A combined experimental and theoretical study of 1-phenylpropane-1,2-dione hydrogenation over heterogeneous cinchonidine-modified Pt catalyst

Article abstract of DOI:10.1016/j.jcat.2004.03.022

The enantioselective hydrogenation of vicinal diketones over cinchonidine-modified Pt resulted in enantiomeric excess of structurally similar (R)-enantiomers. Furthermore, the kinetic resolution was caused due to faster reaction of (S)-hydroxyketone further to diols, resulting in an increase of ee. The diastereoselectivities in diols were similar. The (R,S) or (S,R) diols were always the main products whereas considerably less (R,R) of (S,S) were formed. For the first time in 1-phenylpropane-1,2-dione (A) hydrogenation enantiomeric excesses of both C1O1 and C2O2 group have been reported. The ee_1-OH and ee_2-OH were 50 and 25%, respectively, at 50% conversion of A. Based on batch and continuous reactor experiments it could be concluded that the source of enantioselectivity is an increased formation rate of (R)-enantiomer and decreased formation rate of (S)-enantiomer. Theoretical calculations revealed that in the substrate-modifier diastereomeric complex the reactant forms a nonplanar s-cis conformation and bonds to the protonated cinchonidine either via a bifurcated hydrogen bond or with two hydrogen bonds where the OH group is involved also. Optimized diastereomeric complexes were equal in energy. The calculated proton affinity of CD was high, 1000 kJmol^-1, indicating that protonation is feasible under typical experimental conditions.

Full text of DOI:10.1016/j.jcat.2004.03.022

Journal of Catalysis 224 (2004) 326–339
www.elsevier.com/locate/jcat
A combined experimental and theoretical study
of 1-phenylpropane-1,2-dione hydrogenation over heterogeneous
cinchonidine-modified Pt catalyst
a
a
b
b
Esa Toukoniitty, Ville Nieminen, Antti Taskinen, Juha Päivärinta,
b
a,∗
Matti Hotokka, and Dmitry Yu. Murzin
a
Åbo Akademi University, Process Chemistry Centre, Laboratory of Industrial Chemistry, FIN-20500, Turku-Åbo, Finland
b
Department of Physical Chemistry, Åbo Akademi University, FIN-20500 Turku-Åbo, Finland
Received 8 January 2004; revised 9 March 2004; accepted 11 March 2004
Available online 16 April 2004
Abstract
The enantioselective hydrogenation of vicinal diketones over cinchonidine-modified Pt resulted in enantiomeric excess of structurally sim-
ilar (R)-enantiomers. Furthermore, the kinetic resolution was caused due to faster reaction of (S)-hydroxyketone further to diols, resulting
in an increase of ee. The diastereoselectivities in diols were similar. The (R,S) or (S,R) diols were always the main products whereas con-
siderably less (R,R) of (S,S) were formed. For the first time in 1-phenylpropane-1,2-dione (A) hydrogenation enantiomeric excesses of both
C1=O1 and C2=O2 group have been reported. The ee1
and ee
were 50 and 25%, respectively, at 50% conversion of A. Based on
-OH
2-OH
batch and continuous reactor experiments it could be concluded that the source of enantioselectivity is an increased formation rate of (R)-
enantiomer and decreased formation rate of (S)-enantiomer. Theoretical calculations revealed that in the substrate-modifier diastereomeric
complex the reactant forms a nonplanar s-cis conformation and bonds to the protonated cinchonidine either via a bifurcated hydrogen bond
or with two hydrogen bonds where the OH group is involved also. Optimized diastereomeric complexes were equal in energy. The calculated
−1
proton affinity of CD was high, 1000 kJ mol , indicating that protonation is feasible under typical experimental conditions.
2004 Elsevier Inc. All rights reserved.

Keywords: Diketone; Cinchonidine; Enantioselective hydrogenation; Ab initio calculations
1
. Introduction
tigated modified heterogeneous catalytic systems, i.e., Pt
modified with cinchona alkaloids, which were discovered
in the late 1970s by Orito et al. [2–5]. Nowadays the enan-
tiodifferentiating mechanism of α-keto esters is fairly well
understood [6–9].
Hydrogenation of vicinal diketones including butane-
2,3-dione [10,11], hexane-3,4-dione [11], cyclohexane-1,2-
dione [12], 1,2-diphenyl-1,2-dione [13], hexane-2,3-dione
The use of chiral modifiers, which adsorb on the metal
surface, has proven to be one of the most effective ways
to transfer chirality by utilizing solid, heterogeneous cat-
alysts. Pt dispersed on a high surface area material (e.g.,
Al2O3 or SiO2) is an effective catalyst for the hydrogena-
tion of a carbonyl group (C=O) to a corresponding alcohol.
Prochiral carbonyl compounds are hydrogenated to racemic
product mixtures, 50% (R)- and 50% (S)-enantiomers, over
a conventional supported Pt catalysts. However, when a chi-
ral auxiliary, e.g., a natural alkaloid, is added the situation
changes and, e.g., α-keto esters can be hydrogenated to α-
hydroxy esters with up to 98% enantiomeric excess (ee) [1].
This example represents one of the most intensively inves-
[
11], and 1-phenylpropane-1,2-dione [14,15] can be carried
out enantioselectively over the Pt-cinchona alkaloid catalytic
system (Fig. 1). Although the reaction mechanism has not
been studied extensively, as is the situation with α-keto es-
ters, there are evident mechanistic analogies between vici-
nal diketone and α-keto ester hydrogenations. The depen-
dence on, e.g., catalyst properties (pretreatment, activation,
structural properties), solvent, and modifier concentration is
in some cases very similar. The hydrogenation products of
vicinal diketones, optically active hydroxy ketones and di-
*
Corresponding author. Fax: +358 2 215 4479.
E-mail address: dmurzin@abo.fi (D.Yu. Murzin).
0021-9517/$ – see front matter  2004 Elsevier Inc. All rights reserved.
doi:10.1016/j.jcat.2004.03.022

