Base-promoted annulation of amidoximes with alkynes: Simple access to 2,4-disubstituted imidazoles

Article abstract of DOI:10.3390/molecules25163621

An efficient construction of imidazole ring by a Cs2CO3-promoied annulation of amidoximes with terminal alkynes in DMSO has been developed. This protocol provides a simple synehetic ropte with high atom-utilieation for the synthesis of 2,4-disubstituted imidazoles in good yields under transition-metal-free and ligand-free conditions. Intornal alkynes can also undetgo the annulation to give 2,4,5-trisubstituted imidazoles.

Full text of DOI:10.3390/molecules25163621

molecules
Article
Base-Promoted Annulation of Amidoximes with
Alkynes: Simple Access to
2,4-Disubstituted Imidazoles
Hina Mehmood, Muhammad Asif Iqbal, Le Lu and Ruimao Hua *
Key Laboratory of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Department of
Chemistry, Tsinghua University, Beijing 100084, China; hinamehmood123@gmail.com (H.M.);
ykb15@mails.tsinghua.edu.cn (M.A.I.); lul18@mails.tsinghua.edu.cn (L.L.)
* Correspondence: ruimao@mail.tsinghua.edu.cn; Tel.: +86-10-6279-2596
ꢀꢁꢂꢀꢃꢄꢅꢆꢇ
Academic Editor: Andrea Penoni
Received: 30 June 2020; Accepted: 6 August 2020; Published: 9 August 2020
ꢀꢁꢂꢃꢄꢅꢆ
Abstract: An efficient construction of imidazole ring by a Cs2CO3-promoted annulation of amidoximes
with terminal alkynes in DMSO has been developed. This protocol provides a simple synthetic route
with high atom-utilization for the synthesis of 2,4-disubstituted imidazoles in good yields under
transition-metal-free and ligand-free conditions. Internal alkynes can also undergo the annulation to
give 2,4,5-trisubstituted imidazoles.
Keywords: base-promoted; annulation; amidoximes; alkynes; 2,4-disubstituted imidazoles
1. Introduction
Imidazole ring is the important class of nitrogen-heterocyclic structural motif that has been
found in several commercial drugs, such as olmesartan [
1–4] and losartan [5–7], for the treatment
of hypertension, and ondansetron [ 11] for reducing nausea and emesis, which have become the
8–
best-selling five-membered ring heterocyclic pharmaceuticals [12] (Figure 1). Molecules having this
nitrogen-heterocyclic structure often exhibit important and interesting physiological and biological
activities [13
complexes [16
–
15]. In addition, imidazoles have been also used as ligands in organometallic
17]. Therefore, there has been increasing interest in the developments of efficient
,
methodologies for the construction of imidazole ring [18–20].
OH
Cl
N
N
N
N
N
N
N
N
N
N
N
N
NH
NH
O
O
OH
N
O
O
O
O
Olmesartan
Ondansetron
Losartan
Figure 1. Examples of commercial drugs with imidazole skeleton.
Among them, the construction of imidazole starting from alkyne as one of the reactants
has been well developed. As depicted in Scheme 1, one of the classic approaches to synthesize
1,2,4,5-tetrasubstituted or 2,4,5-trisubstituted imidazoles is the three-component cyclization of
α
-diketone, aldehyde, and amine or ammonia sources catalyzed by transition metal complexes or under
Molecules 2020, 25, 3621; doi:10.3390/molecules25163621
www.mdpi.com/journal/molecules

