The Curtin-Hammett Principle and the Winstein …evans.rc.fas.harvard.edu/pdf/smnr_2009_Wzorek_Joseph.pdfThe Curtin-Hammett Principle and the Winstein-Holness Equation Joseph Wzorek

Evans Group Lecture Series

The Curtin-Hammett Principle andthe Winstein-Holness Equation

Joseph Wzorek12/18/2009

Setting the Stage: A Historical Perspective

General view: Cyclohexaneas a planar hexagon

Prior to 1890

1890 - 1927

Three-dimensionality of organic compounds was poorlyunderstood This includes one of the most common structural motifsfound in organic chemistry: cyclohexane

The idea that cyclohexane may indeed be puckered wasproposed by Sachse (1890) and separately by Mohr (1918)

1928 - 1949

Experimental evidence emerged that supported (andrefuted) a “new” proposal: chair cyclohexane X-ray analysis: Bilicke

X-ray, electron diffraction, dipole moment analyses: Hassel

Cyclohexane in achair conformation

Despite this evidence: “…most chemists, especiallyorganic chemists, depicted the molecule [cyclohexane] as aplanar hexagon even as late as 1948.” - Eliel, 1975

Odd Hassel - Nobel Prize, 19691

2

3

4

5

6

Placing tetrahedral carbon atomsin and out of the plane mayproduce a chair or boat

BrBr

Br

Br

BrBr


1950 - present

Important works published in obscure journals Resistance to new ideas that refute old “tested” principles Separation and slow communication Lack of communication between disciplines War

Landmark paper written by Derek Barton was publishedin 1950: Barton, D. H. R. Experentia, 1950, 6, 316.

Derek BartonNobel Prize, 1969

The birth of conformational analysis: “Thus it has beenshown that monosubstituted cyclohexanes adopt theequatorial conformation rather than the polar one.”

R

RH

H

R is polar R is equatorial

R

RH

H

preferred

Presented an unambiguous representation of the steroidnucleus containing the all-chair conformation

Me

Me

Me

Me

OH

OHO

O O

R

O

R

OH

OH

O O

R

O

O R

Slow

Slow

Fast

Fast

Compared the rate of both hydrolysis and esterificationfor cis and trans cyclohexanols Attributed the rate difference to steric hinderanceassociated with the polar (axial) substituents

The following point was also articulated: “…although oneconformation of a molecule is more stable than otherpossible conformations, this does not mean that themolecule is compelled to react as if it were in thisconformation or that it is rigidly fixed in any way.” - Barton,1950.


Critical Overlap at Columbia

David Y. Curtin, 1920 -

1943: A.B. Swarthmore 1945: Ph.D. University of Illinois 1946: Instructor at ColumbiaUniversity 1951: Asst. Prof., University of Illinois

David Curtin, near the end of his stay at Columbia as aninstructor, had a critical exchange with Louis Hammett andgraduate student Peter Pollak

Louis P. Hammett, 1894 - 1987

1916: B.S. Harvard University 1923: Ph.D. Columbia University 1921 - 1961: Faculty of ColumbiaUniversity

“…the idea was prevalent among chemists that one coulddetermine the configuration of a reactant from the structureof a reaction product. At that time Curtin was on the staffat Columbia, and was puzzled about this idea.” - Hammett,1980.

Consider the following rearrangement reported byBachmann and Ferguson (termed type I)

Stereospecific Rearrangement: Type I

An analysis of the proposed mechanism

Migratory preference relies upon relative ability to stabilizepositive charge

OH

Ar

Ph HONO

O

Ph

NH2 Ar

Preferred migration whenAr = p-Tolyl or p-Anisyl

Curtin and Pollak alluded (in non-mathematical terms) tothe Curtin-Hammett principle in 1950 while studying therearrangement of amino alcohol derivatives

OH

Ar

ArOH

Ar

ArNH2

R = Ar, or H

HONO

ArHO

HH

NN

migrationO

Ar

Ar

+ N2

phenonium ion formation

-H

An Early Example of Conformational Analysis: Prelude to the Curtin-Hammett Principle

Experimental results:

A similar results were obtained when comparing p-Tolylanalogues Additional stereocenter may invert migratory preference Why are the two reaction types inconsistent with respect toone another?

Three staggered conformations exist, each placing apotential migrating group antiperiplanar to the leaving group

Destabilization due to steric interactions is also present inthe TS (a stepwise mechanism may also be at play)

Pollak and Curtin recognized the relevance of the transitionstate in the outcome of the reaction rather than relying solelyupon ground state conformational analysis.

OH

PhAr

Ph HONO

O

PhAr

NH2 Ph

or

O

PhPh

Ar

Curtin and Pollak studied a similar system that utilizedsubstrates with two stereocenters as opposed to one

Stereospecific Rearrangement: Type IIH

Ph

OHN2

Ph

Ar

HPh

PhN2

Ar

HO

HPh

ArN2

OH

Ph

Favored

SubstrateRace-mate

!

