Synthesis, crystal structure and density functional studies on 1N-phenyl-3-(2,4-dichlorophenyl)-5-(4-chlorophenyl)-2-pyrazoline

Article abstract of DOI:10.1002/jccs.200800027

1N-Phenyl-3-(2,4-dichlorophenyl)-5-(4-chlorophenyl)-2-pyrazoline has been synthesized and characterized by elemental analysis, IR, UV-Vis and X-ray single crystal diffraction. Density functional calculations have been carried out for the title compound by using the B3LYP method with a 6-311G** basis set. The calculated results show that the predicted geometry can reproduce well the structural parameters. The electronic absorption spectra calculated in the gas phase are better than those calculated in EtOH solvent to model the experimental electronic spectra. Natural Bond Orbital (NBO) analyses suggest that the above electronic transitions are mainly assigned to π → π* transitions. On the basis of vibrational analyses, the thermodynamic properties of the compound at different temperatures have been calculated, revealing the correlations between C⁰_{p, m}, S ⁰_m, H⁰_m and temperature.

Full text of DOI:10.1002/jccs.200800027

Journal of the Chinese Chemical Society, 2008, 55, 183-188
183
Synthesis, Crystal Structure and Density Functional Studies on
1N-Phenyl-3-(2,4-dichlorophenyl)-5-(4-chlorophenyl)-2-pyrazoline
Pu-Su Zhaoa (
Xian Wanga (
), Huan-Mei Guob (
),
) and Fang-Fang Jiana* (
)
aNew Materials & Function Coordination Chemistry Laboratory, Qingdao University of Science and
Technology, Qingdao, Shandong 266042, P. R. China
bDepartment of Chemistry, Weifang University, Weifang, Shandong 261061, P. R. China
1N-Phenyl-3-(2,4-dichlorophenyl)-5-(4-chlorophenyl)-2-pyrazoline has been synthesized and char-
acterized by elemental analysis, IR, UV-Vis and X-ray single crystal diffraction. Density functional calcu-
lations have been carried out for the title compound by using the B3LYP method with a 6-311G** basis
set. The calculated results show that the predicted geometry can reproduce well the structural parameters.
The electronic absorption spectra calculated in the gas phase are better than those calculated in EtOH sol-
vent to model the experimental electronic spectra. Natural Bond Orbital (NBO) analyses suggest that the
above electronic transitions are mainly assigned to p ® p* transitions. On the basis of vibrational analy-
ses, the thermodynamic properties of the compound at different temperatures have been calculated, re-
vealing the correlations between C0p, m, S0 , H0m and temperature.
m
Keywords: Synthesis; Crystal structure; Density functional theory; Electronic absorption spec-
tra; Thermodynamic property.
INTRODUCTION
EXPERIMENT AND COMPUTATIONAL
METHODS
Fluorescent probes are powerful tools in cell biology
for the non-invasive measurement of intracellular ion con-
centrations.1 They have found widespread applications, for
example, to gauge intracellular calcium concentrations,2 to
visualize labile zinc3-6 and iron pools,7 or as pH sensors.8
Among various possible fluorescent probes, pyrazoline-
based fluorophores stand out due to their simple structure
and favorable photophysical properties such as large ex-
tinction coefficient and quantum yields (Ff » 0.6-0.8).9-10
Their attractive properties, including cation- or pH-sensi-
tive probes, have been described,11-14 and the suitability of
pyrazoline fluorophores as probes in a biological environ-
ment have also been explored.15 Because of its modular na-
ture, the synthesis of 1,3,5-triaryl-substituted pyrazoline
fluorophores provides a high degree of structural flexibil-
ity.10,16 In this study, we wish to report a new crystal struc-
ture of 1N-phenyl-3-(2,4-dichlorophenyl)-5-(4-chlorophen-
yl)-2-pyrazoline. At the same time, the theoretical calcula-
tions for the compound by using the DFT method B3LYP
with a 6-311G** basis set are also reported.
