19 and
5
+
Fig. 17 that the 1 and 2 are large band gaps while Sb is diluted into ZnO
submatrix (the calculated gaps of ZnO and Sb O are 1.463 and 2.287 eV,
2
3
5
respectively), and that increases of Sb contents extend conduction band width
+
and result in a larger band gap of 2, comparing with the 1 compound. It also finds
5
from Fig. 19 that the Sb density of states at conduction band is about 2.8 and
+
2
.0 states/eV for 2 and 1, respectively, and O density of states are almost the
ꢄ
2
same (about 20.0 states/eV) between 2 and 1 at valence band edge. These cases
2ꢄ
5+
show that the charge transfers from O to Sb states are stronger for compound
than compound 1, leading to the blue shifts of absorption edge for 2. Further,
2
the charge transfers within centrosymmetric chromophores SbO6 will reduce
charge polarization and descend SHG responses in the KZn SbO comparing
4
7
2
ꢄ
5+
with that of parent ZnO, and the stronger charge transfers from O to Sb
states, the weaker SHG responses are in KZn (SbO ) . Accordingly, we can
assign that the SHG originates from the charge transfers from O 2p to Sb and
4
4 3
5
+
Zn unoccupied atomic states, and the decrease of Sb ions lead to increase of
SHG intensity in ZnO-based compounds of KZn SbO and KZn (SbO ) .
4
7
4
4 3

Structural Designs and Property Characterizations
27
8
7
6
5
4
3
KZn SbO7
4
2
1
0
-
-
1
2
G
A
H
K
G
M
L
H
1
0
8
6
4
2
0
2
4
KZn Sb O
12
4
3
-
-
F
G
Z
1
1
2
0
8
6
4
2
0
2
4
ZnO
Ef
-
-
G
A
H
K
G
M
L
H
Fig. 17 (Continued)

2
8
W.-D. Cheng et al.
8
6
4
2
0
2
Sb O
2
5
Ef
-
L
M
A
G
Z
V
Fig. 17 The band structures of plots. The lowest conduction band is at G-point and the highest
valence band at F-point for KZn Sb 12 crystal; both the lowest conduction band and highest
valence band are at G-point for KZn SbO , ZnO, and Sb crystals
4
3
O
4
7
2 5
O
4 7 4 3 12
Fig. 18 Optical diffuse reflectance spectra of KZn SbO and KZn Sb O
5
A Strong SHG Material Cd BiO(BO ) with 3-Chromophore
4 3 3
Asymmetric Building Units
In Cd BiO(BO ) (hereafter we call CBOB), the strong SHG effect originates from
3 3
4
the cooperation of the 3-chromophore asymmetric structures composed of the polar
1
0
2+
3+
displacement of the d Cd ion, SCALP effect of Bi , and p-delocalization of
BO [29]. It is the first example of SHG with 3-chromophore asymmetrical building
3

Structural Designs and Property Characterizations
29
Fig. 19 Total density of states and O- and Sb- atomic partial density of states. The blue dash dot
and red solid lines symbolize DOS or PDOS of KZn SbO and KZb Sb 12 bulks, respectively
4
7
4
3
O
2
units. Recently, it has been reported in another Cd -rich compound of Cd InVO , in
+
2
+
6
2
3+
which the major part of the SHG coefficient may originate from the Cd - and In -
centered polyhedra with strong distortions [73].
5
.1 Preparation and Structure of Single Crystal of CBOB
Single crystals of CBOB were prepared by the high-temperature solid-state reaction
in CdO–Bi O –B O ternary system, and the obtained crystals by this reaction
2
3
2 3
method have better chemical and thermal stability to ensure the feasibility of the
industrial applications [29]. Crystallographic analysis revealed that the CBOB
crystal belongs to the space group Cm. Its structure exhibits a complicated three-
dimensional (3D) network composed of BiO , CdO (n ¼ 6,7) distorted polyhedra,
6
n
and p-delocalization BO groups that are interconnected via corner or edge sharing
3
as shown in Fig. 20a, b. In a Cd1O octahedron, the Cd1-O2, Cd1-O3 (2) distances
6
˚
of 2.278, 2.313, and 2.327 A are all shorter than the corresponding distances
2
Cd1-O6, Cd1-O4 (2) of 2.286, 2.329, and 2.337 A, and the (Cd1) cation
+
˚

3
0
W.-D. Cheng et al.
Fig. 20 View of the structure of Cd
environments
4
BiO(BO
3
)
3
down the (a) c axis and (b) cation coordinate
Fig. 21 The coordination of oxygen atoms around (a) Cd1, (b) Cd2, and (c) Bi cations
displacement is along the threefold rotational axis of the octahedron that pass
0
0
through the triangle faces O3O2O3 and O4O6O4 , as shown in Fig. 21a. This
displacement of the cation leads to loss of symmetrical center of Cd1O polyhedra.
6
The Cd2O is a distorted pentagonal bipyramid with Cd2–O bond distances ranging
7
2
+
from 2.263(14) to 2.832(2) A, as plotted in Fig. 21b. The 6-coordination Bi is
˚
localized within the distorted octahedron BiO resulting from the repulsive
6
2
interactions between lone-pair electron of Bi and electron pairs of Bi–O bonding.
+
˚
There are a larger Bi–O1 distance 2.472 A and a smaller O1-Bi-O1 angle 144.1
0
ꢁ
ꢁ
(perfect value 180 ) due to the repulse interaction in the BiO octahedron, as shown
in Fig. 21c. Cd1O and Cd2O polyhedra are interconnected via sharing edges into
6
6
7
a 1D double chain along the c axis (Fig. 22). The double chains are further
interconnected via sharing corner into a 3D framework with the eight-member