Kinetic isotope effect
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The '''kinetic isotope effect''' ('''KIE''') is a variation in the [[reaction rate]] of a [[chemical reaction]] when an [[atom]] in one of the reactants is replaced by one of its [[isotope]]s. It is also called '''isotope fractionation''', although this term is technically somewhat broader in meaning. A KIE involving [[hydrogen]] and [[deuterium]] is represented as:
:<math>KIE = \frac{k_H}{k_D}</math>
with k<sub>H</sub> and k<sub>D</sub> [[reaction rate constant]]s.
An isotopic substitution will greatly modify the [[reaction rate]] when the isotopic replacement is in a [[chemical bond]] that is broken or formed in the [[rate limiting step]]. In such a case, the rate of change is termed a '''primary isotope effect'''. When the substitution is not involved in the bond that is breaking or forming, one may still observe a smaller rate change, termed a '''secondary isotope effect'''. Thus, the magnitude of the kinetic isotope effect can be used to elucidate the [[reaction mechanism]]. If other steps are partially rate-determining, the effect of isotopic substitution will be masked.
Isotopic rate changes are most pronounced when the relative [[mass]] change is greatest. For instance, changing a [[hydrogen]] atom to [[deuterium]] represents a 100% increase in mass, whereas in replacing [[carbon]]-12 with carbon-13, the mass increases by only 8%. The rate of a reaction involving a C-H bond is typically 6 to 10 times faster than the corresponding C-D bond, whereas a <sup>12</sup>C reaction is only ~1.04 times faster than the corresponding <sup>13</sup>C reaction (even though, in both cases, the isotope is one [[atomic mass unit]] heavier).
Isotopic substitution can modify the rate of reaction in a variety of ways. In many cases, the rate difference can be rationalized by noting that the mass of an atom affects the vibration [[frequency]] of the [[chemical bond]] that it forms, even if the [[electron configuration]] is nearly identical. Heavier atoms will ([[classical physics|classically]]) lead to lower vibration frequencies, or, viewed [[quantum mechanics|quantum mechanically]], will have lower [[zero-point energy]]. With a lower zero-point energy, 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]]).
The [[Swain equation]] relates the kinetic isotope effect for the proton/tritium combination with that of the proton/deuterium combination.
==Mathematical details in a diatomic molecule==
One approach to studying the effect is for that of a diatomic molecule. The fundamental vibrational frequency (''ν'') of a chemical bond between atom A and B is, when approximated by a [[harmonic oscillator]]:
:<math>\nu = \frac{1}{2 \pi} \sqrt{\frac{k}{\mu}}</math>
where ''k'' is the spring constant for the bond, and ''μ'' is the [[reduced mass]] of the A-B system:
:<math>\mu = \frac{m_A m_B}{m_A + m_B}</math>
(<math>m_i</math> is the mass of atom <math>i</math>). Quantum mechanically, the energy of the <math>n</math>-th level of a harmonic oscillator is given by:
:<math>E_n = h \nu \left ( n + \frac{1}{2} \right ).</math>
Thus, the zero-point energy (<math>n</math> = 0) will decrease as the reduced mass increases. With a lower zero-point energy, more energy is needed to overcome the activation energy for bond cleavage.
In changing a carbon-hydrogen bond to a carbon-deuterium bond, k remains unchanged, but the reduced mass µ is different. As a good approximation, on going from C-H to C-D, the reduced mass increases by a factor of approximately 2. Thus, the frequency for a C-D bond should be approximately 1/√2 or 0.71 times that of the corresponding C-H bond. Still, this is a much larger effect than changing the carbon-12 to carbon-13.
