C O M M U N I C A T I O N S
constant for eq 2 has the value of k1/(2Kdimer
) 0.98).14
)
0.5 ) 12 M-0.5 s-1 (R2
2k1k2[PhB(OH)2(1)][MVK(2)][Rh]total
A + {A2 + 8Kdimer(k2[MVK(2)])2[Rh]total
ν )
0.5
}
A ) k1[PhB(OH)2(1)] + k2 [MVK(2)]
(1)
(2)
k1
0.5
ν )
0.5[PhB(OH)2(1)][Rh]total
(2Kdimer
)
Figure 2. eeprod vs eecat (left) and νee/ν100%ee vs eecat (right). Simulation
(solid lines) and observation (squares) of the nonlinear effect in the reaction
of 1 to 7.
The existence of the dominant dimeric species prompted us to
carry out a quantitative nonlinear effect (NLE) analysis, because
NLE is generally attributed to the formation of diastereomeric
species or higher-order agglomerates.15 31P NMR of the racemic
binap-hydroxorhodium complex (10 mM in 1,4-dioxane/H2O (10/
1) at 29 °C) showed only one doublet at δ 54.9 Hz (JP-Rh ) 185
Hz), which is the same as that of enantiopure binap-hydroxo-
rhodium complex, indicating that the homochiral dimer is over-
whelmingly more stable than the heterochiral dimer. Kitamura and
Noyori described mathematical treatment of NLE in their reports
on asymmetric alkylation of aldehydes with dialkylzinc reagents.16
A negative NLE in eeprod and an amplified reaction rate are expected
in our reaction system characterized by the preferential formation
of homochiral dimer.15,16 Considering that the formation of het-
erochiral dimer RS-9 is negligible, calculation to obtain the
concentrations of monomers [R-5] and [S-5] is very simple, readily
available from the dimerization constant Kdimer obtained for the
homochiral dimer. The equations for eeprod and the reaction rate
(νee) are defined by the concentrations of active monomeric rhodium
complexes [R-5] and [S-5], where ee100%ee (>99% ee) and ν100%ee
are the enantioselectivity and the rate of the reaction by the
enantiopure catalyst, respectively.17
the inactive dimer species RR-4 is the resting state. These results
are consistent with our previous reaction mechanism proposed by
the NMR studies of key intermediates.4
Acknowledgment. This work was partially supported by a
Grant-in-Aid for Scientific Research, the Ministry of Education,
Culture, Sports, Science and Technology, Japan. A.K. thanks the
Japan Society for the Promotion of Science for the award of a
fellowship for graduate students.
Supporting Information Available: Experimental procedures and
detailed kinetic study data. This material is available free of charge
References
(1) A review on 1,4-addition reactions: Perlmutter, P. Conjugate Addition
Reactions in Organic Synthesis; Pergamon Press: Oxford, 1992.
(2) For the first example of Rh-catalyzed asymmetric 1,4-addition of aryl-
and alkenylboronic acids to enones, see: Takaya, Y.; Ogasawara, M.;
Hayashi, T.; Sakai, M.; Miyaura, N. J. Am. Chem. Soc. 1998, 120, 5579.
(3) Reviews: (a) Hayashi, T.; Yamasaki, K. Chem. ReV. 2003, 103, 2829.
(b) Fagnou, K.; Lautens, M. Chem. ReV. 2003, 103, 169. (c) Bolm, C.;
Hildebrand, J. P.; Muniz, K.; Hermanns, N. Angew. Chem., Int. Ed. 2001,
40, 3284. (d) Hayashi, T. Synlett 2001, 879.
(4) Hayashi, T.; Takahashi, M.; Takaya, Y.; Ogasawara, M. J. Am. Chem.
Soc. 2002, 124, 5052.
(5) Helfferich, F. G. Kinetics of Homogeneous Multistep Reactions; Elsevier
Science: Amsterdam, 2001.
νee
[R-5] - [S-5]
[R-5] + [S-5]
[R-5]100%ee
eeprod ) ee
,
)
(3)
100%ee[R-5] + [S-5]
ν100%ee
(6) An expert review: Blackmond, D. G. Angew. Chem., Int. Ed. 2005, 44,
4302.
