Phenyliodonium diacetate mediated direct synthesis of benzonitriles from styrenes through oxidative cleavage of C=C bonds

Article abstract of DOI:10.1021/jo401919h

A metal-free PhI(OAc)₂ mediated nitrogenation of alkenes through C=C bond cleavage using inorganic ammonia salt as nitrogen source under mild conditions was developed, affording nitriles in moderate to good yields. The advantages of this reaction are mild reaction conditions, operational simplicity, and use of an ammonium salt as nitrogen source. Based upon experimental observations, a plausible reaction mechanism is proposed.

Full text of DOI:10.1021/jo401919h

Article
pubs.acs.org/joc
Phenyliodonium Diacetate Mediated Direct Synthesis of
Benzonitriles from Styrenes through Oxidative Cleavage of CC
Bonds
Jin-Hui Xu, Qing Jiang, and Can-Cheng Guo*
College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, China
S
* Supporting Information
ABSTRACT: A metal-free PhI(OAc)2 mediated nitrogena-
tion of alkenes through CC bond cleavage using inorganic
ammonia salt as nitrogen source under mild conditions was
developed, affording nitriles in moderate to good yields. The
advantages of this reaction are mild reaction conditions,
operational simplicity, and use of an ammonium salt as
nitrogen source. Based upon experimental observations, a
plausible reaction mechanism is proposed.
method toward the synthesis of nitriles from readily available
starting materials.
INTRODUCTION
■
Carbon−carbon double bond cleavage represents a broad class
of fundamental transformations in organic chemistry.1,2 In this
regard, both well-known and representative examples are the
catalytic cleavage of CC bonds to new CC bonds (olefin
metathesis)1 and the oxidative cleavage of CC bonds to C
O bonds.2 In the past decades, olefin metathesis catalyzed by
transition-metal carbene complexes has been developed as a
powerful and straightforward synthetic approach in the
manipulation of carbon−carbon double bonds, which has an
important synthetic impact on fields ranging from materials
science3 to biochemistry4 to natural-product synthesis.5 Like-
wise, the oxidative cleavage of CC bonds is among the most
powerful and broadly applicable synthetic tools of modern
organic chemistry,2 resulting in the formation of carbonyl
compounds that widely occur in natural and synthetic bioactive
molecules.6 While successful for olefin metathesis and the
oxidative cleavage of CC bonds to CO bonds, the cleavage
of CC bonds to construct CN bonds is much under-
developed.7 In 1950, Denton et al. reported the alumina-
supported molybdic oxide catalyzed CC bond cleavage of
styrenes to produce aromatic nitriles at elevated tempareture
(524−552 °C).7a Later on, Chow presented the CC bond
cleavage of olefins to form nitriles through the combination of
photoaddition and Beckmann reaction using organic com-
pounds as nitrogen sources, which caused the formation of
organic wastes.7b More recently, significant progress was made
by Jiao with TEMPO-catalyzed CC double-bond cleavage to
produce oxo nitriles using molecular oxygen as the terminal
oxidant and TMSN3 as the nitrogen source.7c Despite these
advances, some challenges still remain in this promising field.
Therefore, it is extraordinarily important to find new methods
to broaden this area. Herein, we report a metal-free
nitrogenation reaction of alkenes through CC bond cleavage
in the presence of phenyliodonium diacetate (PIDA) and
NH4HCO3 in aqueous medium, which illustrates a convenient
Nitriles are an important class of structural motifs that
frequently occur in agrochemically useful and pharmaceutically
active compounds.8 Also, their widespread synthetic utility is
highlighted by a myriad of possible nitrile transformations,9
including the synthesis of benzoic acids/esters, amides, amines,
aldehydes, and nitrogen-containing heterocycles.10 Generally,
nitriles are prepared through the Sandmeyer reaction of
aryldiazonium salts;11 the transition-metal-mediated cyanation
of aryl halides with a cyanide source that generally is toxic;12
the dehydration approach of amines, alcohols, or oximes;13 and
other methods.14 However, these reactions suffered from the
harsh reaction conditions, multiple steps, poor functional group
tolerance, or the use of expensive and toxic reagents. Therefore,
the development of direct, mild, and environmentally benign
processes to access nitriles from basic chemical materials is
always highly desirable. To the best of our knowledge, no
examples in which nitriles were prepared from direct oxidative
CC bond cleavage of alkenes using ammonium salt as
nitrogen source under metal-free conditions have been
reported.
