Lewis acid catalyzed C-N bond formation: Synthesis of quinoxalines via CuX (X = Cl, Br, I) catalyzed cyclotrimerization of alkynes with o-phenylendiamines

Article abstract of DOI:10.14233/ajchem.2015.18532

An efficient one-pot cycloisomerization reaction has been developed for the synthesis of quinoxaline derivatives from alkynes and o-phenylendiamines using CuX (X = Cl, Br, I) as a catalyst. This method provides a flexible and rapid route to synthesize qui

Full text of DOI:10.14233/ajchem.2015.18532

Asian Journal of Chemistry; Vol. 27, No. 11 (2015), 3921-3924
A
SIAN
J
OURNAL OF HEMISTRY
C
http://dx.doi.org/10.14233/ajchem.2015.18532
Lewis Acid Catalyzed C-N Bond Formation: Synthesis of Quinoxalines via CuX
(X = Cl, Br, I) Catalyzed Cyclotrimerization of Alkynes with o-Phenylendiamines
1,*
2
1
1
YING LIANG , PEI-ZHEN LIU , CHAN-CUI WU and QIAN ZHANG
1School of Life and Environmental Sciences, Guilin University of Electronic Technology, Guilin 541004, PR. China
2Key Laboratory for Chemistry and Molecular Engineering of Medicinal Resources (Ministry of Education of China), School of Chemistry &
Chemical Engineering of Guangxi Normal University, Guilin 541004, P.R. China
*Corresponding author: Tel/Fax: +86 773 2291581; E-mail: YingL@aliyun.com
Received: 30 July 2014;
Accepted: 28 May 2015;
Published online: 16 July 2015;
AJC-17376
An efficient one-pot cycloisomerization reaction has been developed for the synthesis of quinoxaline derivatives from alkynes and
o-phenylendiamines using CuX (X = Cl, Br, I) as a catalyst.This method provides a flexible and rapid route to synthesize quinoxaline derivatives.
Keywords: Alkynes, o-Phenylendiamines, Cycloisomerization, CuX, Quinoxaline derivatives.
CuX (X = Cl, Br, I)-catalyzed cycloisomerization reaction of
alkynes with o-phenylendiamines, leading to the synthesis of
quinoxaline derivatives.
INTRODUCTION
Quinoxaline is a heteroaromatic unit of extensive interests
owing to its occurrence in a diverse range of biological activities
including antitumor1, antibacterial, anthelmintic, antiinfla-
mmatory, kinase inhibitory and anticancer activities2. They
also have a wide application in dyes3, efficient electron lumine-
scent material4, organic semiconductors5, DNA cleaving agents6,
photoinitiators in UV-cured coatings7 and donor materials8.
Therefore, a number of methods have been developed for the
synthesis of substituted quinoxalines9-13. Quinoxalines can be
prepared from α-hydroxy ketones and 1,2-diamines using
transition metal complexes as catalysts14. The most common
method for their preparation relies on the condensation of an
aryl 1,2-diamine with a 1,2-dicarbonyl compound15. However,
the current studies are mainly focused on the same substrate
such as dicarbonyl compounds or α-hydroxy ketones as the
starting materials by different methodologies for the synthesis
of quinoxaline derivatives16-19. Therefore, it is highly significant
to construct quinoxaline rings by developing new synthesis
methodologies from readily available materials. Recently, the
work reported by Chen’s group attracted our attention20. Chen
et al.20 have developed a Cu(OAc)2-catalyzed method for
synthesis of quinoxaline by using o-phenylenediamines and
terminal alkynes in the presence of 3 equiv of DMAP and
Cs2CO3. However, when we repeat their work, it is found that
the product composition is complicated and a large number of
the coupling product of phenylacetylene are obtained due to
the strong base conditions. Herein, we reported an efficient
EXPERIMENTAL
All compounds are commercially available and were used
without further purification. NMR spectra were recorded on a
Bruker AVANCE DPX-400 or Bruker AVANCE DRX-500
instrument with TMS as an internal reference. MS measure-
ments were performed on Bruker Reflex III mass spectrometer
(ESI). Elemental analyses were done with an ElementarVario
Micro Cube in School of Chemistry & Chemical Engineering
of Guangxi Normal University, China. Flash chromatography
was performed with QingDao silica gel (300-400 mesh).
