Editing Kinetic isotope effect (section)

== Case studies ==

=== Primary hydrogen isotope effects ===
Primary hydrogen KIEs refer to cases in which a bond to the isotopically labeled hydrogen is formed or broken at a rate- and/or product-determining step of a reaction.<ref name="Simmons_2012" /> These are the most commonly measured KIEs, and much of the previously covered theory refers to primary KIEs. When there is adequate evidence that transfer of the labeled hydrogen occurs in the rate-determining step of a reaction, if a fairly large KIE is observed, e.g. k{{sub|H}}/k{{sub|D}} of at least 5-6 or k{{sub|H}}/k{{sub|T}} about 10–13 at room temperature, it is quite likely that the hydrogen transfer is linear and that the hydrogen is fairly symmetrically located in the transition state. It is usually not possible to make comments about tunneling contributions to the observed isotope effect unless the effect is very large. If the primary KIE is not as large, it is generally considered to be indicative of a significant contribution from heavy-atom motion to the reaction coordinate, though it may also mean that hydrogen transfer follows a nonlinear pathway.<ref name="Saunders" />

=== Secondary hydrogen isotope effects ===
Secondary hydrogen isotope effects or secondary KIE (SKIE) arise in cases where the isotopic substitution is remote from the bond being broken. The remote atom nonetheless influences the internal vibrations of the system, which via changes in [[zero-point energy]] (ZPE) affect the rates of chemical reactions.<ref>{{cite journal | vauthors = Hennig C, Oswald RB, Schmatz S | title = Secondary kinetic isotope effect in nucleophilic substitution: a quantum-mechanical approach | journal = The Journal of Physical Chemistry A | volume = 110 | issue = 9 | pages = 3071–9 | date = March 2006 | pmid = 16509628 | doi = 10.1021/jp0540151 | bibcode = 2006JPCA..110.3071H }}</ref> Such effects are expressed as ratios of rate for the light isotope to that of the heavy isotope and can be "normal" (ratio ≥ 1) or "inverse" (ratio < 1) effects.<ref name="cleland">{{cite journal | vauthors = Cleland WW | title = The use of isotope effects to determine enzyme mechanisms | journal = The Journal of Biological Chemistry | volume = 278 | issue = 52 | pages = 51975–84 | date = December 2003 | pmid = 14583616 | doi = 10.1074/jbc.X300005200 | doi-access = free }}</ref> SKIEs are defined as ''α,β'' (etc.) secondary isotope effects where such prefixes refer to the position of the isotopic substitution relative to the reaction center (see [[alpha and beta carbon]]).<ref name=goldbook-sie>{{GoldBookRef |file=S05523 |title=Secondary isotope effect}}</ref> The prefix ''α'' refers to the isotope associated with the reaction center and the prefix ''β'' refers to the isotope associated with an atom neighboring the reaction center and so on.

In physical organic chemistry, SKIE is discussed in terms of [[electronic effect]]s such as induction, bond hybridization, or [[hyperconjugation]].<ref>{{cite web |title=Definition of isotope effect, secondary | url = http://www.chemicool.com/definition/isotope_effect_secondary.html | work = Chemistry Dictionary | publisher = Chemitool }}</ref> These properties are determined by electron distribution, and depend upon vibrationally averaged bond length and angles that are not greatly affected by isotopic substitution. Thus, the use of the term "electronic isotope effect" while legitimate is discouraged from use as it can be misinterpreted to suggest that the isotope effect is electronic in nature rather than vibrational.<ref name="goldbook-sie" />

SKIEs can be explained in terms of changes in orbital hybridization. When the hybridization of a carbon atom changes from sp{{sup|3}} to sp{{sup|2}}, a number of vibrational modes (stretches, in-plane and out-of-plane bending) are affected. The in-plane and out-of-plane bending in an sp{{sup|3}} hybridized carbon are similar in frequency due to the symmetry of an sp{{sup|3}} hybridized carbon. In an sp{{sup|2}} hybridized carbon the in-plane bend is much stiffer than the out-of-plane bending resulting in a large difference in the frequency, the ZPE and thus the SKIE (which exists when there is a difference in the ZPE of the reactant and transition state).<ref name="anslyn" />
The theoretical maximum change caused by the bending frequency difference has been calculated as 1.4.<ref name="anslyn" />