RESULTS AND DISCUSSION
■
Inspired by recent reports that, using PIDA as the oxidant,
alkenes can be oxidized to produce aldehydes15 and the fact
that the synthesis of nitriles from aldehydes is well documented
in the literature,16 we envisioned that nitriles could be
generated directly from alkenes in the presence of PIDA. To
test this hypothesis, we initially chose styrene in a model
reaction to test different reaction conditions. Selected data from
this study are listed in Table 1. First, when the reaction was
Received: August 29, 2013
© XXXX American Chemical Society
A
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a
temperature of NH4HCO3), 12 h (for details, see Table S1 in
the Supporting Information). However, when reaction of
phenylacetylene was carried out under the optimized
conditions, benzonitrile was obtained in only 10% yield.
With the optimized protocol in hand, we set out to explore
the scope and limitation of the reaction with respect to various
terminal alkenes (Table 2). We found that the reaction worked
Table 1. Screening of Reaction Conditions
PIDA
NH4HCO3
(equiv)
convn
b
yield
b
entry
(equiv)
solvent
CH3CN
(%)
(%)
1
1.2
0
6.0
6.0
0
37
0
15
0
2
CH3CN
CH3CN
CH3CN
CH3CN
CH3CN
CH3CN
CH3CN
CH3CN
CH3CN
CH2Cl2
dioxane
EtOH
Table 2. Transformation of Terminal Olefins 1 to Nitriles 2
3
1.2
3.0
5.0
5.5
6.5
5.5
5.5
5.5
5.5
5.5
5.5
5.5
5.5
0
0
4
6.0
6.0
6.0
6.0
5.0
3.0
10
70
96
>99
>99
98
86
>99
91
87
79
90
93
43
66
70
72
69
60
72
28
21
61
77
81
5
6
7
8
9
10
11
12
13
14
6.0
6.0
6.0
6.0
6.0
CH3OH
c
15
CH3OH/
H2O
d
16
5.5
5.5
5.5
5.5
6.0
6.0
6.0
6.0
CH3OH/
H2O
94
95
95
95
86
83
86
86
e
17
CH3OH/
H2O
f
18
CH3OH/
d
H2O
g
19
CH3OH/
d
H2O
a
Unless otherwise noted, the reaction was carried out with 1a (0.2
mmol), PIDA, NH4HCO3, and solvent (2.0 mL) at 36 °C for 12 h.
b
c
d
Determined by GC. 0.1 mL water was added. 0.5 mL water was
e
f
g
added. 1.0 mL water was added. 40 °C. 50 °C.
carried out in the presence of phenyliodonium diacetate
(PIDA) and NH4HCO3 as the nitrogen source in acetonitrile at
36 °C for 12 h, much to our delight the desired nitrile product
2a was produced in 15% yield (Table 1, entry 1). Control
experiments showed that the reaction did not proceed in the
absence of either PIDA or NH4HCO3 (Table 1, entries 2 and
3). Increasing the amount of PIDA increased the yield of 2a
and led to almost full conversion (Table 1, entries 4−7).
Decreasing the amount of NH4HCO3 resulted in a slight drop
in terms of product yield (Table 1, entries 8 and 9), while a
comparable yield (72%) was obtained when the amount of
NH4HCO3 was increased to 10 equiv (Table 1, entry 10). The
influence of the solvent was also studied. When other solvents,
such as CH2Cl2, dioxane, EtOH, and CH3OH, were applied
instead of CH3CN, better yield (77%) was obtained in CH3OH
(Table 1, entries 11−14). The addition of water led to an
increased yield (Table 1, entry 15). This promising result
encouraged us to do further optimization with regard to the
volume of water. Indeed, the best yield of 86% was obtained in
the presence of 0.5 mL of water (Table 1, entries 16 and 17). A
reaction temperature of 36 °C was selected because NH4HCO3
decomposes at this temperature and no further improvement
was seen at higher temperatures (40−50 °C) (Table 1, entries
18 and 19). In addition, this reaction was repeated five times,
and five runs were almost consistent in conversions and yields
(see Figure S1 in the Supporting Information). From these
experiments, we determined the optimized conditions to be
PIDA (5.5 equiv), NH4HCO3 (6.0 equiv), CH3OH (2 mL),
H2O (0.5 mL), 36 °C (this temperature is decomposition
a
Standard conditions: alkenes (0.2 mmol), PIDA (5.5 equiv),
NH4HCO3 (6 equiv), and CH3OH/H2O (2 mL/0.5 mL) at 36 °C
for 12 h. Isolated yield. GC yield. Determined by GC−MS.
