New method for the synthesis of α-chlorocinnamonitriles

Article abstract of DOI:10.1023/B:RUCB.0000024853.81460.6a

A novel method for the preparation of nitriles of α-chlorocinnamic acid from aldehydes and ketones was proposed. Transformation of carbonyl compounds into hydrazones followed by treatment of the reaction mixture with CCl₃CN in the presence of copper chloride(I) yields α-chlorocinnamonitriles.

Full text of DOI:10.1023/B:RUCB.0000024853.81460.6a

228
Russian Chemical Bulletin, International Edition, Vol. 53, No. 1, pp. 228—232, January, 2004
New method for the synthesis of αꢀchlorocinnamonitriles
b
а
а
а
V. G. Nenajdenko,а A. V. Shastin, I. V. Golubinskii, O. N. Lenkova, and E. S. Balenkova
ꢀ
aDepartment of Chemistry, Moscow State University,
Leninskie Gory, 119992 Moscow, Russian Federation.
Fax: +7 (095) 932 8846. Eꢀmail: nen@acylium.chem.msu.ru
bInstitute of Problems of Chemical Physics, Russian Academy of Sciences,
142432 Chernogolovka, Moscow Region, Russian Federation.
Eꢀmail: shastin@icp.ac.ru
A novel method for the preparation of nitriles of αꢀchlorocinnamic acid from aldehydes
and ketones was proposed. Transformation of carbonyl compounds into hydrazones followed
by treatment of the reaction mixture with CCl3CN in the presence of copper chloride(I) yields
αꢀchlorocinnamonitriles.
Key words: catalytic olefination reaction, copper salts, trichloroacetonitrile, αꢀchloroꢀ
cinnamonitriles, hydrazones.
Polyfunctional but still rather simple building blocks
aldehyde hydrazone (1a) as an example to study the roles
of various factors and to optimize the reaction conditions,
because previously it had been shown that the natures of
the solvent and the base that is complexed with the cataꢀ
lyst and the counterꢀion have a pronounced effect on the
course of the process. The effects of the natures of the
base and the solvent on the yield of the target alkene were
studied using an invariable amount of the CuCl catalyst
(10 mol.%) and a fivefold molar excess of Cl3CCN with
respect to hydrazone. A number of solvents (DMSO,
EtOH, and MeCN) and bases (aqueous NH3, ethyleneꢀ
1,2ꢀdiamine, Et3N, TMEDA, and DBU) were tested. The
highest yield of the target 2ꢀchloroꢀ3ꢀ(4ꢀchloropheꢀ
nyl)acrylonitrile (2a) (61%) was obtained using DMSO as
the solvent and Et3N as the base. It should be mentioned
that with aqueous NH3, no target product was formed.
The highest yield of the product was attained with a fiveꢀ
fold molar excess of Cl3CCN. When 2.5 or 1 equiv. of
Cl3CCN were used, the product yield decreased to 46
or 39%, respectively. Under standard conditions, we comꢀ
pared the catalytic properties of various copper salts. As
shown by experiments, copper(I) chloride as the catalyst
provides the highest yields of the target product.
that can be involved in chemoꢀ, regioꢀ, and stereoselective
reactions are very significant in modern organic synthesis.
This type of compound can be exemplified by nitriles of
αꢀchlorocinnamic acids, which have found wide use in
organic synthesis.1 In particular, a broad range of Nꢀ, Sꢀ,
and Oꢀcontaining heterocycles have been synthesized by
reactions of derivatives of αꢀchloroꢀ and αꢀbromoacrylic
acid nitriles and esters with various binucleophiles.1
This study describes a new method for the synthesis of
αꢀchlorocinnamonitriles on the basis of the catalytic
olefination reaction (COR) of carbonyl compounds proꢀ
posed in our previous studies.2—6 This method can serve
as a convenient alternative to the known methods used to
prepare these substances, for example, the Wittig reacꢀ
tion,7,8 the addition of chlorine to cinnamonitriles folꢀ
lowed by elimination of HCl,9 the reaction of alkyl
αꢀcyanocinnamates with chlorine followed by decarboxyꢀ
lation,10 and the reaction of carbonyl compounds with
1ꢀchloroꢀ1ꢀcyanoketene.11
Results and Discussion
Previously, it was shown that Nꢀunsubstituted hydrꢀ
azones of aromatic aldehydes and ketones are transformed
into the corresponding substituted alkenes on treatment
with polyhaloalkanes in the presence of catalytic amounts
of CuCl. The double carbon—carbon bond is formed
stereoselectively, the thermodynamically more stable alkꢀ
ene isomer being formed predominantly.12
Catalyst
Yield (%)
CuCl CuCl2 CuSO4 Cu(OAc)2 Cu(OTf)2
61 41 59 55 53
The reaction of 4ꢀchlorobenzaldehyde hydrazone (1а)
with trichloroacetonitrile affords a mixture of the Eꢀ and
Zꢀisomers of the corresponding αꢀchlorocinnamonitrile
2а (Scheme 1).
