New developments in zinc-catalyzed asymmetric hydrosilylation of ketones with PMHS

Article abstract of DOI:10.1016/j.tet.2004.01.051

The influence of structural modifications of the diamine ligand and the ZnR₂ precursor in the [ZnR₂-diamine]-catalyzed asymmetric hydrosilylation of prochiral ketones with PMHS in aprotic medium is reported. A new diamine ligand giving up to 91% ee in the reduction of acetophenone is described. The scope of this reduction system has been investigated using variously functionalized ketones and some deactivation pathways have been identified.

Full text of DOI:10.1016/j.tet.2004.01.051

Tetrahedron 60 (2004) 2837–2842
New developments in zinc-catalyzed asymmetric hydrosilylation
of ketones with PMHS
a
Virginie Bette, Andre Mortreux, Diego Savoia and Jean-Franc¸ois Carpentier
a
b
c
,
*
´
a
´
´
Chimie Organique Appliquee, UPRESA 8010 CNRS-Universite de Lille 1, ENSCL, BP 108, 59652 Villeneuve d’Ascq Cedex, France
`
b
Dipartimento di Chimica ‘G. Ciamician’, Universita di Bologna, via Selmi 2, 40126 Bologna, Italy
´ ´
Organometalliques et Catalyse, UMR 6509 CNRS-Universite de Rennes 1, Institut de Chimie, Campus de Beaulieu,
35042 Rennes Cedex, France
c
Received 3 December 2003; revised 16 January 2004; accepted 20 January 2004
Abstract—The influence of structural modifications of the diamine ligand and the ZnR2 precursor in the [ZnR2–diamine]-catalyzed
asymmetric hydrosilylation of prochiral ketones with PMHS in aprotic medium is reported. A new diamine ligand giving up to 91% ee in the
reduction of acetophenone is described. The scope of this reduction system has been investigated using variously functionalized ketones and
some deactivation pathways have been identified.
q 2004 Elsevier Ltd. All rights reserved.
1. Introduction
to improve eventually on the enantioselectivity in the
hydrosilylation of simple alkyl aryl ketones; and (ii) to
investigate the scope of this reduction system for variously
functionalized ketones.
Enantiomerically pure chiral alcohols are key intermediates
in the synthesis of numerous biologically active molecules.1
For this reason, much effort has been paid in the last 30
years to develop efficient techniques for asymmetric
reduction of prochiral ketones. In particular, asymmetric
catalysis provides organic chemists with a whole tool of
efficient methods,2 none of them being yet optimal.3 Among
others, asymmetric hydrosilylation leads to very high
enantiomeric excesses on a large range of substrates, the
best results being usually obtained with Rh- and Ti-based
catalysts.4 Nevertheless, the toxicity, price and low stability
of the reagents (molecular hydrosilanes and hydrosiloxanes)
and/or catalysts limit its industrial applications. The recent
rediscovery of polymethylhydrosiloxane (PMHS), a stable
inexpensive and non-toxic hydrosilane, has opened new
perspectives to asymmetric hydrosilylation.5 In this context,
we got particularly interested in an original Zn–diamine
catalytic system reported by Mimoun et al. for chemo-
selective hydrosilylation/reduction of aldehydes, ketones
and esters.6 An asymmetric version was also described,
limited to the enantioselective reduction of acetophenone.7
2. Results and discussion
2.1. Influence of ligand structure
In the results disclosed by Mimoun et al.,7 the best ees for
the reduction of acetophenone (K1) were reached with
(R,R)-N,N0-ethylene-bis(1-phenylethylamine) (ebpe, 1a,
Scheme 1) (76% ee, Table 1, entry 1) and (S,S)-N,N0-
dibenzyl-1,2-diphenyl-1,2-ethanediamine (N-Bn-dpen, 3a)
(88% ee, entry 6). Alternatively, we first modified the
substituents on the skeleton of ebpe with the series of
ligands 1b–d (Scheme 1). It appears that replacing the
phenyl ring by a bulkier aromatic substituent does not affect
the catalyst activity (1b, entry 2). On the other hand, a
significant decrease in activity is observed with a p-chloro-
phenyl substituted ligand (1c, entry 3); the latter decrease is
tentatively ascribed to competitive reversible coordination
of chlorine to the zinc center, leading to a catalytically less
active or inactive species. Nevertheless, the level of
enantioselectivity for the reduction of K1 is equivalent
irrespective of the aryl-derivative used within this series
(1a–c). In sharp contrast, a dramatic loss of enantio-
selectivity is observed with the cyclohexyl-ebpe derivative
(1d, entry 4), which likely accounts for the influence of
electronic factors (vide infra). Moreover, the rigidity
provided by a propylene bridge in ligand 2 seems
We report here complementary studies on this zinc-based
catalytic system. Our goals were (i) to further explore the
influence of reaction parameters, for example, structural
modifications of the diamine ligand and the ZnR2 precursor,
Keywords: Asymmetric catalysis; Diamines; Hydrosilylation; Ketones;
PMHS; Zinc.