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acidic conditions (Equation (1)). Recently, this protocol has been evolved using internal alkynes as
starting materials via generating 1,2-diketones in situ by oxidation reaction [21 24]. On the other hand,
–
the formal [3+2] annulation of substituted amidines with alkyne forming imidazole ring usually shows
high atom-utilization, and two representative procedures are concluded in Scheme 1. One of the known
procedures is the annulation of amidines with terminal alkynes catalyzed by CuCl2 2H2O in pyridine in
·
the presence of Na2CO3 under atmospheric oxygen to afford 1,2,4-trisubstituted imidazoles in modest
to good yields (Equation (2)) [25]. The other involves the cyclocondensation of amidine hydrochlorides
with bromoacetylenes promoted by K2CO3 under air in the presence of 2,20-bipyridine and water
affording various 2,5-disubstituted imidazoles in good yields (Equation (3)) [26]. It is readily apparent
to find that, in addition to the requirement of CuCl2
2H2O and/or ligand (pyridine and 2,20-bipyridine),
·
in both cases, inorganic bases were used as the additives, indicating that base is the key promoter to
realize the formation of imidazoles. Therefore, in continuation of our interest in developing alkyne
annulation in the synthesis of nitrogen-heterocyclic compounds [27–30] and base/DMSO-promoted
C-N bond formation [31 34], we decided to explore the possibility of constructing an imidazole ring
–
with the use of inorganic bases as the promoters, without the use of ligands under transition-metal-free
conditions. In this paper, we would like to report a new, simple and efficient procedure to afford a
variety of 2,4-disubstituted imidazoles starting with amidoximes and terminal alkynes in the presence
of Cs2CO3 in DMSO (Equation (4)) [35].
Scheme 1. Synthesis of diverse position-substituted imidazoles from alkynes.

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2. Results and Discussion
We firstly examined the reaction of benzamidoxime (N0-hydroxybenzimidamide) (1a) with phenyl
◦
acetylene (2a, 2.0 equivalent) in the presence of Na2CO3 (4.0 equivalent) in DMSO at 100 C for
24 h; fortunately, 2,4-diphenylimidazole (3aa) could be isolated from the reaction mixture in a 10%
1
yield (Table 1, entry 1). The structure of 3aa was characterized by its H- and 13C-NMR spectral
data, which are the same as the reported ones. In addition, 3aa was recrystallized in a mixed
solvents of petroleum/EtOAc/EtOH as white crystals, its X-ray diffraction studies confirm the structure
unambiguously [36].
Several other inorganic bases, such as K2CO3, KOH, KOtBu and Cs2CO3, were then examined,
and 3aa could be obtained in a 34~75% yield (Table 1, entries 2–5). These results indicate that, in DMSO,
Cs2CO3 is the best base for the present transformation, thus, the influence of other solvents and the
amounts of 1a and Cs2CO3 were investigated. As shown in entries 6–8, when THF, 1,4-dioxane and
DMF were used as solvents to replace DMSO, the yields of 3aa were decreased significantly. In addition,
decreasing amounts of 2a (from 2.0 equivalent to 1.5 equivalent or 1.0 equivalent) resulted in the
considerable decrease of yields (Table 1, entries 9–10). Although the use of 2.5. of Cs2CO3 also gave
results similar to those in entry 5 (Table 1, entry 11 vs. entry 5), the yields of 3aa were reduced when
1.0 equivalent or 0.5. of Cs2CO3 were used (Table 1, entries 12–13). In addition, as discussed above,
the base is the key promoter to promote the formation of imidazoles, the absence of Cs2CO3 led to no
3aa formation at all (Table 1, entry 14).
Table 1. Optimizing reaction conditions for imidazole synthesis a.
Entry
2a (equiv)
Base(equiv)
Solvent
Yield(%)b
1
2
3
4
5
6
7
8
9
10
11
12
13
14
2.0
2.0
2.0
2.0
2.0
2.0
2.0
2.0
1.0
1.5
2.0
2.0
2.0
2.0
Na2CO3(4)
K2CO3(4)
KOH(4)
DMSO
DMSO
DMSO
DMSO
DMSO
THF
10
34
53
41
75
10
14
21
59
68
73
33
19
0
KOtBu(4)
Cs2CO3(4)
Cs2CO3(4)
Cs2CO3(4)
Cs2CO3(4)
Cs2CO3(4)
Cs2CO3(4)
Cs2CO3(2.5)
Cs2CO3(1.0)
Cs2CO3(0.5)
–
Dioxane
DMF
DMSO
DMSO
DMSO
DMSO
DMSO
DMSO
a
The reactions were carried out using 1a (1.0 mmol), 2a (1.0~2.0 equiv), and base in 4.0 mL of solvent in a sealed
tube at 100 oC for 24 h. yields of 3aa are isolated yields.
b
With the optimized conditions established (Table 1, entry 11), we then investigated the scope and
generality of the imidazole formation with the use of various alkynes bearing electron-donating and
electron-withdrawing groups, as well as several amidoximes, and the obtained results are concluded
in Scheme 2. The reactions of 1a with various aromatic terminal alkynes bearing electron-donating
groups and electron-withdrawing groups could occur smoothly, to give the corresponding imidazoles
in moderate to good yields. It was noted that para-alkyl-substituted aromatic alkynes (R” = Me, 2b; Et,
2c; n-Pr, 2d; n-Bu, 2e; t-Bu, 2f; 40-n-pentylcyclohexyl, 2g) showed high reactivity to produce the desired
products (3ab
~ 3ag) in 69–84% yields. para-Phenyl phenyl acetylene (2h) reacted with 1a afforded 3ah

