Editing Kinetic isotope effect (section)

== Experiments ==

Simmons and [[John F. Hartwig|Hartwig]] refer to the following three cases as the main types of KIE experiments involving C-H bond functionalization:<ref name="Simmons_2012">{{cite journal | vauthors = Simmons EM, Hartwig JF | title = On the Interpretation of Deuterium Kinetic Isotope Effects in C–H Bond Functionalizations by Transition-Metal Complexes | journal = Angewandte Chemie International Edition | date = March 2012 | volume = 51 | issue = 1 | pages = 3066–72 | doi = 10.1002/anie.201107334 | pmid = 22392731 }}</ref>

:'''A) '''KIE determined from absolute rates of two parallel reactions
[[File:KIE determined from absolute rates of two parallel reactions.png|center]]
In this experiment, the rate constants for the normal substrate and its isotopically labeled analogue are determined independently, and the KIE is obtained as a ratio of the two. The accuracy of the measured KIE is severely limited by the accuracy with which each of these rate constants can be measured. Furthermore, reproducing the exact conditions in the two parallel reactions can be very challenging. Nevertheless, a measurement of a large kinetic isotope effect through direct comparison of rate constants is indicative that C-H bond cleavage occurs at the rate-determining step. (A smaller value could indicate an isotope effect due to a pre-equilibrium, so that the C-H bond cleavage occurs somewhere before the rate-determining step.)

:'''B) '''KIE determined from an intermolecular competition
[[File:KIE determined from an intermolecular competition.png|center]]
This type of experiment, uses the same substrates as used in Experiment A, but they are allowed in to react in the same container, instead of two separate containers. The KIE in this experiment is determined by the relative amount of products formed from C-H versus C-D functionalization (or it can be inferred from the relative amounts of unreacted starting materials). One must quench the reaction before it goes to completion to observe the KIE (see the Evaluation section below). Generally, the reaction is halted at low conversion (~5 to 10% conversion) or a large excess (> 5 equiv.) of the isotopic mixture is used. This experiment type ensures that both C-H and C-D bond functionalizations occur under exactly the same conditions, and the ratio of products from C-H and C-D bond functionalizations can be measured with much greater precision than the rate constants in Experiment A. Moreover, only a single measurement of product concentrations from a single sample is required. However, an observed kinetic isotope effect from this experiment is more difficult to interpret, since it may either mean that C-H bond cleavage occurs during the rate-determining step or at a product-determining step ensuing the rate-determining step. The absence of a KIE, at least according to Simmons and Hartwig, is nonetheless indicative of the C-H bond cleavage not occurring during the rate-determining step.

:'''C) '''KIE determined from an intramolecular competition
[[File:KIE determined from an intramolecular competition.png|center]]
This type of experiment is analogous to Experiment B, except this time there is an intramolecular competition for the C-H or C-D bond functionalization. In most cases, the substrate possesses a directing group (DG) between the C-H and C-D bonds. Calculation of the KIE from this experiment and its interpretation follow the same considerations as that of Experiment B. However, the results of Experiments B and C will differ if the irreversible binding of the isotope-containing substrate takes place in Experiment B ''prior'' to the cleavage of the C-H or C-D bond. In such a scenario, an isotope effect may be observed in Experiment C (where choice of the isotope can take place even after substrate binding) but not in Experiment B (since the choice of whether C-H or C-D bond cleaves is already made as soon as the substrate binds irreversibly). In contrast to Experiment B, the reaction need not be halted at low consumption of isotopic starting material to obtain an accurate ''k''{{sub|H}}/''k''{{sub|D}}, since the ratio of H and D in the starting material is 1:1, regardless of the extent of conversion.

