ChE 452 Lecture 21 Potential Energy Surfaces 1

Last Time Collision Theory Assumes reactions occur whenever reactants collide Key equations 2

Preexponentials Really Used By The Same Order As Collision Theory? 3

Comparisons Between Collision Theory And Experiments 4

Why Does Collision Theory Fail For Reaction 7.30? 5 Reaction 7.30 requires a special collision geometry: (7.33) (7.34)

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.

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 + C 2 H 6 → H 2 + C 2 H 5 8

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

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

Simplified Potential Energy Surfaces Simplified example: analytical PE surface 11 Energy AB Bond Length BC Bond Length

PE Surface 12 Spreadsheet

Numerical Values 13 Saddle Point Spreadsheet

Top View 14 A+BC  AB + C Saddle Point AB Distance BC Distance Reactants Products Spreadsheet

Barrierless Reaction 15 Spreadsheet

Barrierless Reaction 16 Spreadsheet

Attractive Interaction 17 Spreadsheet

PE With Van der Waals Well 18 Spreadsheet

PE For Series Reactions 19 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 Separated Neons Ne-Ne Collision Ne Anti- Bonding

Ne-Ne Potential 22

F-F interaction 23 F F FF Separated Fluorines F 2 Pure Quantum Effect

F-F Potential 24

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

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

Cl + F 2 Potential 27

Interaction During H + C 2 H 6 →C H 4 + CH 3 28

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

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