Structural Effects on Stability and ReactivityChapter 3

learning tools to use deciphering reaction mechanisms-> a mechanism can never really be proven.

Energy surfaces and related concepts

Energy surface

Reaction coordinate diagrams

Reaction coordinate: the minimum energy pathways, or the pathway we depict as the weighted average of all the pathways

Reaction coordinate diagram

Activation energy

Intermediates: any chemical structures that last longer than the time for a typical bond vibration (10-13 to 10-14 s)

Rate-determining step: the step with the highest barrier.

Rates and rate constants

Rate constant (k): a proportionality constant between concentration of reactants and reaction rate

Reaction order and rate laws

Rate constant (k): a proportionality constant between concentration of reactants and reaction rate

a + b + c = reaction order-> determined by experimental measurements of the rates of reaction: does not give any information about mechanism

Molecularity: the number of molecules involved in the transition state of the reaction Elementary reaction: single-step reaction ( 단일반응 )Unimolecular: only single molecule is involved in the transition state, eg) Cope rearrangement Bimolecular: two molecules are involved in the transition state, eg) SN2 Termolecular: three molecules are involved in the transition state Molecularity applies only to elementary reactions and is basically a statement about the mechanism of the reaction.

Rate law

Transition state theory and related topics

The mathematics of transition state theory: pre-equilibrium between the reactants and activated complex

A + B C

AB++

K = [AB ]

++

++

[A][B]++

A + B [AB ] → C←→

Equilibrium constant of the formation of activated complex

k++

rate =

= k K [A][B]++ ++

G = H - TS = -RTnK++ ++ ++

++

rate = kBT

h

K = e -G /RT++

++

e -G /RT++ [A][B] : transmission coefficient ~ 1

kB: Boltzmann constant h: Planck’s constantT: absolute temperaturekBT

he -G /RT

++

k =

To understand the nature of the rate constant k -> analyze the energetic and entropic components of reaction process

= k [A][B]

kBTh

e -G /RT++

k =

kBTh

e -H /RT++

= eS /R

kB

he -H /RT

++ = eS /R

++

++

T

e -H /RT++

= TC C = kB

heS /R

++

Relationship to the Arrhenius rate law

Arrhenius rate law

A: frequency factor (pre-exponential factor)Ea: activation energyT: absolute temperature

Eyring equation

Eyring equation: analyzes a microscopic rate constant for a single-step conversion of a reactant to a product. In a multistep process involving reactive intermediates, there is an Eyring equation and thus a G‡ for each and every step.

Arrhenius rate law: arises from empirical observations of the macroscopic rate constants for a particular conversion, such as A going to B by various paths. It is ignorant of any mechanistic considerations, such as whether one or more reactive intermediates are involved in the overall conversion of A to B. Ea describes the overall transformation.

Boltzmann distributions and temperature dependence

The higher temperature reaction proceeds faster due to the larger area under the curve past the activation energy

Boltzmann distribution

Experimental determinations of activation parameters and Arrhenius parameters

Arrhenius equation

Eyring equation

T -> k --- H‡, S‡, G‡

Examples of activation parameters and their interpretations

+

Gas phase H‡ = 15.5 kcal/mol S‡ = -34 eu

N N BuBu 2 Bu + N2

Gas phase H‡ = 52 kcal/mol S‡ = 19 eu

H‡ : the latter > the former why? the former; concerted reaction -> bond making accompanies bond breaking S‡ : the latter > the former why? The former -> two molecules become one molecule -> the loss of translational and rotational degrees of freedom the latter -> one molecule becomes three molecules

O O O

Diels-Alder reaction

Claisen rearrangement

S‡ = -8 eu

1, 2, 4, 6-> molecules combine3,5,7-> bond breaking

1; -26 eu -> 26 cal/mol K x 298 K = 7.75 kcal/mol in G‡

-> decrease in the rate constantby a factor of 500,000, relative to a reaction with a S‡ = 0

Postulates and principles related to kinetic analysis

Hammond postulate

Transition states are transient in nature and generally cannot be directly characterized by experimental means.This postulate is likely the most widely used principle for estimating the structures of activated complexes that give us insights into chemical reactivity.; the activated complex most resembles the adjacent reactant, intermediate, or product that it is closest in energy to.

exothermic endothermic

To obey the Hammond postulate

이런 경우도 있다 . 그러나 대부분의 경우7.9 와 같은 reaction coordinates 를 갖는다

The Hammond postulate does not predict the height of the barrier compared to the reactant and product.

