A novel crystallographic and improved computational study of three ligands of lead ion complex

Article abstract of DOI:10.1016/j.molstruc.2008.05.043

The three novel lead(II) complexes, [Pb (L1) (NO₃)₂] (1), [Pb (L2) (NO₃)₂] (2), and [Pb (L3) (NO₃)₂] (3), were characterized by X-ray diffraction analysis. In order to understand the stereochemical structural nature and thermodynamic properties of these complex molecular systems, a theoretical study was conducted. The spatial coordinate positions of complex compounds 1-3 with lead were obtained from X-ray structural analysis and then used as initial coordinates to conduct density functional theory (DFT) theoretical calculations. This improved computational approach resulted in better accuracy when treating large, electron-rich species and better understanding of the complex compounds between the lariat crown ethers (LCEs) and lead ion. Through experimental data auxiliary of a quantum mechanical calculation approach, a DFT method was used to calculate the B3LYP/CEP-121G, B3LYP/SDD and B3LYP/LanL2DZ levels using the GAUSSIAN 03 package program. The calculations were conducted on the three novel LCEs complexed with lead ion. The theoretical calculation was to confirm the lowest energy, optimum geometric structure so as to receive more accurate thermodynamic properties and relative geometric stabilities of these three complex molecules. The atomic bond lengths, atomic torsion angles, binding energies and binding enthalpies of the three novel complex compounds were also calculated. The results of the DFT calculations show that these different complex compounds are cooperative participations of the oxygen on the C-pivot side arm with the ring oxygen molecules to form a six coordination number ligand of stable lead complex compound, which was also confirmed by the single crystal X-ray crystallography analysis.

Full text of DOI:10.1016/j.molstruc.2008.05.043

Journal of Molecular Structure 892 (2008) 231–238
Contents lists available at ScienceDirect
Journal of Molecular Structure
journal homepage: www.elsevier.com/locate/molstruc
A novel crystallographic and improved computational study
of three ligands of lead ion complex
*
Chia-Ching Su
Department of Applied Science, The ROC Naval Academy, 669, Jiun Shiaw Road, Kaohsiung, Taiwan 813, ROC
a r t i c l e i n f o
a b s t r a c t
Article history:
The three novel lead(II) complexes, [Pb (L1) (NO3)2] (1), [Pb (L2) (NO3)2] (2), and [Pb (L3) (NO3)2] (3), were
characterized by X-ray diffraction analysis. In order to understand the stereochemical structural nature
and thermodynamic properties of these complex molecular systems, a theoretical study was conducted.
The spatial coordinate positions of complex compounds 1–3 with lead were obtained from X-ray struc-
tural analysis and then used as initial coordinates to conduct density functional theory (DFT) theoretical
calculations. This improved computational approach resulted in better accuracy when treating large,
electron-rich species and better understanding of the complex compounds between the lariat crown
ethers (LCEs) and lead ion. Through experimental data auxiliary of a quantum mechanical calculation
approach, a DFT method was used to calculate the B3LYP/CEP-121G, B3LYP/SDD and B3LYP/LanL2DZ lev-
els using the GAUSSIAN 03 package program. The calculations were conducted on the three novel LCEs
complexed with lead ion. The theoretical calculation was to confirm the lowest energy, optimum geomet-
ric structure so as to receive more accurate thermodynamic properties and relative geometric stabilities
of these three complex molecules. The atomic bond lengths, atomic torsion angles, binding energies and
binding enthalpies of the three novel complex compounds were also calculated. The results of the DFT
calculations show that these different complex compounds are cooperative participations of the oxygen
on the C-pivot side arm with the ring oxygen molecules to form a six coordination number ligand of sta-
ble lead complex compound, which was also confirmed by the single crystal X-ray crystallography
analysis.
Received 20 March 2008
Received in revised form 21 May 2008
Accepted 22 May 2008
Available online 7 June 2008
Keywords:
Lariat crown ether
SDD
CEP-121G
LanL2DZ
Binding energies
Binding enthalpies
Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
important. Therefore, the understanding of the preferred ligands
of Pb(II) and the stereochemistry of those complexes are necessary.