One non-C-H activation example of different isotope effects being observed in the case of intermolecular (Experiment B) and intramolecular (Experiment C) competition is the [[photodissociation|photolysis]] of diphenyldiazomethane in the presence of ''t''-butylamine. To explain this result, the formation of diphenylcarbene, followed by irreversible nucleophilic attack by ''t''-butylamine was proposed. Because there is little isotopic difference in the rate of nucleophilic attack, the intermolecular experiment resulted in a KIE close to 1. In the intramolecular case, however, the product ratio is determined by the proton transfer that occurs after the nucleophilic attack, a process which has a substantial KIE of 2.6.<ref>{{Cite journal|last1=Newall|first1=A. Raymond|last2=Hayes|first2=John|last3=Bethell|first3=Donald|date=1974-01-01|title=Intermediates in the decomposition of aliphatic diazo-compounds. Part XI. Mechanistic studies on the reaction of diphenylmethylene with amines in solution|journal=Journal of the Chemical Society, Perkin Transactions 2|language=en|issue=11|pages=1307–1312|doi=10.1039/P29740001307|issn=1364-5471}}</ref>
[[File:Inter vs intramolecular competition KIE.png|center|frameless|600x600px]]
Thus, Experiments A, B, and C will give results of differing levels of precision and require different experimental setup and ways of analyzing data. As a result, the feasibility of each type of experiment depends on the kinetic and stoichiometric profile of the reaction, as well as the physical characteristics of the reaction mixture (e.g. homogeneous vs. heterogeneous). Moreover, as noted in the paragraph above, the experiments provide KIE data for different steps of a multi-step reaction, depending on the relative locations of the rate-limiting step, product-determining steps, and/or C-H/D cleavage step.

The hypothetical examples below illustrate common scenarios. Consider the following reaction coordinate diagram. For a reaction with this profile, all three experiments (A, B, and C) will yield a significant primary KIE:
[[File:Reaction energy profile for when C-H cleavage occurs at the RDS.png|thumb|center|350px|Reaction energy profile for when C-H cleavage occurs at the RDS]]
On the other hand, if a reaction follows the following energy profile, in which the C-H or C-D bond cleavage is irreversible but occurs after the rate-determining step (RDS), no significant KIE will be observed with Experiment A, since the overall rate is not affected by the isotopic substitution. Nevertheless, the irreversible C-H bond cleavage step will give a primary KIE with the other two experiments, since the second step would still affect the product distribution. Therefore, with Experiments B and C, it is possible to observe the KIE even if C-H or C-D bond cleavage occurs not in the rate-determining step, but in the product-determining step.
[[File:Reaction energy profile for when the C-H bond cleavage occurs at a product-determining step after the RDS.png|thumb|center|350px|Reaction energy profile for when the C-H bond cleavage occurs at a product-determining step after the RDS]]

{{hidden|toggle=left|1=Evaluation of KIEs in a Hypothetical Multi-Step Reaction|2=
A large part of the KIE arises from vibrational ZPE differences between the reactant ground state and the transition state that vary between the reactant and its isotopically substituted analog. While one can carry out involved calculations of KIEs using computational chemistry, much of the work done is of simpler order that involves the investigation of whether particular isotopic substitutions produce a detectable KIE or not. Vibrational changes from isotopic substitution at atoms away from the site where the reaction occurs tend to cancel between the reactant and the transition state. Therefore, the presence of a KIE indicates that the isotopically labeled atom is at or very near the reaction site.

The absence of an isotope effect is more difficult to interpret: It may mean that the isotopically labeled atom is away from the reaction site, but it may also mean there are certain compensating effects that lead to the lack of an observable KIE. For example, the differences between the reactant and the transition state ZPEs may be identical between the normal reactant and its isotopically labeled version. Alternatively, it may mean that the isotopic substitution is at the reaction site, but vibrational changes associated with bonds to this atom occur after the rate-determining step. Such a case is illustrated in the following example, in which ABCD represents the atomic skeleton of a molecule.

