Kinetic isotope effect

An example of the kinetic isotope effect. In the reaction ofmethyl bromide with cyanide, the kinetic isotope effect of the car-bon in the methyl group was found to be 1.082 ± 0.008.[1][2]

The kinetic isotope effect (KIE) is the change in therate of a chemical reaction when one of the atoms in thereactants is substituted with one of its isotopes. Formally,it is the ratio of rate constants for the reactions involvingthe light (kL) and the heavy (kH) isotopically substitutedreactants:

KIE =kLkH

1 Background

The kinetic isotope effect is considered to be one of themost essential and sensitive tools for the study of reactionmechanisms, the knowledge of which allows the improve-ment of the desirable qualities of the corresponding reac-tions. For example, kinetic isotope effects can be usedto reveal whether a nucleophilic substitution reaction fol-lows a unimolecular (SN1) or bimolecular (SN2) path-way.In the reaction of methyl bromide and cyanide (shown inintro section), the observed methyl carbon kinetic isotopeeffect indicates an SN2 mechanism.[1] Depending on thepathway, different strategies may be used to stabilize thetransition state of the rate-determining step of the reac-tion and improve the reaction rate and selectivity, whichare important for industrial applications.

Isotopic rate changes are most pronounced when therelative mass change is greatest, since the effect is re-lated to vibrational frequencies of the affected bonds.

For instance, changing a hydrogen atom (H) to its iso-tope deuterium (D) represents a 100% increase in mass,whereas in replacing carbon−12 with carbon-13, themass increases by only 8 percent. The rate of a reac-tion involving a C–H bond is typically 6–10 times fasterthan the corresponding C–D bond, whereas a 12C reac-tion is only 4 percent faster than the corresponding 13Creaction (even though, in both cases, the isotope is oneatomic mass unit heavier).Isotopic substitution can modify the rate of reaction in avariety of ways. In many cases, the rate difference canbe rationalized by noting that the mass of an atom af-fects the vibrational frequency of the chemical bond thatit forms, even if the electron configuration is nearly identi-cal. Heavier isotopes will (classically) lead to lower vibra-tion frequencies, or, viewed quantum mechanically, willhave lower zero-point energy. With a lower zero-pointenergy, more energy must be supplied to break the bond,resulting in a higher activation energy for bond cleavage,which in turn lowers the measured rate (see, for example,the Arrhenius equation).

2 Classification

2.1 Primary kinetic isotope effects

A primary kinetic isotope effect may be found when abond to the isotopically labeled atom is being formed orbroken. For the previously mentioned nucleophilic sub-stitution reactions, primary kinetic isotope effects havebeen investigated for both the leaving groups, the nucle-ophiles, and the α-carbon at which the substitution oc-curs. Interpretation of the leaving group kinetic isotopeeffects had been difficult at first due to significant contri-butions from temperature independent factors. Kineticisotope effects at the α-carbon can be used to developsome understanding into the symmetry of the transitionstate in SN2 reactions, although this kinetic isotope ef-fect is less sensitive than what would be ideal, also due tocontribution from non-vibrational factors.[1]

2.2 Secondary kinetic isotope effects

A secondary kinetic isotope effect is observed when nobond to the isotopically substituted atom in the reactant isbroken or formed in the rate-determining step of a reac-tion. By its definition, secondary kinetic isotope effects

1

2 3 THEORY

tend to be much smaller than primary kinetic isotope ef-fects; however, since kinetic isotope effects can be cal-culated and measured to very high precision, secondarykinetic isotope effects are still very useful for elucidatingreaction mechanisms.For the aforementioned nucleophilic substitution reac-tions, secondary hydrogen kinetic isotope effects at theα-carbon provide a direct means to distinguish betweenSN1 and SN2 reactions. It has been found that SN1 reac-tions typically lead to large secondary kinetic isotope ef-fects, approaching to their theoretical maximum at about1.22, while SN2 reactions typically yield kinetic isotopeeffects that are very close to or less than unity. Kineticisotope effects that are greater than 1 are referred to asnormal kinetic isotope effects, while kinetic isotope ef-fects that are less than one are referred to as inverse ki-netic isotope effects. In general, smaller force constantsin the transition state are expected to yield a normal ki-netic isotope effect, and larger force constants in the tran-sition state are expected to yield an inverse kinetic isotopeeffect when stretching vibrational contributions dominatethe kinetic isotope effect.[1]

The magnitudes of such secondary isotope effects at theα-carbon are largely determined by the Cα-H(D) vibra-tions. For an SN1 reaction, since the carbon is convertedinto an sp2 hybridized carbenium ion during the transitionstate for the rate-redermining step with an increase in Cα-H(D) bond order, an inverse kinetic isotope effect wouldbe expected if only the stretching vibrations were impor-tant. The observed large normal kinetic isotope effectsare found to be caused by significant out-of-plane bend-ing vibrational contributions when going from the reac-tants to the transition state of carbenium formation. ForSN2 reactions, bending vibrations still play an importantrole for the kinetic isotope effect, but stretching vibra-tional contributions are of more comparable magnitude,and the resulting kinetic isotope effect may be normal orinverse depending on the specific contributions of the re-spective vibrations.[1][3][4]

