Highly Efficient Enantioselective Synthesis of Chiral Sulfones by Rh-Catalyzed Asymmetric Hydrogenation

Article abstract of DOI:10.1021/jacs.8b12657

A highly efficient and enantioselective Rh-(R,R)-f-spiroPhos complex catalyzed hydrogenation of a series of unsaturated sulfones has been developed. With Rh-(R,R)-f-spiroPhos catalyst under mild conditions, not only the asymmetric hydrogenation of both the 3,3-diaryl and exocyclic α,β-unsaturated sulfones was first realized with up to 99.9% ee but also 3-alkyl-3-aryl and benzo[b]thiophene-1,1-dioxides were successfully hydrogenated to the corresponding chiral sulfones with excellent enantioselectivities (up to 99.4% ee) regardless of the steric hindrance, electronic property, and geometry of the substrates. Moreover, this reaction offers a route to (S)-(+)-ar-turmerone as a spice flavor, which is an important synthetic intermediate of pharmaceuticals.

Full text of DOI:10.1021/jacs.8b12657

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Article
Highly Efficient Enantioselective Synthesis of Chiral
Sulfones by Rh-Catalyzed Asymmetric Hydrogenation
Qiaozhi Yan, Guiying Xiao, Ying Wang, Guofu Zi, Zhanbin Zhang, and Guohua Hou
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Journal of the American Chemical Society
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Highly Efficient Enantioselective Synthesis of Chiral Sulfones by Rh-
Catalyzed Asymmetric Hydrogenation
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Qiaozhi Yan,‡ Guiying Xiao,‡ Ying Wang, Guofu Zi, Zhanbin Zhang, Guohua Hou*
Key Laboratory of Radiopharmaceuticals, College of Chemistry, Beijing Normal University, Beijing 100875, China
Asymmetric hydrogenation, Unsaturated sulfones, Chiral sulfones, Rhodium catalysts, Enantioselectivity, f-spiroPhos.
ABSTRACT: A highly efficient and enantioselective Rh-(R, R)-f-spiroPhos complex catalyzed hydrogenation of a series of un-
saturated sulfones has been developed. With Rh-(R, R)-f-spiroPhos catalyst under mild conditions, not only the asymmetric hydro-
genation of both the 3,3-diaryl and exocyclic α,β-unsaturated sulfones was first realized with up to 99.9% ee, but also 3-alkyl-3-aryl
and benzo[b]thiophene 1,1-dioxides were successfully hydrogenated to the corresponding chiral sulfones with excellent enantiose-
lectivities (up to 99.4% ee) regardless of the steric hindrance, electronic property and geometry of the substrates. Moreover, this
reaction offers a route to (S)-(+)-ar-turmerone as a spice flavor, which is an important synthetic intermediate of pharmaceuticals.
1. INTRODUCTION
asymmetric conjugate reduction of prochiral unsaturated sul-
fones is of interest as one of the most straightforward ap-
proaches for chiral sulfone synthesis. However, only a few
efficient catalyst systems for the preparation of chiral sulfones
have been reported so far.10-11
Chiral sulfones represent an important functional group
prevalently found in many biologically active compounds and
pharmaceutical intermediates to produce ar-turmerone,1 (R)-
curcuphenol,1b (S)-curcudiol,1b Remikiren,2 r-secretase inhibi-
tor,3 and inflammatory cytokines inhibitor (Figure 1).4 Sul-
fones serve as useful intermediates and can be converted into
other chiral functional groups by alkylation, halogenation,
oxidation, desulfonylation and Julia olefinations.5
Catalytic asymmetric hydrogenation represents one of the
most efficient, straightforward, and well-established ap-
proaches to chiral compounds.12 To date, only a few examples
of asymmetric hydrogenation of unsaturated sulfones have
been reported.13-17 Andersson and co-workers reported the
efficient asymmetric hydrogenation of vinylic, allylic, homoal-
lylic and cyclic sulfones catalyzed by a chiral Ir/N, P complex
achieving good to high enantioselectivities.13 Recently, Pfaltz
and co-workers also developed two chiral iridium N, P-ligand
complexes which exhibited good activity and enantioselectivi-
ty in the asymmetric hydrogenation of benzothiophene 1,1-
dioxides. But only moderate to good enantioselectivities were
achieved in the hydrogenation of the corresponding alkyl sub-
stituted substrates.14 Zhang and co-workers developed Rh-
catalyzed asymmetric hydrogenation of α-substituted vinyl
sulfones and β-acetylamino acrylosulfones using DTBM-
SegPhos and Tangphos, respectively, achieving high enanti-
oselectivities for the (Z)-β-acetylamino acrylosulfones.15, 16 But
(E)-substrates only provided low to moderate enantioselectivi-
ties. Thus, the substrate scope of the asymmetric hydrogena-
tion of sulfones remains limited.
