ChE 452 Lecture 16 Quantum Effects In Activation Barriers

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Last Time Three Models

Polayni’s model: Marcus equation:

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E = E + Ha ao

P r E 1H

4EEA

r

a0

2

a0

(10.14)(10.33)

BM

E

0 When H E

w + 0.5 H V - 2w H

V 4 w + HWhen -1 H E

H When H E

a

r Ao

O r P O r2

P O2

rr A

o

r r Ao

/

/

/

4 1

4 1

4 1

2 2

Works Most Of The Time

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-100 -50 0 50 1000-20

0

20

40

60

80

100

Heat Of Reaction, kcal/mole

Act

ivat

ion

Bar

rier,

kca

l/mol

e

Marcus

Blowers Masel

Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR1 RH + R1 with wO = 100 kcal/mole and EA

O = 10 kcal/mole.

Fails for 4 Center Reactions

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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

Quantum Effects Control Chemical Processes

Consider 2 hydrogen atoms coming together – can a bond form?

Classical result: Nuclei repel each other Electrons repel each other Electron-nuclei attraction

Classically no bond can form

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Slight net repulsion

Quantum Effects Allow Bonds To Form

Wavefunctions are “antisymmetric” Electrons rapidly exchange (i.e switch places) When exchange happens the sign of the

wavefunction changes Leads to a cancelation of the couloumb

repulsion The net result is that two electrons in the

same orbital with the opposite spin do not repel!

The absence of repulsion allows bonds to form

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Implications

All chemistry is quantum We would not be alive without

quantum

Electron-electron repulsions during reactions can be reduced via exchange That is why I called it a “Pauli repulsion” Need way to compute the result

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Quantum Methods For Reaction Rates

Solve schroedinger equation

(11.39)

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H r,R r,R E r,R

Approximation To Solve Schroedinger Equation

Hartree Fock (HF) Approximation Treat each electron as though it moves

independently of all others (i.e. In the average field of all others)

Configuration Interaction (CI) Consider how motion of each electron

affects the motion of all of the other electrons

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Hartree Fock Approximation

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321Hf∀=′

HF′

∀

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= Wavefunction for molecule

= Antisymmenizer

… One electron wavefunctions

Solution Of HF Equation For Stationary Atoms

Kinetic Energy Electron-Electron

of Electrons Repulsions Electron Core Exchange

EnergyAttraction

Exchange energy: Extra energy term that eliminates electron-electron repulsion when electrons pair up in a bond.

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(E =( )+( )( )) -

Correlation Energy Missing From Hartee Fock

Physics: When electron atom moves into an area others move out of the way.

Leads to a lowering of electron-electron repulsion.

Correlation Energy – Lowers the total energy.

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How big is the correlation energy

Methodology: Used a program called Gaussian to calculate the Hartree fock and approximate correlation energy for the electrons in ethane

Result: HF energy= -49885. kcal/moleCorrelation energy = -168.5 kcal/mol

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Conservation Of Orbital Symmetry

Signs of orbitals, electron spins, do not change during normal chemical reactions Can switch in light

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Reactants ComeTogether,NonbondingLobe Distorts

TransitionState

H CC

Separated Reactants

H CH CH 33

Non-bonding Lobes

C-C bond

Rea

ctio

n P

rogr

ess

Bonds Break:

New BondsForm

Products

CH3 4

CH

ReactantsBegin ToSeparate

NonbondingLobe PushsInto C-C Bond

Formulation In terms Of MO’s Of The System

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H H

D D

H H

D D

H H

D D

1

2

1

2

1

2

Molecular Orbitals At The Transition State

H H H H H H H H

D D D D D D D D

* * *

1

2

1

2

1

2

1

2

*

Correlation Diagram

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H H H H H H H H

D D D D D D D D

* * *

1

2

1

2

1

2

1

2

*

Ene

rgy

Reactants

ReactionCoordinate

Products

*

*

* *

*

*

* *

Other Cases

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Figure 10.34 Configuration mixing diagram for a) NaClNaCl b) conversion of cis-butene to trans-2-butene.

[Na Cl ]

[Na Cl ]-+

Ene

rgy

Reactants

ReactionCoordinate

Products

[Na Cl ]

[Na Cl ]-+

Reactants

ReactionCoordinate

Products

[ 2 ]

[ * ]

[ ]

[ * ]( )2

*

triplet

singlet

[ 2 ]

[ * ]

[ ]

[ * ]( )2

*

triplet

singlet

ba

Conclusion

Quantum Effects Matter To Chemical reactions No chemical bonds without quantum

Main effects seen in correlation diagrams Bond breaking because bonds cannot

move smoothly from reactants to products

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Query

What did you learn new in this lecture?

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