N(2)-Monosubstituted bishydrazides of oxalic acid as new efficient components of the system for the copper-catalyzed C-N cross-coupling in water

Article abstract of DOI:10.1007/s11172-012-0130-6

N(2)-Monosubstituted bishydrazides of oxalic acid in the presence of hexane-2,5-dione in situ form efficient ligands for the copper catalyzed C-N cross-coupling. A scaled pre-parative method for the synthesis of diarylamines was developed based on the results obtained.

Full text of DOI:10.1007/s11172-012-0130-6

Russian Chemical Bulletin, International Edition, Vol. 61, No. 5, pp. 1009—1013, May, 2012
1009
N(2)ꢀMonosubstituted bishydrazides of oxalic acid
as new efficient components of the system for the copperꢀcatalyzed
C—N crossꢀcoupling in water
D. V. Kurandina, E. V. Eliseenkov, A. A. Petrov, and V. P. Boyarskiy
Saint Petersburg State University, Department of Chemistry,
2
6 Universitetskii prosp., 198504 Saint Petersburg, Russian Federation.
Fax: +7 (812) 428 6939. Eꢀmail: vadimpb@yahoo.com
N(2)ꢀMonosubstituted bishydrazides of oxalic acid in the presence of hexaneꢀ2,5ꢀdione
in situ form efficient ligands for the copper catalyzed C—N crossꢀcoupling. A scaled preꢀ
parative method for the synthesis of diarylamines was developed based on the results obꢀ
tained. aaa
Key words: C—N crossꢀcoupling, catalysis, copper complexes, amination, aryl bromides,
diarylamines, substituted oxalylhydrazides.
Reactions of the C—N bond formation catalyzed by
Scheme 1
1
,2
transition metal complexes (mainly by palladium, nickꢀ
3
4—10
el, and copper
complexes) play an important role in
the synthesis of pharmaceutical drugs and synthetic mateꢀ
rials. As a rule, traditional methods of the C—N crossꢀ
coupling which use copper (such as the Ullmann or the
Goldberg reaction) are of limited practical application,
primarily because they require a large amount of copper
and drastic conditions, in contrast to the palladiumꢀcomꢀ
plex catalyzed Buchwald—Hartwig crossꢀcoupling. At the
same time, the use of copper complexes as catalysts of this
reaction is preferable since they are more available and
less expensive. Moreover, copper belongs to the "life metꢀ
1
1
als" and its microimpurities in the reaction products are
not harmful.
In this connection, much attention in the last years is
paid to the search of efficient ligands for the copperꢀcataꢀ
lyzed C—N crossꢀcoupling. Significant efforts are directꢀ
ed toward development of methods allowing one to avoid
the use of toxic or highꢀboiling organic solvents. In particꢀ
ular, Cuꢀcatalyzed C—N crossꢀcoupling in aqueous meꢀ
MW stands for microwave induction.
yields of diarylamines. We attempted to combine obvious
advantages of these ligands, using a catalyst system based
on monosubstituted oxalyldihydrazide.
The objective of the present work is to search for new,
more efficient ligands for the copper oxalylhydrazideꢀcomꢀ
plexes catalyzed Nꢀarylation of aromatic amines in water.
It is desirable to avoid microwave induction, taking into
account possible practical application of the method.
dia has been reported.1
2—16
In the works,
14—16
the process
was carried out in the presence of the phaseꢀtransfer cataꢀ
lyst Bu NBr under microwave irradiation; oxalyldihydrꢀ
4
azide dihydrazones were used as ligands (either preꢀpreꢀ
1
2
pared or formed in situ; Scheme 1, L and L ), as well as
formed in situ substituted pyrroles (from hexaneꢀ2,5ꢀdiꢀ
2
14,15
Results and Discussion
one in the case of L )
or N(2),N(2´)ꢀdisubstituted diꢀ
hydrazides of oxalic acid16 (L ).
3
These methods have disadvantage. The systems conꢀ
taining dihydrazones require the use of up to 50 mol.%
ligand, whereas N(2),N(2´)ꢀdisubstituted oxalyldihydrꢀ
azides with 20—25 mol.% loading, as a rule, give lower
We investigated reactions of aryl bromides 1—6
(Scheme 2) with aniline 7, pꢀtoluidine (8), and pꢀanisiꢀ
dine (9) catalyzed by copper complexes with different
N(2)ꢀmonosubstituted bishydrazides of oxalic acid as
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1004—1008, May, 2012.