In this study we used trichloroacetonitrile as the
polyhalogenated compound. We took 4ꢀchlorobenzꢀ
To determine the configuration of the resulting prodꢀ
uct, the 13C NMR spectrum without proton decoupling
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 218—222, January, 2004.
1066ꢀ5285/04/5301ꢀ0228 © 2004 Plenum Publishing Corporation

Synthesis of αꢀchlorocinnamonitriles
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 1, January, 2004
229
Scheme 1
Table 1. Reactions of hydrazones 1a—m with trichloroacetoꢀ
nitrile
Comꢀ
pound
Ar
R
Method Yield (Z : E)*
(%)
2a
2b
2c
2d
2e
2f
2g
2h
2i
4ꢀClC6H4
H
H
H
H
H
H
H
Me
Me
Me
Me
A, B
B
B
B
B
B
B
A
A
61
66
57
29
26
40
37
74
52
78
63
61
1 : 4
4ꢀMeOC6H4
2,4ꢀMe2C6H3
4ꢀO2NC6H4
2,6ꢀCl2C6H3
4ꢀMe2NC6H4
3ꢀO2NC6H4
4ꢀClC6H4
4ꢀO2NC6H4
4ꢀMeOC6H4
4ꢀBrC6H4
1 : 1.6
1 : 2.3
1 : 2.2
1 : 2
1 : 1.2
1 : 1.5
1 : 1.6
1 : 3.8
1 : 1.3
1 : 1.75
1 : 1.5
2j
2k
2l
A
A
A
was recorded and the spinꢀspin coupling constant beꢀ
tween the nitrile C atom and the proton at the double
bond was measured. By comparing the results with pubꢀ
lished data,13 we found that the reaction gives predomiꢀ
3,5ꢀMe2ꢀ4ꢀMeOC6H2 Me
2m
Me
A
44
1 : 2
3
nantly the Eꢀisomer, for which the JC,H constant is
* Ratio of isomers.
11.6 Hz; for the minor Zꢀisomer, this value is 6.7 Hz.
In the case of aromatic aldehydes, oneꢀpot method in
which the hydrazone of the carbonyl compound is preꢀ
pared prior to the reaction directly in the reaction vessel
and used without isolation proved to be efficient. This
method has undeniable advantages, as the isolation of the
hydrazone is thus bypassed. Hence, not only the reaction
time and the number of steps are decreased but also the
difficulties associated with the isolation of unstable
hydrazones of aldehydes are eliminated.
mational energies are 0.17 and 0.43 kcal mol–1, respecꢀ
tively), for the ethoxycarbonyl group, the conformational
energy equals 1.2 kcal mol–1 15
.
It was also shown that hydrazones of various acetoꢀ
phenones including heterocyclic derivatives can also be
introduced in this reaction. All products were obtained in
good yields; however, the process selectivity is somewhat
lower with acetophenones. Nevertheless, the reaction is
applicable to a broad range of substrates and gives prodꢀ
ucts in good yields.
We found that the reaction follows the mechanism
we proposed previously for catalytic olefination and
can be described by the following catalytic cycle
(Scheme 3).
A broad range of aromatic aldehydes both with donor
and with acceptor substituents were introduced in the
reaction under the conditions of choice (Scheme 2,
Table 1).
Scheme 2
The first step is oxidation of copper(I) to copper(II).
