Synthesis and characterization of sulfonyl-functionalized ionic liquids

Article abstract of DOI:10.1081/SCC-200057264

Novel sulfonyl-functionalized ionic liquids (SFIL) with -SO₃H and -SO₂Cl groups have been designed, synthesized, and characterized. Being strong acidic substances, these ionic liquids have great potential as media and catalysts in ma

Full text of DOI:10.1081/SCC-200057264

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Synthesis and Characterization
of Sulfonyl‐Functionalized Ionic
Liquids
a
a
a
Zhengyin Du , Zuopeng Li & Youquan Deng
a
Centre for Green Chemistry and Catalysis ,
Lanzhou Institute of Chemical Physics, Chinese
Academy of Science & Graduate School of the
Chinese Academy of Sciences , Lanzhou, China
Published online: 16 Aug 2006.
To cite this article: Zhengyin Du , Zuopeng Li & Youquan Deng (2005) Synthesis and
Characterization of Sulfonyl‐Functionalized Ionic Liquids, Synthetic Communications:
An International Journal for Rapid Communication of Synthetic Organic Chemistry,
35:10, 1343-1349, DOI: 10.1081/SCC-200057264
To link to this article: http://dx.doi.org/10.1081/SCC-200057264
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Synthetic Communications , 35: 1343–1349, 2005
Copyright # Taylor & Francis, Inc.
ISSN 0039-7911 print/1532-2432 online
DOI: 10.1081/SCC-200057264
Synthesis and Characterization of
Sulfonyl-Functionalized Ionic Liquids
Zhengyin Du, Zuopeng Li, and Youquan Deng
Centre for Green Chemistry and Catalysis, Lanzhou Institute of Chemical
Physics, Chinese Academy of Science & Graduate School of the Chinese
Academy of Sciences, Lanzhou, China
3
Abstract: Novel sulfonyl-functionalized ionic liquids (SFIL) with –SO H and
22 SO Cl groups have been designed, synthesized, and characterized. Being strong
acidic substances, these ionic liquids have great potential as media and catalysts in
2
many acid-catalyzed reactions.
Keywords: Characterization, potential applications, sulfonyl-functionalized ionic
liquids, synthesis
In recent years, ionic liquids have gained recognition as environmentally
benign alternatives to more volatile organic solvents. They possess many
interesting properties such as wide liquid range, negligible vapor pressure,
high thermal stability, and good solvating ability for a wide range of substrates
and catalysts. In many cases, the use of ionic liquids provides many advan-
tages over reactions in conventional organic solvents in terms of activity,
enantioselectivity, stability, and the reusability of the solvent–catalyst
[
1–7]
systems.
because their chemical and physical properties can be adjusted by a careful
They have also been refereed to as “designable solvents”
choice of cation/anion.
Received in Japan November 24, 2004
Address correspondence to Youquan Deng, Centre for Green Chemistry and
Catalysis, Lanzhou Institute of Chemical Physics, Chinese Academy of Science &
Graduate School of the Chinese Academy of Sciences, Lanzhou 730000, China.
Fax: þ86-931-4968116; E-mail: ydeng@lzb.ac.cn
1
343

1344
Z. Du, Z. Li, and Y. Deng
Recent advances in ionic-liquids research provided another route for
achieving task-specific ionic liquids in which a functional group is covalently
tethered to the cation or anion of the ionic liquid, especially to the two N atoms
of the imidazole ring. It was expected that these task-specific ionic liquids
might further enlarge the application scope of ionic liquids in chemistry.
This suggests that the chances for preparing a broad array of ionic liquids
with ions incorporating functional groups are rather good. Moreover, certain
of these new ionic liquids have proven useful in both synthetic, catalytic,
[
8–12]
and separations applications.
Being acidic ionic liquids, functionalized ionic liquids containing chloro-
sulfonyl groups grafted on the side chain of imidazolium with chloride and
hexafluorophosphate anions as counter ions were synthesized and used in
[
13,14]
material chemistry and Beckmann rearrangement.
acidic ionic liquids containing sulfonyl end groups have been used success-
Furthermore, Brønsted
[
15]
[16]
[16–18]
fully in oligomerization of olefins,
etherification,
[19]
Friedel–Crafts alkylation,
esterification,
nitration of aromatic
[
16]
Pinacol rearrangement,
[20]
[21]
compounds,
ted only the range of imidazolium cation and triflate anion.
and Beckmann rearrangement.