066ꢀ5285/12/6105ꢀ1009 © 2012 Springer Science+Business Media, Inc.
1

1
010
Russ.Chem.Bull., Int.Ed., Vol. 61, No. 5, May, 2012
Kurandina et al.
Scheme 2
Ar = Ph (1), 4ꢀMeC H (2), 4ꢀClC H (3), 4ꢀMeOC H (4), 4ꢀAcC H (5), 2ꢀNaphthyl (6); Ar´ = Ph (7), 4ꢀMeC H (8), 4ꢀMeOC H4 (9);
6
4
6
4
6
4
6
4
6
4
6
4
t
5
6
7
t
11
12
R = Me (L ), Bu (L ), Ph (L ), 4ꢀO NC H (L ); R´ = Bu (L ), H NCO (L
)
2
6
4
2
4
7
9
10
Note. Hexaneꢀ2,5ꢀdione was added in the equivalent amounts when the ligands L —L , L , and L containing the free hydrazide
group C(O)NHNH were used.
2
ligands. The reaction was carried out in water under conꢀ
with hexaneꢀ2,5ꢀdione. This system was used to deterꢀ
mine the TON (turnover number) for the reaction carried
out under various conditions (Table 2). The values obꢀ
1
6
ditions similar to those described in the work for disubꢀ
stituted oxalyldihydrazides, however, without microwave
induction.
Initially, we compared catalytic activity of systems
based on different ligands in a model reaction between
compounds 1 and 7, determining the yields of diphenylꢀ
amine 10 as a measure of relative efficiency of the ligands
Table 1. Yields of diphenylamine 10 in the Nꢀphenyꢀ
lation of aniline under standard conditions for 1 h at
100 Caaa
(
by GLC, Table 1).
It turned out that the catalysis was the most efficient
Entry
Ligand
Yield of diphenylamine* (%)
when the ligands containing the fragment RNHNHCOꢀ
CONHN< were used. The catalyst systems based on hexꢀ
aneꢀ2,5ꢀdione in combination with malonic acid bishydrꢀ
4
1
2
3
4
5
6
7
8
9
10
L
L
L
L
20
42
66
33
3
5
0
0
0
5
6
1
0
azide (L ) were found to be inactive at all. Among derivaꢀ
7
1
1
12
tives of oxalic acid hydrazides, compounds L and L
8
L
8
9
have proved inefficient, compounds L and L showed low
efficiency. At the same time, the catalyst systems based on
hexaneꢀ2,5ꢀdione in combination with N(2)ꢀmonosubstiꢀ
tuted bishydrazides of oxalic acid RNHNHCOCONHꢀ
NH (L —L ) have proved to be very efficient, as well as
the compound Bu NHNHCOCONHNHCH(Me)C H ꢀ
9
1
1
1
1
L
L
L
L
L
0
1
2
3
4
7
54
2
t
6
4
* The standard conditions: 400 mol.% of aniline,
00 mol.% of KOH, 20 mol.% of Bu NBr, 2 mol.% of
1
3
OMeꢀ4 (L ). The highest yield of diphenylamine (66%)
2
4
under standard conditions was achieved in the case of the
copper acetate, 8 mol.% of the ligand, 0.7 mL of water
per 1 mmol of bromobenzene.
6
ligand PhNHNHCOCONHNH (L ) in combination
2

NꢀArylation of anilines
Russ.Chem.Bull., Int.Ed., Vol. 61, No. 5, May, 2012
1011
Table 2. Determination of the catalyst turnover number (of the
copper(II) compound) in the arylation of aniline with bromobenꢀ
zene at 100 C
the data obtained, the effect of substituents in both reacꢀ
tants is in good agreement with the mechanism of the
transition metalꢀcomplex catalyzed C—N crossꢀcoupling
reactions suggested in the literature. Electronꢀdonating
substituents in the aryl bromide decelerate the reaction,
those in aniline, on the contrary, facilitate the reaction,
however, this effect is small. Because of the relatively low
susceptibility of the rate of the reaction under study to the
variations in substituent on the aromatic ring in molecules
of both electrophile and nucleophile, we may expect that
the found by us optimal conditions for the model reaction
of compounds 1 and 7 would also be optimal for the reacꢀ
tions of analogous substrates.
