An efficient synthesis of 2-trifluoromethyl quinolines via gold-catalyzed cyclization of trifluoromethylated propargylamines

Article abstract of DOI:10.1016/j.jfluchem.2011.11.002

A highly efficient cyclization reaction of trifluoromethylated propargylamines leading to 2-trifluoromethyl-4-aryl quinolines was developed by using gold(I) as a catalyst under extremely mild conditions.

Full text of DOI:10.1016/j.jfluchem.2011.11.002

Journal of Fluorine Chemistry 135 (2012) 195–199
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Journal of Fluorine Chemistry
journal homepage: www.elsevier.com/locate/fluor
An efficient synthesis of 2-trifluoromethyl quinolines via gold-catalyzed
cyclization of trifluoromethylated propargylamines
b
a
a
a
Mei Zhu a, Weijun Fu a, , Guanglong Zou , Chen Xun , Dongsheng Deng , Baoming Ji
*
a College of Chemistry and Chemical Engineering, Luoyang Normal University, Luoyang 471022, PR China
b School of Chemistry and Environmental Science, Guizhou University for Nationalities, Guiyang 550025, PR China
A R T I C L E I N F O
A B S T R A C T
highly efficient cyclization reaction of trifluoromethylated propargylamines leading to 2-
Article history:
A
Received 5 October 2011
trifluoromethyl-4-aryl quinolines was developed by using gold(I) as a catalyst under extremely mild
Received in revised form 30 October 2011
Accepted 8 November 2011
Available online 28 November 2011
conditions.
ß 2011 Elsevier B.V. All rights reserved.
Keywords:
Cyclization
Gold
Propargylamine
Quinoline
1. Introduction
coupling-cyclization N-aryl-fluorinated imidoyl iodides with termi-
nal alkynes proceeded successfully to give 2-trifluoromethylated
Quinolines are important chemicals that exhibit a wide range of
biological activities. The quinolines are found as key structural
elements in various natural products, especially in alkaloids, and
used for the construction of many synthetic compounds with
diverse pharmacological properties [1–3]. In particular, fluorine-
containing quinolines are of significant interest because fluorine
atoms enhance biological and therapeutic activities of organic
compounds, and they provide a further avenue for structural
elaboration [4–12]. Examples include antimalarial agents [13],
PDE4 inhibitors [14,15], antituberculosis agents [16,17], DPP-IV
inhibitors [18], and leishmanicidal agents [19]. As a consequence,
much attention has been paid to the synthesis of fluorinated
quinoline derivatives. The traditional methods for the introduction
of a CF3 group into aromatic systems have been fluorination of a
suitablefunctionalgroup(e.g., halogenexchangeof–CCl3, –CBr3 [20]
and fluorination of –CO2H [21]) or by Ullmann-type reaction of
perfluoroalkyl iodides and aryl halides using copper powder [22].
Recently, transition-metal-catalyzed heteroannulation reactions
have been developed with remarkable improvements in terms of
efficiency and wide scope of application. Uneyama developed an
efficient Rh(I)-catalyzed 2-trifluoromethylated quinolines forma-
tionbytandemcoupling-cyclizationreactionoftrifluoroacetimidoyl
chlorides with alkynes [23]. Wu and co-workers reported that
quinolines in the presence of copper(I) iodide catalyst [24].
Nevertheless, it is still of interest to develop efficient methods for
the synthesis of trifluoromethylated functionalized quinoline
derivatives.
The previous investigations have shown that Au(III) salts and
Au(I) complex display considerable catalytic activity under
moderate conditions [25–38]. The activation of alkynes or allenes
with carbophilic, Lewis-acidic gold salts is the most widespread
application of homogeneous gold catalysis, and it is also utilized for
the construction of carbocyclic or heterocyclic compounds [39–
49]. Recently, the design of gold-catalyzed hydroarylation of
alkynes has attracted attention because of the application to
efficient construction of molecular structures [50–52]. As a
continuation of our interest in the design and discovery of new
reactions for the synthesis of heterocycles [53–55], we envisioned
that trifluoromethyl propargylamines 1 might cyclize via hydro-
arylation of alkynes to afford 2-trifluoromethyl quinolines
(Scheme 1). In this paper, we wish to describe our results on
the synthesis of 2- trifluoromethyl quinolines starting from
propargyl amines 1 catalyzed by gold(I) under mild conditions.