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in a high yield (81%). The reaction of para-chlorophenyl acetylene (2i), an electron-poor alkyne, with 1a
gave the product 3ai in a moderate yield (68%). In addition, the reaction of 1a with para-bromophenyl
acetylene (2j) afford 3aj in a 59% yield. These results were apparent that the electron-donating group
on aromatic terminal alkynes would benefit the formation of imidazoles.
When meta-substituted aromatic terminal alkynes were used, the reactions gave slight
decrease in yields as compared to para-substituted ones. For example, the reactions of 1a with
(3-methylphenyl)ethyne (2k), or with (3-chlorophenyl)ethyne (2l) gave 3ak in a 63% yield (vs. 3ab
75%) and 3al in a 54% yield (vs. 3ag 68%), respectively. It was noted that, in these cases, alkyne bearing
electron-donating group also show relatively high reactivity (3ak vs. 3al), similar to the results as R” at
para-position.
In addition, the present reaction conditions are also suitable for the annulation of 1a with
2-naphthylacetylene (2m), and with 2-thienylacetylene (2n), a heteroaromatic terminal alkyne, afforded
3am and 3an in 55% and 56% yields, respectively.
R''
OH
N
N
R'
NH2
Cs2CO3 (2.5 equiv.)
DMSO, 100 oC, 24 h
+
N
R'
H
R''
1
2
3
R''
R" = Me 3ab 75%
Et 3ac 77%
R''
3ad
n-Bu 3ae 73%
n-Pr
79%
N
t-Bu 3af 84%
N
N
Ph
3ag
4'-n-pentylcyclohexyl
phenyl 3ah 81%
chloro 3ai 68%
bromo 3aj 59%
69%
H
3ak
63%
chloro 3al 54%
N
H
R'' = Me
Ph
R
N
N
S
N
R
N
N
N
N
Ph
Ph
Ph
N
H
Ph
H
H
N
N
H
Ph
Ph
R'
3aq 67%
3ar 76%
H
R = phenyl 3ao 61%
m-tolyl 3ap 55%
3am 55%
3an 56%
R
Ph
N
N
N
N
H
N
N
3ba
R' = 4-Me
72%
H
H
S
4-CF3 3ca 65%
R = 4-n-propylphenyl
3ed
3da
83%
49%
a
1
2
Reactions were carried out using (1.0 mmol), (2.0 mmol), and Cs2CO3 (2.5 mmol)
in 4.0 mL of DMSO in a sealed tube at 100 oC for 24 h.
Scheme 2. Substrate scope of imidazole synthesis a.
Moreover, under the similar conditions, internal alkynes can also undergo the cyclocondensation
with 1a to produce the corresponding 2,4,5-trisubstituted imidazoles. For instance, the reactions of 1a
with 1,2-diphenyacetylene (2o), or with 1,2-bis(m-tolyl)acetylene (2p) gave 3ao and 3ap in 61% and
55% yields.