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
327
Fig. 1. Vicinal diketones and excess enantiomer (ee in brackets) in hydrogenation over cinchonidine-modified Pt catalyst.
ols, are utilized in the synthesis of pharmaceuticals; e.g.,
ephedrine [16] is synthesized from (R)-1 (Fig. 2).
over cinchona alkaloid-modified Pt catalysts. 1-Phenyl-1,2-
propanedione is used as a model molecule because it com-
prises all the aspects of the inherently complex vicinal dike-
tone hydrogenation reaction network. Extensive kinetic ex-
periments in continuous and batch reactors are utilized in
parallel with theoretical calculations and in connection with
the available spectroscopic data on the Pt/cinchona alkaloid
system to develop an enantiodifferentiation model.
In mechanistic studies of asymmetric heterogeneous
metal catalysts the crucial questions are: what is the na-
ture of a chiral site, and how does the enantiodifferentiation
take place on the metal surface? These questions are par-
ticularly difficult to answer when three-phase systems are
involved. The interplay of all participating elements can
be very complex involving solid catalyst, the liquid phase
(
solvent, dissolved reactants and products, chiral catalyst
2
. Experimental
modifier), and the gas phase. Surface-sensitive spectroscopic
techniques, theoretical calculations, and traditional kinetics
each have their own disadvantages. However, when used in
combination, these methods can yield valuable mechanistic
information.
2
.1. Catalyst and chemicals
Commercial 5 wt% Pt/Al O catalyst (Strem Chemicals,
2
3
78-1660) was used in the hydrogenations (BET specific sur-
face area 95 m g , the mean metal particle size 8.3 nm
(XRD), dispersion 40% (H2 chemisorption), and the mean
2
−1
The aim of this study is to develop an enantiodiffer-
entiation model for the hydrogenation of vicinal diketones

328
E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
Fig. 2. Simplified reaction scheme of 1-phenylpropane-1,2-dione (A) hydrogenation and cinchonidine (CD).
◦
catalyst particle size 18.2 µm (Malvern). Catalyst character-
ization has been described in detail previously [14,17].
The chemicals, 1-phenylpropane-1,2-dione (Aldrich,
25 C and 5 bar hydrogen. The catalyst bed was composed of
25 mg catalyst (particle size 45–90 µm) diluted with 200 mg
of Al O (JM, EN AL4174P), resulting in the catalyst bed
2
3
2
2303-4, 99%), toluene (J.T. Baker, 8077, > 99.5%), ethyl
acetate (Lab-Scan, A3511, 99.8%), and (−)-cinchonidine
Fluka, 27350, 98%), were used as received.
thickness of 1.0 cm. Prior to the reaction, the catalyst was
reduced in situ under flowing hydrogen at 400 C and 1 bar
for 2 h. The liquid phase containing the modifier, the solvent,
and the reactant was bubbled with hydrogen for 25 min prior
to commencing the reaction. Typically the experiments were
◦
(
2
.2. Hydrogenation experiments
-Phenylpropane-1,2-dione (A) was hydrogenated in a
3
−1
carried out with concurrent downward gas (50 cm min
)
3
−1
1
and liquid flows (2.8 cm min ).
.3. Definitions of selectivities and yield
Enantiomeric excess of (R)-1-hydroxy-1-phenyl-2-pro-
3
pressurized batch reactor (Parr, 300 cm ) under kinetic con-
trol. The hydrogen (AGA, 99.999%) pressure and tempera-
ture were 6.5 bar and 15 C, respectively. Typically, in the
kinetic experiments, the catalyst mass and liquid volume
were 0.15 g and 150 cm , respectively, and the stirring ve-
locity was 1950 rpm. The catalyst was activated prior to the
reaction under hydrogen flow (100 cm min ) for 2 h at
4
situ modification procedure was utilized; i.e., the hydrogen
degassed reactant solution containing reactant, modifier, and
solvent was injected into the reactor and the reaction was
commenced immediately by starting agitation. The initial
concentrations of 1-phenylpropane-1,2-dione and cinchoni-
2
◦
3
panones and (R)-2-hydroxy-1-phenyl-1-propanones, (R)-1
and (R)-2, respectively, are defined:
3
−1
◦
00 C and cooled down to the reaction temperature. An in
[
[
(R)-1] − [(S)-1]
(R)-1] + [(S)-1]
ee1-OH =
× 100%,
[
(R)-2] − [(S)-2]
ee2-OH =
× 100%.
[(R)-2] + [(S)-2]
−3
−3
dine (CD) were 0.025 and 0–2.7 × 10 mol dm , respec-
The yield of compound i has been defined accordingly
tively.
Continuous hydrogenation was carried out in a fixed-
bed reactor (10 cm length and 0.9 cm internal diameter) at
[i]
Yi = ꢀ
× 100%.
[
products]