General procedure for synthesis of quinoxaline deriva-
tives: The reaction mixture of o-phenylendiamine (2.5 mmol),
alkynes (1 mmol), CuCl (0.1 mmol), chlorobenzene (2 mL) in a
10 mL sealed tube was stirred at 70 °C and monitored periodically
by TLC. Upon completion, chlorobenzene was removed under
reduced pressure by an aspirator and then the residue was purified
by silica gel column chromatography (eluent, PE/EA = 50:1) to
afford corresponding quinoxaline derivatives.
2-Phenyl-3-(phenylethynyl)quinoxalne (3aa): Yellow
solid, m.p.: 109-111 °C. 1H NMR (500 MHz, CDCl3): δ 8.15-
8.05 (m, 4H), 7.76-7.72 (m, 2H), 7.60-7.53 (m, 3H), 7.51-
7.47 (m, 2H), 7.39-7.25 (m, 3H). 13C NMR (125 MHz, CDCl3):
δ 155.06, 140.97, 140.68, 138.04, 137.61, 132.08, 130.63,
130.25, 129.66, 129.56, 129.27, 128.72, 128.41, 128.12,
121.66, 95.04, 88.33. MS: m/z = 307 [M+H+].

3922 Liang et al.
Asian J. Chem.
2-(p-Tolyl)-3-(p-tolylethynyl)quinoxaline (3ba): Yellow
129.85, 129.22, 128.70, 128.56, 97.22, 78.90, 77.25, 77.00,
76.75, 38.34, 29.69, 21.97, 21.78, 21.69, 14.08, 13.64. MS:
m/z = 239 [M+H+].Anal calcd for C16H18N2: C, 80.63; H, 7.61;
N, 11.76. Found: C, 80.80; H, 7.40; N, 11.80.
solid, m.p.: 112-114 °C. 1H NMR (500 MHz, CDCl3): δ 8.12-
8.10 (m, 2H), 8.05 (d, J = 8.1 Hz, 2H), 7.74-7.72 (m, 2H),
7.42 (d, J = 8.4 Hz, 2H), 7.37 (d, J = 7.5 Hz, 2H),7.17 (d, J =
7.5 Hz, 2H), 2.48 (s, 3H), 2.37 (s, 3H). 13C NMR (125 MHz,
CDCl3): δ 154.9, 140.9, 140.7, 139.93, 139.78, 138.2, 134.9,
132.0, 130.4, 129.98, 129.65, 129.2, 128.8, 128.68, 127.4,
118.8, 95.3, 88.2, 21.60, 21.44. MS: m/z = 335 [M+H+]
2-(4-Ethylphenyl)-3-[(4-ethylphenyl)ethynyl]quino-
xaline (3ca): Yellow solid, m.p.: 113-115 °C. 1H NMR (500
MHz,CDCl3): δ 8.15-8.09 (m, 2H), 8.06 (d, J = 8.0 Hz, 2H),
7.75 (dd, J = 6.2, 3.2 Hz, 2H), 7.44 (d, J = 8.0 Hz, 2H), 7.39
(d, J = 7.9 Hz, 2H), 7.19 (d, J = 7.8 Hz, 2H), 2.78 (q, J = 7.5
Hz, 2H), 2.66 (q, J = 7.6 Hz, 2H), 1.32 (t, J = 7.6 Hz, 3H),
1.24 (t, J = 7.6 Hz, 3H). 13C NMR (125 MHz, CDCl3): δ 155.0,
146.2, 146.1, 140.9, 140.7, 138.3, 135.1, 132.1, 130.4, 129.9,
129.7, 129.2, 128.7, 128.0, 127.6, 119.0, 95.4, 88.2, 28.9, 28.8,
15.6, 15.0. MS: m/z = 363 [M+H+]. Anal calcd for C26H22N2:
C, 86.15; H, 6.12; N, 7.73. Found: C, 86.37; H, 6.01; N, 7.62.