(7) In the experiments, phenylboroxine ((PhBO)3) was used as a precursor
of phenylboronic acid (1), because the boroxine is easier to be purified.
Arylboroxine and water is in a fast equilibrium with arylboronic acid,
and hence the reaction starting from phenylboronic acid and that starting
from arylboroxine in water should result in the same outcome. Tokunaga,
Y.; Ueno, H.; Shimomura, Y.; Seo, T. Heterocycles 2002, 57, 787.
(8) In the reaction of reactive MVK, hydrolysis of 1 giving benzene as a side
Scheme 3. Nonlinear Effect and Equilibrium Scheme
1
reaction is negligible. H NMR analysis of the reaction mixture showed
<3% formation of benzene.
(9) An excess of boric acid was added to minimize the change of its
concentration throughout the reaction.
(10) The methodology of reaction progress kinetic analysis is described in ref
6 and in the following literature: (a) Rosner, T.; Le Bars, J.; Pfaltz, A.;
Blackmond, D. G. J. Am. Chem. Soc. 2001, 123, 1848. (b) Singh, U. K.;
Strieter, E. R.; Blackmond, D. G.; Buchwald, S. L. J. Am. Soc. Chem.
2002, 124, 14104. (c) Mathew, S. P.; Gunathilagan, S.; Roberts, S. M.;
Blackmond, D. G. Org. Lett. 2005, 7, 4847.
(11) The parameter [“excess”] is defined as the difference in the initial
concentrations of two substrates, [reagent]0 - [substrate]0 to manipulate
the large number of data pairs. The two reactions carried out at the same
[“excess”] reveal unsteady-state influence on kinetic behavior, and the
reactions at the different [“excess”] give sufficient data required for the
determination of kinetic constants within a kinetic model.
A negative NLE was actually observed in Rh/binap-catalyzed
asymmetric addition of PhB(OH)2 (1) to 2-cyclohexenone (7),
giving phenylation product 82-4 ([R] > [S], Scheme 3, and squares
in Figure 2). The dimerization constant was estimated to be Kdimer
) 8 × 102 M-1 by fitting the deviation from the linear relationship
as well as the increase in the reaction rate to eq 3 (solid lines, Figure
2). By substituting this Kdimer value for the slope of eq 2
(k1/(2Kdimer)
0.5 ) 12 M-0.5 s-1), the rate constant for transmetalation
(12) The half-order kinetics in [catalyst] was reported in ref 10a.
(13) We observed that the hydrolysis is much faster than the insertion (ref 4).
(14) Kinetic modeling of the data to fit the proposed rate expression in eq 2
was carried out using the Excel least-squares program.
k1 is readily extracted to be k1 ) 0.5 M-1 s-1. Thus, we finally
obtained kinetic constants for both k1 and Kdimer. Unfortunately, it
is statistically difficult to extract the constant k2 under our
experimental conditions.
In conclusion, our detailed kinetic study and quantitative
simulation of nonlinear effect determined the rate constant for rate-
determining transmetalation and the dimerization constant, revealing
that the reaction mechanism involves the equilibrium between the
catalytically inactive dimeric hydroxorhodium complex [Rh(OH)-
((R)-binap)]2 (RR-4) and the active monomeric species R-4 and that
(15) For the first example, see: (a) Puchot, C.; Samuel, O.; Dunach, E.; Zhao,
S.; Agami, C.; Kagan, H. B. J. Am. Chem. Soc. 1986, 108, 2353. For
reviews, see: (b) Girard, C.; Kagan, H. B. Angew. Chem., Int. Ed. 1998,
37, 2922. (c) Blackmond, D. G. Acc. Chem. Res. 2000, 33, 402.
(16) (a) Kitamura, M.; Okada, S.; Suga, S.; Noyori, R. J. Am. Chem. Soc.
1989, 111, 4028. (b) Kitamura, M.; Suga, S.; Oka, H.; Noyori, R. J. Am.
Chem. Soc. 1998, 120, 9800.
(17) This type of mathematical treatment has been reported in refs 15c and
16b.
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