These ionic liquids restric-
We report herein the synthesis and characterization of novel sulfonyl
–SO H) and sulfonyl chloride (–SO Cl) functionalized ionic liquids with
3 2
(
imidazolium, pyridinium, and triphenylphosphonium cations coupled with
triflate, trifluoroacetate, and p-toluenesulfonate anions (Scheme 1). To the
best of our knowledge, most of them are reported for the first time. All
1
sulfonyl-functionalized ionic liquids (SFILs) are characterized with IR, H-
1
NMR, C-NMR, and elemental analysis.
3
In conclusion, several novel SFILs were synthesized in excellent yields
and characterized with spectroscopies. Being acidic ionic liquids, they have
great potential applications as catalysts and/or media in many reactions,
Scheme 1. Synthesis of sulfonyl functionalized ionic liquids.

Sulfonyl-Functionalized Ionic Liquids
1345
such as oligomerization, etherification, esterification, Friedel–Crafts reaction,
Pinacol and Beckmann rearrangement, and so on. Some investigations about
application of SFILs are in progress at our laboratory.
EXPERIMENTAL
Trifluoromethanesulfonic acid and 1,4-butane sultone were from Fluka
Chemical Corporation; the others were all from Beijing Chemical Reagent
Corporation Ltd. and used directly without additional treatment.
Instrumental Analysis and Measurements
The C and H elemental analyses were performed on a Yanaco CHN FOER
MT-3 element analyzer. IR spectra (FTIR) were recorded on a Nicolet
1
NEXUS 670 FTIR spectrometer using liquid film or KBr tablet. H NMR
1
3
(
400 MHz) and C NMR (100MHz) were obtained as solutions in deuterium-
substituted reagent. Chemical shifts were reported in parts per million
ppm, d). Melting points were recorded on SGW X-4 Micro-meltingpoint-
(
meter of Shanghai.
General Procedures for the Synthesis of SFILs
The SFILs were prepared by three-step synthesis through 1-methylimidazole,
pyridine, and triphenylphosphine combined first with 1,4-butane sultone to
form zwitterions, which then react with an acid to obtain –SO H acidic ionic
3
liquids, followed by addition of thionyl chloride to yield –SO Cl ionic liquids.
2
The typical synthetic procedure of SFILs is described with 1a and 2a as
examples, which is according to the lately reported references,
some changes.
[16,19]
but has
From the combination of 1-methylimidazole and 1,4-butane, sultone
was formed in excellent yield (ca. 99%). After washing the salt with diethyl
ether and toluene to remove any unreacted starting materials, the solid was
dried in vacuo. Then, a stoichiometric amount of trifluoromethanesulfonic
acid was added and the mixture was stirred for 10 h at 408C, during
which time the solid zwitterion dissolved/liquefied and resulted in the
formation of –SO H acidic ionic liquid (IL) 1a with yield of 98%. The IL
3
phase was then washed repeatedly with toluene and ether to remove
nonionic residues and dried in vacuo. Then, thionyl chloride was added
with an excess of 5 mol and refluxed for 24 h. The unreacted thionyl
chloride was removed by evaporation. The product was formed with 97%
yield and in high purity.
The other functionalized ionic liquids were prepared like 1a and 2a
under the similar conditions and procedures listed in Scheme 1. Among of

1346
Z. Du, Z. Li, and Y. Deng
them, 1a and 2a were previously reported and the others are reported for the
first time.
The spectral data of 22 SO H and 22 SO Cl ionic liquids are as follows.
3
2
1
1a): A colorless viscous liquid with yield of 98%. H-NMR (400 MHz, d -
-(4-Sulfonylbutyl)-3-methylimidazolium trifluoromethanesulfonate
1
(
6
DMSO):d 14.63 (s, 1H), 9.18 (s, 1H), 7.83 (t, J ¼ 2.0, 1H), 7.78 (t, J ¼ 1.8,
1
H), 4.25 (t, J ¼ 6.8, 2H), 3.91 (t, J ¼ 7.0, 3H), 2.62 (t, J ¼ 7.6, 2H), 1.97
1
3
(
quint, J ¼ 8.0, 2H), 1.60 (q, J ¼ 7.6, 2H). C NMR (100 MHz, d -
6
DMSO):d 138.41, 126.21, 124.70, 125.02 (q, J ¼ 320.0, CF ), 52.61,
C-F
3
21
5
1.45, 38.17, 30.61, 23.47. IR (cm ): 3158, 1572, 1364, 1168, 639.
