N-Heterocyclic carbenes as ligands in palladium-catalyzed Tsuji-Trost allylic substitution

Article abstract of DOI:10.1016/j.jorganchem.2005.07.043

A Pd(0)-catalyzed allylic substitution (i.e., Tsuji-Trost reaction) using N-heterocyclic carbene as a ligand was investigated. It has been proven that an imidazolium salt 2d having bulky aromatic rings attached to the nitrogens in its imidazol-2-ylidene skeleton is suitable as a ligand precursor and that a Pd₂dba₃-imidazolium salt 2d-Cs₂CO₃ system is highly efficient for producing a Pd-NHC catalyst in this reaction. Allylic substitution using a Pd-NHC complex differed from that using a Pd-phosphine complex as follows: (1) the reaction using a Pd-NHC complex required elevated temperature (50 °C or reflux in THF), (2) allylic carbonates were inert to a Pd-NHC complex, and (3) nitrogen nucleophiles such as sulfonamide and amine did not react with allylic acetate. It was also found that allylic substitution with a soft nucleophile using a Pd-NHC catalyst proceeds via overall retention of configuration to give the product in a stereospecific manner, the stereochemical reaction course obviously being the same as that of the reaction using a Pd-phosphine complex.

Full text of DOI:10.1016/j.jorganchem.2005.07.043

Journal of Organometallic Chemistry 690 (2005) 5753–5758
www.elsevier.com/locate/jorganchem
N-Heterocyclic carbenes as ligands in palladium-catalyzed
Tsuji–Trost allylic substitution
a,
a
b
Yoshihiro Sato *, Taro Yoshino , Miwako Mori
a
Graduate School of Pharmaceutical Sciences, Hokkaido University, Kita Ku Kita 12 Nishi 6, Sapporo Hokkaido 060-0812, Japan
b
Health Sciences University of Hokkaido, Ishikari-Tobetsu, Hokkaido 061-0293, Japan
Received 9 June 2005; accepted 11 July 2005
Available online 30 August 2005
Abstract
A Pd(0)-catalyzed allylic substitution (i.e., Tsuji–Trost reaction) using N-heterocyclic carbene as a ligand was investigated. It has
been proven that an imidazolium salt 2d having bulky aromatic rings attached to the nitrogens in its imidazol-2-ylidene skeleton is
suitable as a ligand precursor and that a Pd2dba3–imidazolium salt 2d–Cs2CO3 system is highly efficient for producing a Pd–NHC
catalyst in this reaction. Allylic substitution using a Pd–NHC complex differed from that using a Pd–phosphine complex as follows:
(1) the reaction using a Pd–NHC complex required elevated temperature (50°C or reflux in THF), (2) allylic carbonates were inert to
a Pd–NHC complex, and (3) nitrogen nucleophiles such as sulfonamide and amine did not react with allylic acetate. It was also
found that allylic substitution with a soft nucleophile using a Pd–NHC catalyst proceeds via overall retention of configuration
to give the product in a stereospecific manner, the stereochemical reaction course obviously being the same as that of the reaction
using a Pd–phosphine complex.
Ó 2005 Published by Elsevier B.V.
Keywords: N-Heterocyclic carbene; Palladium; Allylation; Tsuji–Trost reaction
1. Introduction
NHCs as ligands (e.g., Suzuki–Miyaura coupling [3],
Kumada–Tamao–Corriu-type coupling [4], Mizoroki–
Heck reaction [5], amination of aryl halide [6], Sono-
gashira coupling [7]).
After the first isolation and X-ray crystallographic
characterization of nucleophilic N-heterocyclic carb-
enes (NHCs) [1], the chemistry of the NHC has rapidly
developed, since NHCs are attractive not only as a sta-
ble isolable carbene species but also as molecules able
to coordinate to various transition metals [2]. NHCs
are regarded as strong r-donor ligands and have reac-
tivities similar to those of sterically bulky tertiary phos-
phines. Recently, high catalytic efficiency has been
found in a variety of reactions, especially those cata-
lyzed by a palladium complex, by virtue of using
The reaction of a p-allylpalladium complex with soft
carbon nucleophiles to give an allylated product was re-
ported for the first time by Tsuji in 1965 [8]. The reaction
was expanded to a catalytic process by Hata and Atkins
[9], and its synthetic utility was greatly enhanced by
Trost [10]. Pd(0)-catalyzed allylic substitution is now
called ‘‘Tsuji–Trost reaction’’ and has been recognized
as one of the most synthetically useful C–C bond form-
ing reactions. However, Pd(0)-catalyzed allylic substitu-
tion using NHCs as ligands has not been investigated in
detail [11,12]. We describe herein results of our contin-
uing studies on Pd(0)-catalyzed allylic substitution using
NHCs as ligands.
