che 553 lecture 25 theory of activation barriers 1
TRANSCRIPT
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ChE 553 Lecture 25 Theory Of Activation
Barriers
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Objective
• Describe more quantitative models of activation barriers– Marcus– Blowers-Masel
• Show one can get reasonable estimates of activation barriers
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Review: 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.
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Polayni’s Model
• Assumptions– Bond stretching dominates– Ignore Pauli repulsions, quantum effects– Linearize energy vs bond stretch
• Result Ea varies linearly with heat of reaction
– Only fair approximation to data
4
E = E + Ha ao
P r
-2.4 -4.8 -7.2 -9.6
-6
-4
-2
0
2
Lo
g kac
, kcal/molerH
MarcusEquation
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Seminov Approximation: Use Multiple Lines
5
-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.
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Marcus Model
• Assumptions– Bond stretching dominates– Ignore Pauli repulsions, quantum effects– Parabolic energy vs bond stretch
• Prediction
6
E 1H
4EEA
r
a0
2
a0
-2.4 -4.8 -7.2 -9.6
-6
-4
-2
0
2
Log kac
, kcal/molerH
MarcusEquation
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Derivation: Fit Potentials To Parabolas Not Lines
7
Figure 10.13 An approximation to the change in the potential energy surface which occurs when Hr changes.
Ener
gy
rX
E a
ApproximationActual
Potential
r1
r2
E1
E2
Eleft E
right
1
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Derivation
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Figure 10.13 An approximation to the change in the potential energy surface which occurs when Hr changes.
Ene
rgy
rX
E a
ApproximationActual
Potential
r1
r2
E1
E2
Eleft
Eright
1
E (r ) SS (r r ) Eleft X 1 X 1
21
(10.21)
E (r ) SS (r r ) H Eright X 2 X 22
r 2
(10.22)
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Solving
9
r22
2
‡
212
1‡
1H+E+)r(rSS=E+)r(rSS
SS SS1 2
Result
E 1H
4EE wA
r
a0
2
a0
r
(10.23)
(10.24)
(10.31)
E 1H
4EEA
r
a0
2
a0
(10.33)
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Qualitative Features Of The Marcus Equation
10
-2.4 -4.8 -7.2 -9.6
-6
-4
-2
0
2L
og k
ac
, 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.
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Marcus Is Great For Unimolecular Reactions
11
0 50 100 150 200 250
rate
, sec-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
Figure 10.17 The activation energy for intramolecular electron transfer across a spacer molecule plotted as a function of the heat of reaction. Data of Miller et. al., J. Am. Chem. Soc., 106 (1984) 3047.
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Marcus Not As Good For Bimolecular Reactions
12
-25 0 25 50 75 100 125
rate
, lit
mol s
ec
-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
-1
Figure 10.18 The activation energy for florescence quenching of a series of molecules in acetonitrite plotted as a function of the heat of reaction. Data of Rehm et. al., Israel J. Chem. 8 (1970) 259.
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Comparison To Wider Bimolecular Data Set
13
-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 = 10 kcal/mole.
EAO
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Why Inverted Behavior?
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rAB
rAB
rAB
E =0aEa
Medium distance Smaller Distance
InvertedRegion
Even Smaller Distance
At small distances bonds need to stretch to to TS.
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Limitations Of The Marcus Equation
• Assumes that the bond distances in the molecule at the transition state does not change as the heat of reaction changes– Good assumption for
unimolecular reactions – In bimolecular reactions
bonds can stretch to lower barriers
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rAB
rAB
rAB
E =0aEa
Medium distance Smaller Distance
InvertedRegion
Even Smaller Distance
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Explains Why Marcus Better For Unimolecular Than Bimolecular
16
-25 0 25 50 75 100 125
rate
, lit
mol s
ec
-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
-1
0 50 100 150 200 250
rate
, sec-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
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Blowers-Masel Equation
• Assumptions– Bimolecular reaction– Pauli repulsions important– Include bond stretching but ignore quantum
limitations
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Blowers-Masel Derivation
• Fit potential energy surface to empirical equation.
• Solve for saddle point energy.
• Only valid for bimolecular reaction.
