1,4-addition of lithium diisopropylamide to unsaturated esters: Role of rate-limiting deaggregation, autocatalysis, lithium chloride catalysis, and other mixed aggregation effects

Article abstract of DOI:10.1021/ja105855v

Lithium diisopropylamide (LDA) in tetrahydrofuran at -78 °C undergoes 1,4-addition to an unsaturated ester via a rate-limiting deaggregation of LDA dimer followed by a post-rate-limiting reaction with the substrate. Muted autocatalysis is traced to a lithium enolate-mediated deaggregation of the LDA dimer and the intervention of LDA-lithium enolate mixed aggregates displaying higher reactivities than LDA. Striking accelerations are elicited by <1.0 mol % LiCl. Rate and mechanistic studies have revealed that the uncatalyzed and catalyzed pathways funnel through a common monosolvated-monomer-based intermediate. Four distinct classes of mixed aggregation effects are discussed.

Full text of DOI:10.1021/ja105855v

Published on Web 10/20/2010
1,4-Addition of Lithium Diisopropylamide to Unsaturated
Esters: Role of Rate-Limiting Deaggregation, Autocatalysis,
Lithium Chloride Catalysis, and Other Mixed Aggregation
Effects
Yun Ma, Alexander C. Hoepker, Lekha Gupta, Marc F. Faggin, and
David B. Collum*
Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell UniVersity,
Ithaca, New York 14853-1301
Received July 2, 2010; E-mail: dbc6@cornell.edu
Abstract: Lithium diisopropylamide (LDA) in tetrahydrofuran at -78 °C undergoes 1,4-addition to an
unsaturated ester via a rate-limiting deaggregation of LDA dimer followed by a post-rate-limiting reaction
with the substrate. Muted autocatalysis is traced to a lithium enolate-mediated deaggregation of the LDA
dimer and the intervention of LDA-lithium enolate mixed aggregates displaying higher reactivities than
LDA. Striking accelerations are elicited by <1.0 mol % LiCl. Rate and mechanistic studies have revealed
that the uncatalyzed and catalyzed pathways funnel through a common monosolvated-monomer-based
intermediate. Four distinct classes of mixed aggregation effects are discussed.
Introduction
familiar to synthetic organic chemists (LDA/THF/-78 °C),
strange decays are observed that are neither first- nor second-
1,4-Additions of lithium amides have been reported on
numerous occasions.1-3 In one of the earliest reports, Schlessing-
er and co-workers found that attempted enolizations of unsatur-
ated esters using lithium diisopropylamide (LDA) in tetrahy-
drofuran (THF) at -78 °C afforded ꢀ-amino esters instead.1,4
They solved the problem by adding hexamethylphosphoramide
(HMPA). Davies and co-workers, recognizing the medicinal
importance of ꢀ-amino esters, developed highly enantioselective
1,4-additions of structurally analogous ꢀ-phenethylamine-
derived lithium dialkylamides.3
order (Figure 1, curve A). The near linearity of these decays
seems more akin to a zeroth-order dependence on ester.8,9
Moreover, traces of LiCl (<1 mol %) elicit a 70-fold
acceleration accompanied by curvature that appears decidedly
more normal (Figure 1, inset).
Our interest was piqued by the 1,4-addition of LDA
described in eq 1. Previous studies of the 1,4-addition in the
presence of HMPA showed that addition occurs to the
exclusion of enolization via highly solvated LDA dimers
suggested to be triple ions.5-7 When the reaction is carried
out in the absence of HMPA under conditions that would be
We describe herein rate and mechanistic studies of the 1,4-
addition in eq 1. The superposition of rate-limiting deaggrega-
tion, intervention of LDA-lithium enolate mixed aggregates,
muted autocatalysis, and marked catalysis by LiCl presents
considerable mechanistic complexity.10 Such overt complexity
is exhilarating in a mechanistic context, yet the growing number
of examples of such odd effects affiliated with LDA/THF/-78
°C are troubling in light of the prevalence of these conditions
in organic synthesis.11,12 Furthermore, the LiCl catalysis, which
is detectable using as little as 1.0 ppm LiCl, represents a mixed
aggregation effect that is, to the best of our knowledge,
undocumented.13-15
(1) (a) Herrman, J. L.; Kieczykowski, G. R.; Schlessinger, R. H.
Tetrahedron Lett. 1973, 14, 2433. (b) Doi, H.; Sakai, T.; Iguchi, M.;
Yamada, K.; Tomioka, K. J. Am. Chem. Soc. 2003, 125, 2886. (c)
Uyehara, T.; Asao, N.; Yamamoto, Y. J. Chem. Soc., Chem. Commun.
1987, 1410. (d) Amputch, M. A.; Matamoros, R.; Little, R. D.
Tetrahedron 1994, 50, 5591. (e) Hase, T. A.; Kukkola, P. Synth.
Commun. 1980, 10, 451. (f) Inokuchi, T.; Kawafuchi, H. J. Org. Chem.
2007, 72, 1472.
(2) Bellasoued, M.; Ennigrou, R.; Gaudemar, M. J. Organomet. Chem.
1988, 338, 149.
The Results describes strategies and tactics for specialists who
wish to understand the details of the rate studies; the section
(3) Davies, S. G.; Smith, A. D.; Price, P. D. Tetrahedron: Asymmetry
2005, 16, 2833.
(4) (a) Bakker, W. I. I.; Wong, P. L.; Snieckus, V. Lithium Diisopropy-
lamide. In e-EROS; Paquette, L. A., Ed.; Wiley: New York, 2001. (b)
Clayden, J. Organolithiums: SelectiVity for Synthesis; Baldwin, J. E.,
Williams, R. M., Eds.; Pergamon Press: New York, 2002.
(5) Ma, Y.; Collum, D. B. J. Am. Chem. Soc. 2007, 129, 14818.
(6) For a review summarizing rate studies of LDA-mediated reactions,
see: Collum, D. B.; McNeil, A. J.; Ramirez, A. Angew. Chem., Int.
Ed. 2007, 46, 3002.
(7) For an attempted comprehensive bibliography of triple ions of lithium
salts, see: Ma, Y.; Ramirez, A.; Singh, K. J.; Keresztes, I.; Collum,
D. B. J. Am. Chem. Soc. 2006, 128, 15399.
(8) (a) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms, 2nd
ed.; McGraw-Hill: New York, 1995; Chapter 2, p 44. Atkins, P. W.;
Jones, L. L. Chemical Principles: The Quest for Insight, 2nd ed.; W. H.
Freeman: New York, 2002.
9
15610 J. AM. CHEM. SOC. 2010, 132, 15610–15623
10.1021/ja105855v  2010 American Chemical Society

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
Figure 2. Representative 6Li NMR spectrum of a 60:40 mixture of [6Li]5
and [6Li]3 showing resonances of the homodimers (A2 and E2) and the mixed
dimer [6Li]4 (AE).
Figure 1. Plot of IR absorbance vs time in THF (6.10 M) for 1,4-addition
of ester 1 (0.004 M) with LDA (0.10 M) at -78 °C in the presence of
various amounts of LiCl: (A) no LiCl; (B) 0.01 mol % LiCl; (C) 0.4 mol
% LiCl. The inset shows an expanded view of curve C.
(DMEA). DMEA accelerates the reduction yet does not remain
bound to the recrystallized LDA.21 Despite taking these precau-
tions, however, we observed some variability when stock
solutions prepared from a common batch of LDA were used.
Control experiments examining the influence of LDA aging,
traces of H2O and O2, contaminants in solvents, joint greases,
and even the specific researcher carrying out the work failed to
uncover the source of this residual variability. The consequences
were not large, although triplicate measurements proved neces-
sary in some instances.
culminates in a mechanistic hypothesis that accounts for the
disparate behaviors. The Discussion summarizes the results for
a more general audience and describes how mixed aggregates
influence the reactivity.
Results
Solution Structures. Reaction of 2.0 equiv of LDA with
unsaturated ester 1 in THF at -78 °C with slow warming to
room temperature afforded ꢀ-amino ester 2 in 82% yield (eq
1).5 Monitoring the reaction of [6Li,15N]LDA with ester 1 using
6Li and 15N NMR spectroscopy revealed the presence of
LDA-lithium enolate mixed dimer 4 along with a concentra-
tion-independent pair of resonances in a nearly 1:1 ratio that
was shown by the absence of 6Li-15N coupling to be attributable
to enolate 5 (Figure 2). Although we were tempted to presume
that the two resonances derived from an E/Z mixture, we
suspected that they were homochiral and heterochiral dimers
5a. (The existence of chelation is depicted out of convenience;
the typically small Li-N coupling anticipated for a Li-NR3
interaction22 was not observed.) By varying the proportions of
LDA and lithium enolate and monitoring LDA homodimer 3,
mixed dimer 4, and the enolate homoaggregates (an A2-AE-En
ensemble), we used the method of continuous variation (the
method of Job23) to show that the enolate (En) is indeed a dimer
(Figure 3). Detailed descriptions of this method for character-
izing lithium enolates have been reported.24 Although mono-
Caveat: Purification of LDA. We previously showed by
potentiometry16 and ion chromatography17 that recrystallized
LDA18 prepared from recrystallized n-BuLi19 contains <0.02
mol % LiCl.11,12 Accelerations of the 1,4-addition in eq 1 by
as little as 0.001 mol % LiCl, however, prompted us to modify
a literature synthesis20 of rigorously LiCl-free LDA from lithium
metal, diisopropylamine, isoprene, and dimethylethylamine
(9) For other examples of odd linearities that may or may not have origins
similar to those described herein, see: (a) Blackmond, D. G.; Ropic,
M.; Stefinovic, M. Org. Process Res. DeV. 2006, 10, 457. (b) Akao,
A.; Nonoyama, N.; Mase, T.; Yasuda, N. Org. Process Res. DeV. 2006,
10, 1178. (c) Rowley, J. M.; Lobkovsky, E. B.; Coates, G. W. J. Am.