It is known that lead has the highest atomic number of all stable
elements. It is a soft, heavy, toxic, malleable poor metal. Lead is
bluish white when freshly cut but tarnishes to dull gray when ex-
posed to air. Lead is regarded as a serious environmental contam-
inant [1]. The knowledge of its environmental and health effects
has led many authorities to forbid some of their uses in many
developed countries that have contributed to a decrease in ambi-
ent lead levels in the environment. However, lead remains a high
hazard to human health, and continues to be one of the most com-
mon pollutants. Lead was commonly used in building construction,
lead storage batteries, pewter, and fusible alloys. Lead may result
in a range of health effects, from behavioral problems and learning
disabilities, to seizures and death. As a result, the development of
medicines to counteract the effects of lead poisoning is especially
Coordination chemistry plays an essential role in chemical
science [2]. Coordination bonding can be regarded as a kind of
electrostatic force between the metal ion (Lewis acid) and ligand
(Lewis base). Currently, we are interested in the coordination
chemistry of lead(II) complexes supported by lariat crown ethers.
The study of the interactions of ligand and metal ion, e.g. be-
tween lariat crown ethers and lead ions, is useful to establish
the relationship between stereochemical structure and the sta-
bility of a complex. Ligands have many donor atoms that can
form thermodynamically more stable complexes than their anal-
ogous containing unidentate ligands. In general, a crown ether
has many neutral nitrogen or oxygen atoms which allows it to
act as donor binding sites in multidentate ligands interacting
with metal ions. Because of the highly favored complexation
due to the chelate and macrocyclic effects, complex and macro-
cyclic ligands have been widely used for metal extractions or as
chelating agents. The removal of toxic heavy metal contaminants
from aqueous waste streams is one of the most important envi-
ronmental issues. Predominantly, lariat crown ethers have been
recognized as a very effective class of compounds to achieve
* Tel.: +886 7 583 4700x1213; fax: +886 7 347 2802.
E-mail address: ccsu@cna.edu.tw
0022-2860/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2008.05.043

232
C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
selective separation of heavy metal ions from aqueous solutions.
However, the chemistry of lead ions in natural systems is very
complex and the exact form of lead in a sample depends on
many circumstances [3].
(s, 3H, OCH2CH2OCH2CH3), 3.56 (q, 2H, OCH2CH2OCH2CH2CH3),
3.64 (t, 2H, OCH2CH2OCH2CH3), 3.92 (t, 2H, OCH2CH2OCH2CH3),
3.97 (m, 4H, OCH2CH2O CH2CH2O), 4.15 (m, 3H, OCHH0CHCHH0O;
4H, OCH2CH2O CH2CH2O), 4.33 (m, 2H, OCHH0CHCHH0O), 6.84-7.01
(m, 8H, benzo group).
Owing to significant progress in computer technology and
algorithms of computational chemistry, molecular modeling has
provided a powerful and reliable tool for exploring the complex
molecular system. Accurate theoretical modeling has become an
important tool to characterize coordination complex compounds.
Over the last decade, the number of experimental and theoreti-
cal methods for stereochemical structural studies has grown
markedly [4–16]. The application of quantum chemical calcula-
tion approaches to the interpretation of experimental data has
became one of the most powerful tools for chemical investiga-
tion. However, no known theoretical investigations have been
made on the lead–LCEs related complex compounds. To the best
of our knowledge, the improved DFT calculation method is ap-
plied for the first time to the three novel complex molecules.
In this research, we applied DFT theoretical calculation success-
fully through experimental data auxiliary to determine the opti-
mal geometrical structure, binding energies, and binding
enthalpies of the three novel complex compounds. DFT geometry
optimization at the B3LYP/CEP-121G, B3LYP/SDD and B3LYP/
LanL2DZ level of theory was used for the three novel complex
compounds. The spatial coordinate positions of the three novel
complex compounds were obtained from X-ray structural analy-
sis and used as initial coordinates for the theoretical calculations.
The main goal of this research is to more accurately determine
the lowest energy of the optimal complex molecular structure
and to attain more accurate thermodynamic properties. This re-
search showed that a more accurate theoretical method should
be useful to those interested in modeling the three novel com-
plex molecules. The research is also helpful for searching and
determining the lowest energy of the optimal geometric struc-
ture and the influences of the different LCEs on the lead ion’s
binding capability.
2.3. Synthesis of lead and lariat crown complex 1–3 and X-ray
structure determination
The complex of lariat 16-crown-5 ether with Pb (NO3)2 was pre-
pared by having [Pb (NO3)2] (0.0662 g, 0.2 mmol) dissolved in
methanol–water (4:1, V:V) and lariat crown ether (0.1 mmol) in
chloroform (1 mL). The mixture was filtered and then put into a
crystal-growing bottle, and ethanol vapor was diffused into the
product until a perfect crystal was produced. The structure of the
resulting single crystals was then analyzed by X-ray crystallogra-
phy. Data was then collected using a Nonius CAD-4 diffractometer
with graphite-monochromated Mo-K
a radiation at 25 °C. Then,
atomic scattering factors were taken from the International Tables
for X-ray Crystallography, and data reduction and structural refine-
ment were performed using NRCVAX packages. Cell parameters
were then obtained from 25 reflections with 2h at 20.70–27.12°,
18.74–26.44°, and 16.94–26.22°, respectively.