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V E E VCC CH CC CC CH CH Pauli ,
(10.52)
V , w exp ( ) 1 1 w
w exp ( ) 1 1
V exp
CC CH CC CC CC CCe 2
CC
CH CH CH CHe 2
O CC CC CH CH
(10.56)
Blowers-Masel Derivation
Approximate VE by:
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Plot Of Potential
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C-C distance, Angstroms
C-C
dis
tan
ce,
An
gstr
om
s
Figure 10.28 A potential energy surface calculated from equation (10.59) with wCC = 95 kcal/mole, wCH = 104 kcal/mole,
VP = 300 kcal/mole, qCC = 0.7, qCH = 0.5.
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Derive Analytical Expression
21
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
w w wO CC CH / 2
Bond energies(10.63)
(10.64)
V ww E
w EP O
O AO
O AO
2
(10.65)
Only parameter
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Comparison To Experiments
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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 = 10 kcal/mole.
EAO
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Comparison Of Methods
23
-100 -50 0 50 1000
0
50
100A
ctiv
atio
n E
nerg
y ,
kca
l/mole
Heat of Reaction, Kcal/mole
Blowers Masel
Marcus
Polanyi
Blowers Masel
MarcusPolanyi
Figure 10.32 A comparison of the Marcus Equation, The Polanyi relationship and the Blowers Masel approximation for =9 kcal/mole and wO = 120 kcal/mole.
Ea
o
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Example: Activation Barriers Via The Blowers-Masel Approximation
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Use a) the Blowers-Masel approximation b) the Marcus equation to estimate the activation barrier for the reaction H + CH3CH3 H2 + CH2CH3
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Solution: Step 1 Calculate VP
VP is given by:
25
V ww E
w EP o
o A
o A
2
0
0
(11.F.2)
Where EA0 is the intrinsic barrier given in
Table 11.3. According to table 11.3 EA0=10
kcal/mole. One could calculate a value of wo from data in the CRC. However, I decided to assume a typical value for a C-H bond, i.e. 100 kcal/mole. I choose H r=-2 kcal/mole from example 11.C
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Step 1 Continued
Substituting into equation (11.F.2) shows
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V kcal molekcal mole kcal mole
kcal mole kcal molekcal moleP
2 100
100 10
100 10244 4/
/ /
/ /. /
(11.F.3)
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Step 2: Plug Into Equation 11.F.1
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E mole mole
mole mole mole
w Hmolea
p o r
100kcal 0.5 2kcal
244.4kcal 2 100kcal 2kcal
49.0Kcal
2
2 2 2/ * // / /
(V )/
(11.F.1)
E w HV w H
V w Ha o r
p o r
p o r
0 5
2
4
2
2 2 2. *
( )
By comparison the experimental value from Westley is 9.6 kcal/mole.
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Solve Via The Marcus Equation:
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E EH
Ea A
A
0
0
2
14
From the data above EA0 =10 kcal/mole,
H r =-2 kcal/mole. Plugging into equation (11.F.4)
E kcal mole
kcal mole
kcal molekcal molea
10 1
2
4 109 0
2
//
/. /
which is the same as the Blowers-Masel approximation.
(11.F.4)
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Limitation Of The Model: Quantum Effects:
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Figure 10.39 A hypothetical four-centered mechanism for H2/D2 exchange. The
dotted lines in the figure denotes mirror planes which are preserved during the reaction (see the text). This reaction is symmetry forbidden.
Note one electron has to be spin up and spin down at the same time.
H H
D D
H H
D D
H H
D D
1
2
1
2
1
2
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Consider H2 + D2 2 HD
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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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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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Orbital 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
*
Figure 10.40 A schematic of the key molecular orbitals for the transition state of reaction (10.92). Positive atomic orbitals are depicted as open circles, negative orbitals are depicted as shaded circles. Symmetry forbidden reactions Woodward hoffman rules
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Summary
• Bonds need to stretch or distort during reaction. It costs energy to stretch or distort bonds. Bond stretching and distortion is one of the major causes of barriers to reaction.
• In order to get molecules close enough to react, the molecules need to overcome Pauli repulsions (i.e., electron electron repulsions) and other steric effects. The Pauli repulsions are another major cause of barriers to reaction.
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Summary Continued
• In certain special reactions, there are quantum effects which prevent the bonds in the reactants from converting smoothly from the reactants to the products. Quantum effects can produce extra barriers to reaction.
• There are also a few special cases where the reactants need to be promoted into an excited state before a reaction can occur. The excitation energy provides an additional barrier to reaction.
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Summary Continued
Polayni: linear potential
Marcus: parabolic potential
Blowers-Masel – size of TST varies
Fails with quantum effects ( varies)
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oAE