*
Corresponding author. Tel./fax: +81117064982.
E-mail address: biyo@pharm.hokudai.ac.jp (Y. Sato).
0022-328X/$ - see front matter Ó 2005 Published by Elsevier B.V.
doi:10.1016/j.jorganchem.2005.07.043

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Y. Sato et al. / Journal of Organometallic Chemistry 690 (2005) 5753–5758
2. Results and discussion
improved the yield of the desired product. The use of
3d, having a sterically bulky substituent on the aromatic
ring, showed the best reactivity in this reaction, giving 5
in 77% yield (run 4).
2.1. Reaction of allylic acetates with dimethyl malonate
using NHCs as ligands
It has been reported that Pd–NHC species can be
formed in situ from a palladium complex and imidazo-
lium salts in the presence of Cs2CO3 as a base, and this
Pd–NHC catalyst has been used in various C–C cou-
pling reactions [3c]. Thus, reactions of 1 with dimethyl
malonate were again investigated using a Pd–NHC cat-
alyst formed from Pd2dba3 Æ CHCl3 and imidazolium
salt 2d in the presence of Cs2CO3 (Table 2).
Initially, reactions of acetate 1 with sodium dimethyl-
malonate (4) were investigated using various Pd–NHC
catalysts (3a)–(3d) formed by treatment of PdCl2 with
BuLi in the presence of imidazolium salts (2a)–(2d)
(Table 1) [13].
R
N
PdCl2
(5 mol %)
Cl-
(5 mol %)
2a-2d
N
Pd2dba3·CHCl3
(2.5 mol %)
R
OAc
CH(CO2Me)2
BuLi (15 mol %)/THF
CH2(CO2Me)2
2d (5.0 mol %)
R
N
Ph
Ph
Ph
Ph
base (2 equiv)
THF, 50 ˚C
Cs2CO3 (0.1 equiv)
1
5
Pd
N
R
3a-3d
Surprisingly, when a THF solution of acetate 1 and
sodium dimethylmalonate (4) was treated with a Pd–
NHC catalyst formed from Pd2dba3 Æ CHCl3
OAc
CH(CO2Me)2
OH
+
NaCH(CO2Me)2 (4)
(2 equiv)
Ph
Ph
Ph
Ph
Ph
Ph
5
1
6
THF, 50 ˚C
(2.5 mol%), imidazolium salt 2d (5.0 mol%), and
Cs2CO3 (10 mol%), the reaction was completed in 2 h
to give the desired product 5 in excellent yield (98%)
(Table 2, run 1). In addition, the reaction of 1 and di-
methyl malonate using Pd2dba3 Æ CHCl3 and imidazo-
lium salt 2d in the presence of an excess amount of
Cs2CO3 at 50 °C gave the desired product 5 in quantita-
tive yield, although the reaction was slightly prolonged
(run 2). These results indicate that the Pd–NHC species
generated from Pd2dba3 Æ CHCl3, 2d, and Cs2CO3 is
more reactive than the above-mentioned Pd–NHC cata-
lyst prepared from PdCl2, 2d, and BuLi and that a prior
preparation of sodium dimethylmalonate (4) from di-
methyl malonate and NaH is unnecessary in this catalyst
system.
To a THF suspension of PdCl2 (5 mol%) and imi-
dazolium salt 2a (5 mol%) was added a solution of
BuLi–hexane (15 mol%) at 0 °C, and the mixture was
stirred for about 1 h at this temperature. To the mixture
of a Pd–NHC catalyst (3a) was added a THF solution of
1 followed by addition of a solution of 4 at 0 °C, and the
mixture was heated at 50 °C for 24 h. As a result, the
desired substitution product 5 was afforded in only 6%
yield, and the starting material 1 was recovered in 76%
yield along with alcohol 6, which would be derived from
1 although the mechanism was not clear, in 13% yield
(Table 1, run 1). It was found that the reaction of 1
and 4 with Pd–NHC catalyst 3c or 3d, having aromatic
rings on nitrogens in the imidazol-2-ylidene skeleton,
A control experiment without imidazolium salt 2d
was carried out in order to confirm that a NHC, gener-
ated from imidazolium salt 2d and Cs2CO3, operates as
a ligand in this reaction (Scheme 1).