Chem. Soc. 2007, 129, 4948. (d) Yin, C.-X.; Finke, R. G. J. Am. Chem.
Soc. 2005, 127, 13988.
(10) For examples of reactions that are fast relative to aggregate-aggregate
exchanges, see: (a) McGarrity, J. F.; Ogle, C. A. J. Am. Chem. Soc.
1985, 107, 1810. (b) Jones, A. C.; Sanders, A. W.; Bevan, M. J.; Reich,
H. J. J. Am. Chem. Soc. 2007, 129, 3492. (c) Thompson, A.; Corley,
E. G.; Huntington, M. F.; Grabowski, E. J. J.; Remenar, J. F.; Collum,
D. B. J. Am. Chem. Soc. 1998, 120, 2028. (d) Jones, A. C.; Sanders,
A. W.; Sikorski, W. H.; Jansen, K. L.; Reich, H. J. J. Am. Chem. Soc.
2008, 130, 6060. (e) Reference 11.
(11) Singh, K. J.; Hoepker, A. C.; Collum, D. B. J. Am. Chem. Soc. 2008,
130, 18008.
(12) Gupta, L.; Hoepker, A. C.; Singh, K. J.; Collum, D. B. J. Org. Chem.
2009, 74, 2231.
(20) (a) Marck, W.; Huisgen, R. Chem. Ber. 1960, 93, 608. (b) Gaudemar-
Bardone, F.; Gaudemar, M. Synthesis 1979, 463. (c) Reetz, M. T.;
Maier, W. F. Liebigs Ann. Chem. 1980, 1471. (d) Williard, P. G.;
Carpenter, G. B. J. Am. Chem. Soc. 1986, 108, 462. Williard, P. G.;
Salvino, J. M. J. Org. Chem. 1993, 58, 1. (e) Morrison, R. C.; Hall,
R. W.; Rathman, T. L. Stable Lithium Diisopropylamide and Method
of Preparation. U.S. Patent 4,595,779, June 17, 1986.
(13) For leading references and discussions of mixed aggregation effects,
see: (a) Seebach, D. Angew. Chem., Int. Ed. Engl. 1988, 27, 1624. (b)
Tchoubar, B.; Loupy, A. Salt Effects in Organic and Organometallic
Chemistry; VCH: New York, 1992; Chapters 4, 5, and 7. (c) Briggs,
T. F.; Winemiller, M. D.; Xiang, B.; Collum, D. B. J. Org. Chem.
2001, 66, 6291. (d) Caube`re, P. Chem. ReV. 1993, 93, 2317.
(14) Seebach, D. In Proceedings of the Robert A. Welch Foundation
Conferences on Chemistry and Biochemistry; Wiley: New York, 1984;
p 93.
(21) See: Zhao, P.; Collum, D. B. J. Am. Chem. Soc. 2003, 125, 14411,
and references cited therein.
(22) Lucht, B. L.; Collum, D. B. J. Am. Chem. Soc. 1996, 118, 3529.
Waldmu¨ller, D.; Kotsatos, B. J.; Nichols, M. A.; Williard, P. G. J. Am.
Chem. Soc. 1997, 119, 5479. Sato, D.; Kawasaki, H.; Shimada, I.;
Arata, Y.; Okamura, K.; Date, T.; Koga, K. J. Am. Chem. Soc. 1992,
114, 761. Reich, H. J.; Goldenberg, W. S.; Gudmundsson, B. O.;
Sanders, A. W.; Kulicke, K. J.; Simon, K.; Guzei, I. A. J. Am. Chem.
Soc. 2001, 123, 8067. Johansson, A.; Davidsson, O. Chem.sEur. J.
2001, 7, 3461. Aubrecht, K. B.; Lucht, B. L.; Collum, D. B.
Organometallics 1999, 18, 2981.
(15) Ramirez, A.; Sun, X.; Collum, D. B. J. Am. Chem. Soc. 2006, 128,
10326, and references cited therein.
(16) Evans, A. Potentiometry and Ion-SelectiVe Electrodes; Wiley: New
York, 1987.
(17) Fuji, T. Anal. Chem. 1992, 64, 775.
(18) Kim, Y.-J.; Bernstein, M. P.; Galiano-Roth, A. S.; Romesberg, F. E.;
Fuller, D. J.; Harrison, A. T.; Collum, D. B.; Williard, P. G. J. Org.
Chem. 1991, 56, 4435.
(23) Job, P. Ann. Chim. 1928, 9, 113. For more recent examples and leading
references, see: Huang, C. Y. Methods Enzymol. 1982, 87, 509.
Hubbard, R. D.; Horner, S. R.; Miller, B. L. J. Am. Chem. Soc. 2001,
123, 5810. Potluri, V.; Maitra, U. J. Org. Chem. 2000, 65, 7764.
(19) Kottke, T.; Stalke, D. Angew. Chem., Int. Ed. Engl. 1993, 32, 580.
Rennels, R. A.; Maliakal, A. J.; Collum, D. B. J. Am. Chem. Soc.
1998, 120, 421.
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15611

A R T I C L E S
Ma et al.
Figure 3. Plot of the relative integrations of [6Li]3 (A2), [6Li]4 (AE), and
[6Li]5 (E2) vs the mole fraction of LDA (A). The curves were derived from
a parametric fit as described previously.24
Figure 4. Plot showing IR absorbance of ester 1 vs time for the 1,4-addition
of ester 1 (0.10 M) with LDA (0.10 M) in neat THF at -78 °C. The dashed
line shows the poor first-order fit (A ) aebt).
described below (e2 mol % LiCl) afford a LiCl-concentration-
independent 1:8 mixture of 6 and 7 to the exclusion of free
LiCl.27,28
meric enolate was not observed, it is invoked as an intermediate.
Density functional theory (DFT) computations at the B3LYP/
6-31G(d) level of theory25 suggested disolvated monomer 5b
as the fleetingly stable resting state.
Kinetics: General Protocols. LDA used in rate studies was
prepared as described above. Exogenous LiCl was generated
in situ from Et3N·HCl.29 (The Et3N byproduct is a poor ligand21
that has no effect on LDA structure or reactivity.) The
disappearance of ester 1 (1715 cm-1) during the 1,4-additions
was monitored using in situ IR spectroscopy.30 Formation of
lithium enolate 5 (1630 cm-1) was correlated with the loss of
1. It should be noted, however, that the absorbance at 1630 cm-1
arises from the superposition of mixed and homoaggregated
6
dimers 4 and 5a, respectively. Using Li NMR spectroscopy,
we were able to show that this IR spectral simplicity belies a
substantial underlying complexity (see below).31
Strange Curvatures. Monitoring addition of LDA to ester 1
by IR spectroscopy under pseudo-first-order conditions (excess
LDA) showed a linear decay, suggesting a zeroth-order depen-
dence on ester 1. Equimolar mixtures of LDA and ester 1
(second-order conditions) afforded the decay depicted in Figure
4. If the linearity in Figure 1 derived solely from a zeroth-order
dependence on ester 1, this dependence in conjunction with a
first-order dependence on LDA would cause the decay in Figure
4 to be first-order overall. The first-order fit in Figure 4 (dashed
line) is poor, suggesting a persistent linearity stemming from
autocatalysis (see below). (Previous studies of arylcarbamate
lithiations revealed linear decays that were traced to straighten-
ing of first-order decays by autocatalysis.11)
6Li NMR spectroscopy allowed us to follow the loss of LDA
dimer 3, mixed dimer 4, and enolate dimer 5a (Figure 5). The
concentrations of the aggregates also allowed us to calculate
the concentration of the spectroscopically silent ester 1. The
calculated linear decay of ester 1 correlated well with the
experimentally measured linear decay detected by IR spectros-
copy. The curved loss of LDA dimer 3 (the noncorrelation with
Catalysis by LiCl is discussed in light of the structures of
LDA-LiCl mixed aggregates. Previous studies have shown that
LiCl is dimeric in THF solution.26,27 Mixtures of LDA with
LiCl at the very low LiCl concentrations used in the rate studies
(24) (a) Liou, L. R.; McNeil, A. J.; Ramirez, A.; Toombes, G. E. S.; Gruver,
J. M.; Collum, D. B. J. Am. Chem. Soc. 2008, 130, 4859. (b) Gruver,
J. M.; Liou, L. R.; McNeil, A. J.; Ramirez, A.; Collum, D. B. J. Org.
Chem. 2008, 73, 7743.
(28) Galiano-Roth, A. S.; Kim, Y.-J.; Gilchrist, J. H.; Harrison, A. T.; Fuller,
D. J.; Collum, D. B. J. Am. Chem. Soc. 1991, 113, 5053. Also see:
Hall, P. L.; Gilchrist, J. H.; Collum, D. B. J. Am. Chem. Soc. 1991,
113, 9571.