When carbon undergoes a reaction that changes its hybridization from sp{{sup|3}} to sp{{sup|2}}, the out-of-plane bending force constant at the transition state is weaker as it is developing sp{{sup|2}} character and a "normal" SKIE is observed with typical values of 1.1 to 1.2.<ref name="anslyn" /> Conversely, when carbon's hybridization changes from sp{{sup|2}} to sp{{sup|3}}, the out of plane bending force constants at the transition state increase and an inverse SKIE is observed with typical values of 0.8 to 0.9.<ref name="anslyn" />

More generally the SKIE for reversible reactions can be "normal" one way and "inverse" the other if bonding in the transition state is midway in stiffness between substrate and product, or they can be "normal" both ways if bonding is weaker in the transition state, or "inverse" both ways if bonding is stronger in the transition state than in either reactant.<ref name="cleland" />

An example of an "inverse" α SKIE can be seen in the work of Fitzpatrick and Kurtz who used such an effect to distinguish between two proposed pathways for the reaction of [[d-amino acid oxidase]] with [[nitroalkane]] anions.<ref>{{cite journal
 | vauthors = Kurtz KA, Fitzpatrick PF
 |year=1997
 |title=pH and Secondary Kinetic Isotope Effects on the Reaction of D-Amino Acid Oxidase with Nitroalkane Anions: Evidence for Direct Attack on the Flavin by Carbanions
 |journal=[[Journal of the American Chemical Society]]
 |volume=119 |issue=5 |pages=1155–1156
 |doi=10.1021/ja962783n
|bibcode=1997JAChS.119.1155K
 }}</ref> Path A involved a nucleophilic attack on the coenzyme [[flavin adenine dinucleotide]] (FAD), while path B involves a free-radical intermediate. As path A results in the intermediate carbon changing hybridization from sp{{sup|2}} to sp{{sup|3}} an "inverse" SKIE is expected. If path B occurs then no SKIE should be observed as the free radical intermediate does not change hybridization. An SKIE of 0.84 was observed and Path A verified as shown in the scheme below.

[[File:Secondaryradicalneucleophilicdetermination.svg]]

Another example of SKIE is oxidation of benzyl alcohols by dimethyldioxirane, where three transition states for different mechanisms were proposed. Again, by considering how and if the hydrogen atoms were involved in each, researchers predicted whether or not they would expect 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 on the observed isotope effect.<ref>{{cite journal
 | vauthors = Angelis YS, Hatzakis NS, Smonou I, Orfanopoulos M
 |year=2006
 |title=Oxidation of benzyl alcohols by dimethyldioxirane. The question of concerted versus stepwise mechanisms probed by kinetic isotope effects
 |journal=[[Tetrahedron Letters]]
 |volume=42 |issue= 22|pages=3753–3756
 |doi=10.1016/S0040-4039(01)00539-1
}}</ref>

Secondary hydrogen isotope effects from the methylene hydrogens were also used to show that Cope rearrangement in 1,5-hexadiene follow a concerted bond rearrangement pathway, and not one of the alternatively proposed allyl radical or 1,4-diyl pathways, all of which are presented in the following scheme.<ref name=Houk>{{cite journal | vauthors = Houk KN, Gustafson SM, Black KA | title = Theoretical secondary kinetic isotope effects and the interpretation of transition state geometries. 1. The Cope rearrangement. | journal = Journal of the American Chemical Society | date = October 1992 | volume = 114 | issue = 22 | pages = 8565–72 | doi = 10.1021/ja00048a032 | bibcode = 1992JAChS.114.8565H }}</ref>
[[File:Cope rearrangement mechanisms.png|center|400px]]
Alternative mechanisms for the Cope rearrangement of 1,5-hexadiene: (from top to bottom), allyl radical, synchronous concerted, and 1,4-dyil pathways. The predominant pathway is found to be the middle one, which has six delocalized π electrons corresponding to an aromatic intermediate.<ref name="Houk" />