[[File:KIE General Background Hypothetical Reaction.png|none]]

Assuming steady state conditions for the intermediate ABC, the overall rate of reaction is the following:

: <math>\frac{d[A]}{dt} = \frac{k_1k_3[ABCD]}{k_2[D]+k_3}</math>

If the first step is rate-determining, this equation reduces to:

: <math>\frac{d[A]}{dt} = k_1[ABCD]</math>

Or if the second step is rate-determining, the equation reduces to:

: <math>\frac{d[A]}{dt} = \frac{k_1k_3[ABCD]}{k_2[D]}</math>

In most cases, isotopic substitution at A, especially if it is a heavy atom, will not alter ''k''{{sub|1}} or ''k''{{sub|2}}, but it will most probably alter ''k''{{sub|3}}. Hence, if the first step is rate-determining, there will not be an observable kinetic isotope effect in the overall reaction with isotopic labeling of A, but there will be one if the second step is rate-determining. For intermediate cases where both steps have comparable rates, the magnitude of the kinetic isotope effect will depend on the ratio of ''k''{{sub|3}} and ''k''{{sub|2}}.

Isotopic substitution of D will alter ''k''{{sub|1}} and ''k''{{sub|2}} while not affecting ''k''{{sub|3}}. The KIE will always be observable with this substitution since ''k''{{sub|1}} appears in the simplified rate expression regardless of which step is rate-determining, but it will be less pronounced if the second step is rate-determining due to some cancellation between the isotope effects on ''k''{{sub|1}} and ''k''{{sub|2}}. This outcome is related to the fact that equilibrium isotope effects are usually smaller than KIEs.

Isotopic substitution of B will clearly alter ''k''{{sub|3}}, but it may also alter ''k''{{sub|1}} to a lesser extent if the B-C bond vibrations are affected in the transition state of the first step. There may thus be a small isotope effect even if the first step is rate-determining.

This hypothetical consideration reveals how observing KIEs may be used to investigate reaction mechanisms. The existence of a KIE is indicative of a change to the vibrational force constant of a bond associated with the isotopically labeled atom at or before the rate-controlling step. Intricate calculations may be used to learn a great amount of detail about the transition state from observed kinetic isotope effects. More commonly, though, the mere qualitative knowledge that a bond associated with the isotopically labeled atom is altered in a certain way can be very useful.<ref name=Buncel3>{{cite book | vauthors = Buncel E, Lee CC | title = Carbon-13 in Organic Chemistry | series = Isotopes in Organic Chemistry | publisher = Elsevier | location = Amsterdam | date = 1977 | volume = 3 | isbn = 978-0-444-41472-4 | oclc = 606113159}}</ref>
}}

=== Evaluation of rate constant ratios from intermolecular competition reactions ===
In competition reactions, KIE is calculated from isotopic product or remaining reactant ratios after the reaction, but these ratios depend strongly on the extent of completion of the reaction. Most often, the isotopic substrate consists of molecules labeled in a specific position and their unlabeled, ordinary counterparts.<ref name="Saunders" /> One can also, in case of {{sup|13}}C KIEs, as well as similar cases, simply rely on the natural abundance of the isotopic carbon for the KIE experiments, eliminating the need for isotopic labeling.<ref name="Singleton_1995">{{cite journal|last1=Singleton|first1=Daniel A.|last2 = Thomas | first2 = Allen A. | name-list-style = vanc |title=High-Precision Simultaneous Determination of Multiple Small Kinetic Isotope Effects at Natural Abundance|journal=Journal of the American Chemical Society|date=September 1995|volume=117|issue=36|pages=9357–9358|doi=10.1021/ja00141a030|bibcode=1995JAChS.117.9357S }}</ref>
The two isotopic substrates will react through the same mechanism, but at different rates. The ratio between the amounts of the two species in the reactants and the products will thus change gradually over the course of the reaction, and this gradual change can be treated as follows:<ref name="Saunders" /> Assume that two isotopic molecules, A{{sub|1}} and A{{sub|2}}, undergo irreversible competition reactions:
:<math chem>\begin{align}
\ce{ {A1} + {B} + {C} + \cdots}\ &\ce{->[k_1] P1}\\
\ce{ {A2} + {B} + {C} + \cdots}\ &\ce{->[k_2] P2}
\end{align}</math>
The KIE for this scenario is found to be:

:<math>\text{KIE} = {k_1 \over k_2} = \frac{\ln (1-F_1)}{\ln (1-F_2) }</math>

Where F{{sub|1}} and F{{sub|2}} refer to the fraction of conversions for the isotopic species A{{sub|1}} and A{{sub|2}}, respectively.