(25) Frisch, M. J.; et al. Gaussian 03, revision B.04; Gaussian, Inc.:
Wallingford, CT, 2004.
(29) Snaith and coworkers underscored the merits of R3NHX salts as
precursors to anhydrous LiX salts. See: Barr, D.; Snaith, R.; Wright,
D. S.; Mulvey, R. E.; Wade, K. J. Am. Chem. Soc. 1987, 109, 7891.
Also see: Hall, P. L.; Gilchrist, J. H.; Collum, D. B. J. Am. Chem.
Soc. 1991, 113, 9571.
(26) (a) Reich, H. J.; Borst, J. P.; Dykstra, R. R.; Green, D. P. J. Am. Chem.
Soc. 1993, 115, 8728. (b) Wong, M. K.; Popov, A. I. J. Inorg. Nucl.
Chem. 1972, 34, 3615. (c) Yakimansky, A. V.; Mu¨ller, A. H.; Beylen,
M. V. Macromolecules 2000, 33, 5686. (d) Goralski, P.; Chabanel,
M. Inorg. Chem. 1987, 26, 2169, and references cited therein.
(27) Studies of LDA-LiCl at ultralow LiCl concentrations as well as
confirmation of LiCl in THF as a dimer will be reported in due course.
(30) Rein, A. J.; Donahue, S. M.; Pavlosky, M. A. Curr. Opin. Drug
DiscoVery DeV. 2000, 3, 734.
(31) Addition of excess i-Pr2NH to the metalation had no measurable effect
on the rates or curvatures.
9
15612 J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
Figure 5. Time-dependent concentrations measured by 6Li NMR spec-
troscopy using 0.05 M 3 (0.10 N) and 0.05 M 1 in 6.1 M THF at -78 °C.
Legend: ester ) 1; A2 ) LDA dimer 3; E2 ) enolate dimer 5a; AE )
enolate mixed dimer 4. The curves represent a parametric fit to eqs 17-22
(described below). The best-fit values for the rate constants are listed in
the Supporting Information.
Figure 7. Time-dependent concentrations measured by 6Li NMR spec-
troscopy using 0.05 M 3 (0.10 N) and 0.05 M ester 12 in 6.1 M THF at
-78 °C. Legend: ester ) 12; A2 ) LDA dimer 3; E′ ) enolate dimer of
2
ester 12; AE′ ) enolate mixed dimer. The curves represent a parametric fit
to eqs 17-22 (described below). The best-fit values for the rate constants
are listed in the Supporting Information.
Figure 6. Time-dependent concentrations measured by 6Li NMR spec-
troscopy using 0.05 M 3 (0.10 N) and 0.025 M 1 in 6.1 M THF at -78 °C.
Legend: ester ) 1; A2 ) LDA dimer 3; E2 ) enolate dimer 5a; AE )
enolate mixed dimer 4. The curves represent a parametric fit to eqs 17-22
(described below). The best-fit values for the rate constants are listed in
the Supporting Information.
Figure 8. Time-dependent concentrations measured by 6Li NMR spec-
troscopy using 0.05 M 3 (0.10 N) and 0.10 M 12 in 6.1 M THF at -78 °C.
Legend: ester ) 12; A2 ) LDA dimer 3; E′2 ) enolate dimer of 12; AE′ )
enolate mixed dimer. The curves represent a parametric fit to eqs 17-22
(described below). The best-fit values for the rate constants are listed in
the Supporting Information.
the ester) reflects the consumption of 3 by both metalation and
formation of mixed dimer 4. The time dependencies of 4 and
5a (represented as AE and E2 in Figures 5 and 6) clearly
departed from conventional behavior. Minor changes in the
initial concentration of ester 1 produced overt visual changes
(Figure 6). Even more striking curvatures and discontinuities
were observed when n-alkyl ester 12 was used (Figures 7 and
8). (Ester 12, n-C7H15CHdCHCO2-t-Bu, was introduced in the
context of the competition studies described below.) The
overshoot of the concentration of enolate dimer 5a relative to
the final equilibrium value and the discontinuity in the mixed
dimer concentration place significant constraints on a mecha-
nistic model. The rate studies described below were employed
to extract the critical details required to account for the strange
time-dependent concentrations, and best-fit numerical integra-
tions afforded the curves (see below).
Figure 9. Plots of IR absorbance of ester 1 vs time for selected initial
concentrations of 1: (A) 0.10 M; (B) 0.050 M; (C) 0.025 M; (D) 0.004 M.
Kinetics: Uncatalyzed 1,4-Additions. The mechanism of the
uncatalyzed 1,4-addition (i.e., the addition before the appearance
of mixed dimers and the onset of autocatalysis) was examined
by monitoring the rates at early conversion using IR spectros-
copy. Plots of ester concentration versus time for different initial
concentrations of ester 1 (Figure 9) showed linear, parallel
decays consistent with a zeroth-order dependence on 1, which
was confirmed by a plot of the initial rates versus initial ester
concentration (Figure 10). Plots of initial rate versus LDA
concentration (Figure 11)32 and THF concentration (Figure 12)
revealed first-order dependencies in both instances. The ideal-
(32) The concentration of LDA, although expressed in units of molarity,
refers to the concentration of the monomer unit (normality).
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15613

A R T I C L E S
Ma et al.
introducing the following shorthand: A ) an LDA monomeric
subunit and S ) THF (e.g., A2S2 ) 3).
d[1]
dt
-
) k[A2S2][S]
(2)
(3)
A2S2 + S
9
k8 [A2S3]q
Scheme 1
Figure 10. Plot of initial rate vs [1] in THF (6.1 M) for the 1,4-addition
of ester 1 with LDA (0.10 M) at -78 °C. The curve depicts an unweighted
least-squares fit to y ) k[1] + k′ [k ) (1.2 ( 1) × 10-5; k′ ) (3.9 ( 0.4)
× 10-6].
Figure 11. Plot of initial rate vs [LDA] in THF (6.10 M) for the 1,4-
addition of ester 1 (0.004 M) at -78 °C. The curve depicts an unweighted
least-squares fit to y ) k[LDA]n [k ) (3.1 ( 0.4) × 10-5; n ) 0.92 (
0.03].
DFT computations showed that trisolvated-dimer-based tran-
sition structures representing rate-limiting open dimer formation
(8) and deaggregation (9) are both plausible (Scheme 1).35 The
dimer-based rate-limiting step does not attest to whether the
post-rate-limiting 1,4-addition is monomer- or dimer-based, but
strong support for a monomer-based 1,4-addition emerged from
studies of catalysis (see below).
Autocatalysis. Product-derived accelerationsso-called autoca-
talysissin its most extreme form manifests sigmoidal decays
of substrate versus time36,37 and should be most easily observed
(35) Open dimers were first proposed for the isomerization of oxiranes to
allylic alcohols by mixed-metal bases. See: Mordini, A.; Rayana, E. B.;
Margot, C.; Schlosser, M. Tetrahedron 1990, 46, 2401. For a
bibliography of lithium amide open dimers, see ref 15.
Figure 12. Plot of initial rate vs [THF] in hexane cosolvent for the 1,4-
addition of ester 1 (0.004 M) with LDA (0.10 M) at -78 °C. The curve
depicts an unweighted least-squares fit to y ) k[THF]n + k′ [k ) (8.1 (
0.2) × 10-7; n ) 0.95 ( 0.03; k′ ) (4.05 ( 0.04) × 10-7].
(36) (a) Besson, C.; Finney, E. E.; Finke, R. G. J. Am. Chem. Soc. 2005,
127, 8179. (b) Besson, C.; Finney, E. E.; Finke, R. G. Chem. Mater.
2005, 17, 4925. (c) Huang, K. T.; Keszler, A.; Patel, N.; Patel, R. P.;
Gladwin, M. T.; Kim-Shapiro, D. B.; Hogg, N. J. Biol. Chem. 2005,
280, 31126. (d) Huang, Z.; Shiva, S.; Kim-Shapiro, D. B.; Patel, R. P.;
Ringwood, L. A.; Irby, C. E.; Huang, K. T.; Ho, C.; Hogg, N.;
Schechter, A. N.; Gladwin, M. T. J. Clin. InVest. 2005, 115, 2099. (e)
Tanj, S.; Ohno, A.; Sato, I.; Soai, K. Org. Lett. 2001, 3, 287. (f)
Barrios-Landeros, F.; Carrow, B. P.; Hartwig, J. F. J. Am. Chem. Soc.
2008, 130, 5842.
ized33 rate law given by eq 2 is consistent with a mechanism
involving rate-limiting deaggregation (eq 3) followed by post-
rate-limiting reaction with ester 1.34 To describe some
fairly complex mechanistic scenarios, we take the liberty of
(37) (a) Depue, J. S.; Collum, D. B. J. Am. Chem. Soc. 1988, 110, 5524.
(b) McNeil, A. J.; Toombes, G. E. S.; Gruner, S. M.; Lobkovsky, E.;
Collum, D. B.; Chandramouli, S. V.; Vanasse, B. J.; Ayers, T. A.
J. Am. Chem. Soc. 2004, 126, 16559. (c) Nudelman, N. S.; Velurtas,
S.; Grela, M. A. J. Phys. Org. Chem. 2003, 16, 669. (d) Alberts, A. H.;
Wynberg, H. J. Am. Chem. Soc. 1989, 111, 7265. (e) Alberts, A. H.;
Wynberg, H. J. Chem. Soc., Chem. Commun. 1990, 453.