3. Computational approaches
All computations were conducted using the GAUSSIAN 03 pro-
gram package, and the standard CEP-121G, SDD and LanL2DZ dif-
ferent basis sets. Electron correlation was partially taken into
account by means of density function theory (DFT) using the
GAUSSIAN 03 version of the hybrid three-parameter function
developed by Becke and denoted as B3LYP. The B3LYP method
has been proved to be the best compromise between computa-
tional cost and accuracy. From experimental data auxiliary, we
conducted the theoretical calculation studies of 16-crown-5
(16c5) ether and its lead ion complexes. The improved DFT calcu-
lations were performed to analyze the complex molecular system
with more accuracy. The large total number of atoms and the pre-
cise lead ion with 16c5 complex of three-dimensional spatial posi-
tions in the complex compounds of molecular system resulted in
computational convergence difficulty. All calculated structures
were completely optimized by GAUSSIAN 03 program package.
For each optimized structure, a frequency calculation was also per-
formed using these basis sets. Zero point energies obtained from
these frequency calculations were used to correct free energy val-
ues for each structure. All calculated frequencies were positive.
Therefore, we are confident that a definite absolute minimum in
the potential energy surface was found.
2. Experimental details
2.1. Reagents and chemicals
All chemicals were obtained from commercial sources and used
without further purification. Only analytical reagent grade chemi-
cals were used in the preparation of these titled complex com-
pounds. The hydroxy-sym-dibenzo-16-crown-5 ether was
synthesized according to the literature method [17] and used after
recrystallization from chloroform–hexane (1:5, V:V). 3-Phenylpro-
pyl sym-dibenzo-16-crown-5 ether (L2) and 4-methoxybenzyl
sym-dibenzo-16-crown-5 ether (L3) synthesized have been re-
ported earlier [18,19].
3.1. Free ligands
2.2. Synthesis of 20-ethoxyethyl sym-dibenzo-16-crown-5-ether L1
The spatial positions of uncomplexed lariat crown ether 1–3,
obtained from X-ray structural analysis with no lead, were used
as initial coordinates for DFT theoretical calculations. The geome-
try of all ligands was fully optimized and the minima with all real
harmonic frequencies were obtained.
Hydroxy-sym-dibenzo-16-crown-5-ether (1.73 g, 5 mmol) was
dissolved in 50 mL anhydrous THF. NaH (0.8 g, 20 mmol) was added
under nitrogen and the reaction mixture was heated under reflux for
30–40 min. After the addition of 2-bromoethyl ethyl ether (5 mmol),
the mixture was refluxed for another 1 h. Deionized water was then
added slowly to destroy theexcess NaH and quench thereaction. The
reaction mixture was then purified by column chromatography (sil-
ica gel, 70–230 mesh, CHCl3 eluent) to give the desired product in
70% (1.86 g) yield. m.p. 61.0–62.0 °C. MS (EI, 70 eV): m/z 418.0 (M+_,
100%), 175 (12%), 149 (16%), 136.0 (72%), 121.0 (44%), 109.0 (12%),
80 (17%), 73.0 (48%). Elemental analysis: Calc. (found) for
C23H30O7; C, 66.01 (66.08); H, 7.23 (7.20). 1H NMR(CDCl3): d 1.24
3.2. Ligands complexes of Pb2+
The theoretical study of the conformational and electronic
properties of the three novel complex compounds was carried
out using crystallographic data. The initial three-dimensional coor-
dinates of the complex compounds 1–3 obtained from the X-ray
structural analysis were used in the DFT calculation. The calculated
structure of the six coordinate LCEs reproduced almost the same

C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
233
general features as the observed values in distorted octahedral, six
coordinate lead complex compounds. Furthermore, binding ener-
gies ( E) between 16-crown-5 ether (16c5) and lead ion were cal-
culated. The binding affinities of the 16-crown-5 ethers for the lead
ion were evaluated by computing the energies of the association
reactions
4.1. Molecular parameters
D
The DFT theoretical calculation was conducted through
experimental data auxiliary to search for the minimal energy
and optimal stereochemical structures of the three novel com-
plex compounds. With the improved DFT calculation, the input
coordinate data has more accuracy. It was also found that the
DFT calculations could achieve convergence more rapidly. The
converged calculations can then result in the optimal geometric
bond lengths, bond angles and dihedral angles of the three no-
vel complex compounds.
