Crystal structure and geometry-optimization study of 4-methyl-3′,5′-dinitro-4′-methyl benzylidene aniline

Article abstract of DOI:10.1016/j.molstruc.2006.02.042

Schiff base 4-methyl-3′,5′-dinitro-4′-methyl benzylidene aniline was synthesized by the condensation of 4-amino-2,6-dinitrotoluene with 4-methylbenzaldehyde. The crystal of the title compound was obtained and it was characterized by X-ray single crystal d

Full text of DOI:10.1016/j.molstruc.2006.02.042

Journal of Molecular Structure 794 (2006) 255–260
www.elsevier.com/locate/molstruc
Crystal structure and geometry-optimization study of
0 0 0
4
-methyl-3 ,5 -dinitro-4 -methyl benzylidene aniline
Wei Yu, Li Yang, Tong-lai Zhang , Jian-guo Zhang, Fu-jian Ren, Yan-hong Liu,
*
Rui-feng Wu, Jin-yu Guo
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
Received 1 January 2006; received in revised form 14 February 2006; accepted 16 February 2006
Available online 30 March 2006
Abstract
0
0
0
Schiff base 4-methyl-3 ,5 -dinitro-4 -methyl benzylidene aniline was synthesized by the condensation of 4-amino-2,6-dinitrotoluene with 4-
methylbenzaldehyde. The crystal of the title compound was obtained and it was characterized by X-ray single crystal diffraction analysis, EA,
1
FTIR and H NMR. The geometry and normal vibrations have been obtained from the density functional theory (DFT) method with the B3LYP
method employing the 6-31G** and 6-311G** basis sets. The calculated results propose that the latter is more accurate to the experimental data.
The structural parameters from the theory are close to those of the crystal, and the computational frequencies are in agreement with the
experimental data.
q 2006 Elsevier B.V. All rights reserved.
Keywords: Crystal structure; Benzylidene aniline; Density functional theory; Geometry-optimization
1
. Introduction
properties of some compounds [6,7]. Mondal et al. [8] have
successfully predicted the properties of the Schiff base of
2-benzyliminiomethylene-4-nitrophenolate, John [9] predicted
some structures of benzylidene anilines containing the
4-dimethyl amino group at one end of the molecule and the
Condensation of primary amines with aldehydes or ketones
yields Schiff bases containing imine (CaN) function group [1].
Some of these compounds are donor–acceptor benzene
derivatives, which can conform conjugated p-electron systems
easily, and they are known to exhibit extremely large second-
0
4 -nitro group at the other.
0
0
0
In this work, we synthesized 4-methyl-3 ,5 -dinitro-4 -
methyl benzylidene aniline (MDNMBA) containing the methyl
group at one benzene ring of the molecule and two nitro groups
at the other, which was alike with NMBA and NMOBA in the
molecular structure. We obtained the crystal of MDNMBA,
0
order optical non-linearities, such as 4-nitro-4 -methyl benzyl-
0
idene aniline (NMBA) [2], 4-nitro-4 -methoxy benzylidene
0
aniline (NMOBA) [3], N-2-[3 -(methoxysalicylideneimino)
0
0
benzyl]-3 -methoxysalicylideneimine [4]. Organic crystals in
terms of non-linear optical property possess advantages when
compared to their inorganic counterparts, and they have larger
structural diversity [5], so the preparation of this kind of
materials has gained increasing importance.
1
which was also characterized by EA, FTIR, H NMR. The
geometry and normal vibrations were obtained from the DFT
method with the B3LYP method [10,11] employing the
6-31G** and 6-311G** basis sets. All the electronic structure
calculations were carried out using GAUSSIAN 98 program [12].
With the advance of quantum chemistry method and high
performance computers, the structures of some organic
compounds can be theoretically predicted in high accuracy.
Density functional theory (DFT) method has recently been
successfully applied to investigate the structures and predict
2. Experiment and computational methods
2.1. Synthesis
*
Corresponding author. Tel./fax: C86 10 68913818.
E-mail address: ztlbit@bit.edu.cn (T.-l. Zhang).
