Quantitative analysis of the chiral amplification in the amino alcohol- promoted asymmetric alkylation of aldehydes with dialkylzincs

Article abstract of DOI:10.1021/ja981740z

Asymmetric reaction of dimethylzinc and benzaldehyde in the presence of (2S)-3-exo-(dimethyl-amino)isoborneol [(2S)-DAIB] exhibits unusual nonlinear phenomena. The enantiomeric purity of the product is much higher than that of the chiral source, DAIB, while the rate of the enantioselective catalysis decreases considerably as the enantiomeric excess (ee) of DAIB is lowered. Such effects originate from the reversible homochiral and heterochiral interaction of the coexistent enantiomeric zinc amino alkoxide catalysts which are formed from dimethylzinc and (2S)- and (2R)-DAIB. The thermodynamics of the five-component equilibration between the two monomers and three dimers, when coupled with the kinetics of the alkylation, strongly affects the extent of enantioselectivity and the reaction rate of the alkylation reaction. The overall profile of the nonlinear effects has been clarified mathematically using experimentally available parameters, viz., the equilibrium constants of the dimer/monomer conversion and the association of the monomeric catalyst with the organozinc and aldehyde, the rate constant of alkyl transfer from the catalyst/dimethylzinc/aldehyde mixed complex, the ee of DAIB, and the concentrations of DAIB, dimethylzinc, and aldehyde. 3D graphics are presented for the correlation of the enantiomeric purity of the product with DAIB ee and the concentrations of dimethylzinc and aldehyde and for the relationship between the reaction rate, DAIB ee, and the concentrations of the organozinc and aldehyde. The computer simulation is in good agreement with the experimental results, confirming thai the nonlinear effects result from the competition of two enantiomorphic catalytic cycles involving the monomeric chiral zinc catalysts rather than the diastereomorphic catalytic cycles with dinuclear zinc catalysts. Furthermore, this study indicates that the degree of nonlinear effects in asymmetric catalysis could be affected not only by the catalyst ee but also by various reaction parameters, particularly the concentrations of the catalyst, reagent, and substrate as well as the extent of conversion.

Full text of DOI:10.1021/ja981740z

9800
J. Am. Chem. Soc. 1998, 120, 9800-9809
Quantitative Analysis of the Chiral Amplification in the Amino
Alcohol-Promoted Asymmetric Alkylation of Aldehydes with
Dialkylzincs
Masato Kitamura, Seiji Suga, Hiromasa Oka, and Ryoji Noyori*
Contribution from the Department of Chemistry and Research Center for Materials Science,
Nagoya UniVersity, Chikusa, Nagoya 464-8602, Japan
ReceiVed May 19, 1998
Abstract: Asymmetric reaction of dimethylzinc and benzaldehyde in the presence of (2S)-3-exo-(dimethyl-
amino)isoborneol [(2S)-DAIB] exhibits unusual nonlinear phenomena. The enantiomeric purity of the product
is much higher than that of the chiral source, DAIB, while the rate of the enantioselective catalysis decreases
considerably as the enantiomeric excess (ee) of DAIB is lowered. Such effects originate from the reversible
homochiral and heterochiral interaction of the coexistent enantiomeric zinc amino alkoxide catalysts which
are formed from dimethylzinc and (2S)- and (2R)-DAIB. The thermodynamics of the five-component
equilibration between the two monomers and three dimers, when coupled with the kinetics of the alkylation,
strongly affects the extent of enantioselectivity and the reaction rate of the alkylation reaction. The overall
profile of the nonlinear effects has been clarified mathematically using experimentally available parameters,
viz., the equilibrium constants of the dimer/monomer conversion and the association of the monomeric catalyst
with the organozinc and aldehyde, the rate constant of alkyl transfer from the catalyst/dimethylzinc/aldehyde
mixed complex, the ee of DAIB, and the concentrations of DAIB, dimethylzinc, and aldehyde. 3D graphics
are presented for the correlation of the enantiomeric purity of the product with DAIB ee and the concentrations
of dimethylzinc and aldehyde and for the relationship between the reaction rate, DAIB ee, and the concentrations
of the organozinc and aldehyde. The computer simulation is in good agreement with the experimental results,
confirming that the nonlinear effects result from the competition of two enantiomorphic catalytic cycles involving
the monomeric chiral zinc catalysts rather than the diastereomorphic catalytic cycles with dinuclear zinc catalysts.
Furthermore, this study indicates that the degree of nonlinear effects in asymmetric catalysis could be affected
not only by the catalyst ee but also by various reaction parameters, particularly the concentrations of the
catalyst, reagent, and substrate as well as the extent of conversion.
In most asymmetric catalyses, the sense and extent of
amino)isoborneol [(2S)-DAIB] in 15% ee (S:R ) 57.5:42.5)
affords after aqueous workup (S)-1-phenyl-1-propanol in 95%
ee (S:R ) 97.5:2.5), which is close to the 98% ee achieved
with enantiomerically pure (2S)-DAIB.5 Furthermore the reac-
tion rate is highly dependent on the enantiomeric purity of the
DAIB ancillary; the reaction aided by enantiomerically pure
DAIB is much faster than that with racemic DAIB. The catalyst
is considered to be a chiral tricoordinate alkylzinc amino
alkoxide formed from diethylzinc and DAIB, which tends to
dimerize in toluene. When the S and R catalysts coexist, both
the homochiral interaction, giving S-S or R-R, and the
heterochiral interaction leading to S-R are possible.6 The
dynamic monomer/dimer equilibrium coupled with the kinetics
stereoselection are determined by the relative stabilities of the
diastereomeric transition states in the first irreversible step.1 In
certain cases, however, the profile of asymmetric catalysis is
highly affected by molecular interaction of the chiral catalyst
with coexisting chiral or achiral molecules, and consequently,
very unusual phenomena are seen.2,3 A notable example is the
amino alcohol-promoted asymmetric reaction of dialkylzincs and
aldehydes that shows a remarkable nonlinear relation between
the enantiomeric purities of the chiral source and the alkylation
products.4-9 Reaction of diethylzinc and benzaldehyde in
toluene containing a small amount of (2S)-3-exo-(dimethyl-
(1) Asymmetric Catalysis; Bosnich, B., Ed.; Martinus Nijhoff Publish-
ers: Dordrecht, 1986.
(2) Review: Noyori, R.; Kitamura, M. Angew. Chem., Int. Ed. Engl.
1991, 30, 49.
(5) (a) Kitamura, M.; Suga, S.; Kawai, K.; Noyori, R. J. Am. Chem.
Soc. 1986, 108, 6071. (b) Noyori, R.; Suga, S.; Kawai, K.; Okada, S.;
Kitamura, M.; Oguni, N.; Hayashi, M.; Kaneko, T.; Matsuda, Y. J.
Organomet. Chem. 1990, 382, 19. The first catalytic asymmetric addition
of diethylzinc to benzaldehyde: Oguni, N.; Omi, T. Tetrahedron Lett. 1984,
25, 2823.
(6) For the structural origin of differences between the homochiral and
heterochiral dimers, see: Kitamura, M.; Yamakawa, M.; Oka, H.; Suga,
S.; Noyori, R. Chem. Eur. J. 1996, 2, 1173.
(3) Early reports on the nonlinear effect in asymmetric reactions: (a)
Puchot, C.; Samuel, O.; Dun˜ach, E.; Zhao, S.; Agami, C.; Kagan, H. B. J.
Am. Chem. Soc. 1986, 108, 2353. (b) Agami, C.; Levisalles, J.; Puchot, C.
J. Chem. Soc., Chem. Commun. 1985, 441. (c) Agami, C. Bull. Soc. Chim.
Fr. 1988, 499. For the original works on discrimination between homo-
and heterochiral pairs and nonlinear effects, see (for physical properties):
Horeau, A. Tetrahedron Lett. 1969, 3121. Horeau, A.; Guette´, J. P.
Tetrahedron 1974, 30, 1923. (For asymmetric synthesis) Wynberg, H.;
Feringa, B. Tetrahedron 1976, 32, 2831.
(7) Kitamura, M.; Okada, S.; Suga, S.; Noyori, R. J. Am. Chem. Soc.
1989, 111, 4028.
(4) (a) Noyori, R.; Suga, S.; Kawai, K.; Okada, S.; Kitamura, M. Pure
Appl. Chem. 1988, 60, 1597. (b) Oguni, N.; Matsuda, Y.; Kaneko, T. J.
Am. Chem. Soc. 1988, 110, 7877. (c) Bolm, C.; Schlingloff, G.; Harms, K.
Chem. Ber. 1992, 125, 1191.
(8) Kitamura, M.; Suga, S.; Niwa, M.; Noyori, R. J. Am. Chem. Soc.
