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ChE 452 Lecture 21 Potential Energy Surfaces 1
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Last Time Collision Theory Assumes reactions occur whenever reactants collide Key equations 2
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Preexponentials Really Used By The Same Order As Collision Theory? 3
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Comparisons Between Collision Theory And Experiments 4
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Why Does Collision Theory Fail For Reaction 7.30? 5 Reaction 7.30 requires a special collision geometry: (7.33) (7.34)
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Next Few Lectures Will Cover Conventional Transition State Theory Model reaction as motion over a potential energy surface Use stat mech to estimate key terms 6 Figure 7.5 Polanyi’s picture of excited molecules.
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Objective For Today Overview of Potential Energy Surfaces What do they look like How to interpret the plots How to interpret motion 7
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Figure 7.6 PE Surface For H + C 2 H 6 → H 2 + C 2 H 5 8
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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+C 2 H 6 H 2 + C 2 H 5, 27 degrees of freedom since 9 atoms 3 translations 3 rotations, 21 others 9
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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
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Simplified Potential Energy Surfaces Simplified example: analytical PE surface 11 Energy AB Bond Length BC Bond Length
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PE Surface 12 Spreadsheet
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Numerical Values 13 Saddle Point Spreadsheet
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Top View 14 A+BC AB + C Saddle Point AB Distance BC Distance Reactants Products Spreadsheet
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Barrierless Reaction 15 Spreadsheet
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Barrierless Reaction 16 Spreadsheet
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Attractive Interaction 17 Spreadsheet
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PE With Van der Waals Well 18 Spreadsheet
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PE For Series Reactions 19 Spreadsheet
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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
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Ne-Ne Interaction 21 Ne Separated Neons Ne-Ne Collision Ne Anti- Bonding
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Ne-Ne Potential 22
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F-F interaction 23 F F FF Separated Fluorines F 2 Pure Quantum Effect
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F-F Potential 24
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Morse Potential 25 V(r)=W(exp(-2x(r-r o )-2exp(-x(r-r o ))) Wherew=bond energy r=distance between atoms r o =Equilibrium distance X=range parameter
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Cl + F 2 Interaction 26 F During Reaction Separated Reactants F F Fluorine-Fluorine Bond Cl Non-bonding Lobe Cl F Fluorine-Fluorine Bond Non-bonding Lobe
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Cl + F 2 Potential 27
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Interaction During H + C 2 H 6 →C H 4 + CH 3 28
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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 Variant v = 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 + w v = 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)) Then v = 20 + Abs(hr) End If End Function
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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
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Question What did you learn new in this lecture? 31
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