MDNMBA has been synthesized by the condensation
reaction of 4-amino-2,6-dinitrotoluene (ADNT) with 4-methyl-
benzaldehyde, and the equation of the reaction is shown as
follows:
0
022-2860/$ - see front matter q 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2006.02.042

256
W.Yu et al. / Journal of Molecular Structure 794 (2006) 255–260
Table 1
Crystallographic and refinement parameters of MDNMBA
Molecular formula
Formula weight
Crystal color
Size
15 13 3 4
C H N O
299.28
Yellow
0.54!0.34!0.24 mm
Monoclinic
Crystal system
Space group
P2(1)/n
˚
Unit cell parameters
aZ19.441(4) A
˚
bZ7.544(1) A
˚
cZ19.997(3) A
bZ99.68(1)8
2891.16(94) A
3
˚
Volume
Z
8
F(000)
1248
K3
Density (calculated)
Theta range for data collection
Limiting indices
1.375 g cm
1.35–25.508
0%h%23, 0%k%9, K24%l%23
6212
K1
Reflections collected
Absorption coefficient
Reflections collected
Data/restraints/parameters
Independent reflections
Extinction coefficient
Final R indices [IO2s(I)]
R indices (all data)
Largest diff. peak and hole
0.102 mm
6212
5386/0/400
5386 [R(int)Z0.0162]
0.0068(5)
R1Z0.0520, wR2Z0.1127
R1Z0.1396, wR2Z0.1340
˚
0.266 and K0.210 e A
K3
O2N
H3C
O N
O2N
NHOH + H3C
O2N
O N
2
2
H S2
KI
NO2
NH2
H C
NH2
O2N
H3C
O2N
NH2
CH3
Equation 1
Equation 2
3
p-dioxane
O N
O N
2
2
O N
2
ethanol
refluxing
H3C
O N
+
OHC
CH3
H3C
O N
N
C
H
2
2
The ADNT was prepared by adopting the method of Mehilal
et al. [13]. Fifty grams of 2,4,6-trinitrotoluene was dissolved in
To a solution of 0.04 mol aldehyde in 100 ml ethanol was
added a solution of 0.04 mol amine in 75 ml ethanol. The
resulting solution was boiled under reflux for 3 h, then
concentrated and cooled in an ice bath until crystallization
was observed, which was the title compound. The yellow solid
was suction filtered, dried and recrystallized from dichloro-
methane–methanol with the yield 86%, m.p. 147–149 8C. IR
1
00 ml of p-dioxane. One millilitre concentrated ammonium
hydroxide solution (0.25 ml, four times) was added giving a
deep red solution. Hydrogen sulfide gas was bubbled into the
stirred solution at a rate sufficient to maintain the temperature
below 35 8C, after 1 h H S addition was stopped. The
2
precipitated sulfur was filtered and dried giving a mixture of
K1
K1 1
(KBr): nCaN: 1632 cm , nNO : 1602, 1533, 1362 cm . H
2
4
4
-amino-2,6-dinitrotoluene and the partial reduction product
-hydroxylamino-2,6-dinitrotoluene.
Ten grams of this mixture was suspended in 500 ml of
NMR (acetone): 8.77 ppm (s, 1H, HCaN), 8.05 ppm (s, 2H,
Ar-H), 7.90 ppm (d, 2H, Ar-H), 7.39 ppm (d, 2H, Ar-H),
2.52 ppm (s, 3H, CH ), 2.43 ppm (s, 3H, CH ). Elemental
3
3
K1
3
mol L hydrochloric acid, 3.12 g of potassium iodide was
analysis for MDNMBA: calcd: C 60.20, H 4.35, N 14.05;
found: C 59.91, H 4.49, N 14.06.
added, and the stirred solution was heated to reflux. After 1 h
an additional 1.56 g KI was added. Following additional half
an hour at reflux, the hot solution was filtered to give a clear red
solution. The cooled solution was neutralized to pH 8 by
addition of concentrated ammonium hydroxide solution. The
precipitated yellow solid was filtered and dried.
2.2. Physical measurements
FTIR spectra for MDNMBA were recorded by KBr pellet
K1
technique between the range of 400 and 4000 cm
using
1
Recrystallization from methanol gave the pure 4-amino-2,6-
dinitrotoluene with the yield w58%, m.p. 169–171 8C. IR
Bruker Equinox 55 FTIR spectrometer. H NMR spectra were
obtained with acetone as solvent and internal TMS as standard
using an AV400 spectrometer. Elemental analysis of C, H and
N were carried out on a Perkin–Elmer 2400 (USA)
K1
K1
(
KBr): nNH : 3478, 3380 cm , nNH: 1658 cm , nNO2:
2
K1
1
536, 1352 cm
.