2-(4-Methoxyphenyl)-3-[(4-methoxyphenyl)ethynyl]-
quinoxaline (3da):Yellow solid, m.p.: 124-126 °C. 1H NMR
(500 MHz, CDCl3): δ 8.13-8.05 (m, 4H), 7.73 (td, J = 1.8 Hz,
6.0 Hz, 2H), 7.49-7.47 (m, 2H), 7.09-7.06 (m, 2H), 6.89-6.86
(m, 2H), 3.91 (s, 3H), 3.82 (s, 3H). 13C NMR (125 MHz,
CDCl3): δ 160.90, 160.65, 154.2, 140.7, 138.1, 133.7, 131.2,
130.33, 130.08, 129.87, 129.06, 128.5, 114.1, 113.6, 95.5,
87.8, 55.40, 55.31. MS: m/z = 367 [M+H+].
2-Hexyl-3-(oct-1-yn-1-yl) quinoxaline (3ja): Colourless
1
oil. H NMR (500 MHz, CDCl3): δ 8.05-7.95 (m, 2H), 7.68
(m, 2H), 3.20-3.10 (t, J = 5.0 Hz, 2H), 2.56 (t, J = 7.1 Hz, 2H),
1.85 (m, 2H), 1.76-1.59 (m, 2H), 1.56-1.41 (m, 4H), 1.41-
1.29 (m, 8H), 0.91 (t, J = 5.0 Hz, 3H), 0.90 (t, J = 6.7 Hz, 3H).
13C NMR (125 MHz, CDCl3): δ 158.9, 140.9, 140.7, 140.1,
130.0, 129.3, 128.8, 128.6, 97.6, 78.9, 36.6, 31.8, 31.5, 29.8,
29.5, 28.9, 28.8, 28.4, 22.70, 22.69, 19.9, 14.2. MS: m/z =
323 [M+H+].
2-(Butyl)-3-(hex-1-yn-1-yl)quinoxaline (3ka): Colour-
less oil, 1H NMR (500 MHz, CDCl3): δ 8.00 (m, 2H), 7.68 (m,
2H), 3.14 (t, J = 7.5 Hz, 2H), 2.57 (t, J = 7.2 Hz, 2H), 1.90-
1.80 (m, 2H), 1.74-1.64 (m, 2H), 1.60-1.43 (m, 4H), 1.02-
0.95(m, 6H); 13C NMR (125 MHz, CDCl3): δ158.7, 140.63,
140.42, 139.9, 129.79, 129.14, 128.58, 128.40, 97.2, 78.6,
36,1, 30.74, 30.19, 22.73, 22.04, 19.2, 13.84, 13.50. MS: m/z
= 267 [M+H+].
6-Chloro-2-phenyl-3-(phenylethynyl)quinoxaline
1
(3ab): White solid, m.p.: 220-225 °C. H NMR (500 MHz,
CDCl3):δ 8.13-8.09 (m, 4H), 7.71 (dd, J = 8.9, 2.2 Hz, 1H),
7.56-7.58 (m, 3H), 7.50-7.48 (m, 2H), 7.42-7.34 (m, 3H).13C
NMR (125 MHz, CDCl3):δ 155.4, 141.4, 139.40, 139.15,
137.5, 136.3, 132.4, 131.7, 130.67, 130.05, 129.96, 129.82,
128.66, 128.35, 127.7, 121.7, 96.1, 88.3. MS: m/z = 341
[M+H+].Anal calcd for C22H13ClN2: C, 77.53; H, 3.84; N, 8.22.
Found: C, 77.82; H, 3.69; N, 8.13.
2-(4-Fluorophenyl)-3-[(4-fluorophenyl)ethynyl]quino-
1
xaline (3ea): White solid, m.p.: 212-218 °C. H NMR (500
MHz, CDCl3): δ 8.12 (m, 4H), 7.79 (m, 2H), 7.49 (dd, J = 8.7,
5.4 Hz, 2H), 7.26 (d, J = 8.0 Hz, 3H), 7.07 (m, 2H). 13C NMR
(125 MHz, CDCl3):δ 164.84, 164.37, 153.9, 141.0, 140.7,
137.70, 134.20, 134.13, 133.75, 131.77, 131.71, 130.87,
130.45, 129.55, 129.27, 128.77, 116.12, 115.94, 115.33,
115.16, 94.0, 88.0. MS: m/z = 363 [M+H+].
