ChE 452 Lecture 21 Potential Energy Surfaces 1. Last Time Collision Theory Assumes reactions occur...
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Transcript of ChE 452 Lecture 21 Potential Energy Surfaces 1. Last Time Collision Theory Assumes reactions occur...
ChE 452 Lecture 21 Potential Energy Surfaces
1
Last Time Collision Theory Assumes reactions occur whenever
reactants collide Key equations
2
k = v 0 A BC A BCc
(7.26)
v 2.52 10 Åsec
T300K
1AMUABC
131/2
ABC
1/2
(7.29)
Preexponentials Really Used By The Same Order As Collision Theory?
3
Table 7.2 a selection of the preexponentials reported by Wesley [1980]Reaction Preexponential
Å3/molecule SecReaction Preexponential
Å3/molecule SecH+C2H6
C2H5+H2 1.6 1014 O+C2H6 OH+C2H5 2.5 1013
H+CH H2+C 1.1 1012 O+C3H8 (CH3)2CH+OH 1.4 1010
H+CH4 H2+CH3 1 1014 O2+H OH+O 1.5 1014
O+H2 OH+H 1.8 1013 OH+OH H2O+O 1 1013
O+OH O2+H 2.3 1013 OH+CH4 H2O+CH3 5 1013
O+CH4 CH3+OH 2.1 1013 OH+H2CO H2O+HCO 5 1013
O+CH3 H+CH3O 5 1013 OH+CH3
H+CH3O 1 1013
O+HCO H+CO2 5 1012 OH+CH3 H2O+CH2 1 1013
Comparisons Between Collision Theory And Experiments
4
Calculated Preexponential
assuming bcoll=van Der Waals radius
Calculated Preexponential assuming bcoll=covalent radius
Experimental
Å3/molec sec Å3/molec sec Preexponential
6.2 1014 2.0 1014 1.6 1014
4 1014 2.0 1014 1.1 1012
1.9 1014 7.6 1013 2.5 1013
1.25 1014 5.8 1013 1 1013
4.0 1014 2 1014 1.5 1014
Table 7.3 Preexponentials calculated from equation (7.30) for a number of reactions compared to experimental data.
Reaction
25262 HHCHCH
H CH H C2
O C H OH C H2 6 2 5
OH OH H O+O2
H O OH O2
Why Does Collision Theory Fail For Reaction 7.30?
5
Reaction 7.30 requires a special collision geometry:
(7.33)
(7.34)
•
3 2 3 3 3
3 2 3 2 2 3
CH CH CH +O: CH C HCH +•OH (7.32a)CH CH CH +O: CH CH CH +•OH (7.32b)
B
SkConfigurations = e
†
B
ΔSk configurations which lead to reactions e =
average number of configurations of the reactants
Next Few Lectures Will Cover Conventional Transition State Theory
Model reaction as motion over a potential energy surface
Use stat mech to estimate key terms6
Reaction Cordinate
Ene
rgy
ReactantsProducts
Barrier
A‡
Figure 7.5 Polanyi’s picture of excited molecules.
Objective For Today Overview of Potential Energy
Surfaces What do they look like How to interpret the plots How to interpret motion
7
Figure 7.6 PE Surface For H + C2H6 →H2 + C2H5
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1 1.5 2 2.5 3
1
1.5
2
2.5
3
C-H Distance (Angstroms)
*
H-H
DIS
TAN
CE
(AN
GST
RO
MS)
C-H Distance
X
X
Y
Y
transition stateEnergy
H-H
Dist
ance
transition state
Potential Energy Surfaces
Potential energy surface is defined as the energy of the system as a function of the coordinates of all of the atoms in a reaction
Many coordinates: For H+C2H6 H2 + C2H5, 27
degrees of freedom since 9 atoms
3 translations 3 rotations, 21 others
9
C-H DistanceX
Y
Saddle point
Energy
H-H
Dist
ance
Simplified Potential Energy Surfaces
Only consider bonds that break and form
Treat ligands as united atoms For A+BC AB + C, 9 degrees of
freedom since 3 atoms 3 translations 3 rotations, 3
others (AB distance, BC distance and ABC bond angle).