C H F O N S (368.35) calcd: C, 29.32; H, 4.07. Found: C, 28.86; H, 3.91.
9
15 3 6 2 2
1
sulfonate (2a): A brown liquid with yield of 97%. H-NMR (400 MHz, d -
-(4-Chlorosulfonylbutyl)-3-methylimidazolium trifluoromethane-
1
6
DMSO): d 9.21 (s, 1H), 7.79 (t, J ¼ 2.0, 1H), 7.73 (t, J ¼ 1.8, 1H), 4.21
(
t, J ¼ 6.8, 2H), 3.88 (t, J ¼ 7.0, 3H), 2.68 (t, J ¼ 7.6, 2H), 1.91 (quint,
1
3
J ¼ 8.0, 2H), 1.59 (q, J ¼ 7.6, 2H). C NMR (100 MHz, d -DMSO):
6
d136.81, 123.78, 122.47, 121.08 (q, J ¼ 320.0, CF ), 50.59, 48.63, 35.92,
C-F
3
2
1
2
8.61, 21.53. IR (cm ): 3156, 3116, 1369, 1165, 593. C H F O N S Cl
9 14 3 5 2 2
(386.58) calcd: C, 27.96; H, 3.62. Found: C, 27.81; H, 3.72.
1-(4-Sulfonylbutyl)-3-methylimidazolium trifluoroacetate (1b): A
1
hygroscopic white solid with yield of 97%. H-NMR (400 MHz, d6-
DMSO): d 13.82 (s, 1H), 9.51 (s, 1H), 7.91 (t, J ¼ 2.0, 1H), 7.87
(
t, J ¼ 1.8, 1H), 4.36 (t, J ¼ 7.2, 2H), 4.07 (s, 3H), 3.75 (t, J ¼ 6.4, 2H),
1
3
2
DMSO): d 139.12, 125.91, 123.79, 52.63, 50.64, 37.47, 30.44, 28.69, 22.92.
2
IR (cm ): 3156, 1787, 1574, 1171. C H F O N S (332.31) calcd: C,
.04 (quint, J ¼ 7.2, 2H), 1.78 (q, J ¼ 6.4, 2H). C-NMR (100 MHz, d -
6
1
1
0 15 3 5 2
3
6.11; H, 4.51. Found: C, 35.86; H, 4.42.
-(4-Chlorosulfonylbutyl)-3-methylimidazolium trifluoroacetate (2b):
1
An orange liquid with yield of 95%. H-NMR (400MHz, d -DMSO): d
1
6
9
3
2
3
.43(s, 1H), 7.88 (t, J ¼ 2.0, 1H), 7.81 (t, J ¼ 1.8, 1H), 4.30 (t, J ¼ 7.2, 2H),
.93 (s, 3H), 3.69 (t, J ¼ 6.4, 2H), 1.97 (quint, J ¼ 7.2, 2H), 1.72 (q, J ¼ 6.4,
1
H). C-NMR (100 MHz, d -DMSO): d 137.04, 123.98, 122.62, 50.79, 48.82,
3
6
21
6.19, 28.86, 27.37, 21.71. IR (cm ): 3147, 3092, 1365, 1167, 592.
C H F O N SCl (350.81) calcd: C, 34.21; H, 3.99. Found: C, 34.47; H, 3.76.
1
0 14 3 4 2
1
colorless viscous liquid with yield of 95%. H-NMR (400 MHz, d -DMSO):
-(4-Sulfonylbutyl)-3-methylimidazolium p-toluenesulfonate (1c): A
1
6
d 9.68 (s, 1H), 7.96 (t, J ¼ 1.6, 1H), 7.89 (t, J ¼ 1.6, 1H), 7.52 (m, J ¼ 6.4,
2
H), 7.31 (m, J ¼ 6.4, 2H), 4.38 (t, J ¼ 6.8, 2H), 4.09 (s, 3H), 3.81
1
3
(
t, J ¼ 6.8, 2H), 2.11 (quint, J ¼ 7.2, 2H), 1.87 (q, J ¼ 6.8, 2H). C-NMR
(
100 MHz, d -DMSO): 138.64, 130.21, 124.92, 124.16, 49.81, 46.48, 37.53,
6
2
1
2
9.97, 28.91. IR (cm ): 3153, 3094, 2962, 1573, 1174. C H O N S
15 22 6 2 2
(390.5) calcd: C, 46.09; H, 5.63. Found: C, 45.82; H, 5.47.