Entry
Amount (mol.%)
/h Yield of 10 TON
(%)
L6
Cu(OAc) •H O
2
2
1
2
3
0.04
0.108
0.65
0.30
0.86
5.15
11.5
6
5
5
23
86
117
212
133
Note:  is the reaction time, TON is the turnover number.
tained were several times higher than the results in the
The performed experiments enabled us to develop
a preparative procedure for the synthesis of diarylamines
by Nꢀarylation of aromatic amines with aryl bromides
without applying microwave irradiation: diarylamines 11—17
were synthesized with satisfactory yields. The procedure
2
case of ligand L (see Ref. 15).
It was logically to suppose that under the reaction conꢀ
6
ditions ligand L reacts with hexaneꢀ2,5ꢀdione to form
pyrrole derivative L1 (Scheme 3). At the same time, it
turned out that this preꢀsynthesized compound showed
twice as lower catalytic activity as compared to the ligand
4
developed is more economic than analogous methods usꢀ
14—16
ing other ligands
(Table 3). From the given results, it
6
formed in situ from compound L and hexaneꢀ2,5ꢀdione.
follows that the yields of the target products for our apꢀ
proach are comparable with the literature data for considꢀ
erably lower loading of copper compounds, ligands, as
well as a phaseꢀtransfer catalyst. The results obtained are
not inferior to the described in the literature Cuꢀcatalyzed
1
5
Similar picture was reported by the authors of the work
2
for ligand L and cyclohexanone. Therefore, we decided
to concentrate on the investigation of threeꢀcomponent
system copper(II) compound—Nꢀphenyloxalyldihydrꢀ
azide—hexaneꢀ2,5ꢀdione, especially as this allowed us to
avoid preliminary synthesis of the pyrrole ligand.
17—19
arylation which uses dipolar aprotic solvents either.
A possibility of scaling was demonstrated by the preparaꢀ
tion of diarylamine 14 taken as an example: a fourteenꢀ
fold increase in the loading allowed us not only to obtain
the product 14 in nearly the same yield, but also to deꢀ
crease the excess of aniline used.
Scheme 3
6
In conclusion, the new ligand system L —hexaneꢀ2,5ꢀ
dione found by us has proved considerably more efficient
in the copperꢀcomplex catalyzed C—N crossꢀcoupling reꢀ
1
3
action as compared to the ligands L —L described in the
1
4—16
literature.
This allows one to decease amount of the
Table 3. Comparison of the yields of diarylamines obtained in
the present work with the literature data
Diarylꢀ
amine
Yield (%)
Present worka
Literature data
From the data given in Table 2, it follows that the
catalyst system developed by us is several times more acꢀ
tive than the most efficient catalyst described in the literature.
To determine the scope of the reaction, we evaluated
effects of substituents in the electrophile (aryl bromide)
and nucleophile (arylamine) on the rate of the reaction
under consideration. Using method of competitive reacꢀ
tions, we determined relative rate constants of arylation of
1
1
1
1
2
3
68
57
83
4814,b; 7015,c
6615,c
5214,b; 7815,c; 6915,d
a
The reaction conditions: 1.3 mol.% of CuO, 8 mol.% of L6,
mol.% of hexaneꢀ2,5ꢀdione, 8 mol.% of Bu NBr, H O, 100 C,
h.
2
8
8
b
4
2
2
5 mol.% of CuO, 50 mol.% of L , 50 mol.% of Bu NBr, 130 C,
4
5
c
min (MW).
compound 7 with the mixture of 1 and 2 (k = 0.74±0.05)
1
5 mol.% of CuO, 50 mol.% of oxalyldihydrazide, 100 mol.% of
and of arylation of the mixture of 7 and 8 with bromobenꢀ
hexaneꢀ2,5ꢀdione, 25 mol.% of Bu NBr, 120 C, 5 min (MW).
4
d
zene (1) at 100 C (k = 1.89±0.13) based on the amount of
5 mol.% of CuO, 50 mol.% of oxalyldihydrazide, 100 mol.% of
2
accumulated products (GLCꢀanalysis). As it follows from
hexaneꢀ2,5ꢀdione, 25 mol.% of Bu NBr, 90 C, 5 min (MW).
