ChE 553 Lecture 24Theory Of Activation

Barriers

1

New Topic• Why do we get activation barriers• How can one manipulate activation

barriers

2

Key Concept: Barriers To Reaction Are Caused By

• Uphill reactions• Bond stretching and distortion.• Orbital distortion due to Pauli

repulsions.• Quantum effects.• Special reactivity of excited states.

3

Plan for Today• Describe each of the effects

• Start to develop models

4

Qualitative Picture Of Free Energy Changes During A Reaction

5

Free

ene

rgy,

kca

l/mol

e of

bro

min

e at

oms

-50

0

50

1/2Br2

Br

H+HBr

Br+2HBr

1/2 Br2+2HBr

Reaction Progress

Gas Phase

+H2

+Br2 H2 + Br2 2HBr

Barrier since uphill

Extra barrier due to orbital distortions

This Case Has Two Key Effects

• Uphill reactions• Orbital distortion due to Pauli repulsions• Bond stretching and distortion• Quantum effects• Special reactivity of excited states

6

Uphill Reactions Obvious

7

Free

ene

rgy,

kca

l/mol

e of

bro

min

e at

oms

-50

0

50

1/2Br2

Br

H+HBr

Br+2HBr

1/2 Br2+2HBr

Reaction Progress

Gas Phase

+H2

+Br2 H2 + Br2 2HBr

Barrier since uphill

Extra barrier due to orbital distortions

Dominant cause of barriers in bond scission (SN1) reactions

Bond Stretching And Distortion

• Bonds bend and stretch as reactions occur

• Bond distortion costs energy – leads to barrier

8

H-NC H\NC NC-H

Dominant cause of barriers in unimolecular reactions

Orbital Distortion• Orbitals distort as reactions occur due

to Pauli repulsions• Leads to barriers

9

Dominant cause of barriers in exothermic atom and ligand transfer (SN2) reactions

Orbital Notation

10

Positive orbital

Negative orbital

Orbital Distortions D + H2 HD+ H

11

Reactants ComeTogether,H-H BondDistorts

TransitionState

Separated Reactants

HD

C-H bond

Rea

ctio

n P

rogr

ess

ProductsD

Incoming DeuteriumPushes H-H Bond Off Of Hydrogen

HydrogenMoves Out Of H-HBond and IntoD-H Bond

D

H

HD

H

D

H

H

Notice that the shading of the bond is preserved

Orbital Distortions H + C2H6 H2+ C2H5

12

Reactants ComeTogether,C-H BondDistorts

TransitionState

HCC

Separated Reactants

H

C-H bond

Rea

ctio

n P

rogr

ess

Products

2

H

HH

Incoming HydrogenPushes CH Bond Off Of Methyl-Hydrogen

HH

H

Methyl HydrogenMoves Out Of C-HBond and IntoH-H Bond

H

H

H

CH CH3 2CH CH3 3

Orbital Distortions H + C2H6 CH3+ CH4

13

Reactants ComeTogether,NonbondingLobe Distorts

TransitionState

H CC

Separated Reactants

H CH CH 33

Non-bonding LobesC-C bond

Rea

ctio

n P

rogr

ess

Bonds Break:

New BondsForm

Products

CH3 4CH

ReactantsBegin ToSeparate

NonbondingLobe PushsInto C-C Bond

Quantum Effects: Orbital Symmetry Conservation

• Sign of orbital, electron spin does not change during a concerted reaction

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Reactants ComeTogether,NonbondingLobe Distorts

TransitionState

H CC

Separated Reactants

H CH CH 33

Non-bonding LobesC-C bond

Rea

ctio

n P

rogr

ess

Bonds Break:

New BondsForm

Products

CH3 4CH

ReactantsBegin ToSeparate

NonbondingLobe PushsInto C-C Bond

Consider H2 + D2 2 HD

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H2

D2

HD HD

Can Reaction Occur?

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No Net Force To Distort Orbitals

Net Force, but product is HD + H + D (i.e. two atoms)Such a reaction is 104 kcal/mole endothermic

Conservation Of Orbital Symmetry

• Quantum effect leading to activation barriers

• Orbital symmetry/sign conserved during concerted reactions– Sometimes bonds must break before new

bonds can form

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Special Reactivity Of Excited States

• Related Quantum Effect: sometimes only excited states can lead easily to products

3 H + N + X NH3 + X• Ground state of N has only 1 unpaired

electron – not reactive to NH3 formation• Excited state of N has 3 unpaired electrons

– much more reactive

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Surfaces Can Change Each Form Of Barrier

• Change free energy of intermediates• Stretch bonds• Modify electron flow• Ameliorate quantum limitations (one

electron in adsorbate replaced by electron from solid)

• Stabilize excited sites

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Polanyi’s Model:Consider a proton transfer reaction (assume

bond stretching controls):

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Ener

gy

E a

rBH

B RHrBH

rRH

Figure 10.2 The energy changes which occur when a proton H is transferred between a conjugate base B and a reactant R. The solid line is the energy of the B-H bond while the dotted line is the energy of the H-R bond.

