Energy Surfaces and Kinetic AnalysesChapter 7

Chapters 7 and 8: learning tools to use deciphering reaction mechanisms-> a mechanism can never really be proven.

7.1 Energy surfaces and related conceptsKinetics of a reaction: determine how quickly product forms as a function of concentrations,

temperature, and other variables. -> goal is to relate experimental observations to molecular scale concepts, such as molecular motions, molecular collisions, and molecular vibrations, as well as energy concepts such as free energy, enthalpy, and entropy.

Reaction dynamics: the molecular scale analysis of reaction rates.When we are talking about individual (or small groups of) molecules traversing a well-defined

surface, we will tend to call such analyses “dynamics studies”.Discussion of macroscopic measurements of real reacting systems will be termed “kinetics”.

7.1.1 Energy surface

7.1.2 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.

7.1.4 Rates and rate constants

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

7.1.5 Reaction order and rate laws

Rate constant (k): a proportionality constant between concentration of reactantsand 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 reactionElementary 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

7.2 Transition state theory and related topics7.2.1 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]++ ++

ΔG = ΔH - TΔS = -RTnK++ ++ ++

++

rate = κkBT

h

K = e -ΔG /RT++++

e -ΔG /RT++

[A][B] κ: transmission coefficient ~ 1kB: Boltzmann constant h: Planck’s constantT: absolute temperatureκkBT

he -ΔG /RT

++ k =

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

= k [A][B]

κkBTh

e -ΔG /RT++

k =

κkBTh

e -ΔH /RT++

= eΔS /R

κkBh e -ΔH /RT

++ = eΔS /R

++

++ T

e -ΔH /RT++

= TC C = κkBh

eΔS /R++

7.2.2 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 ΔG‡ 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.

7.2.3 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

7.2.5 Experimental determinations of activation parameters and Arrhenius parameters

Arrhenius equation

Eyring equation

T -> k --- ΔH‡, ΔS‡, ΔG‡

7.2.6 Examples of activation parameters and their interpretations

+

Gas phase ΔH‡ = 15.5 kcal/molΔS‡ = -34 eu

N N BuBu 2 Bu + N2

Gas phase ΔH‡ = 52 kcal/molΔS‡ = 19 eu

ΔH‡ : the latter > the formerwhy? the former; concerted reaction -> bond making accompanies bond breakingΔS‡ : 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

ΔS‡ = -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 ΔG‡

-> decrease in the rate constantby a factor of 500,000, relative

to a reaction with a ΔS‡ = 0

7.3 Postulates and principles related to kinetic analysis

7.3.1 Hammond postulateTransition 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 postulate이런경우도있다. 그러나대부분의경우7.9와같은 reaction coordinates를갖는다

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

7.3.2 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

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

κkBTh

e -ΔG1 /RT++

κkBTh

e –ΔG2 /RT++

= x e –(-ΔGo /RT)

ΔGo

ΔG1 ΔG2++ ++

= e (-ΔG1 + ΔG2 + ΔGo)/RT++

++

ΔG1 , ΔG2 >> ΔGo very rapid equilibrium++ ++

= e (-ΔG1 + ΔG2 )/RT++

++

Br

H3C H

H

CH3H

Br

H CH3

H

CH3H

anti elimination

anti elimination

-OEt

H3C

CH3

H3C CH3

-OEt

59%

20%

(21%)

7.3.5 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 EtOHWeak base, thermodynamic control-> thermodynamic enolates

LDA

NaOH

O

LDAO-

HH

less hindered proteon

more hinderedproteon

less stable enolate

major

no equilibrium

NaOH

O-

more stable enolate

O

O-

less stable enolate

-H++H+ -H+

+H+

7.4.2 Kinetic analyses for simple mechanisms

7.4 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

ii가 rds에관여하지않는다.-> Support a rate-determining unimoleculardecomposition 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

7.5.1 Steady state kinetics

7.5 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 reactionsince 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

kcatE·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]0Km << [S]

1/rate

1/[S]

1/Vmax

slope = Km/Vmax

Lineweaver-Burk plot

각 substrate 농도에따른 initial rate 측정 (실험) 계산

Vmax

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

2. Km : apparent dissociation constant that may be treated as the overall dissociation constants

of all enzyme-bound species.

B에대하여 zero order kinetics

7.6.1 Reactions with half-lives greater than a few seconds

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

7.6.2 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 photolysisPulse radiolysis