3 Theory

The theoretical treatment of isotope effects relies heavilyon transition state theory, which assumes a single poten-tial energy surface for the reaction, and a barrier betweenthe reactants and the products on this surface, on top of

which resides the transition state.[5][6] The kinetic isotopeeffect arises largely from the changes which the isotopicperturbation produces along the minimum energy path-way on this reaction energy surface, which may only beaccounted for with quantummechanical treatments of thesystem. Depending on the mass and energy of the re-acting species, quantum mechanical tunneling may alsomake a large contribution to an observed kinetic isotopeeffect.[5]

Of the various theoretical treatments of kinetic isotopeeffects, Bigeleisen’s seems to be the most popular. Hisbasic general equation for the hydrogen/deuterium ki-netic isotope effects is given below, neglecting tunnellingcontributions which can be introduced as a separate fac-tor. The subscripts H and D refer to hydrogen and deu-terium substituted substrates, respectively.[4]

kHkD

=

(s‡HsD

s‡DsH

)(M‡

HMD

M‡DMH

)3/2(I‡AHI‡BHI‡CH

I‡ADI‡BDI‡CD

IADIBDICD

IAHIBHICH

)1/2

×

3N‡−7∏i=1

1−e−u‡iD

1−e−u‡iH

3N−6∏i=1

1−e−uiH

1−e−uiD

e−1/2(

3N‡−7∑i=1

(u‡iH−u‡

iD)−3N−6∑i=1

(uiH−uiD))

The S factors are the symmetry numbers for the reac-tants and transition states. The M factors are the molec-ular masses of the corresponding species, and the I fac-tors are the moments of inertia about the three princi-pal axes. The uᵢ factors are determined from the corre-sponding vibrational frequencies, νᵢ, through uᵢ = h νᵢ/kT.N and N‡ are the number of atoms in the reactants andthe transition states, respectively.[4] The complex expres-sion given above can be represented as the product of fourseparate factors, as shown below, from which some pos-sible simplifications for hydrogen/deuterium kinetic iso-tope effects can be more easily seen.[4]

kHkD

= S ×MMI × EXC × ZPE

The S factor is the ratio of the symmetry numbers for thevarious species. These symmetry numbers do not leadto isotopic fractionation, so the S factor can be set to be1.000. The MMI factor refers to the ratio of the molec-ular masses and the moments of inertia. Since hydrogenand deuterium tend to be much lighter compared to mostreactants and transition states, the MMI factor is usuallyalso approximated as unity. The EXC factor corrects forthe kinetic isotope effect caused by the reactions of vibra-tionally excited molecules. The contribution of this factoris also negligible when the reactions are carried out at ornear room temperature. Hence, for hydrogen/deuteriumkinetic isotope effects, the observed values are typicallygoverned by the zero-point energy contributions, whichcan be represented as follows:[4]

3.1 Tunneling 3

kHkD

∼= e−1/2{

3N‡−7∑i=1

(u‡iH−u‡

iD)−3N−6∑i=1

(uiH−uiD)}

= e1/2{

3N−6∑i=1

∆ui−3N‡−7∑

i=1

∆u‡i}

If the zero-point energy difference between the stretchingvibrations of a carbon-hydrogen and carbon-deuteriumbond is allowed to disappear in the transition state, theexpression given above predicts a maximum for kH/kDas 6.9. If the weakening of two bending vibrations arealso taken into account, kH/kD values as large as 15-20can be predicted. Bending frequencies are very unlikelyto vanish in the transition state, however, and quite fewkH/kD values exceed 7-8 near room temperature. Fur-thermore, it is often found that tunneling is a major factorwhen they do exceed such values. Hence, more often thannot, weakening of bending frequencies is not an impor-tant cause of large kinetic isotope effects.For isotope effects involving elements other than hydro-gen, most of these simplifications are not valid, and maydepend largely on some of the neglected factors. In manycases and especially for hydrogen-transfer reactions, con-tributions to kinetic isotope effects from tunneling aresignificant (see below).As mentioned, especially for hydrogen/deuterium substi-tution, most kinetic isotope effects arise from the differ-ence in zero-point energy (ZPE) between the reactantsand the transition state of the isotopologues in question,and this difference can be understood qualitatively withthe following description: within the Born–Oppenheimerapproximation, the potential energy curve is the same forboth isotopic species. However, a quantum-mechanicaltreatment of the energy introduces discrete vibrationallevels onto this curve, and the lowest possible energy stateof a molecule corresponds to the lowest vibrational en-ergy level, which is slightly higher in energy than the min-imum of the potential energy curve. This difference,referred to as the zero-point energy, is a manifestationof the Heisenberg uncertainty principle that necessitatesan uncertainty in the C-H or C-D bond length. Sincethe heavier (in this case the deuterated) species behavesmore “classically,” its vibrational energy levels are closerto the classical potential energy curve, and it has a lowerzero-point energy. The zero-point energy differences be-tween the two isotopic species, at least in most cases, di-minish in the transition state, since the bond force con-stant decreases during bond breaking. Hence, the lowerzero-point energy of the deuterated species translates intoa larger activation energy for its reaction, as shown inthe following figure,leading to a normal kinetic isotopeeffect.[7]

The following simple expressions relating deuterium andtritium kinetic isotope effects, which are also known asthe Swain equation (or the Swain-Schaad-Stivers equa-tions), can be derived from the general expression given

ZPE energy differences and corresponding differences in the ac-tivation energies for the breaking of analogous C-H and C-Dbonds

above using some simplifications:[5][8]

(ln(kH

kT)

ln(kH

kD)

)s

=1−

√mH/mT

1−√mH/mD

=1−

√1/3

1−√1/2

∼= 1.44

i.e.,(kH

kT

)s=(

kH

kD

)1.44s

In deriving these expressions, symmetry terms are omit-ted. The subscript “s” refers to these “semiclassical” ki-netic isotope effects, which disregard quantum tunneling.Tunneling contributions must be treated separately as acorrection factor.

