Study of enantioselective hydrogenation of bulky esters of phenylglyoxylic acid on Pt-CD and Pt-β-ICN chiral catalysts: Steric effect of ester groups and inversion of enantioselectivity

Article abstract of DOI:10.1016/j.jcat.2006.04.027

Enantioselective hydrogenation of seven different esters of phenylglyoxylic acid was investigated by variation of the bulkiness at ester side of the substrates [Ph{single bond}C(O){single bond}C(O)OR, R = Me (l), cyclohexyl (2), adamantyl (3), cis-decahyd

Full text of DOI:10.1016/j.jcat.2006.04.027

Journal of Catalysis 241 (2006) 149–154
www.elsevier.com/locate/jcat
Study of enantioselective hydrogenation of bulky esters
of phenylglyoxylic acid on Pt-CD and Pt-β-ICN chiral catalysts:
Steric effect of ester groups and inversion of enantioselectivity
Kornél Szo˝ri a, Katalin Balázsik a, Károly Felföldi b, Mihály Bartók a,b,∗
a
Organic Catalysis Research Group of the Hungarian Academy of Sciences, Dóm tér 8, H-6720 Szeged, Hungary
b
Department of Organic Chemistry, University of Szeged, Dóm tér 8, H-6720 Szeged, Hungary
Received 6 March 2006; revised 14 April 2006; accepted 19 April 2006
Abstract
Enantioselective hydrogenation of seven different esters of phenylglyoxylic acid was investigated by variation of the bulkiness at ester side of
the substrates [Ph–C(O)–C(O)OR, R = Me (l), cyclohexyl (2), adamantyl (3), cis-decahydro-1-naphthyl (4), phenyl (5), 1-naphthyl (6), 2-naph-
thyl (7)] on Pt-alumina-cinchonidine (CD) and Pt-alumina-β-isocinchonine (β-ICN) chiral catalysts using mild experimental conditions (273 K
and room temperature, hydrogen pressure of 1–25 bar) in solvents of AcOH and toluene. Hydrogenation on Pt-alumina-CD chiral catalyst pro-
duced high values of ee for all but the 5 and 7 compounds. The formation of (R)-mandelic acid esters was 86–91% in AcOH and 79–94% in
toluene. The experiments verified the general applicability of the Orito reaction in the preparation of enantiomers of α-hydroxyesters. Under the
experimental conditions applied, the magnitude of ee is affected by the steric size of α-ketoesters and by solvents. In the enantioselective hy-
drogenation of substrates over a Pt-alumina-β-ICN catalyst in toluene, inversion of enantioselectivity occurred; (R)-mandelic acid esters formed
with a medium ee of 30–54%. The conformation of the adsorbed modifier plays a more determining role than the bulkiness of the substrate in the
formation of the intermediate complex responsible for enantioselection.
© 2006 Elsevier Inc. All rights reserved.
Keywords: Chiral hydrogenation; Pt-alumina; Cinchonidine and β-isocinchonine; Phenylglyoxylic acid esters; Intermediate; Conformation; Inversion of
enantioselectivity
1. Introduction
vated ketones has been the subject of numerous reviews since
2000 [4–9]. The main objectives of these complex research
efforts have been to interpret the reaction mechanism (specif-
ically, the origin of chiral induction), and to extend the reaction
to compounds other than MePy. Industrial application of the re-
action has also been realized [10]. The main model compound
for these studies has been ethyl pyruvate (EtPy); the maximal
ee achieved in with EtPy has been 97–98% [11,12].
Previous studies have shown that the Orito reaction produces
high ee in hydrogenation of the so-called “activated ketones,”
compounds with an electron-withdrawing function on the car-
bon atom next to the oxo group [4–9]. Activated ketones of this
type include α-ketoesters, α-ketoacids, α-ketoamides, α-di-
ketones, α-ketoacetals, and α-trifluoromethyl ketones [7,13].