2. Results and discussion
Our initial investigation focused on the reaction of 1-
trifluoromethyl-substituted propargylamine 1a as an example
for the optimization of the reaction conditions. We found that
treatment 1a with AuCl3 (5 mol%) in 1,2-dichloroethane at 80 8C
* Corresponding author. Fax: +86 379 69810261.
E-mail address: wjfu@lynu.edu.cn (W. Fu).
0022-1139/$ – see front matter ß 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jfluchem.2011.11.002

196
M. Zhu et al. / Journal of Fluorine Chemistry 135 (2012) 195–199
R1
higher reaction temperature could shorten the reaction time and
R2
N
the yield showed moderate improvement (Table 1, entry 5).
Subsequently, other catalysts were further scanned. It was found
that Cu(OTf)2 and InCl3 were active, but low yields were obtained
after long reaction times (Table 1, entries 6–7). In contrast,
employment of CuI as the catalyst, product 2a was formed in trace
amount. It was worthwhile to note that protonic acids were turned
out to be totally disfavored (Table 1, entries 9–10). Finally, the
annulation was failed when heating propargylamine 1a in toluene
at 80 8C for 24 h in the absence of any catalysts (Table 1, entry 11).
After having established the optimized conditions for the
present reaction, various trifluoromethylpropargylamine deriva-
tives 1a–m were subjected to the above conditions, and the results
are summarized in Table 2. As indicated, the cyclization reaction of
1-trifluoromethylpropargylamine derivatives 1a–m proceeded
smoothly to provide the corresponding products 2a–m in
moderate to good yields. The reaction could tolerate various
R1
HN
Ph3PAuCl, AgOTf
PhCH3, 110 oC
F3C
CF3
R2
2
1
Scheme 1. Gold(I)-catalyzed cyclization of propargyl amines.
afforded the desired product 2a in 55% yield after 24 h (Table 1,
entry 1). With this encouraging result, we first examined the
influence of the gold source on the reaction. AuCl and Ph3PAuOTf
worked well to give 2a in 63% and 77% yield, respectively (Table 1,
entries 2–3). Reaction with Ph3PAuOTf as catalyst gave better
results. Significantly, we found that using toluene as the solvent at
Table 1
a
Optimization of the reaction conditions
OCH3
Ph
catalyst
H3CO
HN
5 mol%
conditions
N
CF3
F3C
Ph
1a
2a
Entry
Catalyst
Solvent
Temp. (8C)
Time (h)
Yield (%)b
1
AuCl3
DCE
80
80
24
24
24
24
18
36
36
36
10
24
24
55
63
2
AuCl
DCE
3
Ph3PAuOTf
Ph3PAuOTf
Ph3PAuOTf
Cu(OTf)2
InCl3
DCE
80
77
4
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
80
76
5
110
110
110
110
110
110
110
90
6
65
7
70
8
CuI
Trace
NR
NR
NR
9c
10
11
TfOH
TsOH
No catalyst
a
Reaction conditions:1a (0.5 mmol), catalyst (5 mol%), solvent (5.0 mL) and the reactions were carried out at various temperatures.
b
c
Isolated yield.
A complex mixture was obtained.
R1
R1
R1
Ph3PAu
HN
HN
HN
F3C
F3C
F3C
R2
R2
LAu
AuL
R2
1
A
Ph3PAu
R1
R2
N
O
R1
N
CF3
F3C
R2
B
2
Scheme 2. Possible mechanisms of the Au-catalyzed transformation.

M. Zhu et al. / Journal of Fluorine Chemistry 135 (2012) 195–199
197
Table 2
Synthesis of 2-trifluoromethyl quinolines.a
Entry
Propargyl amines
Product
Yield (%)b
Ph
N
R1
R1
HN
CF3
F3C
Ph
1
2
3
4
5
6
R1 = OCH3
R1 = CH3
R1 = H
R1 = OCH3
R1 = CH3
R1 = H
2a, 90
2b, 91
2c, 88
2d, 82
2e, 74
2f, 69
R1 = Cl
R1 = Cl
R1 = F
R1 = F
R1 = CF3
R1 = CF3
R2
OCH3
H3CO
HN
N
CF3
F3C
R2
7
R2 = 4-CH3OC6H4
R2 = 4-CH3C6H4
R2 = 4-ClC6H4
R2 = 4-CH3OC6H4
R2 = 4-CH3C6H4
R2 = 4-ClC6H4
2g, 88
2h, 92
2i, 81
2j, 75
2k, 90
2l, 89
8
9
10
11
12
R2 = 4-FC6H4
R2 = 4-FC6H4
R2 = 3-CH3OC6H4
R2 = 3-CH3OC6H4
OCH3
S
HN
H3CO
F3C
S
N
CF3
13
2m, 83
OCH3
HN
H3CO
F3C
N
CF3
a
Reaction conditions:1 (0.5 mmol), Ph3PAuCl/AgOTf (5 mol%), toluene (5.0 mL), at 110 8C.