W.Yu et al. / Journal of Molecular Structure 794 (2006) 255–260
257
Fig. 1. The ORTEP view of the molecular structure of MDNMBA.
microanalyzer. Single crystal X-ray diffraction analysis was
performed for MDNMBA crystal using a Siemens P4 four-
circle diffractometer with graphite monochromatized Mo Ka
are ascertained, while those of C15 methyl are unascertained,
and the occupancy of every site is 0.5.
From the data of the crystal, the N–O bond lengths in all the
nitro groups are around the normal N–O double bond in nitro
˚
radiation (lZ0.71073 A) at 296(2) K using u scan mode. The
˚
group (about 1.20 A) [14]. The lengths of C–C bond in benzene
ring are as normal length, and all of the C–N bond lengths
˚
except for N1–C7 are in the range of 1.46–1.48 A and are
around the normal C–N single bond which is referred to
crystals suitable for X-ray diffraction analysis were obtained
from a saturated solution of dry acetone. Crystallographic and
refinement parameters are given in Table 1. The structure was
solved by direct methods. Anisotropic displacement par-
ameters were applied to all non-hydrogen atoms in full-matrix
˚
˚
1.47 A, while the bond length of N1–C7 is 1.189 or 1.244 A,
which is smaller than those of N3–C4 and N2–C2, showing that
the bond between N1 and C7 is double bond.
2
least-squares refinements based on F . All hydrogen atoms
were calculated using a riding model. ORTEP view of the
molecular structure of the title compound is given in Fig. 1,
which shows the experimental geometry of MDNMBA. The
crystallographic-information-file (CIF) has been deposited
with the Cambridge Crystallographic Database Center as a
supplementary publication No. CCDC 282113.
The endocyclic angles have a rule that if the C of the
benzene ring has methyl substitute it has smaller angles (less
than 1208) than that has nitro group substitute (more than 1208)
[15]. For the title compound, the endocyclic angles of C1–C2–
C3 (about 1248) and C3–C4–C5 (about 1258) are larger than
those of C2–C3–C4 (about 1128) and C10–C11–C12 (about
1188), which is expected due to the nitro groups attraction
affect and the methyl repulsion affect.
2
.3. Computational methods
From the crystal data, it is found that the two N atoms of the
two nitro groups are almost co-planar to the benzene ring, and
the largest torsion angle is only 2.68. The two C atoms of the
two methyl groups at the two ends of the molecule are also co-
planar to the benzene ring, and the largest torsion angle is 4.08.
Geometry optimization and frequency analysis of 4-methyl-
0 0
0
2
,6 -dinitro-4 -methyl benzylidene aniline were performed
using the B3LYP hybrid density functional method of theory
with the 6-31G** and 6-311G** basis sets. Here, B3LYP
denotes the combination of the Becke’s three parameter
exchange with the Lee–Yang–Parr (LYP) correlation
functional. All the electronic structure calculations were
carried out using the GAUSSIAN 98 program packages.