Subsequently, CuII reacts with the aldehyde or ketone
hydrazone to give a copper—carbene complex through
the intermediate formation of the corresponding diazoꢀ
alkane. The copper—carbene complex, similar to the
metal—carbene complexes described in the literature,16—18
is the key intermediate of the reaction. It reacts with
CCl3CN to give αꢀchlorocinnamonitrile and copper(II),
the latter being involved again in the catalytic cycle. We
confirmed the presence of the reduction product of
CCl3CN into CHCl2CN by mass spectrometry. The other
product formed in the catalytic olefination is the correꢀ
sponding azine of the carbonyl compound.
Thus, in this work, we developed a new strategy for
the synthesis of αꢀchlorocinnamonitriles, valuable for synꢀ
thetic purposes. This method appears to be a convenient
alternative to the known methods for the preparation of
these compounds. The advantages of this method include,
apart from the ready availability of the starting compounds,
Note. For the description of substituents, see Table 1.
Most often, the target products 2a—m are formed in
satisfactory yields ranging from 26 to 78% (see Table 1).
The reaction is sensitive to steric factors, the lowest prodꢀ
uct yield (26%) being obtained for sterically crowded 2,6ꢀ
dichlorobenzaldehyde. In all cases, Eꢀisomers are formed
as the major products. It is noteworthy that the stereꢀ
ochemistry of this process is opposite to that observed in
the reaction with ethyl trichloroacetate.14 In our opinion,
this may be due to the difference between the steric bulks
of the cyanoꢀ and ethoxycarbonyl groups. Whereas the
cyano group is less bulky than the Cl atom (the conforꢀ

230
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 1, January, 2004
Nenajdenko et al.
Scheme 3
R = H, Me
L = Et3N, Cl–
(0.12 mL, 5 mmol) in DMSO (5 mL). A mixture was stirred
until the starting aldehyde disappeared (TLC monitoring). Then
Et3N (3.5 mL) and freshly purified CuCl (50 mg, 0.5 mmol)
were added to the resulting solution of hydrazone. Then a soluꢀ
tion of CCl3CN (2.5 mL, 25 mmol) in DMSO (5 mL) was added
dropwise at ∼20 °C over a period of 2 min, the temperature being
maintained at ∼20 °C by waterꢀbath cooling. The reaction mixꢀ
ture was stirred for 2 h and quenched with 0.1 M HCl (200 mL).
The products were isolated as described in procedure А.
2ꢀChloroꢀ3ꢀ(4ꢀchlorophenyl)acrylonitrile (2а) (isomer mixꢀ
ture, E : Z = 4 : 1) was formed as yellow crystals, Rf 0.54 and 0.46
for Eꢀ and Zꢀisomers, respectively (hexane—CH2Cl2, 1 : 2).
1H NMR, δ, Eꢀisomer: 7.62, 7.42 (both d, 2 H each, H arom.,
J = 8.5 Hz); 7.30 (s, 1 H, CH); Zꢀisomer: 7.67, 7.42 (both d,
2 H each, H arom., J = 8.8 Hz); 7.29 (s, 1 H, CH). The data of
the 1H NMR spectra correspond to those reported previously.11
13C NMR, δ, Eꢀisomer: 143.8 (CH), 137.2, 129.7, 129.6, 129.4,
114.7 (CN), 100.7 (CCl); Zꢀisomer: 140.8 (CH), 137.2, 131.4,
130.0, 129.0, 116.0 (CN), 101.8 (CCl).
2ꢀChloroꢀ3ꢀ(4ꢀmethoxyphenyl)acrylonitrile (2b) (isomer mixꢀ
ture, E : Z = 1.6 : 1) was formed as yellow oil, Rf 0.54 and 0.42
for Eꢀ and Zꢀisomers, respectively (hexane—CH2Cl2, 1 : 2).
1H NMR, δ, Eꢀisomer: 7.59 (d, 2 H, H arom., J = 8.8 Hz);
7.19 (s, 1 H, CH); 6.87 (d, 2 H, H arom., J = 8.8 Hz); 3.78 (s,
3 H, OMe); Zꢀisomer: 7.67 (d, 2 H, H arom., J = 9.1 Hz);
7.18 (s, 1 H, CH); 6.89 (d, 2 H, H arom., J = 9.1 Hz); 3.8 (s,
3 H, OMe). The NMR data correspond to those reported previꢀ
ously.11
mild conditions of the reaction and simplicity of the proꢀ
cedure.