"

OH

Ph

NH2

Ph

MeO

OH

Ph

NH2

Ph

MeO

Product

O

Ph

PhMeO

Yield (%)

97

97

O

Ph

Ph

OMe

note: ! and " designate that the two substrates are different diastereomers

of unknown relative configuration.

HPh

Ph

N2

Ar

HO

HPh

OH

N2

Ph

Ar

HPh

Ar

N2

O

Ph

H

“It seems possible that VIa may be of sufficiently lowerenergy than VIb to influence the relative rates of the twomigrations.” - Pollak and Curtin, 1950.

Development of the Curtin-Hammett Principle

A2 A3A1 A4

k21 k34k23

k32

The Basic Curtin-Hammett Kinetic Scheme

Consider a compound that exists in two different isomericforms, A2 and A3, that reacts by first-order or psuedo first-order kinetics to yield product, A1 or A4, respectively

Three boundary conditions exist to describe extremeswithin this kinetic scheme

Condition I:

Condition II:

Condition III:

k21,k34

<< k23,k32

k21,k34! k

23,k32

k21,k34

>> k23,k32

Product distribution reflects the initial conformer distribution Requires that reaction is faster than isomer interconversion

Boundary Condition 1: Kinetic Quench

k21,k34

>> k23,k32

3 possible cases as proposed by McKenna, 1974

Case 1: Excess of highly reactive reagent producedsuddenly (flash photolysis)

Case 2: Highly reactive reagent produced slowly(conventional photochemical reactor, thermally, or viaslow addition [strong acids])

Case 3: Intramolecular reactionA2 A3A1 A4

k21 k34k23

k32

Fast FastSlow

Slow

Note: While the scheme shown above is the basic Curtin-Hammett kinetic scheme, more complicated scenarios existinvolving higher-order kinetics

Examples of “Kinetic Quench” Experiments

Another method of kinetic quenching (Lewis, 1972) Consider the geminally disubstituted cyclohexane below

Most common example: proton transfer Protonation of a tertiary amine with acid (Booth, 1972)

These rates reflects both ground-state conformationalpopulations and efficiency of product formation

Determined that A:B is between 1:1.1 and 1:4.4 Value determined via 13C NMR: 2.7:1

Me

OHPh

O

Ph

+

k*AB ! 7 x 104 s-1

k! = 2.5 x 107 s-1 k" = 1.8 x 108 s-1

Results are complicated due to a “mixing” problem (pocketsof protonated amine and free base that allow equilibration)

O

OH

H

KHMDS, 18-c-6

THF, -40ºC

1 N HCl-40ºC

O

O

H

H

Kinetic quench

H

KO

O

H

KO

O

H

H59% yield

N

Me

MeMe

kAB

A B

N

Me

Me

Me

kequat. kaxial

N

Me

MeMe N

Me

Me

MeH

H

O2CCF3

TFA, 0ºC

O2CCF3

TFA, 0ºC

>15:1

kBA

Me

OPhH

k*AB

Me

O

Ph

Me

OPhH

Me

O

PhkAB

h! h!

* *

excitation >> kAB

(Franck-Condonprinciple)

A B

A* B*

A kinetic quench was used to access a single diastereomerfollowing an oxy-Cope rearrangement (Snapper, 2003)

Development of the Curtin-Hammett Principle

Boundary Condition II: Curtin-Hammett Conditions

k21,k34

<< k23,k32

Considered a very common phenomena sinceconformational interconversion is often a very fast process

The Curtin-Hammett principle states: “the relative amountsof product formed from two critical conformations arecompletely independent of the relative populations of theconformations and depend only upon the difference in freeenergy of the transition states, provided the rates of reactionare slower than the rates of conformational interconversion.”

A2 A3A1 A4

k21 k34k23

k32

Slow SlowFast

FastCurtin-Hammett Principle: Derivation

Two derivations exist, allowing the ratio of productconcentrations to be expressed in terms of:

K, k34, and k21 (Derivation 1) ∆G‡

TS (Derivation 2)

d[A1]

dt= k

21[A

2]

d[A4]

dt= k

34[A

3]

Consider the following two rates of formation:

One can arrive at the ratio of rates by dividingequation 2 by equation 1:

d[A4]/dt

d[A1]/dt

=d[A

4]

d[A1]

=k34[A

3]

k21[A

2]

(1, 2)

(3)

A representative condition II system:

Derivation 1:

Derivation of the Curtin-Hammett Principle

Rearranging equation 3 leads to:

Equation 4 may be integrated from 0 to [A]:

d[A4]

0

[A4 ]

! =k34

k21

[A3]

[A2]d[A

1]

0

[A1 ]

!

d[A4] =

k34[A

3]

k21[A

2]d[A

1]

If then is a constant (K).