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Interestingly, when 1-(trimethylsilyl)acetylene (2q) and 1-methyl-2-trimethylsilylacetylene (2r
)
were employed, the reactions with 1a produced 2-phenylimidazole (3aq, 67%) and 2-phenyl-4-
methylimidazole (3ar, 76%), indicating that desilylation took place smoothly under the used
basic conditions.
On the other hand, the substituent (R0) effect on the aryl group of
1 was also investigated,
and the results from two representative examples with the use of either electron-donating group
(para-Me, 1b) or electron-withdrawing group (para-CF3, 1c) were reported. As shown in Scheme 2,
the corresponding products of 3ba and 3ca could be obtained in 72% and 65% yields, respectively.
Again, the electron-donating group is favorable for the formation of imidazole ring.
Additionally, the present reaction conditions could be applied to heteroarylamidoximes and
alkylamidoximes. For example, the reaction between 2-thienylamidoxime (1d) and 2a afford 3da in a
83% yield, and the reaction of acetamidoxime (1e) with 2d produced the expected product of 3ed in a
49% yield.
It is worth noting that the present reaction conditions are tolerant to C(sp2)-Cl and C(sp2)-Br bonds,
the obtained products bearing C(sp2)-X bonds have a highly potential application in organic synthesis
via their cross-coupling reactions.
Amidoximes have been well known to be the useful building blocks for the construction
of nitrogen-heterocyclic compounds, and the five-membered nitrogen-heterocyclic compounds
formation is usually proposed to involve the step of N-O bond cleavage via 3,3-sigmatropic
rearrangement [37–39]. Therefore, on the basis of our results and the known chemistry of amidoximes,
a possible reaction mechanism for the formation of imidazole ring is shown in Scheme 3. It involves the
regioselective nucleophilic addition of O-H bond to alkyne under basic conditions, giving an o-vinylated
amidoxime (4), which undergoes sequential 3,3-sigmatropic rearrangement forming intermediate
5, and intramolecular nucleophilic addition of nitrogen atom to aldehyde affording five-membered
heterocyclic intermediate 6, followed by dehydration to form imidazole ring.
Scheme 3. Proposed mechanism for the formation of imidazoles.
In order to support the proposed mechanism, a theoretical calculation was conducted by using
the quantum chemistry program Gaussian 16 [40], and all structures were optimized by using M06-2X
Minnesota functional with the 6-31G(d,p) basis set [41]. Figure 2 shows the free energy changes in the
base-promoted annulation of 1a with 2a forming 3aa with the transition states for the formation of
key intermediates
(from TS1) and (from TS3) can be found with low activation energies. The key step for the formation
of imidazole ring is the 3,3-sigmatropic rearrangement to give intermediate . The transition state
(TS2) between R4 (intermediate ) and R5 (intermediate ) is not very high in activation energy,
43.2 kcal/mol. These
4–6. It clearly indicates that the transition state for the formation of intermediates 4
6
5
4
5
with 30.8 kcal/mol (TS2-R4), and the Gibbs free energy change in this step is
−
results have confirmed that at 100 ◦C (373.15 K, reaction temperature), 3,3-sigmatropic rearrangement
can occur smoothly to construct imidazole ring as the proposed routes shown in Scheme 3.

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Figure 2. Free energy profile for the base-promoted annulation of 1a with 2a affording 3aa.
3. Materials and Methods
3.1. General Methods
All commercial reagents are analytically pure and used directly without further purification.
Nuclear magnetic resonance (NMR) spectra were recorded on an ECA-400 spectrometer (JEOL,
1
Tokyo, Japan) using DMSO-d6 as solvent at 298 K. H-NMR (400 MHz) chemical shifts (
δ) were
referenced to internal standard TMS (for 1H,
δ
= 0.00 ppm). 13C-NMR (100 MHz) chemical shifts were
referenced to internal solvent DMSO-d6 (for 13C,
δ
= 39.52 ppm). Mass spectra (MS) were obtained
on a GC-MS-QP2010S (Shimadzu, Tokyo, Japan), and the high-resolution mass spectra (HRMS) with
electron spray ionization (ESI) were obtained with a micrOTOF-Q spectrometer (Agilent, California,
CA, USA). Single crystals of 3aa were obtained by slow evaporation of their solution in a mixture
solvents of petroleum, ethyl acetate and EtOH.
3.2. Typical Experimental Procedure for the Synthesis of 2,4-Diphenyl-1H-imidazole (3aa)
A mixture of benzamidoxime (1a, 136.1 mg, 1.0 mmol), phenylacetylene (2a, 204.1 mg, 2.0 mmol)
and Cs2CO3 (815.1 mg, 2.5 mmol) in DMSO (4.0 mL), in a 25 mL screw-capped thick-walled Pyrex tube
was stirred at 100 ◦C for 24 h in an oil bath. After the reaction mixture was cooled to room temperature,
it was poured into a solvent mixture of water (50.0 mL) and ethyl acetate (20.0 mL), and the two phases
were then separated. The aqueous layer was extracted with ethyl acetate (3
×
20.0 mL). The combined
organic extracts were dried over anhydrous Na2SO4. After removal of the solvent under reduced
pressure, the residue was purified by column chromatography on silica gel with petroleum ether/ethyl
acetate (gradient mixture ratio from 100:0 to 70:20) as eluent, to afford 3aa as a white solid (160.4 mg,
73%).
The characterization data for known products of 3aa
3ca and 3da reported in the Supplementary Materials. Each of 3ac
new compounds, and their spectroscopic data are reported below.
,
3ab
,
3af
,
3ah
-
3al
,
3an
,
3ao
, 3aq, 3ar, 3ba,
,
3ad
,
3ae
,
3ag
,
3am
,
3ap and 3ed are