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
329
The regioselectivity (rs) is defined as
3. Results
[
[
(R)-1] + [(S)-1]
(R)-2] + [(S)-2]
rs =
.
The pertinent kinetic observations for vicinal diketones
are presented. The main focus is on factors which affect
enantioselectivity and reaction rate.
2
.4. Analytical procedure
3
.1. Influence of solvent
Samples were withdrawn from the reactor at different
time intervals and analyzed with a Varian 3300 gas chro-
matograph (GC) equipped with a chiral column (β-Dex
Solvent plays an important role and affects the reaction
rate and enantioselectivities considerably. Bad choice of sol-
vent can lead, for instance, to almost racemic reaction. The
ee1-OH depends strongly on solvent polarity [32] in the hy-
drogenation of A. Toluene, ee1-OH = 65%, and ethyl ac-
etate, ee1-OH = 62%, give the highest ee1-OH at maximum
yield. In preliminary experiments with A in acetic acid the
ee1-OH = 6% and activity decreased considerably. Applica-
tion of alcohols, e.g., ethanol (ee1-OH = 12%) and methanol
2
25). A new (previously not used) chiral column that could
separate (R)- and (S)-2-hydroxy-1-phenyl-1-propanoneswas
utilized in the present work. With time the column’s ability
to separate (R)- and (S)-2-hydroxy-1-phenyl-1-propanones
decreases rapidly and therefore in previous reports these
enantiomers could not be separated with an aged column.
Details of the analytical procedure, calibration, and GC stan-
dard synthesis can be found in [14].
(
ee1-OH = 4%), resulted in low ee1-OH, although the reaction
rate was about the same as in ethyl acetate.
2
.5. Calculations
In other vicinal diketone hydrogenation experiments,
similar observations have been reported. For butane-2,3-
dione (C) the ee decreased in acidified toluene (1 M AcOH
in toluene) with respect to neat toluene from 45 to 28% [33]
and alcohols reduced the ee from the highest value ob-
tained in toluene. Cyclohexane-1,2-dione (D) hydrogena-
tion [12] gave high 81% ee of (1R,2R)-cyclohexane-1,2-
diol in toluene whereas in acetic acid, tetrahydrofurane,
2
.5.1. Protonated cinchonidine-1-phenylpropane-1,2-dione
complexes
The source of enantiodifferentiation is the interaction be-
tween catalyst modifier and reactant. Therefore, different
substrate-modifier complexes were evaluated by using ab
initio calculations with Gaussian98 software [18]. Differ-
ent starting geometries for the reactant, 1-phenylpropane-
2
-propanol, and acetonitirle, reduced ee and a lowered ac-
1
,2-dione (A), having s-cis and s-trans conformations, were
tivity was observed (the ee in this context is the ee of final
product diol and not the (R)-2 hydroxyketone).
first preoptimized by using Hartree–Fock (HF) approxima-
tion with the 3-21G basis set. Modifier cinchonidine was
assumed to be protonated having an Open(3) conformation
in analogy with the previous calculations for methyl pyru-
vate [19]. These starting geometries of the cinchonidine-
reactant complexes were fully optimized by using HF ap-
proximation with the 6-31G* basis set [20–22]. The effects
of the complex formation on the relative energies of 1-
phenylpropane-1,2-dione bonding and antibonding orbitals
in the keto carbonyl moiety were evaluated.
In conclusion relatively nonpolar solvents such as toluene
are the best ones for achieving high enantioselectivity in vic-
inal diketone hydrogenation. The utilization of acetic acid,
which is commonly known as the best solvent for α-keto es-
ters, particularly for ethyl pyruvate, leads to decreased ee and
activity in hydrogenation of A, C, and D. However, ketopan-
tolactone (KPL), also an α-keto ester which has a fixed s-cis
conformation, has a very similar dependence on solvent po-
larity [34,35] as A [32]. Namely, toluene is clearly the best
solvent for KPL hydrogenation, and acetic acid and alcohols
lead to considerably reduced ee. Although the reason for the
negative effect of acetic acid and alcohols as solvents is not
understood completely, it seems to be characteristic of vici-
nal diketones.
2
.5.2. Proton affinity of cinchonidine
In order to calculate the gas-phase proton affinity of cin-
chonidine, i.e., the negative of ꢀH for the reaction CD +
+
+
H
→ CDH in the standard conditions (at 298.15 K in
pressure of 1 bar), the equilibrium structures and vibra-
tional spectra of CD and CDH were computed with den-
+
3
.2. Rate acceleration
sity functional theory (DFT) using the resolution-of-the-
identity (RI) approximation [23] and the analytic second
derivative program AOFORCE [24] as implemented in the
TURBOMOLE program package [25,26]. For these calcu-
lations the BP86 functional [27,28] and TZVP [29,30] ba-
sis set were used. The frequencies were scaled by a factor
of 0.95. The single-point energies of the DFT-BP86/TZVP-
optimized structures were calculated with Gaussian98 using
second-order Møller–Plesset perturbation theory (MP2) [31]
with the standard 6-31G* basis set.
It has been reported that an overall rate acceleration is
a general feature of the Pt/cinchona system (the Orito re-
action) for α-functionalized ketones [6–8]. In principle this
means that in the presence of a catalyst modifier, e.g., cin-
chonidine, the overall reaction rate is considerably higher
than in the absence of modifier. For ethyl pyruvate up to
100-fold increase of reaction rate has been reported [36].
Furthermore, Wells and co-workers [37] stated that the rate