1995, 117, 4832.
(9) Kitamura, M.; Suga, S.; Niwa, M.; Noyori, R.; Zhai, Z.-X.; Suga, H.
J. Phys. Chem. 1994, 98, 12776.
S0002-7863(98)01740-5 CCC: $15.00 © 1998 American Chemical Society
Published on Web 09/15/1998

Asymmetric Alkylation of Aldehydes with Dialkylzincs
J. Am. Chem. Soc., Vol. 120, No. 38, 1998 9801
of the catalysis results in the deviation of the S:R catalyst ratio
from the original ratio of DAIB enantiomer and in turn the
nonlinear phenomenon.7-9 This article describes the quantitative
analysis of the overall profile of stereoselectivity and the reaction
rate of the amino alcohol-aided alkylation.
Scheme 1a
Kagan has done a mathematical analysis on a related, but
different, case using the titanium tartrate-catalyzed oxidation
of allylic alcohols and sulfides, where homochiral and hetero-
chiral Ti catalysts are involved in the stereodetermining transi-
tion states.3a,10,11 In these reactions, metal modification by a
partially resolved chiral auxiliary results in the irreVersible,
nonstatistical formation of diastereomeric Ti complexes with
two chiral auxiliary molecules of types ML*2 or M2L*2 (M )
metallic species; L* ) chiral ligand). The differences in the
stabilities and reactivities of the stereoisomers are believed to
cause the nonlinear effect.12 In contrast, the organozinc
chemistry is characterized by the reversibility of the chiral
recognition of the enantiomeric catalysts of type ML* as well
as the involvement of a single chiral molecule in the stereo-
determining transition state. Thus, the nonlinear effects of the
Zn chemistry are based on the relative significance of enantio-
morphic catalytic cycles, in contrast to the unusual phenomena
of the Ti chemistry that arise from the competition of diaste-
reomorphic catalytic cycles. This study aims to confirm this
view. The present mathematical treatment, as a complement
to Kagan’s accomplishment,3a,11 will help to deepen the
understanding of the origin and mechanism of the nonlinear
phenomena in various asymmetric catalysis.3,4
a P ) product, PR or PS.
between the catalysts and the homochiral and heterochiral
dimers, S-S, R-R, and S-R, as illustrated in the center of
Scheme 1. The catalytically unreactive dimers dissociate into
the reactive monomers with the given dissociate constants, Khomo
9
and Khetero
.
Monomeric S and R assemble a reactant (Rea) and
a substrate (Sub), with a given associate constant Kassoc to form
the catalyst/reactant/substrate mixed complexes, S-Rea-Sub
and R-Rea-Sub, which are converted with the same rate
constant k to the catalyst/product complexes, S-P and R-P.
Finally, the enantiomeric products, PS and PR, are released from
these complexes by the action of Rea or Sub to complete the
catalytic cycle. To establish a smooth catalytic cycle, all steps
must proceed at a reasonable rate; inhibition by the reactant,
substrate, or product should be avoided. The enantiomeric
purity of the product, eeP, limited by the enantioselectivity,
eePmax, which may be obtained with the enantiomerically pure
catalyst, is determined by the relative turnovers of the two
enantiomorphic catalytic cycles.
General Mathematical Treatment
For mathematical purposes, a steady-state approximation is
applied to the concentrations of S-Rea-Sub and R-Rea-Sub.
These intermediates are irreversibly and stereoselectively con-
verted to S-P or R-P, and the turnover of the catalytic cycles
is limited by this step. Thus, when Rea and Sub exist in
We assume a disubstrate-monoproduct catalysis that follows
the Michaelis-Menten-type kinetic law. Supposing that enan-
tiomeric catalysts, S and R, are coexistent in the same reaction
system ([S] g [R]) and that there exists a dynamic equilibrium
max
sufficient excess to the catalyst, the eeP is determined by eeP
and the relative concentration of S-Rea-Sub to R-Rea-Sub.
The initial reaction rate ν0 can be expressed by multiplication
of the sum of [S-Rea-Sub] and [R-Rea-Sub] and the rate
constant k. Equations 1 and 2 are thus established. Since the
(10) Other asymmetric reactions showing nonlinear effects. (Sharpless
epoxidation of geraniol or sulfide): Reference 3a. (Ene reaction): Terada,
M.; Mikami, K. J. Chem. Soc., Chem. Commun. 1994, 833. (Diels-Alder
reaction): Iwasawa, N.; Hayashi, Y.; Sakurai, H.; Narasaka, K. Chem. Lett.
1989, 1581. Mikami, K.; Motoyama, Y.; Terada, M. J. Am. Chem. Soc.
1994, 116, 2812. Kobayashi, S.; Ishitani, H.; Araki, M.; Hachiya, I.
Tetrahedron Lett. 1994, 35, 6325. (Silylcyanation of benzaldehyde):
Hayashi, M.; Matsuda, T.; Oguni, N. J. Chem. Soc., Chem. Commun. 1990,
1364. (Conjugate addition of organometallics to R,â-unsaturated carbonyl
compounds): Bolm, C.; Ewald, M.; Felder, M. Chem. Ber. 1992, 125, 1205.
Tanaka, K.; Matsui, J.; Suzuki, H. J. Chem. Soc., Perkin Trans. 1 1993,
153. Rossiter, B. E.; Eguchi, M.; Miao, G.; Swingle, N. M.; Herna´ndez, A.
E.; Vickers, D.; Fluckiger, E.; Patterson, R. G.; Reddy, K. V. Tetrahedron
1993, 49, 965. Zhou, Q.-L.; Pfaltz, A. Tetrahedron 1994, 50, 4467. de Vries,
A. H. M.; Jansen, J. F. G. A.; Feringa, B. L. Tetrahedron 1994, 50, 4479.
(Hajos-Wiechert intramolecular aldol reaction): References 3b and 3c.
(Nitro-aldol reaction): Sasai, H.; Suzuki, T.; Itoh, N.; Shibasaki, M.
Tetrahedron Lett. 1993, 34, 851. (Allylation of aldehydes using organotin
compounds): Keck, G. E.; Krishnamurthy, D.; Grier, M. C. J. Org. Chem.
1993, 58, 6543. (Meerwein-Ponndorf-Verley reduction): Evans, D. A.;
Nelson, S. G.; Gagne´, M. R.; Muci, A. R. J. Am. Chem. Soc. 1993, 115,
9800. (Oxidation of sulfides): Komatsu, N.; Hashizume, M.; Sugita, T.;
Uemura, S. J. Org. Chem. 1993, 58, 4529. (Reduction of acetophenone by
diisopinocamphenyl chloroborate): Girard, C.; Kagan, H. B. Tetrahedron:
Asymmetry 1997, 8, 3851.
max[S-Rea-Sub] - [R-Rea-Sub]
eeP ) eep
(1)
(2)
[S-Rea-Sub] + [R-Rea-Sub]
ν0 ) k([S-Rea-Sub] + [R-Rea-Sub])
total catalyst concentration, [Ctot], is approximated by the sum
of the concentrations of the chiral source existing before the
rate-determining step as the monomeric catalysts, the dimers,
and the Rea and Sub complexes, the enantiomeric purity of the
chiral source, eeC , can be expressed by eq 3.
tot
eeC ) (([S] + 2[S-S] + [S-R] + [S-Rea-Sub] -
tot
([R] + 2[R-R] + [S-R] + [R-Rea-Sub]))/[Ctot] (3)
To correlate eeP and ν0 with eeCtot using the equilibrium
constants, Khomo, Khetero, and Kassoc, and the concentrations of
Ctot, Rea, and Sub,13 the concentration terms of the dimers and
catalyst/reactant/substrate complexes can be eliminated from eqs
1-3 by using eqs 4-6 and eq 7. Here for simplification, R
(11) Guillaneux, D.; Zhao, S.-H.; Samuel, O.; Rainford, D.; Kagan, H.
B. J. Am. Chem. Soc. 1994, 116, 9430. In the Kagan reservoir effect,
catalytic species are considered to be preserved as their associates. See
also: Blackmond, D. G. J. Am. Chem. Soc. 1997, 119, 12934.
(12) For the nonlinear effect based on the asymmetric activation of
racemic catalysts, see: Matsukawa, S.; Mikami, K. Tetrahedron: Asymmetry
1997, 8, 815. Matsukawa, S.; Mikami, K. Enantiomer 1996, 1, 69. Mikami,
K.; Matsukawa, S. Nature 1997, 385, 613. Ohkuma, T.; Doncet, H.; Pham,
T.; Mikami, K.; Korenaga, T.; Terada, M.; Noyori, R. J. Am. Chem. Soc.
1998, 120, 1086.