==== Steric isotope effects ====

{| style="float: right;"
| [[File:racemization.svg|250px]]
|-
| {{center|<math>\frac{k_{(X=D)}}{k_{(X=H)}} = 1.15</math>}}
|}

The steric isotope effect (SIE) is a SKIE that does not involve bond breaking or formation. This effect is attributed to the different vibrational amplitudes of [[isotopologue]]s.<ref>{{GoldBookRef |file=S06001 |title=steric isotope effect}}</ref> An example of such an effect is the [[racemization]] of 9,10-dihydro-4,5-dimethylphenanthrene.<ref>{{cite journal
 | vauthors = Mislow K, Graeve R, Gordon AJ, Wahl GH
 |authorlink1=Kurt Mislow
 |year=1963
 |title=A Note on Steric Isotope Effects. Conformational Kinetic Isotope Effects in The Racemization of 9,10-Dihydro-4,5-Dimethylphenanthrene
 |journal=[[Journal of the American Chemical Society]]
 |volume=85 |issue=8 |pages=1199–1200
 |doi=10.1021/ja00891a038
|bibcode=1963JAChS..85.1199M
 }}</ref> The smaller amplitude of vibration for {{sup|2}}H than for {{sup|1}}H in C–{{sup|1}}H, C–{{sup|2}}H bonds, results in a smaller van der Waals radius or effective size in addition to a difference in the ZPE between the two. When there is a greater effective bulk of molecules containing one over the other this may be manifested by a steric effect on the rate constant. For the example above, {{sup|2}}H racemizes faster than {{sup|1}}H resulting in a SIE. A model for the SIE was developed by Bartell.<ref>{{Cite journal| vauthors = Bartell LS |date=1961-09-01|title=The Role of Non-bonded Repulsions in Secondary Isotope Effects. I. Alpha and Beta Substitution Effects.1 |journal=Journal of the American Chemical Society|volume=83|issue=17 |pages=3567–3571 |doi= 10.1021/ja01478a006 |bibcode=1961JAChS..83.3567B }}</ref> A SIE is usually small, unless the transformations passes through a transition state with severe steric encumbrance, as in the racemization process shown above.

Another example of the SIE is in the deslipping reaction of rotaxanes. {{sup|2}}H, due to its smaller effective size, allows easier passage of the stoppers through the macrocycle, resulting in faster deslipping for the deuterated [[rotaxane]]s.<ref>{{cite journal | vauthors = Felder T, Schalley CA | title = Secondary isotope effects on the deslipping reaction of rotaxanes: high-precision measurement of steric size | journal = Angewandte Chemie | volume = 42 | issue = 20 | pages = 2258–60 | date = May 2003 | pmid = 12772156 | doi = 10.1002/anie.200350903 }}</ref>

[[File:chemicalrotaxane.svg]]

=== Inverse kinetic isotope effects ===
Reactions are known where the deuterated species reacts ''faster'' than the undeuterated one, and these cases are said to exhibit inverse KIEs (IKIE). IKIEs are often observed in the [[reductive elimination]] of alkyl metal hydrides, e.g. ([[TMEDA|(Me{{sub|2}}NCH{{sub|2}}){{sub|2}}]])PtMe(H).{{efn|"Me" means [[methyl group|methyl]], CH{{sub|3}}.}} In such cases the C-D bond in the transition state, an [[agostic]] species, is highly stabilized relative to the C–H bond.<ref>{{cite journal |last1=Churchill |first1=David G. |last2=Janak |first2=Kevin E. |last3=Wittenberg |first3=Joshua S. |last4=Parkin |first4=Gerard |title=Normal and Inverse Primary Kinetic Deuterium Isotope Effects for C−H Bond Reductive Elimination and Oxidative Addition Reactions of Molybdenocene and Tungstenocene Complexes: Evidence for Benzene σ-Complex Intermediates |journal=J. Am. Chem. Soc. |date=11 January 2003 |volume=125 |issue=5 |pages=1403–1420 |doi=10.1021/ja027670k |pmid=12553844 |bibcode=2003JAChS.125.1403C |url=https://pubs.acs.org/doi/abs/10.1021/ja027670k |access-date=26 January 2023|url-access=subscription }}</ref>