*
Corresponding author. Tel.: þ33-223-235-950; fax: þ33-223-236-939;
e-mail address: jean-francois.carpentier@univ-rennes1.fr
0040–4020/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tet.2004.01.051

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V. Bette et al. / Tetrahedron 60 (2004) 2837–2842
Scheme 1.
point of view, the results show that no cooperative effect of
the a and (1,2) chiral centers takes place within ligand 4a.
Indeed, although both (S,S)-dpen (3a) and (S,S)-ebpe (1a)
lead to the same major product of absolute configuration
(R), the performance of the ‘matched’ ligand 4a (84% ee,
entry 8) is only in between that of each individual ebpe 1a
and dpen 3a. Thus, with respect to 3a, the introduction of a
a-methyl substituent on the N-benzyl arm only lowers the
catalyst performances. Nevertheless, further improvement
of enantioselectivity in the hydrosilylation/reduction of K1
was obtained with the 2-methoxyphenyl-substituted dia-
mine 4b, which delivers the best ee with the so-called
matched-pair of this ligand (91% ee, entry 9). This
improvement is possibly due to the hindered rotation of
the phenyl moiety, assisted in this case by the a-methyl
arms.
Table 1. Zinc-catalyzed reduction of acetophenone (K1) with PMHS using
ligands 1–7a
Entry
Ligand
Timeb (h) Yield (mol%) ee (conf.) (%)
1c
2
3
4
(R,R)-1a
(R,R)-1b
(R,R)-1c
(R,R)-1d
(R,R)-2
(S,S)-3a
(S,S)-3b
(1S,2S)-a(S,S)-4a
(1S,2S)-a(S,S)-4b
(R,R)-5
18
6
6
6
4
18
72
170
288
16
18
2
.99
94
14
68
76 (S)
78 (S)
76 (S)
22 (S)
0
88 (R)
83 (R)
84 (R)
91 (R)
0
5
15
6c
7
.99
.99
56
66
91
8
9
10
11
12
(R,R)-6
(R,R)-7
.99
2
22 (R)
,5
a
PMHS/K1/ZnEt2/diamine¼60:50:1:1 [K1]¼0.89 M in toluene.
Reaction time not optimized.
Results from Ref. 7.
b
c
2.2. Other reaction parameters: zinc precursor,
hydrosilane
insufficient to enable effective activation and enantio-
differentiation for the reduction, as reflected by the limited
racemic conversion (entry 5). C2-symmetric secondary
diamine ligands 5 and 6 that bear no aromatic substituents
proved also inefficient in terms of enantioselectivity, and
bis-aniline-type diamine 7 showed only poor activity
(entries 10–12). In light of these results, it appears thus
important to keep both a C2-symmetric 1,2-ethylenediamine
ligand backbone as well as a N-benzyl group, either a to the
nitrogen or on the 1,2 positions of the ethylene bridge.