(13) The initial concentrations of Rea and Sub approximate [Rea] and
[Sub], because S-Rea-Sub and R-Rea-Sub are present only in small
quantities.

9802 J. Am. Chem. Soc., Vol. 120, No. 38, 1998
[S]2 [R]2
Kitamura et al.
point, the enantiomer ratio of the catalyst molecules present in
the whole system is identical to the [S-Rea-Sub] to [R-Rea-
Sub] ratio, resulting in a linear relationship between eeP and
eeCtot. When Khomo becomes greater than 2Khetero, chirality of
the product is amplified, and the denominator of eq 13 must be
positive. Solving the second-order inequality 13 in combination
with eeCtot e 1, the R ranges for the positive nonlinear effects
are given in eq 14. The highest and the lowest R values are
Khomo
)
)
(4)
(5)
(6)
[S-S] [R-R]
[S][R]
Khetero
)
[S-R]
[S-Rea-Sub] [R-Rea-Sub]
Kassoc
)
)
[S][Rea][Sub]
[R][Rea][Sub]
(-Khomo(1 + Kassoc[Rea][Sub]) + (Khomo(8[Ctot] + Khomo
2KhomoKassoc[Rea][Sub] + KhomoKassoc2[Rea]2[Sub]2))1/2)/
+
[Ctot] ) [S] + 2[S-S] + [S-R] + [S-Rea-Sub] + [R] +
2[R-R] + [S-R] + [R-Rea-Sub] (7)
4 g R g KhomoKhetero (1 + Kassoc[Rea][Sub])2 +
and â are introduced, where R ) [S] + [R] (R > 0) and â )
[S][R] (â g 0). Modification of the two equations by assuming
[S] g [R] gives
(
((
2[Ctot]
+
1/2 - (1 + Kassoc[Rea][Sub]) /
1
2
(
))
))
Khetero Khomo
2
(Khomo - 2Khetero) (14)
x
x
[S] ) (R + R - 4â)/2
(8)
(9)
reversed for the negative nonlinear effect. In addition, modi-
fication of eq 2 using eqs 6, 8, and 9 affords the rate eq 15.
2
[R] ) (R - R - 4â)/2
As the equation eeP ) eePmax([S] - [R])/([S] + [R]) is
established by substitution of eq 6 into eq 1, rearrangement with
eqs 8 and 9 affords
ν0 ) kKassoc[Rea][Sub]R
(15)
Now all the important variants eeP, eeCtot, and ν0 are described
by the four or six factors through parameter R: eeP ) f1(Khomo
,
max
2
x
eeP ) eeP
R - 4â/R
(10)
K
hetero, Kassoc, [Ctot], [Rea], [Sub], R) as seen from eqs 10 and
12. eeCtot ) f2(Khomo, Khetero, Kassoc, [Ctot], [Rea], [Sub], R) from
eqs 11 and 12. ν0 ) f3(k, Kassoc, [Rea], [Sub], R) from eq 15.
The selectivity profile and the kinetic behavior of a given
asymmetric reaction system can be clarified by graphical
expression with the Khomo, Khetero, and Kassoc values, which can
be experimentally determined by spectroscopic methods, mo-
lecular weight measurement, and kinetic analysis. Six frames,
a-f, in Figure 1 illustrate R-parametrically plotted curves
derived from eqs 10-12 by changing four factors, Khomo:Khetero
ratio, [Ctot], [Rea], and [Sub], and the association constant Kassoc
When eqs 4-6 are substituted into eq 3 to eliminate [S-S],
[R-R], [S-R], [S-Rea-Sub], and [R-Rea-Sub] followed by
replacement of [S] and [R] using eqs 8 and 9 gives eq 11 in
2
x
(2R/Khomo) + 1 + Kassoc[Rea][Sub] R - 4â
eeC
)
(11)
tot
[Ctot]
which eeCtot is related to Khomo, Kassoc, [Ctot], [Rea], [Sub], R,
and â. Combination of eq 7 with eqs 4-6, 8, and 9 followed
by rearrangement for â establishes eq 12. Since â is expressed
using theoretical values for the other parameters. As the Khomo
:
Khetero ratio decreases, the positive deviation diminishes and
finally returns to linearity (frame a). After passing the Khomo
) 2Khetero boundary, a negative nonlinearity begins to appear
(frame b). Frames c-e predict that only a weak nonlinear effect
will be observed with a very low [Ctot], very high [Rea] and
[Sub], and high association constants for catalyst S or R, Rea,
and Sub. As seen from frame f, the extent of the positive
nonlinear effect is enlarged when [Rea] and [Sub] are decreased
from 1000 to 100 mM with the Ctot, Rea, and Sub ratio fixed to
1:50:50. A further decrease of concentrations, however, tends
to diminish the nonlinear effect.
Figure 2 expresses graphically the influence of eeCtot as well
as [Rea] and [Sub] on the reaction velocity. Substantial rate
reduction is anticipated with the decrease of the enantiomeric
purity of the catalyst. Increasing the Khomo:Khetero ratio enhances
the sensitivity. The concentrations of Rea and Sub affect the
rate more strongly in the reaction using an enantiomerically pure
catalyst (eeCtot ) 1) than in the reaction with the racemic catalyst
(eeCtot ) 0). The velocity with an enantiopure catalyst is also
more easily maximized than that with a racemic catalyst.
A Case Study: Amino Alcohol-Promoted Asymmetric
Reaction of Dialkylzincs and Aldehydes. Dialkylzincs react
with prochiral aldehydes in the presence of a catalytic amount
of nonracemic DAIB to give, after hydrolysis, optically active
secondary alcohols.5 Frame a of Figure 3 illustrates the
enantioselectivity observed in the reaction of dimethylzinc
(DMZ) (420 mM) and benzaldehyde (BzH) (420 mM) in the
presence of (2S)-DAIB (8 mM) in toluene at 40 °C. The
â )
-Khetero(2R2 + RKhomo - ([Ctot] - Kassoc[Rea][Sub]R)Khomo
)
2(Khomo - 2Khetero
)
(12)
as a function of R, eeP is now given as a function of eeCtot
through R by using Khomo, Khetero, Kassoc, [Ctot], [Rea], and [Sub]
with a fixed eePmax value in a given asymmetric reaction. Once
these constants are determined, the overall profile of stereose-
lectivity is defined by the five-component monomer/dimer
equilibration of the chiral catalysts, bounded by solid lines in
Scheme 1, and the reversible formation of the product-
determining complexes, S-Rea-Sub and R-Rea-Sub. Here,
the conditions (1) R2 - 4â > 0, (2) 0 e eeCtot e 1, and (3) 0
e eeP e eeP
nonlinearity in the eeCtot/eeP relation is decided by the R range.
The requirements of 0 e eeCtot and 0 e eeP e eePmax are filled
when R2 - 4â > 0, as seen from eqs 11 and 10, respectively.
Substitution for â in the first inequality using eq 12 affords
max
must be satisfied. The type and degree of
R2 - 4â ) ((Khomo + 2Khetero)R2 + 2KhomoKhetero(1 +
Kassoc[Rea][Sub])R - 2KhomoKhetero[Ctot])/(Khomo
-
2Khetero) > 0 (13)
This equation shows that Khomo ) 2Khetero is the branching
condition which determines the type of nonlinearity. At this

Asymmetric Alkylation of Aldehydes with Dialkylzincs
J. Am. Chem. Soc., Vol. 120, No. 38, 1998 9803
Figure 1. Simulation of the nonlinear relationship between eeP and eeCtot in a theoretical asymmetric catalysis with the following parameters. a:
Khomo ) 1.0 × 10-2 M; Kassoc ) 5.0 × 101 M-2; [Ctot] ) 10 mM; [Rea] ) [Sub] ) 500 mM. b: Khomo ) 1.0 × 10-2 M; Kassoc ) 5.0 × 101 M-2
;
[Ctot] ) 10 mM; [Rea] ) [Sub] ) 500 mM. c: Khomo ) 1.0 × 10-2 M; Khetero ) 1.0 × 10-5 M; Kassoc ) 5.0 × 101 M-2; [Rea] ) [Sub] ) 500 mM.
d: Khomo ) 1.0 × 10-2 M; Khetero ) 1.0 × 10-5 M; Kassoc ) 5.0 × 101 M-2; [Ctot] ) 10 mM. e: Khomo ) 1.0 × 10-2 M; Khetero ) 1.0 × 10-5 M;
[Ctot] ) 10 mM; [Rea] ) [Sub] ) 500 mM. f: Khomo ) 1.0 × 10-2 M; Khetero ) 1.0 × 10-5 M; Kassoc ) 5.0 × 101 M-2
.
enantiomeric purity of (S)-1-phenylethanol obtained at an early
stage of reaction ranges from 95% with enantiomerically pure
(2S)-DAIB to 0% with racemic DAIB, where the variation is
not proportional to the enantiomeric purity of DAIB.14 In
addition, as shown in frame b, the reaction with enantiomerically
pure DAIB proceeds ∼6 times faster than with racemic DAIB.
