KIE = k H. k D SM H SM! D PDT H PDT D. Kine%c Isotope Effects. Ques%ons: What is the mechanism of a reac%on?

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1 Kine%c Isotope Effects Ques%ons: What is the mechanism of a reac%on? Is a certain bond broken in the rate- determining step? What is the transi%on state geometry? Ideas: Minimally perturb the reac%on by isotopically labeling one of the atoms in the reactants. Isotopic labeling cannot change the mechanism of the reac%on! Defini%on: The KIE is the rate constant ra%o, with the lighter isotopomer in the numerator. The most common isotopomers are pro%um and deuterium, but many other choices are possible. SM SM! D k PDT k D PDT D KIE = k k! D

2 Defini%ons Primary KIE: A bond is broken or formed to the isotope in the rds. e.g. E2 elimina%on: /D Cl (/D) + + Cl Secondary KIE: The isotope is not directly involved in the rds. e.g. Claisen rearrangement: /D /D Normal KIE: The lighter isotopomer reacts faster: k /k D > 1.0. Inverse KIE: The lighter isotopomer reacts slower: k /k D < 1.0. Equilibrium Isotope Effect (EIE): The isotope affects the posi%on of an equilibrium, rather than the rate of a reac%on.

3 Primary Isotope Effects k /k D _ T + 2 _ + _ T 6.26 C* 3 Br 2 C* 2 -Br + *-Br 4.6 C* 3 Cl 2 C* 2 -Cl + *-Cl 1.5 * 6 N 3 / 2 S 4 N 2 ca. 1 g(cl gcl 4 ) 2 4 * C C 3 * Cr 4 3 C C 3 7.7

4 rigin of the KIE The KIE mainly arises from zero point energy differences. Quantum harmonic oscillator model: The frequency of the oscillator is: v = 1! 2π k µ k is the force constant, which is how s%ff the spring is. µ is the reduced mass, which is the effec%ve mass of the system in the center of mass frame: µ = m m 1 2 m! 1 + m 2

5 rigin of the KIE The energy levels are given by: E n = n+ 1 2 hv n = 0,1,2,...! For n=0, the energy is 0.5hv. This is the zero- point energy (ZPE). Frequency depends on reduced mass, so isotopic subs%tu%on will change the ZPE. Since the ground and transi%on states contain different amounts of ZPE, isotopic subs%tu%on will change the reac%on barrier.

6 rigin of the KIE Consider a homoly%c bond dissocia%on of a C- bond: There is no ZPE in the transi%on state, so the barrier to homolysis will be equal to the difference in zero- point energy. Because the lighter isotope has more ZPE, it has a smaller barrier and reacts faster. This means most KIEs k /k D will be greater than 1.0 (i.e., normal ).

7 rigin of the KIE Consider a homoly%c bond dissocia%on of a C- bond: C- vs C- D stretch: 3000 cm - 1 and 2200 cm - 1, a difference of 800 cm - 1. The ZPE difference is 0.5*h*c*800 = 1.15 kcal/mol. The molar gas constant is kcal/k mol. At 298 K, this is 0.6 kcal/mol. The rate difference is exp( 1.15/0.6) = 6.8. This is the maximum primary KIE.

8 rigin of the KIE In most reac%ons, the bond is not completely broken in the transi%on state: The KIE will be the difference between the ground and transi%on state ZPEs. If the transi%on state retains some ZPE, the difference in ZPEs will be smaller. This means that most KIEs will be less than 6.8.

9 Non- linear Transi%on States Linear transi%on states have larger KIEs than non- linear transi%on states. A B symmetric stretch of linear transition state: central atom is fixed A B asymmetric stretch of nonlinear transition state: central atom moves a lot When the central atom has a small displacement, the frequency of the vibra%on will be hardly affected by which isotope is present. The means the transi%on state will not be affected by the isotope, but the ground state will be. This leads to a larger KIE.

10 ammond Postulate In highly exothermic reac%ons, the transi%on state resembles the star%ng material. This means bonds are mostly s%ll formed in the transi%on state. The difference in KIEs will be small, so a small KIE will be observed. The bonds in a thermoneutral reac%on will largely broken, so larger KIES are expected.

11 ammond Postulate A classic example is from Bruice (JACS ), who studied the KIEs of nitroethane deprotona%on by various amines: Amines whose pk a is closest to that of nitroethane (8.5) will undergo a thermoneutral deprotona%on reac%on. These are the reac%ons with the largest KIEs.