Effects Of Changes

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Ener

gy

E a

rBH

B RHr

BHr

RH

Figure 10.3 A diagram illustrating how an upward displacement of the B-H curve affects the activation energy when the B-R distance is fixed.

Ener

gyrBH

B RHrBH rRH

Reactants

Products

Figure 10.4 A diagram illustrating a case where the activation energy is zero.

Derivation Of Polayni Equation

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Ener

gy

rAB

Ea

ActualPotential

LinearFit

Line 1

Line 2r1 r2

BCAB

Figure 10.6 A linear approximation to the Polanyi diagram used to derive equation (10.11).

  

E E + Sl r - r (reactants)1 Reactant 1 ABC 1

E E + Sl r - r (products)2 product 2 2 ABC

(10.9)

(10.10)

Solving For The Intersection Of The Two Lines

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E =Sl Sl

Sl Slr r +

SlSl Sl

Ha1 2

1 22

1

1 2r

1

(10.11)

Put In Standard Form

Defining

Yields

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ESl Sl

Sl Slr ra

o 1 2

1 22 1

P

1

1 2

SlSl Sl

E = E + Ha ao

P r

(10.12) (10.13)

(10.14)

Case Where Polayni Works (Over A limited data set)

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-20 -15 -10 -5 0 5 10 15 20

-20 -15 -10 -5 0 5 10 15 20

0

5

10

15

20

25

, kcal/molerH

, kca

l/mol

eaE

Figure 10.7 A plot of the activation barriers for the reaction R + H R RH + R with R, R = H, CH3, OH plotted as a function of the heat of reaction Hr.

Equation Does Not Work Over Wide Range Of H

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-2.4 -4.8 -7.2 -9.6

-6

-4

-2

0

2Lo

g kac

, kcal/molerH

MarcusEquation

Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977]. Note Ln (kac) is proportional to Ea.

Equation Does Not Work Over A Wide Data Set

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-30 -20 -10 0 10 20 300

-30 -20 -10 0 10 20 300

0

5

10

15

20

25

30

, kcal/molerH

, kca

l/mol

eaE

Figure 10.10 A Polanyi relationship for a series of reactions of the form RH + R R + HR. Data from Roberts and Steel[1994].

Seminov Approximation: Use Multiple Lines

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-40 -20 0 20 400

0

10

20

30

40

Heat Of Reaction, kcal/mole

Act

ivat

ion

Bar

rier,

kcal

/mol

e Seminov

-100 -50 0 50 1000-20

0

20

40

60

80

100

Heat Of Reaction, kcal/moleA

ctiv

atio

n B

arrie

r, kc

al/m

ole Seminov

Figure 11.11 A comparison of the activation energies of a number of hydrogen transfer reactions to those predicted by the Seminov relationships, equations (11.33) and (11.34)

 

Figure 11.12 A comparison of the activation energies of 482 hydrogen transfer reactions to those predicted by the Seminov relationships, over a wider range of energies.

 

Key Prediction Stronger Bonds Are Harder To Break

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Ener

gy

rAB

Weak Bond

rAB

EaEa

Bond E

nergyStrong Bond

Figure 10.8 A schematic of the curve crossing during the destruction of a weak bond and a strong one for the reaction AB + C A + BC.

Experiments Do Not Follow Predicted Trend

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50 60 70 80 90 100 110 12030

35

40

45

50

55

60

65

70

75

, kca

l/mol

eaE

Predicted Trend

Experimental Trend

Figure 10.9 The activation barrier for the reaction X- +CH3X XCH3 +

X-. The numbers are from the calculations of Glukhoustev, Pross and Radam[1995].

Summary: Barriers To Reaction Are Caused By

• Uphill reactions– Dominates for many gas phase SN1 reactions

• Bond stretching and distortion– Dominates for unimolecular reactions

• Orbital distortion due to Pauli repulsions• Quantum effects• Special reactivity of excited states

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Need Models To Quantify Ideas

• Polanyi’s model– Bond stretching dominates– Ignore Pauli repulsions, quantum effects– Linearize energy vs bond stretch

• Ea varies linearly with heat of reaction– Only fair approximation to data

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