Table 2
˚
Selected bond distances (A) of crystal data and theoretical calculations of
MDNMBA
Distance
MDNMBA-a
MDNMBA-b
B3LYP/
-31G**
B3LYP/
6
6-311G**
3
. Results and discussion
O(1)–N(2)
O(2)–N(2)
O(3)–N(3)
O(4)–N(3)
N(1)–C(7)
N(1)–C(6)
N(2)–C(2)
N(3)–C(4)
C(3)–C(14)
C(7)–C(8)
C(11)–C(15)
1.180(3)
1.202(3)
1.204(4)
1.218(4)
1.189(4)
1.462(4)
1.483(4)
1.468(4)
1.500(4)
1.529(4)
1.512(4)
1.165(3)
1.169(3)
1.203(3)
1.230(3)
1.244(3)
1.428(3)
1.473(4)
1.476(4)
1.504(4)
1.469(4)
1.503(4)
1.229
1.229
1.220
1.230
1.280
1.390
1.470
1.470
1.510
1.460
1.500
1.222
1.222
1.222
1.222
1.270
1.390
1.480
1.480
1.500
1.460
1.500
3
.1. Molecular and crystal structure
From the molecular structure, it is found that there are two
crystallographically independent but structurally very similar
molecules in the unit cell of the title compound, and the
selected bond distances, bond angles of the two molecules are
given in Tables 2 and 3, respectively. The hydrogen of CH are
3
different for C14 and C15. The sites of H atoms of C14 methyl

258
W.Yu et al. / Journal of Molecular Structure 794 (2006) 255–260
Table 3
Selected bond angles (8) of crystal data and theoretical calculations of
MDNMBA
Angles
MDNMBA-a MDNMBA-b B3LYP/6-
1G**
B3LYP/6-
311G**
3
b
C(7)–N(1)–C(6)
C(2)–C(1)–C(6)
C(1)–C(2)–C(3)
C(1)–C(2)–N(2)
C(3)–C(2)–N(2)
C(4)–C(3)–C(2)
C(4)–C(3)–C(14)
C(2)–C(3)–C(14)
C(5)–C(4)–C(3)
C(5)–C(4)–N(3)
C(3)–C(4)–N(3)
C(6)–C(5)–C(4)
C(1)–C(6)–C(5)
C(1)–C(6)–N(1)
C(5)–C(6)–N(1)
N(1)–C(7)–C(8)
C(9)–C(8)–C(13)
C(9)–C(8)–C(7)
C(13)–C(8)–C(7)
C(10)–C(11)–C(12)
116.2(4)
120.1(3)
124.8(3)
114.8(3)
120.4(3)
112.4(3)
122.7(3)
124.8(3)
125.0(3)
115.5(3)
119.5(3)
118.9(3)
118.8(3)
116.0(3)
124.9(3)
120.0(4)
119.4(3)
117.7(4)
122.9(4)
118.5(3)
118.0(3)
120.7(3)
124.3(3)
115.4(3)
120.4(3)
112.4(3)
121.7(3)
125.8(3)
125.3(3)
115.2(3)
119.4(3)
119.7(3)
117.6(3)
118.0(3)
124.2(3)
122.4(3)
118.2(3)
119.4(3)
122.4(3)
118.2(3)
120.04
120.34
124.23
114.97
120.79
113.22
123.43
123.18
124.24
114.83
120.92
124.24
117.64
118.22
124.06
122.89
118.81
119.48
121.70
118.27
120.38
120.28
124.28
115.04
120.66
113.22
123.48
123.16
124.25
114.87
120.86
120.23
117.64
118.28
123.98
122.98
118.76
119.54
121.68
118.24
a
500
1000
1500
Wavenumber (cm–1
2000
2500
3000
3500
)
Fig. 2. The calculated FTIR spectra of MDNMBA, a and b are the calculated
results by using B3LYP/6-31G** and B3LYP/6-311G** level of theory,
respectively.
It is found that the bond lengths and bond angles have subtle
differences between the data obtained at B3LYP/6-311G**
level and the average values of crystal, in which all bond
˚
distances deviate by less than 0.055 A, and the largest bond-
angle error is 3.2808.
The calculated results obtained at B3LYP/6-311G** level
predict that the angles of C11–C2–C2, C2–C3–C4, C3–C4–C5,
C4–C5–C6 and C5–C6–C1 are 120.38, 124.28, 113.22, 124.25,
For most of the benzylidene anilines, the central four atoms of
C–CaN–C is almost co-planar [16–18], which is the same with
the title compound, and the torsion of C6–N1–C7–C8 for
molecular a and b are both 176.28.
120.23 and 117.648, which is in agreement with the rule of
endocyclic angles mentioned above.