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3.3. Characterization Data of Products
4-(4-Ethylphenyl)-2-phenyl-1H-imidazole (3ac):
1
White solid (190.4 mg, 77%). H-NMR (400 MHz, DMSO-d6)
δ
12.71 (s, 1H), 8.17 (d, J = 7.6 Hz, 2H),
7.87 (d, J = 7.6 Hz, 2H), 7.70 (s, 1H), 7.50 (t, J = 7.6 Hz, 2H), 7.37 (t, J = 7.3 Hz, 1H), 7.25 (d, J = 8.0 Hz,
2H), 2.61 (q, J = 7.5 Hz, 2H), 1.20 (t, J = 7.5 Hz, 3H); 13C-NMR (100 MHz, DMSO-d6)
δ 146.1, 141.9, 130.8,
128.7, 128.0, 127.9, 125.0, 124.5, 28.0, 15.6 HRMS (ESI) m/z: [M + H]+ calcd for C17H16N2, 249.1386;
found 249.1388.
2-Phenyl-4-(4-n-propylphenyl)-1H-imidazole (3ad):
1
White solid (206.7 mg, 79%). H-NMR (400 MHz, DMSO-d6)
δ 12.64 (sbr, 1H), 8.15 (d, J = 7.7 Hz, 2H),
7.85 (d, J = 7.7 Hz, 2H), 7.66 (s, 1H), 7.49 (t, J = 7.5 Hz, 2H), 7.38 (t, J = 7.3 Hz, 1H), 7.22 (d, J = 7.8 Hz,
2H), 2.56 (t, J = 7.4 Hz, 2H), 1.69–1.53 (m, 2H), 0.91 (t, J = 7.4 Hz, 3H); 13C-NMR (100 MHz, DMSO-d6)
δ
146.0, 140.2, 130.8, 129.3, 128.5, 128.4, 127.9, 125.0, 124.4, 118.7, 115.3, 37.0, 24.0, 13.5; HRMS (ESI) m/z:
[M + H]+ calcd for C18H18N2, 263.1543; found 263.1540.
4-(4-Butylphenyl)-2-phenyl-1H-imidazole (3ae):
1
White solid (201.3 mg, 73%). H NMR (400 MHz, DMSO-d6)
δ
12.64 (sbr, 1H), 8.14 (d, J = 7.4 Hz, 2H),
7.83 (d, J = 7.3 Hz, 2H), 7.65 (s, 1H), 7.48 (t, J = 7.2 Hz, 2H), 7.36 (t, J = 7.0 Hz, 1H), 7.21 (d, J = 7.5 Hz,
2H), 2.58 (t, J = 7.3 Hz, 2H), 1.63–1.50 (m, 2H), 1.40–1.22 (m, 2H), 0.90 (t, J = 7.1 Hz, 3H); 13C-NMR
(100 MHz, DMSO-d6) δ 146.0, 140.3, 130.8, 129.3, 128.5, 128.3, 127.8, 124.9, 124.4, 34.6, 33.1, 21.7, 13.7;
HRMS (ESI) m/z: [M + H]+ calcd for C19H20N2, 277.1699; found 277.1698.
4-(4-(4-n-Pentylcyclohexyl)phenyl)-2-phenyl-1H-imidazole (3ag):
1
White Solid (256.7 mg, 69%). H-NMR (400 MHz, DMSO-d6)
δ
12.58 (s, 1H), 8.00 (d, J = 7.6 Hz, 2H),
7.74 (d, J = 7.8 Hz, 2H), 7.63 (s, 1H), 7.46 (t, J = 7.6 Hz, 2H), 7.35 (t, J = 7.3 Hz, 1H), 7.22 (d, J = 8.0 Hz,
2H), 2.50–2.38 (m, 1H), 1.83–1.80 (m, 4H), 1.52–1.37 (m, 2H), 1.35–1.13 (m, 10H), 1.10–0.95 (m, 2H), 0.88
(t, J = 6.6 Hz, 3H); 13C-NMR (100 MHz, DMSO-d6)
δ 145.8, 145.4, 130.6, 128.6, 128.0, 126.7, 124.8, 124.3,
43.9, 36.8, 36.6, 33.8, 33.1, 31.6, 26.0, 22.1, 13.9; HRMS (ESI) m/z: [M + H]+ calcd for C26H32N2, 373.2638;
found 373.2635.
4-(Naphthalen-2-yl)-2-phenyl-1H-imidazole (3am):
1
White solid (148.3 mg, 55%). H-NMR (400 MHz, DMSO-d6)
δ 12.72 (s, 1H), 8.39 (s, 1H), 8.09–7.85 (m,
7H), 7.55–7.34 (m, 5H); 13C-NMR (100 MHz, DMSO-d6)
δ 146.0, 140.9, 133.3, 132.1, 131.8, 130.5, 128.6,
128.1, 127.7, 127.6, 127.4, 126.1, 125.1, 125.0, 124.9, 123.7, 121.7, 114.9; HRMS (ESI) m/z: [M + H]+ calcd
for C19H14N2, 271.1230; found 271.1235.
2-Phenyl-4,5-di-m-tolyl-1H-imidazole (3ap):
1
White solid (178.1 mg, 55%). H-NMR (400 MHz, DMSO-d6)
δ
12.59 (s, 1H), 8.08 (d, J = 8.3 Hz, 3H),
7.50–7.43 (m, 3H), 7.40–7.24 (m, 5H), 7.22–7.12 (m, 2H), 7.04 (d, J = 6.9 Hz, 1H), 2.34 (s, 3H), 2.27 (s,
3H); 13C-NMR (100 MHz, DMSO-d6)
δ 145.2, 137.6, 137.0, 135.0, 130.9, 130.3, 129.5, 128.8, 128.5, 128.3,
128.2, 128.1, 128.0, 127.8, 127.6, 127.0, 125.5, 125.1, 124.1, 21.0, 20.9; HRMS (ESI) m/z: [M + H]+ calcd for
C23H20N2, 325.1699; found 325.1697.
2-Methyl-4-(4-n-propylphenyl)-1H-imidazole (3ed):
Waxy oil (98.1 mg, 49%). 1H-NMR (400 MHz, DMSO-d6)
7.09 (d, J = 8.2 Hz, 2H), 2.50–2.41 (m, 2H), 2.26 (s, 3H), 1.60–1.46 (m, 2H), 0.85 (t, J = 7.3 Hz, 3H);
13C-NMR (100 MHz, DMSO-d6)
144.1, 1, 139.5, 131.5, 128.4, 123.9, 36.9, 24.0, 13.9, 13.6; HRMS (ESI)
m/z: [M + H]+ calcd for C13H16N2, 201.0681; found 201.0687.
δ 7.55 (d, J = 8.1 Hz, 2H), 7.28 (s, 1H),
δ