6-Chloro-3-(p-tolyl)-2-(p-tolylethynyl)quinoxaline
(3bb1) and 6-chloro-2-(p-tolyl)-3-(p-tolylethynyl)quino-
xaline (3bb2); 3bb1:3bb2 = 1:1: Yellow solid, m.p.: 150-153
1
°C. H NMR (500 MHz, CDCl3): δ8.08-8.04 (m, 4H), 7.65
(dd, J = 2.4 Hz, 8.7 Hz, 1H), 7.41-7.33 (m, 4H), 7.17-7.14 (d,
J = 8.4 Hz, 2H), 2.47 (s, 3H), 2.36(s, 3H). 13C NMR (125
MHz, CDCl3): δ154.89, 141.03, 140.88, 140.20, 140.12,
140.03, 139.30, 139.13, 138.95, 136.14, 135.73, 134.39,
134.33, 132.07, 132.01, 131.25, 130.96, 139.36, 129.77,
129.63, 129.57, 129.22, 128.82, 128.07, 127.38, 118.50,
118.44, 96.12, 95.82, 87.91, 21.63, 21.46. MS: m/z = 369
[M+H+].
2-(4-Bromophenyl)-3-[(4-bromophenyl)ethynyl]quino-
1
xaline (3fa): White solid, m.p.: 210-217 °C. H NMR (500
MHz, CDCl3):δ 8.13 (dd, J = 6.3, 2.7 Hz, 2H), 8.00 (d, J = 8.5
Hz, 2H), 7.80 (dd, J = 6.4, 3.4 Hz, 2H), 7.70 (d, J = 8.4 Hz,
3H), 7.53 (d, J = 8.3 Hz, 3H), 7.36 (d, J = 8.4 Hz, 2H). 13C
NMR (125 MHz, CDCl3): δ 141.19, 140.84, 139.3, 136.5,
133.42, 132.39, 131.99, 131.43, 131.30, 131.04, 130.87,
130.64, 129.4, 128.9, 114.0, 94.1, 89.1. MS: m/z = 464
[M+H+]. Anal calcd for C22H12Br2N2: C, 56.93; H, 34.43; N,
6.04. Found: C, 57.25; H, 34.15; N, 6.12.
6-Methyl-2-phenyl-3-(phenylethynyl)quinoxaline
(3ac1) and 6-methyl-3-phenyl-2-(phenylethynyl)quinoxaline
(3ac2); 3ac1:3ac2 = 2.0:1: Yellow solid, m.p.: 138-142 °C.
1H NMR (500 MHz, CDCl3): δ 8.10-8.07 (m, 2H), 8.02 (d, J =
9.0 Hz, 1H), 7.89 (s, 1H), 7.57-7.53(m, 4H), 7.49-7.46 (m,
2H), 7.35-7.72 (m, 3H), 2.59 (S, 3H). 13C NMR (125 MHz,
CDCl3): δ 154.5, 141.67, 141.30, 141.11, 139.4, 138.10,
138.02,133.2, 132.8, 132.30, 132.26, 130.64, 130.23, 129.88,
129.80, 129.72, 129.45, 129.0, 128.88, 128.64, 128.49,128.38,
128.32, 127.7, 122.1, 95.0, 88.7, 22.19, 22.13. MS: m/z = 321
[M+H+].
2-(Thiophen-2-yl)-3-(thiophen-2-ylethynyl)quino-
xaline (3ha): Yellow solid,m.p.: 94-96 °C. 1H NMR (500 MHz,
CDCl3): δ 8.43 (d, J = 1.8 Hz, 1H), 8.08-8.04 (m, 2H), 8.01
(d, J = 4.2 Hz, 1H), 7.73-7.69 (m, 3H), 7.44 (dd, J = 3.0 Hz, J
= 5.4 Hz, 1H), 7.32 (dd, J = 3.0 Hz, 4.8 Hz, 1H), 7.27(d, J =
5.1 Hz, 1H); 13C NMR (125 MHz, CDCl3): δ 149.33, 140.59,
138.93, 137.13, 131.28, 130.55, 129.96, 129.63, 129.03,
128.81, 128.58, 127.93, 125.87, 125.21,120.78, 90.32, 88.37.