Physical Measurements
Elemental analyses for carbon, hydrogen and nitro-
gen were performed by a Perkin-Elmer 240C elemental in-
strument. The melting points were determined on a Yanaco
MP-500 melting point apparatus. IR spectra (4000-400
cm-1), as KBr pellets, were recorded on a Nicolet FT-IR
spectrophotometer. Electronic absorption spectra were
measured on a Shimadzu UV3100 spectrophotometer in
EtOH solution.
Synthesis
All chemicals were obtained from a commercial
source and used without further purification.
1-(2,4-Dichlorophenyl)-3-(p-chlorophenyl)-2-pro-
penyl-1-ketone (0.01 mol) and phenylhydrazine (0.015
mol) were mixed in acetic acid (40 mL) and stirred in
refluxing for 6 h, then the mixture was poured into ice-wa-
ter to afford yellow solids. The solids were filtrated and
washed with water until the pH of solution is about 7. Fi-
* Corresponding author. Fax: 0086-0532-84023606; E-mail: zhaopusu@yahooo.com.cn

184 J. Chin. Chem. Soc., Vol. 55, No. 1, 2008
Zhao et al.
nally, the yellow solid crystals were dried at room tempera-
ture. Yield 85%. mp. 128.5-129.5 oC. IR: n 3089 (m), 2918
(m), 1928 (w), 1734 (m), 1655 (w), 1596 (vs), 1555 (s),
1530 (m), 1502 (vs), 1472 (s), 1399 (s), 1364 (vs), 1338
(m), 1313 (s), 1240 (s), 1231 (s), 1175 (m), 1132 (vs), 1106
(vs), 1072 (s), 1042 (m), 1015 (m), 1001 (m), 953 (m), 870
(s), 827 (vs), 798 (s), 769 (w), 749 (vs), 691 (s), 667 (s)
cm-1. Found: C, 62.74; H, 3.35; N, 6.79%. Calc. for
C21H15Cl3N2: C, 62.84; H, 3.49; N, 6.98 %. Electronic ab-
sorption spectra in EtOH (nm, log e): lmax = 206 (1.20), l =
248 (0.79), l = 364 (0.76).
Table 1. Summary of crystallographic results for the title
compound
Empirical formula
C21H15Cl3N2
Formula weight
401.7
Temperature
293(2) K
Wavelength
0.71073 Å
Crystal system, space group
Unit cell dimensions
Monoclinic, P21/c
a = 8.4779(17) Å
b = 15.706(3) Å b = 97.98(3)°
c = 14.185(3) Å
1870.5(6) Å3
Volume
Z, Calculated density
Absorption coefficient
F(000)
4, 1.426 Mg/m3
0.497
For the compound, single crystals suitable for X-ray
measurements were obtained by recrystallization from ace-
tic ether at room temperature.
824
q range for data collection
Limiting indices
1.94 to 27.06°
-10 £ h £ 10, -12 £ k £ 20, -15 £
l £18
Reflections collected/unique 8659/3932 [Rint = 0.0209]
Refinement method
Crystallographic Study
Full-matrix least-squares on F2
3932/0/235
The selected crystal of the title compound was
mounted on an Enraf-Nonius CAD4 diffractometer. Re-
flection data were measured at 20 °C using graphite
monochromated Mo-Ka (l = 0.71073 Å) radiation and a
w-2q scan mode. The correction for Lp factors and empiri-
cal absorption were applied to the data. The structures were
solved by direct methods and refined by full-matrix
least-squares method on Fobs2 using the SHELXTL soft-
ware package.17 All non-H atoms were anisotropically re-
fined. The hydrogen atom positions were fixed geometri-
cally at calculated distances and allowed to ride on the par-
ent C atoms. The final least-squares cycle gave R = 0.0677,
wR2 = 0.1604. Atomic scattering factors and anomalous
dispersion corrections were taken from the International
Table for X-ray Crystallography.18 A summary of the key
crystallographic information is given in Table 1.