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4. Conclusions
In summary, we developed a simple and efficient method to prepare 2,4-disubstituted imidazoles
in moderate to good yields from easily available starting materials of amidoximes and terminal alkynes
promoted by Cs2CO3 in DMSO. The significant advantages of the present procedure include the
formation of imidazoles under transition-metal-free and ligand-free conditions, high atom-utilization,
and a broad substrate scope. 2-substituted and 2,4,5-trisubstituted imidazoles could be also prepared
under the similar conditions by using 1-(trimethylsilyl)acetylene and internal alkynes.
Supplementary Materials: The following are available online. The characterization data of the known
products, copies of 1H- and 13C-NMR charts of all products, X-ray structural details (including CIF files)
of 3aa, and computational predicted energies and cartesian coordinates.
Author Contributions: Investigation, writing—original draft preparation, H.M.; investigation, M.A.I. & L.L.;
conceptualization, supervision, writing—review and editing, R.H. All authors have read and agreed to the
published version of the manuscript.
Funding: This research was funded by National Natural Science Foundation of China (21673124). Hina Mehmood
and Muhammad Asif Iqbal thank the China Scholarship Council (CSC) for generous support for their study in
Tsinghua University as PhD candidates.
Acknowledgments: We thank Tsinghua Xuetang Talents Program for computational hardware and software support.
Conflicts of Interest: The authors declare no conflict of interest.
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