Isolated yield.
b
substituents on the aromatic groups. Generally, electron-donating
Au(I) species first coordinates to the triple bond to generate an
intermediate A, which then undergoes an intramolecular nucleo-
philic attack by the N-substituted aromatic ring to give dihy-
droquinoline intermediate B and regenerates the Au(I) catalyst.
Subsequent oxidation of the dihydroquinoline intermediate B by
air O2 produces the corresponding quinoline.
substituent on the benzene ring such as methoxy (Table 2, entry 1)
and methyl (Table 2, entry 2) proceeded well. On the other hand,
electron-withdrawing aryl groups including chloro, fluoro and
trifluoromethyl (Table 2, entries 4–6) would reduce the yield.
Subsequently, the scope of alkynes in this reaction was further
investigated, and it was found that substituted phenylacetylenes
with electron-donating or electron-withdrawing groups were
perfectly suitable substrates for this transformation, and the
expected products were obtained in moderate to excellent yields
(Table 2, entries 7–11). Interestingly, substrates like 1l–m with
heteroaromatic alkyne or bulky naphthylacetylene also gave the
corresponding cyclization compounds 2l–m in good yields.
Based on the experimental results above and together with our
previous work [54], a mechanism for the formation of the
quinoline derivatives is proposed in Scheme 2. Initially, a cationic
3. Conclusion
In conclusion, we have developed a gold-catalyzed cyclization
reaction of trifluoromethylated propargylamines that provides an
efficient route to 2-trifluoromethyl-4-aryl quinolines under mild
conditions. The substrates can be readily prepared from the
corresponding imidoyl iodide and alkynes [56]. Further studies,
including the reaction mechanism and synthetic application of this
methodology, are in progress.

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M. Zhu et al. / Journal of Fluorine Chemistry 135 (2012) 195–199
4. Experimental
4.1. General
J = 35.2 Hz, J = 3.0 Hz), 144.6, 135.9, 133.0 (d, J = 9.8 Hz), 129.5,
129.3, 128.5 (d, J = 10.1 Hz), 121.6 (q, J = 275.8 Hz), 120.0 (d,
J = 25.7 Hz), 117.3, 109.5 (d, J = 23.5 Hz); MS (EI) m/z 291 (M+);
Anal. Calcd. For C16H9F4N: (%) C, 65.98; H, 3.11; N, 4.81. Found: C,
65.18; H, 3.26; N, 4.81.
Chemicals used were obtained from commercial suppliers and
used without further purifications. Trifluoromethylated propargy-
lamines 1a–n were prepared as described previously [57]. 1H NMR
spectra and 13C NMR spectra were measured in CDCl3 and recorded
on Bruker Avance-400 spectrometer (400 MHz for 1H NMR,
100 MHz for 13C NMR) with TMS as an internal standard. EIMS
were determined with a HP5989B mass spectrometer. Elemental
analyses were performed on an EA-1110 instrument. Melting
points were measured on a Melt-Temp apparatus and uncorrected.
4.2.6. 2,6-bis(trifluoromethyl)-4-phenylquinoline (2f)
White solid, mp 94–95 8C; 1H NMR (400 MHz, CDCl3)
d
8.40 (d,
J = 8.8 Hz, 1H), 8.32 (s, 1H), 8.05 (dd, J = 8.8 Hz, J = 2.0 Hz, 1H), 7.78
(s, 1H), 7.60–7.51 (m, 5H); 13C NMR (100 MHz, CDCl3):
152.5,
d
149.7 (q, J = 35.5 Hz), 148.6, 136.0, 131.9, 130.2 (q, J = 33.2 Hz),
129.5, 129.4, 129.2, 126.5, 126.2 (d, J = 3.0 Hz), 123.8 (q, J = 4.7 Hz),
123.5 (d, J = 274.5 Hz), 121.5 (q, J = 276.0 Hz), 117.9; MS (EI) m/z
341 (M+); Anal. Calcd. For C17H9F6N: (%) C, 59.83; H, 2.66; N, 4.10.