Figure 1. Key structural elements in chiral pharmaceuticals.
The synthesis of chiral sulfones has attracted increased at-
tention due to their utility as intermediates. Previous reported
methods for the synthesis of chiral sulfones have included
asymmetric arylations/alkenylations of α-bromosulfones,6
rhodium- and organo-catalyzed asymmetric conjugate addition
to unsaturated sulfones,7 asymmetric radical additions,8 and
asymmetric conjugate reduction of prochiral unsaturated sul-
fones.9-11,13-16 Amongst the reported methods, metal-catalyzed
Figure 2. Some challenging substrates of unsaturated sulfones.
Representative challenging sulfone containing moieties for
asymmetric hydrogenation are shown in Figure 2. The follow-
ing sterically hindered substrates including 3,3-diaryl unsatu-
rated sulfones and the cyclic unsaturated sulfones have so far
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remain unexplored as substrates for asymmetric hydrogenation.
Page 2 of 8
trace products were afforded (Table 1, entries 7−10). (S, S)-f-
Binaphane gave higher conversion (29%) and ee value (68%).
Thus demonstrating that the rigidity and bulkier steric hin-
drance of the spiro-backbone in f-spiroPhos had a significant
positive effect on the conversion and enantioselectivity in this
hydrogenation.
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It is not surprising because the bigger aromatic system and the
bulkier steric hindrance in the substrates results in their inert-
ness, which requires much higher catalytic activity. So far
only a few successful examples of asymmetric hydrogenation
of the substrates bearing diaryl substituents at the stereogenic
center were reported.18 In addition, most of present catalysts
are only efficient for either of two isomers of unsaturated sul-
fones. Therefore, the development of efficient catalysts for
asymmetric hydrogenation of unsaturated sulfones to afford
chiral sulfones is still highly desirable.
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Recently, we prepared and demonstrated the chiral diphos-
phine ligand, f-spiroPhos, containing the 1,1′-spirobiindane
skeleton, as a highly efficient and enantioselective ligand in
the hydrogenation of various substrates including unsaturated
nitriles, carboxylic acids and imines.19 Encouraged by the pre-
vious work, we decide to attempt to tackle the asymmetric
hydrogenation of these challenging unsaturated sulfones. We
herein report the first example of highly enantioselective Rh-
catalyzed hydrogenation of 3,3-diaryl and exocyclic unsaturat-
ed sulfones with up to 99.9% ee. The reaction also showed
high substrate scope, E- and Z-isomers of a wide range of sub-
strates including 3,3-diaryl, 3-alkyl-3-aryl, exocyclic α, β-
unsaturated sulfones and benzo[b]thiophene 1,1-dioxide can
also be hydrogenated with excellent enantioselectivities under
mild reaction conditions (Scheme 1).
Figure 3. Structures of the phosphine ligands for hydrogenation
of (E)-1-chloro-3-(1-phenyl-2-(phenylsulfonyl)vinyl)benzene 1a.
Table 1. Asymmetric Hydrogenation of (E)-1-chloro-3-(1-
phenyl-2-(phenylsulfonyl)vinyl)benzene 1a.a
Scheme 1
entry
1
ligand
solvent
CH2Cl2
MeOH
THF
conv.(%)b ee(%)c
(R, R)-f-spiroPhos
(R, R)-f-spiroPhos
(R, R)-f-spiroPhos
(R, R)-f-spiroPhos
(R, R)-f-spiroPhos
(R, R)-f-spiroPhos
(R)-BINAP
60
5
96
ND
ND
ND
ND
98
2
3
3
4
DCE
6
5
dioxane
toluene
toluene
toluene
toluene
toluene
toluene
3
6
99
0.5
2
2. RESULTS AND DISCUSSION
2.1. Asymmetric Hydrogenation of Diaryl α,β-
Unsaturated Sulfones.