Table 1
Allylic substitution of 1 with 4 using a Pd–NHC complex
Run
1
Imidazolium salt
(–R)
Time
(h)
Yield (%)
Recover of 1
(%)
5
6
24
6
13
76
Ph
Table 2
Reaction of 1 with dimethyl malonate using Pd2dba3 and imidazolium
salt 2d
(2a)
Run
Base
Time (h)
Yield (%)
2
3
15
18
–
11
16
79
30
1
2
NaH
Cs2CO3
2
10
98
100
(2b)
(2c)
25
2.5 mol %
Pd2dba3•CHCl3
OAc
CH(CO2Me)2
Ph
5: 3%
recovery of 1: 97%
NaCH(CO2Me)2 (4)
Ph
Ph
Ph
i
4
37
77
–
16
Pr
(2 equiv)
THF, 50 ˚C
1
(2d)
i
Pr
Scheme 1.

Y. Sato et al. / Journal of Organometallic Chemistry 690 (2005) 5753–5758
5755
The reaction of 1 and sodium dimethylmalonate (4)
with Pd2dba3 Æ CHCl3 (2.5 mol%) in the absence of imi-
dazolium salt 2d in THF at 50 °C produced a trace
amount of desired product 5 in 3%, and the starting
material 1 was recovered in 97% yield. This result indi-
cates that the NHC formed from 2d actually operates
as a ligand in this reaction.
It is well known that Pd(0)-catalyzed allylic substitu-
tion of the allylic carbonate proceeds without addition
of bases bacause an alkoxide is formed via oxidative
addition of the carbonate to the Pd(0) complex followed
by decarbonylation [14]. Thus, allylic substitution of
carbonate 11 using a Pd–NHC complex was investigated
(Table 3).
Unexpectedly, reaction of 11 with dimethyl malonate
using Pd–NHC complex generated in situ from Pd2dba3
and imidazolium salt 2d in the presence of Cs2CO3 gave
allylation product 5 in a very low yield (5%) and un-
changed 11 was recovered in 90% (run 1). The use of a
Pd–NHC catalyst generated by treatment of PdCl2–imi-
dazolium salt 2d with BuLi showed the same tendency
and only a trace amount of the desired product was ob-
tained along with unchanged 11 in 85% (run 2). At pres-
ent, the reason why a Pd–NHC catalyst system is
ineffective for the allylic substitution of carbonates is
not clear.
Next, the reaction of allylic acetate with other nucle-
philes instead of malonate was investigated. The reac-
tion of allylic acetate 1 with b-ketoester 12 using the
above-mentioned Pd–NHC complex, generated from
Pd2dba3 and 2d, in the presence of Cs2CO3, gave allyla-
tion product 13 in 38% yield as a mixture of diastereo-
mers (ratio of 1:1) along with 130 in 48% yield
(Scheme 4). The product 130, which would be formed
via isomerization from 13, was obtained as a sole
2.2. Scope and limitations of allylic substitution by
Pd–NHC complex
To evaluate the scope of this reaction, allylic substitu-
tion of various substrates using a Pd–NHC complex,
generated in situ from Pd2dba3 and imidazolium salt
2d in the presence of Cs2CO3, was investigated. The
reaction of unsymmetrically substituted allylic actetate
7 and dimethyl malonate required heating to reflux,
and allylation products were produced in a total 89%
yield (linear-allylation product 8a, 55%; branched-
allylation product 8b, 18%; double-allylation product
8c, 16%) (Scheme 2).
In the case of cyclic lactone 9, the reaction with di-
methyl malonate proceeded at 50 °C to give the product
10 in 63% yield as a single diastereomer (Scheme 3).