3.1 Tunneling

In some cases, an additional rate enhancement is seen forthe lighter isotope, possibly due to quantum mechanicaltunnelling. This is typically only observed for reactionsinvolving bonds to hydrogen atoms. Tunneling occurswhen a molecule penetrates through a potential energybarrier rather than over it.[9][10] Although not allowed bythe laws of classical mechanics, particles can pass throughclassically forbidden regions of space in quantum me-chanics based on wave–particle duality.[11]

The potential energy well of a tunneling reaction. The dash-redarrow shows the classical activated process, while the red arrowshows the tunneling path.[9]

Analysis of tunneling can be made using Bell’s modifica-tion of the Arrhenius equation, which includes the addi-tion of a tunneling factor, Q:

4 4 KINETIC ISOTOPE EFFECT EXPERIMENTS

k = QAe−E/RT

where A is the Arrhenius parameter, E is the barrierheight and

Q =eα

β − α(βe−α − αe−β)

where α = ERT and β = 2aπ2(2mE)1/2

h

Examination of the β term shows exponential dependencyon the mass of the particle. As a result, tunneling is muchmore likely for a lighter particle such as hydrogen. Sim-ply doubling the mass of a tunneling proton by replacingit with its deuterium isotope drastically reduces the rateof such reactions. As a result, very large kinetic isotopeeffects are observed that can not be accounted for by dif-ferences in zero point energies.

Donor-Acceptor Model of a proton transfer.[12]

In addition, the β term depends linearly with barrierwidth, 2a. As with mass, tunneling is greatest for smallbarrier widths. Optimal tunneling distances of protonsbetween donor and acceptor atom is 0.4 Å.[13]

3.2 Transient kinetic isotope effect

Main article: Transient kinetic isotope fractionation

Isotopic effect expressed with the equations given aboveonly refer to reactions that can be described with first-order kinetics. In all instances in which this is not possi-ble, transient kinetic isotope effects should be taken intoaccount using the GEBIK and GEBIF equations.[25]

4 Kinetic isotope effect experi-ments

Simmons and Hartwig refer to the following three casesas the main types of kinetic isotope effect experimentsinvolving C-H bond functionalization:[26]

A) KIE determined from absolute rates of two parallelreactions In this experiment, the rate constants for the

normal substrate and its isotopically labeled analogue aredetermined independently, and the KIE is obtained as aratio of the two. The accuracy of the measured KIE isseverely limited by the accuracy with which each of theserate constants can be measured. Furthermore, reproduc-ing the exact conditions in the two parallel reactions canbe very challenging. Nevertheless, this measurement ofthe kinetic isotope effect is the only one that may tell thatC-H bond cleavage occurs in the rate-determining stepwithout a doubt.B) KIE determined from an intermolecular competitionIn this type of experiment, the same substrates that are

used in Experiment A are employed, but they are allowedin to react in the same container, instead of two separatecontainers. The kinetic isotope effect from this exper-iment is determined by the relative amount of products

4.1 Evaluation of Rate Constant Ratios from Intermolecular Competition Reactions 5

formed from C-H versus C-D functionalization (or it canbe inferred from the relative amounts of unreacted start-ing materials). It is necessary to quench the reaction be-fore it goes to completion to observe the kinetic isotopeeffect (see the Evaluation section below). This experi-ment type ensures that both C-H and C-D bond function-alizations occur under exactly the same conditions, andthe ratio of products from C-H and C-D bond function-alizations can be measured with much greater precisionthan the rate constants in Experiment A. Moreover, onlya single measurement of product concentrations from asingle sample is required. However, an observed ki-netic isotope effect from this experiment is more diffi-cult to interpret, since it may either mean that C-H bondcleavage occurs during the rate-determining step or ata product-determining step ensuing the rate-determiningstep. The absence of a kinetic isotope effect, at least ac-cording to Simmons and Hartwig, is nonetheless indica-tive of the C-H bond cleavage not occurring during therate-determining step.C) KIE determined from an intramolecular competitionThis type of experiment is analogous to Experiment B,

except this time there is an intramolecular competition forthe C-H or C-D bond functionalization. Inmost cases, thesubstrate possesses a directing group (DG) between theC-H and C-D bonds. Calculation of the kinetic isotopeeffect from this experiment and its interpretation followthe same considerations as that of Experiment B.Apart from the differences in feasibility and precision be-tween the different kinds of experiments, they may alsodiffer in terms of the information they may provide. Forexample, if a reaction follows the following energy pro-file, all three experiments will yield a significant primarykinetic isotope effect:

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 cleavageis irreversible but occurs after the rate-determining step(RDS), no significant kinetic isotope effect will be ob-served with Experiment A, since the overall rate is notaffected by the isotopic substitution. Nevertheless, the ir-reversible C-H bond cleavage step will give a primary ki-netic isotope effect with the other two experiments, sincethe second step would still affect the product distribution.Therefore, with Experiments B and C, it is possible to ob-serve the kinetic isotope effect even if C-H or C-D bondcleavage occurs not in the rate-determining step, but inthe product-determining step.