7
ND
ND
ND
ND
68
8
(R)-JosiPhos-1
Our initial investigation began with the hydrogenation of
(E)-1-chloro-3-(1-phenyl-2-(phenylsulfonyl)vinyl)benzene 1a
as the model substrate under 80 atm of H2 in CH2Cl2 at room
temperature using 1.0 mol% the complex of [Rh(COD)2]BF4
and (R, R)-f-spiroPhos. Although only a moderate conversion
was provided, a high enantioselectivity was achieved, 96% ee
(Table 1, entry 1). To increase substrate conversion, we subse-
quently investigated the solvent effect. The role of solvent was
found to play an important role in the asymmetric hydrogena-
tion of chiral sulfones. Poor conversion was observed in most
of the solvents such as MeOH, THF, DCE and 1,4-dioxane,
(Table 1, entries 2−5). To our delight, performing reactions in
toluene as the solvent, complete conversion and high enanti-
oselectivity (98% ee) was achieved (Table 1, entry 6). Follow-
ing solvent optimization, a screening of commercially availa-
ble chiral phosphorus ligands (Figure 3) revealed that (S)-
BINAP, electron-rich (R)-JosiPhos, (S, S)-Me-Duphos and (R,
R)-Ph-BPE were ineffective in this transformation and only
9
(R, R)-Me-Duphos
(R, R)-Ph-BPE
1
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11
a
1
(S, S)-f-Binaphane
29
Reaction conditions: Rh(COD)2BF4/ligand/substrate ratio =
1.0 : 1.1 : 100, 80 atm H2, 24 h, rt. b Determined by GC analysis. c
Determined by chiral SFC using a chiral stationary phase Lux 5u
Cellulose-3 (250 × 4.60 mm ), MeOH : CO2 = 30 : 70, 3.0
mL/min, 210 nm.
Encouraged by the promising results obtained by the asym-
metric
hydrogenation
of
(E)-1-chloro-3-(1-phenyl-2-
(phenylsulfonyl)vinyl)benzene 1a, we then prepared a variety
of 3,3-diaryl unsaturated sulfones 1 and applied them to the
hydrogenation in toluene under the catalyst loading of 1.0 mol%
[Rh(COD)2]BF4/(R, R)-f-spiroPhos and 80 atm H2 (Table 2).
All of the substrates examined (1a − 1o) could be successfully
hydrogenated to produce the corresponding chiral sulfones in
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high yields with excellent enantioselectivities, 94 − 99.9% ee.
1
Neither the electron property nor position of the substituents at
the two aryl rings of the substrates had an apparent effect on
the enantioselectivity. In general, the substrates with electron-
donating substituents including Me, MeO group exhibited
relatively lower reactivity compared with those bearing elec-
tron-withdrawing substituents. For instance, the fluro- or chlo-
ro-substituted substrates 1a − 1g were hydrogenated in full
conversions with 96 − 99.9% ee, while the substrates bearing
electron-donating substituents Me, MeO 1h − 1l provided 94
− 97% conversions. Notably, even if the substrate contained
the same substituent present at different position of the two
phenyl ring (i.e meta and para), excellent enantioselectivity
was achieved. This is shown in the following example (sub-
strates 1i and 1n) substituted by a methyl group at meta-
position of one phenyl ring or both meta- and para-position of
the two phenyl rings respectively provided the highest enanti-
oselectivity, 99.9% ee. Remarkably, this catalyst could also
exhibited the comparable activity and enantioselectivity in the
hydrogenation of the corresponding (Z)-isomers to afford the
products with an opposite absolute configuration compared
with that obtained by (E)-isomers. For example, the substrates
(Z)-1b and (Z)-1d were hydrogenated providing the desired
products 2b and 2d with 99.9% and 98% ee respectively. It
was found that the (Z)-substrates provided the hydrogenation
products with an opposite absolute configuration compared
with that afforded by (E)-isomers by comparison with the sign
of the specific rotation and order of elution for major and mi-
nor enantiomers from the chiral column. The absolute configu-
ration of hydrogenation product 2l was determined and as-
signed to be (R) configuration by X-ray crystallographic anal-
ysis of the corresponding single-crystal structure (Figure 4). It
was demonstrated that this method could produce chiral sul-
fones with either desired configuration, (S) or (R)-enantiomer
in excellent enantioselectivities by the asymmetric hydrogena-
tion of (E)- or (Z)-α,β-unsaturated sulfones.