==The secondary Isotope effect==
The secondary kinetic isotope effect (SKIE) arises when an isotopic substitution that is not involved in the reaction influences the internal vibrations of the system that via changes in the zero point energy (ZPE) affect the rates of chemical reactions <ref>J. Phys. Chem. A 2006, 110, 3071-3079</ref>. Such effects are expressed as ratios of rate for the light isotope to that of the heavy isotope and can be "normal" (ratio is greater than or equal to 1) or "inverse" (ratio is less than 1) effects.<ref name = cleland>{{cite journal | author = W. W. Cleland | title = The Use of Isotope Effects to Determine Enzyme Mechanisms | year = 2003 | journal = [[J. Biol. Chem.]] | volume = 278 | issue = 52 | pages = 51975–51984 | doi = 10.1074/jbc.X300005200 | pmid = 14583616}}</ref>
SKIE 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.<ref name=goldbook-sie>{{GoldBookRef | file = S05523 | title = secondary isotope effect}}</ref> The prefix α refers to the isotope associated with the reaction center while 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>[http://www.chemicool.com/definition/isotope_effect_secondary.html Defintion of isotope_effect_secondary - Chemistry Dictionary<!-- Bot generated title -->]</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 incorrectly suggests that the isotope effect is electronic in nature rather than vibrational.<ref name = goldbook-sie/>
SKIE detection in physical organic chemistry can be explained in terms of changes in orbital hybridisation. When a carbon atom changes from sp<sup>3</sup> to sp<sup>2</sup> hybridization a number of vibrational modes (stretches, in-plane and out-of-plane bending) undergo large changes. The in-plane and out-of-plane bending in an sp<sup>3</sup> hybridized carbon are similar in frequency due to the symmetry of an sp<sup>3</sup> hybridized carbon. In an sp<sup>2</sup> 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>{{cite book | title = Modern Physical Organic Chemistry | author = E.V. Anslyn, D.A. Dougherty | publisher = University Science Books | pages = 428-431 | isbn = 1-891389-31-9}}</ref> The theoretical maximum change caused by the bending frequency difference has been calculated as 1.4.<ref name = anslyn/>
When undergoing a reaction that changes the hybridization of carbon from sp<sup>3</sup> to sp<sup>2</sup> the force constant at the transition state is weaker as it is developing sp<sup>2</sup> character and a "normal" SKIE is observed with typical values of 1.1 to 1.2.<ref name = anslyn/> Similarly when going from sp<sup>2</sup> to sp<sup>3</sup> character the force constants at the tranistion state increase and an inverse SKIE is observered 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 secondary kinetic isotope effect 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 | author = K. A. Kurtz and P. F. Fitzpatrick | 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 | year = 1997 | journal = [[J. Am. Chem. Soc.]] | volume = 119 | issue = 5 | pages = 1155–1156 | doi = 10.1021/ja962783n}}</ref> Path A involved a neucleophilic attack while path B involves a free-radical intermediate. As path A results in the intermediate carbon changing hybridization from sp<sup>2</sup> to sp<sup>3</sup> an "inverse" a 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.
[[Image:secondaryradicalneucleophilicdetermination.jpg]]
Another example of an SKIE is the Oxidation of benzyl alcohols by dimethyldioxirane where three transition states for different mechanisms were proposed. Work by Y. S. Angelis et al<ref>Y. S. Angelis et al. / Tetrahedron Letters 42 (2001) 3753–3756</ref> used b SKIE to show that TS<sub>1</sub> was the transition state as TS<sub>11</sub> and TS<sub>111</sub> should due to the hyperconjugative effect of the five hydrogen atoms in 6-d0 versus the five deuterium atoms in 6-d5 should show large SKIE (kH/kD = 1.03–1.1 per deuterium atom)11. This did not match observed SKIE of approx. 1 which eliminates TS<sub>11</sub> and TS<sub>111</sub>.
[[Image:ProposedTS.jpg]]
[[Image:BetaSKIE.jpg]]
== Steric Isotope Effect ==
The steric isotope effect is an SKIE that does not involve bond breaking or formation. This effect is attributed to the different vibrational amplitudes of isotopologues (molecular entities differing in isotopic composition only.<ref>{{GoldBookRef | title = isotopologue | file = I03351}}</ref>)<ref>{{GoldBookRef | file = S06001 | title = steric isotope effect}}</ref> An example of such an effect can be seen in the work of Kurt Mislow et al.<ref>{{cite journal | author = K. Mislow, R. Graeve, A. J. Gordon and G. H. Wahl | title = A Note on Steric Isotope Effects. Conformational Kinetic Isotope Effects in The Racemization of 9,10-Dihydro-4,5-Dimethylphenanthrene | year = 1963 | journal = [[J. Am. Chem. Soc.]] | volume = 85 | issue = 8 | pages = 1199–1200 | doi = 10.1021/ja00891a038}}</ref> who demonstrated through the racemization of 9,10-dihydro-4,5-dimethylphenanthrene that the smaller amplitude of vibration for deuterium as compared to hydrogen in C-H (Carbon -Hydrogen), C-D (Carbon -Deuterium) 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 deuterium racemizes faster than the hydrogen isotopologue resulting in a steric isotope effect.
[[Image:racemization.jpg]]
Another example of the Steric isotope effect has been reported by Schalley and Felder in the deslipping reaction of rotaxanes where the deuterium isotope due to its smaller effective size allows faster passage through the stoppers resulting in faster rates of deslipping for the deuterated rotaxanes.<ref>{{cite journal | author = T. Felder and C. A. Schalley | title = Secondary Isotope Effects on the Deslipping Reaction of Rotaxanes: High-Precision Measurement of Steric Size | year = 2003 | journal = [[Angewandte Chemie International Edition]] | volume = 42 | issue = 20 | pages = 2258–2260 | doi = 10.1002/anie.200350903}}</ref>
A depiction of the deslippage reaction of rotaxanes where the mechanical bond is broken and the components freed without cleavage of chemical bonds.
