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Kinetic Isotope Effects - Theory

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Kinetic Isotope Effects - Theory Chemistry 202 - Organic Reaction Mechanisms II Some Common Mechanistic Tools David Van Vranken University of California, Irvine Crossover Experiment ■ Crossover experiments allow one to distinguish intramolecular processes from those that involve dissociation and recombination. Stevens "1,2-shift" + N CO Et + KOt-Bu N CO Et Bn 2 2 Bn intramolecular, concerted + N - CO2Et Bn .. or dissociative + stepwise N - CO Et +.N - CO Et N CO Et Bn .. 2 2 .. 2 . .. Bn Bn. ■ Formation of mixed products rules out an intramolecular mechanism. t-BuOK + N CO2Me + N CO2Et N CO2Me N CO2Me N CO2Et N CO2Et + + + Ph Tol Ph Tol Ph Tol ∴Can’t be intramolecular Stevens, T.S.; et al. J. Chem. Soc. 1928, 3193 Primary Kinetic Isotope Effects - Theory ■ Isotopes (e.g., H vs. D) exhibit the same chemical reactivity. ■ Bonds to lighter isotopes vibrate more quickly. ■ Biggest difference for 1H vs 2H as opposed to 12C vs 13C. ■ C-H reacts faster than C-D. Using linear stretch frequencies, you can estimate the maximum ratio of rates for a primary kinetic isotope effect to be a factor of 7. Planck from IR spectra h (νH - νD) k H = 2kT = kD e 6.9 Boltzmann ■ Primary K.I.E.: If H transfer is the rate-determining step, then the D analog will be up to 7x slower. primary R R K.I.E. R C H X R C D X transition states: R faster R slower ■ Theoretically, rates of H transfer can be up to 15 times faster than D transfer due to bending contributions in the T.S., but in practice, they aren’t higher than a factor of 8. Primary Kinetic Isotope Effect - Example ■ A primary K.I.E. is established by determining relative rate constants with two different substrates: one with H and one with D. Consider the following case of electrophilic aromatic substitution. + HgClO experimental detn: 4 Hg(ClO ) HgClO4 4 2 +2 rate = kH[C6H6][Hg ] +2 rate = kD[C6D6][Hg ] non-basic O - Cl kH :O O = 6.75 + H O RDS kD HgClO4 ••• H xfer in RDS ■ Contrast Hg(ClO4)2 with a typical E.A.S. where the formation of the arenium ion is the RDS and proton transfer comes after. O + N cat HA O NO2 k HNO3 H = 1 kD - :A H RDS + NO2 won't affect the rate Primary Kinetic Isotope Effect - Example ■ Where does the cyclopropane come from? Ph Li Ph Cl Ph mechanism? Magid, R.; Welch, J.G. Et2O JACS 1966, 88, 5681 35 °C, 5 h 55% 1% displacement mechanism: H Ph Cl Ph H Ph Li H C H Cl C - CH C C C CH .. 2 H2C CH2 H H H2 carbene mechanism: carbene Ph H H H H Li Ph Cl Cl C H C H C H H C H CH Ph Li H C C C C C C .. C CH2 H C CH - .. H 2 2 H H H H ■ ClH2C–CH=CH2 reacts more quickly than ClD2C–CH=CH2. Th e strong primary K.I.E. (kH/kD > 2) with rules out the displacement mechanism. Kinetic Isotope Effects - The Easy Way ■ kH/kDratios can come from simple competition experiments and determined from the product ratios using simple techniques like 1H NMR or GCMS. ■ You often don’t observe the maximum primary deuterium isotope effect as high as 7. kH/kD >2 is taken as strong evidence for C-H cleavage in the RDS. CONMe2 CONMe2 Ph Ph Ph K.I.E. H cat. Ru(II) consistent 2.1 with: H Ph AcOH .. RDS NMe CONMe2 CONMe2 1 2 D4 D 4 Ph O D Ru(II) H H Ph Hashimoto, Y.; et al. JOC 2013, 78, 638 Kinetic Isotope Effects - The Easy Way ■ kH/kDratios can come from simple competition experiments and determined from the product ratios using simple techniques like 1H NMR or GCMS. ■ Here’s a cool visual demonstration of the K.I.E. by comparing two colorimetric reactions. orange green H CrO OH O O 2 4 O HO O C + .C HO OH . OH O O C RDS H O: O OH 2 H O’Leary, D.J.; et al. J. Chem. Educ. 2013, 90, 1044 Secondary Kinetic Isotope Effects – they're small ■ Secondary kinetic isotope effect: If H is attached to a carbon that undergoes changes in bonding in the RDS, then a very small secondary K.I.E. will be observed. sp2 to sp3 secondary L.G.δ- L.G.δ- Nuδ- K.I.E. faster slower faster! transition states: R Cδ+ R Cδ+ R C H Ph D Ph D Oδ- sp3 to sp2 isotopes ■ Here are the trends: • Dissociative sp3 to sp2 = about 1.1 - 1.2 • Associative sp2 to sp3 = about 0.8 - 0.9 (inverse KIE) ■ Yo u need precise methods for measuring relative rates in order to employ secondary kinetic isotope effects. 