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Kinetic Isotope Effects in Organic Chemistry

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Kinetic Isotope Effects in Organic Chemistry Kinetic Isotope Effects in Organic Chemistry Rob Knowles MacMillan Group Meeting Sept. 14, 2005 Key References Wiberg, K.B. Chem. Rev. 1955, 55, 713 Westheimer, F.H. Chem. Rev. 1961, 61, 295 Saunders, W.H., Melander, L. Reaction Rates of Isotopic Molecules , Wiley, New York, 1981 Dougherty, D.A., Anslyn, E.V. Modern Physical Organic Chemistry, University, Sausalito, 2005 Lowry, T.H., Richardson, K.S. Mechanism and Theory in Organic Chemistry, Harper and Row, New York, 1987 Entering the Deuterated Age 1929 Giauque and Johnston discover heavy oxygen isotopes 17O and 18O. Based upon the accurately measured molecular mass of water this result leads to speculation that hydrogen must also have a heavy isotope. 1932 Urey and coworkers reported the first spectroscopic evidence for a heavy isotope of hydrogen. Shortly thereafter Urey reported the enrichment of Urey heavy hydrogen in water upon electrolysis. natural isotope abundance 2H 0.0015% 1933 Gilbert Lewis and coworkers isolated a pure sample of heavy water 3H 0.0001% 13C 1.108% 15N 0.365% 17O 0.037% 1933 Eyring and Polanyi independently and correctly postulate that protonated and deuterated compounds should react at different rates based upon differences in zero-point energies. 1934 Interest and the availability of deuterated compounds lead to an explosion of research into isotopically labelled molecules. More than 200 papers dealing with the prepartation and uses of deuterated compounds were published. Urey is awarded the Nobel Prize for his work on deuterium. Eyring Wiberg, K.B. Chem. Rev. 1955, 55, 713 What Are Kinetic Isotope Effects? ! A kinetic isotope effect is a mechanistic phenomenon wherein isotopically substituted molecules react at different rates. Key Assumptions Krel O O cat H+ 1. Isotopic substitution does not affect the potential energy surface 7.0 H3C CH3 H3C CH2Br of the reaction or the energies of Br2, H2O the electronic states. O 2. Only mass dependent properties O cat H+ are affected, most importantly 1.0 vibrational frequencies. D C CD D3C CD2Br 3 3 Br2, H2O ! Interpretation of the rate differences provides information on the nature of the rate-determining step. Me HO OH (D)H Me NaOEt OsO4 Me Me C R Cl E1 or E2? R Me Me3C 3+2 or 2+2? 3 ! There are several different classifications for KIE's Primary isotope effect: Occurs when labelled bond is made or broken in the rate determining step Secondary isotope effect: Occurs when labelled bond is not made or broken in the rate determining step Normal isotope effect: Occurs when KH/KD is greater than 1 Inverse isotope effect: Occurs when KH/KD is less than 1 Quick Review of Vibrational Spectroscopy ! All bonds have quantized vibrational energy levels ! The vibrational energies (En) are dependent on the frequency of the bond stretch (!), which is in turn dependent on the reduced mass of the two connected atoms (µ). Three Key Equations bond µ r C-H 0.92 1 k C H ! = C-D 1.71 2"c µ 12C-12C 6.00 12C-13C 6.24 µ = m1 · m2 y g m1 + m2 r e n E n=3 En = (n + 1) h! n=2 n=1 n=0 Zero-Point Energy 99.9 % of C-H bonds are in the ground vibrational state (n=0) at room temperature Internuclear Distance (r) ! The energy the molecule possesses in the ground vibrational state is known as the zero-point energy, and it forms the basis for the reactivity differences between isotopomers. Physical Origins of Primary Kinetic Isotope Effects ! Simplest case to treat is the homolytic cleavage of C - H/D bond where the bond is considered to be fully broken at the transition state. Reaction progress followed by observing the C - H/D bond stretch. frequency (cm-1) ZPE (kcal/mol) rel. rate (300 K) C - H stretch 2900 4.15 ~6.9 C - D stretch 2100 3.00 1.0 y g r e r n E Activation energy for C D C-D bond homolysis Activation energy for n=0 (C-H) C-H bond homolysis r C H n=0 (C-D) !!G = !ZPE Internuclear Distance (r) ! As the C - H/D bond breaks at the transition state the stretch becomes a translation. As a result there is no new stretch in the TS that corresponds to the stretch of ground state bond. For this mechanism, the isotope effect is entirely controlled by the difference in the ground state ZPE's. Wesheimer, F.H. Chem. Rev. 1961, 61, 295 Using Primary KIE's to Distinguish Between Reaction Mechanisms ! KIE's