The reactivity vs. selectivity principle

The more reactive a compound is, the less selective it will be.

More reactive molecules -> being higher in energy or having more exothermic reactions.

-> the more reactive species will produce a transition state that more resembles the reactant.

Thus, the transition state is not very sensitive to the structure of other components involved

in the reaction, and it is affected little by the structure of the product.

-> If the reaction is not sensitive to the structure of the product, it can not select between different

products and hence is not selective.

Cl· is much more reactive than Br· (H-Cl > H-Br).-> H· abstraction by Cl· is an exothermic reaction-> very little radical character on carbon in TS-> quite indiscriminate about which H is abstracted (chlorination is much less selective than bromination)H· abstraction by Br· is an endothermic reaction -> large radical character on carbon in TS-> H· abstraction by Br· is quite selective

Bond strength

The Curtin-Hammett principleThis principle states that the ratio of products is determined by the relative heights of the highest energy

barriers leading to the different products, and is not significantly influenced by the relative energies of

any isomers, conformers, or intermediates formed prior to the highest energy transition states.

This principle is applicable when the barriers interconverting the different starting points is much lower

than the barriers to form products.

Product ratio = [P1]/[P2] = (d[P1]/dt) / (d[P2]/dt)

= ka[I1]/kb[I2] = (ka / kb) x (1/Keq)

I1 ←→ I2 → P2←P1

Rapidequilibrium

ka kb

Keq

kBTh

e -G1 /RT++

kBTh

e –G2 /RT++

= x e –(-Go /RT)

Go

G1 G2

++

++

= e (-G1 + G2 + Go)/RT++

++

G1 , G2 >> Go very rapid equilibrium

++

++

= e (-G1 + G2 )/RT++

++

Br

H3C H

H

CH3H

Br

H CH3

H

CH3H

anti elimination

anti elimination

-OEt

H3C

CH3

H3C CH3

-OEt

59%

20%

(21%)

Kinetic vs. thermodynamic control

Thermodynamic control: product composition is governed by equilibrium of the system.

Kinetic control: product composition is governed by reaction rate or activation energy.

LDA (lithium diisopropylamide)

Li+ -N(iPr)2 -> strong, sterically hindered base in tetrahydrofuran (THF)

-> kinetic enolates

NaOH in H2O or EtOH

Weak base, thermodynamic control

-> thermodynamic enolates

LDA

NaOH

O

LDA

O-

HH

less hindered proteon

more hindered proteon

less stable enolate

major

no equilibrium

NaOH

O-

more stable enolate

O

O-

less stable enolate

-H++H+ -H+

+H+

Kinetic analyses for simple mechanisms

Kinetic experiments

Goal of kinetics: to establish a quantitative relationship between the concentrations of reactants

and / or products, and the rate of the reactions.

First order kinetics

A -> P

v =

half-life time (t1/2): time required for 50% of the starting material to be consumed

[A] = [A]0/2 -> t1/2

t1/2 =ln2/k = 0.693/k

t

ln[A]slope = -k (1/sec)

- plot of ln[A] vs t will be linear - t1/2 is constant - k should not depend on [A]0

[A]0 = [A] + [P]

Bimolecular reaction

rds

ii 가 rds 에 관여하지 않는다 .-> Support a rate-determining unimolecular decomposition of i to give cyclopentyne

Second order kinetics

A + B -> P

[A]0 = [A] + [P] [B]0 = [B] + [P] [A]- [A]0 = [B] - [B]0

= k[A]([B]0 - [A]0 +[A]) = -d[A]/dt

1

[B]0 - [A]0

ln[A]0([B]0 - [A]0 +[A])

[B]0[A]= kt

no SN2 reaction

Pseudo-first order kinetics

Second order kinetics: too complicating -> Pseudo-first order kinetics

A + B -> P

B -> a large excess (usually 10 equivalents or more) -> [B] will change little during the course of the reaction : [B] ~ [B]0

-> pseudo-first order kinetics

k’ = kobs = k[B]0

t

ln[A]slope = -kobs = -k[B]0

Determination of k

Vary concentration of the excess [B]

[B]

slope = kkobs

kobst

Initial rate kinetics

- In case that the reaction is slow, it is difficult to follow the reaction to several half-lives

in order to obtain a reliable rate constant

- Many reactions start to have significant competing pathways as the reaction proceeds,

causing deviations from the ideal behaviors.