Regarding systematic studies on the effect of α-ketoester
structure on ee, the results obtained in AcOH (the solvent found
Optically active α-hydroxy carboxylic acid derivatives are
important building blocks in organic synthesis [1]. Synthesis
of these compounds by a heterogeneous catalytic method was
carried out using the Orito reaction [2,3] (Table 1). Orito et
al. recognized the reaction that produces (R)- and (S)-methyl-
lactates (MeLt) in high enantioselectivity (ee) in 1979 while
studying hydrogenation of methyl pyruvate (MePy) on heat-
treated Pt/C catalyst in the presence of cinchona alkaloids
(Fig. 1) as chiral modifiers [2,3]. By now, more than 400 pub-
lications have reported on the details of the Orito reaction. The
state of research on the enantioselective hydrogenation of acti-
*
Corresponding author. Fax: +36 62 544 200.
E-mail address: bartok@chem.u-szeged.hu (M. Bartók).
0021-9517/$ – see front matter © 2006 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcat.2006.04.027

150
K. Szo˝ri et al. / Journal of Catalysis 241 (2006) 149–154
Fig. 1. The structures of parent cinchona alkaloids (CD, CN, Q, QD) and β-ICN.
Table 1
Enantioselective hydrogenations of α-ketoesters over Pt-alumina in AcOH
Entry
Substrate
ee
Reference
(%)
1
2
R
R
a
a
a
1
2
3
4
5
6
7
8
9
10
11
12
13
Me
Me
Me
Me
Me
Me
Me
Me
i-Pr
i-Bu
t-Bu
Ph
Me
Et
Pr
i-Pr
Bu
i-Bu
t-Bu
Neo-pentyl
Et
Et
Et
Et
Et
97–98
92–94
90–96
a
[11,14,15]
[11,14,15]
[11,15]
[11,14]
[11]
[11,15]
[15]
[15]
[14,15]
[15]
[14,15]
[14,15]
[14,15]
77 –80
a
91
a
92–93
93
92
a
54–95
Scheme 1. Investigated esters of phenylglyoxylic acid in Orito reaction.
91
50–81
b
b
84–98
cinchonine (β-ICN) was synthesized as described previously
[17–19]. The 2–7 esters were synthetised by the reaction of
phenylglyoxylic acid chloride (not isolated) [20] and the appro-
priate alcohols (or phenols) in dichloromethane at room tem-
perature [21].
b
Ph(CH )
90–93
2 2
a
Pt-colloidal cluster.
In optimized conditions.
b
to be the best) are summarized in Table 1. Some of the com-
pounds listed in Table 1 have also been studied by others. Be-
cause those authors did not examine the correlation of ee with
substrate structure, these data are not included in Table 1. From
the table, it appears that increasing the bulkiness of R1 pre-
vented higher ee; however, ee could be increased by optimizing
the experimental conditions. Despite the fact that in the cases
where R1 = phenyl and R2 = Et (EBF, entry 12), the hydro-
genation reaction was considerably slower than that for EtPy,
the highest ee was attained (98%) [16]. The high ee prompted
us to study the effect of increasing the bulkiness of the ester
group on ee.1 Toward this end, synthesis and study of the new
compounds outlined in Scheme 1 were initiated.
2.1.1. General method for the synthesis of the 2–7 esters
To a stirred solution of 1.5 g (10 mmol) of phenylglyoxylic
acid and 0.1 mL of DMF in 20 mL of dichloromethane, 1.3 mL
of oxalyl chloride was added dropwise at 273 K. The mixture
was stirred for 4 h at room temperature, then evaporated in
vacuo at 313 K. Then 30 mL of dichloromethane was added
to the residue. A small amount of 4-dimethylamino pyridine
(DMAP) was added to the solution, followed by a solution of
10 mmol of alcohol (or phenol) and 4 mL of triethylamine
in 10 mL of dichloromethane dropwise under stirring. The
mixture was stirred at room temperature for 24 h; diluted in
20 mL of dichloromethane; washed with water (2 × 10 mL),
10% NaOH solution (1 × 10 mL) and saturated NaCl solution
(15 mL); and then dried (Na2SO4), filtered, and concentrated
in vacuo. The crude products were purified by vacuum dis-
tillation or recrystallyzation or column chromatography using
hexane/acetone (5:2) as an eluent. Silica gel 60 (Fluka 60741)
was used for column chromatography.