{{hidden|toggle=left|1=Evaluation|2=
In this treatment, all other reactants are assumed to be non-isotopic. Assuming further that the reaction is of first order with respect to the isotopic substrate A, the following general rate expression for both these reactions can be written:

:<math chem>\text{rate} = {-d[\ce A_n]\over dt} = k_n \times [\ce A_n] \times f([\ce B],[\ce C],\cdots) \text{ where } n=1 \text{ or } 2</math>

Since f([B],[C],...) does not depend on the isotopic composition of A, it can be solved for in both rate expressions with A{{sub|1}} and A{{sub|2}}, and the two can be equated to derive the following relations:

:<math chem>{1\over k_1} \times \ce{\mathit{d}[A1]\over [A1]} = {1\over k_2} \times \ce{\mathit{d}[A2] \over [A2]}</math>

:<math chem>{1\over k_1} \times \int \limits_\ce{[A1]^0}^\ce{[A1]} {d[\ce A'_1]\over [\ce A'_1]} = {1\over k_2} \times \int \limits_\ce{[A2]^0}^\ce{[A2]}{d[\ce A'_2] \over [\ce A'_2]}</math>

Where [A{{sub|1}}]{{sup|0}} and [A{{sub|2}}]{{sup|0}} are the initial concentrations of A{{sub|1}} and A{{sub|2}}, respectively. This leads to the following KIE expression:

:<math chem>{k_1 \over k_2} = \frac\ce{\ln ([A1]/[A1]^0)}\ce{\ln ([A2]/[A2]^0) }</math>

Which can also be expressed in terms of fraction amounts of conversion of the two reactions, F{{sub|1}} and F{{sub|2}}, where 1-F{{sub|n}}=[A{{sub|n}}]/[A{{sub|n}}]{{sup|0}} for n = 1 or 2, as follows:

:<math chem>{k_1 \over k_2} = \frac{\ln (1-F_1)}{\ln (1-F_2) }</math>

[[File:F2 vs. F1 in KIE Competition Reactions.png|thumb|center|500px|Relation between the fractions of conversion for the two competing reactions with isotopic substrates. The rate constant ratio ''k''{{sub|1}}/''k''{{sub|2}} (KIE) is varied for each curve.]]

As for finding the KIEs, mixtures of substrates containing stable isotopes may be analyzed with a mass spectrometer, which yields the ratios of the isotopic molecules in the initial substrate (defined here as [A{{sub|2}}]{{sup|0}}/[A{{sub|1}}]{{sup|0}}=R{{sub|0}}), in the substrate after some conversion ([A{{sub|2}}]/[A{{sub|1}}]=R), or in the product ([P{{sub|2}}]/[P{{sub|1}}]=R{{sub|P}}). When one of the species, e.g. 2, is a radioisotope, its mixture with the other species can also be analyzed by its radioactivity, which is measured in molar activities that are proportional to [A{{sub|2}}]{{sup|0}} / ([A{{sub|1}}]{{sup|0}}+[A{{sub|2}}]{{sup|0}}) ≈ [A{{sub|2}}]{{sup|0}}/[A{{sub|1}}]{{sup|0}} = R{{sub|0}} in the initial substrate, [A{{sub|2}}] / ([A{{sub|1}}]+[A{{sub|2}}]) ≈ [A{{sub|2}}]/[A{{sub|1}}] = R in the substrate after some conversion, and [R{{sub|2}}] / ([R{{sub|1}}]+[R{{sub|2}}]) ≈  [R{{sub|2}}]/[R{{sub|1}}] = R{{sub|P}}, so that the same ratios as in the other case can be measured as long as the radioisotope is present in tracer amounts. Such ratios may also be determined using NMR spectroscopy.<ref name=Jankowski>{{cite journal | vauthors = Jankowski S | title = Application of NMR spectroscopy in isotope effects studies. | journal = Annual Reports on NMR Spectroscopy | date = January 2009 | volume = 68 | pages = 149–191 | doi = 10.1016/S0066-4103(09)06803-3 | isbn = 978-0-12-381041-0 }}</ref>