b
c
d
very well for a wide variety of substituted styrenes, affording the
desired substituted benzonitriles in yields ranging from 65% to
93%. Styrene derivatives with electron-withdrawing substituents
afforded the desired benzonitriles in 65−88% yield (Table 2,
entries 2−7), while styrene derivatives bearing electron-
donating substituents provided the desired benzonitriles in
83−93% yield (Table 2, entries 8 −12). It is worth pointing out
that the CC bond cleavage/hydrolyzation occurred in the
B
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reaction of 1j to produce 2j in 83% yield (Table 2, entry 10).
Notably, F, Cl, Br, and MeO substituents on the phenyl ring
were well tolerated, which enables a potential application in
further functionalization.17 Additionally, a more bulky substrate,
2-vinylnaphthalene, also efficiently reacted to provide the
product in 89% yield (Table 2, entry 13). While the results of
styrenes were all favorable, the reactions of aliphatic alkenes
were almost unreactive. For instance, when 1-octene was
subjected to the same reaction conditions, only a trace amount
of the desired product was detected by GC−MS (Table 2, entry
14). To investigate the possible on- carbon product, reaction of
styrene was carried out under the optimized conditions. After
the reaction, dimethoxymethane as another product was
detected in the solvent by GC−MS (see Supporting
Information).
proceed smoothly under the standard reaction conditions, and
only trace amount of the desired product was detected by GC−
MS (Table 3, entry 8).
To gain insight into the reaction mechanism, some
information has been gathered. As shown in Scheme 1a,
Scheme 1. Control Experiments
Next, we applied our method to a range of internal alkenes
(Table 3). Various β-substituted styrenes proceeded in a
Table 3. Transformation of Internal Olefins to Nitriles
when the reaction was carried out at 0 °C, an intermediate
benzaldehyde was detected by GC and GC−MS in the initial
stage of the reaction. When the reaction temperature was
increased to 36 °C and then reacted for 12 h under this
conditions, benzaldehyde was completely consumed and
benzonitrile was obtained in 84% yield (Scheme 1a). Also,
we used NMR spectroscopy to monitor the reaction progress.
An intermediate benzaldehyde was likewise observed in the
initial stage of styrene reaction (see Supporting Information).
To further support this, when benzaldehyde was reacted under
the standard reaction condition, benzaldehyde was equally
converted to benzonitrile (Scheme 1b). From this point, the
1,1-diphenylethylene would generate the corresponding ketone
under the same reaction conditions. Unsurprisingly, the
reaction of 1,1-diphenylethylene gave benzophenone in 93%
yield (Scheme 1c). The data indicate that the reaction proceeds
via the benzaldehyde as an intermediate. In addition, the
bubbles generated during the reaction process were demon-
strated to be CO2 since it obviously could make limewater
become turbid (see Figure S2 in the Supporting Information).
On the basis of these preliminary results and related
reports,15,16,18 a possible mechanism is proposed (Scheme 2).
Initially, the alkene is oxidized to give the corresponding
aldehydes (step a). Alternatively, the alkene undergoes
dihydroxylation first to generate 1,2-diols, and its subsequent
oxidative cleavage affords aldehydes.18a Next, the condensation
of aldehyde with ammonia provides imine (step b). Finally, the
imine is further oxidized to produce the desired nitrile (step c).