Found: C, 59.80; H, 2.41; N, 4.25.
4.2. Typical procedure for synthesis of 2-trifluoromethyl-4-aryl
quinolines
4.2.7. 2-(trifluoromethyl)-6-methoxy-4-(4-
methoxyphenyl)quinoline(2g)
A solution of trifluoromethylated propargylamine 1 (0.5 mmol)
in dry toluene was added to a solution of Ph3AuOTf (generated by
mixing equal equivalents of Ph3PAuCl and AgOTf, 5 mol% in
toluene). The mixture was then stirred at 110 8C until the substrate
had been consumed completely, cooled to room temperature and
filtered through a short silica gel column using CH2Cl2 as eluent.
After evaporation of the solvent, the residue was purified by SiO2
gel column chromatography to give the corresponding product 2.
White solid, mp 60–62 8C; 1H NMR (400 MHz, CDCl3):
d 8.14 (d,
J = 9.2 Hz, 1H), 7.60 (s, 1H), 7.46–7.42 (m, 2H), 7.41 (dd, J = 9.2,
J = 2.8 Hz, 1H), 7.24 (d, J = 2.8 Hz, 1H), 7.06–7.00 (m, 2H), 3.86 (s,
3H), 3.79 (s, 3H); 13C NMR (100 MHz, CDCl3):
d 160.3, 159.3, 148.7,
144.8 (q, J = 35.2 Hz), 143.7, 131.8, 130.3, 129.4, 128.8, 123.2, 121.8
(q, J = 275.0 Hz), 117.1, 114.3, 103.3, 55.4, 55.3; MS (EI) m/z 333
(M+); Anal. Calcd. For C18H14F3NO2: (%) C, 64.86; H, 4.23; N, 4.20.
Found: C, 64.95; H, 4.48; N, 4.06.
4.2.1. 2-(trifluoromethyl)-6-methoxy-4-phenylquinoline (2a)
White solid, mp 68–70 8C. 1H NMR (400 MHz, CDCl3):
J = 9.2 Hz, 1H), 7.61 (s, 1H), 7.50–7.56 (m, 5H), 7.45 (dd, J = 9.2,
2.8 Hz, 1H), 7.21 (d, J = 2.8 Hz, 1H), 3.78 (s, 3H); 13C NMR (100 MHz,
d
8.16 (d,
4.2.8. 2-(trifluoromethyl)-6-methoxy-4-p-tolylquinoline (2h)
White solid, mp 138–140 8C; 1H NMR (400 MHz, CDCl3):
d
8.15
(d, J = 9.2 Hz, 1H), 7.61 (s, 1H), 7.45–7.32 (m, 5H), 7.25 (d, J = 2.8 Hz,
1H), 3.82 (s, 3H), 2.47 (s, 3H); 13C NMR (100 MHz, CDCl3):
159.4,
CDCl3):
d
159.4, 148.8, 145.0 (q, J = 35.7 Hz), 143.6, 137.5, 131.9,
d
129.3, 128.9, 128.8, 128.6, 123.4, 121.7 (q, J = 276 Hz), 117.4, 103.4,
55.4; MS (EI) m/z 303 (M+); Anal. Calcd for C17H12F3NO: (%) C,
67.32; H,3.99; N, 4.62. Found: C, 67.48; H, 3.82; N, 4.68.
149.1, 145.0 (q, J = 35.0 Hz), 138.8, 134.5, 131.8, 129.6, 129.1,
128.8, 125.9, 123.3, 121.8 (q, J = 275.2 Hz), 117.2, 103.3, 55.3, 21.5;
MS (EI) m/z: 317 (M+); Anal. Calcd. For C18H14F3NO: (%) C, 68.13; H,
4.45; N, 4.41. Found: C, 68.25; H, 4.28; N, 4.53.