When the substrate composition is followed, the following KIE expression in terms of R{{sub|0}} and R can be derived:

:<math>\text{KIE} = \frac{k_1}{k_2} = \frac {\ln(1-F_1)}{\ln[(1-F_1)R/R_0]}</math>
}}

{{hidden|toggle=left|1=Measurement of F{{sub|1}} in terms of weights per unit volume or molarities of the reactants|2=
Taking the ratio of R and R{{sub|0}} using the previously derived expression for F{{sub|2}}, one gets:
:<math chem>{R \over R_0} = \ce{\frac {[A2]/[A1]}{[A2]^0/[A1]^0}} = \ce{\frac {[A2]/[A2]^0}{[A1]/[A1]^0}} = \frac{1-F_2}{1-F_1}=(1-F_1)^{(k_2/k_1)-1}</math>

This relation can be solved in terms of the KIE to obtain the KIE expression given above. When the uncommon isotope has very low abundance, both R{{sub|0}} and R are very small and not significantly different from each other, such that 1-''F''{{sub|1}} can be approximated with ''m''/''m''{{sub|0}} or ''c''/''c''{{sub|0}}.
}}

Isotopic enrichment of the starting material can be calculated from the dependence of ''R/R''{{sub|0}} on ''F''{{sub|1}} for various KIEs, yielding the following figure. Due to the exponential dependence, even very low KIEs lead to large changes in isotopic composition of the starting material at high conversions.

[[File:R to R0 vs. F1 in KIE Competition Reactions.png|thumb|center|500px|The isotopic enrichment of the relative amount of species 2 with respect to species 1 in the starting material as a function of conversion of species 1. The value of the KIE (''k''{{sub|1}}/''k''{{sub|2}}) is indicated at each curve.]]

When the products are followed, the KIE can be calculated using the products ratio ''R{{sub|P}}'' along with ''R''{{sub|0}} as follows:

:<math>{k_1 \over k_2} = \frac {\ln(1-F_1)} {\ln[1-(F_1R_P/R_0)]}</math>

=== Kinetic isotope effect measurement at natural abundance ===
'''KIE measurement at natural abundance''' is a simple general method for measuring KIEs for [[chemical reaction]]s performed with materials of [[natural abundance]]. This technique for measuring KIEs overcomes many limitations of previous KIE measurement methods. KIE measurements from isotopically labeled materials require a new synthesis for each isotopically labeled material (a process often prohibitively difficult), a competition reaction, and an analysis.<ref name="Simmons_2012" /> The KIE measurement at [[natural abundance]] avoids these issues by taking advantage of high precision quantitative techniques ([[nuclear magnetic resonance spectroscopy]], [[isotope-ratio mass spectrometry]]) to site selectively measure [[kinetic fractionation]] of [[isotope]]s, in either product or starting material for a given [[chemical reaction]].