Thus, the rate depends on the enantiomeric purity of DAIB but
the extent is not straightforward. The origin of these unusual
phenomena has been explained qualitatively in terms of the
enantiomer recognition of the asymmetric catalyst as outlined
in Scheme 2.6-9,11 The tricoordinate Zn complex 1, which is
in equilibrium with the dimer 2, acts as catalyst of the
enantioselective reaction of DMZ and BzH. When (2S)- and
(2R)-1 are coexistent, the homochiral and heterochiral dimer-
izations, leading to (2S,2′S)- and (2R,2′R)-2 and (2S,2′R)-2,
respectively, are possible, with the latter overwhelmingly
favored. The higher stability of (2S,2′R)-2 reduces the total
amount of 1 and also causes its enantiomeric purity to deviate
with the added DAIB auxiliary. As a consequence, substantial
nonlinearity is seen for both the reactivity and enantioselectivity.
We here analyze such effects quantitatively using experiments
and computer simulation.
2.5), while (2R)-3 gives (2R)-4 selectively.15 The final product
4, upon reaction with DMZ or BzH, affords tetrameric meth-
ylzinc 1-phenylethoxide (5), and a 1/DMZ or 1/BzH complex,
respectively, and then 3 to establish the catalytic cycle. The
formation of the stable tetrameric alkoxide 5 is important to
minimize the undesired product inhibition. The two catalytic
cycles are enantiomorphic. This mechanism is consistent with
the experimental results7 and the ab initio MO calculations.16
Seven parameters are required for the quantitative analysis
of Scheme 2. Three of these, [Ctot], [Rea], and [Sub], are
defined arbitrarily as the concentrations of (2S)-DAIB, DMZ,
and BzH, whereas the remaining key constants, Khomo, Khetero
assoc, and k, are obtained experimentally.
The molecular weight measurement of stereoisomeric 2 by
,
K
vapor pressure osmometry in toluene at 40 °C indicated that
the homochiral and heterochiral dimers dissociate into catalytic
1 with dissociation constants, Khomo ) (3.0 ( 1.0) × 10-2
M
and Khetero ) 1 × 10-5 M, respectively.9 Thus, in a 10 mM
toluene solution of (2S,2′S)- or (2R,2′R)-2, ∼60% of the
homochiral dimer is dissociated into the monomer, while, under
the same conditions, the degree of dissociation of (2S,2′R)-2 is
only ∼3%.
Equilibrium and Rate Constants. Scheme 2 consists of
the five-component equilibration of the chiral catalysts, 1 a 2,
the formation of the 1/DMZ/BzH mixed-ligand complex 3, and
the turnover-limiting alkyl transfer in 3. (2S)-3 produces (2S)-
415 predominantly containing (S)-1-phenylethoxide (S:R ) 97.5:
The rate constant k and the equilibrium constant Kassoc can
be determined by kinetic experiments using enantiomerically
pure DAIB. Figure 4a shows the initial rate as a function of
the concentration of an equimolar mixture of DMZ and BzH.
(15) The molecular weight is unknown. Complex 4 may be in equilibrium
with the dimer and other aggregates formed with coexisting organozinc
complexes.
(14) The optical yield of the reaction of DMZ and BzH using optically
pure DAIB ranges from 91 to 95%. Use of freshly distilled DMZ gives the
product in 95% ee.
(16) Yamakawa, M.; Noyori, R. J. Am. Chem. Soc. 1995, 117, 6327.

9804 J. Am. Chem. Soc., Vol. 120, No. 38, 1998
Kitamura et al.
Figure 2. Graphical expression of the ν0-eeCtot relation (a) and the
relation of ν0 with [Rea] and [Sub] (b) in a theoretical asymmetric
reaction with the following parameters. a: Khomo ) 1.0 × 10-2 M;
Kassoc ) 5.0 × 101 M-2; k ) 1.0 min-1; [Ctot] ) 10 mM; [Rea] )
[Sub] ) 500 mM. b: Khomo ) 1.0 × 10-2 M; Khetero ) 1.0 × 10-6 M;
Kassoc ) 5.0 × 101 M-2; k ) 1.0 min-1; [Ctot] ) 10 mM.
The reaction using an 8 mM solution of pure (2S)-DAIB in
toluene at 40 °C proceeds with a zero-order kinetics in the
reactant and substrate concentration when they are greater than
800 mM, although the rate depends on the concentration in a
range of 0-800 mM. Thus, in the presence of a large excess
of DMZ and BzH, (2S)-1 is completely converted to (2S)-3,
Figure 3. Nonlinear relationship between the enantiomeric purities
of the product and DAIB at <30% conversion (a) and between the
initial rate and DAIB ee (b) in the enantioselective methylation of
benzaldehyde. Conditions: [DAIB] ) 8 mM; [DMZ] ) [BzH] ) 420
mM; toluene; 40 °C.
giving saturation kinetics. The maximal velocity, ν0sat, at this
) 8-34 mM. Frame a predicts that the eeP nonlinearly will
increase with an increase of the ee value of DAIB when [DMZ]
and [BzH] are fixed. With a fixed DAIB ee, the degree of
nonlinearity is expected to decrease with an increase of [DMZ]
and [BzH]. The surface of frame b denotes the reaction rate ν0
calculated by varying eeCtot and [DMZ] and [BzH] with [DAIB]
) 8 mM. Frame c gives a simulated profile of the reaction
with [DAIB] ) 16 mM, suggesting rate enhancement by
increasing [DAIB] from 8 to 16 mM and, particularly, [DMZ]
and [BzH]. The ν0-DAIB ee projected planes predict that the
initial methylation rate is nonlinearily enhanced by increasing
the ee value of DAIB, as expected from the 1 a 2 equilibration
in favor of the heterochiral dimerization. In all cases, the
computer-generated curves (lines) provide a good fit with the
experimental results (dots) obtained at the early stage of the
reaction, indicating the validity of the theoretical analysis. This
confirms the mechanistic assumption as well; the nonlinear
effects originate from competition of the two enantiomorphic
catalytic cycles involving (2S)-1 and (2R)-1 under standard
reaction conditions.
sat
point is correlated with k and [Ctot] to give the equation ν0
)
k[Ctot], where [Ctot] corresponds to the concentration of DAIB
since 1 is formed quantitatively from DAIB and DMZ. Thus
the rate constant k of the (2S)-DAIB-promoted reaction is
calculated to be 2.5 × 10-1 min-1 by using the observed
velocity, ν0sat ) 2.0 mM min-1 and [Ctot] ) 8 mM. The reaction
using racemic DAIB did not attain saturation kinetics even with
high concentrations of DMZ and BzH because of the high
stability of (2S,2′R)-2. The association constant Kassoc is
determined to be 2.0 × 101 M-2 by curve-fitting between the
observed kinetics (Figure 4a) and the simulated kinetics (Figure
4b) with Kassoc in the range of 5-100 M-2
.
Validity of the Mathematical Treatment. Methylation is
normally conducted with [DAIB] e 34 mM and [DMZ] )
[BzH] < 840 mM. Figure 5 illustrates the graphic expression
of the three-dimensional (3D) correlation between eeP, ee of
DAIB (eeCtot in the general discussion), and [DMZ] and [BzH]
(1:1 molar ratio), and between ν0, DAIB ee, and [DMZ] and
[BzH] (1:1 molar ratio). The curved surfaces of frames a-c
have been obtained by simulation using the experimentally
determined Khomo, Khetero, Kassoc, and k where [Ctot] ) [DAIB]
Obtaining High eeP Values Using Partially Resolved
DAIB. This chirality amplification is based on the difference

Asymmetric Alkylation of Aldehydes with Dialkylzincs
J. Am. Chem. Soc., Vol. 120, No. 38, 1998 9805
Scheme 2
high chirality amplification is realized only when dissociation
of the heterochiral dimer to the racemic catalysts is insignificant.
Therefore, to gain a high degree of nonlinearity, the reaction
conditions must be selected for decreasing the dissociation of
(2S,2′R)-2.
When the concentrations of DMZ and BzH are lowered, the
mixed-ligand complexes (2S)- and (2R)-3 tend to release (2S)-
and (2R)-1, which equilibrate with the homochiral and hetero-
chiral dimers. The resulting higher stability of the heterochiral
dimer then increases the relative amount of (2S)-1 to (2R)-1,
thereby enhancing the degree of nonlinearity. For example,
when the reaction using an 8 mM solution of (2S)-DAIB in
20% ee was conducted with [DMZ] ) [BzH] ) 420 mM, an
eeP of only 68% was obtained. However, the ee value was
increased to 80 and 89% by decreasing [DMZ] and [BzH] to
210 and to 84 mM. Figure 5a illustrates the general trend.