Thus, the equation 5 may be integrated, resulting in:

k23,k32

>> k21,k34

[A3]

[A2]

[A4]! [A

4]0

[A1]! [A

1]0

=k34k23

k21k32

= Kk34

k21

[A4]

[A1]

= Kk34

k21

when

[A4]0

= [A1]0

= 0

Equation 6 may be further simplified, leading to:

The product ratio is dependant on the ratio k34/k21 The ground state conformational preference has a direct(proportional) role in the value of the product ratio

Derivation 2:

Consider the following familiar equations:

K =[A

3]

[A2]

= e!"G

0/RT

Substitution of equations 8-10 into the equation 7produces:

Note: the transmission coefficients k34 and k21 areassumed to be equal.This equation, in turn can be simplified further:

If we state that then:

!GTS

‡= !G

34

‡+ !G

0" !G

21

‡

[A4]

[A1]

= e!("G34

‡+"G

0!"G21

‡) /RT

[A4]

[A1]

= Kk34

k21

= e!"G

0/RT e

!"G34‡/RT

e!"G21

‡/RT

[A4]

[A1]

= e!"G

TS

‡/RT

The product ratio is dependant on the difference in energybetween the two transition states This expression is also only true if [A3]/[A2] is constant

(4)

(5)

(6)

(7)

(8-10)

(11)

(12)

(13)

k21

= !21kh

"1Te

"#G21‡/RT

k34

= !34kh

"1Te

"#G34‡/RT

The Curtin-Hammett Principle

Recall that the basic stipulation for Curtin-Hammett kinetics(termed “condition II”) is the following:

Analysis of this system with the recently derivedmathematical expression of the Curtin-Hammett principlepresents two interesting subsets of condition II

Subset 1:

Subset 2:

k21,k34

<< k23,k32

Extremes within Condition II Systems

K ! 1, "GTS

‡! 0

K ! 1, "GTS

‡= 0

Within subset 2 exist another two extremes exist (see treebelow)

Condition II

k21,k34

<< k23,k32

K ! 1, "GTS

‡! 0

K ! 1, "GTS

‡= 0

K ! 1, "GTS

‡! 0,

"G0

< "GTS

‡

K ! 1, "GTS

‡! 0,

"G0

> "GTS

‡

K ! 1, "GTS

‡= 0

Subset 1

Consider the following free-energy diagram

Few examples exist for this subset Eliel has presented a possible situation

I I*

I*

+ I


Treating cyclohexyl iodide with radiolabeled iodide couldresult in a completely symmetric transition state leading totwo different products

Of course, this is only hypothetical due to productequilibration

I

I

kea

kae

ke kaI* I*

I*

I*

kea

kae

via:

I

I H

Part 1:

Subset 2

This situation implies that the ground-state conformerdistribution heavily favors one conformer However, this selectivity is degraded in the transition state,leading to a less selective reaction Note: While this free-energy diagram shows the majorconformer leading to the major product, the inverse couldexist as well

Consider the following example (Solladié, 1972):

K ! 1, "GTS

‡! 0,

"G0

> "GTS

‡

K ! 1, "GTS

‡! 0,

"G0

> "GTS

‡

MeN

Ph D3C I NPh

D3C Me

I

NPh

Me

NPh

Me


This reaction involves stereogenicity at nitrogen

Due to rapid inversion at nitrogen, this system is underCurtin-Hammett conditions

The transition state is slightly favored for axial alkylation The selectivity in the ground-state conformer distribution isdegraded due to emerging quaternization of the amine

17 : 1

1.9 : 1

NMe

Ph

H

H

H

N

Ph

H

H

H

Me

NMe

Ph

H

H

H

CD

DD

I

NC

Ph

H

H

MeD

DDH I

Favored Favored

I NPh

Me

CD3

NPh

MeD3C

I

Another example (Giese, 1996)

CN

CNH

t-Bu

MeCN

CNMe

H

t-Bu

Two major conformers are proposed

A(1,3) minimized

99:1

Transition state energies are dictated primarily by: A(1,3) strain Steric hinderance associated with incoming R radical

t-Bu CN

CNMe

MeI t-Bu CN

CNMe

Me

+

t-Bu CN

CNMe

Me

Zn/CuI

Favored

CN

CNH

t-Bu

MeH Me

CN

CNMe

H

t-BuMe H

61:39t-Bu CN

CNMe

Me

t-Bu CN

CNMe

Me

D3C

I

NPh

Me

CD3

I

NPh

MeCD3

D3C I

I


Consider the following example (Winstein, Holness, 1955) Much more soon regarding this paper

14:1

ke:ka = 1:70

minimally

Despite the large conformational preference, the reactionproceeds almost exclusively through the minor conformer Note: This specific case would be described by a slightlydifferent free-energy diagram where the minor conformerleads to the product:

Part 2:

K ! 1, "GTS

‡! 0,

"G0

< "GTS

‡

K ! 1, "GTS

‡! 0,

"G0

< "GTS

‡

Systems of this type involve an increase in selectivitythrough the transition state in comparison to the ground state