However, when R2 group was hydrogen, it would be trapped by
methanol to provide dimethoxymethane (step d).
a
Standard conditions: alkenes (0.2 mmol), PIDA (5.5 equiv),
NH4HCO3 (6 equiv), and CH3OH/H2O (2 mL/0.5 mL) at 36 °C
b
c
for 12 h. GC yield. 2o, 2q, and 2v were detected by GC−MS; 2r was
CONCLUSION
d
e
■
not detected by GC−MS. Isolated yield. CH3CN/H2O (2 mL/0.5
In summary, a novel way of synthesizing nitriles from alkenes
through CC bond cleavage was developed. By treating
alkenes with NH4HCO3 in the presence of phenyliodonium
diacetate (PIDA) in aqueous medium, the alkenes were found
to proceed via the benzaldehyde as an intermediate, thus
affording a variety of nitriles in moderate to good yields. This
method features metal-free, mild reaction conditions, opera-
tional simplicity, good functional group tolerance, and use of
NH4HCO3 as nitrogen source without the use of expensive and
mL).
normal fashion to afford the desired nitriles in 13−90% yield
(Table 3, entries 1−7). The reaction of trans- and cis-stilbene
gave the same product benzonitrile in 51% and 67% yield,
respectively (Table 3, entries 5 and 6). Moreover, better yields
were obtained when 1s and 1u were used in this protocol
(Table 3, entries 5 and 7). Unfortunately, cyclohexene did not
C
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Scheme 2. Proposed Reaction Mechanism
(as shown in Scheme 1c). The reaction of 1,1-diphenylethylene was
performed according to the general procedure. After cooling to room
temperature, the reaction mixture was diluted with 20 mL ethyl
acetate, dried over Na2SO4, filtered, and concentrated under vacuum.
The crude residue was purified by column chromatography to afford
the benzophenone in 93% yield. 1H NMR (400 MHz, CDCl3) δ 7.72−
7.56 (m, 3H), 7.48 (dd, J = 7.9, 7.4 Hz, 2H). 13C NMR (101 MHz,
CDCl3) δ 196.78, 137.61, 132.44, 130.08, 128.30.
toxic organic compounds as nitrogen source while avoiding the
formation of organic wastes. From the results of the present
study and on the basis of the proposed mechanism, it should be
possible to develop novel chemical transformations through
C−C bond cleavage, which should be of interest to both
industrial and academic researchers.
EXPERIMENTAL SECTION
Benzonitrile (2a). Following the general procedure, a colorless oil
was obtained. The yield was determined by GC using bromobenzene
as internal standard. Benzonitrile was obtained from 1a, 1o, 1q−u in
86% (17.7 mg), 84% (17.3 mg), 29% (6.0 mg), 13% (2.7 mg), 51%
■
General Comments. All reagents and solvent used were obtained
commercially and used without further purification unless indicated
otherwise. Deionized water was used. PhI(OAc)2 was prepared
according to literature procedures.19 All products were characterized
by GC−MS, 1H NMR, and 13C NMR. Mass spectra were measured on
a mass instrument (EI). Analyses of the yield and conversion of
styrene were performed by gas phase chromatography, using a RTX-5
1
(10.5 mg), 67% (13.8 mg), and 72% (14.8 mg) yield, respectively. H
NMR (400 MHz, CDCl3) δ 7.70−7.58 (m, 3H), 7.48 (dd, J = 7.9, 7.4
Hz, 2H). 13C NMR (101 MHz, CDCl3) δ 132.81, 132.15, 129.15,
118.87, 112.43. LRMS: m/z calcd for C7H5N (M + H) 104, found 104.
2-Bromobenzonitrile (2b).20a Following the general procedure,
the product was isolated as a colorless solid in 65% yield (23.5 mg),
mp = 53−55 °C. 1H NMR (400 MHz, CDCl3) δ 7.69 (m, 2H), 7.50−
7.41 (m, 2H). 13C NMR (101 MHz, CDCl3) δ 134.35, 133.90, 133.23,
127.64, 125.37, 117.16, 115.92. LRMS: m/z calcd for C7H4BrN (M +
H) 183, found 183.
1
capillary column and a frame ionization detector (FID). H NMR
spectra were recorded on 400 MHz in CDCl3, and 13C NMR spectra
were recorded on 100 MHz in CDCl3 using TMS as internal standard.
Multiplicities are indicated as s (singlet), d (doublet), t (triplet), q
(quintet), and m (multiplet), and coupling constants (J) are reported
1
in hertz. Copies of H NMR and 13C NMR spectra are provided as
3-Bromobenzonitrile (2c).20b Following the general procedure,
the product was isolated as a colorless solid in 72% yield (26.1 mg),
mp = 38−40 °C. 1H NMR (400 MHz, CDCl3) δ 7.81 (s, 1H), 7.75 (d,
J = 8.1 Hz, 1H), 7.61 (d, J = 7.7 Hz, 1H), 7.37 (t, J = 8.0 Hz, 1H). 13C
NMR (101 MHz, CDCl3) δ 136.15, 134.79, 130.73, 130.63, 122.94,
117.32, 114.23. LRMS: m/z calcd for C7H4BrN (M + H) 183, found
183.