Second, increasing the DAIB concentration raises the con-
centrations of the catalyst dimers resulting in a higher chirality
amplification. This is based on the tendency of even the stable
heterochiral dimer to considerably dissociate to the monomers
at lower concentrations. When DMZ and BzH (420 mM each)
were reacted with an 8 mM concentration of DAIB in 20% ee,
the methylation product was obtained in 68% ee as described
above, while the reaction using a 34 mM concentration of DAIB
with the same ee under otherwise identical conditions formed
the adduct in 82% ee (Figure 5a). In a like manner, the ee
values were improved from 82 to 94% by increasing the
concentration of DAIB in 40% ee from 8 to 34 mM (Figure
5a).
Figure 4. Determination of the rate constant k and the association
constant Kassoc. a: Initial rate of reaction of dimethylzinc and benzal-
dehyde in the presence of enantiomerically pure (2S)-DAIB (8 mM)
in toluene at 40 °C. k ) ν0sat/[Ctot] ) 2.5 × 10-1 min-1. b: Simulation
of kinetics under the conditions, Khomo ) 3.0 × 10-2 M; Khetero ) 1 ×
10-5 M; k ) 2.5 × 10-1 min-1; [Ctot] ) 8 mM. Kassoc is estimated to
be 2.0 × 101 M-2 by curve-fitting of graphs a and b.
in the thermodynamic stability of the homochiral and hetero-
chiral dimers 2 (Scheme 2), where the extent of participation
in the second equilibrium, forming (2S)- or (2R)-3, strongly
influences the degree of nonlinearity. In the reaction system
of Scheme 2, the enantiomeric purity of the 1-phenylethoxide
is determined simply by the ratio of [(2S)-3] and [(2R)-3] and
then [(2S)-1] and [(2R)-1], which are dynamically balanced
through the five equilibria: 2(2S)-1 a (2S,2′S)-2, 2(2R)-1 a
(2R,2′R)-2, (2S)-1 + (2R)-1 a (2S,2′R)-2, (2S)-1 + DMZ +
BzH a (2S)-3, and (2R)-1 + DMZ + BzH a (2R)-3. The
Finally, changing the total concentration of the catalyst and
reactants, DAIB, DMZ, and BzH, while keeping their mole
ratios constant, exerts an intricate effect on the nonlinearity
(Figure 6). Thus, when the reaction system with [DAIB (20%
ee)] ) 8 mM and [DMZ] ) [BzH] ) 420 mM was diluted by
a factor of 3 by increasing the amount of solvent, the eeP
increased from 68 to 83%. With a 7-fold-diluted system
([DAIB] ) 2.7 mM and [DMZ] ) [BzH] ) 140 mM to [DAIB]
) 0.4 mM and [DMZ] ) [BzH] ) 21 mM), the eeP value
decreased from 83 to 65%. These phenomena originate from
the balance of two opposite concentration effects, [DMZ] and
[BzH] vs [DAIB] on eeP. The 3-fold dilution intensifies the

9806 J. Am. Chem. Soc., Vol. 120, No. 38, 1998
Kitamura et al.
Figure 6. Correlation of eeP with [DMZ]:[DAIB] or [BzH]:[DAIB]
ratio and [DMZ] and [BzH] in the enantioselective methylation in
toluene at 40 °C. Ee of (2S)-DAIB is fixed to 20%. o, [DAIB] ) 0.4
mM, [DMZ] ) [BzH] ) 21 mM. O, [DAIB] ) 2.7 mM, [DMZ] )
[BzH] ) 140 mM. n, [DAIB] ) 8 mM, [DMZ] ) [BzH] ) 420 mM.
X, [DAIB] ) 16 mM, [DMZ] ) [BzH] ) 840 mM. X, [DAIB] ) 34
mM, [DMZ] ) [BzH] ) 1680 mM. b, [DAIB] ) 34 mM, [DMZ] )
[BzH] ) 420 mM. Simulation conditions, [DMZ]/[DAIB] or [BzH]/
[DAIB] ) 1, 12.5, 25, 50, 66.7, 100. Khomo ) 3.0 × 10-2 M; Khetero
)
max
1 × 10-5 M; Kassoc ) 2.0 × 101 M-2, and eeP
) 0.95. The
experimental data X and X do not fit with the calculation because of
[DMZ] ) [BzH] g 840 mM.
contribution of the unstable homochiral dimer relative to the
heterochiral dimer, increasing the eeP value. Once the limiting
condition of [DAIB] ) 2.7 mM where the homochiral dimer
sufficiently dissociates to the monomer is reached, however,
there is significant dissociation of the stable heterochiral dimer
which decreases the (2S)-1:(2R)-1 ratio and in turn lowers the
eeP. Figure 6 illustrates that the experimental results fit well
with the simulation curves when [DMZ] ) [BzH] < 840 mM
(standard conditions). This can then be used to find the
conditions for obtaining the highest eeP value.
Independent vs Competitive Figures. In some asymmetric
reactions that use partially resolved catalysts, a chiral and an
achiral catalytic system coexist without interaction and work
competitively in the same homogeneous medium. Kagan’s
observations in the Ti-catalyzed asymmetric oxidation of allylic
alcohols or sulfides are typical examples.3a Here the term f is
defined as the relative turnover efficiency of the chiral and
achiral catalyst systems. In such cases, the enantiomeric ratio
max
of the product, PS/PR, is determined by eq 16, where eeP
is
eeC (1 + eePmax)f + (1 - eeC
)
)
PS
PR
tot
tot
)
(16)
Figure 5. Simulation and observation of the nonlinear effects in the
DAIB-promoted enantioselective methylation of benzaldehyde in
toluene at 40 °C. a: Correlation of eeP with eeCtot and concentration of
DMZ and BzH (1:1). o, [DAIB] ) 8 mM; [DMZ] ) [BzH] ) 84 mM.
O, [DAIB] ) 8 mM; [DMZ] ) [BzH] ) 210 mM. n, [DAIB] ) 8
mM; [DMZ] ) [BzH] ) 420 mM. Simulation conditions, [DAIB] )
8 mM; [DMZ] ) [BzH] ) 0, 84, 210, 336, 420 mM. B, [DAIB] ) 34
mM; [DMZ] ) [BzH] ) 420 mM. Simulation conditions, [DAIB] )
34 mM; [DMZ] ) [BzH] ) 420 mM. b: Correlation of ν0 with eeCtot
and concentration of DMZ and BzH (1:1). 0, [(2S)-DAIB (100% ee)]
) 8 mM. ], [(()-DAIB] ) 8 mM. 4, [DAIB] ) 8 mM; [DMZ] )
[BzH] ) 420 mM. Simulation conditions, [DAIB] ) 8 mM; [DMZ]
) [BzH] ) 84, 168, 252, 336, 420 mM. c: Correlation of ν0 with
eeCtot and concentration of DMZ and BzH (1:1). 9, [(2S)-DAIB (100%
ee)] ) 16 mM. [, [(()-DAIB ) 16 mM. 2, [(2S)-DAIB (50% ee)] )
16 mM. Simulation conditions, [DAIB] ) 16 mM; [DMZ] ) [BzH]
) 84, 168, 252, 336, 420 mM. In all cases, parameters, Khomo ) 3.0 ×
10-2 M; Khetero ) 1 × 10-5 M; Kassoc ) 2.0 × 101 M-2; k ) 2.5 × 10-1
eeC (1 - eePmax)f + (1 - eeC
tot
tot
the enantiomeric excess of the product obtained by an enan-
tiomerically pure catalyst and eeC is the enantiomeric excess
tot
of the catalyst used. Rearrangement of eq 16 for f in
combination with eeP ) (PS - PR)/(PS + PR) gives eq 17.
eeP(1 - eeC
)
tot
f )
(17)
eeC (eePmax - eeP)
tot
We attempted to analyze the enantioselectivity of the orga-
nozinc reaction in this manner. The reaction of DMZ and BzH
(420 mM each) in the presence of DAIB in 20% ee (8 mM)
gave the eeP value 68%. This may be interpreted as the
competition of the imaginary chiral and achiral catalytic cycles,
giving the S alcohols in 95% ee and racemic alcohol, respec-
max
min-1, and eeP ) 0.95 are used.

Asymmetric Alkylation of Aldehydes with Dialkylzincs
J. Am. Chem. Soc., Vol. 120, No. 38, 1998 9807
contains (2S,2′R)-2 as the overwhelmingly major component,
and at the standard 8 mM concentration, the monomers (2S)-
and (2R)-1 are present only in small quantities, the methylation
reaction proceeds via the monomer 1 but not the dinuclear 2.