(33) We define the idealized rate law as that obtained by rounding the
observed reaction orders to the nearest rational order.
(34) The rate law provides the stoichiometry of the transition structure
relative to that of the reactants. See: Edwards, J. O.; Greene, E. F.;
Ross, J. J. Chem. Educ. 1968, 45, 381.
9
15614 J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
Figure 14. Plot of initial rate vs [LDA] for the condensation of LDA dimer
3 with enolate dimer 5a (0.025 M) in THF (6.10 M) at -78 °C. The curve
depicts an unweighted least-squares fit to y ) k[LDA]n [k ) (1.0 ( 0.3) ×
10-4; n ) 0.93 ( 0.24].
Figure 13. Plot of initial rate versus mole fraction of enolate (XROLi) for
the serial injection of 10 aliquots of ester 1 (10 mol % each relative to
LDA) into 0.10 M LDA in 6.1 M THF/hexane cosolvent at -78 °C. The
dashed line depicts the theoretical behavior of the initial rate in the absence
of autocatalysis, and the solid curve represents a nonlinear least-squares fit
to eq 4.
the Supporting Information) afforded the idealized33 rate law
given in eq 5:
using equimolar mixtures of LDA and substrate. Figure 1 shows
no sigmoid but does show a persistent linearity in the first two
half-lives, suggesting muted autocatalysis. We developed a
method for detecting low levels of mixed aggregation effects
using serial substrate injections as follows.
d[1]
dt
-
) k[A2S2][E2][S]0
(5)
The associative mechanism suggests mixed-tetramer-based
exchange.38 We can imagine ladder-based intermediates (eq
6),39,40 but monomeric LDA would not necessarily be formed
during the exchange, and the role this exchange plays in the
1,4-addition is minor at best (see below).41
In a routine control experiment, the IR baseline was zeroed
at the end of a pseudo-first-order kinetic run, and a second
aliquot of substrate was added. In the absence of autocatalysis,
the rate for the second aliquot should have shown a minor
decrease relative to the first aliquot because of the slight loss
in LDA titer. In the 1,4-addition, however, the second aliquot
afforded a measurably higher rate. This effect was amplified
by serially injecting aliquots containing 10 mol % ester 1 until
the LDA was completely consumed. The initial rate is plotted
versus mole fraction of enolate 5 (XROLi) in Figure 13. The serial
injections correspond to movement from left to right along the
XROLi axis.23 Figure 13 differs from a standard plot of concentra-
tion versus time in that (1) the normal upward curvature resulting
from substrate loss was factored out by adding substrate at
constant concentrations and monitoring initial rates and (2) all
aggregates were allowed to equilibrate between injections.
The maximum at XROLi ) 0.5 in Figure 13 suggests that a
1:1 LDA/enolate ratio is optimal.23,24 The solid curve in Figure
13 corresponds to a nonlinear least-squares fit to eq 4:
LiCl-Catalyzed 1,4-Additions. Very low concentrations of
LiCl (<0.5 mol % relative to LDA) cause marked accelerations
of the 1,4-addition and impart upward curvatures in plots of
ester concentration versus time (Figure 1), which suggests that
LiCl catalysis brings ester 1 into the rate law. The decays
become cleanly first-order at >0.5 mol % LiCl under pseudo-
first-order conditions. Plotting the initial rate versus LiCl
concentration revealed saturation kinetics with rates that plateau
at >0.5 mol % LiCl (Figure 16).42
∆[ester]
m
1.0
-
) k[XROLi]n[1 - XROLi
]
+ k'[1 - XROLi
]
(4)
|
∆t
Saturation often arises when a bimolecular reaction at low
concentration becomes unimolecular at higher concentrations
t)0
(see the Supporting Information). This behavior could arise
either from a key condensation involving LDA dimer 3 and
enolate dimer 5a (affording the mathematically equivalent 2:2
(38) Tetramer-based intermediates have also been implicated in LDA-
mediated ortholithiations. See: Ma, Y.; Hoepker, A. C.; Gupta, L.;
Collum, D. B. Unpublished work.
(39) A four-rung LDA/enolate ladder structure has been characterized
crystallographically. See: Williard, P. G.; Hintze, M. J. J. Am. Chem.
Soc. 1987, 109, 5539.
stoichiometry) or from mixed dimer 4 maximized at XROLi
)
0.5. There is, however, a telling paradox: Figure 13 suggests
that a 1,4-addition from equimolar mixtures of LDA and ester
1 should be markedly faster at 50% conversion than at the start.
Nonetheless, there is no sigmoidal behavior in Figure 4; only a
gentle straightening of the decay appears. (Perfect linearity arises
when the autocatalysis precisely offsets the consumption of
LDA.11)
(40) (a) Gregory, K.; Schleyer, P. v. R.; Snaith, R. AdV. Inorg. Chem. 1991,
37, 47. (b) Mulvey, R. E. Chem. Soc. ReV. 1991, 20, 167. (c) Beswick,
M. A.; Wright, D. S. In ComprehensiVe Organometallic Chemistry
II; Abels, E. W., Stone, F. G. A., Wilkinson, G., Eds.; Pergamon Press:
New York, 1995; Vol. 1, Chapter 1. (d) Mulvey, R. E. Chem. Soc.
ReV. 1998, 27, 339. (e) Rutherford, J. L.; Collum, D. B. J. Am. Chem.
Soc. 1999, 121, 10198.
Using 6Li NMR spectroscopy, we monitored the reaction of
LDA dimer 3 and enolate dimer 5a to give mixed dimer 4. The
reaction using 0.05 M each of 3 and 5a revealed a half-life of
3000 s. First-order dependencies in 3 and 5a (Figures 14 and
15) in conjunction with a zeroth-order THF dependence (see
(41) (a) Pate´, F.; Ge´rard, H.; Oulyadi, H.; de la Lande, A.; Harrison-
Marchand, A.; Parisel, O.; Maddaluno, J. Chem. Commun. 2009, 319.
(b) Arvidsson, P. I.; Ahlberg, P.; Hilmersson, G. Chem.sEur. J. 1999,
5, 1348.
(42) Saturation was also apparent when the observed rate constants from
fits to the exponential decays were plotted.
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15615

A R T I C L E S
Ma et al.
Figure 15. Plot of initial rate vs the concentration of enolate 5 for the
condensation of LDA dimer 3 (0.10 M) with enolate dimer 5a in THF (6.10
M) at -78 °C. The curve depicts an unweighted least-squares fit to y )
k[enolate]n [k ) (7.4 ( 0.3) × 10-5; n ) 1.10 ( 0.14].
Figure 17. Plot of kobsd vs [LDA] in THF (6.10 M) for the 1,4-addition of
ester 1 (0.004 M) in the presence of 1 mol % LiCl at -78 °C. The curve
depicts an unweighted least-squares fit to y ) k[LDA]n [k ) (6.01 ( 0.04)
× 10-2; n ) 0.57 ( 0.08]. The asterisk denotes a point that departed markedly
from pseudo-first-order conditions and was not included in the fit.
Figure 16. Plot of initial rate vs [LiCl] in THF (6.1 M) for the 1,4-addition
of ester 1 (0.004 M) with LDA (0.10 M) at -78 °C. The 0.6 mol % notation
is relative to the LDA concentration.
Figure 18. Plot of kobsd vs [THF] in hexane cosolvent for the 1,4-addition
of ester 1 (0.004 M) with LDA (0.10 M) in the presence of 1 mol % LiCl
at -78 °C. The curve depicts an unweighted least-squares fit to y ) k[THF]
+ k′ [k ) (5.0 ( 0.01) × 10-4; k′ ) (1.2 ( 0.1) × 10-2].
because an observable complex is formed.43 Enzymology offers
a plethora of examples under the rubric of Michaelis-Menten
kinetics.44 A Michaelis-Menten-like saturation behavior, how-
ever, would require g100 mol % LiCl, not a mere 0.5 mol %,
to form observable LDA-LiCl mixed aggregates 6 and 7 as
the dominant species.45
the idealized33 rate law given by eq 8, which implicates the
monosolvated-monomer-based transition structure [AS(ester)]q
formed according to eq 9:34
1/2
Saturation kinetics can also be caused by a change in the
rate-limiting step.43 Indeed, our rate studies are consistent with
a scenario in which LiCl catalyzes a dimer-monomer exchange
(eq 7):
k1
d[ester]
-
)
k2[ester][S]0[A2S2]1/2
(8)
(9)
(
)
dt
k-1
k2
k1[LiClT]
AS + ester
9
8 [AS(ester)]q
1/2A2S2
AS
(7)
k-1[LiClT]
where ester ) 1. Importantly, although LiCl catalyzes the
deaggregation, it has no role in the product-determining 1,4-
addition step (see eq 10 below).
where LiClT ) lithium chloride titer. The competition studies
described below confirmed this assertion. The mechanism at
full saturation (1.0 mol % LiCl) was gleaned from plots showing
a half-order LDA dependence (Figure 17) and zeroth-order THF
dependence (Figure 18). The equilibrium approximation affords
We can now complete the mathematical analysis of the
saturation curve in Figure 16. The transition from a rate-limiting
deaggregation of dimer 3 in the absence of LiCl to a fully
established pre-equilibrium at high LiClT concentration precludes
the equilibrium approximation. The time dependencies of the
concentrations of ester 1 and LDA dimer and monomer are
described by eqs 10-12, respectively:
(43) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms, 2nd
ed.; McGraw-Hill: New York, 1995.