Data/restraints/parameters
Goodness-of-fit on F2
Final R indices [I > 2s (I)]
R indices (all data)
1.098
R1 = 0.0677, wR2 = 0.1604
R1 = 0.0814, wR2 = 0.1685
0.542 and -0.250 e. Å-3
Largest diff. Peak and hole
spectra, Onsager reaction filed model25-29 was utilized to
optimize the solvated systems and calculate relevant prop-
erties. Among all the self-consistent reaction field (SCRF)
methods, the Onsager reaction field25-26 is a classic one and
has been adapted to various kinds of solution calcula-
tions.27-29 In this method, the solute occupies a fixed spheri-
cal cavity of radius a0 within the solvent field, which was
derived from a tight molecular volume calculation pro-
vided in Gaussian 03 on the fully optimized gas-phase sta-
tionary states using the same quantum chemical model for
consistency.
Computational Methods
All calculations were performed on a DELL PE 2850
server and a Pentium IV computer using the default conver-
gence criteria.
DFT calculations with a hybrid functional B3LYP
(Becke’s three-parameter hybrid functional using the LYP
correlation functional) at basis set 6-311G** by the Berny
method19 were performed with the Gaussian 03 software
package.20 Vibrational frequencies calculated ascertain the
structure was stable (no imaginary frequencies). The ther-
modynamic properties of the title compound at different
temperatures were calculated on the basis of vibrational
analyses. Natural Bond Orbital (NBO) analyses and the
time-dependent density functional theory (TD-DFT)21-24
calculations of electronic absorption spectra were also per-
formed on the optimized structure.
RESULTS AND DISCUSSION
Description of the Crystal Structure
The displacement ellipsoid plot with the numbering
scheme for the title is shown in Fig. 1. Fig. 2 shows a per-
spective view of the crystal packing in the unit cell. Atomic
parameters and equivalent isotropic thermal parameters of
non-hydrogen atoms for the title compound are given in Ta-
ble 2. Selected bond lengths and bond angles by X-ray dif-
fractions are listed in Table 3 along with the calculated
In order to investigate solvent effect on the electronic

Crystal Structure and DFT Study on a Pyrazoline Derivative
J. Chin. Chem. Soc., Vol. 55, No. 1, 2008 185
Table 2. Atomic coordinates (´ 104) and equivalent isotropic
displacement parameters (Å2 ´ 103) for the title
compound
bond parameters.
The molecular structure consists of discrete
[PhCl2C3H3N2PhPhCl] entities. All of the bond lengths and
bond angles in the phenyl rings are in the normal range. In
the pyrazolinyl rings of both molecules, the C=N and C-N
bond lengths (Table 3) are all shorter than those found in
similar structures [C=N 1.291(2) ~ 1.300(10) Å, C-N 1.482(2)
~ 1.515(9) Å].15 The N-N bond length is shorter than those
found in the above-cited structures [N-N 1.373(2) ~
1.380(8) Å].15 The pyrazolinyl ring with the phenyl rings at
positions 1 and 5 of the pyrazoline defines two planes P1
and P2, respectively, with the dihedral angle between P1
and P2 being 3.68°. The dihedral angle between P1 and
5-position phenyl ring is 82.22°.
Atom
x
y
Z
Ueq
Cl(1)
Cl(2)
Cl(3)
N(1)
N(2)
C(1)
C(2)
C(3)
C(4)
C(5)
6360(1)
6378(2)
5480(2)
9329(3)
9702(3)
6999(3)
6506(3)
6970(4)
7908(4)
8372(4)
7940(3)
8508(3)
8230(3)
9203(3)
10714(3)
11167(4)
12127(5)
12657(5)
12237(4)
11289(4)
8260(3)
8580(4)
7718(5)
6559(4)
6219(4)
7072(4)
882(1)
151(1)
-2219(1)
-1493(2)
-1655(2)
177(2)
9688(1)
6053(1)
14824(1)
10244(2)
11191(2)
8875(2)
7930(2)
7236(2)
7456(2)
8395(2)
64(1)
92(1)
107(1)
48(1)
54(1)
44(1)
50(1)
54(1)
56(1)
51(1)
40(1)
41(1)
47(1)
46(1)
49(1)
62(1)
82(1)
79(1)
68(1)
57(1)
43(1)
60(1)
70(1)
64(1)
64(1)
54(1)
383(2)
-122(2)
-828(2)
-1022(2)
-531(2)
-803(2)
-400(2)
-975(2)
-2327(2)
-2909(2)
-3584(2)
-3706(3)
-3127(2)
-2434(2)
-1295(2)
-989(2)
-1270(3)
-1860(2)
-2173(2)
-1884(2)
C(6)
C(7)
C(8)
C(9)
9146(2)
10121(2)
11045(2)
11792(2)
11493(2)
10843(2)
11161(3)
12105(3)
12750(3)
12454(2)
12553(2)
13466(2)
14170(2)
13944(2)
13041(3)
12345(2)
In the crystal lattice, there are some weak supramo-
C(10)
C(11)
C(12)
C(13)
C(14)
C(15)
C(16)
C(17)
C(18)
C(19)
C(20)
C(21)
30
...