Reaction energy profile for when the C-H bond cleavage occursat a product-determining step after the RDS

4.1 Evaluation of Rate Constant Ratiosfrom Intermolecular Competition Re-actions

In competition reactions, the kinetic isotope effect is cal-culated from isotopic product or remaining reactant ra-tios after the reaction, but these ratios depend stronglyon the extent of completion of the reaction. Most com-monly, the isotopic substrate will consist of molecules la-beled in a specific position and their unlabeled, ordinarycounterparts.[5] It is also possible in case of 13C kineticisotope effects, as well as similar cases, to simply rely onthe natural abundance of the isotopic carbon for the ki-netic isotope effect experiments, eliminating the need forisotopic labeling.[28] The two isotopic substrates will re-act through the same mechanism, but at different rates.The ratio between the amounts of the two species in thereactants and the products will thus change gradually overthe course of the reaction, and this gradual change can betreated in the following manner:[5] Assume that two iso-topic molecules, A1 and A2, undergo irreversible compe-tition reactions in the following manner:The kinetic isotope effect for this scenario is found to be:

KIE =k1k2

=ln(1− F1)

ln(1− F2)

6 5 CASE STUDIES

Where F1 and F2 refer to the fraction of conversions forthe isotopic species A1 and A2, respectively.Isotopic enrichment of the starting material can be cal-culated from the dependence of R/R0 on F1 for variouskinetic isotope effects, yielding the following figure. Be-cause of the exponential dependence, even very low ki-netic isotope effects lead to large changes in isotopic com-position of the starting material at high conversions.

The isotopic enrichment of the relative amount of species 2 withrespect to species 1 in the starting material as a function of con-version of species 1. The value of the kinetic isotope effect(k1/k2) is indicated at each curve.

When the products are followed, the kinetic isotope effectcan be calculated using the products ratio RP along withR0 as follows:

k1k2

=ln(1− F1)

ln[1− (F1RP /R0)]

5 Case studies

5.1 Primary hydrogen isotope effects

Primary hydrogen kinetic isotope effects refer to casesin which a bond to the isotopically labeled hydrogen isformed or broken in the rate-determining step of the re-action. These are the most commonly measured kinetic

isotope effects, and much of the previously covered the-ory refers to primary kinetic isotope effects. When thereis adequate evidence that transfer of the labeled hydro-gen occurs in the rate-determining step of a reaction, if afairly large kinetic isotope effect is observed, e.g. kH/kDof at least 5-6 or kH/kT about 10-13 at room temper-ature, it is quite likely that the hydrogen transfer is lin-ear and that the hydrogen is fairly symmetrically locatedin the transition state. It is usually not possible to makecomments about tunneling contributions to the observedisotope effect unless the effect is very large. If the pri-mary kinetic isotope effect is not as large, it is generallyconsidered to be indicative of a significant contributionfrom heavy-atom motion to the reaction coordinate, al-though it may also mean that hydrogen transfer follows anonlinear pathway.[5]

5.2 Secondary hydrogen isotope effects

The secondary hydrogen isotope effects or secondary ki-netic isotope effect (SKIE) arises in cases where the iso-topic substitution is remote from the bond being broken.The remote atom, nonetheless, influences the internal vi-brations of the system that via changes in the zero pointenergy (ZPE) affect the rates of chemical reactions.[31]Such effects are expressed as ratios of rate for the lightisotope to that of the heavy isotope and can be “normal”(ratio is greater than or equal to 1) or “inverse” (ratio isless than 1) effects.[32] SKIE are defined as α,β (etc.) sec-ondary isotope effects where such prefixes refer to the po-sition of the isotopic substitution relative to the reactioncenter (see alpha and beta carbon).[33] The prefix α refersto the isotope associated with the reaction center whilethe prefix β refers to the isotope associated with an atomneighboring the reaction center and so on.In physical organic chemistry, SKIE is discussed in termsof electronic effects such as induction, bond hybridiza-tion, or hyperconjugation.[34] These properties are de-termined by electron distribution, and depend upon vi-brationally averaged bond length and angles that are notgreatly affected by isotopic substitution. Thus, the useof the term “electronic isotope effect” while legitimate isdiscouraged from use as it can be misinterpreted to sug-gest that the isotope effect is electronic in nature ratherthan vibrational.[33]

SKIE’s can be explained in terms of changes in orbitalhybridization. When the hybridization of a carbon atomchanges from sp3 to sp2, a number of vibrational modes(stretches, in-plane and out-of-plane bending) are af-fected. The in-plane and out-of-plane bending in an sp3hybridized carbon are similar in frequency due to thesymmetry of an sp3 hybridized carbon. In an sp2 hy-bridized carbon the in-plane bend is much stiffer than theout-of-plane bending resulting in a large difference in thefrequency, the ZPE and thus the SKIE (which exists whenthere is a difference in the ZPE of the reactant and tran-sition state).[9] The theoretical maximum change caused

5.2 Secondary hydrogen isotope effects 7

by the bending frequency difference has been calculatedas 1.4.[9]