4.2.2. 2-(trifluoromethyl)-6-methyl-4-phenylquinoline (2b)
White solid, mp 37–39 8C; 1H NMR (400 MHz, CDCl3):
d
8.16 (d,
J = 8.8 Hz, 1H), 7.69 (s, 1H), 7.75–7.62 (m, 2H), 7.58–7.51 (m, 5H),
2.51 (s, 3H); 13C NMR (100 MHz, CDCl3):
150.2, 146.5 (q,
4.2.9. 4-(4-chlorophenyl)-2-(trifluoromethyl)-6-methoxyquinoline
(2i)
d
White solid, mp 100–101 8C; 1H NMR (400 MHz, CDCl3):
d
8.19
(d, J = 9.2 Hz, 1H), 7.59 (s, 1H), 7.57–7.47 (m, 5H), 7.16 (d, J = 2.8 Hz,
1H), 3.83(s, 3H); 13C NMR (100 MHz, CDCl3):
159.6, 147.7, 145.1
J = 35.1 Hz), 146.3, 139.1, 137.0, 132.8, 130.1, 129.4, 128.9, 128.8,
127.6, 124.1, 121.8 (q, J = 275.4 Hz), 117.2, 21.9; MS (EI) m/z 287
(M+); Anal. Calcd. For C17H12F3N: (%) C, 71.07; H, 4.21; N, 4.88.
Found: C, 71.20; H, 4.50; N, 4.81.
d
(q, J = 34.2 Hz), 143.8, 135.7, 135.1, 131.8, 130.2, 129.0, 128.4,
123.5, 121.7 (q, J = 275.5 Hz), 117.2, 103.0, 55.5; MS (EI) m/z 337
(M+); Anal. Calcd. For C17H11ClF3NO: (%) C, 60.46; H, 3.28; N, 4.15.
Found: C, 60.58; H, 3.12; N, 4.07.
4.2.3. 2-(trifluoromethyl)-4-phenylquinoline (2c)
White solid, mp 60–61 8C; 1H NMR (400 MHz, CDCl3):
d
8.30 (d,
J = 8.4 Hz, 1H), 8.03 (d, J = 8.4 Hz, 1H), 7.71 (s, 1H), 7.69–7.60 (m,
1H), 7.58–7.50 (m, 6H); 13C NMR (100 MHz, CDCl3):
151.5, 148.1,
4.2.10. 2-(trifluoromethyl)-4-(4-fluorophenyl)-6-methoxyquinoline
(2j)
d
147.5 (q, J = 34.8 Hz), 137.7, 131.2, 130.8, 129.9, 129.5, 129.2,
129.1, 127.8, 126.4, 122.0 (q, J = 275.5 Hz), 117.3; MS (EI) m/z 273
(M+); Anal. Calcd for C16H10F3N: (%) C, 70.33; H, 3.69; N, 5.13.
Found: C, 70.21; H, 3.87; N, 4.93.
White solid, mp 100–102 8C; 1H NMR (400 MHz, CDCl3):
d 8.15
(d, J = 9.2 Hz, 1H), 7.59 (s, 1H), 7.55–7.48 (m, 2H), 7.42 (dd, J = 9.2,
2.8 Hz, 1H), 7.15 (d, J = 2.8 Hz, 1H), 7.28–7.21 (m, 2H), 3.81 (s, 3H);
13C NMR (100 MHz, CDCl3):
d 163.1 (d, J = 250.1 Hz), 159.3, 147.8,
144.9 (q, J = 35.0 Hz), 144.0, 133.2 (d, J = 3.2 Hz), 132.1, 130.9 (d,
J = 8.6 Hz), 128.8, 123.3, 121.7 (q, J = 274.9 Hz), 117.3, 115.9 (d,
J = 21.9 Hz), 103.3, 55.5; MS (EI) m/z 321 (M+); Anal. Calcd. For
4.2.4. 6-chloro-2-(trifluoromethyl)-4-phenylquinoline (2d)
White solid, mp 85–87 8C; 1HNMR (400 MHz, CDCl3):
d
8.18 (d,
J = 9.2 Hz, 1H), 7.90 (d, J = 2.1 Hz, 1H), 7.77–7.71 (m, 2H), 7.59–7.54
(m, 3H), 7.52–7.47 (m, 2H); 13C NMR (100 MHz, CDCl3):
150.2,
C17H11F4NO: (%) C, 63.55; H, 3.45; N, 4.36. Found: C, 63.32; H, 3.57;
d
N, 4.28.
