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ChE 452 Lecture 16 Quantum Effects In Activation Barriers 1

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Last Time Three Models Polayni’s model:Marcus equation: 2 (10.14) (10.33) BM

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Works Most Of The Time 3

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Fails for 4 Center Reactions 4 H2H2 D2D2 HD

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Can Reaction Occur? 5 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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Quantum Effects Control Chemical Processes Consider 2 hydrogen atoms coming together – can a bond form? Classical result: Nuclei repel each other Electrons repel each other Electron-nuclei attraction Classically no bond can form 6 Slight net repulsion

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Quantum Effects Allow Bonds To Form Wavefunctions are “antisymmetric” Electrons rapidly exchange (i.e switch places) When exchange happens the sign of the wavefunction changes Leads to a cancelation of the couloumb repulsion The net result is that two electrons in the same orbital with the opposite spin do not repel! The absence of repulsion allows bonds to form 7

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Implications All chemistry is quantum We would not be alive without quantum Electron-electron repulsions during reactions can be reduced via exchange That is why I called it a “Pauli repulsion” Need way to compute the result 8

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Quantum Methods For Reaction Rates Solve schroedinger equation (11.39) 9

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Approximation To Solve Schroedinger Equation Hartree Fock (HF) Approximation Treat each electron as though it moves independently of all others (i.e. In the average field of all others) Configuration Interaction (CI) Consider how motion of each electron affects the motion of all of the other electrons 10

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Hartree Fock Approximation 11 = Wavefunction for molecule = Antisymmenizer … One electron wavefunctions

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Solution Of HF Equation For Stationary Atoms Kinetic Energy Electron-Electron of Electrons Repulsions Electron Core Exchange Energy Attraction Exchange energy: Extra energy term that eliminates electron-electron repulsion when electrons pair up in a bond. 12 ( E = ( ) + ( ) ( ) ) -

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Correlation Energy Missing From Hartee Fock Physics: When electron atom moves into an area others move out of the way. Leads to a lowering of electron-electron repulsion. Correlation Energy – Lowers the total energy. 13

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How big is the correlation energy Methodology: Used a program called Gaussian to calculate the Hartree fock and approximate correlation energy for the electrons in ethane Result: HF energy= -49885. kcal/mole Correlation energy = -168.5 kcal/mol 14

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Conservation Of Orbital Symmetry Signs of orbitals, electron spins, do not change during normal chemical reactions Can switch in light 15

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Formulation In terms Of MO’s Of The System 16 Molecular Orbitals At The Transition State

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Correlation Diagram 17

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Other Cases 18 Figure 10.34 Configuration mixing diagram for a) Na Cl NaCl b) conversion of cis- butene to trans-2-butene.

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Conclusion Quantum Effects Matter To Chemical reactions No chemical bonds without quantum Main effects seen in correlation diagrams Bond breaking because bonds cannot move smoothly from reactants to products 19

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Query What did you learn new in this lecture? 20

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