Supporting Information.
General Procedure for the Synthesis of Nitriles from
Alkenes. A 10 mL sealed tube was charged with NH4HCO3 (1.2
mmol) and CH3OH/H2O (2 mL/0.5 mL). The mixture was stirred at
room temperature until the solid was completely dissolved. Then
alkene (0.2 mmol) was added. After stirring for 2 min, PhI(OAc)2 (1.1
mmol) was added, and the reaction mixture was stirred at 36 °C for 12
h. After cooling to room temperature, the reaction mixture was diluted
by addition of 20 mL ethyl acetate, dried over Na2SO4, filtered, and
concentrated under vacuum. The crude residue was purified by
column chromatography on silica gel to afford the desired product.
Reaction of Styrenes with NH4HCO3 in the Presence of
Phenyliodonium Diacetate (PIDA) in CH3OH/H2O (as shown in
Scheme 1a). In a 10 mL sealed tube, a mixture of 0.2 mmol styrene,
1.1 mmol PhI(OAc)2, and 1.2 mmol NH4HCO3 in CH3OH/H2O(2
mL/0.5 mL) was stirred at 0 °C. After 10 min, an aliquot of sample
was taken from the reaction mixture and analyzed by GC−MS. Then
the reaction mixture was stirred at 36 °C for 12 h. The resulting
mixture was analyzed by GC (bromobenzene as internal standard in
GC analysis).
4-Bromobenzonitrile (2d).20c Following the general procedure,
the product was isolated as a colorless solid in 88% yield (32.0 mg),
1
mp = 110−112 °C. H NMR (400 MHz, CDCl3) δ 7.56 (d, J = 8.1
Hz, 2H), 7.45 (d, J = 8.0 Hz, 2H). 13C NMR (101 MHz, CDCl3) δ
133.43, 132.66, 128.04, 118.08, 111.25. LRMS: m/z calcd for
C7H4BrN (M + H) 183, found 183.
4-Chlorobenzonitrile (2e).20d Following the general procedure,
the product was isolated as a colorless solid in 82% yield (22.5 mg),
1
mp = 90−92 °C. H NMR (400 MHz, CDCl3) δ 7.54 (d, J = 8.5 Hz,
2H), 7.40 (d, J = 8.6 Hz, 2H). 13C NMR (101 MHz, CDCl3) δ 139.58,
133.40, 129.72, 117.99, 116.70, 110.80. LRMS: m/z calcd for
C7H4ClN (M + H) 139, found 139.
4-Fluorobenzonitrile (2f).20d Following the general procedure,
the product was isolated as a colorless solid in 85% yield (20.5 mg),
Reaction of Benzaldehyde with NH4HCO3 in the Presence of
Phenyliodonium Diacetate (PIDA) in CH3OH/H2O (as shown in
Scheme 1b). The reaction of benzaldehyde was performed according
to the general procedure, and the resulting mixture was analyzed by
GC (bromobenzene as internal standard in GC analysis).
Reaction of 1,1-Diphenylethylene with NH4HCO3 in the
Presence of Phenyliodonium Diacetate (PIDA) in CH3OH/H2O
1
mp = 33−35 °C. H NMR (400 MHz, CDCl3) δ 7.19 (t, J = 8.0 Hz,
2H), 7.69 (dd, J = 8.0, 4.0 Hz, 2H). 13C NMR (101 MHz, CDCl3)
δ165.05 (d, J = 256.5 Hz), 134.71 (d, J = 9.3 Hz), 118.05 (s), 116.88
(d, J = 22.7 Hz), 108.58 (d, J = 3.7 Hz). LRMS: m/z calcd for C7H4FN
(M + H) 122, found 122.