2-(Pent-1-yn-1-yl)-3-propylquinoxaline (3ia): Colour-
RESULTS AND DISCUSSION
1
less oil. H NMR (500 MHz, CDCl3):δ 8.04-7.97 (m, 2H),
To identify the optimal conditions for the reactions, a series
of catalysts and solvents were screened (Table-1). Initially,
the reaction conditions were optimized starting from alkyne
(1a) and o-phenylendiamine (2a) in PhCl at 70 °C with CuCl
7.73-7.64 (m, 2H), 3.15 (dd, J = 8.6, 6.9 Hz, 2H), 2.55 (t, J =
7.0 Hz, 2H), 1.91 (dd, J = 15.2, 7.6 Hz, 2H), 1.74 (dd, J =
14.5, 7.2 Hz, 2H), 1.12 (t, J = 7.4 Hz, 3H), 1.07 (t, J = 7.4 Hz,
3H). 13C NMR (125 MHz, CDCl3): δ 158.55, 140.78, 140.03,

Vol. 27, No. 11 (2015)
Synthesis of Quinoxalines via CuX Catalyzed Cyclotrimerization of Alkynes 3923
Cl1
TABLE-1
C22
C21
OPTIMIZATION OF QUINOXALINE
C6
C1
DERIVATIVES FORMATIONa
N2
C17
C5
C16
C15
C20
C8
NH2
NH2
N
N
Catalyst
Solvent
C2
+
C19
C18
C4
C3
C7
N1
2a
1a
3aa
C14
C9
C10
Entry
1
Catalyst
Solvent
PhCl
PhCl
PhCl
PhCl
PhCl
PhCl
PhCl
PhCl
PhCl
PhCl
PhCl
THF
Yield (%)b
82
CuCl (5 mol %)
CuCl (10 mol %)
CuCl (20 mol %)
ZnCl2 (10 mol %)
FeCl3 (10 mol %)
BiCl3 (10 mol %)
CuSO4 (10 mol %)
Cu(OTf)2 (10 mol %)
CuCl2 (10 mol %)
CuBr (10 mol %)
CuI (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
CuCl (10 mol %)
C13
C12
2
3
4
5
6
7
8
9
90
91
NR
NR
NR
45
56
78
89
88
20
40
89
87
33
37
NR
NR
C11
Fig. 1. X-ray Crystal structure of quinoxaline 3aa. The thermal ellipsoids
are at the 50 % probability level
With the optimized reaction conditions in hands, we
started to investigate the scope and limitation of this reaction
and the results are summarized in Table-2. To our delight,
aromatic alkynes bearing both electron-rich and electron-poor
moieties gave the corresponding quinoxaline derivatives in
good to excellent yields. Substrates possessing electron-
donating groups at the aromatic alkyne ring reacted smoothly
and afforded the desired products in moderate yields (Table-
2, entries 2-4). Other alkynes possessing electron-withdrawing
groups at the benzene ring, such as fluoro and bromo also
reacted smoothly, providing substituted quinoxaline derivatives
in higher yields (Table-2, entries 5 and 6). This reaction was
not limited to aromatic alkynes; aliphatic alkynes were also
tested and it turned out that they could react smoothly with o-
phenylendiamines 2 to give quinoxalines (Table-2, entries 9-
11). Additionally, alkynes bearing a heterocyclic aromatic
substituent such as 2-ethynylthiophene was found to afford
10
11
12c
13
14
15c
16
17
18
19
Toulene
ClCH2CH2Cl
CH2Cl2
H2O
–
DMSO
CH3NO2
aReaction conditions: 1a (1 mmol), 2a (2.5 mmol) and catalyst in PhCl
b
(2 mL) at 70 °C. Isolated yield of pure product based on alkyne 1a.
cThe reaction was carried in sealed tube.