When carbon undergoes a reaction that changes its hy-bridization from sp3 to sp2, the out of plane bending forceconstant at the transition state is weaker as it is develop-ing sp2 character and a “normal” SKIE is observed withtypical values of 1.1 to 1.2.[9] Conversely, when carbon’shybridization changes from sp2 to sp3, the out of planebending force constants at the transition state increase andan inverse SKIE is observed with typical values of 0.8 to0.9.[9]

More generally the SKIE for reversible reactions can be“normal” one way and “inverse” the other if bonding inthe transition state is midway in stiffness between sub-strate and product, or they can be “normal” both ways ifbonding is weaker in the transition state, or “inverse” bothways if bonding is stronger in the transition state than ineither reactant.[32]

An example of an “inverse” α secondary kinetic isotopeeffect can be seen in the work of Fitzpatrick and Kurtzwho used such an effect to distinguish between two pro-posed pathways for the reaction of d-amino acid oxi-dase with nitroalkane anions.[35] Path A involved a nu-cleophilic attack on the coenzyme FAD, while path B in-volves a free-radical intermediate. As path A results inthe intermediate carbon changing hybridization from sp2to sp3 an “inverse” a SKIE is expected. If path B occursthen no SKIE should be observed as the free radical inter-mediate does not change hybridization. An SKIE of 0.84was observed and Path A verified as shown in the schemebelow.

N

N

N

N O

HO

R

X NO

O

N

N

N

N O

HO

R

X NO

O

N

N

N

N O

HO

R

X NO

O

Path A

Path BX = H or D

Nitroethaneanion

Probing radical vs. nucleophilic mechanisms

Another example of a SKIE is the oxidation of benzyl al-cohols by dimethyldioxirane where three transition statesfor different mechanisms were proposed. Again, by con-sidering how and if the hydrogen atoms were involvedin each, researchers predicted whether or not they wouldexpect an effect of isotopic substitution of them. Then,analysis of the experimental data for the reaction allowed

them to choose which pathway was most likely based onthe observed isotope effect.[36]

Secondary hydrogen isotope effects from the methylenehydrogens were also used to show that Cope rearrange-ment in 1,5-hexadiene follow a concerted bond rearrange-ment pathway, and not one of the alternatively proposedallyl radical or 1,4-diyl pathways, all of which are pre-sented in the following scheme.[37]

Alternative mechanisms for the Cope rearrangement of1,5-hexadiene: (from top to bottom), allyl radical, syn-chronous concerted, and 1,4-dyil pathways. The middlepathway is found to be the predominant one.[37]

5.2.1 Steric isotope effects

The steric isotope effect is a SKIE that does not involvebond breaking or formation. This effect is attributed tothe different vibrational amplitudes of isotopologues.[38]An example of such an effect is the racemization of9,10-dihydro-4,5-dimethylphenanthrene.[39] The smalleramplitude of vibration for deuterium as compared tohydrogen in C–H (carbon–hydrogen), C–D (carbon–deuterium) bonds results in a smaller van der Waals ra-dius or effective size in addition to a difference in theZPE between the two. When there is a greater effectivebulk of molecules containing one over the other this maybe manifested by a steric effect on the rate constant. Forthe example above deuterium racemizes faster than thehydrogen isotopologue resulting in a steric isotope effect.Another example of the steric isotope effect is in thedeslipping reaction of rotaxanes. The deuterium isotope,due to its smaller effective size, allows easier passage ofthe stoppers through the macrocycle, resulting in fasterrates of deslipping for the deuterated rotaxanes.[40]

8 5 CASE STUDIES

5.2.2 Inverse kinetic isotope effects

Reactions are known where the deuterated speciesreacts faster than the undeuterated analogue, andthese cases are said to exhibit inverse kinetic iso-tope effects (IKIE). IKIE’s are often observed in thereductive elimination of alkyl metal hydrides, e.g.(Me2NCH2CH2NMe2)PtMe(H). In such cases the C-Dbond in the transition state, an agostic species, is highlystabilized relative to the C–H bond.

5.3 Solvent hydrogen kinetic isotope effects

For the solvent isotope effects to be measurable, a fi-nite fraction of the solvent must have a different isotopiccomposition than the rest. Therefore, large amounts ofthe less common isotopic species must be available, lim-iting observable solvent isotope effects to isotopic sub-stitutions involving hydrogen. Detectable kinetic isotopeeffects occur only when solutes exchange hydrogen withthe solvent or when there is a specific solute-solvent in-teraction near the reaction site. Both such phenomena arecommon for protic solvents, in which the hydrogen is ex-changeable, and they may form dipole-dipole interactionsor hydrogen bonds with polar molecules.[5]

5.4 Carbon-13 isotope effects

Most organic reactions involve the breaking and mak-ing of bonds to a carbon; thus, it is reasonable to ex-pect detectable carbon isotope effects. When 13C is usedas the label, the change in mass of the isotope is only~8%, though, which limits the observable kinetic isotopeeffects to much smaller values than the ones observablewith hydrogen isotope effects.

5.4.1 Compensating for variations in 13C naturalabundance

Often, the largest source of error in a study that dependson the natural abundance of carbon is the slight variationin natural 13C abundance itself. Such variations arise be-cause the starting materials used in the reaction are them-selves products of some other reactions that have kineticisotope effects and corresponding isotopic enrichmentsin the products. To compensate for this error when NMRspectroscopy is used to determine the kinetic isotope ef-fect, the following guidelines have been proposed:[29][30]

• Choose a carbon that is remote from the reactioncenter that will serve as a reference and assume itdoes not have a kinetic isotope effect in the reaction.