An inverse effect can also occur in a multistep reaction if the overall rate constant depends on a [[Pre-equilibrium (chemical kinetics)|pre-equilibrium]] prior to the [[rate-determining step]] which has an inverse [[Equilibrium constant#Effect of isotopic substitution|equilibrium isotope effect]]. For example, the rates of [[Acid catalysis|acid-catalyzed]] reactions are usually 2-3 times greater for reactions in D{{sub|2}}O catalyzed by D{{sub|3}}O{{sup|+}} than for the analogous reactions in H{{sub|2}}O catalyzed by H{{sub|3}}O{{sup|+}}<ref name="Laidler_1987" />{{rp|433}} This can be explained for a mechanism of [[Acid catalysis#Specific catalysis|specific hydrogen-ion catalysis]] of a reactant R by H{{sub|3}}O{{sup|+}} (or D{{sub|3}}O{{sup|+}}).
:H{{sub|3}}O{{sup|+}} + R {{eqm}} RH{{sup|+}} + H{{sub|2}}O
:RH{{sup|+}} + H{{sub|2}}O → H{{sub|3}}O{{sup|+}} + P
The rate of formation of products is then d[P]/dt = k{{sub|2}}[RH{{sup|+}}] = k{{sub|2}}K{{sub|1}}[H{{sub|3}}O{{sup|+}}][R] = k{{sub|obs}}[H{{sub|3}}O{{sup|+}}][R]. In the first step, H{{sub|3}}O{{sup|+}} is usually a stronger acid than RH{{sup|+}}. Deuteration shifts the equilibrium toward the more strongly bound acid species RD{{sup|+}} in which the effect of deuteration on zero-point vibrational energy is greater, so that the deuterated equilibrium constant K{{sub|1D}} is greater than K{{sub|1H}}. This equilibrium isotope effect in the first step usually outweighs the kinetic isotope effect in the second step, so that there is an apparent inverse isotope effect and the observed overall rate constant k{{sub|obs}} = k{{sub|2}}K{{sub|1}} decreases.<ref name="Laidler_1987" />{{rp|433}}

=== Solvent hydrogen kinetic isotope effects ===

For the solvent isotope effects to be measurable, a fraction of the solvent must have a different isotopic composition than the rest. Therefore, large amounts of the less common isotopic species must be available, limiting observable solvent isotope effects to isotopic substitutions involving hydrogen. Detectable KIEs occur only when solutes exchange hydrogen with the solvent or when there is a specific solute-solvent interaction near the reaction site. Both such phenomena are common for protic solvents, in which the hydrogen is exchangeable, and they may form dipole-dipole interactions or hydrogen bonds with polar molecules.<ref name="Saunders" />

=== Carbon-13 isotope effects ===
Most organic reactions involve breaking and making bonds to carbon; thus, it is reasonable to expect detectable carbon isotope effects. When {{sup|13}}C is used as the label, the change in mass of the isotope is only ~8%, though, which limits the observable KIEs to much smaller values than the ones observable with hydrogen isotope effects.

==== Compensating for variations in {{sup|13}}C natural abundance ====
Often, the largest source of error in a study that depends on the natural abundance of carbon is the slight variation in natural {{sup|13}}C abundance itself. Such variations arise; because the starting materials in the reaction, are themselves products of other reactions that have KIEs and thus isotopically enrich the products. To compensate for this error when NMR spectroscopy is used to determine the KIE, the following guidelines have been proposed:<ref name=Jankowski />
* Choose a carbon that is remote from the reaction center that will serve as a reference and assume it does not have a KIE in the reaction.
* In the starting material that has not undergone any reaction, determine the ratios of the other carbon NMR peak integrals to that of the reference carbon.
* Obtain the same ratios for the carbons in a sample of the starting material after it has undergone some reaction.
* The ratios of the latter ratios to the former ratios yields R/R{{sub|0}}.
If these as well as some other precautions listed by Jankowski are followed, KIEs with precisions of three decimal places can be achieved.<ref name=Jankowski />