330
E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
acceleration is always observed for both of the enantiomers
with respect to racemic hydrogenation.
In this light a noteworthy observation is that cinchoni-
dine induces ee but not necessarily overall rate acceleration
in vicinal diketone hydrogenation. With A, e.g., no rate ac-
celeration could be observed in the presence of CD over
5
% Pt/Al2O3 (Strem) catalyst [15]. Analogous results were
reported [12] for D for which the CD resulted in consid-
erably reduced reaction rate in the first reaction step to
hydroxyketone over a 5% Pt/Al2O3 (Engelhard 4759) cata-
lyst. For C differing observations have been reported. When
Fig. 4. The yield of excess enantiomers (R)-1 and (R)-2 in hydrogenation of
6
.3% Pt/SiO2 catalyst was used no rate acceleration was
◦
1-phenylpropane-1,2-dione (A) at 15 C in toluene.
reported [11]. However, over 5% Pt/Al2O3 (JM94) cata-
lyst considerable rate acceleration could be observed [10].
Noteworthy is that in both cases similar ee values were
obtained (ee = 40–45%). Furthermore, in C hydrogena-
tion when codeine was used as the catalyst modifier in
dichloromethane or ethanol as solvent up to fivefold rate
acceleration could be observed with zero enantioselectiv-
ity [38]. This suggests that in vicinal diketone hydrogenation
the overall rate acceleration, although observable in some
cases, is not a prerequisite for an enantioselective reaction.
reacts faster to diols than (R)-1 and therefore, the ee1-OH in-
creases. In the hydrogenation of the second carbonyl group
(
C2=O2) the (R)-enantiomer was also formed in excess, al-
though the ee2-OH was notably lower. Not surprisingly, anal-
ogous kinetic resolution was observed also for ee2-OH. The
(S)-2 reacted faster to diols than (R)-2 and therefore, ee2-OH
increases from 25 to 50% at high reactant conversions. In-
crease of ee by kinetic resolution is achieved at the cost of
reduced yield of main product as illustrated in Fig. 4.
Interestingly, with asymmetrical hexane-2,3-dione (B,
Fig. 1) the stereochemical outcome was analogous to the
hydrogenation of A [11]. Structurally analogous (R)-2 and
(R)-3 were obtained in 29 and 35% enantiomeric excess, re-
spectively (Reaction 2 in Fig. 1).
3
.3. Enantioselectivity in vicinal diketone hydrogenation
In the previously reported studies [14,15,17,32,39,44]
in hydrogenation of A over cinchona alkaloid-modified Pt
catalyst the (R)- and (S)-2-hydroxy-1-phenyl-1-propanones
(
(R)-2 and (S)-2 in Fig. 2) could not be separated making
Studer et al. [10] used 5% Pt/Al2O3 and an in situ cata-
lyst modification procedure, whereas Slipszenko et al. [11]
utilized 6.3% Pt/SiO2 (EUROPT-1) catalyst and ex situ aer-
obic modification for the hydrogenation of C. In both in-
vestigations the (R)-3 was obtained in excess (ee = 45% at
maximum yield). The ee of (R)-3 could be increased up to
85–90% by kinetic resolution. In analogy to hydrogenation
of A the (S)-3 reacted much faster to diols, resulting in im-
proved ee of the remaining (R)-3.
In hydrogenation of hexane-3,4-dione (E, Fig. 1) Slip-
szenko et al. [11] applied a 6.3% Pt/SiO2 (EUROPT-1) cat-
alyst and obtained the (R)-4 in 33% excess.
In hydrogenation of D the first hydrogenation step is al-
most racemic, the (R)-2 was obtained with only marginal 6%
ee (calculated from the rate constants) [12]. Regardless of
the low ee, the configuration of the excess enantiomer was
the same as with all other vicinal diketones.
the reaction network incomplete (Fig. 2). However, in the
present work, the unused chiral column that was employed
allowed such a separation (see experimental section for de-
tails) and in Fig. 3 for the first time both the ee1-OH and
ee2-OH are illustrated as a function of conversion of A. The
ee1-OH and ee2-OH increase slightly with conversion of re-
actant A from 20 to 80% after which the increase is more
steep. The ee1-OH has been maximally 65% in the first reac-
tion step under optimized conditions at maximum yield. The
ee1-OH can be increased to nearly 100% by kinetic resolu-
tion of (R)-1 and (S)-1, which is represented by the steeply
increasing ee1-OH at high reactant conversion (Fig. 3). (S)-1
In 1,2-diphenylethane-1,2-dione (F, Fig. 1) hydrogena-
tion, the lack of enantioselectivity over cinchonidine-mod-
ified 6.3% Pt/SiO2 (EUROPT-1) was reported [13]. As an
explanation the steric hindrance caused by the nonplanar
molecule, as it adsorbs on flat Pt surface, was offered. An
additional possibility for the 0% ee was, according to the au-
thor, the hot filtration method used for the product recovery,
which might have racemized the product [13].
To summarize, in the hydrogenation of vicinal diketones,
excluding F, structurally analogous (R)-enantiomers were
obtained in excess with cinchonidine as the catalyst modifier.
Fig. 3. The enantiomeric excesses in hydrogenation of 1-phenyl-
◦
propane-1,2-dione over a 5% Pt/Al O catalyst at 15 C in toluene.
2
3

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
331
Fig. 5. The effect of steric repulsion on the product distribution of diols.
Furthermore, in all reported cases (reactions 1, 3, and 4 in
Fig. 1) analogous kinetic resolution took place due to faster
reactions of the (S)-enantiomer, thus increasing the ee of re-
maining (R)-enantiomer. The similarities indicate that the
underlying reaction mechanism is similar for vicinal dike-
tones.
3 and 4 were the major products [10,11]. Considerably less
(S,S) and (R,R) enantiomers were formed. The contributing
factor to the distribution of diols is evidently steric con-
straints induced by the Pt surface. In (S,S) and (R,R) one
OH group points toward the Pt surface (when fixed in s-
cis conformation, which is the most stable conformation of
intermediate hydroxyketones [12] due to intramolecular hy-
drogen bonding) making their adsorption sterically hindered.
The situation with (S,R) and (R,S) is different in such a way
that both OH groups point away from the Pt surface making
their adsorption sterically favored (Fig. 5). The evident sim-
ilarities in the further reactions to diols support a proposal of
a common reaction mechanism.
3
.4. Regioselectivity
Regioselectivity is an additional factor, which can be de-
fined for reactions 1 and 2 (Fig. 1), where the carbonyl
groups are distinguished from each other. In the case of sym-
metrical diones (C, D, E, and F) regioselectivity cannot be
defined due to molecular symmetry.
Regioselectivity is rather high (rs = 10, in the absence of
modifier rs = 4) in hydrogenation of A, indicating that the
C1=O1 group adjacent to phenyl ring reacts mainly in the
first step of the reaction yielding over 90% (R)-1 + (S)-1
3.6. Kinetics of enantiodifferentiation
The origin of enantiodifferentiation was found to be the
altered formation rate of product enantiomers (R)-1 and
(S)-1 in the presence of cinchonidine [15] (Figs. 6 and 7a).
The formation rate of (R)-1 increased and exhibited a maxi-
mum as a function of cinchonidine concentration, whereas
the formation rate of (S)-1 continuously decreased with
respect to racemic hydrogenation as cinchonidine concen-
tration was increased (Fig. 7). A similar observation was
made in continuous operation in a fixed-bed reactor as well,
i.e., with increasing time-on-stream the amount of (R)-1 in-
creased and (S)-1 decreased (Fig. 6). The overall activity
remains nearly constant as the (R)-1 increase is very much
compensated by the (S)-1 decrease. However, this is not
qualitative compensation as catalyst deactivation contributes
also to the overall activity.
(
Figs. 2 and 4). In hydrogenation of B, regioselectivity equal
to one was reported [11] demonstrating that there is no pref-
erence for different C=O group hydrogenation.
The source of high regioselectivity in A is probably the
delocalization of electrons between the C1=O1 group and
the phenyl ring [39], which makes the C1=O1 group more
reactive that the C2=O2 group.
3
.5. Diastereoselectivity and enantioselectivity of product
diols
Three reactions (1, 3, and 4, Fig. 1) have been stud-
ied further [10,11,14,32] so that the product distribution
among completely hydrogenated diols has been reported.
The product distribution of diols and kinetic resolution (i.e.,
A notable experimental fact is that the maximum in
ee1-OH does not directly correspond to the maximum in
formation rate of (R)-1 nor to a clear minimum in (S)-1
alone (Fig. 7a). However, if the formation rate of (S)-1 is
subtracted from the formation rate of (R)-1 a very good
correlation between the experimentally observed ee and
(
S)-enantiomer reacts faster) in the second hydrogenation
step are similar in these reactions, which indicate similar
reaction mechanisms. The (1S,2R) and (1R,2S) diols in re-
action 1 [32] or the meso diols (S,R) and (R,S) in reactions