The influence of the catalyst precursor ZnR2 was investi-
gated by varying the bulkiness and electronic properties of
the R residues (R¼Et, iPr, Ph). While the use of Zn(iPr)2 in
place of ZnEt2 was not so sensitive in the case of K1, the use
of ZnPh2 greatly affected the reaction rate (Table 2, entries
13 and 14; compare with Table 1, entry 1). A similar trend
was observed in the reduction of methyl phenylglyoxylate
(K2, entries 15–17). For both K1 and K2, the impact of the
R residue on the enantioselectivity is noticeable although
rather limited. Mechanistically, this evidences that at least
one R residue remains coordinated onto the Zn center
throughout catalysis (vide infra).† Though the ZnPh2/(R,R)-
ebpe system leads to 82% ee in the case of K1, i.e., an
increase in DDG # of ca. 0.2 kcal mol21 as compared to
ZnEt2, this parameter can not be, however, advantageously
exploited from a synthetic point of view, due to the poor
The 2-methoxyphenyl-substituted diamine 3b was syn-
thesized in order to assess the effect of a restricted rotation
of the aryl ring on the catalyst performance. As somewhat
lower activity is obtained, the enantioselectivity remains
slightly below that promoted by N-Bn-dpen (3a, entries 6
and 7). The association of the aforementioned two types of
chiral centers (a and 1,2) was realized through the new
diamines 4a,b. ZnEt2-catalyst systems based on these bulky
ligands promote hydrosilylation/reduction of K1, but only
with modest rates (entries 8 and 9). On an enantioselective
†
The enantioselectivity of all the systems reported in this paper is constant
over the whole reaction time, as probed by GLC monitoring.

V. Bette et al. / Tetrahedron 60 (2004) 2837–2842
2839
Table 2. Zinc–(R,R)-ebpe (1a)-catalyzed reduction of acetophenone (K1)
and methyl phenylglyoxylate (K2): influence of the zinc precursor and
silanea
Table 3. Zinc–(R,R)-ebpe (1a)-catalyzed reduction of carbonyl compounds
K3–K8a
Entry
Ketone
Timeb (h)
Yield (mol%)
ee (conf.) (%)
Entry
Ketone
ZnR2
(R)
Silane
Timeb
(h)
Yield
(mol%)
ee
(conf.)
(%)
22
23
24
25
26
27
K3
K4
K5
K6
K7
K8
1
.99
43
0
.99
80
69
27 (R)
62 (R)
—
78 (R)
35 (R)
17 (R)
18
18
48
48
4
13
14
15
16
17
18
19
20
21
K1
K1
K2
K2
K2
K1
K1
K1
K1
iPr
Ph
Et
iPr
Ph
Etc
Et
PMHS
PMHS
PMHS
PMHS
PMHS
PMHS
Et3SiH
Ph2SiH2
PhSiH3
48
18
6
6
4
44
48
5
.99
31
.99
.99
31
19
0
.99
.99
76 (S)
82 (S)
28 (R)
33 (R)
48 (R)
82 (S)
—
a
PMHS/K/ZnEt2/(R,R)-1a¼60:50:1:1, [K]¼0.89 M in toluene.
b
Reaction time not optimized.
Et
Et
79 (S)
76 (S)
2-(1-thienyl)ethanol with excellent chemoselectivity and
78% ee (entry 25). The presence of a strongly electron-
withdrawing group a to the carbonyl function, such as in
a,a,a-trifluoroacetophenone (K3), activates greatly the
reaction, however ending with quite a low enantioselectivity
in this case (entry 22). Also, as already mentioned, higher
a-ketoesters such as methyl phenylglyoxylate (K2) are
quantitatively reduced to the corresponding a-hydroxy-
esters, which can be readily recovered in high yields after
careful hydrolysis (Table 2, entry 15). This result is
noteworthy if one takes into account the excellent activity
of this Zn–diamine system in the chemoselective reduction
of esters and lactones under harsher conditions.6 In spite of
these encouraging results, limitations of this system
appeared. For instance, the final hydrolysis step proved
somehow troublesome, particularly in the case of lower
a-ketoesters such as ethyl and methyl pyruvate, though
initial reduction appeared quantitative and chemoselective
(1H NMR). More problematic is the presence of potentially
coordinating functionalities, such as chlorine (K4) and
amino groups (K7, K8), either on the alkyl or aryl moieties
of the ketones, which lower the activity of the system
(entries 23, 26 and 27). This observation is consistent with
the detrimental effect of a chloro group on the ligand
backbone (vide supra, entry 3) and suggests also poisoning
of the catalytically active zinc species by competitive
coordination of the chloro/amino group onto the metal
center. Moreover, substrates prone to the formation of enols,
for example, b-ketoesters such as K5, cannot be reduced
18
a
SiH/K/ZnR2/(R,R)-1a¼60:50:1:1 [K]¼0.89 M in toluene.
Reaction time not optimized.