(44) Frey, P. A.; Hegeman, A. D. Enzymatic Reaction Mechanisms; Oxford
University Press: New York, 2007; Chapter 2.
(45) In fact, addition of 100 mol % LiCl causes a 3-fold inhibition relative
to native LDA containing 1.0 mol % LiCl. Davies noted inhibition
by LiCl on the 1,4-additions of chiral lithium amides to unsaturated
esters (see: Davies, S. G.; Hermann, G. J.; Sweet, M. J.; Smith, A. D.
Chem. Commun. 2004, 1128). LiCl had no measurable effect on the
stereoselectivity.
d[ester]
-
) -k2[ester][AS]
(10)
dt
9
15616 J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
d[A2S2]
With the monosolvated-monomer-based stoichiometry estab-
lished for the addition under full LiCl catalysis, we turned to
DFT computations. Transition structure 10 is plausible (MP2-
corrected ∆Gq ) 16.3 kcal/mol at -78 °C), although the energy
is large relative to the calculated barrier for the rate-limiting
deaggregation (Scheme 1).
-
) k1[LiClT][A2S2] - k-1[LiClT][AS]2 (11)
dt
) -2k1[LiClT][A2S2] + 2k-1[LiClT][AS]2 +
k2[ester][AS] ≈ 0 (12)
d[AS]
-
dt
Solving for the concentration of monomer AS in eq 12 using
the quadratic equation and substituting the result into eq 10
affords the rate law in eq 13:
k2[ester]
d[ester]
-
)
×
dt
4k-1[LiClT]
2
k [ester]2 + 16k k [A S ][LiCl ]2 - k [ester] + c (13)
(
√
)
2
1
-1
2
2
T
2
where c corresponds to the low basal rate of uncatalyzed
deaggregation. The quantity -d[ester]/dt in eq 13 is equal to
-(∆[ester]/∆t)t)0 obtained by initial rates. The curve in Figure
16 corresponds to a fit to eq 13. Although eq 13 lacks the
intuitive appeal of simple saturation functions, the rate reduces
to c as the LiClT concentration approaches zero and to eq 8 at
high LiClT concentration.46
Since deaggregation is rate-limiting in the absence of LiCl
(eq 3), it is logical that accelerating the deaggregation through
LiCl catalysis would accelerate the reaction. Why LiCl changes
the rate-limiting step is less obvious. Inspection of the mech-
anism in eqs 7 and 8 shows that elevated LiCl concentrations
(k-1[LiClT] . k2[ester]) cause the reaggregation to become
competitive with the 1,4-addition, eventually affording a fully
established pre-equilibrium. Thus, it is formally the catalysis
of the reaggregation of LDA monomer by LiCl that causes the
1,4-addition to become rate-limiting. Such reversibility is also
required for a fractional-order dependence on LDA concentration
to be observed.
The mechanism by which LiCl catalyzes the deaggregation
of LDA is elusive, but a few comments are warranted. In
LDA-LiCl mixtures containing low LiCl concentrations, LiCl
exists exclusively as mixed aggregates 6 and 7 (1:8) to the
exclusion of appreciable free LiCl.27,28 Thus, an apparent first-
order dependence on the total LiCl concentration at the lowest
LiCl concentration47 is tantamount to a first-order dependence
on the mixed aggregates.
Competition Studies. We delineated three pathways for 1,4-
addition that may share a common reactive intermediate: (1)
uncatalyzed 1,4-addition with the key post-rate-limiting addition
opaque to standard kinetic analysis; (2) autocatalyzed (enolate-
mediated) deaggregation with the key 1,4-addition remaining
post-rate-limiting; and (3) LiCl-catalyzed deaggregation with
rate-limiting 1,4-addition (eqs 7 and 8), which was shown to
proceed via LDA monomer 11. (We have chosen to draw the
fleeting monomer 11 as the computationally most stable
trisolvate.48) Standard protocols for examining post-rate-limiting
steps to probe for common (shared) intermediates usually entail
comparing inter- and intramolecular isotope effects.49 Showing
that isotopic substitution affects the selectivity at a key branch
point, but not the reaction rate, confirms that the isotopically
sensitive step is post-rate-limiting. Since the 1,4-addition is
poorly suited for isotopic labeling, we turned to a related
approach using two structurally distinct substrates.
We established the reactivity of monomer 11 toward ester 1
and its n-alkyl analogue 1250 under conditions of fully saturated
LiCl catalysis (eq 14):
(46) Equation 13 would appear to become undefined at [LiClT] ) 0, but
this turns out not to be the case. Qualitatively, the [LiClT]2 term within
the argument of the square root approaches zero at low values of
[LiClT] faster than the [LiClT] term in the denominator. Alternatively,
let a ) k2[ester], b ) 16k1k-1[A2S2]0, d ) 4k-1, and x ) [LiClT]2. Eq
13 can then be rewritten as
d[ester]
a
dx0.5
-
)
[(a2 + bx)0.5 - a] + c
dt
0.5
a
b
a2
)
a 1 +
x
- a + c
dx0.5
(
)
[
]
Whether in competition or in separate vessels, 12 displayed
7-fold greater reactivity. (We used gas chromatography of
serially quenched separate vessels to monitor mixtures of esters
1 and 12 for the competition experiments.) The 7:1 relative
reactivity provides an important benchmark for monomer 11.
Applying the Taylor expansion to [1 + (b/a2)x]0.5 for x , 1 gives
d[ester]
a
dx0.5
b
bx
-
)
a 1 +
x - a + c )
+ c
2a2
2dx0.5
(
)
[
]
dt
Since x approaches zero faster than x0.5, it follows that
bx
(48) Viciu, M.; Gupta, L.; Collum, D. B. J. Am. Chem. Soc. 2010, 132,
6361.
lim
+ c ) c
0.5
(
)
xf0
2dx
(49) (a) Carpenter, B. K. Determination of Organic Reaction Mechanisms;
Wiley: New York, 1984. (b) Whisler, M. C.; MacNeil, S.; Snieckus,
V.; Beak, P. Angew. Chem., Int. Ed. 2004, 43, 2206.
(50) Davies, S. G.; Mulvaney, A. W.; Russell, A. J.; Smith, A. D.
Tetrahedron: Asymmetry 2007, 18, 1554.
.
(47) Although the saturation behavior is not sigmoidal, excluding a higher-
order dependence on LiCl, the data do not exclude a fractional LiCl
dependence.
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15617

A R T I C L E S
Ma et al.
that is poor compared with LiCl. In contrast, treating an
analogous equimolar mixture of LDA and mixed dimer 4
with an equimolar mixture of esters 1 and 12 showed a
relative reactivity of 7:1. This confirmed that the back-
reaction in eq 15 (the reaggregation of LDA) is slow relative
to the 1,4-addition (eq 16) and showed the commonality of
intermediate in the uncatalyzed and LiCl-catalyzed 1,4-
additions.
Figure 19. Plots of ester concentration vs time for the uncatalyzed 1,4-
addition of LDA (0.10 M) to a mixture of esters 1 and 12 (0.005 M each)
in THF (6.10 M) at -78 °C: (9) ester 1; (2) ester 12. Results were analyzed
by GC relative to a decane internal standard.
The uncatalyzed reaction of ester 1 with LDA involves a post-
rate-limiting 1,4-addition: is the key intermediate in that case
also monomer 11? Ester 1 and n-alkyl analogue 12 underwent
1,4-additions at indistinguishable rates despite differing steric
demands, as expected for a rate-limiting deaggregation and post-
rate-limiting 1,4-addition. In contrast, reacting an equimolar
mixture of 1 and 12 with 2.0 equiv of LDA revealed a 7-fold
greater reactivity of 12 relative to 1 (eq 15), as expected if
monomer 11 is the intermediate. We also observed that once
12 was fully consumed, ester 1 reacted at a rate comparable to
that of 12 (Figure 19). Such biphasic kinetics would be expected
for post-rate-limiting 1,4-additions.51
Mechanistic Hypothesis and Numerical Integrations.52,53 The
rate and mechanistic studies were pieced together to form the
mechanistic hypothesis shown in Scheme 2 and described by
the affiliated differential equations given in eqs 17-22. As
mentioned previously, in these equations A stands for an LDA
subunit and E stands for an enolate subunit. We have taken
some liberties with the depiction of the model in Scheme 2 to
optimize the visual presentation. Although the role of the solvent
has been elucidated for a number of steps, it is not germane to
the numerical fitting and has been omitted for clarity. We have
depicted the critical autocatalytic step by affiliating k3 and k-3
with the fleeting mixed trimer A2E; this step is described
numerically in the differential equations by means of the
equilibrium A2 + E a A + AE. The equilibria in Scheme 2
are unbalanced to minimize clutter. However, the differential
equations are all fully balanced to provide a valid mathematical
description.