2. Experimental
2.1. Materials
The AcOH, CD, 1, and compounds used in synthesis of
2–7 were from Fluka or Aldrich and used as received. β-iso-
The purity and characterization of the compounds prepared
were checked by TLC (Fluka 60778 silica gel TLC cards,
hexane/acetone 5:2 as eluent), gas chromatography–mass spec-
troscopy (GC-MS) (Agilent 6890 N with 5973 MSD; tempera-
ture: 10 min → 373 K, 5 K/min → 473 K; 10 psi of He; 15-m
long DB-1 column), and nuclear magnetic resonance (NMR)
1
After submitting our manuscript an significant article was published in a
similar subject (M. Maris, D. Ferri, L. Konigsmann, T. Mallat, A. Baiker, J.
Catal. 237 (2006) 230.), which deals with the hydrogenation of compounds,
1
containing R = aromatic groups.

K. Szo˝ri et al. / Journal of Catalysis 241 (2006) 149–154
151
spectroscopy (Bruker Avance 500 spectrometer; 1H: 500 MHz;
13C: 125.8 MHz, in CDCl3, with chemical shifts are expressed
in ppm downfield from internal tetramethylsilane). The char-
acterization data on the compounds (white solids or colorless
oils) are summarized below. The yields concern the isolated,
pure products.
time. Standard conditions were 12.5 mg of E4759, 1 mmol L−1
of modifier concentration, 1.9 mL of solvent (toluene [T] or
AcOH), 30 min of hydrogenation time, and 100 mg of substrate
(total liquid volume, 2 mL).
The ee was measured as methyl mandelate [PhCH(OH)CO-
OMe = MeMt]. In case of AcOH the crude product was treated
with 10 mL of saturated NaHCO3 solution. The mixture was
extracted by 3 × 10 mL diethyl ether. The combined extrac-
tion was dried by Na2SO4, and the ether was evaporated. For
transesterification, this mixture was refluxed with MeOH in the
presence of a small amount of H2SO4 for 1 h, after which
it was evaporated, neutralized with NaHCO3, extracted with
2 × 10 mL of ether, and analyzed by GC. MeMt was identified,
and enantiomeric excess [ee% = ([R −S]×100/[R +S])] was
monitored by GC (30-m long cyclodex-B Agilent 6890 N+FID
capillary column, 393 K, 21.65 psi of He; uncertainty 2%).
Retention times were 16.9 min for methyl benzoylformate (1),
22.6 min for (R)-MeMt, and 23.2 min for (S)-MeMt.
2.1.2. Characterization data of the compounds
Phenylglyoxylic acid cyclohexyl ester (2): yield: 62%; bp.
407–409 K/1 Hgmm (lit. [22] 440 K/5 Hgmm); n2D0: 1.5236;
TLC: Rf 0.66; 1H NMR: 7.98 (d, 2H), 7.65 (t, 1H), 7.51 (t, 2H),
5.09 (m, 1H), 2.06 (m, 2H), 1.78 (m, 2H), 1.59 (m, 3H), 1.43
(m, 2H), 1.29 (m, 1H); GC-MS (ret. time): 19.3 min.
Phenylglyoxylic acid 1-adamantyl ester (3): yield: 65%;
semi solid; TLC: Rf 0.69; 1H NMR: 8.01 (t, 2H), 7.65 (t, 1H),
7.52 (t, 1H), 2.32–2.21 (m, 9H), 1.74 (m, 6H); 13C NMR: 186.6,
163.4, 134.4, 132.5, 129.8, 128.7, 84.90, 41.3, 36.0, 31.0; GC-
MS (ret. time): 28.0 min.
Phenylglyoxylic acid cis-decahydro-1-naphthyl ester (4):
yield: 67%; mp. 379–380 K (diethyl ether); TLC: Rf 0.68; 1H
NMR: 7.98 (d, 2H), 7.64 (t, 1H), 7.50 (t, 2H), 5.12 (m, 1H),
2.14 (m, 1H), 1.80 (m, 4H), 1.65–1.40 (m, 9H), 1.21 (m, 2H);
13C NMR: 186.7, 163.6, 134.6, 132.6, 129.9, 128.8, 78.7, 40.1,
35.5, 31.5, 25.9, 25.8, 21.2, 19.7; GC-MS (ret. time): 28.1 min.