D
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4-Nitrobenzonitrile (2g).20g Following the general procedure, the
product was isolated as a colorless solid in 82% yield (24.2 mg), mp =
143−145 °C. 1H NMR (400 MHz, CDCl3) δ 7.54 (d, J = 8.5 Hz, 2H),
7.40 (d, J = 8.6 Hz, 2H). 13C NMR (101 MHz, CDCl3) δ 139.58,
133.40, 129.72, 117.99, 116.70, 110.80. LRMS: m/z calcd for
C7H4N2O2 (M + H) 149, found 149.
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4-Methylbenzonitrile (2h).20e Following the general procedure,
the product was isolated as a colorless solid in 88% yield (20.0 mg),
mp = 28−30 °C. 1H NMR (400 MHz, CDCl3) δ 7.47 (d, J = 8.2 Hz,
2H), 7.20 (d, J = 7.9 Hz, 2H), 2.35 (s, 3H). 13C NMR (101 MHz,
CDCl3) δ 143.70, 132.06, 129.85, 119.18, 109.33, 21.85. LRMS: m/z
calcd for C8H4N (M + H) 118, found 118.
4-Tert-butylbenzonitrile (2i).20f Following the general proce-
dure, the product was isolated as a colorless oil in 90% yield (28.4 mg).
1H NMR (400 MHz, CDCl3) δ 7.59 (d, J = 8.5 Hz, 2H), 7.48 (d, J =
8.5 Hz, 2H), 1.33 (s, 9H). 13C NMR (101 MHz, CDCl3) δ 156.66,
131.98, 126.18, 119.19, 109.31, 35.28, 30.96. LRMS: m/z calcd for
C11H4N (M + H) 160, found 160.
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4-Hydroxybenzonitrile (2j).20a Following the general procedure,
the product was isolated as a colorless solid in 78% yield (18.6 mg),
1
mp = 110−112 °C. H NMR (400 MHz, CDCl3) δ 7.55 (d, J = 8.5
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Hz, 2H), 6.93 (d, J = 8.5 Hz, 2H), 6.79 (s, 1H). 13C NMR (101 MHz,
CDCl3) δ 160.16, 134.33, 119.28, 116.46, 103.20. LRMS: m/z calcd
for C7H5ON (M + H) 120, found 120.
4-Methoxybenzonitrile (2k).20a Following the general proce-
dure, the product was isolated as a colorless solid from 1k, 1p, 1u in
92% (24.5 mg), 90% (23.9 mg) and 70% (18.6 mg) yield, respectively,
mp = 57−59 °C. 1H NMR (400 MHz, CDCl3) δ 7.59 (d, J = 8.9 Hz,
2H), 6.95 (d, J = 8.9 Hz, 2H), 3.86 (s, 3H). 13C NMR (101 MHz,
CDCl3) δ 162.85, 134.00, 119.26, 114.76, 103.97, 55.56. LRMS: m/z
calcd for C8H7ON (M + H) 134, found 134.
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2,4,6-Trimethylbenzonitrile (2l).20f Following the general
procedure, the product was isolated as a colorless solid in 90% yield
(25.8 mg), mp = 51−53 °C. 1H NMR (400 MHz, CDCl3) δ 6.93 (d, J
= 0.5 Hz, 2H), 2.48 (s, 6H), 2.32 (s, 3H). 13C NMR (101 MHz,
CDCl3) δ 142.78, 141.99, 128.19, 117.62, 110.48, 21.56, 20.62. LRMS:
m/z calcd for C10H11N (M + H) 146, found 146.
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2-Naphthonitrile (2m).20c Following the general procedure, the
product was isolated as a colorless solid in 89% yield (27.1 mg), mp
=63−65 °C. 1H NMR (400 MHz, CDCl3) δ 8.23 (s, 1H), 7.90 (t, J =
8.9 Hz, 3H), 7.67−7.58 (m, 3H). 13C NMR (101 MHz, CDCl3) δ
134.66, 134.18, 132.26, 129.22, 129.07, 128.43, 128.08, 127.68, 126.36,
119.29, 109.38. LRMS: m/z calcd for C11H7N (M + H) 154, found
154.
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ASSOCIATED CONTENT
■
S
* Supporting Information
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Screening of reaction conditions and copies of H and 13C
1
NMR spectra for the products. This material is available free of
charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: ccguo@hnu.edu.cn.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We are grateful for the financial support from the National
Natural Science Foundation of China (No. 21372068,
J1210040, J1103312).
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