Experimental
IR spectra were measured on a URꢀ20 spectrophotometer in
thin film for liquids and in mineral oil for solids. 1H and
13C NMR spectra were recorded on a Varian VXRꢀ400 specꢀ
trometer (operating at 400 and 100 MHz, respectively) in CDCl3
using Me4Si as the internal standard. TLC was performed using
plates with silica gel 60 F254 (Merck), and column chromatograꢀ
phy was carried out using Merck silica gel (63—200 mesh). The
hydrazones of aromatic aldehydes and ketones were prepared
from commercially available aldehydes by published proceꢀ
dures.19
The synthesis of αꢀchlorocinnamonitriles (general procedure).
А. Triethylamine (3.5 mL) and freshly purified CuCl 3 (50 mg,
0.5 mmol) were added to a solution of freshly prepared hydrꢀ
azone (5 mmol) in DMSO (15 mL). A solution of CCl3CN
(2.5 mL, 25 mmol) in DMSO (5 mL) was added dropwise over a
period of 2 min, the temperature being maintained at ∼20 °C by
waterꢀbath cooling. The reaction mixture was stirred for 2 h and
quenched with 0.1 M HCl (200 mL). The products were exꢀ
tracted with CH2Cl2 (3×50 mL), the combined extracts were
dried over Na2SO4, the solvent was evaporated, and the prodꢀ
ucts (a mixture of isomers) were isolated by column chromatoꢀ
graphy (elution with hexane—CH2Cl2, 1 : 1).
B. A solution of aldehyde (5 mmol) in DMSO (10 mL) was
added dropwise with stirring to a solution of N2H4•H2O
2ꢀChloroꢀ3ꢀ(2,4ꢀdimethylphenyl)acrylonitrile (2c) (isomer
mixture, E : Z = 2.3 : 1) was formed as a colorless oil, Rf 0.62 and

Synthesis of αꢀchlorocinnamonitriles
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 1, January, 2004
231
0.56 for Eꢀ and Zꢀisomers, respectively (hexane—CH2Cl2, 1 : 2).
1H NMR, δ, Eꢀisomer: 7.68 (d, 1 H, H arom., J = 7.9 Hz); 7.54
(s, 1 H, CH); 7.08 (d, 1 H, H arom., J = 7.9 Hz); 7.06 (s, 1 H,
H arom.); 2.34, 2.31 (both s, 3 H each, Me); Zꢀisomer: 7.70 (d,
1 H, H arom., J = 8.5 Hz); 7.50 (s, 1 H, CH); 7.07 (s, 1 H,
H arom.); 7.06 (d, 1 H, H arom., J = 8.5 Hz); 2.34, 2.31 (both s,
3 H each, Me). 13C NMR, δ, Eꢀisomer: 143.9, 141.4, 137.1,
131.4, 130.5, 127.4, 127.2, 128.0, 115.0 (CN), 100.4 (CCl),
21.29 (Me), 19.57 (Me). Found (%): C, 68.54; H, 5.12.
C11H10ClN. Calculated (%): C, 68.93; H, 5.26.
2ꢀChloroꢀ3ꢀ(4ꢀnitrophenyl)acrylonitrile (2d) (isomer mixture,
E : Z = 4 : 1) was formed as yellow crystals, Rf 0.42 and 0.35 for
Eꢀ and Zꢀisomers, respectively (hexane—CH2Cl2, 1 : 2).
1H NMR, δ, Eꢀisomer: 8.30, 7.85 (both d, 2 H each, H arom.,
J = 8.8 Hz); 7.44 (s, 1 H, CH); Zꢀisomer: 8.29, 7.86 (both d,
2 H each, H arom., J = 8.8 Hz); 7.42 (s, 1 H, CH). The NMR
data correspond to those reported previously.11
Rf 0.52 (hexane—CH2Cl2, 1 : 2). 1H NMR, δ, Eꢀisomer:
7.26, 6.86 (both d, 2 H each, H arom., J = 8.8 Hz); 3.76 (s,
3 H, OMe); 2.36 (s, 3 H, Me); Zꢀisomer: 7.31, 6.86 (both d,
2 H each, H arom., J = 8.8 Hz); 3.76 (s, 3 H, OMe); 2.25
(s, 3 H, Me). 13C NMR, δ, Eꢀisomer: 160.4, 153.5, 129.1,
115.5 (CN), 113.7, 98.8 (CCl), 55.2 (OMe), 24.0 (Me).