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a
Unless otherwise mentioned, all reactions were carried out
with a [Rh(COD)2]BF4/(R,R)-f-spiroPhos/substrate ratio of 1.0 :
1.1 : 100, toluene, 80 atm H2, rt, 24 h. The conversion was deter-
mined by 1H NMR spectroscopy or GC analysis; the enantioselec-
tivity was determined by SFC analysis using a chiral stationary
phase.
Table 2. Rh-Catalyzed Asymmetric Hydrogenation of 3,3-
Diaryl α,β-Unsaturated Sulfones 1.a
Figure 4. X-ray crystal structure of the product (R)-2l.
2.2. Asymmetric Hydrogenation of Cyclic α,β-
Unsaturated Sulfones.
Previously, Charette and co-workers reported the copper-
DuPhos(O) catalyzed enantioselective hydrosilylation of vinyl
phenyl sulfones including two cyclic sulfones and achieved
excellent enantioselectivities.11 Surprisingly, the asymmetric
hydrogenation of cyclic unsaturated sulfones (substrate 3) has
not been reported. To develop the asymmetric hydrogenation
of this class of substrates and extend the substrate scope of the
catalyst, we decided to evaluated the cyclic α,β-unsaturated
sulfone 3a under the previously optimized reaction conditions
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in the hydrogenation of 3,3-diaryl α, β-unsaturated sulfones 1, 2.3. Asymmetric Hydrogenation of Benzo[b]thiophene
Page 4 of 8
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a conversion of 76% conversion and 90% ee was obtained.
After further solvent optimization, dichloromethane was found
to result in full conversion and better enantioselectivity (93%
ee). Lowering the hydrogen pressure from 80 atm to 10 atm
still resulted in complete substrate conversion while preserv-
ing high enantioselectivity. The effect of different electronic
substitutes on the ring was investigated and all resulted in full
conversions and excellent enantioselectivities (> 92% ee). It
was revealed that ring size in the substrates (i.e. cyclopentyl,
cyclohexyl or cycloheptyl) had no apparent influence on the
enantioselectivity (substrates 3a − 3h) and excellent enantiose-
lectivities were observed. However, the reactivity was affected
by the ring size of substrates. The substrates with five-
membered ring 3a − 3d could be hydrogenated to obtain the
corresponding products in satisfactory conversions under 10
atm of H2 at room temperature for 1 h, whereas the substrate
with a six- or seven-membered ring required higher catalyst
loadings and increased hydrogen pressure for complete con-
version. The substrate (E)-3f could be fully hydrogenated un-
der 80 atm of hydrogen pressure in 24 h, while (E)-3g with a
seven-membered ring required 2 mol% catalyst loading. The
catalyst system was also suitable for the (Z) isomer of the cy-
clic unsaturated sulfones, such as the (Z)-3h, providing the
corresponding product 4h with excellent enantioselectivities
(93% ee), with a reversal of the absolute configuration as dis-
cussed above.
1,1-dioxides.
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Recently, Pfaltz’s group reported Ir-P, N complex catalyzed
asymmetric hydrogenation of benzo[b]thiophene 1,1-dioxides,
and the 2- and 3-aryl substituted substrates were hydrogenated
with high conversions and excellent enantioselectivities (up to
99% ee).14 However, poor conversions or moderate to good
enantioselectivities were observed for the 2-alkyl substituted
substrates. The application of the catalyst/ligand investigated
reported herein, Rh-(R, R)-f-spiroPhos, for the hydrogenation
of 2-alkyl-substituted benzo[b]thiophene 1,1-dioxides yielded
excellent enantioselectivities (up to 99% ee) for a wide range
of 2-alkyl-substituted substrates 5 (Table 4). The 2-methyl-, 2-
ethyl- and 2-npropyl-substituted substrates 5a − 5c were hy-
drogenated under 10 atm hydrogen pressure in an hour to pro-
vide the products with high enantioselectivities and conver-
sions. Replacing the alkyl substituent at 2-position with an
isopropyl group ((E)-5d) still maintained the excellent enanti-
oselectivity of 96% ee, but led to a decreased conversion to
81%, and was attributed to the increased steric hindrance. The
2-phenyl substituted substrate (E)-5f also exhibited lower re-
activity but higher hydrogen pressure and longer reaction time
for the satisfactory conversion were required. Inspired by
these exciting results obtained by this cyclic substrates, we
also investigated the hydrogenation of linear α-methyl or phe-
nyl substituted substrate 5g and 5h, but very poor conversions
(5% and 20% conversion, respectively) were observed.