OTs

NaOEt

EtOH+ NaOTs

OTs

OTsH

H

NaOEt

EtOH

NaOEt

EtOHke ka


Other Curtin-Hammett Kinetic Schemes

A2 A3A1 A4

k21 k34k23

k32

Recall the simplest Curtin-Hammett kinetic scheme thatformed the basis for our previous scenarios

While it is easiest to apply Curtin-Hammett concepts toScheme 1 systems, many other schemes apply as well

Scheme 1

A2 A3A1 A4

k21 k34k23

k32

+ R + R

Scheme 2

Now, the rates of product formation (A1 and A4) can bedescribed by the following two equations:

d[A1]

dt= k

21[A

2][R]

d[A4]

dt= k

34[A

3][R]

Following the same logic used previously to derive theCurtin-Hammett principle, we arrive at the following equation:

d[A4]/dt

d[A1]/dt

=k34[A

3][R]

k21[A

2][R]

=k34[A

3]

k21[A

2]

[R] cancels out apparently removing [R] from functionaldependence on [A4]/[A1] However, this approximation is only valid under Curtin-Hammett conditions

Like Scheme 1 systems, Scheme 2 systems have threeconditions Condition I: Kinetic Quench

Condition II: Curtin-Hammett

Condition III:

k21[R],k

34[R]>> k

23,k32

k21[R],k

34[R]<< k

23,k32

k21[R],k

34[R]! k

23,k32

A2 A3A1 A4

k21 k34k23

k32

A0

k0

Scheme 3

Scheme 3 involves an interconverting pair of compoundsthat react to give a different product However, all material is introduced into the system from A0

Second-Order Reactions to Product

The “Feed-In” Mechanism

Consider a second scheme (Scheme 2) which involves twointerconverting substances, each of which reacts with areagent R via second order kinetics

Winstein and Holness

Critical Overlap at UCLA

1934: B.S. UCLA 1938: Ph.D. Cal. Tech. 1941: Instructor at UCLA 1947: Full Professor

During postdoctoral work at UCLA, Holness overlappedwith Winstein, who had a small office in Holness’ lab

Norris J. Holness1927 - ?

1952: Ph.D. Imperial College (Barton) 1952: Postdoctoral studies at UCLA Conducted research at Queen MaryCollege, London

Holness is considered the driving forcebehind the Winstein-Holness equation

Saul Winstein, 1912 - 1969

“the quantitative aspects of this subject [conformationalanalysis] have, however, been scarcely been touched andit is clear that much useful work can be done by physicalorganic chemists in this direction.” - Barton, 1955.

Winstein and Holness knew that conformationalinterconversion was a fast process, thus Curtin-Hammettconditions could potentially apply How can they access K (kea/kae)?

Insight into a Seemingly Intractable Problem

OH

kea

kae

OHH

H

Now that the Curtin-Hammett principle has beenpresented, the relevance of the Winstein-Holness equationto this topic must be addressed

Typically such experiments include low temperature dataacquisition and subsequent peak integration

!G0

= "RT lnK

Aside: This determination is made much easier todaythrough the use of NMR spectroscopy

Consider the following scheme:

A mathematical treatment is now necessary to proceed

The Winstein-Holness Equation

Winstein-Holness Equation: Derivation

Recall the Scheme 1, condition II system previouslyunder scrutiny:

d[A1]

dt= k

21[A

2]

d[A4]

dt= k

34[A

3]

Recall the following two rates of formation:

The Winstein-Holness equation requires examinationof the total rate of product formation:

Like the Curtin-Hammett Princple, two mathematicalderivations exist for the Winstein-Holness equation

Derivation 1: Winstein and Holness, 1955 Derivation 2: Eliel and Ro, 1956; Eliel and Lukach, 1957

Derivation 1

d[A1]

dt+d[A

4]

dt= k

21[A

2]+ k

34[A

3]

At any time t, the total rate of product formation maybe expressed in the following manner:

Note: kWH is defined as the Winstein-Holness rateconstant.Recombining equations 14 and 15 produces:

(14)

(1,2)

(15)

k21[A

2]+ k

34[A

3] = k

WH{[A

2]+ k

34[A

3]} (16)

Solving for kWH:

kWH

=[A

2]

[A2]+ [A

3]k21

+[A

3]

[A2]+ [A

3]k34

(17)(at time t)

This equation is general for any system that adheresto the kinetic scheme defined earlier (not necessarilyCurtin-Hammett conditions)

d[A1]

dt+d[A

4]

dt= k

WH{[A

2]+ [A

3]}

A2 A3A1 A4

k21 k34k23

k32

Slow SlowFast

Fast

The Winstein-Holness Equation

Noting that equation 17 can be simplified usingequations 18 + 19 (mole fractions) yields:

x20

=[A

2]0

[A2]+ [A

3]

x30

=[A

3]0

[A2]+ [A

3]

(18, 19)

kWH

= x20k21

+ x30k34

for all t if k23, k32 >> k21, k34)(Curtin-Hammett conditions)

kWH is considered the weighted average of the specificrate constants for the individual conformers Other properties can be described by this equation aswell including (see equation 21 for the general expression)

pK dipole moment NMR chemical shifts

(20)

P = NiPi

i

!