This view in now confirmed by the agreement between the
experimentally obtained and calculated values as seen in Figures
5-7. Previously we theorized the direct participation of 2
reacting with DMZ and/or BzH.7 The present simulation,
however, excludes such an associative mechanism from con-
sideration, at least under standard reaction conditions. Special
conditions, such as higher concentrations of the catalyst, DMZ,
and BzH,17 may require serious consideration of the contribution
of the associative mechanism.
Degree of Chirality Amplification as a Function of
Conversion. A decrease in [DMZ] and [BzH] and an increase
in [DAIB] lead to a higher degree of chirality amplification,
while a limiting value exists when [DMZ] and [BzH] are varied
with a fixed [DAIB]:[DMZ]:[BzH] ratio. This simulation gives
excellent agreement with the experimental results at the initial
stage of methylation. However, as the reaction proceeds, DMZ
and BzH are consumed and the product accumulates, thereby
shifting the conditions away from the initial state. In addition,
product inhibition becomes nonnegligible at the later stage of
the reaction, causing quantitative disagreement. There is a need
for caution under such a situation.
Figure 7. Conversion of the DAIB-Zn-promoted methylation of
benzaldehyde in the independent and competitive systems with [DMZ]
) [BzH] ) 420 mM. 0, [(2S)-DAIB (100% ee)] ) 8 mM, ν0 ) 1.4
mM min-1. ], [(()-DAIB] ) 8 mM), ν0 ) 0.22 mM min-1. 2, [(2S)-
DAIB (50% ee)] ) 16 mM ([(2S)-DAIB (100% ee)] ) [(()-DAIB )
8 mM, ν0 ) 1.5 mM min-1. The observed rate (2) is lower than the
value expected from the operation of chiral and achiral catalytic cycles
(sum of 0 and ] given by the broken line).
tively, that coexist in a 20:80 ratio and that turn over with a
10:1 relative rate. The competitive figure, f ) 10, is, however,
different from the relative rate observed under the independent
conditions; the catalysis using enantiomerically pure DAIB and
the same concentrations is in fact 6.4 times faster than the
reaction with racemic DAIB. With DAIB in 80% ee, the
difference is further enhanced. The chiral catalyst is calculated
to methylate BzH 23.5 times faster than the achiral catalyst
system does. This large difference between the independent
and competitive figures (6.4 vs 23.5) indicates that such an
interpretation is false. The present system involves the two
enantiomorphic catalytic cycles occurring at the same turnover
rate (Scheme 2), and the enantiomeric purity of the product is
determined simply by the ratio of the concentrations of (2S)-
and (2R)-1 in the catalytic system. The relative contribution
of the S and R catalytic cycle is 5.25 with 20% ee DAIB, giving
a 68% ee product, and 32.3 with 80% ee DAIB to afford the
94% ee product. The relative concentration of the monomeric
catalyst is not linearly correlated with the initial ratio of (S)-
The reaction performed with [(2S)-DAIB (20% ee)] ) 34
mM and [DMZ] ) [BzH] ) 420 mM gave (S)-1-phenylethanol
in 82% ee at 5% conversion but in 89% ee at 84% conversion.
The increase in eeP can be understood in terms of a successive
decrease in [DMZ] and [BzH] (Figure 5a). The overall ee can
be estimated by the integration of eeP from time 0 to time t (for
equations, see Supporting Information). In the highly enanti-
oselective reaction with a high [DAIB], as shown in Figure 8a,
the observed eeP values fit well with the calculated ones even
at the final stage of the reaction.
On the other hand, as shown in Figure 8b, when [DAIB (20%
ee)] was reduced to 8 mM, the reaction became less enantiose-
lective and the observed ee significantly deviates from the
calculated value particularly after the middle stage. This
phenomenon is explained qualitatively by assuming the product
and (R)-DAIB but is determined by the six parameters, Khomo
hetero, Kassoc, [DAIB], [DMZ], and [BzH].
Analysis of the reaction rate also eliminates the possibility
,
1
inhibition, 1 + /4 [CH3ZnOR*]4 [5, OR* ) (S)- or (R)-OCH-
K
(CH3)C6H5] a 4 and species derived therefrom, [1]m[CH3-
ZnOR*]n.15 The product participation is negligible at the initial
stage because of the high stability of the tetrameric alkoxide 5
as well as the existence of a large excess of DMZ and BzH.7
During the course of methylation, however, the decrease of
DMZ and BzH is accompanied by the accumulation of 5. As
a consequence, the equilibrium is shifted in the direction of 4,
and the regeneration of 3 is retarded. Thus the increase in CH3-
ZnOR* promotes the dissociation of 2, resulting in the reduction
of the chirality amplification.18
of competition between the chiral and achiral catalytic cycles.
When the coexistence of independent chiral and achiral (meso)
catalytic cycles is assumed, the rate of reaction using (2S)-DAIB
in 50% ee should be the sum of the rates of the two
diastereomorphic cycles. As shown in Figure 7, however, the
rate of reaction of DMZ and BzH (420 mM each) in the presence
of (2S)-DAIB in 50% ee (16 mM; each 8 mM of chiral and
racemic catalyst), indicated by 2 is significantly less than the
sum of 0 and ] (broken line) expected from the coexistent
chiral and achiral catalytic cycles. Instead, the observed
reactivity is properly analyzed on the basis of the mechanism
of Scheme 2. The rates of reaction with [DMZ] ) [BzH] )
420 mM and [(2S)-DAIB (100% ee)] ) 8 mM, [(()-DAIB] )
8 mM, or [DAIB (50% ee)] ) 16 mM are calculated to be 1.5,
0.32, and 1.6 mM min-1, respectively. These values agree well
with the experimental values. Thus, a buffer effect in the
multiple equilibration system suppresses the increase in the
concentration of 3 that directly correlates with the reaction rate.
Dissociative vs Associative Mechanism. The overall profile
of the organozinc catalysis is fully consistent with the pathway
of Scheme 2. Dissociation of the dinuclear complexes 2
generates the true catalyst 1. Although the heterochiral system
1
This process was confirmed by H NMR experiments. The
dinuclear structure of stable (2S,2′R)-2 was not affected by the
addition of an excess amount of 5 or DMZ. However, when
unstable (2S,2′S)-2 (3 mM) and (S)-5 (7.5 mM) (1:5 Zn-based
ratio) were mixed in toluene-d8, catalyst/product complexes15
were formed in 80% yield based on (2S,2′S)-2. The intensities
of signals due to two C(2) protons of DAIB, one benzylic proton,
and three Zn-methyls (-40 °C) suggested that the major
(17) Reaction with [DAIB (20% ee)] ) 34 mM and [DMZ] ) [BzH] )
1680 mM gave eeP of 44% at 10% conversion, the value being higher than
the expected 27% ee (Figure 6).
(18) Tetrameric (S)-methylzinc 1-phenylethoxide slowly catalyzes the
reaction of DMZ and BzH. This effect is negligible under the standard
conditions allowing smooth alkylation.

9808 J. Am. Chem. Soc., Vol. 120, No. 38, 1998
Kitamura et al.
homochiral and heterochiral dimerization of the enantiomeric
catalysts. The expressions make allowance for the mechanistic
interpretation of the nonlinear effects in the amino alcohol-
promoted enantioselective alkylation of aldehydes. Their valid-
ity has been proven through comparison of computer-simulated
graphs and experimental findings. The chirality amplification
is the consequence of the combination of many structural,
thermodynamic, and kinetic parameters. Most importantly, the
mathematical treatment confirms that the nonlinear phenomena
observed in the organozinc chemistry originate from the relative
significance of the enantiomorphic cycles and not from the
competition between diastereomorphic cycles involving the
chiral and achiral catalysts.23 In such asymmetric reactions, the
quantitative reproduction of nonlinear effects is achievable only
with identical reaction parameters, particularly concentrations
of the catalyst, reagent, and substrate. Note that the reagent
and substrate concentrations vary significantly in the course of
reaction. The product inhibition might affect the profile as well.