T¼220 8C.
b
c
reduction rate associated. Therefore, no further preparation
of Zn(Ar)2 precursor was attempted. Similarly, only a slight
improvement of the enantioselectivity was noticed when the
reduction was carried out at 220 8C, along a neat decrease
of the reaction rate (entry 18). Pre-activation of the catalyst,
through brief heating (50 8C) of ZnEt2, diamine and 1 equiv.
of substrate together, proved useless.
Except trialkylsilanes (entry 19), various molecular mono-
alkyl- and dialkylsilanes lead to as effective systems as
PMHS for the reduction of K1, with ees in the same range
(entries 20 and 21). No specific rate acceleration was
detected with PMHS as compared to other silanes.8
Nevertheless, the intrinsic characteristics of this polymeric
siloxane (low price, low toxicity, stability to air and
moisture) largely justify its use as reducing agent in current
efforts to access inexpensive and efficient reducing systems.
2.3. Scope of the catalytic reaction—deactivation
pathways
Another point of interest was to assess the reductive abilities
of this Zn/diamine catalyst system in toluene towards
functionalized ketones, since only the reduction of simple
alkyl aryl ketones has been reported so far. Using ZnEt2–
(R,R)-1a as the model catalyst, a variety of ketones were
reduced with moderate to good activities, total chemoselec-
tivity for the corresponding alcohol, and interesting levels of
enantioselectivities for some of them (Scheme 2, Table 3).
For instance, reduction of 2-acetylthiophene (K6) provides
1
with this catalyst system in toluene (entry 24). H NMR
analysis of the reaction mixture (before hydrolysis)
indicated that the substrate (K5) remains intact under
those conditions; no silyl ether nor silylated enol was
detected. Also, cross-experiments showed that b-ketoester
K5 inhibits the catalytic reduction of K1 and K2. The
formation of a [Zn–acetylacetonate] species was suspected
to account for this inhibition. Indeed, in a separate reaction,
the addition of 2 equiv. (vs Zn) of benzoylacetoacetate K5
on the dimeric amine–amido Zn precursor I9 was found to
give the zinc–bis(acac) complex II, which was isolated in
high yield and identified by elemental analysis and 1H, 13
C
and 2D NMR (Scheme 3).10 Complex II proved totally
inefficient in promoting the reduction of K1 under standard
conditions in toluene, in contrast to I which is a highly
effective catalyst.
In a parallel experiment, the addition of 1 equiv. (vs Zn) of
methyl phenylglyoxylate (K2) on amine–amido Zn com-
plex I enabled us to isolate, as the major product (50%
1
yield), the 3-hydroxypiperazin-2-one III, identified by H,
Scheme 2.

2840
V. Bette et al. / Tetrahedron 60 (2004) 2837–2842
Scheme 3.
Scheme 4.
13C and 2D NMR, and X-ray diffraction.‡ The formation of
III11 can be explained on the basis of Mimoun’s
mechanism,7 by degradation of a transient (not observed)
intermediate complex of type IV, that would initially arise
from insertion of the carbonyl function of the substrate into
the Zn–N(amido) bond of complex I (Scheme 4). Interest-
ingly, this stoichiometric reaction does not seem to take
place under catalytic conditions with ZnR2–(R,R)-ebpe
systems, since K2 is quantitatively reduced to methyl
mandelate with constant enantioselectivity (Table 2, entries
15 and 16). We assume that the higher bulkiness of ebpe
(1a) (as compared to that of N,N-dibenzylethylenediamine)
may prevent this side reaction.§ Also, the hydrosilane
present under catalytic conditions may likely convert the
[ZnEt2–diamine] precursor into another (hydrido) species,
which has its own reactivity towards K2.
catalyst system. The enantioselectivity (91% ee) reached
with the new 2-methoxyphenyl derivative 4b compares
favorably with recent [Rh]–diphosphine catalysts, such as
those based on EtTRAP-H,12 MiniPHOS13 or BMPF14
leading to 85–94% ee on alkyl aryl ketones. Its reactivity
and chemoselectivity towards a-ketoesters is also remark-
able, though modest enantioselectivity could be achieved so
far. As previously reported,9 the use of similar Zn–diamine
systems in protic solvents (alcohol) is an interesting
alternative to avoid the final hydrolysis step, which turns
out sometimes problematic, and to broaden the scope of this
hydrosilylation reaction. Further results obtained under
these conditions will be reported soon.