332
E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
for the formation rate of (R)-enantiomer. This activation is a
key to the enantiodifferentiation and enantioselectivity.
3
.7. Theoretical calculations
In order to understand the enantiodifferentiation mech-
anism the reactant–modifier interaction should be con-
sidered. According to current understanding a one-to-one
reactant–modifier complex is the source of enantiodifferenti-
ation [6–9] in the Orito reaction. In the following calculation
catalytic Pt surface has not been taken into account. Because
only little information about the effect of modifier structure
in vicinal diketone hydrogenation is available, the analogies
observed with well-studied α-keto ester hydrogenation are
used as a basis for the calculations. Cinchonidine is a com-
plex molecule and exhibits a rich conformational behavior.
Based on detailed experimental and theoretical considera-
tions Open(3) conformer [6–9,35] has been proposed to be
the actor species in enantiodifferentiation. Therefore, in this
work the Open(3) conformer is considered the actor species
and has been used in theoretical calculations. However, one
should keep in mind that the situation is more complex, as
other cinchonidine conformations are present as well and
only about 70% of cinchonidine adopts Open(3) conforma-
tion in toluene.
Previously, in theoretical calculations with methyl pyru-
vate [19], the O=C–C=O system of methyl pyruvate and
the quinoline ring of cinchonidine were restricted to copla-
narity in order to mimic steric constraints induced by a flat
Pt surface. In case of A the constraining to planarity was
not utilized, because the catalyst used in the hydrogenation
had clearly spherical Pt particles. The particle morphology
became evident when analyzing transmission electron mi-
croscopy (TEM) images by comparing the shape of the Pt
particles at the edge and on the center of the catalyst parti-
cle.
Fig. 6. Continuous hydrogenation of 1-phenylpropane-1,2-dione (A). Sym-
bols: (F) ee
, (2) conversion of A, (") [(R)-1], (Q) [(S)-1], (×)
1
-OH
[
(R)-1] − [(S)-1]—product concentration in the reactor outlet, C —inlet
0
concentration of A. The dashed line is obtained by subtraction of [(S)-1]
from [(R)-1].
the remaining “enantioselective” formation rate (R)-1 (see
Fig. 7b) is obtained. This demonstrates that the apparent
formation rate of (R)-1 can well be divided into racemic
(
Rracemic) and enantioselective components (Renantioselective)
where the enantioselective component follows the experi-
mental ee1-OH:
The important reactant-modifier interaction takes place
+
via a hydrogen bond (C=O···H ···N) between carbonyl
oxygen and proton bonded to quinuclidine nitrogen of the
cinchonidine [6–9]. Recently this kind of hydrogen bond be-
tween ketopantolactone (an α-keto ester) and cinchonidine
was observed experimentally by attenuated total reflection
IR concentration modulation spectroscopy [41]. There ex-
ists mechanistic proposals for α-keto esters [6–9], which
include both protonated and nonprotonated CD; however,
in both cases the substrate-modifier interaction takes place
via a hydrogen bond. In this work the protonated cinchoni-
Rapparent = Renantioselective(R)-1 + Rracemic(R)-1
.
Even under optimum conditions the racemic reaction route
contributes considerably to the apparent reaction rate. The
ratio of Renantioselective(R)-1 to Rracemic(R)-1 at maximum
enantiomeric excess is 3.1.
When evaluating the overall reaction rate, one should
keep in mind that adsorption of the modifier decreases the
fraction of free Pt surface available for hydrogenation [40].
Under optimum conditions with respect to CD concentra-
tion a considerable fraction of the Pt surface is covered by
the modifier and therefore, one would expect to observe a re-
duced C=O group hydrogenation rate if no rate-accelerating
+
dine (CDH ) is considered as the source for the hydrogen
bond between A and CD. In the following, molecular level
+
interactions between protonated CD (CDH ) in Open(3)
conformation and A are considered by means of ab initio
calculations.
(
activation) effects are involved. This is actually the situation
for the (S)-1 in the hydrogenation of A (Fig. 7). However,
for the (R)-1 the formation rate increased from the racemic
hydrogenation level (Fig. 7) with increasing cinchonidine
amount. This indicates that CD has some activating effects
3.7.1. Geometries of the complexes
Five minima on the potential energy surface (PES) were
found for the substrate-modifier complexes between pro-

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
333
(a)
(b)
Fig. 7. The formation rates and enantiomeric excess (ee) in 1-phenylpropane-1,2-dione hydrogenation at different molar rations of cinchonidine-to-surface Pt
in batch reactor. Symbols: ee (solid line), initial formation rates (dashed lines).
1-OH
+
tonated cinchonidine (CDH ) in Open(3) conformation
and A, see Figs. 8 and 9. All optimized complexes were
equal in stability, the largest relative energy difference being
matic ring of the modifier and the adjacent C=O group of
the reactant are almost coplanar (see Fig. 8). In the tilted
complex, (Fig. 9), the modifier’s OH group is involved in
the complexation. Two hydrogen bonds are formed: one be-
tween the modifier’s OH hydrogen and the reactant’s oxygen
−1
only 1.9 kJ mol (Table 1). Two essentially different types
of complexes were found, pro-R or pro-S (Fig. 8) and tilted
ones (Fig. 9). In all complexes the reactant adopts an s-cis
conformation, and especially no minimum on the PES for a
complex, in which the reactant would have adopted s-trans
conformation, was found. However, the PES is extremely
flat and the existence of a complex with s-trans structure of
the reactant cannot be completely ruled out. Based on the
HF/3-21G preoptimized geometries, the complexes with the
+
O2 and the second one between the modifier’s NH proton
and the reactant’s oxygen O1.
When evaluating the optimized modifier-reactant com-
plexes one should keep in mind that the reactive C=O group
should have an easy access to the adsorbed hydrogen on
the spherical Pt surface. This limits the possible complex
candidates to be considered as actor species in enantiodiffer-
entiation as well. In the tilted complex (Fig. 9) the carbonyl
groups are oriented in such a way that the addition of hy-
drogen from (below) the spherical Pt surface would not be
possible. On the other hand, in pro-R1 and pro-S1 complexes
the sterical criteria are fulfilled and the complexes can eas-
ily adsorb on a spherical Pt surface while both C=O groups
have relatively easy access to adsorbed hydrogen. However,
in pro-R2 and pro-S2 complexes the phenyl substituent ster-
ically hinders their adsorption.
−1
s-trans conformation of the reactant were ca. 16 kJ mol
less stable than the corresponding complexes with the s-cis
conformation. Pro-S and pro-R complexes were stabilized
by a bifurcated hydrogen bond between the proton and the
two O=C groups of A (Fig. 8). Note that the isolated opti-
mized reactant adopts s-trans conformation [39] (Table 1).
The essential geometrical parameters are given in Tables 1
and 2. All pro complexes (Fig. 8) have a similar bifurcated
hydrogen bond system, which defines the geometry. The aro-