P = weighted average of propertyNi = mole fraction of ith conformationPi = property value of ith conformation

Derivation 2

(21)

Consider the alternative definition of mole fraction ascompared to equations 18 and 19:

x20

+ x30

= 1 (22)

Therefore:

x20

=x20

x20

+ x30

(23)

Dividing the numerator and denominator by x20 or x30produces:

x20

=1

1+x30

x20

=1

1+ K(24,25)

x30

=

x20

x30

x20

x30

+ 1

=K

1+ K

Substituting equations 24 and 25 into 20 produces:

kWH

=k21

+ Kk34

K + 1

Which can be solved for K to yield the more convenient:

K =k21! k

WH

kWH

! k34

(26)

(27)

How can equations 20, 26, or 27 be used to solve a real-life problem?

Application of the Winstein-Holness Equation

The Kinetic Method (of conformational analysis)

OH

kea

kae

OHH

H

Product Product

ke ka

Fast

FastSlow Slow

Recall the following scheme in which cyclohexanol israpidly interconverting from one conformation to the other

Step 1: The system in question is coupled to anirreversible reaction that is much slower than kea or kae

OH O

75% AcOH

CrO3

OH

kea

kae

OHH

H

The Winstein-Holness equation may now be used as abasis for “the kinetic method” to help determine the relativeratio of conformers

This system is now under Curtin-Hammett conditions Winstein and Holness chose several different reactionsfor the slow step to prove the method works, such as:

oxidation of secondary carbinols saponification of acid phthalates solvation of tosylates

For simplicity, only one reaction will be examined:chromic acid oxidation

Step 2: Perform three experiments examining therate constants for oxidation of:

the initial substrate ring-locked axial substrate ring-locked equatorial substrate

Experimental results (Winstein, Holness, 1955):

To continue further, an assumption is needed: ke = k’eand ka = k’a where k’ is the rate constant of oxidation forthe t-Butylcyclohexyl analogue

OH

t-Bu

OH

H

t-Bu

H

OH

substrate temp. (ºC)

103 k2

L(mol-1s-1)

25

50

25

50

25

50

5.84

42.1

4.72

29.9

14.0

76.3

K =k21! k

WH

kWH

! k34

Application of the Winstein-Holness Equation

K =k21! k

WH

kWH

! k34

Step 3: Using the experimental data, solve for K Recall equation 27

In the generic equation 27, if we consider kWH the rate constant for cyclohexanol oxidation k21 the rate constant for cis t-Butylcyclohexanoloxidation (OH axial) k34 the rate constant for trans t-Butylcyclohexanoloxidation (OH equatorial)

(27)

K =k21! k

WH

kWH

! k34

=14.0 ! 5.84

5.84 ! 4.72= 7.29

Which means that if our assumption is true regardingthe applicability of the t-Butyl analogues, the ratio is

K =k21! k

WH

kWH

! k34

=76.3 ! 42.1

42.1! 29.9= 2.80

At 25°C

At 50°C

OH

kea

kae

OHH

H

88

74

12

26

25 ºC

50 ºC

Step 4: Solve for an A-value if so desired

Using the accepted equation:

!G = !H "T!S = "RT lnK (28)

!G = A = "8.3145J

Kmol298K ln 7.29 = "4922

J

mol

!G = A = "8.3145J

Kmol323K ln 2.80 = "2765

J

mol

This means that the A value is between 0.66 and 1.2Kcal/mol in AcOH Winstein and Holness claim 0.8 after averaging

Criticisms of the Kinetic Method

Regardless of the type of reaction chosen, the samevalues for K or A should be obtained if the samesubstituent is used; yet this is not the case The assumption that the t-Butyl group will alwaysreside equatorial is not true

One example involves solvation of a carboxylicacid

Few examples exist in which the reaction does notinvolve a ring atom

Acree-Curtin-Hammett Principle?

Solomon F. Acree (1875 - 1957)

Brief biographical sketch (Andraos, 2008): 1896: B.S. Univ. of Texas 1897: M.S. Univ. of Texas 1902: Ph.D. Univ. of Chicago (John Nef) 1903: Univ. of Berlin (Emil Fischer) 1901-1926: 8 different institutions 1927-retirement: NIST

Acree began his career studying the constitution ofphenylurazoles In 1907, he published a paper that largely outlined theconcepts of the Curtin-Hammett principle and the Winstein-Holness equation Consider the following scheme:

“it is perfectly obvious that such reactions…do not give usdecisive evidence in regard to the relative amounts of theenol and keto forms in any given amide group in which thechange from one tautomeric form to the other is very rapidin comparison with the reactions between the two formsand the alkylating reagents.” Acree, 1907

Of course, no mention of transition states is reasonablesince they were not formalized yet by Eyring

d(C2

+ C3)

dt=kK

3+ k

1

1+ K3

(C + C1! C

2! C

3)2

This equation expresses the observed second order rateconstant as a function of enol and keto forms Note that the derived rate constant is exactly kWH!