• In the starting material that has not undergone anyreaction, determine the ratios of the other carbonNMR peak integrals to that of the reference carbon.

• Obtain the same ratios for the carbons in a sampleof the starting material after it has undergone somereaction.

• The ratios of the latter ratios to the former ratiosyields R/R0.

If these as well as some other precautions listed byJankowski are followed, kinetic isotope effects with pre-cisions of three decimal places can be achieved.[29][30]

5.5 Isotope effects with elements heavierthan carbon

Interpretation of carbon isotope effects are usually com-plicated by simultaneously forming and breaking bondsto carbon. Even reactions that involve only bond cleavagefrom the carbon, such as SN1 reactions, involve strength-ening of the remaining bonds to carbon. In many suchreactions, leaving group isotope effects tend to be eas-ier to interpret. For example, substitution and elimina-tion reactions in which chlorine act as a leaving group areconvenient to interpret, especially since chlorine acts asa monoatomic species with no internal bonding to com-plicate the reaction coordinate, and it has two stable iso-topes, 35Cl and 37Cl, both with high abundance. The ma-jor challenge to the interpretation of such isotope affectsis the solvation of the leaving group.[5]

Owing to experimental uncertainties, measurement ofisotope effect may entail significant uncertainty. Of-ten isotope effects are determined through complemen-tary studies on a series of isotopomers. Accordingly,it is quite useful to combine hydrogen isotope effectswith heavy-atom isotope effects. For instance, de-termining nitrogen isotope effect along with hydrogenisotope effect was used to show that the reaction of2-phenylethyltrimethylammonium ion with ethoxide in

5.6 Other Examples 9

ethanol at 40oC follows an E2 mechanism, as opposedto alternative non-concerted mechanisms. This conclu-sion was reached upon showing that this reaction yields anitrogen isotope effect, k14/k15, of 1.0133±0.0002 alongwith a hydrogen kinetic isotope effect of 3.2 at the leavinghydrogen.[5]

Similarly, combining nitrogen and hydrogen isotope ef-fects was used to show that syn eliminations of simple am-monium salts also follow a concerted mechanism, whichwas a question of debate before. In the following tworeactions of 2-phenylcyclopentyltrimethylammonium ionwith ethoxide, both of which yield 1-phenylcyclopentene,both isomers exhibited a nitrogen isotope effect k14/k15at 60oC. Although the reaction of the trans isomer, whichfollows syn elimination, has a smaller nitrogen kinetic iso-tope effect (1.0064) compared to the cis isomer whichundergoes anti elimination (1.0108), both results arelarge enough to be indicative of weakening of the C-Nbond in the transition state that would occur in a con-certed process.

5.6 Other Examples

Since kinetic isotope effects arise from differences in iso-topic masses, the largest observable kinetic isotope ef-fects are associated with isotopic substitutions of hydro-gen with deuterium (100% increase in mass) or tritium(300% increase in mass). Kinetic isotope effects fromisotopic mass ratios can be as large as 36.4 using muons.They have produced the lightest hydrogen atom, 0.11H(0.113 amu), in which an electron orbits around a posi-tive muon (μ+) “nucleus” that has a mass of 206 electrons.They have also prepared the heaviest hydrogen atom ana-logue by replacing one electron in helium with a negativemuon (μ−) to form Heμ with an atomic mass of 4.116amu. Since the negative muon is much heavier than anelectron, it orbits much closer to the nucleus, effectivelyshielding one proton, making Heμ to behave as 4.1H.With

these exotic species, the reaction of H with 1H2 was in-vestigated. Rate constants from reacting the lightest andthe heaviest hydrogen analogues with 1H2 were then usedto calculate the k₀.₁₁/k₄.₁ kinetic isotope effect, in whichthere is a 36.4 fold difference in isotopic masses. Forthis reaction, isotopic substitution happens to produce aninverse kinetic isotope effect, and the authors report akinetic isotope effect as low as 1.74 x 10−4, which is thesmallest kinetic isotope effect ever reported.[41]

The kinetic isotope effect leads to a specific distributionof deuterium isotopes in natural products, depending onthe route they were synthesized in nature. By NMR spec-troscopy, it is therefore easy to detect whether the alco-hol in wine was fermented from glucose, or from illicitlyadded saccharose.Another reaction mechanisms that was elucidated us-ing the kinetic isotope effect is the halogenation oftoluene:[42]

In this particular “intramolecular KIE” study, a benzylichydrogen undergoes radical substitution by bromine us-ingN-bromosuccinimide as the brominating agent. It wasfound that PhCH3 brominates 4.86x faster than PhCD3.A large KIE of 5.56 is associated with the reaction ofketones with bromine and sodium hydroxide.[43]

10 7 REFERENCES

In this reaction the rate-limiting step is formation of theenolate by deprotonation of the ketone. In this study theKIE is calculated from the reaction rate constants for reg-ular 2,4-dimethyl-3-pentanone and its deuterated isomerby optical density measurements.