The computational results show that C3, N2 and N3 are co-
planar to the aniline ring, and C15 is co-planar to the aldehyde
ring. The four atoms of C6, N1, C7 and C8 are almost co-planar
As a rule, the aromatic ring containing the donor group is
essentially co-planar with the central –CaN-double bond with
typical torsion angles of 5–108, however, the ring containing
the acceptor group is twisted by around 30–508 from the C–
CaN–C plane, such as the four polymorphs of 4-(N,
(176.818), and the aldehyde ring is almost co-planar to the C6–
N1–C7–C8 axis (N1–C7–C8–C9 179.108, and N1–C7–C8–
C13 0.978), and the aniline ring is twisted from the C6–N1–
C7–C8 plane (C7–N1–C6–C1 143.748, and C7–N1–C6–C5
0
N-dimethyl-amino) benzylidene-4 -nitroaniline [16,17],
which is in agreement with the crystal data of the title
compound. For molecular a and b the angles between the C–
CaN–C plane and the C1–C6 benzene ring are 33.6 or 31.18,
the torsion angles of C7–N1–C6–C1 are 151.0 or 152.48, C7–
N1–C6–C5 are 35.4 or 33.38, while the angles between the C–
CaN–C plane and the C8–C13 benzene ring for molecular a
and b are 7.2 or 8.68, the torsion angles of N1–C7–C8–C9 are
39.658), which is in line with the data of the crystal, therefore,
the DFT calculations can give a remarkably good description of
the molecular geometry.
Vibrational frequencies were calculated using two levels of
theories for MDNMBA. The predicted IR spectra using
B3LYP/6-31G** and B3LYP/6-311G** level of theory
1
72.4 or 170.98, N1–C7–C8–C13 are 8.4 or 9.68.
The plane of C1–C6 benzene ring for molecular a is almost
1.1
1.0
0.9
in parallel with that of C8–C13 benzene ring for molecular b,
and the angle is 2.98, and the distance of the two planes is
˚
.444 A, which is in the range of p–p stacking interaction
˚
(3.3–3.7 A) [19], may be the existence of p–p stacking
interaction benefits for the formation of the crystals.
0.8
0.7
3
0.6
0.5
0.4
0.3
0.2
0.1
3
.2. Computational results and discussion
The calculated data of selected bond distances, bond angles
of MDNMBA are given in Tables 2 and 3, respectively. It is
found that the computation results obtained at B3LYP/6-
0.0
5
00
1000
1500
2000
2500
3000
3500 4000
3
1G** and B3LYP/6-311G** level of theories are similar, but
Wavenumber (cm–1
)
on the whole the latter is closer to the data of the crystal
structure from the experiment.
Fig. 3. FTIR spectra of MDNMBA.

W.Yu et al. / Journal of Molecular Structure 794 (2006) 255–260
259
for MDNMBA are shown in Fig. 2 a and b, respectively.
Comparing the two methods, we can find that B3LYP/6-
factor is available for the B3LYP method with the 6-311G**
basis set. We assigned the main vibrational frequencies of
some main function groups.
3
11G** method is more accurate to predict the experimental
IR spectra, which is shown in Fig. 3 so the predicted
frequencies and intensities for MDNMBA are listed in
Table 4 at the B3LYP/6-311G** level of theory. All theoretical
frequencies reported here are listed as calculated, as no scale
Aromatic nitro compounds have strong absorptions due to the
asymmetric and symmetric vibrations of the NO group. From
2
Table 4, it is found that the absorption bands at 1608 and
K1
1379 cm
can be designated to asymmetric stretching and
Table 4
Selected vibrational assignment of MDNMBA based on the B3LYP/6-311G** frequencies and assignment
K1
n
Energy (cm
)
Intensity
Assignment
tC15H
tN2O
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
27.8
52.3
0.16
0.23
3
2
(twist.), tN3O
2
(twist.)
128.8
2.96
dC7–N1
178.4
0.98
gring1
202.1
3.98
gring2
214.7
7.53
gC7–N1, gring1
dC3–C14, dC11–C15
350.4
1.67
471.7
1.50
gN2O
2
(wag.), gN3O
2
(wag.), gring1
484.3
8.66
dring1, dring2
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
500.5
9.72
gring1, gring2, gC7–N1
gring2
531.0
10.60
5.29
645.9
tring1, gC6–N1, dring2
tring2
732.9
6.99
746.5
40.76
9.43
dring1, dN2O
gN3O (wag.), dring2, gC1–H, gC5–H
gring1, gN2O (wag.)
gC9–H, gC10–H, gC12–H, gC13–H
dN2O (sciss.), dN3O (sciss.), dring1, dring2
2 2
(sciss.), dN3O (sciss.)