=== Isotope effects with elements heavier than carbon ===
Interpretation of carbon isotope effects is usually complicated by simultaneously forming and breaking bonds to carbon. Even reactions that involve only bond cleavage from the carbon, such as S{{sub|N}}1 reactions, involve strengthening of the remaining bonds to carbon. In many such reactions, leaving group isotope effects tend to be easier to interpret. For example, substitution and elimination reactions in which [[chlorine]] acts as a leaving group are convenient to interpret, especially since chlorine acts as a monatomic species with no internal bonding to complicate the reaction coordinate, and it has two stable isotopes, {{sup|35}}Cl and {{sup|37}}Cl, both with high abundance. The major challenge to the interpretation of such isotope affects is the solvation of the leaving group.<ref name="Saunders" />

Owing to experimental uncertainties, measurement of isotope effect may entail significant uncertainty. Often isotope effects are determined through complementary studies on a series of isotopomers. Accordingly, it is quite useful to combine hydrogen isotope effects with heavy-atom isotope effects. For instance, determining nitrogen isotope effect along with hydrogen isotope effect was used to show that the reaction of 2-phenylethyltrimethylammonium ion with ethoxide in ethanol at 40°C follows an E2 mechanism, as opposed to alternative non-concerted mechanisms. This conclusion was reached upon showing that this reaction yields a nitrogen isotope effect, ''k''{{sub|14}}/''k''{{sub|15}}, of 1.0133±0.0002 along with a hydrogen KIE of 3.2 at the leaving hydrogen.<ref name="Saunders" />

Similarly, combining nitrogen and hydrogen isotope effects was used to show that syn eliminations of simple ammonium salts also follow a concerted mechanism, which was a question of debate before. In the following two reactions of 2-phenylcyclopentyltrimethylammonium ion with ethoxide, both of which yield 1-phenylcyclopentene, both isomers exhibited a nitrogen isotope effect ''k''{{sub|14}}/''k''{{sub|15}} at 60°C. Though the reaction of the trans isomer, which follows syn elimination, has a smaller nitrogen KIE (1.0064) than the cis isomer which undergoes anti elimination (1.0108); both results are large enough to be indicative of weakening of the C-N bond in the transition state that would occur in a concerted process.{{efn|In the diagrams below, "Et" means [[ethyl radical|ethyl]], C{{sub|2}}H{{sub|5}}; "Ph" means [[phenyl]], C{{sub|6}}H{{sub|5}}. Phenyl is also called by the symbol Φ ([[phi]]).}}
[[File:Elimination reactions of 2-phenylcyclopentyltrimethylammonium isomers.png|center]]

=== Other examples ===
Since KIEs arise from differences in isotopic mass, the largest observable KIEs are associated with substitution of {{sup|1}}H with {{sup|2}}H (2× increase in mass) or {{sup|3}}H (3× increase in mass). KIEs from isotopic mass ratios can be as large as 36.4 using muons. They have produced the lightest "hydrogen" atom, {{sup|0.11}}H (0.113 amu), in which an electron orbits a positive muon (μ{{sup|+}}) "nucleus" that has a mass of 206 electrons. They have also prepared the heaviest "hydrogen" atom by replacing one electron in [[helium]] with a negative muon μ{{sup|−}} to form Heμ (mass 4.116 amu). Since μ{{sup|−}} is much heavier than an electron, it orbits much closer to the nucleus, effectively shielding one proton, making Heμ behave as {{sup|4.1}}H. With these [[exotic atom]]s, the reaction of H with {{sup|1}}H{{sub|2}} was investigated. Rate constants from reacting the lightest and the heaviest hydrogen analogs with {{sup|1}}H{{sub|2}} were then used to calculate ''k''{{sub|0.11}}/''k''{{sub|4.1}}, in which there is a 36.4× difference in isotopic mass. For this reaction, isotopic substitution happens to produce an IKIE, and the authors report a KIE as low as 1.74×10{{sup|−4}}, the smallest KIE ever reported.<ref>{{cite journal | vauthors = Fleming DG, Arseneau DJ, Sukhorukov O, Brewer JH, Mielke SL, Schatz GC, Garrett BC, Peterson KA, Truhlar DG | title = Kinetic isotope effects for the reactions of muonic helium and muonium with H2 | journal = Science | volume = 331 | issue = 6016 | pages = 448–50 | date = January 2011 | pmid = 21273484 | doi = 10.1126/science.1199421 | bibcode = 2011Sci...331..448F | s2cid = 206530683 }}</ref>