334
E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
+
Fig. 8. CDH -A complexes having bifurcated hydrogen bond.
tions as it is involved in hydrogen bond formed between
the cinchonidine and the reactant. The proton affinity (PA)
was calculated in order to get information on how feasi-
ble the protonation of cinchonidine is. Calculation results
demonstrate that cinchonidine has a very high proton affin-
−1
ity (987 and 1000 kJ mol at the BP86/TZVP and MP2/6-
1G*//BP86/TZVP level, respectively) and in case there are
proton donors available the protonation of CD is probable.
3
3
.7.3. Stability of 1-phenylpropane-1,2-dione keto carbonyl
π orbitals
Recently, Vargas et al. [42] proposed that the stabilities
of the bonding and antibonding keto carbonyl π (i.e., π
∗
and π ) orbitals are a good measure for the reactivity of α-
substituted ketones in racemic hydrogenation. Based on the
frontier molecular orbital theory, the energy of the transition
state can be extrapolated from the initial stage of the reac-
tion to the activated complex. Activation, and consequently
hydrogenation, would be correlated to the stabilization of
the keto carbonyl orbitals. The stabilization (lowering of en-
ergy) of keto carbonyl orbitals would result in lowering of
the transition-state energy and thus, decreasing the activa-
Fig. 9. The optimized tilted conformation of the modifier-reactant complex.
3
.7.2. Proton affinity of cinchonidine
In theoretical calculations the protonated cinchonidine
has been commonly utilized as a starting point [19]. The
proton has a central role in the modifier-reactant interac-

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
335
Table 1
The torsion angle D(O=C–C=O) (τ, ), complexation energies (ꢀE
◦
−1
−1
, kJ mol ), and relative energies (kJ mol ) of the keto carbonyl antibonding
complex
∗
a
π
and the two keto carbonyl bonding π orbitals in some complexes formed by 1-phenyl-1,2-propanedione (A) and protonated cinchonidine calculated at
the HF/6-31G* level of theory
b
c
d
e
Complex
τ
ꢀE
ꢀE(A.B.)
ꢀE(B1)
ꢀE(B2)
ꢀE(sum)
complex
f
g
h
i
Pro-R1
Pro-R2
Pro-S1
Pro-S2
Tilted
44.2
−70.9
−70.7
−69.5
−71.4
−70.5
–
0.0
0.0
0.0
0.0
0.2
12.5
49.2
31.0
898.4
−45.2
−41.7
57.9
−74.4
−1.6
0.8
8.0
9.1
1.1
1.8
12.1
7.5
2.7
27.9
24.4
298.3
−1.0
Pure A
144.6
282.0
318.1
a
Energies relative to the energies of the corresponding orbitals in the pro-R1 complex.
Antibonding π orbital.
Bonding π orbital 1.
Bonding π orbital 2.
b
c
d
e
f
∗
ꢀ
Esum = ꢀE(A.B.) + ꢀE(B1) + ꢀE(B2).
+
Etot(pro R1) = −1411.6563301 a.u., Etot(CDH ) = −916.4294386 a.u., and Etot(A) = −495.1998815 a.u.
g
h
i
ε = −0.04739 a.u.
ε = −0.60784 a.u.
ε = −0.67770 a.u.
Table 2
The distance (pm) between the carbonyl oxygens of the reactant and the
+
NH proton of the modifier in some complexes formed by 1-phenyl-1,2-
propanedione and protonated cinchonidine and calculated at the HF/6-31G*
level of theory
+
+
Complex
d (NH ···O1)
d (NH ···O2)
Pro-R1
Pro-R2
Pro-S1
Pro-S2
Tilted
203
204
226
267
196
255
252
221
203
a
228
a
The distance between O2 and the OH hydrogen of the modifier.
tion energy of the hydrogenation. This eventually leads to
intrinsically higher hydrogenation rate.
The bonding π orbitals of 1-phenyl-1,2-propanedione
∗
and antibonding π (LUMO) are illustrated in Fig. 10. The
first keto carbonyl-bonding orbital mixes with the π system
of the aromatic ring and is split to two molecular orbitals,
bonding 1 and bonding 2. The relative energies of LUMO,
bonding 1, bonding 2, and sums of them for 1-phenyl-1,2-
propanedione in optimized complexes with the modifier are
reported in Table 1. Vargas et al. [42] proposed that the sum
of orbital stabilization (HOMO + LUMO) is the most gen-
eral parameter to be used as a measure for the reactivity.
In the pro-R1 complex the differential orbital stabilization
−1
∗
(
ꢀEsumpro-S1 − ꢀEsum pro-R1, Table 1) is 12.5 kJ mol
Fig. 10. Keto carbonyl antibonding π and bonding π orbitals of 1-phenyl-
propane-1,2-dione.
compared to the pro-S1 complexes. This difference could ex-
plain the ee1-OH with kinetic control: in the pro-R1 complex
A reacts faster to the (R)-1 enantiomer than in the pro-S1
complex to the (S)-1 enantiomer due to the stabilization of
the keto carbonyl orbitals. This is in good agreement with the
experimental observations for hydrogenationof A, where the
formation rate of (R)-1 enantiomer increased considerably
in the presence of cinchonidine. However, the ee2-OH cannot
be explained directly in an analogous manner, as the excess
enantiomer (R)-2 (upon hydrogenation of the C2=O2) is
evidently formed from the less stabilized pro-S1 complex
upon hydrogenation. Calculations are currently in progress
to evaluate alternative substrate-modifier complexes involv-
ing, e.g., interactions of A with the OH group of cinchoni-
dine.
In order to further verify the observed keto carbonyl π or-
bital stabilization effect, additional optimization was carried
using protonated cinchonine and A in order to see if analo-