0.96 H 1.02 O O H C 2 3 H 0.96 H3C H secondary 2H and 13C NMR at natural abundance: 13C primary 1.00 H 0.94 O O Singleton, D.A.; Thomas, A. A. H 25 °C JACS 1995, 117, 9357 H 1.02 O O 0.97 Isotopic Labeling ■ Isotopic labeling allows one to rule out implausible mechanisms simply by looking at the products. Tobisu, M.; et al. D D 100% D transfer JOC 2009, 74, 5471 cat. PtCl2 H H toluene 60 °C, 24 h Cl2Pt - D PtCl2 Uh, no. PtCl2 D D ≤50% D transfer H H H + Maybe... D D - D D + PtCl PtCl H 2 C 2 PtCl2 H H PtCl2 D D D H H H PtCl2 PtCl2 Linear Free Energy Relationships ■ Benzoic acid is a little bit like a carbocation; that’s why it is acidic. Groups X that stabilize carbocations make it less acidic. Groups X that destabilize carbocations make it more acidic. O - O O This res. struct. K + H H a helps you understand O O O - why X affects the pKa. X X X ■ The differences in pKas relative to benzoic acid Group σ (X=H) are called values. Values for all common Me2N- -0.62 σ σ MeO- -0.38 substitutents have been tabulated: H- 0 Cl- 0.24 NC- 0.65 • Groups with lower σ stabilize carbocations. O2N- 0.81 • Groups with higher σ stabilize carbanions. ■ Since we understand how substituted benzenes affect the acidity of carboxylic acids, we can use substituted benzenes to tell us about carbon centers in mysterious RDSs. It is common to obtain relative rates by mixing substrates in pair-wise combinations. Br Br Br SN1 or SN2? vs. vs. Compare rates varying X: :OH2 O2N MeO Hammett Plot - Is the Correlation Linear? ■ A Hammett plot compares the effect of benzene substituents on slope MeO kX reaction rates with the effect of log = ρ • σ H kH substituents on benzoic acid acidity. kX Cl log < 0 δ+ in RDS kH CO2Et ρ The slope, ρ (rho) tells you about - NO ρ > 0 δ in RDS whether negative or positive charge is 2 building up in the R.D.S. typical: -6 < ρ < 6 σ O OEt Nuc. Addn RDS ρ = + 2.4 to C=O -OH X δ Br Heck rxn RDS ρ = + 2.5 Oxid. Addn PdL Consorti, C.S.; et al. JACS 2005, 127, 12054 step X L L Pd Difft Heck rxn R ρ = - 0.53 carbapalladation Fristrup, P.; et al. Organomet. 2004, 23, 6160 step RDS X The Taft Equation: Steric Effects in the T.S. ■ The Hammett analysis is restricted to reactions at benzylic positions so the substituents are too far away to exert a steric effect. Robert Taft pioneered the use of linear free energy relationships to estimate steric effects in transition states for rate determining steps. - O δ Use Hammett for this: OEt -OH X δ What about this? S H H R ≠ aryl R SEt R SEt R = Me, Et, i-Pr, s-Bu, t-Bu, c-Hex, n-Bu, adamantyl The Taft Equation: Steric Effects in the T.S. ■ The Hammett analysis is restricted to reactions at benzylic positions so the substituents are too far away to exert a steric effect. Robert Taft pioneered the use of linear free energy relationships to estimate steric effects in transition states for rate determining steps. ■ Like the Hammett relationship, the idea is to compare rates of chemical reactions using substrates with different steric substituents. The equation helps you dissect polar effects from steric effects. The slope ρ* tells you about polar effects; the slope δ tells you about sterics. slope Es σ* kX H 1.24 0.49 Hammett Eq. log = ρ • σ kH CH3 0 0 CH2CH3 -0.07 -0.1 CH2Ph -0.47 -0.19 ks Taft Eq. log = * • * + δ • E CH(CH3)2 -1.54 -0.3 k ρ σ s CH3 C(CH3)3 -0.38 0.22 Ph -2.55 0.6 polar sensitivity factor steric substituent constant polar substituent constant from a reference reaction from reference reaction steric sensitivity factor ■ If you have plausible ideas about the transition states, linear free energy relationships are usually not the best approach. Reaction Predictor: Predicting Arrow-Pushing Mechs ■ ReactionPredictor uses powerful rules related to the interaction of filled orbitals with unfilled orbitals to predict arrow-pushing mechanisms. The system uses large neural networks for “deep learning”. It never forgets and will continue to get smarter… faster than you. N N C C DMSO 70 °C M.A. Kayala, C.A. Azencott, J.H. Chen, P. Baldi. “Learning to predict chemical reactions.” Journal of Chemical Information and Modeling 2011, 51, 2209–2222.
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