4. Experimental
4.1. General
3. Conclusion
GLC analyses were performed on Chrompack CP 9001
apparatuses equipped with a flame ionization detector and,
respectively, a BPX5 (25 m£0.32 mm, SGE) and a chiral
Chirasil-DEX CB (25 m£0.25 mm, Chrompack) column.
1H NMR spectra were recorded on AC-200 and AC-300
Bruker spectrometers at 23 8C in CDCl3; chemical shifts are
reported in ppm downfield from TMS and were determined
Although the ZnR2–diamine–PMHS hydrosilylation sys-
tem in aprotic solvents proved relatively limited in scope, its
activity and enantioselectivity in the reduction of simple
alkyl aryl ketones are noteworthy for such an unusual
‡
Poor final R values (R¼0.1066; wR2¼0.2704) were obtained in this X-ray
diffraction analysis due to poor quality crystals and disorder problems
associated to solvent molecules. However, the data confirmed
unambiguously the atom connectivity of III.
1
by reference to the residual H (d 7.25) solvent peak; all
coupling constants are reported in Hz. Optical rotations
were measured on a Perkin–Elmer 343 polarimeter at 25 8C
in a 1 dm cell. IR spectra were recorded on a Nicolet 510
§
Note that ebpe (1a) reacts with ZnEt2 at room temperature to form the
diamine complex ZnEt2(ebpe),7 while N,N-dibenzylethylenediamine
reacts rapidly with ZnEt2 to form the amine–amido complex I.9

V. Bette et al. / Tetrahedron 60 (2004) 2837–2842
2841
FTIR spectrophotometer in a KBr cell and are expressed by
wave number (cm21). Melting points are uncorrected.
128.10, 128.0, 127.7, 126.9, 126.6 (all C arom.), 89.7
(COH), 52.2 (C(OH)NCH2Ph), 50.7 (CONCH2Ph), 47.0
(CH2N(Bn)CO), 41.1 (CH2N(Bn)C(OH)).
Diamines 1a–d and 2,7 N-Bn-Dpen (3a),15 5,16 and 717
were prepared following slightly modified reported
procedures and strictly purified by distillation or column
chromatography and subsequent recrystallization. The
new diamines 3b and 4a,b were prepared according to
known procedures and their synthesis will be described
elsewhere. Diamine 618 was kindly provided by Pr.
A. Alexakis (University Geneva). ZnEt2 (1.1 M solution
in toluene) was purchased from Aldrich and used as
received. Complex I was prepared as described pre-
viously.9 Ketones were distilled over CaH2 and degassed
before use. PMHS (Aldrich) was degassed before use.
Toluene was freshly distilled from Na/K amalgam and
degassed before use.
4.1.3. Zn–diamine-catalyzed asymmetric hydrosilyl-
ation of acetophenone by PMHS. General procedure.
Catalytic reactions were performed under nitrogen using
standard Schlenk techniques. In a typical experiment
(Table 1, entry 1), to a solution of (S,S)-1a (14.7 mg,
0.055 mmol) in freshly distilled toluene (2.5 mL), were
added ZnEt2 (50 mL of a 1.1 M solution in toluene,
0.055 mmol), then acetophenone (0.32 mL, 2.75 mmol)
and finally PMHS (0.21 mL, 3.30 mmol). The solution
was stirred at room temperature and the reaction was
monitored by GLC as follows: aliquot samples (ca. 0.1 mL)
from the reaction mixture were hydrolyzed by aqueous
KOH (45 wt%), the organic products (K1 and 1-phenyl-
ethanol) were extracted in diethyl ether, and this organic
phase was analyzed by quantitative GLC. The enantiomeric
purity of 1-phenylethanol was assessed by GLC on a
Chirasil-DEX CB column (110 8C, 0.7 bar). When the same
reaction was carried out on a preparative scale, no aliquots
were sampled and the final mixture was hydrolyzed after 3
days and extracted as described above, yielding spectro-
scopically pure 1-phenylethanol in more than 95% isolated
yield.