Phenylglyoxylic acid phenyl ester (5): yield: 48%; bp. 421–
3. Results and discussion
3.1. Hydrogenation on Pt-CD chiral catalyst
Table 2 summarizes results obtained in enantioselective hy-
drogenation of the α-ketoesters shown in Scheme 1. Standard
experimental conditions were selected on the basis of exper-
imental data described previously [15]. The enantioselective
hydrogenation of phenylglyoxylic acid esters was significantly
slower than that of EtPy, as was shown for EBF [16,23]. This is
a good example of the lack of a close correlation between the
reaction rate and high ee. Although substrate hydrogenations
in AcOH and in T were carried out under nonidentical experi-
mental conditions (AcOH-T, 25 bar; T, 1 bar), high ee can be
attained in both solvents. Values of conversion as a function of
substrate type took a similar course in both solvents; however,
in the case of 1 and 6, under identical experimental conditions
and at 1 bar hydrogen pressure, the reaction was significantly
faster in T than in AcOH, producing an increase in ee.
423 K/1 Hgmm; n20: 1.5723; TLC: Rf 0.55; H NMR: 8.10
1
(dd, 2H), 7.68 (m, D1H), 7.54 (m, 2H), 7.43 (m, 2H), 7.28 (m,
3H); 13C NMR: 185.2, 161.7, 149.9, 135.1, 132.4, 130.1, 129.7,
129.0, 126.7, 121.2; GC-MS (ret. time): 18.9 min.
Phenylglyoxylic acid 1-naphthyl ester (6): yield: 35%; mp.
1
364–365 K; TLC: Rf 0.52; H NMR: 8.17 (d, 2H9, 8.01 (m,
1H), 7.88 (m, 1H), 7.79 (d, 1H), 7.69 (t, 1H), 7.57–7.49 (m,
5H), 7.45 (d, 1H); 13C NMR: 184.9, 161.6, 145.3, 134.9, 1345,
132.0, 129.7, 128.7, 127.6, 126.5, 126.4, 126.3, 124.8, 120.5,
117.4; GC-MS (ret. time): 29.3 min.
Phenylglyoxylic acid 2-naphthyl ester (7): yield: 41%; mp.
1
359–360 K; TLC: Rf 0.53; H NMR: 8.15 (d, 2H), 7.92–7.83
(m, 3H), 7.76 (d, 1H), 7.70 (t, 1H), 7.58–7.48 (m, 4H), 7.38
(dd, 1H); 13C NMR: 185.2, 161.9, 147.6, 135.2, 133.7, 132.8,
132.4, 130.2, 129.8, 129.1, 127.9, 127.8, 126.9, 126.2, 120.3,
118.5; GC-MS (ret. time): 30 min.
Based on previous findings, for compounds containing bulky
and aromatic groups (e.g., compounds 1–7), solvents can be ex-
Catalyst: 5% Pt-alumina catalyst from Engelhard (E 4759)
was pretreated before being used in a fixed-bed reactor (or a
quartz vessel) by flushing with 30 mL min−1 of helium at 298–
673 K for 30 min and with 30 mL min−1 of hydrogen at 673 K
for 100 min. After cooling to room temperature in hydrogen,
the catalyst was flushed with helium for 30 min.
Table 2
Experimental data of enantioselective hydrogenation of esters of phenylgly-
oxylic acid on Pt-CD chiral catalyst (standard conditions: see Section 2)
a
b
Substrate
AcOH
Toluene
Conversion
(%)
Ee
(R%)
Conversion
(%)
Ee
(R%)
1
2
3
4
5
6
7
100
80
88
76
65
97
55
50
40
96
88
91
89
86
86
44
73
70
94
27
83
20
16
95
4
84
80
92
82
23
80
28
84
80
2.2. Hydrogenation
The hydrogenation was performed in a conventional at-
mospheric batch reactor or hydrogenation autoclave. The cat-
alytic system including the catalyst and the solvent was flushed
with hydrogen several times and filled to the desired pressure
and stirred (∼1000 rpm). After the prehydrogenation (30 min),
first the modifier and then the reactant were introduced and
stirred in the presence of hydrogen for the required reaction
b
1
6
94
95
b
a
273 K, 25 bar of hydrogen, reaction time: 10 min.
298 K, 1 bar of hydrogen pressure; reaction time: 30 min.
b

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K. Szo˝ri et al. / Journal of Catalysis 241 (2006) 149–154
pected to play significant roles in solvation, in the adsorption–
desorption equilibrium [24–26], and especially in directing sub-
strate adsorption (e.g., in determining the character of adsorp-
tion). For example, the solvent and the size of the ester group
may promote the η1(O)-type (end-on fashion [27,28]) adsorp-
tion of the substrate, which can be a prerequisite of intermediate
complex formation in T [27,28]. Earlier hypotheses have been
verified by recent significant experimental data on the determi-
nant role of solvents in the enantioselective hydrogenation of
α-ketoesters [25,29–31].