Where concentration ofdiazomethane and urazole after time t.

(C + C1! C

2! C

3) =

kWH

=k21

+ Kk34

K + 1

[A4]

[A1]

= Kk34

k21

Also gave the product ratio as:

C2

C3

=kK

3

k1

(26)

N

N

N

HO OH

Ph

N

N

NH

HO O

Ph

N

N

N

HO O

Ph

N

N

N

HO O

Ph

CH2N2 CH2N2

Me

Me

Major, C3 Minor, C2

C1 C

K3

k1 k

recall: (7)

Note: This information was obtained from Andraos, 2008since the Acree,1907 paper is published in a defunct journal Despite this, Ph. D. theses written under Acree supportthese claims

Derived the following expression:

Curtin-Hammett and Winstein-Holness

A Combined Kinetic Treatment

The combined usage of Curtin-Hammett and Winstein-Holness concepts allows determination of k21 and k34 This combined usage may lead to the greatest utility of theseconcepts

Let us now consider in detail, the proposed system

[A4]

[A1]

= Kk34

k21

(7)

kWH

=k21

+ Kk34

K + 1(26)

Using the equations already developed (7, 26), we can solvefor k34 and k21 in terms of kWH, K, and the product ratio (P)

k34

= kWH

K + 1

K

!

"

#

$

P

P + 1

!

"

#

$

k21

= kWH

K + 1

P + 1

!

"

#

$ (29, 30)

Seeman and coworkers were able to determine kcis and ktrans(which correspond to k34 and k21 above using this treatment(Seeman, 1980)

Experimentally determined dataMeN

13CH3I N

13CH3

Me

I

R R

Substrate kWH (10-4) [Ptrans]/[Pcis]

30 1.72

7.61 1.4

5.31 1.3

R = H

R = Me

R = i-Pr

K

17

>30

>30

Using equations 29 and 30, the following rate constants forPtrans and Pcis formation were determined

Substrate kcis ktrans

2.0 x 10-3 2.0 x 10-2

4.6 x 10-4 9.8 x 10-3

3.0 x 10-4 6.9 x 10-3

R = H

R = Me

R = i-Pr

NMe

Ar

H

H

H

N

Ar

H

H

H

Me

NMe

Ar

H

H

H

13CH3

N13CH3

Ar

H

H

H

Me

K

ktrans kcis13CH3I

13CH3I

II

Ptrans Pcis

Consider the following reaction (which is very similar tosomething we have recently discussed)

An Interesting Potential Curtin-Hammett Situation

D. A. Evans and the Anti-Aldol Reaction

In 2001 and 2002 D. A. Evans and coworkers publishedtwo articles regarding the magnesium halide catalyzed anti-aldol reaction (Evans, 2001, 2002)

A table of representative substrates: (Evans, 2001)

Similar results were achieved using the thiazolidinethionevariant and MgBr2·OEt2 (Evans, 2002)

O N

O O

Bn

Me

1) 20 mol% MgCl2, Et3N, TMSCl, EtOAc

2) TFA; MeOH+

O

HArO N

O O

Bn

Me

OH

Ar

O N

O O

Bn

Me

1) 20 mol% MgCl2,30 mol% SbF6, Et3N

TMSCl,N EtOAc2) TFA; MeOH

+O

HRO N

O O

Bn

Me

OH

R

Data points acquired by P. Nagornyy as a graduate studentwith DAE show an interesting temperature dependence

O N

O O

Bn

Me

Mg

Cl Cl

HNR3

O N

O O

Bn

Me

O

R

Mg

Cl Cl

O N

O O

Bn

Me

O

R

Mg

Cl Cl

The trend is toward higher selectivity when the reactions areconducted at higher temperature How are proposed intermediates (below) related?

NO2

O

H

O

H

O

Substrate dr –10 ºC 80 ºC25 ºC

1.5:1 6:1 6:1

2:1 5:1 10:1

NR 1:1 2:1

Ph

O

H

NO2

O

H

Me

O

H Ph

O

H

O

Substrate dr yield

7:1 71

28:1 92

6:1 80

An Interesting Potential Curtin-Hammett Situation

1 3

5

2

4

blue: T = -10 °Cred: T = 77 °C

O N

O O

Bn

Me

Mg

Cl Cl

HNR3

O N

O O

Bn

Me

O

R

Mg

Cl Cl

O N

O O

Bn

Me

O

R

Mg

Cl Cl

TMSCl TMSCl+

O

HR

k1

k1'

k2

k2'k3 k4Product Product

1 32

4 5

Synthesis Examples

NH

NH

NH

O

NH

CO2Me

Bn

!!