give useful information about the rate determining step of the reaction mechanism Case 1 E2 elimination NaOEt Me H EtO– CH3CH2CH2Br C H OH kH/KD = 6.7 H H 2 5 H H H 1° KIE for C - H/D Me NaOEt Me H H Br CH3CD2CH2Br C2H5OH D H ! This KIE is consistent with an E2 elimination in which the C - H/D bond is broken in the rate determining step. Case 2 E1 elimination Me Me Me H2O, ! C Br CH3CH2 H k /K = 1.4 H Me H Me H D Me H Me Me Me 2° KIE for C - H/D H - H2O, ! Br CH3CD2 C Br Me D Me ! This KIE is consistent with an E1 solvolysis in which the C - H/D bond is not broken in the rate determining step. A More Realistic View of Primary Kinetic Isotope Effects ! In most reactions the bond of interest is not fully broken at the TS. Rather, it is only partially broken and thus the TS structure has its own ZPE's. Consider the deprotonation of A-H by B. Important Considerations A H B A H B 1. The A-H stretch in the SM defines the rxn coord. in the TS and does not contribute energetically to the primary KIE. !ZPETS 2. Bending modes have much lower force constants than stretches and consequently contribute very little to the overall primary KIE. y g r 3. The proton is shared between e n A and B in the transition state, E creating a new symmetric stretch that has no analogue in the SM. !!G = !ZPEGS - !ZPETS A H B !ZPEGS This new vibrational mode has a Reaction Coordinate strong force constant and is the major energetic contributor to the KIE ! The ZPE changes between the ground state and the transition state because the force constant of the bond is changing. The difference in energy between the !ZPE's in the ground state and the transition state determine the magnitude of the kinetic isotope effect. Hammond Postulate and Isotope Effects ! The Hammond postulate states the TS structure most resembles the molecule that it is closest in energy to. Therefore, the position of the TS on the reaction coordinate, and thus the KIE, will depend on the thermodynamic difference in energy between the starting material and the product. Exothermic Endothermic Thermoneutral A B A B H H A H B y g r e n E !ZPEGS ~ !ZPETS !ZPEGS ~ !ZPETS !ZPEGS > !ZPETS !!G is small !!G is small !!G is large Small KIE Small KIE Large KIE ! In the exothermic and endothermic reactions, the TS is similar to the SM and product respectively. Thus !ZPETS is very similar to !ZPEGS, yielding a small KIE. In the thermoneutral TS the symetrical stretch is independent of the mass of the isotope, yielding very small values of !ZPETS which in turn yield very large KIE's. Kinetic Isotope Effects in Acid/Base Chemistry ! This concept was nicely demonstrated by Bruice and coworkers in their work on the KIE's of nitroethane deprotonation by a variety of amine bases. R-NH R-NH3 Me NO2 2 Me NO2 ! The greatest KIE is seen when the !pKa = 0 pKa of the nitroethane equals that of the conjugate acid of the amine. 11 ! In this scenario, both reactants are 10 pulling equally on the proton in the transition state, and the reaction is D thermoneutral, giving a a very large K / 9 primary KIE. H K 8 KIE's reflect the 5 6 7 8 9 10 11 12 13 symmetry of the 7 TS structure, and how it varies with + reaction conditions pKa of RNH3 Exothermic Thermoneutral Endothermic A H B A H B A H B Bruice, T.C. JACS 1969, 92, 905 Primary KIE's and Non-Linear Transition States ! All the analysis so far has assumed that the TS is essentially linear, but very often rxns involving proton transfers do not have linear transition states. H H H A B A B A B ! In general primary KIE's for nonlinear TS's are lower than those for more linear TS's for two reasons: Stretch Bend H H 1. In going to a TS with bent bonds, the bending vibrational modes become C more important.However, bending modes are much lower energy than C stretching modes in linear TS's and thus the KIE's associated with bending are diminished. v = 2900 cm-1 v = 1350 cm-1 2.There is a new symmetrical stretch in TS structure in which the hydrogen atom has a significant range of motion. This makes the frequency of this stretch highly mass dependent. H A B ! Generally primary KIE's for proton transfers occuring by non-linear TS's are on the order of 2.5 - 3.5. New symmetric stretch in the TS structure Secondary Deuterium Kinetic Isotope Effects ! Secondary KIE arise from rate differences caused by isotopically labelled bonds that are not made or broken in the rate determining step.
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