336
E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
gous orbital energy stabilization would be observed as well.
Not surprisingly, analogous mirror image complexes could
be optimized with a similar stabilization of the keto carbonyl
π in the pro-S. This is in line with the kinetic experiments
cinchonine yielded the major product (S)-1 in excess [43].
Consequently, the observed keto carbonyl π orbital stabi-
lization effect does not contradict with experimental obser-
vations.
nonprotic media could well take place either in the liquid
phase by the residual water, always present to some extent
or alternatively on the catalyst surface, which is covered by
hydrogen. The adsorbed hydrogen as a source of proton has
been proposed recently for ketopantolactone hydrogenation
in dichloromethane [41] as the residual water and the solvent
could be excluded as proton sources. Normally it is assumed
that the hydrogen resides on the Pt surface in form of hy-
•
drogen atoms (H ) as a result of homolytic cleavage of a
3
.7.4. Summary of theoretical calculations
The CDH -A interaction involves s-cis conformation of
hydrogen molecule (H2). In order for the adsorbed hydrogen
atom to protonate CD it has to lose an electron, and where
would this additional electron go and could the acid sites
of alumina support be involved in the CD protonation are
still open questions. However, regardless on the mechanism
of the CD protonation on the catalyst surface (acid sites of
alumina or dissociatively adsorbed hydrogen on Pt) there is
experimental evidence [41], which supports CD protonation
on the catalyst surface.
+
the reactant. Both carbonyl groups were involved in hydro-
gen bonding with the protonated CD. The hydrogen bond
was either bifurcated (Fig. 8) or involved the hydroxyl group
of cinchonidine (Fig. 9). In the present work complexes in-
volving a bifurcated hydrogen bond were mainly considered;
however, the possible involvement of the OH group of CD
in enantiodifferentiation should not be totally forgotten. The
optimized complexes were energetically identical and, there-
fore, enantioselectivity cannot be accounted by the stability
of the different diastereomeric complexes (thermodynamic
control) considered in this work.
4
.2. Hydrogen addition mechanism
The hydrogen addition mechanism has not been ad-
+
−1
The CDH -A interaction led to 12.5 kJ mol keto car-
dressed considerably in the literature. However, in enan-
tioselective hydrogenation one can question mechanisms
which assume that the proton in protonated CD would be
involved in the actual hydrogenation step [6]. This is due
bonyl group stabilization of pro-R1 compared to the pro-S1
(
Table 1). Analogous keto carbonyl molecular orbital stabi-
lization has been observed in substituted acetophenones [42]
and it could be linked to the hydrogenation activity; i.e.,
more profound stabilization means higher hydrogenation
rate, as the energy levels of adsorbed hydrogen and react-
ing carbonyl group become closer to each other. This could
be a contributing factor in enantiodifferentiation and in the
enhancement of formation rate of (R)-enantiomer. However,
the fact that two carbonyl groups of A can react complicates
the situation.
+
to the fact that proton abstraction from CDH by the re-
actant would require passing over a high-energy barrier,
thus making this reaction route less probable at least at
room temperature, which is predominantly used in asym-
metric heterogeneous catalysis. Mechanisms, which involve
a nonprotonated CD [6–9], are also questionable, as CD pro-
tonates readily under typical experimental conditions.
An alternative possibility is that the protonation of the
cinchonidine is an activation step for the reactant-modifier
interactions that occur via a hydrogen bond. Protonated cin-
The proton affinity of CD was around 1000 kJ mol 1
−
.
Based on the high proton affinity of CD one can conclude
that under typical experimental conditions the protonation of
the modifier is feasible as long as proton donors are present
+
chonidine CDH and A have attractive interactions whereas
+
CD and A have negligible ones. After the CDH -A com-
(
e.g., water or adsorbed hydrogen on Pt).
plex is formed it is hydrogenated on a Pt surface releasing
+
the hydrogenation product and creating a free CDH . In this
+
mechanism the proton in CDH is not involved in the hydro-
4
. Discussion
genation cycle.
In the sequel, central mechanistic aspects, which are rele-
vant for the present work, are considered in detail for vicinal
diketones.
4
.3. The role of s-cis conformation and bifurcated
hydrogen bond
It has been proposed [11,12] that vicinal diketones would
require the s-trans conformation to react enantioselectively
to hydroxyketones. This is a reasonable assumption when
results for C and D are compared. The latter has a fixed
nearly planar s-cis structure (ee of (R)-enantiomer only 6%)
(Fig. 1), whereas the former has an s-trans conformation
(ee in the first step is 45%) (Fig. 1). A mechanism for hy-
drogenation of C has been proposed, which is based on ad-
sorption of the reactant in planar s-trans conformation [11]
as illustrated in Fig. 11a. The cinchonidine is in Open (3)
4
.1. Cinchonidine protonation
The vicinal diketones can be successfully hydrogenated
in nonprotic solvents like toluene and under such conditions
the protonation of CD has been questioned [6]. However,
cinchonidine has a very high proton affinity and in case there
are proton donors available the protonation of CD is proba-
ble. It should be noted that the optimum CD concentration
−5
−3
is very low (c = 10 mol dm ) and, therefore, the amount
of proton donors needed is also small. CD protonation in

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
337
Fig. 11. s-trans model for diketones.
conformation (the L-shaped ensemble in Fig. 11) and the
one-to-one substrate-modifier interaction occurs via a hydro-
gen bond between the quinuclidine nitrogen (illustrated as N
in Fig. 11) and the carbonyl group. The adsorption in pro-
repulsion model one cannot explain the observed enantios-
electivities. As can be seen from Fig. 11b for the pro-(R)-
1 and pro-(S)-1 the steric repulsion is similar, nevertheless
(R)-1 is obtained in 65% excess (Fig. 2). For the other case
(Fig. 11c) one would expect greater ee in excess of (R)-2
as the steric repulsion induced by phenyl ring in pro-(S)-2 is
very large; however, experimental results indicate that about
50% lower ee is obtained for the (R)-2 (Fig. 11c) with re-
spect to (R)-1 (Fig. 11b). One can conclude that the steric
factors alone cannot be used a basis for a general model. By
applying this steric repulsion concept to hydrogenation of
A one would arrive in a negligible ee1-OH and considerably
high ee2-OH.
(
R)-3 arrangement is not sterically hindered by the methyl
group-quinoline ring repulsion as is the case in pro-(S)-3 and
therefore, the pro-(R)-3 complex results in the formation of
the excess of (R)-enantiomer (thermodynamic control). As a
source of enantiodifferentiation the steric repulsion induced
by methyl group of C predicts the major enantiomer cor-
rectly as illustrated in Fig. 11a.
Despite the success of the s-trans approach to C and D,
this concept applied for A reveals that by utilizing the steric