lecular C-H p interactions (see Table 4). In the solid
state, all the above supramolecular interactions stabilize
the crystal structure.
Fig. 1. Molecular structure with the atomic numbering
scheme for the title compound.
Optimized Geometry
DFT calculations were performed on the title com-
pound at a B3LYP/6-311G** level of theory. Some opti-
mized geometric parameters are also listed in Table 3. Seen
from Table 3, most of the predicted bond lengths are longer
than those in the crystal structures, as the theoretical values
belong to the isolated molecule in the gas phase and the ex-
perimental values are attributed to the molecule in the solid
state. The geometry of the solid-state structures is subject
to intermolecular forces, such as van der Waals interactions
and crystal packing forces. The biggest differences of bond
lengths and bond angles between the experimental values
and the predicted values are -0.027 Å for the Cl(1)-C(1)
bond and -1.3° for the N(1)-N(2)-C(10) bond angle, which
suggest that the calculational precision is satisfactory31 and
the B3LYP/6-311G** level of theory is suitable for the
Fig. 2. A view of the crystal packing down the c axis
for the title compound.

186 J. Chin. Chem. Soc., Vol. 55, No. 1, 2008
Zhao et al.
system studied here.
Table 3. Selected structural parameters by X-ray and theoretical
calculations
Electronic Absorption Spectra
Bond lengths (Å)
Exp.
Calc.
Experimental electronic spectra were measured in
EtOH solution. Theoretical electronic absorption spectra
were calculated based on the B3LYP/6-311G** level opti-
mized structures in the gas phase and in EtOH solvent, re-
spectively, so as to make comparisons between the experi-
mental and calculated values. The value of the cavity size
(ao) for the title compound recommended by the tight mo-
lecular volume calculation on the fully optimized gas-phase
stationary was 5.89 Å. The dielectric constant of the EtOH
solvent was 24.55, which is the default value in the Gaussi-
an 03 software package. All of the experimental data and
calculated values are listed in Table 5.
Cl(1)-C(1)
Cl(2)-C(3)
Cl(3)-C(19)
N(1)-C(7)
N(1)-N(2)
N(2)-C(10)
N(2)-C(9)
C(6)-C(7)
C(7)-C(8)
C(8)-C(9)
C(1)-C(6)
C(3)-C(4)
1.738(3)
1.737(3)
1.740(3)
1.288(4)
1.361(3)
1.389(4)
1.465(4)
1.464(4)
1.503(4)
1.542(4)
1.391(4)
1.375(4)
1.370(4)
1.515(4)
1.391(4)
1.392(4)
1.371(5)
1.370(4)
1.373(4)
1.380(4)
1.765
1.754
1.759
1.294
1.356
1.398
1.476
1.469
1.521
1.554
1.406
1.393
1.382
1.522
1.406
1.404
1.392
1.396
1.397
1.392
C(4)-C(5)
C(9)-C(16)
C(10)-C(11)
C(10)-C(15)
C(13)-C(14)
C(16)-C(21)
C(16)-C(17)
C(20)-C(21)
Seen from Table 5, both the experimental electronic
spectra and predicted electronic spectra in the gas phase
have three absorption peaks, with the latter having some
red shifts compared with the former, while in EtOH sol-
vent, the predicted electronic spectra have four absorption
peaks. It is evident that, for the system studied here, the
electronic spectra calculated in the gas phase can approxi-
mately model the experimental electronic spectra, while
the predicted electronic spectra in EtOH solvent will intro-
duce bigger errors compared with the experimental data.