Initial rate kinetics:

only follow the reaction to 5% or 10% completion ([A] ~ [A]0), thereby avoiding complications that may arise later in the reaction and/or allowing us to solve for rate constants in a reasonable time period.-> this approach is inherently less accurate than a full monitoring of a reaction over several half-lives, but often it is the best we can do.

= k[A]0

[P] = k[A]0t

slope = k[A]0

Plotting [P] versus t over the first few percent of the reactiongives a line whose slope is k[A]0

k

Steady state kinetics

Complex reactions – deciphering mechanisms

Most organic, bioorganic, and organometallic mechanisms have more than one step,

and frequently involve reactive intermediates.

-> such mechanisms can produce complex rate laws that are difficult to analyze.

The concentration of the reactive intermediate is constant during the reaction

since the reactive intermediate (short life-time) is not accumulated during the reaction

Steady state approximation (SSA)

A + B -> P

Rate of the formation of I = rate of disappearance of I

Enzyme kinetics: steady state kinetics

E + S E·S P + E←→k1

→k-1

kcat

E·S: Michaelis complex

SE + ←→ → P

E·S

rate = d[P]/dt = kcat[ES]

d[ES]/dt = k1[E][S] – k-1[ES] - kcat[ES] = 0

[E]0 = [E] + [ES]

k1([E]0-[ES])[S] – k-1[ES] - kcat[ES] = 0

[E] = [E]0 - [ES]

[E]0[S]Km = (k-1 + kcat)/k1

[ES] =Km + [S]

rate = d[P]/dt = kcat[ES] = kcat[E]0[S]

Km + [S]Michaelis-Menten equation

Kinetic parameters to be determined for enzymatic reactions: kcat and Km

[S]

rate

rate = kcat[E]0[S]

Km + [S]

1/rate = 1/Vmax + Km/(Vmax [S])

Vmax = kcat[E]0

Km << [S]1/rate

1/[S]

1/Vmax

slope = Km/Vmax

Lineweaver-Burk plot

각 substrate 농도에 따른 initial rate 측정 ( 실험 ) 계산

Vmax

1. kcat: catalytic constant turnover number: the maximum number of substrate molecules converted to products per active site per unit time

2. Km : apparent dissociation constant that may be treated as the overall dissociation constants of all enzyme-bound species.

B 에 대하여 zero order kinetics

Reactions with half-lives greater than a few seconds

Methods for following kinetics

No special technique requirement for generating the reactants and/or mixing the reactants

-> the kinetic analysis can be performed with chromatographic and spectroscopic methods.

Chromatographic analysis : HPLC or GC

Spectroscopic analysis: continuous analysis is possible (UV, fluorescence) or NMR

Fast kinetics

Half-life; a few seconds or less

-> Special technique requirement for generating the reactants and/or mixing the reactants .

Stopped flow analysis

Flash photolysis

Pulse radiolysis

Studies of reaction mechanisms

Isotope effects: important for mechanistic studies

k

m1 m2

Hooke’s law

v = 1/(2 k/

k = force constant = reduced mass, m1m2/(m1 +m2)

E = hv = hc/ = hcvv = wavenumber (cm-1)

vCH

vCD

vCH

vCD

= = kCH/CH

kCD/CD

= CD

CH

kCD ~ kCH

= 24/14

12/13= 1.36

vCD =vCH

1.36= 3000/1.36 ~ 2200 cm-1 (IR spectra)

Vibrational energy level

e0 = hv/2 : zero point energy (ZPE) vCH

vCD= 1.36 e0, CH = 1.36 e0, CD

e0, CH = 18 kJ/mole0, CD = 13 kJ/mol

kH

kD

= e(-G +G )/RT = e5000j/RT = e2.00 = 7.4 at 25 oC 20.2 at -73 oC 1026 at -263 oC

‡ ‡H D

e0, CH = 18 kJ/mole0, CD = 13 kJ/mol

Maximum value

C···H or C···D

In general, kH

kD

<7.5

ZPECH,TS = ZPECD,TS

Primary KIE in case that a bond to the isotopically substituted atom is broken in the rate-determining step