The detailed analysis presented in this paper, together with the
earlier qualitative descriptions of the nonlinear effects,4a,7,8
provides a logical basis for understanding the molecular
mechanism of a range of chemical nonlinear phenomena.3,4
Experimental Section
Graphical expression of the mathematical equations in Figures 1, 2,
4, 5, 6, and 8 was aided by the Mathematica program on an Apple
Macintosh computer or a Silicon Graphics computer. The key
parameters, Khomo for the dissociation of (2S,2′S)-2 to (2S)-1 and Khetero
for the dissociation of (2S,2′R)-2 to (2S)-1 and (2R)-1 were taken from
an earlier work.9 The DAIB-promoted asymmetric methylation of BzH
with DMZ was carried out in toluene at 40 °C. The procedures for
the chirality amplification experiments, kinetic studies, NMR studies,
molecular weight determination, and purification of materials are
essentially the same as those reported.7,8 Commercial DMZ (Toyo
Stauffer Chemical Co., Lot No. DMZ-812) was distilled at 25 °C and
at 0.01 mmHg into a Schlenk tube. The purified DMZ (9.76 g, 0.102
mol) was diluted with toluene to a total volume of 30 mL under an
argon stream. The resulting 3.41 M toluene solution of DMZ in a
Schlenk tube equipped with a Young tap was kept at -30 °C in the
dark. Solution that had been stored over 3 weeks was not used for
reactions.14 The crude (S)-5 was obtained as a white solid by
evaporating the volatiles from the mixture of the (S)-DAIB-promoted
reaction [(S)-DAIB (111 mg, 0.564 mmol), DMZ (2.87 M toluene
solution, 10.8 mL, 31.1 mmol), BzH (3.00 g, 28.2 mmol), and hexane
(20 mL), 380 h]. Recrystallization from hexane (5 mL) at 0 °C gave
pure (S)-5 as colorless platelet crystals, mp 108-110 °C. Racemic 5
was prepared from a solution of (()-1-phenylethanol (29.3 mg, 0.237
mmol) in hexane (2 mL) mixed with a 1.88 M DMZ solution in hexane
(0.15 mL, 0.28 mmol) at 0 °C under argon atmosphere. After 24 h,
all volatiles were removed under vacuum to give (()-5 (41.2 mg) as
an oil.
The conversion was confirmed by GC using a Shimadzu GC-14A
gas chromatograph:7 The conditions (capillary column, GL Science
OV-1 0.25 mm × 50 m; column temperature, 90 °C; rate of temperature
increase, 2 °C min-1; carrier gas, He; flow rate, 50 mL min-1; split
ratio, 40:1) afforded good separation of BzH and 1-phenylethanol with
tR values of 8.9 and 11.0 min, respectively. The ee of 1-phenylethanol
was determined by HPLC using a Shimadzu LC-6A model under the
following conditions:7 column, Daicel Co. Chiralcel OB; eluent, 100:2
hexane/2-propanol; flow rate, 1.0 mL min-1; detection, 254-nm light;
tR of the S isomer, 12.6 min; tR of the R isomer, 18.9 min.
Chiral Amplification Experiments. (a) Effect of [DMZ] and
[BzH] with a Fixed [DAIB]. [DAIB] was set to 8 mM and all reactions
were stopped early. The data for 84, 210, and 420 mM DMZ and
BzH are listed in the order, % ee of (2S)-DAIB, reaction time (min),
% conversion, and % ee of (S)-1-phenylethanol. 84 mM: (20, 180,
Figure 8. The eeP conversion curve in the DAIB-promoted enanti-
oselective methylation of benzaldehyde in toluene at 40 °C. a: [(2S)-
DAIB (20% ee)] ) 34 mM, [DMZ] ) [BzH] ) 420 mM. b: [(2S)-
DAIB (20% ee)] ) 8 mM, [DMZ] ) [BzH] ) 420 mM. Simulation
conditions, Khomo ) 3.0 × 10-2 M; Khetero ) 1 × 10-5 M; Kassoc ) 2.0
max
× 101 M-2, and eeP
) 0.95. Line, simulation. Dot, experimental
result.
product was [(2S)-1]2[(S)-CH3ZnOR*] with a six-membered
Zn3O3 structure.19 Upon the addition of 10 molar equiv of
DMZ, the amounts of the new products were reduced to 30%
and gave a C(2)-H signal pattern which had been obtained by
mixing (2S,2′S)-2 and DMZ in a 1:10 (Zn-based) molar ratio.
Reaction of (2S,2′S)-2 and (()-520 gave similar diastereomeric
[(2S)-1]m[CH3ZnOR*]n in 85% combined yield.21 Here, unlike
the enantiopure system, addition of 10 molar equiv of DMZ
reduced the amount of these complexes to only 55%. This
difference reflects the relative stabilities of (S)-5 and (()-5.
Cryoscopic molecular weight determination showed that the
aggregation state of (S)-5 is 3.8, while that of (()-5 is 3.2,22
indicating the lower stability of (()-5 compared to homochiral
(S)-5. This higher tendency of nonenantiopure 5 to cause
product inhibition explains the notable departure from the
calculated values in the less enantioselective reaction (Figure
8b). A mixture of (2S,2′S)-2, (S)-5, and DMZ in a 1:10:5 Zn
ratio, which approximates the conditions at ∼60% conversion,
gave the catalyst/product complex in ∼50% yield based on
(2S,2′S)-2. Thus, since the product inhibition becomes non-
negligible as the reaction proceeds, care must be taken to
evaluate for the nonlinear effect at the late stage of reaction.
Conclusion
General equations have been developed for the quantitative
treatment of nonlinear effects that result from the reversible
(19) van der Schaaf, P. A.; Wissing, E.; Boersma, J.; Smeets, W. J. J.;
Spek, A. L.; van Koten, G. Organometallics 1993, 12, 3624.
(20) Tetrameric (()-5 consists of (S)- and (R)-methylzinc 1-phenylethox-
ide in a statistical ratio.
(21) The 1H NMR spectrum was more complicated than that of the
homochiral system.
(22) Boersma, J. ComprehensiVe Organometallic Chemistry; Wilkinson,
G.; Ed.; Pergamon Press: New York, 1982; Chapter 16.
(23) For a chemical support, see: Kitamura, M.; Oka, H.; Noyori, R.
Tetrahedron, in press.

Asymmetric Alkylation of Aldehydes with Dialkylzincs
J. Am. Chem. Soc., Vol. 120, No. 38, 1998 9809
11.2, 88.9), (40, 180, 26.6, 88.7), (60, 180, 30.6, 92.3), (80, 120, 26.3,
95.9), (100, 100, 25.4, 95.7). 210 mM: (20, 160, 11.8, 80.1), (40,
180, 23.0, 93.3), (60, 180, 29.7, 92.5), (80, 160, 23.8, 92.6), (100, 75,
27.9, 94.9). 420 mM: (20, 120, 6.3, 67.6), (40, 80, 6.0, 82.2), (60,
80, 17.6, 89.8), (80, 40, 13.6, 93.9), (100, 30, 17.2, 94.5).
(b) Effect of [DAIB] with a Fixed [DMZ] and [BzH]. [DMZ]
and [BzH] were set to 420 mM. For [DAIB (20% ee)] ) 8 mM and
[DAIB (40% ee)] ) 8 mM, the data from experiment a was used. For
[DAIB] ) 34 mM the data are listed in the order of reaction time (min),
% conversion, and % ee of (S)-1-phenylethanol. (2S)-DAIB in 20%
ee: (20, 5.1, 81.6). (2S)-DAIB in 40% ee: (20, 16.0, 94.1).
(c) Effect of Total Concentration with a Fixed [DAIB]:[DMZ]:
[BzH] Ratio. The ee of (2S)-DAIB was set to 20%. The collected
data are listed in the order of [DAIB] (mM), [DMZ] and [BzH] (mM),
reaction time (min), % conversion, and % ee of (S)-1-phenylethanol.
[DAIB]:[DMZ]:[BzH] ) 1:50:50: (0.4, 21, 140, 2.3, 64.6), (2.7, 140,
180, 5.0, 83.1), (16, 840, 30, 3.7, 56.5), (34, 1680, 30, 10.0, 44.3).
[DAIB]:[DMZ]:[BzH] ) 1:12.5:12.5: (34, 420, 20, 5.1, 81.6).