Natural population analyses based on the optimized geo-
metrics in the gas phase indicate that the frontier molecular
orbitals are mainly composed of py and pz atomic orbitals,
so electronic transitions corresponding to the above elec-
tronic spectra are mainly assigned to p ® p* transitions.
Fig. 3 shows the surfaces of the HOMO-1, HOMO, LUMO
and LUMO + 1. As seen from Fig. 3, the electrons transfer
from the phenyl ring at the 1 and 5 positions of the pyr-
azolinyl ring to the phenyl ring at the 3 position of the
pyrazolinyl ring, which are corresponding to p ® p* elec-
tron transitions.
Bond angles (°)
Exp.
Calc.
C(7)-N(1)-N(2)
N(1)-N(2)-C(10)
N(1)-N(2)-C(9)
C(10)-N(2)-C(9)
C(2)-C(1)-C(6)
C(2)-C(1)-Cl(1)
C(3)-C(2)-C(1)
C(2)-C(3)-Cl(2)
C(1)-C(6)-C(5)
C(1)-C(6)-C(7)
N(1)-C(7)-C(8)
C(7)-C(8)-C(9)
N(2)-C(9)-C(16)
N(2)-C(9)-C(8)
C(11)-C(10)-C(15)
C(13)-C(12)-C(11)
C(13)-C(14)-C(15)
C(21)-C(16)-C(17)
C(16)-C(17)-C(18)
C(18)-C(19)-C(20)
C(18)-C(19)-Cl(3)
109.8(2)
119.7(2)
113.1(2)
126.2(2)
122.5(3)
114.4(2)
118.9(3)
118.7(2)
115.5(2)
126.5(2)
112.6(2)
102.7(2)
113.3(2)
101.4(2)
118.5(3)
121.9(4)
120.8(3)
118.8(3)
120.8(3)
121.3(3)
119.2(3)
110.6
121.0
112.8
126.0
122.2
115.3
119.4
119.4
115.9
126.1
111.8
102.1
113.3
101.2
119.0
121.1
120.9
118.7
121.1
121.0
119.4
Thermodynamic Properties
On the basis of vibrational analyses and statistical
Table 4. Supramolecular C-H••• p interactions
D-H•••A
Symmetry
D•••A (Å)
ÐD-H•••A (°)
C(2)-H(2A)•••Cg(4)[C(16)~C(21)]
C(4)-H(4A)•••Cg(3)[C(10)~C(15)]
C(5)-H(5A)•••Cg(4)[C(16)~C(20)]
C(9)-H(9A)•••Cg(2)[C(1)~C(6)]
C(19)-H(19A)•••Cg(2)[C(1)~C(6)]
1-x, 1-y, 1-z
x, 1/2-y, 1/2+z
x, 1/2-y, 1/2+z
-x, 1-y, 1-z
3.971 (3)
3.915 (3)
3.857 (3)
3.490 (3)
3.781 (3)
147.40
129.34
119.75
147.40
139.43
-x, -1/2+y, 1/2-z

Crystal Structure and DFT Study on a Pyrazoline Derivative
J. Chin. Chem. Soc., Vol. 55, No. 1, 2008 187
C0p,m = 17.7109 + 1.369 T - 5.4300*10-4 T2
(R2 = 0.99907)
Table 5. Experimental and theoretical electronic absorption
spectra values
S0m = 293.4917 + 1.4684 T - 3.3065*10-4 T2
(R2 = 0.99998)
Calc.
Exp.
in the gas phase
in EtOH solvent
These equations could be used for further studies of
wave length
(nm)
wave length oscillator wave length oscillator
log e
the title compounds.
