1. ChE 553 Lecture 25 Theory Of Activation Barriers 1

2. Objective Describe more quantitative models of activation barriers –Marcus –Blowers-Masel Show one can get reasonable estimates of activation barriers 2

3. Review: 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. Polayni’s Model Assumptions –Bond stretching dominates –Ignore Pauli repulsions, quantum effects –Linearize energy vs bond stretch Result Ea varies linearly with heat of reaction –Only fair approximation to data 4

5. Seminov Approximation: Use Multiple Lines 5 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.

6. Marcus Model Assumptions –Bond stretching dominates –Ignore Pauli repulsions, quantum effects –Parabolic energy vs bond stretch Prediction 6

7. Derivation: Fit Potentials To Parabolas Not Lines 7 Figure 10.13 An approximation to the change in the potential energy surface which occurs when  H r changes.

8. Derivation 8 Figure 10.13 An approximation to the change in the potential energy surface which occurs when  H r changes.

9. Solving 9 Result (10.23) (10.24) (10.31) (10.33)

10. Qualitative Features Of The Marcus Equation 10 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.

11. Marcus Is Great For Unimolecular Reactions 11 Figure 10.17 The activation energy for intramolecular electron transfer across a spacer molecule plotted as a function of the heat of reaction. Data of Miller et. al., J. Am. Chem. Soc., 106 (1984) 3047.

12. Marcus Not As Good For Bimolecular Reactions 12 Figure 10.18 The activation energy for florescence quenching of a series of molecules in acetonitrite plotted as a function of the heat of reaction. Data of Rehm et. al., Israel J. Chem. 8 (1970) 259.

13. Comparison To Wider Bimolecular Data Set 13 Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR 1  RH + R 1 with w O = 100 kcal/mole and = 10 kcal/mole.

14. Why Inverted Behavior? 14 At small distances bonds need to stretch to to TS.

15. Limitations Of The Marcus Equation Assumes that the bond distances in the molecule at the transition state does not change as the heat of reaction changes –Good assumption for unimolecular reactions –In bimolecular reactions bonds can stretch to lower barriers 15

16. Explains Why Marcus Better For Unimolecular Than Bimolecular 16

17. Blowers-Masel Equation Assumptions –Bimolecular reaction –Pauli repulsions important –Include bond stretching but ignore quantum limitations 17

18. Blowers-Masel Derivation Fit potential energy surface to empirical equation. Solve for saddle point energy. Only valid for bimolecular reaction. 18

19. Blowers-Masel Derivation Approximate VE by: 19

20. Plot Of Potential 20 Figure 10.28 A potential energy surface calculated from equation (10.59) with w CC = 95 kcal/mole, w CH = 104 kcal/mole, V P = 300 kcal/mole, q CC = 0.7, q CH = 0.5.

21. Derive Analytical Expression 21 Bond energies (10.63) (10.64) (10.65) Only parameter

22. Comparison To Experiments 22 Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR 1  RH + R 1 with w O = 100 kcal/mole and = 10 kcal/mole.

23. Comparison Of Methods 23 Figure 10.32 A comparison of the Marcus Equation, The Polanyi relationship and the Blowers Masel approximation for =9 kcal/mole and w O = 120 kcal/mole.

24. Example: Activation Barriers Via The Blowers-Masel Approximation 24

25. Solution: Step 1 Calculate V P V P is given by: 25 (11.F.2)

26. Step 1 Continued Substituting into equation (11.F.2) shows 26 (11.F.3)

27. Step 2: Plug Into Equation 11.F.1 27 (11.F.1) By comparison the experimental value from Westley is 9.6 kcal/mole.

28. Solve Via The Marcus Equation: 28 which is the same as the Blowers-Masel approximation. (11.F.4)

29. Limitation Of The Model: Quantum Effects: 29 Figure 10.39 A hypothetical four-centered mechanism for H 2 /D 2 exchange. The dotted lines in the figure denotes mirror planes which are preserved during the reaction (see the text). This reaction is symmetry forbidden. Note one electron has to be spin up and spin down at the same time.

30. Consider H 2 + D 2  2 HD 30 H2H2 D2D2 HD

31. Can Reaction Occur? 31 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

32. 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 32

33. Orbital Diagram 33 Figure 10.40 A schematic of the key molecular orbitals for the transition state of reaction (10.92). Positive atomic orbitals are depicted as open circles, negative orbitals are depicted as shaded circles. Symmetry forbidden reactions Woodward hoffman rules

34. Summary Bonds need to stretch or distort during reaction. It costs energy to stretch or distort bonds. Bond stretching and distortion is one of the major causes of barriers to reaction. In order to get molecules close enough to react, the molecules need to overcome Pauli repulsions (i.e., electron electron repulsions) and other steric effects. The Pauli repulsions are another major cause of barriers to reaction. 34

35. Summary Continued In certain special reactions, there are quantum effects which prevent the bonds in the reactants from converting smoothly from the reactants to the products. Quantum effects can produce extra barriers to reaction. There are also a few special cases where the reactants need to be promoted into an excited state before a reaction can occur. The excitation energy provides an additional barrier to reaction. 35

36. Summary Continued Polayni: linear potential Marcus: parabolic potential Blowers-Masel – size of TST varies Fails with quantum effects ( varies) 36