The results of X-Ray diffraction studies upon single crystals of
the three novel complex compounds between lead and LCEs are
shown in Figs. 1–3. The geometric optimization was then con-
ducted using the B3LYP method with SDD, CEP-121G and
LanL2DZ basis set. We analyzed the available experimental data
and DFT calculation positions of the six oxygen atoms relative
to the three novel complex compounds. The bridge oxygen atom
and the parent group of five oxygen atoms in the 16-crown-5
ether with lead ion form a six coordination number of a stable
complex compound. In the three novel complex compounds 1–
3, lead ion shows a positive charge and all six oxygen atoms
are negatively charged. As a result, distortions to geometric struc-
tures are expected to have a significant impact on the Lewis ba-
sicity of the six oxygen donor atoms.
Pb2þ þ 16c5 ! Pb2þ=16c5
ð1Þ
where the free ligands is corrected to the lowest energy of optimal
geometric structure. Basis set superposition error was accounted for
in an approximate manner by the full counterpoise correction of
Boys and Bernardi [20].
The binding enthalpies,
DH, for the reaction of lead ion with li-
gands [Pb2+ + Lꢀ ? PbL] are given by the following equation:
D
H ¼
D
HðPb2þ::ligandÞ ꢀ f
D
HðPb2þÞ þ
D
HðligandÞg
ð2Þ
where
D
H (Pb2+) and
D
H (ligand) are the enthalpy of the lead ion
H (Pb2+..ligand) is the en-
E) and binding
and ligand molecules, respectively, and
thalpy of the complex. The binding energies (
enthalpies ( H) could be estimated in detail according to the liter-
ature [21,22].
D
D
D
4. Results and discussions
According to the DFT theoretical calculations, the three novel
complex compounds 1–3 all shown no symmetric geometrical
structure of C1 point group. Table 1 provides the resulting Pb–O
bond lengths of the complex compounds 1–3 from the X-ray crys-
tallography structural analysis and DFT theoretical calculations.
The observed X-ray crystal structures of the three novel complex
compounds were compared to the optimized geometries obtained
from the DFT calculations.
The DFT calculation of the asymmetric complex molecular sys-
tem showed that the six lead–oxygen coordinate atoms have bond
distances in the range of 2.410–2.679 Å. In all three complex com-
pounds the calculated PbꢁꢁꢁO distance is shorter than that in the
In all three independent complex molecules, lead ion forms six
strong Pb–O bonds. The ligand molecule provides lead ion with the
correct number and types of binding sites to form stable complex
molecules. Thus, six oxygen atoms occupy four equatorial and
two axial positions to form six coordination numbers of complex
compounds. A distorted octahedral geometrical structure is there-
fore predicted. The optimal geometric structures of the three novel
complex compounds show that the lead ion was coordinated with
the six donor atoms of the LCEs. The results of the study indicate
that the theoretical calculation can result in more accurate deter-
mination of the optimal complex molecular structure and thermo-
dynamic properties between lead ion and lariat 16-crown-5 ether.
Fig. 1. X-ray crystal structure of ORTEP diagram of lead ion in complex compound 1 with atom labeling; hydrogen atoms omitted for simplicity.

234
C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
Fig. 2. X-ray crystal structure of ORTEP diagram of lead ion in complex compound 2 with atom labeling; hydrogen atoms omitted for simplicity.
crystal. The average lengths of the Pb–O bond predicted by the
B3LYP calculations are ca. 0.1–0.4 Å shorter than the corresponding
experimental X-ray data. It is therefore indicated that the three
complex compounds can formed a more stable geometric structure
of complex molecules than from X-ray crystallographic analysis. As
from my previous research result [22], the improved DFT calcula-
tion can gain more optimal and accurate complex geometric
molecular structure.
As a result, the structures of complex 1 and 3 molecules show
the same crystal systems and space groups. However, complex
compound 2 has a different crystal system and space group. Table
4 shows the binding energies and enthalpies of the three complex
compounds of lariat 16-crown-5 ether–Pb2+
.
4.2. Molecular first ionization potentials, HOMO and LUMO energies,
and energy gaps
Table 2 provides the resulting Pb-connected torsion angles of
the complex compounds 1–3 from the X-ray crystallographic
structural analysis and the DFT theoretical calculations. The two
tables show that both the bond lengths and torsion angles of com-
plex compounds 1–3 obtained from the theoretical calculations are
in good agreement with those from experimental investigations
using X-ray crystallography. The crystallographic data collected
are listed in Table 3.