(5 mol %) and the desired quinoxaline derivative (3aa) was
isolated in 82 % yield (Table-1, entry 1). The yield of 3aa was
increased to 90 % when the amount of CuCl was increased to
10 mol % (Table-1, entry 2). However, no further improvement
in the yield of 3aa could be achieved, when the amount of
CuCl was increased up to 20 mol % (Table-1, entry 3).The
crystallization of quinoxaline 3aa from anhydrous ethanol gave
single crystals suitable for X-ray analysis. Fig. 1 illustrates
the molecular structure of quinoxaline 3aa. CuSO4,Cu(OTf)2
and CuCl2 were also effective, albeit affording the products
with diminished yields (Table-1, entries 7-9). It is noted that
the CuBr and CuI also smoothly promoted the reactions in
excellent yields (Table-1, entries 10 and 11). Other Lewis acid
catalysts, such as ZnCl2, FeCl3 and BiCl3 did not promote the
reaction (Table-1, entries 4-6). In addition, it was found that
the solvent played a crucial role in this reaction (Table-1, entries
1 and 12-19). The reactions were obviously restrained when
they were performed in tetrahydrofuran or toluene (Table-1,
entries 12 and 13). Further inspection of the reaction conditions
revealed that this reaction also proceeded efficiently in solvents
such as ClCH2CH2Cl, CH2Cl2 (Table-1, entries 14 and 15),
whereas DMSO and CH3NO2 were found to be unfavourable
(Table-1, entries 18 and 19). Furthermore, H2O as solvent was
also able to facilitate the reaction and the reaction could be
carried out under solvent-free conditions (Table-1, entries 16
and 17). On the basis of the above experiments, the optimized
reaction conditions were summarized as follows: CuCl (10
mol %) in chlorobenzene as solvent.
TABLE-2
SYNTHESIS OF QUINOXALINE DERIVATIVES FROM
ALKYNES 1 AND o-PHENYLENEDIAMINES 2a
R1
NH2
NH2
N
N
CuCl ( 10 mol%)
PhCl, 70 oC
R1
R2
+
R2
R1
1
2
3
Time Yield
(h)
7
8
8
12
5
Entry
Alkyne
R1=C6H4
R1=4-CH3C6H4
Diamine
Product
(%)b
90
81
78
68
95
93
Trace
58
57
88
56
71
65
NR
91
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
R2=H
R2=H
3aa
3ba
3ca
3da
3ea
3fa
3ga
3ha
3ia
R1=-CH2CH3 C6H4 R2=H
R1=4-OCH3C6H4
R1=4-FC6H4
R1=4-BrC6H4
R1=TMS
R2=H
R2=H
R2=H
5
R2=H
24
12
8
7
7
7
7
24
7
R1=Thienyl
R1=C3H7
R2=H
R2=H
R1=C6H13
R2=H
3ja
R1=C4H9
R2=H
3ka
3ab
3bb
NR
3ac
R1=C6H4
R2=4-Cl
R2=4-Cl
R2=4-NO2
R2=4-CH3
R1=4-CH3C6H4
R1=C6H4
R1=C6H4
aReaction conditions: 1 (1 mmol), 2 (2.5 mmol) and CuCl (10 mol %)
in PhCl (2 mL) at 70 °C.
bIsolated yield of pure product based on alkyne 1.

3924 Liang et al.
Asian J. Chem.
NH2
NH2
R2
H2
N
Cu
H
2
R1
Cu+
R1
R2
R1
- H+
N
H
Cu+
A
1
R1
H
N
H
R1
N
R1
Cu+
- H+
-CuOH
O2
R2
R2
Ph
Cu
N
H
C
N
H
B
H
H
H
N
R1
N
N
R1
-CuOH
O2
Air
R2
R2
N
H
R1
R1
D
3
Scheme-I: Proposed mechanism
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the desired product 3ha in moderate yield (Table-2, entry 8).
Next, the reaction scope of o-phenylenediamine was studied
(Table-2, entries 12-15). Obviously, electron-rich o-phenylene-
diamine provided the desired products in higher yields than
electron-poor o-phenylenediamine (Table-2, entry 15 vs. entries
12-14).
On the basis of previous work21-23, our postulated reaction
pathways are summarized in Scheme-I. The proposed initiated
complex A would lose H+ and Cu+ to give B. Subsequently, a
second equivalent of alkyne was attacked by B to form C.
After the losing another H+ and Cu+, a precursor of quinoxaline
D was obtained. Next, D could be easily aromatized to the
target compound quinoxaline 3 by air.
Conclusion
In summary, we have developed an effective CuX (X =
Cl, Br, I)-catalyzed cycloisomerization reaction of alkynes with
o-phenylendiamines to synthesize the quinoxaline derivatives.
A wide range of alkynes, bearing not only aryl groups but
also alkyl groups, effectively participated in the reactions and
the reaction conditions were relatively mild.
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ACKNOWLEDGEMENTS
This work was supported by the National Natural Science
Foundation of China (No. 41206077).
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