6 See also

• Chemical kinetics

• Reaction mechanism

• Transient kinetic isotope fractionation

• Magnetic isotope effect

• Crossover experiment

7 References[1] Westaway, Kenneth C. (2006). “Using kinetic isotope ef-

fects to determine the structure of the transition states ofSN2 reactions”. Advances in Physical Organic Chemistry41: 217–273. doi:10.1016/S0065-3160(06)41004-2.

[2] Lynn, K. R.; Yankwich, Peter E. (5 August 1961). Jour-nal of the American Chemical Society 83 (15): 3220–3223. doi:10.1021/ja01476a012. Missing or empty |ti-tle= (help)

[3] Poirier, Raymond A.; Wang, Youliang; Westaway, Ken-neth C. (March 1994). “A Theoretical Study of theRelationship between Secondary .alpha.-Deuterium Ki-netic Isotope Effects and the Structure of SN2 TransitionStates”. Journal of the American Chemical Society 116 (6):2526–2533. doi:10.1021/ja00085a037.

[4] Buncel, E.; Lee, C.C. Isotopes in Organic Chemistry. El-sevier: Amsterdam, 1977, Vol. 5.

[5] Melander, L.; Saunders, W.H., Jr. Reaction Rates of Iso-topic Molecules. Wiley: New York, 1980.

[6] Bigeleisen, J.; Wolfsberg, M. Adv. Chem. Phys. 1958, 1,15.

[7] Carpenter, B.K. Nature Chem. 2010, 2, 80.

[8] Swain, C. Gardner; Stivers, Edward C.; Reuwer, JosephF.; Schaad, Lawrence J. (1 November 1958). “Use ofHydrogen Isotope Effects to Identify the Attacking Nucle-ophile in the Enolization of Ketones Catalyzed by AceticAcid”. Journal of the American Chemical Society 80 (21):5885–5893. doi:10.1021/ja01554a077.

[9] Anslyn, E. V.; Dougherty, D. A. (2006). Modern PhysicalOrganic Chemistry. University Science Books. pp. 435–437. ISBN 1-891389-31-9.

[10] Razauy, M. (2003). Quantum Theory of Tunneling.World Scientific. ISBN 981-238-019-1.

[11] Silbey, R. J.; Alberty, R. A.; Bawendi, M. G. (2005).Physical Chemistry. John Wiley & Sons. pp. 326–338.ISBN 0-471-21504-X.

[12] Borgis, D.; Hynes, J. T. (1993). “Dynamical the-ory of proton tunneling transfer rates in solution: Gen-eral formulation”. Chemical Physics 170 (3): 315–346. Bibcode:1993CP....170..315B. doi:10.1016/0301-0104(93)85117-Q.

[13] Krishtalik, L. I. (2000). “The mechanism of the pro-ton transfer: An outline”. Biochimica et Biophysica Acta1458: 6–27. doi:10.1016/S0005-2728(00)00057-8.

[14] Zuev, P. S. (2003). “Carbon tunnelingfrom a single quantum state”. Science 299(5608): 867–70. Bibcode:2003Sci...299..867Z.doi:10.1126/science.1079294. PMID 12574623.

[15] Atkins, P.; de Paula, J. (2006). Atkins’ Physical Chemistry.Oxford University Press. pp. 286–288, 816–818. ISBN978-0-19-870072-2.

[16] Fujisaki, N.; Ruf, A.; Gaeumann, T. (1987). “Tunnel ef-fects in hydrogen-atom-transfer reactions as studied by thetemperature dependence of the hydrogen deuterium ki-netic isotope effects”. Journal of Physical Chemistry 91(6): 1602. doi:10.1021/j100290a062.

[17] Lewis, E. S.; Funderburk, L. (1967). “Rates and isotopeeffects in the proton transfers from 2-nitropropane to pyri-dine bases”. Journal of the American Chemical Society 89(10): 2322–2327. doi:10.1021/ja00986a013.

[18] Dewar, M. J. S.; Healy, E. F.; Ruiz, J. M. (1988).“Mechanism of the 1,5-sigmatropic hydrogen shift in 1,3-pentadiene”. Journal of the American Chemical Society110 (8): 2666–2667. doi:10.1021/ja00216a060.

[19] von Eggers Doering, W.; Zhao, X. (2006). “Effecton Kinetics by Deuterium in the 1,5-Hydrogen Shiftof a Cisoid-Locked 1,3(Z)-Pentadiene, 2-Methyl-10-methylenebicyclo[4.4.0]dec-1-ene: Evidence for Tunnel-ing?". Journal of the American Chemical Society 128 (28):9080–9085. doi:10.1021/ja057377v. PMID 16834382.

[20] In this study the KIE is measured by sensitive protonNMR. The extrapolated KIE at 25 °C is 16.6 but the mar-gin of error is high

[21] Kohen, A.; Klinman, J. P. (1999). “Hydrogen tunnel-ing in biology”. Chemistry & Biology 6 (7): R191–198.doi:10.1016/S1074-5521(99)80058-1. PMID 10381408.

[22] Wilde, T. C.; Blotny, G.; Pollack, R. M. (2008). “Ex-perimental evidence for enzyme-enhanced coupled mo-tion/quantum mechanical hydrogen tunneling by ketos-teroid isomerase”. Journal of the American ChemicalSociety 130 (20): 6577–6585. doi:10.1021/ja0732330.PMID 18426205.