OHO-

Br2

O

Br

O-

Br-Brfast

rds

kH

kD

= 6.1 (25 oC) -> deprotonation is rds

If the second step is rds, what happens?Answer) kH

kD

= 1

kH

kD

= 4.6 (77 oC)

kH

kD

= 1.5 (77 oC)

Product-like TS; large radical character (largely broken) -> large KIE

Reactant-like TS; small radical character (a little broken) -> small KIE

Ph-CH2-HBr2

hvPh-CH2-Br + HBr

Ph-CH2-HCl2

hvPh-CH2-Cl + HCl

Secondary KIE in case that substituted hydrogen atom is not directly involved in the reaction

kH

kD

= 0.7 ~ 1.5

kH

kD

> 1; normal KIEkH

kD

< 1; inverse KIE

PE

Distance (r)rC-D

rC-H

rC-D < rC-H

-effect

sp3 -> sp2 (transition state)

sp2 -> sp3 (transition state)

H (D)

*H H*

*H H*

*H H*

*H H* *H2C CH2*kH

kD

= 1.37 (50 oC)

bond length; sp3 > sp2

C D

C H

C D

C H

sp3 sp2

kH

kD

> 1 (normal KIE)

H*

O

MeO

H*

OH

MeO

NC

HCN H*

OH

MeO

NC

kH

kD

= 0.73 (25 oC)

bond length; sp3 > sp2

kH

kD

< 1 (inverse KIE)C D

C H

C D

C H

sp2 sp3

D-amino acid oxidase

Pathway A: nucleophilic addition to the flavin

sp2 -> sp3 ; expected, inverse KIE

sp2

Pathway B: an electron transfer to the flavin

sp2 -> ~sp2 ; expected, little KIE

kH

kD

= 0.84 large inverse KIE

Support pathway A

-effect H (D)

H (D)

*H3C CH3*

H Br

*H3C CH3*

H OHH2O kH

kD

= 1.31

H*

H*

H*

H*

Br

*H H*

*H H*

H*

H*

H*

Br

*H H*

*H

sp2-like

H*

H*

H*

H*

Br

*H H*

*H

Bond energy; EC-D > EC-H

Why? hyperconjugation

-> the contribution of C-D bond hyperconjugation is smaller than that of C-H.

*H H*H3C Cl

*Hcarbocation -> product

H2O

solvolysis

kH

kD

= 1.14 per D

1

2

1

kH

kD

= 0.99 no KIE2

Orthogonal (no orbital overlap)

Long range KIE

rC-D < rC-H Size: CD3 < CH3

kH

kD

= 0.86

kH

kD

= 1.107

Size: C(CD)3 < C(CH)3

HH

O

*H3C CH3*CH3*

S NO2

O

OH

HO

*H3C CH3*CH3*

S NO2

O

O

Steric hindrance is released by going to TS

Tunneling

Sometimes KIE of 50 or larger are observed for comparisons of H vs D.-> Tunneling is a quantum mechanical phenomenon involving penetration of the wavefunction for the molecule through the barrier for the reaction than over it.-> the tunneling is very sensitive to the mass of the tunneling particle.-> tunneling is usually associated with proton or hydrogen transfers or electron transfers.

kH

kD

= 74

Substituent effects

The origin of substituent effects

Field effects

- is one of that originates from such a through-space interaction- is often very hard to separate from inductive effects

A quaternary ammonium with a full positive charge produces an electric field that can influence distant atoms in the same or neighboring molecules.

Inductive effects- results from the ability of an atom or group of atoms to withdraw or donate electrons through bond.

F; poor at making HBs; but more stable collagen; inductive effects

Resonance effects

- the ability of an atom or group of atoms to withdraw or donate electrons through bonds.

Polarizability effects

- defined as the extent to which the electron cloud of the structure can undergo distortion.

Steric effects

Solvation effects

Field effects, Inductive effects, Resonance effects, Polarizability effects: electronic effects