4

1
012
Russ.Chem.Bull., Int.Ed., Vol. 61, No. 5, May, 2012
Kurandina et al.
catalyst by a factor of a few for the acceptable yields of the
products to be achieved. Based on the results obtained, we
have developed an easily scaled preparative method for the
synthesis of diarylamines.
(390 mg, 6 mmol, 200 mol.%), Bu4NBr (242 mg, 0.75 mmol),
hexaneꢀ2,5ꢀdione (27 mg, 0.24 mmol, 8 mol.%), aryl bromide
(
3 mmol), aniline (12 mmol), and water (2 mL) were successively
placed into a 10ꢀmL glass tube, argon was bubbled through the
reaction mixture for 1 min. The tube was sealed and the reaction
mixture was magnetically stirred in a boiling water bath for 8 h.
After the reaction was complete, the tube was unsealed, the
reaction mixture was poured into a 50ꢀmL flask (washing the
tube with ethyl acetate (5 mL)), diluted with water (20—25 mL),
and excess arylamine was steam distilled off. The reaction prodꢀ
uct was extracted with ethyl acetate (3×8 mL), the extract was
sequentially washed with water (2×8 mL) and brine (8 mL),
dried with anhydrous Na SO , then the solvent was slowly evapꢀ
Experimental
NMR spectra were recorded on a Bruker DPXꢀ300 specꢀ
1
trometer (300.13 MHz ( H)) in CDCl . GLC analysis was perꢀ
3
formed on a Tsvetꢀ104 chromatograph, a flameꢀionizing detecꢀ
tor, two types of glass columns 3 mm in diameter and 2500 mm
in length: with the stationary phases SEꢀ30 (5%) and OVꢀ225
2
4
(
5%) (on Chromaton NꢀSuper, 80—100 mesh in both cases).
Commercially available KOH was used (Reakhim, reagent grade,
5%). Commercial inorganic reagents (analytically pure grade)
orated. The solid products obtained were recrystallized from the
corresponding solvent.
8
NꢀArylation of amines with aryl bromides (preparative synꢀ
thesis with 4ꢀmethylꢀNꢀ(4ꢀmethylphenyl)aniline (14) as an example).
4ꢀBromotoluene (2) (7.2 g, 42 mmol), 4ꢀmethylaniline (8) (9.0 g,
84 mmol), copper(II) acetate monohydrate (200 mg, 1 mmol),
ligand L6 (656 mg, 3.4 mmol), hexaneꢀ2,5ꢀdione (385 mg,
and commercial aryl bromides and anilines (analytically pure
grade) were used as purchased, as well as hexaneꢀ2,5ꢀdione
(
procedures. Ligands were obtained by the known procedures,
the purity was monitored by H NMR.
Acros, 97%). Solvents were purified according to the standard
14—16
1
3.4 mmol), Bu NBr (3.4 g, 10.5 mmol), KOH (5.5 g, 84 mmol),
4
NꢀArylation of amines with aryl bromides (general procedure).
A reaction mixture containing accurately weighed amounts of
bromobenzene (1) and aniline (7) (in the molar ratio 1 : 4), as
well as 1,2ꢀdiphenylethane (internal standard) was preꢀprepared.
A 2—4ꢀmL glass tube was filled with the accurately measured
amounts of the thus prepared reaction mixture (containing
and water (42 mL) were placed into a 100ꢀmL Schlenk flask
equipped with a magnetic stirrer and a reflux condenser. The
reaction mixture was stirred at 100 C for 10 h under argon. The
product was extracted with a mixture of hexane—CH Cl (1 : 1)
(2×75 mL), the organic layer was filtered from insoluble impuriꢀ
ties, sequentially washed with 5% aq. HCl (150 mL), saturated
2
2
0
.2 mmol of bromobenzene), KOH (26 mg, 0.4 mmol), Bu NBr
aq. NaHCO (150 mL), and water (2×100 mL). The solvent was
4
3
(
13 mg, 0.04 mmol), ligand (0.016 mmol, 8 mol.%), hexaneꢀ2,5ꢀ
evaporated at reduced pressure, the product obtained was reꢀ
crystallized from 80% aq. methanol, preliminary having removed
resins by reflux the solution with activated charcoal. The yield of
14 was 6.0 g (71%), m.p. 77—78 C.
dione (0.016 mmol) (in the case of ligands containing free hydrꢀ
azide group —C(O)NHNH ), copper acetate monohydrate
(
2
0.008 mmol, as a 0.1 M aqueous solution), and water (100 mg).