==== Single-pulse NMR ====
Quantitative single-pulse [[nuclear magnetic resonance spectroscopy]] (NMR) is a method amenable for measuring [[kinetic fractionation]] of [[isotope]]s for natural abundance KIE measurements. Pascal et al. were inspired by studies demonstrating dramatic variations of deuterium within identical compounds from different sources and hypothesized that NMR could be used to measure {{sup|2}}H KIEs at natural abundance.<ref>{{Cite journal| vauthors = Martin GJ, Martin ML |title=Deuterium labelling at the natural abundance level as studied by high field quantitative 2H NMR |journal=Tetrahedron Letters|language=en|year=1984|volume=22|issue=36|pages=3525–3528|doi=10.1016/s0040-4039(01)81948-1}}</ref><ref name=":0" /> Pascal and coworkers tested their hypothesis by studying the [[insertion reaction]] of dimethyl diazomalonate into [[cyclohexane]]. Pascal et al. measured a KIE of 2.2 using {{sup|2}}H NMR for materials of natural abundance.<ref name=":0">{{cite journal| vauthors = Pascal Jr RA, Baum MW, Wagner CK, Rodgers LR |title=Measurement of deuterium kinetic isotope effects in organic reactions by natural-abundance deuterium NMR spectroscopy|journal=Journal of the American Chemical Society|date=September 1984|volume=106|issue=18|pages=5377–5378|doi=10.1021/ja00330a071 |bibcode=1984JAChS.106.5377P }}</ref>

[[File:Chemical reaction 1.png|frameless|none|500px]]

Singleton and coworkers demonstrated the capacity of {{sup|13}}C NMR based natural abundance KIE measurements for studying the mechanism of the [4 + 2] [[cycloaddition]] of [[isoprene]] with [[maleic anhydride]].<ref name="Singleton_1995" /> Previous studies by Gajewski on isotopically enrich materials observed KIE results that suggested an asynchronous transition state, but were always consistent, within error, for a perfectly synchronous [[reaction mechanism]].<ref>{{cite journal| vauthors = Gajewski JJ, Peterson KB, Kagel JR, Huang YJ |date=December 1989|title=Transition-state structure variation in the Diels-Alder reaction from secondary deuterium kinetic isotope effects. The reaction of nearly symmetrical dienes and dienophiles is nearly synchronous|journal=Journal of the American Chemical Society|volume=111|issue=25|pages=9078–9081|doi=10.1021/ja00207a013 |bibcode=1989JAChS.111.9078G }}</ref>

[[File:Chemical reaction 2.png|frameless|none|500px]]

This work by Singleton et al. established the measurement of multiple {{sup|13}}C KIEs within the design of a single experiment. These {{sup|2}}H and {{sup|13}}C KIE measurements determined at natural abundance found the "inside" hydrogens of the diene experience a more pronounced {{sup|2}}H KIE than the "outside" hydrogens and the C1 and C4 experience a significant KIE. These key observations suggest an asynchronous [[reaction mechanism]] for the [[cycloaddition]] of [[isoprene]] with [[maleic anhydride]].

[[File:KIE measurements.png|frameless|274x274px]]

The limitations for determining KIEs at natural abundance using NMR are that the recovered material must have a suitable amount and purity for NMR analysis (the signal of interest should be distinct from other signals), the reaction of interest must be irreversible, and the [[reaction mechanism]] must not change for the duration of the [[chemical reaction]].

Experimental details for using quantitative single pulse NMR to measure KIE at natural abundance as follows: the experiment needs to be performed under quantitative conditions including a relaxation time of 5 T{{sub|1}}, measured 90° flip angle, a digital resolution of at least 5 points across a peak, and a signal:noise greater than 250. The raw FID is zero-filled to at least 256K points before the Fourier transform. NMR spectra are phased and then treated with a zeroth order baseline correction without any tilt correction. Signal integrations are determined numerically with a minimal tolerance for each integrated signal.<ref name="Singleton_1995" />{{clarify|date=November 2018}}

