Chapter 7: Kinetic Isotope Effects I. Isotope Effects A. Equilibrium Isotope Effects

1. Chapter 7: Kinetic Isotope Effects I. Isotope Effects A. Equilibrium Isotope Effects RSH + R'OD RSD + R'OH Keq = 0.4-0.5 14NH4+ + 15NH314NH3 + 15NH4+ Keq = 1.0393 H12CN + 13CN- H13CN + 12CN- Keq = 1.026

2. B. Kinetic Isotope Effects (L = H or D)

4. II. Isotope Effect Theory A. Equilibrium Isotope Effects K1 R1 P1 K2 R2 P2 Qtot = QtrQrotQvibQele0tot =e0el +e0vib Since Qel = 1: Qtot = QtrQrotQvib

5. Born-Oppenheimer Approximation:

6. Substituting partition functions and vibrational zero-point energies: MMI EXC ZPE ui = hi/kT i  reactant indexl  product index

7. MMI = isotope effects on translation and rotation. ZPE = isotope effects on i at 0 K. EXC = isotope effects on population of vibrational excited states at T (density of vibrational states).

9. ‡ ‡ ‡ ‡ ‡ ‡ B. Kinetic Isotope Effects K1‡ A1 ‡1 P1 K2‡ A2 ‡2 P2

10. ‡ ‡ ‡ ‡ ‡ ‡ Approximations: κ1κ2, m2‡/m1‡  m2/m1, I2‡/I1‡  I2/I1; for i> 500 cm-1 e-ui < 0.08 at 25 C and  EXC  1.

11. ‡ ‡ Rules: 1. Isotopically heavier molecule has lower ZPE. 2. ZPE between isotopic isomers increases as f increases. 3. Heavier isotope accumulates in the state where binding is stronger (e.g. for C-L, where vibrational well is steeper). 4. Lighter isotope accumulates where binding is weaker. 5. ZPE is greatest for hydrogen isotopes.

12. ‡ ‡ ‡ D0,D De0,H III. Primary Hydrogen Isotope Effects A. Simplest Model

13. ‡ ‡ ‡ ‡ kH/kD = e-ZPEH,D/kT ‡ ‡ ‡ ‡ All of reactant state ZPEH,D is lost in the transition state: ZPEH,D = e0,H - e0,D ‡ Since 0,H = 0,D: ‡ ‡

15. For H = 3000 cm-1 D = 2200 cm-1 kH/kD = 6.75

16. B. Westheimer-Melander Model 1. Background ‡ Linear Transition State Four transition state vibrations are considered, two stretches and two degenerate bends.

17. Stretches: r1 r2 Antisymmetric C………H………B r1 – r2  Symmetric C………H………Br1 + r2  ‡

18. r1 r2 r1 + r2 r1 – r2 E C:- H+-B C-H :B

19. 2. Variation of Primary Isotope Effect with Extent of Proton Transfer C……H…………BReactant-like transition state  CHBSymmetric transition state  C…………H……BProduct-like transition state  

20. CHB CDB Isotopic ZPE difference remains in the transition state. C-H C-D

21. Extent of proton transfer varies as the basicity of the base increases. Why? Consider Hammond’s Postulate: d-d+ [CHB]‡  

22. Consider the symmetric stretch of the transition state: Short-Dashed Line: pKaC-H<< pKaHB+ [CHB]‡  Early transition state Solid Line: pKaC-H ~ pKaHB+ [CHB]‡   Symmetrical transition state Long-Dashed Line: pKaC-H >> pKaHB+ [CHB]‡  Late transition state

23. 3. Example: Base-catalyzed ester enolate formation resonance stabilized

24. fCH = 608 J m-2 fBH = 712 J m-2 λ = 63200 J mol-1 G‡int = 15800 J mol-1 Reference: Barnes and Bell, Proc. Royal Soc. London, Ser. A318, 421 (1970)

25. ‡ ‡ ‡ ‡ 4. Marcus Theory of Isotope Effects: DGH‡ - DGD‡ = NDZPEH,D‡ = NDe0,H‡ -NDe0,D‡ ‡ f1 = fCH(1 - x‡) f2 = fBHx‡

26. ‡ ‡ ‡ ‡ ‡ kH/kD = e-DZPEH,D/kT

27. C. Other Factors 1. Additional Transition State Vibrational Modes Two degenerate bending modes Transition state bending motions decrease kH/kD. + - +

28. ‡ Nonlinear transition state Symmetric stretch not separable from bending motions. Common for H- transfer reactions

29. 2. Quantum Mechanical Tunneling • = 2p2mn/h x = r - req Barrier is narrower for C-H species. Ψ2 for C-H falls off more slowly with increasing x than does C-D.

30. IV. Isotope Effects on Multistep Reactions * denotes isotopically sensitive step

31. DkobskobsH/kobsD (observed isotope effect) Dk3 k3H/k3D (intrinsic isotope effect) Dkobs = f1 + f3 Dk3 wherein f1 and f3 are fractions of rate determination by k1 and k3, respectively.

32. k3>> k2 kobs = k1 k3<< k2 kobs = k1k3/k2 f1 = 1 Dkobs = 1 f3 = 1 Dkobs = Dk3

33. A. Electrophilic Aromatic Substitutions

35. B. H/D Exchange of Toluene

36. Applying the steady-state approximation:

37. V. Heavy Atom Isotope Effects

38. Example 1: Decarboxylation of 2-Benzoyl Propionic Acid k12/k14 isotope effects C-1: 1.074 C-2: 1.051 C-3: 1.000

39. Mechanistic Rationale: Stepwise reaction can also explain the isotope effects.

40. Example 2: Nucleophilic Displacement of Cl- From p-Nitrobenzyl Chloride Nu: = H2O k35/k37 = 1.0076 Nu: = -CN k35/k37 = 1.0057

41. Example 3: Baeyer-Villager Oxidation of Acetophenone Stepwise mechanism:

42. Concerted mechanism: k12/k14 = 1.048  0.002 at 32 C Isotope effect is consistent with the concerted mechanism.

43. VI. Secondary Isotope Effects The bond to the isotopic atom is neither made nor broken in the kinetic or equilibrium process. A. -Deuterium Isotope Effects

44. L OH C C O H L H L -CL sigma bond electrons are delocalized by hyperconjugation in sp2 reactant. Hyperconjugation is no longer possible in sp3 product.

46. D3k  kH3/kD3 = 0.90 D3k = (D3Khyd)F F = 0.65

47. B. Factors Affecting the Magnitude of -D Effects 1. Demand for Hyperconjugation kH3/kD3 = 1.89 (1.24 per D)  Transition state resembles ion pair or carbonium ion:

48. 2. Dependence on Dihedral Angle kH/kD = 1.14 per D at L1. kH/kD = 0.99 per D at L2.

49. C. -Deuterium Effects

50. Why? Streitwieser Model