Scheme 2
We suspected that the weak autocatalysis arises because
ester enolate 5 is an inferior deaggregation catalyst in
comparison with LiCl. A reaction was carried out to 50%
conversion by adding 0.5 equiv of ester 1sconditions to
establish lithium enolate-induced accelerationsand subse-
quently treating the mixture with either 1 or 12 (separate
reactions); the accelerations were indistinguishable for the
two substrates. These results indicate that the formation of
monomer 11 is still rate-limiting, as expected for a catalyst
d[ester]
) k2[A][ester]
(17)
(18)
dt
d[A2]
) -k1[A2] + k-1[A]2 - k3[A2][E] + k-3[A][AE]
dt
d[A]
dt
) 2k1[A2] - 2k-1[A]2 - k2[A][ester] + k3[A2][E] -
k-3[A][AE] - k4[A][E] + k-4[AE] (19)
(51) The curves in Figure 16 correspond to numerical integration of the
following highly simplified model:
1/2A2 a A
d[AE]
dt
) k3[A2][E] - k-3[A][AE] + k4[A][E] - k-4[AE] (20)
A + 1 f 5
A + 12 f 13
9
15618 J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
numerical simulations failed to reproduce the curvatures. How
the simulations failed was key, in that the simulations kept
suggesting a source of AE independent of the simple reaggre-
gation of A and E. Of course, there was considerable experi-
mental evidence of autocatalysis, which could only arise by
accelerating the rate-limiting deaggregation of LDA dimer A2.
(4) One might ask why the autocatalytic step is depicted as
proceeding via A2E rather than through a dimer-dimer con-
densation via A2E2 that we studied kinetically. Again, the simple
answer is that no amount of tinkering could force the curves to
fit using an A2E2-based pathway. One could justify a provision
for A2E2 in addition to A2E on the basis of the kinetics of mixed
aggregation described in eqs 5 and 6, but the improvement in
the fit was statistically insignificant.
d[E]
dt
) k2[A][ester] - k3[A2][E] + k-3[A][AE] -
k4[A][E] + k-4[AE] - 2k5[E]2 + 2k-5[E2] (21)
d[E2]
) k5[E]2 - k-5[E2]
(22)
dt
It is nearly impossible to reproduce in prose how the model
came into being, but we can describe the general strategy as
well as the most critical constraints. We hasten to add at the
outset that despite aphorisms proclaiming that anything can be
fit given enough differential equations, our experience with
complex systems containing a large number of restrictions and
observables (see Figures 5-8) is quite the opposite. The model
in Scheme 2 is the simplest model that fits the data, and many
others failed to do so quite decisively.
The components of the model in Scheme 2 are well-founded
by the rate and mechanistic studies. As can be seen from Figures
5-8, the best-fit numerical integrations of eqs 17-22 are
exceptional.
First, a few comments about general tactics are warranted.
The rate data placed significant constraints on the model. In
other instances, seemingly reasonable hypotheses were excluded
only through numerical simulations showing that key curvatures
were not reproduced. Once the data in Figures 5-8 were
qualitatively reproduced through numerical simulations, best-
fit numerical integrations of eqs 17-22 afforded the functions
displayed.
The key constraints imparted by the curvatures in Figures
5-8 include the following: (1) the linear decay of ester; (2) the
two obvious discontinuities (most easily seen in Figure 8),
namely, the maximum in enolate dimer (E2) concentration and
the marked change in the rate of formation of the mixed dimer
(AE), that coincide with the consumption of ester; (3) an
overshoot in the concentration of E2 relative to the equilibrium
population; and (4) the coincident formation of AE and E2 at
the outset of the reaction (most easily observed in Figure 5),
indicating that AE is not a requisite precursor to E2 (or vice
versa).54
Discussion
It is becoming evident that reactions of LDA in THF at -78
°C are mechanistically complex even by the standards of
organolithium chemistry.11,12 Nature could not have chosen a
more inauspicious opportunitysa more synthetically relevant
reagent under the most commonly used conditionssto insert
confusion. The complexity stems from aggregate exchanges that
occur at rates comparable to those of the reaction with
substrate.10 The result is that aggregation events can become
rate-limiting, and LDA-containing aggregates are not at full
equilibrium on the time scales of their reactions with substrates.
The first detailed investigations of such phenomena focused on
ortholithiations of fluorinated aryl carbamates.11 Almost per-
fectly linear decays normally attributed to zeroth-order ester
dependencies were traced to the superposition of a first-order
ester dependence and autocatalysis. In the case of the 1,4-
addition, seemingly analogous linear decays were traced to the
superposition of a zeroth-order ester dependence and much less
pronounced autocatalysis. A summary of the mechanism
customized for mathematical treatment is provided in Scheme
2. The more structurally illuminating version with the full
complement of intermediates and transition structures is sum-
marized in Scheme 3. A compartmentalized summary follows.
Rate-Limiting Deaggregation. Monitoring the initial rates of
the uncatalyzed 1,4-addition to ester 1 revealed a true zeroth-
order ester dependence: deaggregation of LDA is rate-limiting,
and the 1,4-addition step is post-rate-limiting. The trisolvated-
dimer-based deaggregation is either a partial deaggregation to
form the open dimer35 via transition structure 8 or a complete
deaggregation to form the monomer via transition structure 9.
Computational studies indicate that 9 has the higher barrier.
Even if the rate-limiting step involves formation of the open
dimer via 8, however, standard rate studies do not peer past the
rate-limiting step to distinguish between the monomer-based
and dimer-based reactions with ester 1. A combination of rate
studies in the presence of LiCl and competition studies (both
discussed below) support monomeric intermediate 11 and
monosolvated-monomer-based transition structure 10.
The model was assembled as follows:
(1) Rate-limiting deaggregation of A2 gives monomer A,
which subsequently reacts in a post-rate-limiting step with ester
to give enolate. This enolate necessarily forms as a monomer
(E). Thus, the A2 f A f E sequence representing the top half
of Scheme 2 was fully established by traditional kinetic methods.
(2) The fate of enolate monomer E was a central issue. Self-
condensation of E is one logical source of E2 (the other logical
source would be direct reaction of AE with ester). The
condensation of A and E is an obvious source of the mixed
dimer AE. A critical insight was that the bifurcation of E to
form E2 and AE allows for their concurrent formation (with no
induction period in either case).
(3) Two factors elicited the inclusion of the pathways
involving the condensation of E with A2 (via A2E) to give the
mixed dimer AE and monomer A. (To reiterate, this was
modeled as a net conversion and does not connote a single-
barrier pathway.) The most important factor was that the
(52) For an explanation of Levenberg-Marquardt nonlinear least-squares
optimization, see: Press, W. H.; Flannery, B. P.; Teukolsky, S. A.;
Vetterling, V. T. Numerical Recipes in C; Cambridge University Press:
London, 1988; Chapter 14.4.
Autocatalysis. The rate-limiting deaggregation of dimer 3 that
is dominant at the onset of 1,4-addition is overlaid by contribu-
tions from muted autocatalysis as the reaction progresses. It is
very tempting to focus on mixed dimer 4 for an explanation,
but that would be wrong. Neither the elevated concentration
nor higher reactivity of mixed dimer 4 causes the autocatalysis.
(53) Brown, P. N.; Byrne, G. D.; Hindmarsh, A. C. J. Sci. Stat. Comput.
1989, 10, 1038.
(54) Given a reaction coordinate SM f I f P in which I builds to
appreciable concentrations, the rate of formation of P will show an
induction period (see ref 43).
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15619

A R T I C L E S
Ma et al.
Scheme 3
Mixed dimer 4 could react with ester 1 instantaneously, and
this still would not constitute autocatalysis. An autocatalyst must
catalyze the rate-limiting deaggregation of LDA. To understand
the autocatalysis, it is instructive to focus on the structurally
simplified model in Scheme 2.
Autocatalysis stems from acceleration of the rate-limiting
deaggregation of LDA dimer, denoted as A2. Notably, enolate
homodimer E2 is an ineffectual catalyst: it reacts with LDA
dimer Very slowly. The autocatalysis was traced to the reaction
of enolate monomer E. When LDA monomer A reacts with ester
to form enolate monomer E, E can dimerize to form E2 or react
with an LDA monomer A to form the mixed dimer AE.
Occasionally, however, E reacts with LDA dimer A2 to form
AE and monomer A. This is autocatalysis.
The data, however, seem paradoxical. The plot of the reaction
rate versus time when equimolar LDA and ester were used
(Figure 4) shows some straightening that hints at autocatalysis,
but a marked sigmoidal decay characteristic of virulent auto-
catalysis is notably absent. In short, the reaction is not faster at
50% conversion. In contrast, however, incremental additions
of ester 1 to LDA (Figure 13) showed a marked increase in
rate with each increment, reaching a net 4-fold higher rate at
50% consumption of LDA and 50% formation of enolate. An
analogous 4-fold autocatalysis certainly would have elicited a
quite distinct sigmoidal curvature in Figure 4.
How do we reconcile these two contrasting views? The key
to understanding Figure 13 is to note that under normal reaction
conditions, the aggregates are not at full equilibrium, so the
LDA-enolate mixed dimer AE remains well below its equi-
librium concentration. In contrast, the incremental additions in
Figure 13 allow full equilibration of the aggregates between
increments. As a consequence, AE attains substantial equilibrium
concentrations. When the subsequent increment of ester is added,
the key LDA monomer is generated either from rate-limiting
deaggregation of A2 or by a more facile (and only partially rate-
limiting) deaggregation of mixed dimer AE. The rate maximum
in Figure 13 corresponds to the maximum concentration of the
kinetically labile AE mixed dimer. Thus, an experiment initially
intended to explicitly probe autocatalysis uncovered an alto-
gether different mixed aggregation effect. We will return to these
distinctions below.