Pd2dba3·CHCl3
(2.5 mol %)
2d (5 mol %)
Ph
CH(CO2Me)2
8a: 55%
Ph
OAc
CH(CO2Me)2
CH2(CO2Me)2 (2 equiv)
Cs2CO3 (2.1 equiv)
7
Ph
THF, reflux
Table 3
8b: 18%
Allylic substitution of carbonate 11 with dimethyl malonate using
Pd–NHC complex
Ph
C(CO2Me)2
2
Pd catalyst, base
OCO2Me
Ph
CH(CO2Me)2
2d (5.0 mol %)
8c: 16%
CH2(CO2Me)2 (1.2 equiv)
THF, 50 ˚C, 26 h
Ph
Ph
Ph
Scheme 2.
5
11
Run Pd catalyst
(mol%)
Base
(mol%)
Yield Recovery of
11 (%)
Pd2dba3·CHCl3
(2.5 mol %)
2d (5 mol %)
CH(CO2Me)2
1
2
Pd2dba3 Æ CHCl3 (2.5) Cs2CO3 (10)a 5%
PdCl2 (5) Trace 85
BuLi (15)b
90
O
CH2N2
Et2O
a
O
10 mol% of Cs2CO3 was used for preparation in situ of a Pd–NHC
CH2(CO2Me)2 (2 equiv)
Cs2CO3 (2.1 equiv)
CO2Me
10: 63%
complex from Pd2dba3 and imidazolium salt 2d.
b
Pd–NHC complex was prepared by treatment of PdCl2 and 2d with
9
THF, 50 ˚C
BuLi and then carbonate 11 and dimethyl malonate were added to the
Scheme 3.
catalyst mixture.
Pd2dba3·CHCl3
(2.5 mol %)
O
O
OH O
OAc
O
O
2d (5 mol %)
OEt
OEt
Ph
+
+
Cs2CO3 (2.1 equiv)
THF, reflux, 37 h
Ph
Ph
OEt
Ph
Ph Ph
1
12
13: 38%
13': 48%
(2 equiv)
(1:1 diastereomer) (single isomer)
Scheme 4.

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Y. Sato et al. / Journal of Organometallic Chemistry 690 (2005) 5753–5758
O
O
Pd2dba3·CHCl3 (2.5 mol %)
2d (5.0 mol %)
Pd2dba3·CHCl3
(2.5 mol %)
2d (5 mol %)
O
O
O
O
OEt
OAc
CO2Me
OAc
Cs2CO3 (0.1 equiv)
CO2Me
OEt
+
Cs2CO3 (2.1 equiv)
THF, reflux, 17 h
15
(2 equiv)
NaH (1.1 equiv)
THF, reflux, 13 h
14
16: 72%
21
22: 46%
Scheme 5.
Scheme 8.
Intramolecular allylic substitution of 21 was also
carried out under similar conditions, and the cyclized
product 22 was obtained in a moderate yield [15]
(Scheme 8).
product, although the geometry of the alkene fragment
of 130 was not determined.
Allylic substitution of allyl acetate 15 with cyclic b-
ketoester 14 under similar conditions also proceed
smoothly to afford the product 16, having a quaternary
carbon center, in good yield (Scheme 5).
On the other hand, the reaction of 1 with a nitrogen
nucleophile, N-methyltosylamide (17), under similar
conditions and under conditions using NaH as a base
did not afford the product 18, and the starting material
1 was recovered in 86% and 83% yields, respectively
(Scheme 6). Similarly, the reaction of 1 with benzyl-
amine did not afford the coupling product 19, only pro-
ducing deacetylation product 20 in 41% yield (E/
Z = 2.7:1) along with the starting material 1 in 43%
yield. Although the reason is not clear, allylic substitu-
tion using a Pd–NHC complex seems to be inapplicable
to nitrogen nucleophiles (Scheme 7).
2.3. Stereochemistry in the allylic substitution using a
Pd–NHC catalyst
In order to examine the stereochemical reaction
course in the allylic substitution using a Pd–NHC cata-
lyst, reactions of 23-a and 23-b were investigated
(Scheme 9).
In the reactions of 23-a and 23-b under similar condi-
tions, 24-a and 24-b were stereospecifically produced in
83% and 94% yields, respectively. These results indicate
that allylic substitution using a Pd–NHC catalyst pro-
ceeds via an overall retention of configuration in a man-
ner similar to when Pd–phosphine complexes are used.
cat.
