The Curtin-Hammett Principle
∂[B2]
∂t
GTS2 - GTS1
∂[B1]
(
=e
−(GTS2 - GTS1)
RT
)
∂t
ΔG1‡
ΔG2‡
ΔG21O
B1
k1
A1
A2
k2
B2
So, relative reaction rates
depend only on relative
transition-state energies,
and not on starting-material
ground-state energies.
The Curtin-Hammett Principle
Example: Dynamic Kinetic Resolution
Question:
O
How can enantioselective chemistry convert a
racemic mixture into exclusively one diastereomer?
O
O
OCH3
O
+
OCH3
(R)
(S)
H2
enantioselective
reduction of ketone
(S) to (S,S) makes sense—
just incorporate new chiral
center by enantioselective
reduction.
But how to convert
(R) to (S,S)?
H OH O
OCH3
(S,S)
Ryoji Noyori, Nagoya University
(Nobel Prize, 2001)
The Curtin-Hammett Principle
Example: Dynamic Kinetic Resolution
O
O
(S)-BINAP-RuBr2
OCH3
H OH O
OCH3
H2
(S)
(S,S)
Ph
(R) is converted to (R,S)
much more slowly than (S)
to (S,S) with this catalyst.
Diastereospecific yield of
reaction on racemic mixture
could not exceed 50%.
Ph
P
Ru
P
Ph
(S)-BINAP-RuBr2
Br
Br
Ph
(S)-BINAP
BINAP ligand creates
two sterically
hindered quadrants.
Tokunaga, M.; Kitamura, M.; Noyori, R. J. Am. Chem. Soc. 1993,
115, 144-152.
Noyori, R.; et al. J. Am. Chem. Soc. 1989, 111, 9134-9135.
The Curtin-Hammett Principle
Example: Dynamic Kinetic Resolution
O
O
(S)-BINAP-RuBr2
OCH3
H OH O
OCH3
H2
(S)
(R) is converted to (R,S)
much more slowly than (S)
to (S,S) with this catalyst.
(S,S)
‡
lower-energy
(rate-determining)
transition state
(S)-BINAP +
‡
steric
congestion
(S)-ketoester
(S)-BINAP +
higher-energy
(rate-determining)
transition state
(R)-ketoester
The Curtin-Hammett Principle
Example: Dynamic Kinetic Resolution
O
O
(S)-BINAP-RuBr2
OCH3
OH
O
OCH3
H2
(S)
(S,S)
+
O
O
?
OCH3
(R)
So, how to convert (R)-ketoester
to (S,S)-β-hydroxyester?
The Curtin-Hammett Principle
Example: Dynamic Kinetic Resolution
O
O
(S)-BINAP-RuBr2
OCH3
O
OH
OCH3
H2
(S)
O
O
(S,S)
+
OCH3
achiral ester
enolate
O
O
(S)-BINAP-RuBr2
OCH3
(R)
Equilibrate two enantiomeric starting
materials through achiral enolate, by
tuning Lewis acidity in solvent.
H2
OH
O
OCH3
(R,S)
Curtin-Hammett ensures that all
racemate goes to (S,S), as long as
equilibration is faster than catalysis.
The Curtin-Hammett Principle
Example: Dynamic Kinetic Resolution
(S)-BINAP-Ru
(S)-ketoester
(S)-BINAP-Ru
(R)-ketoester
‡
O
‡
O
OCH3
OH
O
O
O
(S)
OH
O
OCH3
OCH3
OCH3
(S,S)
O
O
(R)
OCH3
(R,S)
(not observed)
Kinetic vs. Thermodynamic Control
increase frequency of going
over reaction barriers (e.g.,
by lowering TS energy w/ catalyst,
or by increasing T)
E
B1
A1
A2
B2
Under kinetic control, make product
with lowest-energy transition state
B1
A1
A2
B2
Under thermodynamic control,
make product with lowest
ground-state energy
Kinetic vs. Thermodynamic Control
Br
more δ+
on 2o carbon
+
-80 °C
δ+
HBr
δ−
Br
δ+
δ+
δ−
δ+
+
40 °C
Br
kinetic
product
δ+
Br
thermodynamic
product
δ+
Br
Br
Principle of Microscopic Reversibility
The lowest-energy pathway from reactant to product must
also be the lowest-energy pathway from product to reactant.
Pathway I
Pathway II
A→P
and
P→A
choose this path.
If I were hiking, I’d take Pathway I from A → P, and Pathway II from P → A.
But molecules aren’t hikers. They’d always take Pathway II.
Principle of Microscopic Reversibility
An interesting corollary: Catalysts activate both forward and
reverse reactions.
O
+ H2O
N
H
subtilisin,
trypsin,
papain
subtilisin,
trypsin,
papain
O
OH
Enzymes that catalyze
protein cleavage…
+
H2N
…also catalyze protein
synthesis!
So, how does our body selectively degrade the proteins it wants to eat,
and synthesize the proteins it wants to use?
Principle of Microscopic Reversibility
Answer: Isolate different reactions in different places.
In the gut…
Inside cells…
O
O
+ H2O
N
H
N
H
subtilisin,
trypsin,
papain
O
+ H2O
+ ADP
+ Pi
ribosome
O
OH
+
H2N
…proteolysis is
driven by water.
OH
+
H2N
+ ATP
…protein synthesis is
driven by energy (ATP).
Enzymes work both ways, but thermodynamics drives reactions in desired directions.