1.0 ppm). At the risk of stating the obvious, we note that this is
remarkably efficient catalysis.13 Readers might be unsurprised
that this catalysis plagued the rate studies until we adapted
protocols for preparing rigorously LiCl-free LDA from lithium
metal.20 (Ironically, the modified synthesis is also more
convenient than our standard method.)
Lithium chloride accelerates the 1,4-addition by catalyzing
the deaggregation of LDA, as summarized in eqs 7 and 8.
Saturation behavior (Figure 16) with an onset of saturation at
>0.5 mol % LiCl derives from a LiCl-catalyzed exchange of
LDA dimers and monomers, resulting in a change from rate-
limiting deaggregation to rate-limiting 1,4-addition. How LiCl
catalyzes LDA deaggregation is still unclear and the subject of
ongoing investigations. Nonetheless, the rate studies revealed
a monosolvated monomer-based pathway for the addition, and
the computational studies filled in the intimate details of
transition structure 10.
Competition Studies: Commonality of Intermediate. Compet-
ing esters 1 and 12 having different steric demands allowed us
to probe the post-rate-limiting reactivity (eqs 14-16). These
studies are tactically analogous to comparisons of inter- and
intramolecular isotope effects.50
The substrate-dependent rates under LiCl catalysis showed
that the 1,4-addition is rate-limiting. Ester 12 is 7 times more
reactive than ester 1 toward monomer 11 (eq 14) both in separate
reactions and in competition. Most importantly, this 7:1 prefer-
ence serves as a benchmark for the monomer-based addition.
In the 1,4-addition under uncatalyzed conditions, where partial
or total deaggregation is rate-limiting, the rates of 1,4-addition
were identical for 1 and 12 when measured independently,
confirming a post-rate-limiting addition. Using mixtures of 1
and 12 in competition, however, produced the same 7-fold
higher reactivity of 12 (eq 15) characteristic of trapping of
monomer 11.
A competition was carried out using equimolar mixtures of
LDA and lithium enolate 5 to examine the influence of mixed
dimer 4 (eq 16). When compared independently, esters 1 and
12 showed identical reactivities, indicating that the deaggrega-
tions of 3 and 4 remain rate-limiting. In contrast, competition
of 1 and 12 revealed the 7-fold greater reactivity of 12
characteristic of reaction with monomer 11.
LiCl Catalysis. The 1,4-addition of LDA to ester 1 is
measurably accelerated by as little as 0.001 mol % LiCl (i.e.,
Do the 7:1 selectivities for the uncatalyzed, LiCl-catalyzed,
and enolate-mediated additions rigorously show the commonal-
9
15620 J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
ity of intermediate 11 and transition structure 10? In a word,
no. The selectivities do, however, make for a compelling
circumstantial case.
Mixed Aggregation Effects: Four Variants. Effects of lithium
salts on organolithium reactivitysso-called mixed aggregation
effectsswere first documented decades ago.14 Examples of
mixed aggregation effects on rates and selectivities, whether
LiX salts are added explicitly or formed in situ, are now legion.13
Mechanistically well-defined examples, however, are quite rare
by comparison.15 We take this opportunity to discuss four
distinct classes of mixed aggregation effects using LDA
emblematically.
Case 1. Probably the most often cited and certainly the most
intuitively simple salt effect derives from the direct reaction of
mixed aggregates (such as 4, 6, and 7) with substrate (eq 23).
Because the steric and electronic properties of LDA-LiX mixed
aggregates are markedly different than those of homoaggregated
LDA dimer 3 and the LiX salt is assumed to be strategically
located in the rate- and product-determining transition structures,
it is easy to understand how LiX could markedly influence both
the rate and selectivity. We have documented the direct reaction
of LDA mixed dimers.15 Although the mixed aggregates could
be either fleetingly stable or observable quantitatively, inhibition
by observable mixed aggregates is prevalent.15,55 The critical
requirement common to all examples in case 1, whether
inhibiting or accelerating, is that the LiX salt remain intimately
involved in the rate- or product-determining transition structure.
Case 3. The mixed aggregation effects described in this paper
involve LiX-catalyzed deaggregation. We must point out that
there is jargon in the literature that loosely refers to LDA-LiX
mixed aggregates as deaggregated because the mixed aggregate
contains only one LDA subunit. We find this usage to be
unconstructive. In the case described herein, however, the role
of LiX salts (LiCl and, to a much lesser extent, lithium enolate)
is to catalyze the formation of true LDA monomer (eq 26). To
the best of our knowledge, this catalysis is undocumented. It
could be observed only for reactions in which deaggregation is
either rate-limiting or precluded altogether by a high barrier
(forcing the reaction to occur with the aggregated form). No
catalysis by LiCl will be observed if all of the aggregation states
fully equilibrate on the time scale of the reaction without added
catalyst. Of course, to the extent that a rate-limiting deaggre-
gation is accelerated, the overall reaction will be accelerated
also. If that catalysis affords the same intermediate as the
uncatalyzed deaggregation (monomer 11), only faster, then the
accelerations and even changes in the rate-limiting step will
not be accompanied by changes in regio- or stereoselectivity.
However, if the preferred pathway for the uncatalyzed reaction
is dimer-based because of a prohibitively high barrier to
deaggregation and LiX catalyzes monomer formation, the
acceleration could be accompanied by a change in selectivity.
We suspect that regioselective ortholithiations may be a fruitful
place to look for such phenomena.
Case 2. Rate reductions are not the only consequence of
inhibition. Imagine that a mixed aggregate forms quantitatively
and shows no reactivity toward substrate (eq 24). The only
available avenue of reaction is via free LDA. To the extent that
the steady-state concentration of LDA is decreased to very low
levels, representing a dilution of sorts, monomer-based pathways
will be promoted relative to dimer-based pathways.56 The
influence of such a mass-action effect on the efficacies of the
monomer- and dimer-based pathways is illustrated in eq 25.15
Indeed, an LDA-dimer-based ester enolization was diverted by
an intervening LDA-lithium enolate mixed dimer through both
mixed-dimer-based and monomer-based pathways. To the extent
that LiX can divert a dimer-based pathway to a monomer-based
pathway, an LiX-dependent change in selectivity could arise
without intimate association of LiX with the product-determining
transition structure.
Case 4. In cases 1 and 2, we have implicitly assumed that
the aggregate exchanges are fast relative to reactions with
substrate. Under this criterion, mixed aggregation must neces-
sarily inhibit a reaction according to the principle of detailed
balance56 unless the mixed aggregate can react with the substrate
directly and rapidly. Case 4 addresses the consequences of mixed
aggregation when aggregate exchanges are not at equilibrium
during the course of the reaction. If, for example, deaggregations
of LDA dimer 3 and mixed dimer 4 are rate-limiting (i.e., if
the reaction with LDA monomer is at least competitive with
reaggregation, as the model in Scheme 2 suggests), the result
would be a scenario in which facile deaggregation of mixed
dimer 4 increases the rate that monomeric LDA is released and
subsequently trapped. Formally, this is not autocatalysis because
autocatalysis requires a provision for accelerating the deaggre-
gation of LDA dimer 3. Solutions containing considerable
concentrations of labile mixed dimer 4, however, would show
a higher reactivity than analogous solutions containing only
LDA dimer 3. This scenario accounts for 1,4-additions in the
presence of enolate that are more rapid than would be predicted
on the basis of the low levels of autocatalysis.
(55) (a) Sun, X.; Collum, D. B. J. Am. Chem. Soc. 2000, 122, 2459. (b)
See the references cited in ref 6.
(56) The principle of detailed balance asserts that individual equilibria
within an ensemble of equilibria are maintained.57b-d It is particularly
useful in understanding the complex equilibria observed in organo-
lithium chemistry. See: (a) Alberty, R. A. J. Chem. Educ. 2004, 81,
1206–1209. (b) Casado, J.; Lopez-Quintela, M. A.; Lorenzo-Barral,
F. M. J. Chem. Educ. 1986, 63, 450. (c) Hammes, G. G. Principles of
Chemical Kinetics; Academic Press: New York, 1978; pp 14-15.
Conclusion
A number of consequences of the work described herein are
clear. Because traces of LiCl may contaminate LDA, source
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15621

A R T I C L E S
Ma et al.
and batch dependencies could become acute. Synthetic chemists
carrying out LDA-mediated reactions in THF at -78 °C might
notice enormous differences between commercial LDA (which
tends to be LiCl-free) and LDA generated in situ from n-BuLi
(which contains ample LiCl to catalyze exchanges). Indeed, this
is the case for the 1,4-addition in eq 1. Adding traces of LiCl
(in the form of Et3NHCl) to commercial LDA equalizes the
two protocols. Moreover, marked catalysis by traces of LiCl
and inhibitions by molar excesses of LiCl suggest that the
quantity of LiCl is important. We are reminded of LDA-
mediated 3-pentanone enolizations, in which the E/Z selectivities
are maximized using fractional-equivalent amounts of LiCl.28
Could a composite of mixed aggregation effects be operative?