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Table 4. Rh-Catalyzed Asymmetric Hydrogenation of Ben-
zo[b]thiophene 1,1-Dioxides 5. a
Table 3. Rh-Catalyzed Asymmetric Hydrogenation of Cy-
clic α,β-Unsaturated Sulfones 3.a
a
Unless otherwise mentioned, all reactions were carried out
with a [Rh(COD)2]BF4/(R,R)-f-spiroPhos/substrate ratio of 1.0 :
a
Unless otherwise mentioned, all reactions were carried out
1.1 : 100, CH2Cl2, 10 atm H2, rt, 1 h. The conversion was deter-
with a [Rh(COD)2]BF4/(R,R)-f-spiroPhos/substrate ratio of 1.0 :
1
mined by H NMR spectroscopy; the enantioselectivity was de-
1.1 : 100, CH2Cl2, 10 atm H2, rt, 1 h. The conversion was deter-
termined by HPLC analysis using a chiral stationary. b 80 atm H2,
24 h.
1
mined by H NMR spectroscopy; the enantioselectivity was de-
termined by HPLC analysis using a chiral stationary. b 80 atm H2,
c
d
24 h.
[Rh(COD)2]BF4 (2.0 mol%), 80 atm H2, 24 h.
[Rh(COD)2]BF4 (3 mol%), 80 atm H2, 24 h.
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2.4. Asymmetric Hydrogenation of 3-Alkyl-3-aryl α,β-
1
Unsaturated Sulfones.
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Finally, we turned our attention to the asymmetric hydro-
genation of 3-alkyl-3-aryl α,β-unsaturated sulfones. Initially,
we chose (E)-((2-phenylprop-1-en-1-yl)sulfonyl)benzene 7a as
the model substrate under 80 atm of H2 in CH2Cl2. Both full
conversion and high enantioselectivity of 94% ee were ob-
tained. For comparison, other electron-rich ligands including
(R)-JosiPhos-1, (S, S)-Me-Duphos, (R, R)-Ph-BPE and (S, S)-
f-Binaphane were also evaluated, but only poor conversions
and enantioselectivities were obtained except the ligand (S,S)-
f-Binaphane achieving relatively better results, 71% conver-
sion and 77% ee.20 As shown above, the hydrogen pressure
can be lowered to 10 atm without any deleterious effects on
enantioselectivity or reaction time (1 hour). Further lowering
the hydrogen pressure to 5 atm, high conversion (97%) and
high enantioselectivity were achieved. In addition to CH2Cl2,
1,4-dioxane was also proved as the suitable solvent for this
hydrogenation and an extremely high enantioselectivity of 99%
ee with full conversion could be achieved.
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a
Unless otherwise mentioned, all reactions were carried out
It was revealed that a variety of (E)-3-alkyl-3-aryl α,β-
unsaturated sulfones 7 could be successfully hydrogenated to
produce the corresponding chiral sulfones with 93 − 99.4% ee
(Table 5) using the catalyst system. The electron property and
position of the substituents at the phenyl ring of the substrates
had no obvious influence on both the reactivity and enantiose-
lectivity. Generally, the substrates with electron-donating sub-
stituents on the phenyl ring gave higher enantioselectivities
than those with electron-withdrawing substituents. For exam-
ple, the substrate (E)-7i and (E)-7j with a para-fluoro or chlo-
ro substituent gave 93 − 94% ee, while the substrate (E)-7k
with a para-methyl substituent yielded 8k with as high as 99%
ee. The substrates with a larger 3-alkyl substituent such as
ethyl group ((E)-7l) could also give comparable enantioselec-
tivity with substrate (E)-7a. Both the 1-naphthyl substrate (E)-
7m and 2-naphthyl (E)-7n exhibited higher enantioselectivity,
and (E)-7n provided product 8n with the highest 99.4% ee
value. The hydrogenation of the (Z)-isomers such as the sub-
strates (Z)-7o and (Z)-7p could also be performed smoothly
providing the desired products 8o and 8p with 97% and 96%
ee respectively, which was the highest enantioselectivity in the
hydrogenation of the (Z)-isomers of 3-alkyl-3-aryl α,β-
unsaturated sulfones so far. It was also found that the products
obtained by the (E)- and (Z)-isomers were opposite enantio-
mers.