2
0
The tube was purged with a weak flow of argon for 1 min, sealed,
and placed into refluxing water bath for 1—12 h with vigorous
magnetic stirring of the reaction mixture. After the tube was
unsealed, ethyl acetate (0.2—0.6 mL) and water (0.3—0.8 mL)
were added, followed by stirring for 1 min with a magnetic stirꢀ
rer. The organic phase (0.1—0.2 mL) was separated, dried with
sodium sulfate, and analyzed by GLC. The TON was calculated
as the amount of the reaction product moles (compound 10)
formed per 1 mole of the copper(II) compound.
4ꢀMethylꢀNꢀphenylaniline (11) . The yield was 374 mg,
1
68%), m.p. 82—84 C (from hexane). H NMR (CDCl ), : 2.33
3
(s, 3 H, CH ); 5.62 (br.s, 1 H, NH); 6.90 (t, 1 H, Ph, J = 7.3 Hz);
3
7.01—7.05 (m, 4 H, Ph, Ar); 7.11 (d, 2 H, Ar, J = 8.0 Hz);
7.23—7.29 (t, 2 H, Ph, J = 7.6 Hz).
2
1
1ꢀ[4ꢀ(Phenylamino)phenyl]ethanone (12) . The yield was
361 mg, 57%), m.p. 94—96 C (from a mixture of hexane—ethyl
1
acetate (1 : 1)). H NMR (CDCl ), : 2.55 (s, 3 H, CH ); 6.14
3
3
(br.s, 1 H, NH); 7.01 (d, 2 H, Ph, J = 8.7 Hz); 7.11 (t, 1 H, Ph´,
J = 7.3 Hz); 7.20 (d, 2 H, Ph, J = 8.0 Hz); 7.37 (t, 2 H, Ph,
J = 7.6 Hz); 7.89 (d, 2 H, Ph, J = 8.7 Hz).
NꢀArylation of amines with aryl bromides (procedure for deꢀ
termination of relative rate constants). Reaction mixtures conꢀ
tained accurately measured amounts of bromobenzene (1),
2
2
4ꢀMethoxyꢀNꢀphenylaniline (13) . The yield was 496 mg,
4
ꢀbromotoluene (2), 1,2ꢀdiphenylethane (internal standard), and
aniline (7) (the reaction mixture 1) or bromobenzene (1),
,2ꢀdiphenylethane, aniline (7), and pꢀtoluidine (8) (the reacꢀ
83%), m.p. 100—102 C (from a mixture of hexane—CCl (1 : 1)).
4
1
H NMR (CDCl ), : 3.82 (s, 3 H, CH ); 5.63 (br.s, 1 H, NH);
3
3
1
6.86 (t, 1 H, Ph, J = 7.3 Hz); 6.88 (d, 2 H, Ar, J = 8.7 Hz); 6.93
(d, 2 H, Ph, J = 8.0 Hz); 7.11 (d, 2 H, Ar, J = 8.7 Hz); 7.23
(t, 2 H, Ph, J = 7.6 Hz).
tion mixture 2). Besides the reaction mixture, the tubes were
filled with KOH (230 mol.%), Bu NBr (26 mol.%), ligand L
6
4
2
3
(
9 mol.%), hexaneꢀ2,5ꢀdione (9 mol.%), aqueous solution conꢀ
taining a desired amount of copper acetate (usually 1—2 mol.%,
70 mg), as well as the solvent chlorobenzene (0.8 mL per 1 mmol
4ꢀMethylꢀNꢀ(4ꢀmethylphenyl)aniline (14) . The yield was
1
426 mg, 72%), m.p. 74—76 C (from hexane). H NMR (CDCl ),
3
1
: 2.31 (s, 6 H, 2 CH ); 5.37 (br.s, 1 H, NH); 6.97 (d, 4 H, Ar,
3
of a mixture of aryl bromides). After the reaction has been carꢀ
ried out according to the general procedure, the reaction mixꢀ
ture was analyzed by GLC. Several identical experiments were
performed simultaneously, having being quenched and analyzed
after the certain periods of time. Values of relative rate constants
were averaged over the data of 4—5 independent trials.
