1. ChE 553 Lecture 24 Theory Of Activation Barriers 1

2. New Topic Why do we get activation barriers How can one manipulate activation barriers 2

3. Key Concept: 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. 3

4. Plan for Today Describe each of the effects Start to develop models 4

5. Qualitative Picture Of Free Energy Changes During A Reaction 5 Free energy, kcal/mole of bromine atoms -50 0 50 1/2Br 2 Br H+HBr Br+2HBr 1/2 Br 2 +2HBr Reaction Progress Gas Phase +H 2 +Br 2 H 2 + Br 2  2HBr Barrier since uphill Extra barrier due to orbital distortions

6. This Case Has Two Key Effects Uphill reactions Orbital distortion due to Pauli repulsions Bond stretching and distortion Quantum effects Special reactivity of excited states 6

7. Uphill Reactions Obvious 7 Free energy, kcal/mole of bromine atoms -50 0 50 1/2Br 2 Br H+HBr Br+2HBr 1/2 Br 2 +2HBr Reaction Progress Gas Phase +H 2 +Br 2 H 2 + Br 2  2HBr Barrier since uphill Extra barrier due to orbital distortions Dominant cause of barriers in bond scission (S N 1) reactions

8. Bond Stretching And Distortion Bonds bend and stretch as reactions occur Bond distortion costs energy – leads to barrier 8 H-N  C  H \ N  C  N  C-H Dominant cause of barriers in unimolecular reactions

9. Orbital Distortion Orbitals distort as reactions occur due to Pauli repulsions Leads to barriers 9 Dominant cause of barriers in exothermic atom and ligand transfer (S N 2) reactions

10. Orbital Notation 10 Positive orbital Negative orbital

11. Orbital Distortions D + H 2  HD+ H 11 Notice that the shading of the bond is preserved

12. Orbital Distortions H + C 2 H 6  H 2 + C 2 H 5 12

13. Orbital Distortions H + C 2 H 6  CH 3 + CH 4 13

14. Quantum Effects: Orbital Symmetry Conservation Sign of orbital, electron spin does not change during a concerted reaction 14

15. Consider H 2 + D 2  2 HD 15 H2H2 D2D2 HD

16. Can Reaction Occur? 16 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

17. 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 17

18. Special Reactivity Of Excited States Related Quantum Effect: sometimes only excited states can lead easily to products 3 H + N + X  NH 3 + X Ground state of N has only 1 unpaired electron – not reactive to NH 3 formation Excited state of N has 3 unpaired electrons – much more reactive 18

19. Surfaces Can Change Each Form Of Barrier Change free energy of intermediates Stretch bonds Modify electron flow Ameliorate quantum limitations (one electron in adsorbate replaced by electron from solid) Stabilize excited sites 19

20. Polanyi’s Model: Consider a proton transfer reaction (assume bond stretching controls): 20 Figure 10.2 The energy changes which occur when a proton H is transferred between a conjugate base B and a reactant R. The solid line is the energy of the B-H bond while the dotted line is the energy of the H-R bond.

21. Effects Of Changes 21 Figure 10.3 A diagram illustrating how an upward displacement of the B-H curve affects the activation energy when the B-R distance is fixed. Figure 10.4 A diagram illustrating a case where the activation energy is zero.

22. Derivation Of Polayni Equation 22 Figure 10.6 A linear approximation to the Polanyi diagram used to derive equation (10.11). (10.9) (10.10)

23. Solving For The Intersection Of The Two Lines 23 (10.11)

24. Put In Standard Form Defining Yields 24 (10.12) (10.13) (10.14)

25. Case Where Polayni Works (Over A limited data set) 25 Figure 10.7 A plot of the activation barriers for the reaction R + H R  RH + R with R, R = H, CH 3, OH plotted as a function of the heat of reaction  H r.

26. Equation Does Not Work Over Wide Range Of  H 26 Figure 10.11 A Polanyi plot for the enolization of NO 2 (C 6 H 4 )O(CH 2 ) 2 COCH 3. Data of Hupke and Wu[1977]. Note Ln (k ac ) is proportional to E a.

27. Equation Does Not Work Over A Wide Data Set 27 Figure 10.10 A Polanyi relationship for a series of reactions of the form RH + R  R + HR. Data from Roberts and Steel[1994].

28. Seminov Approximation: Use Multiple Lines 28 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.

29. Key Prediction Stronger Bonds Are Harder To Break 29 Figure 10.8 A schematic of the curve crossing during the destruction of a weak bond and a strong one for the reaction AB + C  A + BC.

30. Experiments Do Not Follow Predicted Trend 30 Figure 10.9 The activation barrier for the reaction X - +CH 3 X  XCH 3 + X -. The numbers are from the calculations of Glukhoustev, Pross and Radam[1995].

31. Summary: Barriers To Reaction Are Caused By Uphill reactions –Dominates for many gas phase S N 1 reactions Bond stretching and distortion –Dominates for unimolecular reactions Orbital distortion due to Pauli repulsions Quantum effects Special reactivity of excited states 31

32. Need Models To Quantify Ideas Polanyi’s model –Bond stretching dominates –Ignore Pauli repulsions, quantum effects –Linearize energy vs bond stretch Ea varies linearly with heat of reaction –Only fair approximation to data 32