The experimental conversion and ee data suggest that both
electronic and steric factors may affect the rate of enantiose-
lective hydrogenation and ee. In compounds containing methyl
(1) and cycloalkyl groups (2–4), steric factors predominate,
whereas in aromatic groups (5–7), mainly electronic factors nat-
urally predominate. Although the experimental conditions were
not optimized, it can be established that under the conditions
applied, ee is not reduced even in compounds containing bulky
ester groups; ee values of 86–91% in AcOH and 79–92% in T
were obtained. Thus, it appears that the size of the ester group
has no significant effect on ee (except for 5 and 7); in other
words, the increased size does not hinder formation of the in-
termediate complex responsible for enantioselection.
Table 3
Inversion of enantioselectivity in the hydrogenation of 1–7 on Pt-alumina-
β-ICN chiral catalyst in toluene (for conditions, see Section 2; [β-ICN] =
−1
0.1 mmol L , 1 bar of hydrogen pressure, reaction time: 30 min)
Substrate
Solvent
Temperature
(K)
Conversion
(%)
Ee
(R%)
1
1
2
3
4
5
6
7
T
298
295
294
294
298
295
298
298
98
60
15
38
36
5
50
0–3
46
50
35
8
AcOH
T
T
T
T
T
T
70
3
54
20
Regarding the exception, in both solvents the highly diver-
gent value of the hydrogenation rate, and even more so of the
ee, observed in the case of compounds 5, 6, and 7 [contain-
ing phenyl (5), 1-naphthyl (6), and 2-naphthyl (7) groups, re-
spectively], is quite remarkable and the interpretation of these
results requires further consideration. For compounds 5 and 7,
the presence of microcontaminants not detectable by GC analy-
sis could also contribute to the decreased ee.
3.2. Hydrogenation on Pt-β-ICN chiral catalyst
Fig. 2. Enantioselective hydrogenation of 1 and 6: effect of modifiers (CD,
β-ICN) on relationship between conversion and ee (conditions: see Section 2,
2.5 mL of toluene, 1 bar of hydrogen pressure, reaction time: 5–45 min (in case
of β-ICN), 2–10 min (in case of CD)).
The unexpected results of research on the inversion of enan-
tioselection [32–43] have prompted studies on the hydrogena-
tion of phenylglyoxylic acid esters (1–7) on Pt-alumina-β-
ICN chiral catalyst. It has been shown that on this catalyst
in T, because of inversion, EtPy gave rise to (R)-EtLt in
50% ee [41,44]. Based on earlier experience, in the pres-
ence of cinchona alkaloids containing C8(R) and C9(S) chiral
carbon atoms (cinchonine and quinidine), an ee of (S)-EtLt
should have formed [4–7]. To study the possibility of inver-
sion, phenylglyoxylic acid esters 1–7 were hydrogenated on
Pt-alumina catalyst modified with β-ICN in T at 1 bar hydrogen
pressure and room temperature (Table 3).
Because hydrogenation of 1 in AcOH was accompanied
by very little enantioselectivity, studying the hydrogenation of
compounds 2–7 in AcOH seemed pointless. According to Ta-
ble 3, in T, hydrogenation of all compounds but 5 and 7 yielded
products of (R) configuration in a medium ee; compounds 5
and 7 produced low ee values. That is, in T, inversion of enan-
tioselection occurred. The rate of hydrogenation on Pt-β-ICN
chiral catalyst and the magnitude of ee depend on the sub-
stituent, but the tendencies are similar to those for hydrogena-
tion on Pt-CD chiral catalyst; the reaction is faster and ee is
higher for compounds 1–4 than for compounds 5 and 7, and
the behavior of compound 6 is markedly different. We see the
absence of enantioselection in AcOH and the inversion ob-
served in T as confirming the earlier supposition of different
mechanisms in these two solvents [40,41,44]. Experimental re-
sults obtained so far do not allow interpretation of the low
ee achieved in hydrogenation of compounds containing phenyl
and 2-naphthyl groups (5 and 7).