1-(4-Chlorosulfonylbutyl)-3-methylimidazolium p-toluenesulfonate
1
2c): A dark brown viscous liquid with yield of 92%. H-NMR (400 MHz,
(
d6-DMSO): d 9.51 (s, 1H), 7.89 (t, J ¼ 1.6, 1H), 7.79 (t, J ¼ 1.6, 1H), 4.24

Sulfonyl-Functionalized Ionic Liquids
1347
(
t, J ¼ 6.8, 2H), 3.84 (s, 3H), 3.64 (t, J ¼ 6.8, 2H), 1.87 (quint, J ¼ 7.2, 2H),
1
3
1
1
1
4
.65 (q, J ¼ 6.8, 2H). C-NMR (100 MHz, d -DMSO):d 136.86, 128.35,
6
2
1
23.68, 122.28, 47.92, 44.71, 35.80, 28.63, 27.02. IR (cm ): 3147, 3091,
571, 1171. C H O N S Cl (408.5) calcd: C, 44.06; H, 5.14. Found: C,
1
5 21 5 2 2
4.17; H, 5.04.
-(4-Sulfonylbutyl)pyridinium trifluoromethanesulfonate (3a): A
1
brown viscous liquid with yield of 94%. H-NMR (400 MHz, d -DMSO):
1
6
d 9.23 (s, 2H), 8.69 (s, 1H), 8.27 (s, 2H), 4.78 (s, 2H), 2.73 (s, 2H), 2.15
1
3
(
s, 2H), 1.74 (s, 2H). C-NMR (100 MHz, d -DMSO): d 147.83, 146.52,
6
1
29.94, 122.19 (q, J ¼ 320.0, CF ), 76.44, 62.65, 52.76, 31.86, 23.54. IR
10 14 6 3 2
C-F
3
2
1
cm ): 3075, 2976, 1373, 1264, 1166. C H O NF S (365.25) calcd: C,
(
3
2.85; H, 3.83. Found: C, 32.59; H, 3.71.
-(4-Chlorosulfonylbutyl)pyridinium trifluoromethanesulfonate (4a):
1
A dark brown viscous liquid with yield of 96%. H-NMR (400 MHz, d -
1
6
DMSO): d 9.07 (s, 2H), 8.53 (s, 1H), 8.09 (s, 2H), 4.60 (s, 2H), 2.65
1
3
(
s, 2H), 1.97 (s, 2H), 1.56 (s, 2H). C-NMR (100 MHz, d -DMSO): d
6
1
46.10, 145.31, 128.68, 125.64 (q, J ¼ 320.0, CF ), 60.89, 50.86, 30.26,
10 13 5 3 2
C-F
3
2
1.74. IR (cm ): 3072, 1370, 1261, 1163. C H O NF S Cl (383.75)
1
2
calcd: C, 31.27; H, 3.39. Found: C, 30.85; H, 3.51.
-(4-Sulfonylbutyl)pyridinium trifluoroacetate (3b): A white wax
1
solid with yield of 92%. H-NMR (400 MHz, d -DMSO): d 9.45
1
6
(
d, J ¼ 3.6, 2H), 8.74 (t, J ¼ 7.6, 1H), 8.32 (t, J ¼ 6.8, 2H), 4.90
(
t, J ¼ 7.2, 2H), 3.82 (t, J ¼ 6.8, 2H), 2.13 (quint, J ¼ 7.2, 2H), 1.81 (quint,
1
3
J ¼ 6.8, 2H). C-NMR (100 MHz, d -DMSO): d 148.21, 146.38, 129.45,
6
2
1
6
1.59, 46.31, 29.69. IR (cm ): 3057, 1636, 1491, 1179. C H O NF S
11 14 5 3
(
329.21) calcd: C, 40.09; H, 4.25. Found: C, 39.62; H, 3.98.