Table 5 lists the calculated values of the first ionization poten-
tials, HOMO, LUMO, and energy gap (DeHOMOꢀLUMO) of the three
novel complex compounds. All DFT calculation results show that
the first ionization potential of complex compound 3 was the low-
est. On the other hand, the energy gap of complex compound 1 was
found to be the highest, indicating the lowest conductivity, reactiv-
ity and formation a more stable complex compound. It also shows
Fig. 3. X-ray crystal structure of ORTEP diagram of lead ion in complex compound 3 with atom labeling; hydrogen atoms omitted for simplicity.

C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
235
Table 1
Table 2
Crystallographic data and selected optimal Pb–O bond lengths (Å) of complex
compound 1–3 obtained using improved DFT calculations
Crystallographic data and optimal structure Pb-connected atomic torsion angle (°) of
complex compound 1–3 obtained improved DFT calculations
Complex
compound
Atomic bond
lengths (Å)
Crystallographic B3LYP/CEP- B3LYP/ B3LYP/
Complex
compound
Atomic torsion
angle (°)
Crystallographic B3LYP/
data CEP-121G
B3LYP/
SDD
B3LYP/
LanL2DZ
data
121G
SDD
LanL2DZ
1
2
3
Pb–O2
Pb–O3
Pb–O4
Pb–O5
Pb–O6
Pb–O7
2.681(7)
2.800(7)
2.803(7)
2.728(6)
2.879(7)
2.864(6)
2.487
2.410
2.481
2.526
2.503
2.411
2.640
2.524
2.609
2.663
2.650
2.527
2.546
2.441
2.530
2.598
2.575
2.446
1
O2–Pb–O3
O2–Pb–O4
O2–Pb–O5
O2–Pb–O6
O2–Pb–O7
O3–Pb–O4
O3–Pb–O5
O3–Pb–O6
O3–Pb–O7
O4–Pb–O5
O4–Pb–O6
O4–Pb–O7
O5–Pb–O6
O5–Pb–O7
O6–Pb–O7
C4–O2–Pb
C5–O2–Pb
C6–O3–Pb
C12–O4–Pb
C13–O4–Pb
C14–O5–Pb
C15–O5–Pb
C16–O6–Pb
C17–O6–Pb
C22–O7–Pb
C23–O7–Pb
61.5 (2)
69.0
132.0
152.9
118.6
69.0
65.9
126.5
167.6
118.7
65.4
67.4
129.4
160.6
118.6
66.9
116.0(2)
167.2 (2)
110.6(2)
59.9(2)
54.6(2)
65.6
62.5
64.3
112.4(2)
102.6(2)
63.2(2)
59.8(2)
86.9 (2)
92.8(2)
58.4(2)
107.5(2)
54.1(2)
132.2(7)
110.6(6)
116.5(5)
120.0(6)
115.1(6)
117.7(6)
108.5(6)
119.1(6)
126.5(6)
127.2(5)
115.2(6)
131.9
128.4
73.3
125.0
122.4
72.8
128.7
126.3
73.8
Pb–O1
Pb–O2
Pb–O3
Pb–O4
Pb–O5
Pb–O6
2.712(3)
2.750(3)
2.878(3)
2.715(4)
2.851(3)
2.867(3)
2.473
2.432
2.487
2.523
2.496
2.421
2.618
2.546
2.610
2.654
2.651
2.538
2.528
2.461
2.531
2.586
2.572
2.457
66.4
63.0
64.4
101.6
110.7
65.4
128.4
65.2
138.7
103.7
117.3
119.8
117.8
115.8
108.7
121.2
120.0
123.0
117.0
100.7
110.4
62.4
121.4
62.4
139.8
103.2
117.9
119.1
120.0
115.5
109.8
121.6
120.1
124.3
117.9
101.9
111.7
63.5
124.5
63.9
139.1
103.8
118.1
119.2
120.2
115.2
109.7
121.9
119.8
124.0
117.9
Pb–O2
Pb–O3
Pb–O4
Pb–O5
Pb–O6
Pb–O7
2.708(19)
2.907(18)
2.882(23)
2.709(21)
2.765(23)
2.796(19)
2.466
2.415
2.511
2.540
2.492
2.413
2.604
2.536
2.665
2.679
2.621
2.525
2.509
2.454
2.587
2.611
2.546
2.440
that 2 and 3 have almost the same energy gap that is lower indicat-
ing higher conductivity.