Taking into account the experience of earlier studies [45],
we examined the relationship between ee and conversion in the
enantioselective hydrogenation of compounds 1 and 6 under
the conditions of inversion, that is, in T using the chiral cata-
lyst Pt-β-ICN (Fig. 2). No differences between the ee versus
conversion relationship in inversion-free hydrogenation and in
hydrogenation accompanied by inversion were seen.
On the basis of investigations into the hydrogenation of the
bulkier α-ketoesters, it seems that steric effects are more impor-
tant in the inversion of enantioselection than in hydrogenation
without inversion. In our opinion, this new finding may point
to the directional effect of ester groups on substrate adsorp-

K. Szo˝ri et al. / Journal of Catalysis 241 (2006) 149–154
153
R: Me, cyclohexyl, adamantyl, cis-decahydro-1-naphthyl, phenyl, 1-naphthyl, 2-naphthyl
Scheme 2. Enantioselective hydrogenation of bulky esters of phenylglyoxylic acids on Pt-CD and Pt-β-ICN chiral catalysts.
Fig. 3. The proposed structures of adduct complexes of CD (A, C) and β-ICN (B) with esters of phenylglyoxylic acids.
tion, presumably by promoting η1-type substrate adsorption
on the one hand and by the fact that the relatively bulky cy-
cloalkyl group of the ester is situated not on the surface, but
in the solution solvated by T, on the other hand. To be able to
draw unambiguous conclusions regarding the role of steric fac-
tors in the Orito reaction, specifically designed and accurately
arranged studies should be carried out, such as those reported
previously [46], in which case a significant difference could be
detected even between MePy and EtPy.
surface complex of this type has been experimentally verified in
the ultrahigh vacuum conditions [51]. More recent studies [52]
do not support the role of intermediates of types B and C, be-
cause the nitrogen atom of quinuclidine is capable of removing
a proton from the surface under nonreducing conditions; that is,
as reported previously [52], even in aprotic solvents, the forma-
tion of type A intermediates is responsible for enantioselection.
These findings reconfirm previous suggestions regarding the
effect of solvents and the sense of enantioselection. The reac-
tion mechanism may differ depending on solvent, and the sense
of enantioselection is controlled by the conformation of the
modifier–substrate–Pt surface intermediate complex.
4. Conclusion
The Orito reaction for bulky esters of phenylglyoxylic acid
was investigated on Pt-CD- and Pt-β-ICN chiral catalysts. The
results are shown in Scheme 2. The experimental data listed
in Table 1 and discussed herein lead to the conclusion that the
Orito reaction may be used for the enantioselective hydrogena-
tion of α-ketoesters, that is, for the synthesis of α-hydroxyesters
in general, independent of the steric size of the molecule.
The results on the enantioselective hydrogenation of phenyl-
glyoxylic acid esters are interpreted through a somewhat sup-
plemented/modified variation of the intermediate complexes of
the type proposed earlier [41]. For a Pt-CD-chiral catalyst in
AcOH, the intermediate is generated through the interaction of
the protonated CD [47–50] acting as electrophilic agent with
the nucleophilic oxygen atom of the keto group of compounds
of 1–7 (Fig. 3, A). As reported previously [41], the hydrogena-
tion of 1–7 to an appropriate (R)-compound on a Pt-β-ICN
chiral catalyst in T (when inversion occurs) is assumed on the
formation of surface intermediates B (Fig. 3). The surface com-
plex responsible for the enantioselection is probably formed by
interaction between the nucleophilic N atom of the quinucli-
dine skeleton and the electrophilic C atom of the keto group
of the substrate. The assumed intermediate on a Pt-CD chiral
catalyst in T is shown in Fig. 3 (C) as well. In our opinion,
the H-bridge(s) linking the C5ꢀ-H and/or C6ꢀ-H of the quino-
line skeleton with the carbonyl group of the substrate plays a
determinant role in the formation of intermediates B and C, re-
sponsible for enantioselection. The formation of an H-bridged
Acknowledgments
Financial support was provided by the Hungarian National
Science Foundation (OTKA grants TS 044690, T 042466,
T 048764 and M 045606). K.B. acknowledges financial support
from the HAS through a Bolyai János Research grant and from
the Hungarian National Science Foundation through a postdoc-
toral research grant (OTKA D 048513).
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