338
E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
The protonated modifier stabilized the s-cis conformer
omeric complex yielded the major enantiomer as a result
of a faster reaction. However, based on the present work
one cannot explain unequivocally the enantiodifferentiation
mechanism.
of A to such extent that no s-trans conformers as an en-
ergy minimum on PES were found. The importance of s-
cis conformation can be demonstrated by comparing A and
acetophenone, which is structurally similar to A. The reac-
tions of the C1=O1 carbonyl group of A are expected to
be similar to that of acetophenone (note that the two car-
bonyl groups of A are not conjugated). However, it is the
C2=O2 carbonyl group in A that makes the hydrogenation
of C1=O1 of A (ee1-OH = 65%) very different from ace-
tophenone (ee = 5%) in the presence of CD.
5. Conclusions
The available data on six vicinal diketones revealed that
the reactions exhibit many similarities. In all cases the enan-
tiomeric excess of structurally similar (R)-enantiomer was
obtained with cinchonidine as catalyst modifier. Toluene
gave the highest enantioselectivity whereas acetic acid re-
sulted in considerably reduced enantioselectivity and reac-
tion rate. Furthermore, the kinetic resolution was caused due
to faster reaction of (S)-hydroxyketone further to diols, re-
sulting in an increase of ee. The diastereoselectivies in di-
ols were similar, the (R,S) or (S,R) diols were always the
main products whereas considerably less (R,R) of (S,S) were
formed. The overall rate acceleration could not be linked
to enantioselective reaction in vicinal diketone hydrogena-
tion.
An explanation for these differences in enantioselectivi-
ties can be the s-cis conformation and bifurcated hydrogen
bond (or two separate hydrogen bonds involving –OH of
CD). In acetophenone (ee = 5%) this kind of complex with
CD is not possible, while the C2=O2 group of A participates
in stabilization of the s-cis conformation with the protonated
cinchonidine and contributes to high enantioselectivity.
It has been proposed [44] that an electron-withdrawing
substituent in α-position to C=O group is needed for enan-
tioselective reaction. A plausible explanation for this “sub-
strate specificity” based on our calculations is that the
“
electron-rich α-substituent” is needed for the stabilization
For the first time enantiomeric excesses for both C=O
group hydrogenation of 1-phenylpropane-1,2-dione (A) hy-
drogenation have been reported, making the reaction net-
work complete. The ee1-OH and ee2-OH were 50 and 25%,
respectively, at 50% conversion of A. From both batch
and continuous reactor experiments it could be concluded
that the source of enantioselectivity is increased forma-
tion rate of (R)-enantiomer and decreased formation rate
of (S)-enantiomer. The reaction exhibits a high regios-
electivity (rs = 10). The C1=O1 group adjacent to the
phenyl ring hydrogenates faster probably due to delocal-
ization of electrons between the C1=O1 and the phenyl
ring.
Theoretical calculation revealed that in the substrate-
modifier diastereomeric complex the reactant forms a non-
planar s-cis conformation and bond to the protonated cin-
chonidine either via a bifurcated hydrogen bond or with two
hydrogen bonds where the OH group is involved also. All
diastereomeric complexes were equal in energy, an indica-
tion that enantioselectivity cannot be explained directly by
thermodynamic control. The keto carbonyl π-orbitals stabi-
lization could be an explanation for the increased formation
rate of (R)-1. The calculated proton affinity of CD was high,
indicating that protonation is feasible under experimental
conditions.
of the s-cis conformation. Stabilization occurs via a bifur-
cated hydrogen bond (Fig. 8) or alternatively with two hy-
drogen bonds where the OH of CD (Fig. 9) is included in hy-
drogen bonding. There are several model substrates, which
follow this criteria [7,8], e.g., acetophenone (ee = 5%) vs
trifluoroacetophenone (ee = 92%) or A (ee1-OH = 65%).
4
.4. Source of enantiodifferentiation
In principle there are two contributing factors in enan-
tioselectivity [42], namely stability of the diastereomeric
cinchonidine-reactant complexes (thermodynamic control)
and the activation energy barrier for the hydrogenation (ki-
netic control). Both of these factors can either work in favor
or disfavor of the apparent enantioselectivity.
The diastereomeric complexes (Figs. 8 and 9) are al-
most equal in energy, which implies that enantioselectivity
cannot be explained solely by thermodynamic control. The
geometry of A in complexes pro-R1 and pro-S1 is such that
C1=O1 has optimal access to adsorbed hydrogen on the
catalyst surface, whereas for the other complexes the ori-
entation of A is nonoptimal. However, regardless on the
assumed geometry of the Pt surface (spherical of planar)
one cannot explain enantioselectivities by steric factors. The
experimentally observed increase of (R)-1 formation rate
−1
(
Figs. 6 and 7) could be due to the 12.5 kJ mol stabi-
Acknowledgments
lization of the reactant’s keto carbonyl π-orbitals [42] in
complex pro-R1 (Table 1). This would explain enantios-
electivity in the hydrogenation of the C1=O1 group by
means of kinetic control. An example of kinetically con-
trolled enantioselectivity has been presented in the classical
work of Landis and Halpern [45] and later on elaborated by
Boudart [46] who demonstrated that the less stable diastere-
Prof. Andreas Liese is gratefully acknowledged for pro-
viding (R)-2- and (S)-2-hydroxy-1-phenylpropanones as GC
standards. This work is part of the activities at the Åbo
Akademi Process Chemistry Centre within the Finnish Cen-
tre of Excellence Programme (2000–2005) by the Academy
of Finland.

E. Toukoniitty et al. / Journal of Catalysis 224 (2004) 326–339
339
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