(d) Effect of the Conversion on the Degree of Chirality Ampli-
fication. The data are listed in the order of reaction time (min), %
conversion, and % ee of (S)-1-phenylethanol. [DAIB (20% ee)] ) 34
mM and [DMZ] ) [BzH] ) 420 mM: (20, 5.1, 81.6), (40, 11.6, 85.8),
(85, 22.1, 85.2), (175, 38.3, 87.1), (320, 54.1, 88.3), (495, 66.0, 88.7),
(765, 72.2, 88.6), (1400, 79.3, 89.7), (3305, 84.5, 89.0). [DAIB (20%
ee)] ) 8 mM and [DMZ] ) [BzH] ) 420 mM: (120, 6.3, 67.6), (240,
14.5, 68.3), (480, 25.5, 68.3), (910, 42.2, 69.2), (1530, 59.2, 70.1),
(2840, 75.4, 69.1), (20000, 96.8, 66.4).
original data for the time-conversion relationship and the initial rates
are listed. 0% ee: (10, 0.58), (20, 1.2), (30, 1.7), (40, 2.5), (50, 3.1),
(60, 3.8), (120, 7.1), (180, 9.8), (240, 12.5), (300, 16.1); 0.053% min-1
) 0.22 mM min-1. 20% ee: (60, 4.0), (120, 8.5), (180, 13.4), (240,
17.5), (300, 21.3), (360, 24.5), (420, 26.5); 0.074% min-1 ) 0.31 mM
min-1. 40% ee: (60, 8.1), (120, 16.6), (180, 25.1), (240, 32.2), (300,
37.6), (360, 41.2); 0.14% min-1 ) 0.59 mM min-1. 60% ee: (40,
8.4), (80, 16.9), (120, 25.1), (160, 32.9), (200, 38.9), (240, 45.0); 0.21%
min-1 ) 0.88 mM min-1. 80% ee: (20, 6.1), (40, 12.2), (60, 18.9),
(80, 24.6), (100, 29.8), (120, 37.4); 0.32% min-1 ) 1.3 mM min-1
100% ee: (10, 3.5), (20, 6.6), (30, 10.8), (40, 13.2), (50, 16.9), (60,
20.0); 0.33% min-1 ) 1.4 mM min-1
.
.
The correlation between ν0 and ee of (2S)-DAIB with [DAIB] ) 16
mM was deduced from the results obtained under the following
conditions: (2S)-DAIB in 0, 50, and 100% ee; [DMZ] ) [BzH] ) 84,
252, and 420 mM. The original data for the time-conversion relation-
ship and the initial rates are listed. [DMZ] ) [BzH] ) 84 mM: 0%
ee: (120, 1.9), (180, 2.7), (240, 4.6), (300, 5.3), (360, 5.9); 0.017%
min-1 ) 0.014 mM min-1. 50% ee: (15, 4.6), (30, 8.0), (45, 8.2),
(60, 15.9), (75, 19.6), (90, 22.2); 0.25% min-1 ) 0.21 mM min-1. 100%
ee: (15, 7.2), (30, 13.7), (45, 21.3), (60, 26.6), (75, 29.0), (90, 34.6);
0.38% min-1 ) 0.32 mM min-1. [DMZ] ) [BzH] ) 252 mM: 0%
ee: (80, 3.2), (120, 4.6), (160, 5.0), (200, 8.5), (240, 12.7); 0.049%
min-1 ) 0.12 mM min-1. 50% ee: (15, 5.3), (30, 11.3), (45, 16.8),
(60, 23.5), (75, 28.9), (90, 32.3); 0.37% min-1 ) 0.94 mM min-1. 100%
ee: (10, 5.2), (25, 15.0), (35, 20.3), (45, 26.3), (55, 34.4), (70, 41.8);
0.61% min-1 ) 1.5 mM min-1. [DMZ] ) [BzH] ) 420 mM: 0% ee:
(40, 1.7), (80, 4.7), (120, 6.9), (160, 12.2), (200, 13.6), (240, 18.0);
0.076% min-1 ) 0.32 mM min-1. 50% ee: (10, 3.2), (20, 6.8), (30,
10.6), (40, 13.5), (60, 19.6), (80, 25.3), (100, 30.2), (120, 34.6), (180,
45.4); 0.35% min-1 ) 1.5 mM min-1. 100% ee: (10, 6.8), (20, 13.8),
(30, 20.5), (40, 26.2), (50, 32.3), (60, 38.8); 0.64% min-1 ) 2.7 mM
Kinetic Studies. (a) ν0 to ([DMZ] and [BzH]) Relationship Using
Optically Pure DAIB. The kinetic experiments using 8 mM (2S)-
DAIB in 100% ee were conducted by varying [DMZ] or [BzH] over a
range of 42-840 mM with a fixed 1:1 DMZ to BzH ratio. The time-
conversion relationship and the initial rates are listed for each
concentration of DMZ and BzH. 42 mM: (20, 4.0), (40, 11.5), (60,
15.8), (80, 22.1), (100, 25.3), (120, 30.5); 0.28% min-1 ) 0.12 mM
min-1. 84 mM: (20, 4.7), (40, 13.5), (60, 18.5), (80, 27.7), (100, 32.1),
min-1
.
Determination of Aggregation States of 5. The molecular weights
of (S)-5 and (()-520 were determined by depression of the freezing
(120, 34.4); 0.34% min-1 ) 0.29 mM min-1
. 126 mM: (20, 6.0),
point in benzene solution according to the reported procedure.7
A
(40, 15.0), (60, 23.6), (80, 30.0), (100, 36.2), (120, 41.7); 0.38% min-1
) 0.48 mM min-1. 168 mM: (20, 7.1), (40, 14.5), (60, 22.8), (80,
29.0), (100, 35.0), (120, 40.6); 0.39% min-1 ) 0.65 mM min-1. 252
mM: (20, 7.5), (40, 17.1), (60, 24.4), (80, 32.2), (100, 37.8), (120,
43.6); 0.42% min-1 ) 1.1 mM min-1. 336 mM: (20, 9.0), (40, 16.9),
(60, 25.8), (80, 32.1), (100, 40.0), (120, 45.3); 0.40% min-1 ) 1.4
mM min-1. 420 mM: (10, 3.5), (20, 6.6), (30, 10.8), (40, 13.2), (50,
16.9), (60, 20.0); 0.33% min-1 ) 1.4 mM min-1. 630 mM: (20, 6.1),
(40, 13.5), (60, 19.9), (80, 25.5), (100, 31.9), (120, 37.3); 0.30% min-1
) 1.9 mM min-1. 840 mM: (20, 4.5), (40, 10.2), (60, 15.3), (80, 20.3),
(100, 25.0), (120, 30.2); 0.24% min-1 ) 2.0 mM min-1. These data
was used to determine the rate constant k and the association constant
standard freezing point depression apparatus was used, equipped with
a sidearm through which the cell could be connected to a dual-manifold
vacuum/argon system. Molecular weight was calculated in each case
from ∆T ) Kfω/MW, where ∆T is the depression (degrees), Kf is the
molar depression of the solvent, ω is the weight (g) of solute in 1000
g of solvent, and MW is molecular weight. The Kf value of this
apparatus was calculated to be 5.16 on the basis of the depression of
a benzene (10.53 g) solution by naphthalene (118.6-566.6 mg). The
averaged ∆T values for (S)-5 and (()-5 obtained from four runs were
0.318 and 0.37 (0.35-0.39), respectively. The molecular weights of
(S)-5 and (()-5 were calculated to be 759 and 647 (620-690),
indicating the aggregation state to be 3.8 and 3.2, respectively.
Kassoc
.
(b) ν0 to ([DMZ] and [BzH]) Relation Using Racemic DAIB. All
the collected time-conversion data obtained with 8 mM of (()-DAIB
by varying [DMZ] or [BzH] over a range of 84-420 mM with a fixed
1:1 DMZ to BzH ratio are listed. 84 mM: (120, 1.7), (180, 2.1), (240,
2.9), (300, 3.9), (360, 4.5); 0.012% min-1 ) 0.010 mM min-1. 168
mM: (60, 1.9), (120, 3.5), (180, 5.4), (240, 7.4), (300, 8.5), (360, 11.7);
0.031% min-1 ) 0.052 mM min-1. 252 mM: (60, 2.9), (120, 5.2),
(180, 8.1), (240, 10.8); 0.045% min-1 ) 0.11 mM min-1. 336 mM:
(60, 2.9), (120, 5.8), (180, 8.5), (240, 10.5); 0.047% min-1 ) 0.16
mM min-1. 420 mM: (10, 0.58), (20, 1.2), (30, 1.7), (40, 2.5), (50,
3.1), (60, 3.8), (120, 7.1), (180, 9.8), (240, 12.5), (300, 16.1); 0.053%
Acknowledgment. We thank Professor H. Suga (Osaka
University) for suggestions and encouragement. We also
acknowledge Mr. Y. Takezawa, Wolfram Research, Inc., for
his quick and kind technical suggestion for the use of the
Mathematica program. This work was aided by Grand-in-Aid
for COE Research (07CE2004) from the Ministry of Education,
Science, Sports and Culture, Japan.
Supporting Information Available: Induction of equations
for graphical expression of Figures 4b, 5b, 6, and 8 as well as
1H NMR experiments (5 pages, print/PDF). See any current
masthead page for ordering information and Web access
instructions.
min-1 ) 0.22 mM min-1
.
(c) Relation between ν0, eeCtot, and [DMZ] and [BzH]. The
correlation between ν0 and ee of (2S)-DAIB was deduced from the
results obtained under the following conditions: 8 mM (2S)-DAIB in
0, 20, 40, 60, 80, and 100% ee; [DMZ] ) [BzH] ) 420 mM. The
JA981740Z