che 553 lecture 24 theory of activation barriers 1
DESCRIPTION
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. 3TRANSCRIPT
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
14
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
15
H2
D2
HD HD
Can Reaction Occur?
16
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
17
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
18
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
19
Polanyi’s Model:Consider a proton transfer reaction (assume
bond stretching controls):
20
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
21
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
22
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
23
E =Sl Sl
Sl Slr r +
SlSl Sl
Ha1 2
1 22
1
1 2r
1
(10.11)
Put In Standard Form
Defining
Yields
24
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)
25
-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
26
-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
27
-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
28
-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
29
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
30
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
31
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
32