The KIE leads to a specific distribution of {{sup|2}}H in natural products, depending on the route they were synthesized in nature. By NMR spectroscopy, it is therefore easy to detect whether the alcohol in wine was fermented from [[glucose]], or from illicitly added [[saccharose]].

Another [[reaction mechanism]] that was elucidated using the KIE is [[halogenation]] of [[toluene]]:<ref>{{cite journal
 | vauthors = Wiberg KB, Slaugh LH
 |year=1958
 |title=The Deuterium Isotope Effect in the Side Chain Halogenation of Toluene
 |journal=[[Journal of the American Chemical Society]]
 |volume=80 |issue=12 |pages=3033–3039
 |doi=10.1021/ja01545a034
|bibcode=1958JAChS..80.3033W
 }}</ref>

:[[File:KineticIsotopeEffectHalogenation.png|400px|KIE in halogenation of toluene]]

In this particular "intramolecular KIE" study, a benzylic hydrogen undergoes [[radical substitution]] by bromine using [[N-Bromosuccinimide|''N''-bromosuccinimide]] as the brominating agent. It was found that PhCH{{sub|3}} brominates 4.86x faster than PhC{{sup|2}}H{{sub|3}} (PhCD{{sub|3}}). A large KIE of 5.56 is associated with the reaction of [[ketone]]s with [[bromine]] and [[sodium hydroxide]].<ref>{{cite journal
 | vauthors = Lynch RA, Vincenti SP, Lin YT, Smucker LD, Subba Rao SC
 |year=1972
 |title=Anomalous kinetic hydrogen isotope effects on the rate of ionization of some dialkyl substituted ketones
 |journal=[[Journal of the American Chemical Society]]
 |volume=94 |issue=24 |pages=8351–8356
 |doi=10.1021/ja00779a012
|bibcode=1972JAChS..94.8351L
 }}</ref>

:[[File:KineticIsotopeEffectEnolateFormation.png|500px|KIE in bromination of ketone]]

In this reaction the rate-limiting step is formation of the [[enolate]] by deprotonation of the ketone. In this study the KIE is calculated from the [[reaction rate constant]]s for regular 2,4-dimethyl-3-pentanone and its deuterated isomer by [[optical density]] measurements.

In asymmetric catalysis, there are rare cases where a KIE manifests as a significant difference in the enantioselectivity observed for a deuterated substrate compared to a non-deuterated one. One example was reported by Toste and coworkers, in which a deuterated substrate produced an enantioselectivity of 83% ee, compared to 93% ee for the undeuterated substrate. The effect was taken to corroborate additional inter- and intramolecular competition KIE data that suggested cleavage of the C-H/D bond in the enantiodetermining step.<ref>{{cite journal | vauthors = Zi W, Wang YM, Toste FD | title = An in situ directing group strategy for chiral anion phase-transfer fluorination of allylic alcohols | journal = Journal of the American Chemical Society | volume = 136 | issue = 37 | pages = 12864–7 | date = September 2014 | pmid = 25203796 | pmc = 4183625 | doi = 10.1021/ja507468u | bibcode = 2014JAChS.13612864Z }}</ref>

[[File:EnantioselectivityKIE.png|frameless|700x700px]]