[23] Truhlar, D. G.; Gao, J.; Alhambra, C.; Garcia-Viloca, M.;Corchado, J.; Sánchez, M.; Villà, J. (2002). “The Incor-poration of Quantum Effects in Enzyme Kinetics Mod-eling”. Accounts of Chemical Research 35 (6): 341–349.doi:10.1021/ar0100226.

11

[24] Kohen, A.; Klinman, J. P. (1998). “Enzyme Catalysis:Beyond Classical Paradigms”. Accounts of Chemical Re-search 31 (7): 397–404. doi:10.1021/ar9701225.

[25] Maggi, F.; Riley, W. J. (2010). “Mathematical treatmentof isotopologue and isotopomer speciation and fractiona-tion in biochemical kinetics”. Geochimica et Cosmochim-ica Acta 74 (6): 1823. Bibcode:2010GeCoA..74.1823M.doi:10.1016/j.gca.2009.12.021.

[26] Simmons, E.M.; Hartwig, J.F. Angew. Chem. Int. Ed.2012, 51, 3066-3072.

[27] Buncel, E.; Lee, C.C. Isotopes in Organic Chemistry. El-sevier: Amsterdam, 1977, Vol. 3.

[28] Singleton, Daniel A.; Thomas, Allen A. (September1995). “High-Precision Simultaneous Determination ofMultiple Small Kinetic Isotope Effects at Natural Abun-dance”. Journal of the American Chemical Society 117(36): 9357–9358. doi:10.1021/ja00141a030.

[29] Jankowski, S. Ann. Rep. NMR Spec. 2009, 68, 149.

[30] Kwan, Eugene. “CHEM 106 Course Notes - Lecture 14 -Computational Chemistry”. Retrieved 2 November 2013.

[31] Hennig, C.; Oswald, R. B.; Schmatz, S. (2006).“Secondary Kinetic Isotope Effect in NucleophilicSubstitution: A Quantum-Mechanical Approach”.Journal of Physical Chemistry A 110 (9): 3071–3079.doi:10.1021/jp0540151.

[32] Cleland, W. W. (2003). “The Use of Isotope Ef-fects to Determine Enzyme Mechanisms”. Journalof Biological Chemistry 278 (52): 51975–51984.doi:10.1074/jbc.X300005200. PMID 14583616.

[33] IUPAC, Compendium of Chemical Terminology, 2nd ed.(the “Gold Book”) (1997). Online corrected version:(2006–) "Secondary isotope effect".

[34] “Definition of isotope effect, secondary”. Chemistry Dic-tionary.

[35] Kurtz, K. A.; Fitzpatrick, P. F. (1997). “pH and Sec-ondary Kinetic Isotope Effects on the Reaction of D-Amino Acid Oxidase with Nitroalkane Anions: Evidencefor Direct Attack on the Flavin by Carbanions”. Journalof the American Chemical Society 119 (5): 1155–1156.doi:10.1021/ja962783n.

[36] Angelis, Y. S.; Hatzakis, N. S.; Smonou, I.; Or-fanopoulos, M. (2006). “Oxidation of benzyl alco-hols by dimethyldioxirane. The question of concertedversus stepwise mechanisms probed by kinetic isotopeeffects”. Tetrahedron Letters 42 (22): 3753–3756.doi:10.1016/S0040-4039(01)00539-1.

[37] Houk, K.N.; Gustafson, S.M.; Black, K.A. JACS 1992,114, 8565.

[38] IUPAC, Compendium of Chemical Terminology, 2nd ed.(the “Gold Book”) (1997). Online corrected version:(2006–) "steric isotope effect".

[39] Mislow, K.; Graeve, R.; Gordon, A. J.; Wahl, G. H.(1963). “A Note on Steric Isotope Effects. Confor-mational Kinetic Isotope Effects in The Racemizationof 9,10-Dihydro-4,5-Dimethylphenanthrene”. Journalof the American Chemical Society 85 (8): 1199–1200.doi:10.1021/ja00891a038.

[40] Felder, T.; Schalley, C. A. (2003). “Secondary Iso-tope Effects on the Deslipping Reaction of Rotax-anes: High-Precision Measurement of Steric Size”.Angewandte Chemie International Edition 42 (20): 2258–2260. doi:10.1002/anie.200350903. PMID 12772156.

[41] Fleming, D. G.; Arseneau, D. J.; Sukhorukov, O.; Brewer,J. H.; Mielke, S. L.; Schatz, G. C.; Garrett, B. C.; Pe-terson, K. A.; Truhlar, D. G. (27 January 2011). “Ki-netic Isotope Effects for the Reactions of Muonic Heliumand Muonium with H2”. Science 331 (6016): 448–450.doi:10.1126/science.1199421. PMID 21273484.

[42] Wiberg, K. B.; Slaugh, L. H. (1958). “The Deuterium Iso-tope Effect in the Side Chain Halogenation of Toluene”.Journal of the American Chemical Society 80 (12): 3033–3039. doi:10.1021/ja01545a034.

[43] Lynch, R. A.; Vincenti, S. P.; Lin, Y. T.; Smucker, L. D.;Subba Rao, S. C. (1972). “Anomalous kinetic hydrogenisotope effects on the rat of ionization of some dialkylsubstituted ketones”. Journal of the American ChemicalSociety 94 (24): 8351–8356. doi:10.1021/ja00779a012.

12 8 TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES

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