12 Electronic Tuning of Enantioselectivity Ph Ph X N N Mn Cl t-bu t-bu X X N N Mn Cl t-bu t-bu X log (ratio of enantiomers) 2.0 X = C 3, C 3,, Cl, N 2 n X = Me (96% ee) n ρ = -1.37, r = n 1.0 n X = N 2 (22% ee) n σ para 0.8 Jacobsen JACS 1991, 113, 6703

13 X = N 2 X = X = Me ΔE X = N 2 Ar R X = X = Me X Mn IV X Ar R X Mn V X X Mn III X Ar R

14 Basis for the Electronic Effect Ph (D) + NaCl (D) X N N Mn X Cl t-bu t-bu X = C 3, C 3,, Cl, N 2 Ph (D) (D) 6 X k / k D 5 N 2 Cl C 3 C enantiofacial selectivity Jacobsen JACS 1998, 120, 948 Theoretical analysis: Jacobsen JC 2003, 68, 6202 k /k D

15 Rehybridiza%on Considering bends as well as stretches allows us to understand secondary KIEs: sp 3 In-plane Bend ut-of-plane Bend 1350 cm cm -1 sp cm cm -1 Changing from sp 3 to sp 2 decreases the bend frequency from 1350 cm - 1 to 800 cm - 1. This means the transi%on state has less ZPE than the ground state and a normal SKIE is observed (typical: ). Changing from sp 2 to sp 3 increases the bend frequency, leading to an inverse SKIE (typical: ). + (D) k /k D = 0.95 (D)

16 Secondary Isotope Effects k /k D * * Tf * * Ac * * Ac * * 2.06 Me * + CN Me * CN 0.73 * * Cl 2 * * 1.30 Me Et Me * 2 C C* 2 50 ºC * 2 C C* 2

17 Tunnelling Some reac%ons proceed by passing directly through the barrier. /D KIEs of up to 100 can be observed! Left: tunnelling in a [1,2]-shift of a carbene, which has a half-life of one hour at 11 K, despite a barrier of 28 kcal. The deuterated analog is completely stable, which is an infinite KIE! Schreiner and Allen, /science The tunnelling rate depends on barrier width and mass, rather than the barrier height. This results in temperature- independent rates. Tunnelling is common in proton transfers.

18 eavy Atom Isotope Effects eavy atom isotope effects can also be measured, but are much smaller because of the much smaller difference in reduced mass. For example, a primary 12 C/ 13 C KIE is These can be measured by absolute rates: SM SM! D k PDT k D PDT D That is, the rates are measured in separate flasks and then compared. There are two drawbacks to this method: - - Isotopically pure sta%ng materials must be prepared. The result is inaccurate because the error bar in the measurement is on the order of the expected isotope effect.

19 eavy Atom Isotope Effects Alterna%vely, one can measure the rates by intermolecular compe%%on:! SM + SM D k,k D PDT + PDT D That is, an isotopic mixture of star%ng materials are reacted in the same flask, and the KIE inferred from the product distribu%on. Specifically, for a normal KIE, we expect: - - the product to be enriched in the faster- reac%ng light isotopomer the star%ng material to be enrinched in the slower- reac%ng heavy isotopomer The advantages are that: - - product distribu%ons can be determined much more accurately than absolute rates the ini%al isotopic distribu%on can be arbitrary In fact, Singleton has shown that heavy atom carbon isotope effects can be measured for many reac%ons at natural abundance (JACS ).

20 eavy Atom Isotope Effects For example, consider the Bayer Villiger oxida%on of cyclohexanone: + R addition R migration This reac%on has two steps: nucleophilic addi%on and migra%on. For the nucleophilic addi%on step, we expect reac%on to be slightly faster with the unlabeled isotopomer: + R fast R * + R slow * R * = 13 C label If we recover star%ng material, it should be enriched in the slower reac%ng 13 C isotopomer. (The KIE in the second step doesn t maner because the first step is irreversible.) This is the same principle as that for kine%c resolu%ons.

21 eavy Atom Isotope Effects The enrichment is related to the KIE by the following equa%on: R ( ) k 2 = 1 F R 1! 0 1 k 1 where R is the isotopic ra%o in the recovered star%ng material, R 0 is the original isotopic ra%o, 1- F 1 is the conversion, and k 2 /k 1 is 1/KIE. Using quan%ta%ve 13 C and 2 NMR: (assumed) 1.00 (assumed) There is a large primary kine%c isotope effect at the carbonyl carbon and an inverse secondary KIE from the hybridiza%on change at the adjacent protons.

22 eavy Atom Isotope Effects If we apply the same analysis to product arer running the reac%on to low conversion, we will find an en%rely different result! 1.00 (assumed) These measure the intramolecular KIE! We are actually measuring a post- rate- determining selec%vity: * + R rate-determining addition KIE=1 * R slow primary KIE * either of the enantiotopic carbons can migrate fast * (The natural abundance of carbon- 13 is 1.1%, so we can assume there is only one label per molecule.)