CONCLUSIONS
1N-Phenyl-3-(2,4-dichlorophenyl)-5-(4-chlorophen-
(nm)
strength
(nm)
strength
206
1.20
219.08
240.31
260.92
393.05
0.1709
0.1070
0.2595
0.6965
240
262
385
0.1013
0.2226
0.5743
248
364
0.79
0.76
yl)-2-pyrazoline has been synthesized and characterized
by elemental analysis, IR, UV-Vis and X-ray single crystal
diffraction. DFT calculations at the B3LYP/6-311G** level
for the compound show that the optimized geometry closely
resembles the crystal structure. The electronic absorption
spectra calculated in the gas phase are better than those cal-
culated in EtOH solvent to model the experimental elec-
tronic spectra. NBO analysis suggests that the electronic
transitions for the title compound are mainly assigned p ®
p* transitions, which correspond to the electron transition
from the phenyl rings at the 1 and 5 positions of the pyr-
azolinyl ring to the phenyl ring at the 3 position of the pyr-
azolinyl ring. The correlations between the thermodynamic
thermodynamics, the standard thermodynamic functions:
heat capacity (C0p,m), entropy (S0m) and enthalpy (H0
)
m
were obtained and are listed in Table 6. The scale factor for
frequencies is 0.96, which is a typical scaled factor for the
B3LYP method.
As observed from Table 6, all the values of C0p,m, S0
m
and H0 increase with the increase of temperature from
m
100.0 to 600.0 K, which is attributed to the enhancement of
the molecular vibration while the temperature increases.
The linear equations between C0p,m, S0m and tempera-
ture T are as follows:
Fig. 3. Surfaces of HOMO-1, HOMO, LUMO and LUMO+1 for the title compound.

188 J. Chin. Chem. Soc., Vol. 55, No. 1, 2008
Zhao et al.
12. de Silva, A. P.; Gunaratne, H. Q. N.; Gunnlaugsson, T.;
Nieuwenhuizen, M. Chem. Commun. 1996, 1967.
13. Rurack, K.; Resch-Genger, U.; Bricks, J. L.; Spieles, M.
Chem. Commun. 2000, 2103.
14. Rurack, K.; Bricks, J. L.; Schulz, B.; Maus, M.; Reck, G.;
Resch-Genger, U. J. Phys. Chem. A. 2000, 104, 6171.
15. Fahrni, C. J.; Yang, L. C.; VanDerveer, D. G. J. Am. Chem.
Soc. 2003, 125, 3799.
Table 6. Thermodynamic properties of the title compound at
different temperatures at the B3LYP/6-311G** level
T
C0
S0
H0
p,m
m
m
(J·mol-1·K-1)
(kJ·mol-1)
(J·mol-1·K-1)
(K)
100.0
200.0
298.1
300.0
400.0
500.0
600.0
154.29
262.17
375.67
377.78
484.08
571.06
639.53
0436.27
0575.68
0701.49
0703.82
0827.46
0945.20
1055.62
009.98
030.71
062.01
062.71
105.94
158.87
219.54
16. Wagner, A.; Schellhammer, C. W.; Petersen, S. Angew.
Chem., Int. Ed. Engl. 1966, 5, 699.
17. Sheldrick, G. M. SHELXTL, v5 Reference Manual; Siemens
Analytical X-Ray Systems: Madison, WI, 1997.
18. Wilson, A. J. International Table for X-Ray Crystallogra-
phy; Kluwer Academic: Dordrecht, 1992; Vol. C, pp
219-222, pp 500–502.
properties C0p,m, S0m and temperatures T are also obtained.
19. Peng, C.; Ayala P. Y.; Schlegel, H. B.; Frisch, M. J. J.
Comput. Chem. 1996, 49, 17.
ACKNOWLEDGMENT
20. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven,
Jr., T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S.
S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.;
Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;
Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.;
Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.;Cross, J. B.;
Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.;
Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski,
J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.;
Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels,
A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A.
D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.;
Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.;
Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R.
L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.;
Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A.
Gaussian, Inc., Wallingford CT, 2004.
This work was supported by the Natural Science
Foundation of Shandong Province (No. Y2005B04), P. R.
China, Doctoral Fund of Shandong Province, P. R. China,
(No. 2006BS01043) and Doctoral Fund of Qingdao Uni-
versity of Science & Technology.
Received June 1, 2007.
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