-(4-Chlorosulfonylbutyl)pyridinium trifluoroacetate (4b): A brown
1
semisolid with yield of 95%. H-NMR (400 MHz, d -DMSO): d 9.32
1
6
(
d, J ¼ 3.6, 2H), 8.62 (t, J ¼ 7.6, 1H), 8.18 (t, J ¼ 6.8, 2H), 4.76
(
t, J ¼ 7.2, 2H), 3.65 (t, J ¼ 6.8, 2H), 2.01 (quint, J ¼ 7.2, 2H), 1.69 (quint,
1
3
J ¼ 6.8, 2H). C-NMR (100 MHz, d -DMSO):d145.64, 144.97, 128.18,
6
21
5
9.64, 44.67, 28.46. IR (cm ): 3053, 1634, 1489, 1176. C H O NF SCl
11 13 4 3
(
347.71) calcd: C, 37.96; H, 3.74. Found: C, 37.69; H, 3.53.
-(4-Sulfonylbutyl)pyridinium p-toluenesulfonate (3c): A colorless
1
viscous liquid with yield of 91%. H-NMR (400 MHz, D O): d 7.45
1
2
(
d, J ¼ 2.8, 2H), 7.03 (t, J ¼ 7.6, 1H), 6.60 (d, J ¼ 3.2, 2H), 3.19
t, J ¼ 8.0, 2H), 2.16 (q, J ¼ 5.6, 2H), 0.71 (quint, J ¼ 6.4, 2H),
(
1
3
0
.36 (quint, J ¼ 6.0, 2H). C-NMR (100 MHz, D O):d 149.73, 148.51,
2
2
1
1
32.86, 65.59, 48.75, 32.67, 31.92. IR (cm ): 3057, 1637, 1492,
179. C H O NS (387.38): calcd: C, 49.56; H, 5.42. Found: C, 49.48;
H, 5.27.
1
1
6
21
6
2
1
dark brown slurry with yield of 93%. H-NMR (400 MHz, D O): d 7.21
-(4-Chlorosulfonylbutyl)pyridinium p-toluenesulfonate (4c): A
1
2
(
(
d, J ¼ 2.8, 2H), 6.89 (t, J ¼ 7.6, 1H), 6.42 (d, J ¼ 3.2, 2H), 3.00
t, J ¼ 8.0, 2H), 1.98 (q, J ¼ 5.6, 2H), 0.52 (quint, J ¼ 6.4, 2H),

1348
Z. Du, Z. Li, and Y. Deng
1
3
0
.18 (quint, J ¼ 6.0, 2H). C-NMR (100 MHz, D O): d 148.23, 146.77,
2
2
1
1
30.88, 63.68, 46.94, 30.85, 30.63. IR (cm ): 3055, 1634, 1489,
177. C H O NS Cl (405.88) calcd: C, 47.30; H, 4.93. Found: C, 47.61;
H, 4.78.
1
1
6
20
5
2
Triphenyl(4-sulfonylbutyl)phosphonium trifluoromethanesulfonate
1
5a): A hygroscopic pale brown slurry with yield of 95%. H-NMR
(
(
400 MHz, CDCl ): d 7.96 (s, 3H), 7.85 (m, J ¼ 3.2, 12H), 3.97 (t, J ¼ 6.4,
3
1
3
2
H), 3.54 (q, J ¼ 7.2, 2H), 2.48 (t, J ¼ 6.8, 2H), 2.06 (d, J ¼ 3.6, 2H). C-
NMR (100 MHz, CDCl ): d 137.68, 135.51, 132.58, 119.85(q, J ¼ 320.0,
3 C-F
21
CF ), 66.37, 27.34, 23.54, 22.43. IR (cm ): 2948, 1277, 1259, 1164, 1032.
3
C H O PF S (548.53) calcd: C, 50.32; H, 4.38. Found: C, 50.24; H, 4.27.
2
3
24
6
3 2
Triphenyl(4-chlorosulfonylbutyl)phosphonium trifluoromethanesul-
fonate (6a): A pale brown solid with yield of 94%. Melting point:
1
9
1
1
1
0–92 8C. H-NMR (400 MHz, CDCl ): d 7.84 (s, 3H), 7.72 (m, J ¼ 3.2,
3
2H), 3.88 (t, J ¼ 6.4, 2H), 3.41 (q, J ¼ 7.2, 2H), 2.34 (t, J ¼ 6.8, 2H),
1
3
.93 (d, J ¼ 3.6, 2H). C-NMR (100 MHz, CDCl ): d 135.37, 133.45,
3
30.62, 117.63 (q, J ¼ 320.0, CF ), 64.17, 24.80, 21.65, 20.30. IR
C-F
3
2
cm ): 2945, 1276, 1257, 1163, 1029. C H O PF S Cl (567.03) calcd:
1
(
C, 48.67; H, 4.06. Found: C, 48.32; H, 3.91.