Textbook examples also usually assume that bond angle dependence is small
10
C-H DistanceX
Y
Saddle point
Energy
H-H
Dist
ance
Simplified Potential Energy Surfaces
Simplified example: analytical PE surface
11
1
11
21
31
S1 S4 S7 S10
S13
S16
S19
S22
S25
S28
S31
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Ener
gyAB Bond Length
BC Bond Length
PE Surface
12
1
7
13
19
25
31
37
S1 S3 S5 S7 S9 S11
S13
S15
S17
S19
S21
S23
S25
S27
S29
S31
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Spreadsheet
Numerical Values
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r2\r1 0.5 0.70 0.90 1.10 1.30 1.50 1.70 1.90 2.10 2.30 2.50 2.70 2.90 3.10 3.30 3.50 3.70 3.90 4.10 4.300.5 20.0 20.0 20.0 20.0 20.0 20.0 20.0 19.1 15.5 12.8 10.7 9.1 7.9 7.0 6.3 5.7 5.3 4.9 4.6 4.40.7 20.0 20.0 20.0 20.0 20.0 16.8 12.4 9.2 6.9 5.2 4.0 3.1 2.4 1.9 1.5 1.2 0.9 0.7 0.6 0.50.9 20.0 20.0 20.0 20.0 13.8 9.7 6.9 5.1 3.9 3.1 2.5 2.1 1.8 1.6 1.5 1.4 1.3 1.2 1.2 1.11.1 20.0 20.0 20.0 13.1 8.8 6.3 5.0 4.2 3.8 3.7 3.6 3.6 3.7 3.7 3.8 3.8 3.9 3.9 3.9 4.01.3 20.0 20.0 13.8 8.8 6.3 5.2 4.9 5.0 5.2 5.6 6.0 6.3 6.6 6.8 7.0 7.2 7.4 7.5 7.6 7.61.5 20.0 16.8 9.7 6.3 5.2 5.1 5.7 6.4 7.2 8.0 8.7 9.3 9.8 10.2 10.5 10.8 11.0 11.2 11.3 11.41.7 20.0 12.4 6.9 5.0 4.9 5.7 6.9 8.1 9.4 10.4 11.4 12.2 12.8 13.3 13.8 14.1 14.4 14.6 14.8 14.91.9 19.1 9.2 5.1 4.2 5.0 6.4 8.1 9.8 11.4 12.7 13.8 14.8 15.6 16.2 16.7 17.1 17.4 17.7 17.9 18.02.1 15.5 6.9 3.9 3.8 5.2 7.2 9.4 11.4 13.2 14.7 16.0 17.0 17.9 18.6 19.2 19.6 20.0 20.0 20.0 20.02.3 12.8 5.2 3.1 3.7 5.6 8.0 10.4 12.7 14.7 16.4 17.8 19.0 19.9 20.0 20.0 20.0 20.0 20.0 20.0 20.02.5 10.7 4.0 2.5 3.6 6.0 8.7 11.4 13.8 16.0 17.8 19.3 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.02.7 9.1 3.1 2.1 3.6 6.3 9.3 12.2 14.8 17.0 19.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.02.9 7.9 2.4 1.8 3.7 6.6 9.8 12.8 15.6 17.9 19.9 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.03.1 7.0 1.9 1.6 3.7 6.8 10.2 13.3 16.2 18.6 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.03.3 6.3 1.5 1.5 3.8 7.0 10.5 13.8 16.7 19.2 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.03.5 5.7 1.2 1.4 3.8 7.2 10.8 14.1 17.1 19.6 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.03.7 5.3 0.9 1.3 3.9 7.4 11.0 14.4 17.4 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.03.9 4.9 0.7 1.2 3.9 7.5 11.2 14.6 17.7 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.04.1 4.6 0.6 1.2 3.9 7.6 11.3 14.8 17.9 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0
Saddle Point
Spreadsheet
Top View
14
A+BC AB + C1 4 7 10 13 16 19 22 25 28 31 34 37
S1
S4
S7
S10
S13
S16
S19
S22
S25
S28
S31
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Saddle Point
AB Distance
BC D
istan
ce
Reactants
Prod
ucts
Spreadsheet
Barrierless Reaction
15
1
12
23
34
S1 S4 S7 S10
S13
S16
S19
S22
S25
S28
S31
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Spreadsheet
Barrierless Reaction
16
1 4 7 10 13 16 19 22 25 28 31 34 37
S1
S4
S7
S10
S13
S16
S19
S22
S25
S28
S31-2
.00.