OAc
CH(CO2Me)2
Pd2dba3·CHCl3 (2.5 mol %)
2d (5.0 mol %)
Cs2CO3 (2.1 equiv)
Pd2dba3·CHCl3/ 2d
TsNMe
Ph
CH2(CO2Me)2, Cs2CO3
Ph
THF, reflux, 25 h
OAc
THF, 50 ˚C
18: trace
(recovery of 1: 86%)
Ph
Ph
23-
OAc
24- : 83%
1
Pd2dba3·CHCl3 (2.5 mol %)
2d (5.0 mol %)
Cs2CO3 (0.1 equiv)
+
cat.
CH(CO2Me)2
Pd2dba3·CHCl3/ 2d
TsNHCH3
(2.0 equiv)
CH2(CO2Me)2, Cs2CO3
TsNMe
17
Pd-NHC complex
THF, reflux, 21 h
Ph
Ph
NaH (2 equiv)
THF, 50 ˚C
18: trace
(recovery of 1: 83%)
23-
24- : 94%
Scheme 6.
Scheme 9.
NHBn
Pd2dba3·CHCl3 (2.5 mol %)
2d (5.0 mol %)
Cs2CO3 (2.1 equiv)
Ph
Ph
OAc
19: not obtained
BnNH2
(2 equiv)
+
Ph
Ph
THF, reflux, 37 h
1
Ph
Ph
20: 41%
(E:Z = 2.7:1)
recovery of 1: 43%
Scheme 7.

Y. Sato et al. / Journal of Organometallic Chemistry 690 (2005) 5753–5758
5757
2.4. Conclusions
the residue was purified by column chromatography
on silica gel (hexane–EtOAc, 8/1) to give 5 in 77%
yield.
A Pd(0)-catalyzed allylic substitution using N-het-
erocyclic carbene (NHC) as a ligand was investigated,
and it was found that an imidazolium salt 2d having
bulky aromatic rings attached to the nitrogens in its
imidazol-2-ylidene skeleton is suitable as a ligand pre-
cursor. It has also been proven that a Pd2dba3–imi-
dazolium salt 2d–Cs2CO3 system is highly efficient
for producing a Pd–NHC catalyst in this reaction.
Allylic substitution using a Pd–NHC complex is differ-
ent from that using a Pd–phosphine complex as
follows: (1) the reaction using a Pd–NHC complex
requires elevated temperature (50 °C or reflux in
THF), (2) allylic carbonates are inert to a Pd–NHC
complex, and (3) nitrogen nucleophiles such as sulfon-
amide or amine do not react with allylic acetate in the
Pd–NHC catalyst system. It was also found that allylic
substitution with a soft nucleophile such as a malonate
using a Pd–NHC catalyst proceeds via overall reten-
tion of configuration to give the product in a stereo-
specific manner, the stereochemical reaction course
obviously being the same as that of the reaction using
a Pd–phosphine complex.
3.2. Typical procedure for allylic substitution of 1 with 4
using a Pd–NHC catalyst generated from
Pd2dba3 Æ CHCl3 and imidazolium salt 2d in the
presence of Cs2CO3 (Table 2, run 2)
To a reddish-brown suspension of Pd2dba3 Æ CHCl3
(10.4 mg, 0.01 mmol), imidazolium salt 2 d (8.5 mg,
0.02 mmol) and Cs2CO3 (273.7 mg, 0.84 mmol) in
THF (0.4 mL) were added a solution of acetate 1
(100.9 mg, 0.4 mmol) in THF (2 mL) and a solution
of dimethyl malonate (0.09 mL, 0.8 mmol) in THF
(2 mL) at 0 °C, and the mixture was heated at 50 °C
for 10 h. To the mixture was added sat. NH4Cl aque-
ous solution at 0 °C, and the organic layer was ex-
tracted with Et2O. The combined organic layer was
washed with brine and dried over Na2SO4. After re-
moval of the solvent, the residue was purified by col-
umn chromatography on silica gel (hexane–EtOAc,
4/1) to give 5 in 100% yield.