==== Organometallic reaction mechanism elucidation examples ====
Colletto et al. developed a regioselective β-arylation of benzo[b]thiophenes at room temperature with aryl iodides as coupling partners and sought to understand the mechanism of this reaction by performing natural abundance KIE measurements via single pulse NMR.<ref name=":1">{{cite journal | vauthors = Colletto C, Islam S, Juliá-Hernández F, Larrosa I | title = Room-Temperature Direct β-Arylation of Thiophenes and Benzo[b]thiophenes and Kinetic Evidence for a Heck-type Pathway | journal = Journal of the American Chemical Society | volume = 138 | issue = 5 | pages = 1677–83 | date = February 2016 | pmid = 26788885 | pmc = 4774971 | doi = 10.1021/jacs.5b12242 | bibcode = 2016JAChS.138.1677C }}</ref>
[[File:Reaction scheme for the beta arylation of benzo b thiophenes.png|none|thumb|553x553px|Regioselective β-arylation of benzo[b]thiophenes. HFiP (usually HFIP) refers to [[hexafluoroisopropanol]], or CF<small>3</small>-CHOH-CF<sub>3</sub>]]

[[File:1H KIEs for beta arylation of benzo b thiophenes.png|none|thumb|200x200px|{{sup|2}}H KIEs measured at natural abundance]]

[[File:13C KIEs for beta arylation of benzo b thiophenes.png|none|thumb|200x200px|{{sup|13}}C KIEs measured at natural abundance]]

The observation of a primary {{sup|13}}C isotope effect at C3, an inverse {{sup|2}}H isotope effect, a secondary {{sup|13}}C isotope effect at C2, and the lack of a {{sup|2}}H isotope effect at C2; led Colletto ''et al.'' to suggest a Heck-type reaction mechanism for the regioselective {{math|β}}-arylation of benzo[b]thiophenes at room temperature with aryl iodides as coupling partners.<ref name=":1" />

Frost ''et al.'' sought to understand the effects of [[Lewis acid]] additives on the mechanism of enantioselective [[palladium]]-catalyzed C-N bond activation using natural abundance KIE measurements via single pulse NMR.<ref name=":2">{{cite journal | vauthors = Frost GB, Serratore NA, Ogilvie JM, Douglas CJ | title = Mechanistic Model for Enantioselective Intramolecular Alkene Cyanoamidation via Palladium-Catalyzed C-CN Bond Activation | journal = The Journal of Organic Chemistry | volume = 82 | issue = 7 | pages = 3721–3726 | date = April 2017 | pmid = 28294618 | doi = 10.1021/acs.joc.7b00196 | pmc = 5535300 }}</ref>
[[File:Enantioselective intramolecular alkene cyanoamidation reaction scheme.png|none|thumb|513x513px|Enantioselective intramolecular alkene cyanoamidation]]
[[File:13C KIEs for enantioselective intramolecular alkene cyanoamidation reaction scheme.png|none|thumb|542x542px|{{sup|13}}C KIEs for enantioselective intramolecular alkene cyanoamidation reaction (left no additive, right add BPh{{sub|3}})]]
The primary {{sup|13}}C KIE observed in the absence of BPh{{sub|3}} suggests a reaction mechanism with rate limiting cis oxidation into the C–CN bond of the [[cyanoformamide]]. The addition of BPh{{sub|3}} causes a relative decrease in the observed {{sup|13}}C KIE which led Frost et al. to suggest a change in the rate limiting step from cis oxidation to coordination of palladium to the cyanoformamide.<ref name=":2" />