J = 8.0 Hz); 7.08 (d, 4 H, Ar, J = 8.0 Hz).
4ꢀChloroꢀNꢀ(4ꢀmethylphenyl)aniline (15) . The yield was
470 mg, 72%), m.p. 84—86 C (from methanol). H NMR
2
4
1
(CDCl ), : 2.33 (s, 3 H, CH ); 5.60 (br.s, 1 H, NH); 6.94 (d, 2 H,
3
3
Ar, J = 8.7 Hz); 6.99 (d, 2 H, Ar´, J = 8.0 Hz); 7.12 (d, 2 H, Ar´,
J = 8.0 Hz); 7.20 (d, 2 H, Ar, J = 8.7 Hz).
2
5
NꢀArylation of amines with aryl bromides (procedure for the
NꢀPhenylnaphthalenꢀ2ꢀamine (16) . The yield was 434 mg,
1
reaction scaled for 1 mmol). Copper(II) oxide (3 mg, 0.038 mmol,
66%), m.p. 106—107 C (from methanol). H NMR (CDCl ),
: 5.90 (br.s, 1 H, NH); 7.01 (t, 1 H, Ph, J = 7.3 Hz); 7.18—7.47
3
6
1
.3 mol.%), ligand L (47 mg, 0.24 mmol, 8 mol.%), KOH

NꢀArylation of anilines
Russ.Chem.Bull., Int.Ed., Vol. 61, No. 5, May, 2012
1013
(
m, 8 H, Ar, Ph); 7.67 (d, 1 H, Ar, J = 8.3 Hz); 7.77 (d, 2 H, Ar,
J = 8.7 Hz).
ꢀ[4ꢀ(Methoxyphenylamino)phenyl]ethanone (17)26. M.p.
10. F. Monnier, M. Taillefer, Angew. Chem., Int. Ed., 2009,
48, 6954.
11. M. R. Bleackley, R. T. A. MacGillivray, Biometals, 2011,
24, 785.
1
1
1
12—114 C (from ethanol). H NMR (CDCl ), : 2.53 (s, 3 H,
3
C(O)CH ); 3.84 (s, 3 H, OCH ); 5.94 (br.s, 1 H, NH); 6.83
12. M. Carril, R. Sanmartin, E. Dominguez, Chem. Soc. Rev.,
2008, 37, 639.
13. D. Dallinger, C. O. Kappe, Chem. Rev., 2007, 107, 2563.
3
3
(
(
d, 2 H, Ar, J = 8.7 Hz); 6.93 (d, 2 H, Ar´, J = 8.7 Hz); 7.16
d, 2 H, Ar´, J = 8.7 Hz); 7.85 (d, 2 H, Ar, J = 8.7 Hz).
1
4. X. Zhu, Y. Ma, L. Su, H. Song, G. Chen, D. Liang, Y. Wan,
Synthesis, 2006, 3955.
This work was financially supported by the Ministry of
Education and Science of the Russian Federation (Federal
Target Program "Scientific and ScientificꢀPedagogical
Personnel of the Innovative Russia", measure 1.2.1, State
Contract Pꢀ676, 20.05.2010), St.ꢀPetersburg State Univerꢀ
sity (Grant SPSU for performing scientific research in
years 2011—2013), and the Russian Foundation for Basic
Research (Project Nos 11ꢀ03ꢀ00048ꢀa and 10ꢀ03ꢀ00600ꢀa).
15. X. Zhu, L. Su, L. Huang, G. Chen, J. Wang, H. Song, Y. Wan,
Eur. J. Org. Chem., 2009, 635.
1
6. F. Meng, C. Wang, J. Xie, X. Zhu, Y. Wan, Appl. Organomet.
Chem., 2011, 25, 341.
1
1
7. H. Zhang, C. Qian, D. Ma, J. Org. Chem., 2005, 70, 5164.
8. J. Xie, X. Zhu, M. Huang, F. Meng, W. Chen, Y. Wan, Eur.
J. Org. Chem., 2010, 3219.
1
9. X. Guo, H. Rao, H. Fu, Y. Jiang, Y. Zhao, Adv. Synth. Catal.,
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006, 348, 2197.
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Received November 15, 2011;
in revised form April 10, 2012
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