Found (%): C, 63.20; H, 4.60. C11H10ClNO. Calculated (%):
C, 63.62; H, 4.85.
3ꢀ(4ꢀBromophenyl)ꢀ2ꢀchlorobutꢀ2ꢀenonitrile (2k) (isomer
mixture, E : Z = 1.8 : 1) was formed as yellowꢀbrown crystals,
Rf 0.62 (hexane—CH2Cl2, 1 : 2). 1H NMR, δ, Eꢀisomer: 7.49,
7.14 (both d, 2 H each, H arom., J = 8.5 Hz); 2.36 (s, 3 H, Me);
Zꢀisomer: 7.50, 7.22 (both d, 2 H each, H arom., J = 8.5 Hz);
2.27 (s, 3 H, Me). 13C NMR, δ, Eꢀisomer: 153.0, 135.6,
131.7, 128.9, 123.7, 114.8 (CN), 99.2 (CCl), 24.0 (Me).
Found (%): C, 46.59; H, 2.73. C10H7BrClN. Calculated (%):
C, 46.32; H, 2.75.
2ꢀChloroꢀ3ꢀ(2,6ꢀdichlorophenyl)acrylonitrile (2e) (isomer
mixture, E : Z = 2 : 1) was formed as a yellow oil, Rf 0.61 and
0.53 for Eꢀ and Zꢀisomers, respectively (hexane—CH2Cl2, 1 : 2).
1H NMR, δ, Eꢀisomer: 7.35—7.30 (m, 2 H, H arom.); 7.26 (s,
1 H, CH); 7.25—7.18 (m, 1 H, H arom.). Found (%): C, 46.93;
H, 6.05. C9H4Cl3N. Calculated (%): C, 46.49; H, 6.02.
2ꢀChloroꢀ3ꢀ(4ꢀN,Nꢀdimethylaminophenyl)acrylonitrile (2f)
(isomer mixture, E : Z = 1.2 : 1) was formed as yellow crystals,
Rf 0.50 and 0.45 for Eꢀ and Zꢀisomers, respectively (hexꢀ
ane—CH2Cl2, 1 : 2). 1H NMR, δ, Eꢀisomer: 7.59 (d, 2 H,
H arom., J = 7.6 Hz); 7.16 (s, 1 H, CH); 6.66 (d, 2 H, H arom.,
J = 7.6 Hz); 3.03 (s, 6 H, NMe2); Zꢀisomer: 7.60 (d, 2 H,
H arom., J = 9.0 Hz); 7.05 (s, 1 H, CH); 6.60 (d, 2 H, H arom.,
J = 9.0 Hz); 2.99 (s, 6 H, NMe2). The NMR data correspond to
those reported previously.11
2ꢀChloroꢀ3ꢀ(3ꢀnitrophenyl)acrylonitrile (2g)10 (isomer mixꢀ
ture, E : Z = 1.5 : 1) was formed as yellow crystals, Rf 0.44 and
0.37 for Eꢀ and Zꢀisomers, respectively (hexane—CH2Cl2, 1 : 2).
1H NMR, δ, Eꢀisomer: 8.44 (s, 1 H, H arom.); 8.30 (d, 1 H,
H arom., J = 8.2 Hz); 8.09 (d, 1 H, H arom., J = 8.0 Hz); 8.30
(t, 1 H, H arom., J = 8.2 Hz); 7.45 (s, 1 H, CH); Zꢀisomer: 8.60
(s, 1 H, Ar); 8.02 (d, 1 H, H arom., J = 8.0 Hz); 7.43 (s, 1 H,
CH); other proton signals are superimposed by the signals of the
major isomer.
2ꢀChloroꢀ3ꢀ(4ꢀchlorophenyl)butꢀ2ꢀenonitrile (2h) (isomer
mixture, E : Z = 1.6 : 1) was formed as a yellow oil, Rf 0.60
(hexane—CH2Cl2, 1 : 2). 1H NMR, δ, Eꢀisomer: 7.32, 7.20
(both d, 2 H each, H arom., J = 8.5 Hz); 2.36 (s, 3 H, Me);
Zꢀisomer: 7.33, 7.28 (both d, 2 H each, H arom., J = 8.8 Hz);
2.26 (s, 3 H, Me). 13C NMR, δ, Eꢀisomer: 153.0, 136.0,
135.4, 129.0, 128.7, 114.8 (CN), 92.2 (CCl), 24.0 (Me).