2
O1–Pb–O2
O1–Pb–O3
O1–Pb–O4
O1–Pb–O5
O1–Pb–O6
O2–Pb–O3
O2–Pb–O4
O2–Pb–O5
O2–Pb–O6
O3–Pb–O4
O3–Pb–O5
O3–Pb–O6
O4–Pb–O5
O4–Pb–O6
O5–Pb–O6
Pb–O1–C1
Pb–O1–C2
Pb–O2–C11
Pb–O2–C12
Pb–O3–C17
Pb–O3–C18
Pb–O4–C19
Pb–O4–C20
Pb–O5–C21
Pb–O5–C22
Pb–O6–C27
Pb–O6–C28
63.2(1)
115.9(1)
158.5(1)
101.9(1)
56.8(1)
67.9
129.7
153.6
120.6
68.6
65.4
125.9
168.4
118.4
65.1
66.9
128.2
160.9
119.7
66.7
4.3. Complex of binding energies and binding enthalpies
53.8(1)
65.3
62.3
64.1
The B3LYP/CEP-121G theoretical calculation shows that the
112.2(1)
111.5(1)
63.9(1)
59.3(1)
91.3 (1)
84.8(1)
59.0(1)
101.8(1)
55.1(1)
109.2(3)
134.5(3)
114.0(3)
114.3(3)
110.9(3)
114.1(3)
116.9(3)
108.6(3)
118.4(3)
125.1(3)
124.7(3)
116.2(3)
131.8
126.5
73.0
121.8
121.8
72.2
128.6
124.6
73.3
binding energies (DE) for the three novel complex compounds
are between ꢀ288.74 and ꢀ297.81 kcal molꢀ1. However, the calcu-
66.5
63.2
64.6
lated binding enthalpies
(
D
H) are between ꢀ288.32 and
101.8
112.7
65.6
129.1
65.1
105.1
133.2
117.6
122.3
120.1
117.7
115.7
108.6
121.1
120.4
122.9
117.8
100.4
109.5
62.5
121.1
62.3
104.6
137.4
117.9
121.8
119.4
119.6
115.5
109.7
121.4
120.3
124.1
118.3
101.4
112.3
63.6
125.0
63.7
105.0
136.7
118.0
122.2
119.6
119.5
115.6
109.8
121.7
120.1
123.9
118.3
ꢀ296.70 kcal molꢀ1 for the three novel complex compounds. Addi-
tionally, the B3LYP/SDD theoretical calculation shows that the
binding
energies
(
D
E)
are
between
ꢀ230.95
and
ꢀ241.45 kcal molꢀ1 and the binding enthalpies (
DH) are between
ꢀ230.45 and ꢀ240.37 kcal molꢀ1. On the other hand, the B3LYP/
LanL2DZ theoretical calculation shows that the binding energies
(
D
E) are between ꢀ255.30 and ꢀ265.84 kcal molꢀ1 and the bind-
ing enthalpies (
D
H) are between ꢀ254.75 and ꢀ264.69 kcal molꢀ1
.
As a result, complex compound 1 has the largest binding energy
(D
E) and binding enthalpy (
3 and complex compound 2. Overall, the formation of the three no-
vel complex compounds 1–3 is exothermic ( H < 0) and therefore
DH) followed by complex compound
D
the complex molecules are more rigid. This is probably the reason
why the entropy change for the reaction is slightly negative. Thus,
the DFT calculation results also indicate that the three complex
compounds are formed most readily and are also the most stable
ones.
3
O2–Pb–O3
O2–Pb–O4
O2–Pb–O5
O2–Pb–O6
O2–Pb–O7
O3–Pb–O4
O3–Pb–O5
O3–Pb–O6
O3–Pb–O7
O4–Pb–O5
O4–Pb–O6
O4–Pb–O7
O5–Pb–O6
O5–Pb–O7
O6–Pb–O7
C8–O2–Pb
C10–O3–Pb
C11–O3–Pb
C16–O4–Pb
C17–O4–Pb
C18–O5–Pb
C19–O5–Pb
C20–O6–Pb
C21–O6–Pb
C26–O7–Pb
C27–O7–Pb
59.4(6)
110.2(6)
166.8 (6)
114.5(6)
60.5(7)
54.0(6)
107.6(6)
92.8(6)
68.9
118.1
154.0
131.7
68.9
65.6
118.6
168.3
126.4
65.9
67.2
119.2
161.0
129.2
67.5
65.0
62.1
63.6
127.6
110.6
73.5
120.6
109.5
72.9
124.1
111.7
74.0
5. Summary
63.8(6)
58.7(7)
65.2
62.2
63.3
Three novel complex compounds 1–3 were synthesized and the
optimal geometric structures were determined through experi-
mental data auxiliary together with DFT theoretical calculations.