4.1.1. Complex II. Methyl benzoylacetoacetate (K5,
0.19 mL, 1.20 mmol, 2.0 equiv. vs Zn) was added dropwise
under nitrogen to a solution of complex I (0.200 g,
0.30 mmol of dimer, 0.60 mmol of Zn) in toluene (5 mL)
cooled at 220 8C. The resulting solution was stirred with a
magnetic stir bar for 20 min at 220 8C, and then for 30 min
at 25 8C. Volatiles were removed under vacuum to give a
yellow oil which was triturated with pentane (5 mL). The
resulting precipitate was separated off from the liquid phase,
washed with pentane (2£5 mL), and dried under vacuum to
give II as a white powder (0.260 g, 70%). 1H NMR
(C6D5CD3): d 8.13 (d, J¼6.4 Hz, 4H, o-Ph), 7.70–6.85 (m,
16H, arom.), 6.00 (s, 2H, CH acac), 4.09 (s, 4H, NHCH2Ph),
3.50 (s, 6H, OCH3), 2.25 (s, 4H, CH2NHBn). 13C{1H} NMR
(C6D5CD3): d 183.4 (ZnOC(Ph)v), 175.4 (COOMe),
143.1, 139.1, 133.6, 130.0, 129.3, 129.2, 129.0, 128.6,
127.5 (all C arom.), 82.2 (CH), 53.2 (NHCH2Ph), 50.6
(OCH3), 45.7 (CH2NHBn). Anal. calcd for C36H38N2O6Zn
(660.09): C 65.44, H 5.75, N 4.24; found C 65.79, H 5.88, N
3.89.
Acknowledgements
We thank the CNRS and PPG-SIPSY for financial support
of this research (PhD grant to V. B.) and Professor
A. Alexakis (Univ. Geneva) for providing us the diamine 6.
References and notes
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Collins, A. N., Ed.; Wiley: New York, 1997; p 99.
2. (a) Noyori, R. Asymmetric catalysis in organic synthesis;
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4.1.2. 3-Hydroxy-1,4-dibenzyl-piperazin-2-one (III).
Methyl phenylglyoxylate (K2, 0.13 mL, 0.92 mmol,
1.03 equiv. vs Zn) was added dropwise under nitrogen to
a solution of complex I (0.296 g, 0.445 mmol of dimer,
0.890 mmol of Zn) in toluene (10 mL) cooled at 230 8C.
The solution was stirred for 30 min at 230 8C, then for 1 h
at 25 8C. Volatiles were removed under vacuum to give a
white solid which was triturated with pentane (5 mL). The
resulting precipitate was separated off from the liquid phase,
washed with pentane (2£5 mL), and dried under vacuum to
give a small amount of III (0.020 g). The residue was dried
under vacuum (0.206 g) and extracted with pentane
(5£5 mL). The solution was filtered and volatiles were
removed under vacuum to afford III as a white powder
(total: 0.164 g, 50%). Crystals for X-ray diffraction were
grown from toluene/pentane (2:1) at 230 8C. 1H NMR
(CDCl3): d 7.74 (d, J¼7.0 Hz, 2H, arom.), 7.40–7.10 (m,
13H, arom.), 4.69 (d, J¼14.3 Hz, 1H, CONCHHPh), 4.56
(d, J¼14.3 Hz, 1H, CONCHHPh), 3.74 (d, J¼14.6 Hz, 1H,
4. Carpentier, J.-F.; Bette, V. Curr. Org. Chem. 2002, 6,
913–936.
5. For a review on PMHS see: Lawrence, N. J.; Drew, M. D.;
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L. Synlett 1997, 989–991.
C(OH)NCHHPh),
3.54
(d,
J¼14.3 Hz,
1H,
C(OH)NCHHPh), 3.55 (m, 1H, CHHN(Bn)CO), 3.15 (m,
2H, CHHN(Bn)COþCHHN(Bn)C(OH)), 2.83 (s, 1H, OH),
2.70 (m, 1H, CHHN(Bn)C(OH)). 13C{1H} NMR (CDCl3): d
170.4 (CO), 142.5, 138.9, 136.3, 129.9, 128.8, 128.3, 128.2,
9. Bette, V.; Mortreux, A.; Lehmann, C. W.; Carpentier, J.-F.
Chem. Commun. 2003, 332–333.
10. Although no suitable crystals of II could be grown for X-ray
diffraction analysis, the octahedral structure proposed here is

2842
V. Bette et al. / Tetrahedron 60 (2004) 2837–2842
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