3.3. Spectral data
3. Experimental
3.3.1. (E)-Methyl-9-acetoxy-3-oxonon-7-enoate (21)
The compound 21 was synthesized by acetylation of
(E)-methyl-9-hydroxy-3-oxonon-7-enoate [15b]. 1H
NMR (270 MHz, CDCl3) d 1.71 (tt, J = 7.3, 7.3 Hz,
2H), 2.05–2.11 (m, 2H), 2.06 (s, 3 H), 2.55 (t, J = 7.3
Hz, 2H), 3.45 (s, 2H), 3.74 (s, 3H), 4.51 (d, J = 6.4 Hz,
2H), 5.54–5.61 (m, 1H), 5.72 (dt, J = 15.7, 6.4 Hz, 1
H); IR (neat) 2952, 1740, 1717, 1235 cmꢀ1; EI LRMS
m/z 242 (M+), 211 (M+ ꢀ OCH3), 182 (M+ ꢀ AcOH),
150, 122. EI HRMS Calc. for C11H15O4 (M+ ꢀ OCH3)
211.0970, found 211.0980.
All manipulations were performed under an argon
atmosphere unless otherwise stated. All solvents and re-
agents were purified when necessary using standard pro-
cedures. Imidazolium salts were dried in vacuo at 80 °C
just before its use. Column chromatography was per-
formed on silica gel 60 (Merck, 70–230 mesh), and flash
chromatography was performed on silica gel 60 (Merck,
230–400 mesh).
3.1. Typical procedure for allylic substitution of 1 with 4
using a Pd–NHC catalyst generated from PdCl2,
imidazolium salt 2d, and BuLi (Table 1, run 4)
3.3.2. rel-4S-Isopropenyl-6R-(1,1-bis(methoxycarbony)-
methyl)-1-methyl-cyclohexene (24-a)
1H NMR (400 MHz, CDCl3) d 1.62–1.92 (m, 9H),
2.10–2.20 (m, 2H), 2.92 (m, 1H), 3.61 (d, J = 7.6 Hz,
1H), 3.73 (s, 3 H), 3.74 (s, 3H), 4.69 (s, 1H), 4.72 (s,
1H), 5.45 (m, 1H); 13C NMR (100 MHz, CDCl3) d
20.7, 22.5, 30.5, 31.2, 36.2, 38.9, 52.3, 52.4, 54.8, 108.9,
125.1, 132.5, 148.6, 168.8, 169.3; IR (neat) 2952, 1738,
1645, 1435, 1251 cmꢀ1; EI LRMS m/z 266, 234, 207,
203, 191, 149, 134, 119, 105. Anal. Calc. for C15H22O4:
C, 67.64; H, 8.33. Found C, 67.40; H, 8.26.
To a suspension of PdCl2 (12.6 mg, 0.07 mmol) and
imidazolium salt 2d (29.6 mg, 0.07 mmol) in THF was
added BuLi (1.52 M in hexane, 0.14 mL, 0.21 mmol) at
0 °C, and the mixture was stirred at the same temper-
ature for 45 min. To the reddish-brown mixture were
added a solution of acetate 1 (353.2 mg, 1.4 mmol) in
THF (7 mL) and a solution of sodium dimethylmalo-
nate in THF (21 mL), which was prepared from di-
methyl malonate (0.32 mL, 2.8 mmol) and NaH (60%
oil suspension, 112.2 mg, 2.8 mmol), at room tempera-
ture, and the mixture was heated at 50 °C for 37 h. To
the mixture was added sat. NH4Cl aqueous solution at
0 °C, and the organic layer was extracted with Et2O.
The combined organic layer was washed with brine
and dried over Na2SO4. After removal of the solvent,
3.3.3. CAS registry numbers of other compounds known in
the literature
1, 96482-68-7; 5, 95071-02-6; 6, 62668-02-4; 7, 1566-
65-0; 8a, 119793-72-5; 8b, 129047-20-7; 8c, 119784-73-5;
9, 68217-48-1; 10, 79644-04-5; 11, 121440-72-0; 13,
191542-57-1; 16, 61771-75-3; 20-(E), 65149-83-9; 20-(Z),

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Y. Sato et al. / Journal of Organometallic Chemistry 690 (2005) 5753–5758
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1596;
65149-82-8; 22, 75351-30-3; 23-a, 5258-01-5; 23-b, 76704-
27-3; 24-b, 77517-64-7.
(f) D.S. Clyne, J. Jin, E. Genest, J.C. Gallucci, T.V. RajanBabu,
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This work was financially supported by a Grant-in-Aid
for Scientific Research on Priority Areas (No. 16033203,
‘‘Reaction Control of Dynamic Complexes’’) from the
Ministry of Education, Culture, Sports, Science and
Technology, Japan and by the Naito Foundation, which
are gratefully acknowledged.
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