==== DEPT-55 NMR ====
Though KIE measurements at natural abundance are a powerful tool for understanding reaction mechanisms, the amounts of material needed for analysis can make this technique inaccessible for reactions that use expensive reagents or unstable starting materials. To mitigate these limitations, Jacobsen and coworkers developed {{sup|1}}H to {{sup|13}}C polarization transfer as a means to reduce the time and material required for KIE measurements at natural abundance. The [[distortionless enhancement by polarization transfer]] (DEPT) takes advantage of the larger [[gyromagnetic ratio]] of {{sup|1}}H over {{sup|13}}C, to theoretically improve measurement sensitivity by a factor of 4 or decrease experiment time by a factor of 16. This method for natural abundance kinetic isotope measurement is favorable for analysis for reactions containing unstable starting materials, and catalysts or products that are relatively costly.<ref>{{cite journal | vauthors = Kwan EE, Park Y, Besser HA, Anderson TL, Jacobsen EN | title = 13C Kinetic Isotope Effect Measurements Enabled by Polarization Transfer | journal = Journal of the American Chemical Society | volume = 139 | issue = 1 | pages = 43–46 | date = January 2017 | pmid = 28005341 | doi = 10.1021/jacs.6b10621 | pmc = 5674980 }}</ref>

Jacobsen and coworkers identified the [[thiourea]]-catalyzed glycosylation of galactose as a reaction that met both of the aforementioned criteria (expensive materials and unstable substrates) and was a reaction with a poorly understood mechanism.<ref>{{cite journal | vauthors = Park Y, Harper KC, Kuhl N, Kwan EE, Liu RY, Jacobsen EN | title = Macrocyclic bis-thioureas catalyze stereospecific glycosylation reactions | journal = Science | volume = 355 | issue = 6321 | pages = 162–166 | date = January 2017 | pmid = 28082586 | pmc = 5671764 | doi = 10.1126/science.aal1875 | bibcode = 2017Sci...355..162P }}</ref> Glycosylation is a special case of nucleophilic substitution that lacks clear definition between S{{sub|N}}1 and S{{sub|N}}2 mechanistic character. The presence of the oxygen adjacent to the site of displacement (i.e., C1) can stabilize positive charge. This charge stabilization can cause any potential concerted pathway to become asynchronous and approaches intermediates with oxocarbenium character of the S{{sub|N}}1 mechanism for glycosylation.

[[File:Reaction Scheme for Thiourea catalyzed glycosylation of galactose.png|alt=Reaction scheme for thiourea catalyzed glycosylation of galactose|none|thumb|492x492px|Reaction scheme for thiourea catalyzed glycosylation of galactose]]
[[File:Kinetic Isotope Effect Measurements for Thiourea catalyzed glycosylation of galactose.png|alt=13C kinetic isotope effect measurements for thiourea catalyzed glycosylation of galactose|none|thumb|350x350px|{{sup|13}}C kinetic isotope effect measurements for thiourea catalyzed glycosylation of galactose]]

Jacobsen and coworkers observed small normal KIEs at C1, C2, and C5 which suggests significant oxocarbenium character in the transition state and an asynchronous reaction mechanism with a large degree of charge separation.

==== Isotope-ratio mass spectrometry ====

High precision [[isotope-ratio mass spectrometry]] (IRMS) is another method for measuring [[kinetic fractionation]] of [[isotope]]s for natural abundance KIE measurements. Widlanski and coworkers demonstrated {{sup|34}}S KIE at natural abundance measurements for the [[hydrolysis]] of [[sulfate]] monoesters. Their observation of a large KIE suggests S-O bond cleavage is rate controlling and likely rules out an associate [[reaction mechanism]].<ref>{{cite journal | vauthors = Burlingham BT, Pratt LM, Davidson ER, Shiner VJ, Fong J, Widlanski TS | title = 34S isotope effect on sulfate ester hydrolysis: mechanistic implications | journal = Journal of the American Chemical Society | volume = 125 | issue = 43 | pages = 13036–7 | date = October 2003 | pmid = 14570471 | doi = 10.1021/ja0279747 | bibcode = 2003JAChS.12513036B }}</ref>
[[File:34S isotope effect on sulfate ester hydrolysis reaction scheme.png|none|thumb|525x525px|34S isotope effect on sulfate ester hydrolysis reaction]]

The major limitation for determining KIEs at natural abundance using IRMS is the required site selective degradation without isotopic fractionation into an analyzable small molecule, a non-trivial task.<ref name="Singleton_1995" />