We have long believed that deconvoluting the roles of LiCl in
E-selective ketone enolizations would remain outside our grasp,
but we are not so pessimistic now. We have also reported LiCl-
accelerated ortholithiations in which traces of LiCl dramatically
accelerated the rates but had no influence on regiocontrol
because the regioisomers were fully equilibrated.57 Some LDA-
mediated ortholithiations are not at equilibrium,58 however, and
may display regioselectivities that are sensitive to traces of LiCl.
mines conventional mechanistic views, but it would be unfor-
tunate if speculation (even unsubstantiated speculation) becomes
stifled.
Experimental Section
Reagents and Solvents. THF and hexanes were distilled from
blue or purple solutions containing sodium benzophenone ketyl.
The hexanes contained 1% tetraglyme to dissolve the ketyl. Esters
1 and 12 were prepared via literature protocols.22,50 Et3NHCl was
recrystallized from THF/2-propanol.
Preparation and Purification of LDA. Modifications of litera-
ture procedures20 were used to prepare LDA as a LiCl-free and
ligand-free solid as follows. A 250 mL Schlenk flask with an
attached fine-mesh glass frit and a 250 mL receiving flask was
charged with lithium shavings (1.11 g, 160 mmol), diisopropylamine
(16.5 g, 160 mmol), and 80 mL of Me2NEt. The flask was
submerged in a bath at 25 °C, and isoprene (5.44 g, 80 mmol) in
30 mL of dry Me2NEt was added over 1.0 h via syringe pump.
The solution was stirred for 1.0 h at 25 °C until the lithium
dissolved. (The reaction became exothermic when isoprene was
added too quickly, affording highly undesirable dark-yellow or
purple solutions if the temperature exceeded 35 °C.) The nearly
homogeneous reaction mixture was filtered through a fine-mesh
glass frit, and the solvent was removed under vacuum (∼6 h) to
afford LDA as a white solid (16.0 g, 90% yield). With the aid of
a glovebox, the LDA (8.0 g) was transferred to a 250 mL round-
bottom flask fitted with a fine-mesh glass frit and a 250 mL pear-
shaped receiving flask fitted with a side arm/stopcock. The apparatus
was attached to a vacuum line, and ∼200 mL of hexanes was
vacuum-transferred into the flask containing the solid LDA. The
slurry was stirred at 63 °C for ∼2 h to afford a pale-yellow solution
of LDA that was subsequently filtered to remove any undissolved
particles. The filtrate was transferred by cannula to a 250 mL round-
bottom flask fitted with a coarse-mesh glass frit and a 250 mL
receiving flask. The solution was cooled to -78 °C by incrementally
raising a dry ice/acetone bath to precipitate the LDA and held at
-78 °C overnight. The mother liquor was carefully removed by
filtration, and the solid was washed three times with 10 mL of
hexanes and then dried in vacuo for 6 h. The assembly was moved
to the glovebox, where the LDA was collected as a white solid in
75-85% yield. The isolated material was spectroscopically indis-
tinguishable from samples prepared previously.18
Synthesis of 2. Unsaturated ester 1 (0.63 g, 3.0 mmol) in 3.0
mL of THF was added to LDA (0.64 g, 6.0 mmol) in 15 mL of
THF at -78 °C. The solution was stirred for 30 min and then
warmed to room temperature with stirring for 1.0 h. The reaction
was quenched with 10 mL of H2O, and the mixture was extracted
with diethyl ether (3 × 10 mL). The extracts were dried using
Na2SO4, and the solvent was removed in vacuo. The residue was
redissolved in CH2Cl2 (5 mL) and extracted with 4.0 M HCl (3 ×
3 mL). The aqueous layer was neutralized with 10% NaOH and
extracted with diethyl ether (3 × 5 mL). The combined organic
layers were dried with MgSO4, and the solvent was removed. Flash
chromatography (30% ethyl acetate/hexane) afforded amino ester
2 (78-82% yield) having the spectral properties described previ-
ously.5
It is instructive to look forward. We have now reported two
extensive studies of LDA-mediated reactions in which inordinate
complexity rears its ugly head under conditions favored by
synthetic chemists: LDA/THF/-78 °C. This is no bizarre
coincidence: under these conditions, aggregation events occur
with half-lives on the order of minutes. Any LDA/THF-mediated
reaction that proceeds on a similar time scale at -78 °C will
be subjected to potentially rate-limiting deaggregation and
display a hypersensitivity to added lithium salts. Subtle changes
in substrate reactivity and product (autocatalyst) structure could
cause marked shifts in the relative efficacies of the competing
steps and consequent baffling changes in rate behavior. Ongoing
studies suggest that there may even be several rate-limiting LDA
deaggregations (depending on the choice of substrate) and
several variants of autocatalysis. We are becoming increasingly
certain that manyspossibly allsLDA/THF-mediated reactions
carried out at -78 °C are influenced by the rates at which
aggregates exchange.
We close with a caveat, but not one readers may expect. In
the earliest studies of organolithium chemistry, when the role
of mixed aggregates was beginning to surface, salt effects were
often couched in a mechanistic context and language that were
inadequate. Chastened by that experience and the daunting
mechanistic and structural complexity, specialists often warn
nonspecialists against invoking overly simplistic interpretations
of salt effects on organolithium rates and selectivities. We admit
some schadenfreude when uncovering complexity that under-
IR Spectroscopic Analyses. IR spectra were recorded using an
in situ IR spectrometer fitted with a 30-bounce silicon-tipped probe.
The spectra were acquired in 16 scans at a gain of 1 and a resolution
of 4 cm-1, and the absorbance at 1715 cm-1 was monitored over
the course of the reaction. For the most rapid reactions, IR spectra
were recorded every 3 s.
A representative reaction was carried out as follows: The IR
probe was inserted through a nylon adapter and O-ring seal into
an oven-dried, cylindrical flask fitted with a magnetic stir bar and
a T-joint. The T-joint was capped by a septum for injections and
a nitrogen line. After the flask was evacuated under full vacuum,
heated, and flushed with nitrogen, it was charged with LDA (107
mg, 1.00 mmol) in THF and cooled in a dry ice/acetone bath
(57) (a) Cottet, F.; Schlosser, M. Eur. J. Org. Chem. 2004, 3793. (b)
Trecourt, F.; Mallet, M.; Marsais, F.; Que´guiner, G. J. Org. Chem.
1988, 53, 1367. (c) Comins, D. L.; LaMunyon, D. H. Tetrahedron
Lett. 1988, 29, 773. (d) Eaton, P. E.; Cunkle, G. T.; Marchioro, G.;
Martin, R. M. J. Am. Chem. Soc. 1987, 109, 948. (e) Bridges., A. J.;
Patt, W. C.; Stickney, T. M. J. Org. Chem. 1990, 55, 773. (f) Tre´court,
F.; Marsais, F.; Gu¨ngo¨r, T.; Que´guiner, G. J. Chem. Soc., Perkin Trans.
1 1990, 2409. (g) Gros, P. C.; Fort, Y. Eur. J. Org. Chem. 2009, 4199.
(h) Cottet, F.; Marull, M.; Lefebvre, O.; Schlosser, M. Eur. J. Org.
Chem. 2003, 1559. (i) Gu¨ngo¨r, T.; Marsais, F.; Queguiner, G. J.
Organomet. Chem. 1981, 215, 139.
(58) (a) Schlosser, M. Angew. Chem., Int. Ed. 2005, 44, 376. (b) Schlosser,
M.; Rausis, T. Eur. J. Org. Chem. 2004, 1018.
9
15622 J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010

1,4-Addition of Lithium Diisopropylamide to Unsaturated Esters
A R T I C L E S
prepared from fresh acetone. LiCl (0.5 mol % relative to LDA)
was added as a stock solution (0.50 mL) containing Et3N·HCl (8.3
mg, 0.06 mmol) and LDA (13.5 mg, 0.12 mmol) in 5 mL of THF.
After recording a background spectrum, we added ester 1 (0.005
mmol) with stirring.
(rate constants). The Levenberg-Marquardt algorithm52 used for
the ꢁ2 minimization is a form of nonlinear least-squares fitting. The
fitting procedure implemented numerical integration based on the
backward-differentiation formula53 to solve the differential equa-
tions, yielding functions describing concentration versus time.
NMR Spectroscopic Analyses. All of the NMR tubes were
prepared using stock solutions and sealed under partial vacuum.
Acknowledgment. We thank the National Institutes of Health
(GM39764 and, in part, GM 077167) for direct support of this work
and Pfizer, Merck, and Sanofi-Aventis for indirect support.
6
Standard Li, 13C, and 15N NMR spectra were recorded on a 500
MHz spectrometer at 73.57, 125.79, and 50.66 MHz, respectively.
The 6Li, 13C, and 15N resonances were referenced to 0.30 M
[6Li]LiCl/MeOH at -90 °C (0.0 ppm), the CH2O resonance of THF
at -90 °C (67.57 ppm), and neat Me2NEt at -90 °C (25.7 ppm),
respectively.
Numerical Integrations. The time-dependent concentration plots
obtained using 6Li NMR spectroscopy (Figures 5-8) were fit to a
mechanistic model expressed by a set of differential equations. The
curve fitting minimized ꢁ2 in searching for the coefficient values
Supporting Information Available: NMR, rate, and compu-
tational data; experimental protocols; details of the numerical
integrations; and complete ref 25. This material is available free
of charge via the Internet at http://pubs.acs.org.
JA105855V
9
J. AM. CHEM. SOC. VOL. 132, NO. 44, 2010 15623