Found (%): C, 56.76; H, 3.36. C10H7Cl2N. Calculated (%):
C, 56.63; H, 3.33.
2ꢀChloroꢀ3ꢀ(4ꢀnitrophenyl)butꢀ2ꢀenonitrile (2i) (isomer mixꢀ
ture, E : Z = 3.8 : 1) was formed as a yellow oil, Rf 0.40 (hexꢀ
ane—CH2Cl2, 1 : 2). 1H NMR, δ, Eꢀisomer: 8.23, 7.43 (both d,
2 H each, H arom., J = 9.1 Hz); 2.42 (s, 3 H, Me); Zꢀisomer:
8.23, 7.54 (both d, 2 H each, H arom., J = 9.1 Hz); 2.33 (s, 3 H,
Me). 13C NMR, δ, Eꢀisomer: 152.2, 148.0, 143.2, 128.3, 124.0,
114.0 (CN), 101.0 (CCl), 23.8 (Me). Found (%): C, 54.00;
H, 3.33. C10H7ClN2O2. Calculated (%): C, 53.95; H, 3.17.
2ꢀChloroꢀ3ꢀ(4ꢀmethoxyphenyl)butꢀ2ꢀenonitrile (2j) (isoꢀ
mer mixture, E : Z = 1.3 : 1) was formed as a yellow oil,
2ꢀChloroꢀ3ꢀ(4ꢀmethoxyꢀ3,5ꢀdimethylphenyl)butꢀ2ꢀenonitrile
(2l) (isomer mixture, E : Z = 1.2 : 1) was formed as a yellow
oil, Rf 0.48 (hexane—CH2Cl2, 1 : 2). 1H NMR, δ, Eꢀisomer:
6.99 (s, 2 H, H arom.); 3.74 (s, 3 H, OMe); 2.30 (s, 3 H,
Me); 2.30 (s, 6 H, Me); Zꢀisomer: 7.07 (s, 2 H, H arom.); 3.74
(s, 3 H, OMe); 2.40 (s, 6 H, Me); 2.30 (s, 3 H, Me). 13C NMR,
δ, Eꢀisomer: 157.8, 154.2, 132.9, 132.1, 131.4, 131.1, 127.9,
115.3 (CN), 98.0 (CCl), 59.6 (OMe), 24.2 (Me), 16.1 (Me).
Found (%): C, 65.71; H, 6.13. C13H14ClNO. Calculated (%):
C, 66.24; H, 5.99.
2ꢀChloroꢀ3ꢀ(2ꢀthienyl)butꢀ2ꢀenonitrile (2m) (isomer mixture,
E : Z = 1.8 : 1) was formed as a yellow oil, Rf 0.60 (hexꢀ
1
ane—CH2Cl2, 1 : 2). H NMR, δ, Eꢀisomer: 7.62, 7.61 (both s,
1 H each, H heteroarom.); 7.16 (t, 1 H, H heteroarom.,
J = 4.7 Hz); 2.59 (s, 3 H, Me); Zꢀisomer: 7.64 (dd, 1 H,
H heteroarom., J = 1.2 Hz, J = 3.8 Hz); 7.48 (dd, 1 H,
H heteroarom., J = 1.1 Hz, J = 5.0 Hz); 7.10 (dd, 1 H,
H heteroarom., J = 3.8 Hz, J = 5.0 Hz); 2.42 (s, 3 H, Me).
13C NMR, δ, Eꢀisomer: 146.4, 138.0, 131.9, 129.1, 127.0, 116.0
(CN), 96.4 (CCl), 22.8 (Me). Found (%): C, 52.05; H, 3.44.
C8H6ClNS. Calculated (%): C, 52.32; H, 3.29.
This work was financially supported by the Russian
Foundation for Basic Research (Project No. 03ꢀ03ꢀ
32052ꢀa).
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Received July 15, 2003;
in revised form October 21, 2003