777.6
2
784.0
4.12
2
832.8
31.45
38.56
25.34
40.93
24.93
1.07
834.5
2
2
878.5
dC7–N1, dring2, gC1–H, gC5–H
gC1–H, gC5–H, dring1, nC2–N2, nC4–N3
gC1–H, gC5–H
918.3
924.8
966.0
gC9–H, gC10–H, gC7–H
dring1, dring2, dC6–N1
994.8
14.85
21.78
6.38
1009.4
1017.7
1035.2
1043.9
1139.4
1197.3
1227.6
1237.4
1319.2
1335.9
1379.5
1387.5
1404.7
1430.1
1477.9
1495.8
1502.6
1578.8
1604.9
1608.5
1616.9
1645.9
1661.0
1689.2
3003.6
3026.8
3109.3
3128.2
dC15H
gC7–H
dring2, dC9–H, dC10–H, dC12–H, dC13–H
dC14H (rock.)
3
(rock.)
9.02
3.60
3
10.77
85.17
59.78
44.16
14.64
21.56
351.94
146.77
12.25
8.64
dC9–H, dC10–H, dC12–H, dC13–H
dC9–H, dC10–H, dC12–H, dC13–H
dring1, dring2, dC7– C8, dC6–N1, dC7–N1
dring2, dC1–H, dC5–H
dring1, dring2, dC7– C8, dC6–N1
dring2, dC7–C8
n
n
s
N2O
N2O
2
, n
, n
s
N3O
N3O
2
, nC2–N2, nC4–N3
, nC2–N2, nC4–N3
s
2
s
2
dC7–H
dring1, dC1–H, dC5–H, dC7–H, dC14–H
3
(sciss.)
16.79
13.24
74.16
10.58
136.69
471.52
78.30
166.18
44.81
272.27
38.02
26.30
18.01
9.26
dC14–H
dC15–H
3
(sciss.)
(sciss.)
3
3
dring1, nC6–N1, dC14–H (sciss.)
dring1, dC6–N1
nC7–N1, dring2
n
n
a
N2O
N2O
2
, n
, n
a
N3O
N3O
2
, dring1, dring2
, dring1
a
2
a
2
nC7–N1, dring1, dring2
nC7–N1, dring1, dring2
nC7–N1, dring1, dring2
nC7–H
nC15–H
3
n
n
a
C15–H
C14–H
3
a
3
ring1, aniline ring; ring2, aldehyde ring; n, stretching; d, in-plane bending; g, out-of-plane bending; t, torsion; s, symmetry; a, asymmetry; rock., rocking; sciss.,
scissoring; twist., twisting; wag., wagging. For numbering of atom refer Fig. 1.

260
W.Yu et al. / Journal of Molecular Structure 794 (2006) 255–260
symmetric stretching of the nitro groups, and the bands at 1604,
1
[7] B. Ivan, K.F. George, J. Am. Soc. Chem. 86 (1964) 1671.
[8] B. Mondal, G.K. lahiri, P. Naumov, S.W. Ng, J. Mol. Struct. 613
(2002) 131.
K1
645 and 1689 cm are assigned to the stretching of CaN, and
K1
K1
the bands above 3000 cm (3003, 3026, 3109, and 3128 cm
are designated to the C–H stretching.
)
[
9] O.M. John, J. Mol. Struct. (Theochem) 340 (1995) 45.
[
10] A. Becke, J. Chem. Phys. 98 (1993) 5648.
From above analysis, we can conclude that the vibrational
frequencies are identical on the whole between theoretical
calculation and the experimental result, and the calculated data
could offer the theoretical bases.
[11] C. Lee, W. Wang, R.G. Parr, Phys. Rev. B 37 (1988) 785.
[12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R.
Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C.
Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C.
Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B.
Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A.
Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D.
Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G.
Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi,
R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y.
Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe,. M.W. Gill, B.
Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-
Gordon, E.S. Replogle, and J.A. Pople, GAUSSIAN 98, Revision A.7,
Gaussian, Inc., Pittsburgh PA, 1998.
Acknowledgements
We are grateful to the National Natural Science Foundation
of China (No. 20471008) and the Foundation for basic research
by the Beijing Institute of Technology.
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