We have performed a combined theoretical and experimental
study of the three novel complex compounds. The result obtained
from the improved DFT calculation was found to be more accurate,
based on which the X-ray crystallography analysis. As a result the
more optimal stereochemical structures of three novel complex
compounds 1–3 were obtained (see Figs. 4–6).
In addition, molecular structural conformation optimized using
the B3LYP/CEP-121G, B3LYP/SDD and B3LYP/LanL2DZ methods
indicated that there were a considerable differences in the energies
of the three novel complex compounds. Moreover, comparison of
88.0 (7)
103.4(7)
60.9(7)
113.1(7)
54.1(6)
132.6(15)
115.8(17)
126.0(17)
126.7(19)
119.1(20)
109.0(18)
116.2(17)
115.7(20)
121.0(21)
120.0(18)
118.7(18)
102.3
128.9
66.0
131.3
65.4
133.0
117.1
123.2
120.0
121.3
108.6
115.1
118.5
119.4
122.6
116.9
100.1
122.3
62.7
124.5
62.2
132.9
117.6
124.6
120.2
121.5
109.4
115.1
120.1
119.0
122.5
117.3
101.2
125.6
64.1
128.1
64.1
132.7
117.7
124.3
119.8
121.9
109.7
115.4
119.9
119.1
122.9
117.4

236
C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
Table 3
Crystallographic data
employed DFT methodologies with respect to the structural and
vibrational properties of the three novel complex compounds were
compared.
Complex compound
1
2
3
The experimental results and the DFT calculations (B3LYP) also
complementarily established the electronic structures of these
complex molecular species and provided insight into the more
accurate molecular mechanics. From the DFT theoretical calcula-
tions using the CEP-121G, SDD and LanL2DZ basis sets, data of
the three complex compounds of conformational analysis was suc-
cessfully obtained. Based on the results of the DFT study, we intro-
duced a novel molecular model for the complexation of LCEs and
lead ion.
The DFT calculated bond lengths and torsion angles of the three
novel complex compounds are very close to the experimental val-
ues and are quite reasonable. As a result, the improved DFT calcu-
lation has been shown to be essential for obtaining accurate
results. The DFT theoretical calculations of binding energies and
binding enthalpies show that the three novel complex compounds
are all located at the stable, minimum points of the potential en-
ergy surfaces. The DFT calculation results support the fact that lead
ion with bridge oxygen and five oxygen atoms of the parent group
of LCE form six coordination number of complex compound.
The results presented here support the hypothesis that, in com-
plexes containing high density ligands, twisted geometries might
be favored by the presence of donor atoms with special affinity to-
Empirical formula
Formula weight
Crystal system
Space group
C23H30N2O13Pb C28H32N2O12Pb
C27H30N2O13Pb
797.73
Monoclinic
P2(1)/a
749.69
Monoclinic
P2(1)/a
795.76
Triclinic
P ꢀ1
Unit cell dimensions
a (Å)
b (Å)
c (Å)
17.124(3)
8.443(2)
19.388(4)
90
103.62
90
9.186(4)
11.541(3)
14.501(4)
94.20
103.47
14.50
1462(1)
2
18.285(2)
8.340(3)
19.341(2)
90
102.37
90
2881(1)
4
1.839
5.94
a
(°)
b (°)
c
(°)
Volume (Å3)
2724(1)
4
Z (atoms/unit cell)
Dcalc (Mg mꢀ3
)
1.828
6.27
1.808
5.85
l
(mmꢀ1
F(000)
)
1472
784
1568
51.8
Range of 2h (°)
Crystal size (mm)
49.8
49.8
0.45 ꢂ .35 ꢂ 0.10 0.40 ꢂ 0.25 ꢂ 0.20 0.30 ꢂ 0.15 ꢂ 0.08
Octants measured
h
k
l
Number of reflections
measured
Number of unique
reflection
ꢀ20 to 19
0 to 10
0 to 23
4912
ꢀ10 to 10
0 to 13
ꢀ22 to 22
0 to 10
0 to 23
5831
ꢀ17 to 17
5353
4763
3649
5130
4597
5657
3504
Number of reflections
with I > 2.5 or 2.0r(I)
Number of variables
Table 5
353
389
389
Comparison of HOMO, LUMO, energy gaps
potentials of three novel complex compounds (eV)
(DeHOMOꢀLUMO), and first ionization
Absorption correction
Rf
0.057–0.273
0.038
0.211–0.294
0.024
0.06–0.295
0.108
Rw
GoF
0.047
2.616
0.027
2.2346
0.131
3.876
Complex
compound
DFT methods
eHOMO
eLUMO
I1st
DeHOMOꢀLUMO
1
2
3
B3LYP/CEP-121G ꢀ11.9759 ꢀ7.1829 11.9759 4.7930
B3LYP/SDD
ꢀ11.8587 ꢀ7.4784 11.8587 4.3803
ꢀ11.9191 ꢀ7.3045 11.9191 4.6145
B3LYP/LanL2DZ
the calculated geometry of the complex compounds 1–3 with the
structure obtained from X-ray diffraction indicates a more stable
geometric structure of complex molecules.