with a [Rh(COD)2]BF4/(R,R)-f-spiroPhos/substrate ratio of 1.0 :
1.1 : 100, CH2Cl2, 10 atm H2, rt, 1 h. The conversion was deter-
mined by 1H NMR spectroscopy or GC analysis; the enantioselec-
tivity was determined by HPLC analysis using a chiral stationary
phase. 10 atm H2, 2 h, 1,4-dioxane. Rh(COD)2PF6 (2 mol%),
80 atm H2, 24 h.
b
c
2.5. Preparative Asymmetric Hydrogenation on a Larg-
er Scale of Unsaturated Sulfones.
Under the optimal reaction conditions, we carried out the
preparative hydrogenation of the following substrates in Fig-
ure 5 on a large scale (1.0 mmol). The desired products were
obtained with maintained high conversions and excellent en-
antioselectivities.
Figure 5. Substrates evaluated on a large scale.
2.6. Application of the Rh-(R,R)-f-spiroPhos Catalyst to
the Synthesis of Biologically Active Compounds and
Pharmaceuticals.
The optical active chiral sulfones are versatile synthetic in-
termediates that can be easily converted to various derivatives.
To illustrate this point, we performed a short synthesis of the
precursor of (S)-(+)-ar-turmerone and (+)-bisacumol (Scheme
2). Product (R)-8k obtained by asymmetric hydrogenation
could be transformed by acylation reaction with 3,3-
dimethylacrylic acid methyl ester and MgBr2-Et2O to the in-
termediate 9. In the following step, intermediate 9 was con-
verted to (S)-(+)-ar-turmerone as a spice flavor of turmeric.
(S)-(+)-ar-turmerone could also be used to the asymmetric
synthesis of (S)-ar-himachalene, which is a pheromone com-
ponent of the flea beetle and (+)-bisacumol, as a member of
the aromatic bisabolane sesquiterpene family isolated from the
rhizome of Curcuma Xanthorrhiza.1b
Table 5. Rh-Catalyzed Asymmetric Hydrogenation of (E)-
3-alkyl-3-aryl α,β-Unsaturated Sulfones 7.a
Scheme 2
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method to allow for the broad screening of chiral sulfones for
Page 6 of 8
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a wide variety of industries including pharmaceuticals, pesti-
cides or chiral polymers.
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ASSOCIATED CONTENT
Supporting Information. Experimental procedures, compound
characterization data, analysis of enantioselectivities of products
and crystal parameters for compound 2l. This material is available
free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
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Corresponding Author
*ghhou@bnu.edu.cn.
Author Contributions
‡These authors contributed equally.
Based on the configurations of hydrogenation products and
the reported mechanism of rhodium and iridium catalyzed
asymmetric hydrogenation reactions,21 we proposed the transi-
tion model determining the enantioselectivity (Scheme 3). The
ferrocenyl group of the ligand blocked one side of the complex
and prevented the coordination of the substrate from this ori-
entation. The substrate could only coordinate with rhodium
from the opposing face of the catalyst. The repulsive steric
interaction of the ligand with the larger sulfonyl group led to
the coordination of the (E)-substrate with rhodium more fa-
vorable from the Re-face than Si-face of the α, β-unsaturated
sulfones, predictably resulting in the (R) product. By X-ray
crystallographic analysis of the corresponding single-crystal
structure or comparison with the sign of the specific rotation
reported, the stereochemistry of some other products was de-
termined. It was demonstrated to be in good agreement with
the predicted stereochemical outcome of the hydrogenation
products.
Notes
The authors declare no competing financial interests.
ACKNOWLEDGMENT
We thank the National Natural Science Foundation of China
(Grant Nos. 21672024, 21272026, and 21472013), Beijing Natu-
ral Science Foundation (2182025), and Beijing Municipal Com-
mission of Education for generous financial support.
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In conclusion, we have developed a highly efficient method
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