02.
04.
06.
08.
010
.012
.014
.016
.018
.020
.0
Spreadsheet
Attractive Interaction
17
1 4 7 10 13 16 19 22 25 28 31 34 37
S1
S4
S7
S10
S13
S16
S19
S22
S25
S28
S31-1
8.0
-16.
0-1
4.0
-12.
0-1
0.0
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Well
Spreadsheet
PE With Van der Waals Well
18
1 4 7 10 13 16 19 22 25 28 31 34 37
S1
S4
S7
S10
S13
S16
S19
S22
S25
S28
S31-4
.0-2
.00.
02.
04.
06.
08.
010
.012
.014
.016
.018
.020
.0
SaddlePoint
Complex
Complex
Spreadsheet
PE For Series Reactions
19
1 4 7 10 13 16 19 22 25 28 31 34 37
S1
S4
S7
S10
S13
S16
S19
S22
S25
S28
S31
-12.
0-1
0.0
-8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
SaddlePoint
Intermediate
SaddlePoint
Spreadsheet
Why Do Plots Look The Way They Do?
Balance between attractive forces and Pauli repulsions
Attractive forces Van der Waals Interactions (Correlation) Bond formation
Repulsive forces Pauli repulsions (quantized electron-
electron repulsions)
20
Ne-Ne Interaction
21
Ne
Ne
Ne
Ne
Separated Neons
Ne-NeCollision
Ne Ne
Anti-Bonding
Bonding
Ne-Ne Potential
22
0 1 2 3 4 5Distance Angstroms
-150
-100
-50
0
50
100E
nerg
y. K
cal/m
ol
-15
-10
-5
0
5
10
Ene
rgy,
Kca
l/mol
e
F
2
2
Ne
F-F interaction
23
F F
F F
Separated Fluorines
F2
Pure Quantum Effect
F-F Potential
24
0 1 2 3 4 5Distance Angstroms
-150
-100
-50
0
50
100
Ene
rgy.
Kca
l/mol
-15
-10
-5
0
5
10
Ene
rgy,
Kca
l/mol
e
F
2
2
Ne
Morse Potential
25
V(r)=W(exp(-2x(r-ro)-2exp(-x(r-ro)))
Wherew=bond energyr=distance between atomsro=Equilibrium distanceX=range parameter
0 1 2 3 4 5Distance Angstroms
-150
-100
-50
0
50
100
Ene
rgy.
Kca
l/mol
-15
-10
-5
0
5
10
Ene
rgy,
Kca
l/mol
e
F
2
2
Ne
Cl + F2 Interaction
26
F
During Reaction
SeparatedReactants
F
F
Fluorine-Fluorine Bond
ClNon-bonding Lobe
Cl F
Fluorine-Fluorine Bond
Non-bonding Lobe
Cl + F2 Potential
27
FF
RClF
R
Energy
Interaction During H + C2H6 →CH4 + CH3
28
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
Analytical PE Surface
29
Table 7.G.1 The module used to calculate the function in equation 7.G.1
Public Function v(r1, r2, r0, a, w, vp, wa, hr) As Variantv = w * (Exp(-2 * a * (r1 - r0)) - 2 * Exp(-a * (r1 - r0)))v = v + (w + hr) * (Exp(-2 * a * (r2 - r0)) - 2 * Exp(-a * (r2 - r0)))v = v + vp * Exp(-a * (r1 + r2 - 2 * r0))v = v + wv = v + wa * Exp(-4 * a * a * ((r1 - r0) ^ 2 + (r2 - 3 * r0) ^ 2))v = v + wa * Exp(-4 * a * a * (((r1 - 3 * r0) ^ 2) + ((r2 - r0) ^ 2)))If (v > 20 + Abs(hr)) Thenv = 20 + Abs(hr)End IfEnd Function
Summary PE surface plot of energy vs internal
coordinates of reactive complex. Attractive interaction due to bonding
and Van der Waals. Repulsions due to Pauli repulsions
(quantized electron-electron repulsions).
Net yields saddle point if reaction not too exothermic.
30
Question What did you learn new in this
lecture?
31