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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
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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.
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Fails for 4 Center Reactions
4
H2
D2
HD HD
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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
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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
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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
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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
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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 =( )+( )( )) -
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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
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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
*
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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
*
*
* *
*
*
* *
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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
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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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