23 23 5 3 2
Triphenyl(4-sulfonylbutyl)phosphonium trifluoroacetate (5b): A
1
white solid with yield of 93%. Melting point: 282–2858C. H-NMR
(
400 MHz, CDCl ): d 7.96 (m, J ¼ 7.6, 15H), 4.18 (s, 2H), 3.91 (s, 2H),
3
1
3
2
.43 (s, 2H), 2.02 (s, 2H). C-NMR (100 MHz, CDCl ): d 136.21, 135.64,
3
2
1
1
32.39, 119.57, 45.58, 39.71, 33.43, 23.46, 20.84. IR (cm ): 2887, 2865,
439, 1112, 531. C H O PF S (512.49) calcd: C, 56.19; H, 4.68. Found:
C, 56.11; H, 4.57.
1
2
4
24
5
3
Triphenyl(4-chlorosulfonylbutyl)phosphonium trifluoroacetate (6b):
1
A yellow powder with yield of 92%. Melting point: 222–2258C. H-NMR
(
400 MHz, CDCl ): d 7.83 (m, J ¼ 7.6, 15H), 4.02 (s, 2H), 3.73 (s, 2H),
3
1
.25 (s, 2H), 1.84 (s, 2H). C-NMR (100 MHz, CDCl ): d 134.90, 133.77,
3
2
1
1
3
2
1
30.42, 118.46, 44.69, 37.87, 31.82, 21.73, 19.67. IR (cm ): 2884, 1436,
109, 530. C H O PF SCl (530.99) calcd: C, 54.24; H, 4.33. Found:
2
4
23
4
3
C, 54.47; H, 4.18.
Triphenyl(4-sulfonylbutyl)phosphonium p-toluenesulfonate (5c): A
1
hygroscopic white solid with yield of 92%. H-NMR (400 MHz, CDCl ):
3
d 7.94 (q, J ¼ 7.6, 6H), 7.86 (q, J ¼ 6.4, 3H), 7.83 (m, J ¼ 3.6, 6H), 4.15
(
q, J ¼ 8.0, 2H), 3.86 (t, J ¼ 6.0, 2H), 2.39 (t, J ¼ 6.4, 2H), 1.95
1
3
(
q, J ¼ 7.2, 2H). C-NMR (100 MHz, CDCl ): d 136.78, 134.96, 132.14,
3
2
1
1
19.83, 45.75, 33.67, 22.93, 20.31. IR (cm ): 2887, 1439, 1112, 532.
C H O PS (570.68) calcd: C, 60.98; H, 5.43. Found: C, 60.89; H, 5.41.
2
9
31
6
2
Triphenyl(4-chlorosulfonylbutyl)phosphonium
p-toluenesulfonate
(
6c): A yellow solid with yield of 90%. Melting point: 221–2238C.
1
H-NMR (400 MHz, CDCl ): d 7.88 (q, J ¼ 7.6, 6H), 7.79 (q, J ¼ 6.4, 3H),
3
7
.71 (m, J ¼ 3.6, 6H), 4.01 (q, J ¼ 8.0, 2H), 3.73 (t, J ¼ 6.0, 2H), 2.24
1
3
(
t, J ¼ 6.4, 2H), 1.83 (q, J ¼ 7.2, 2H). C-NMR (100 MHz, CDCl ):
3

Sulfonyl-Functionalized Ionic Liquids
1349
2
d 134.91, 133.71, 130.42, 118.46, 44.61, 31.88, 21.42, 19.62. IR (cm ): 2884,
1
1
5
437, 1110, 531. C H O PS Cl (589.18) calcd: C, 59.07; H, 5.09. Found: C,
29 30 5 2
9.36; H, 4.85.
ACKNOWLEDGMENT
Financial support from the National Natural Science Foundation of China
No. 20233040) is acknowledged.
(
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