HN

HN

HNHBoc

O

Me

O

HO2C i-Bu

H

H

NH

N

O

NH

HBocHNO

HN

CO2H

i-Bu

Me H

NO

MeO2CBn

H

H

NH2

Baran and coworkers encountered a potential Curtin-Hammett situation during theirsynthesis of both Kapakahines B and F (Baran, 2009)

HOAt, EDC

20:1 CH2Cl2:DMF

HOAt, EDC

20:1 CH2Cl2:DMF

N

NH

NH

O

NH

CO2Me

Bn

!!

HN

HN

HNHBoc

O

Me

O

i-Bu

H

6%

O

H

NH

N

NO

MeO2C Bn

H

H

NH

O

HN

ONH

OBocHN H MeH

i-Bu

64%

"More reactive"

Synthesis Examples

Van Vranken and coworkers disclosed an exceedingly selective Mannich-type cyclizationenroute to the antitumor antibiotic AT2433-A1 (Van Vranken, 2000)

Rational:

N

NH

NH

Me

OO

H H

Cl

SMe

O

O

OH

CHCl3

N

NH

NH2

Me

OO

H H

Cl

H

H

MsO

94%

selectivity: >20:1

N

NH

NH

Me

OO

H H

Cl

H

N

NH

NH

Me

OO

H H

Cl

H

N

NH

NH2

Me

OO

H H

Cl

H

H

MsO

N

NH2

NH

Me

OO

H H

Cl

MsO

H

H

Note: The authors show that Mannich cyclizationis irreversible in chloroform

Favored

Synthesis Examples

Pirrung and coworkers disclosed the following case during their synthesis of (+)-Griseofulvin(Pirrung, 1991)

OMe

MeO

Cl

O

O

N2

MeMe

Rh2(piv)4

PhH, reflux

CO2Me

OMe

MeO

Cl

O

O

CO2Me

Me

Me

62%

OMe

MeO

ClMeO

Cl

O

MeMe

O

Me

O

CO2Me

O

O

CO2Me

Me

Me

MeO

Cl

O

MeMe

O

OMe

CO2Me OMe

MeO

Cl

O

O

CO2Me

Me

Me

[2,3]1,4-methyl shift

exclusive product

Rational:

Quantification of the Curtin-Hammett/Winstein-Holness Kinetic System

To this point, we have always made the followingassumption with regard to Condition II systems:

k21,k34

<< k23,k32

A1(t) =

bk21et!

!+k21Ce

t"

"+ (A

10#bk

21

!#k21C

")

A2(t) = be

t!+ Ce

t"

A3(t) = de

t!+ he

t"

A4(t) =

dk34et!

!+hk

34et"

"+ (A

40#dk

34

!#k34h

")

How might we determine to what extent this assumptionis valid?

Anti-Curtin-Hammett Curtin-Hammett

Several researchers set out to quantify Curtin-Hammett/Winstein-Holness kinetics including:

Zefirov, 1977

Seeman and Farone, 1978

Andraos, 2003

Anti-Curtin-Hammett/Curtin-Hammett Distinction A truncated version of the solution is shown below

A2 A3A1 A4

k21 k34k23

k32

Seeman and Farone

In 1978, Seeman and Farone arrived at the exact solutionfor the following concentration-time dependancies for allfour species present in the familiar kinetic scheme:

For our purposes, the implications of this solution aremore important than the derivation and we will thereforefocus on the former

!WH

= (kWH

" kobsd

kobsd

) *100

kobsd

=d(A

1+ A

4)

dt(A

2+ A

3)!1

!CH

= [K (k34

k21

) "A4

A1

](A4

A1

)"1*100

Scheme 1

Seeman and Farone decided to express deviation fromCurtin-Hammett conditions using the three equationsbelow:

kWH

=k21

+ Kk34

K + 1

[A4]

[A1]

= Kk34

k21

Recall:


An absolute value of 5 was set as the upper limit for non-Curtin-Hammett kinetics (this means ∆CH < 5)

This mirrors assumed experimental error

A clear area in which I∆CHI < 5 is present This area generally shows that each rate needs to besignificantly lower than 10-4 (remember the rate ofinterconversion is 5.64 x 10-4)

A plot of ∆CH contours determined at 100% reaction as afunction of k21 and k34 when k23 = k32 = 5.64 x 10-4 (Seemanand Farone, 1978)

Furthermore, the relationship between k23 (k23=k32) andk21 (or k34) is linear for a given ∆CH as shown below

A similar deviation from Curtin-Hammett kinetics will beobtained for a set of rate constants having the samerelative magnitudes proportional to one another


Due to this uniformity, the following general statementcan be made: “…when the rate of reaction from the lessstable of the two isomers (A2 or A3) is greater than 0.1times as fast as the rate of conversion of that compound toits isomer the C-H/W-H kinetics will not approximate theactual chemistry observed.” - Seeman and Farone, 1978 Andraos shows that quantification of a system can be

experimentally more simple Consider the following the following scheme

Simply stated: You need at least one order of magnitudedifference between your slow and fast steps