147.5 (q, J = 34.7 Hz), 146.0, 136.4, 135.1, 132.3, 131.5, 129.4,
129.3, 128.9, 128.1, 124.7, 121.5 (q, J = 275.5 Hz), 117.5; MS (EI) m/
z 307 (M+); Anal. Calcd. For C16H9ClF3N: (%) C, 62.45; H, 2.95; N,
4.55. Found: C, 62.27; H, 3.16; N, 4.59.
4.2.11. 2-(trifluoromethyl)-6-methoxy-4-(3-
methoxyphenyl)quinoline (2k)
White solid, mp 58–59 8C; 1H NMR (400 MHz, CDCl3):
d 8.18 (d,
J = 9.2 Hz, 1H), 7.62 (s, 1H), 7.51–7.44 (m, 2H), 7.27–7.25 (m, 1H),
4.2.5. 6-fluoro-2-(trifluoromethyl)-4-phenylquinoline (2e)
7.10–7.00 (m, 3H), 3.88 (s, 3H), 3.83 (s, 3H); 13C NMR (100 MHz,
CDCl3): d 163.1 (d, J = 249.8 Hz), 159.8, 159.8, 148.5, 145.0 (q,
J = 35.0 Hz), 138.8, 131.6, 129.5, 128.6, 123.4, 121.7 (q,
J = 275.0 Hz), 121.4, 117.3, 114.8, 114.4, 103.2, 55.5, 55.3; MS
White solid, mp 93–95 8C; 1H NMR (400 MHz, CDCl3):
d
8.27–
8.23 (m, 1H), 7.71 (s, 1H), 7.59–7.45 (m, 7H); 13C NMR (100 MHz,
CDCl3): 161.7 (d, J = 250.9 Hz), 150.4 (d, J = 6.0 Hz), 147.6 (qd,
d

M. Zhu et al. / Journal of Fluorine Chemistry 135 (2012) 195–199
199
(EI) m/z 333 (M+); Anal. Calcd. For C18H14F3NO2: (%) C, 64.86; H,
4.23; N, 4.20. Found: C, 64.57; H, 4.39; N, 4.28.
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4.2.12. 2-(trifluoromethyl)-6-methoxy-4-(thiophen-2-yl)quinoline
(2l)
White solid, mp 95–96 8C; 1H NMR (400 MHz, CDCl3):
d 8.10 (d,
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J = 9.2 Hz, 1H), 7.71 (s, 1H), 7.57 (d, J = 2.8 Hz, 1H), 7.54 (d,
J = 5.2 Hz, 1H), 7.42–7.35 (m, 2H), 7.25–7.20 (m, 2H), 3.85 (s, 3H);
13C NMR (100 MHz, CDCl3):
d 159.9, 145.0 (q, J = 34.7 Hz), 144.0,
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141.1, 138.3, 131.7, 128.7, 128.4, 128.2, 127.9, 123.4, 121.8 (q,
J = 275.5 Hz), 117.6, 103.2, 55.4; MS (EI) m/z 309 (M+); Anal. Calcd.
For C15H10F3NOS: (%) C, 58.25; H, 3.26; N, 4.53. Found: C, 58.47; H,
3.58; N, 4.42.
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White solid, mp 88–90 8C; 1H NMR (400 MHz, CDCl3):
d 8.19 (d,
J = 9.2 Hz, 1H), 8.03–7.89 (m, 4H),7.69 (s, 1H), 7.65–7.55 (m, 3H),
7.47 (dd, J = 9.2 Hz, 2.8 Hz, 1H), 7.25 (d, J = 2.4 Hz, 1H), 3.80 (s, 3H);
13C NMR (100 MHz, CDCl3):
d 159.3, 149.0, 145.3 (q, J = 34.2 Hz),
143.8, 135.1, 133.3, 133.2, 131.9, 128.7, 128.5, 128.4, 128.1, 127.8,
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55.5; MS (EI) m/z 309 (M+); Anal. Calcd. For C21H14F3NO: (%) C,
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Acknowledgments
We are grateful to the National Natural Science Foundation of
China (Project Nos. 20902042; 20902043) and Foundation of
He’nan Educational Committee (No. 2010B150020)
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