Vibrational frequency analyses performed at the B3LYP/CEP-
121G, B3LYP/SDD and B3LYP/LanL2DZ theoretical levels yielded
zero imaginary frequency and confirmed that all optimized
structures were in the ground state. The performances of various
B3LYP/CEP-121G ꢀ10.9422 ꢀ7.1502 10.9422 3.7920
B3LYP/SDD
B3LYP/LanL2DZ
ꢀ10.5978 ꢀ7.5578 10.5978 3.0399
ꢀ10.6296 ꢀ7.3750 10.6296 3.2546
B3LYP/CEP-121G ꢀ10.6758 ꢀ7.1209 10.6758 3.5550
B3LYP/SDD
B3LYP/LanL2DZ
ꢀ10.5847 ꢀ7.4123 10.5847 3.1724
ꢀ10.6010 ꢀ7.2319 10.6010 3.3691
Table 4
Binding energies and binding enthalpies of lariat crown ether–Pb2+
Complex compound
R
B3LYP/CEP-121G
E (kcal molꢀ1
B3LYP/SDD
E (kcal molꢀ1
B3LYP/LanL2DZ
D
)
D
H (kcal molꢀ1
)
D
)
D
H (kcal molꢀ1
)
D
E(kcal molꢀ1
)
D )
H (kcal molꢀ1
1
2
CH2CH2OCH2CH3
CH2CH2CH2Ph
ꢀ297.81
ꢀ288.74
ꢀ296.70
ꢀ288.32
ꢀ241.45
ꢀ230.95
ꢀ240.37
ꢀ230.45
ꢀ265.84
ꢀ255.30
ꢀ264.69
ꢀ254.75
3
ꢀ296.18
ꢀ295.40
ꢀ239.17
ꢀ238.35
ꢀ263.51
ꢀ262.66

C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
237
Fig. 5. Improved DFT calculation diagram of complex compound 2.
the lariat 16-crown-5 ethers can also result in higher differences
in the relative binding energy and binding enthalpy. Therefore,
with different sidearms resulting in conformational change, differ-
ent complex ability between lariat crown ethers and lead ion can
be shown. Thus, the sidearm effect appears to be a strong influence
on lead ion’s binding capability. The estimated binding energies
and binding enthalpies values obtained this way can be used as
the substitutes for unavailable experimental values, especially for
those complex compounds for which the experimental determina-
tion is very difficult.
Fig. 4. Improved DFT calculation diagram of complex compound 1.
ward Pb(II). In the final geometry found in the corresponding lea-
d(II) complex, it is found that not only the nature of the donor atom
present in the ligand molecule but also its charge has a main influ-
ence in the lead(II)-lone pair activity.
The three novel complex compounds have the same parent
macrocycle but contain different sidearms. The sidearm effect of
In sum, the DFT method, through experimental auxiliary, ap-
pears to provide results that were trustworthy and reasonable.
The calculated method also provided a framework for searching

238
C.-C. Su / Journal of Molecular Structure 892 (2008) 231–238
the lowest energy and optimal geometric structure of this class of
complex compounds. The obtained information should be highly
transferable to other theoretical studies on lead ion complexes
and biological systems, as will be demonstrated in forthcoming
application studies.
Acknowledgements
The author thanks the National Science Council of the Republic
of China (Taiwan) for its financial support (NSC 96-2113-M-012-
001). The helpful suggestions from Professor L. Liu-Kao and Oper-
ator T.S. Kuo of National Taiwan Normal University, Department
of Chemistry, are greatly appreciated. Dr. Y.C. Su, P.E., of Houston,
TX, USA, is also greatly appreciated for providing a critical reading
review of this manuscript prior to completion.
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Fig. 6. Improved DFT calculation diagram of complex compound 3.