Exact analytical treatments have not been widely usedby synthetic or mechanistic chemists

Andraos

Let us define X and Y as enantiomers or some otherisomeric substance which can be partitioned Andraos defines [X], [Y], [Px], and [Py] using the Laplacetransform method (see Andraos, 2003)

X YPx Pyk3 k4k1

k2

If k34 > 0.1k32 then not Curtin-Hammett

If the system is truly dynamic, the product ratio should bedescribed by some function of the initial substrateconcentrations and associated rate constants

The Andraos Method

Step 1: For a system in which first-order or psuedo-firstorder kinetics are observed, determine the product ratio forvarious initial concentrations of two enantiomers (orisomers)

[Px]!

[Py]!= "

k3

k4

#

$ %

&

' (

Last topic: An easier way to quantify the dynamic natureof your system and determine K, k34/k21


Step 2: Plot the final product excess as a function of initialsubstrate excess (each with respect to X)

k1

k3=1

2

1! interceptslope

!1"

# $

%

& '

k2

k3=1k4

2k3

1+ intercept

slope!1

"

# $

%

& '

[Px]0

[Py]0= intercept + slope

[X ]0

[Y ]0

!

" #

$

% &

k3

k4

= slope

Step 3: Plot the initial product ratio as a function of initialsubstrate ratio and determine the slope

Step 4: Use the following equations to determine the variousrate constant ratios

K =k1

k2

=

k1

k3

k2

k3

Simply by acquiring the kinetic data for an array of startingmaterial compositions, all relevant rate constant ratios havebeen determined

The Curtin-Hammett principle refers to product ratio whileWinstein-Holness equation refers to reaction rates

It is dangerous to equate product distribution withequilibrium conformer (or isomer) distribution

Brief Conclusion

[A4]

[A1]

= Kk34

k21

kWH

=k21

+ Kk34

K + 1

This graph shows how far the system under scrutiny hasdeviated from the ideal Curtin-Hammett condition

References

Seeman, J. Chem. Rev. 1983, 83, 83. Sachse, H. Chem. Ber. 1890, 12, 1363. Mohr, E. J. Prakt. Chem. 1918, 98, 315. Dickinson, R. G.; Bilicke, C. J. Am. Chem. Soc. 1928, 50, 764. Eliel, E. L. J. Chem. Ed. 1975, 52, 762. Pollak, P. I.; Curtin, D. Y. J. Am. Chem. Soc. 1950, 72, 961. Seeman, J. J. Chem. Ed. 1986, 63, 42. McKenna, J. Tetrahedron. 1974, 30, 1555. Booth, H.; Little, J. H. J. Chem. Soc. Perkin II. 1972, 1848. White, B. H.; Snapper, M. L. J. Am. Chem. Soc. 2003, 125, 14901. Lewis, F. D.; Johnson, R. W. J. Am. Chem. Soc. 1972, 94, 8914. Barton, D. H. Experentia, Suppl. 1955, 121. Solladié-Cavallo, A.; Solladié, G. 1972, 41,4237. Winstein, S.; Holness, N. J. J. Am. Chem. Soc. 1955, 77, 5562. Roth, M.; Wolfgang, D.; Giese, B. Tet. Lett. 1996, 37, 351. Eliel, E. L. Experentia. 1953, 9, 91. Eliel, E. L. J. Am. Chem. Soc. 1957, 79, 5986. Andraos, J. Chem. Educator. 2008, 13, 170. Acree, S.F. Am. Chem. J. 1907, 38, 1-91. Seeman, J. I.; Secor, H. V.; Hartung, H.; Galzerano, R. J. Am. Chem. Soc. 1980, 102, 7741. Evans, D. A.; Tedrow, J. S.; Shaw, J. T.; Downey, C. W. J. Am. Chem. Soc. 2002, 124, 392. Evans, D. A.; Downey, W. C.; Shaw, J. T.; Tedrow, J. S. Org. Lett. 2002, 4, 1127. Newhouse, T.; Lewis, C. A.; Baran, P. S. J. Am. Chem. Soc. 2009, 131, 6360. Chisholm, J. D.; Van Vranken, D. L. J. Org. Chem. 2000, 65, 7541. Pirrung, M. C.; Brown, W. L.; Rege, S.; Laughton, P. J. Am. Chem. Soc. 1991, 113, 8562. Zefirov, N. S. Tetrahedron. 1977, 33, 2719. Seeman, J. I.; Farone, W. A. J. Org. Chem. 1978, 43, 1854. Andraos, J. J. Phys. Chem. A. 2003, 107, 2374.

Documents

The Curtin-Hammett Principle and the Winstein …evans.rc.fas.harvard.edu/pdf/smnr_2009_Wzorek_Joseph.pdfThe Curtin-Hammett Principle and the Winstein-Holness Equation Joseph Wzorek