[[Image:rotaxaneslip.jpg]]
[[Image:chemicalrotaxane.jpg]]
==Applications==
The kinetic isotope effect is applied in [[reaction mechanism]] elucidation, for instance in the [[halogenation]] of [[toluene]]:<ref>{{cite journal | title = The Deuterium Isotope Effect in the Side Chain Halogenation of Toluene | author = Kenneth B. Wiberg and Lynn H. Slaugh | journal = [[J. Am. Chem. Soc.]] | year = 1958 | volume = 80 | issue = 12 | pages = 3033–3039 | doi = 10.1021/ja01545a034}} </ref>
:[[Image:KineticIsotopeEffectHalogenation.png|400px|Kinetic isotope effect in halogenation of toluene]]
In this particular '''intramolecular KIE''' study the [[radical substitution]] of hydrogen by bromine is examined with mono-deuterated toluene (obtained by [[organic reduction]] of [[benzyl chloride]] with [[zinc]] and deuterated [[acetic acid]]) and [[N-Bromosuccinimide|''N''-bromosuccinimide]]. As hydrogen is replaced by bromine faster than deuterium, the reaction product gets enriched in deuterium. In order to analyze the deuterium composition by means of [[mass spectroscopy]] the reaction product is reduced back to toluene with [[lithium aluminium hydride]] and a KIE of 4.86 is calculated. This finding is in accordance with the general accepted view of a radical substitution in which a hydrogen atom is removed by a bromine [[free radical]] species in the [[rate-determining step]].
A large KIE of 5.56 is also reported for reaction of [[ketone]]s with [[bromine]] and [[sodium hydroxide]] forming a [[haloketone]] with the α-carbonyl positions deuterated.<ref>{{cite journal | title = Anomalous kinetic hydrogen isotope effects on the rat of ionization of some dialkyl substituted ketones | author = R. A. Lynch, S. P. Vincenti, Y. T. Lin, L. D. Smucker, and S. C. Subba Rao | journal = [[J. Am. Chem. Soc.]] | year = 1972 | volume = 94 | pages = 8351–8356 | doi = 10.1021/ja00779a012}}</ref>
:[[Image:KineticIsotopeEffectEnolateFormation.png|500px|Kinetic isotope effect in bromination of ketone]]
In this reaction the rate-limiting step is [[enolate]] formation by proton (deuterium) abstraction from the ketone by base. 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.
==Tunneling==
In some cases, an additional rate enhancement is seen for the lighter isotope, possibly due to [[Quantum tunnelling|quantum mechanical tunnelling]]. This is typically only observed for hydrogen atoms, which are light enough to exhibit significant tunnelling.
This effect has been observed in such reactions as the [[deprotonation]] and iodination of [[Nitro compound|nitropropane]] with hindered [[pyridine]] base<ref>{{cite journal | title = Rates and isotope effects in the proton transfers from 2-nitropropane to pyridine bases | author = Edward Sheldon Lewis and Lance Funderburk | journal = [[J. Am. Chem. Soc.]] | year = 1967 | volume = 89 | issue = 10 | pages = 2322–2327 | doi = 10.1021/ja00986a013}}</ref> with a reported KIE of 25 at 25 °C:
:[[Image:KIE effect iodination.png|400px|KIE effect iodination]]
and in a [[Sigmatropic reaction|1,5-sigmatropic hydrogen shift]]<ref>{{cite journal | title = Mechanism of the 1,5-sigmatropic hydrogen shift in 1,3-pentadiene | author = Michael J. S. Dewar, Eamonn F. Healy, and James M. Ruiz | journal = [[J. Am. Chem. Soc.]] | year = 1988 | volume = 110 | issue = 8 | pages = 2666–2667 | doi = 10.1021/ja00216a060}}</ref> although it is observed that it is difficult to extrapolate experimental values obtained at elevated temperatures to lower temperatures:<ref>{{cite journal | title = Effect on Kinetics by Deuterium in the 1,5-Hydrogen Shift of a Cisoid-Locked 1,3(Z)-Pentadiene, 2-Methyl-10-methylenebicyclo<nowiki>[4.4.0]</nowiki>dec-1-ene: Evidence for Tunneling? | author = [[William von Eggers Doering|William von E. Doering]] and Xin Zhao | journal = [[J. Am. Chem. Soc.]] | year =2006 | volume = 128 | issue = 28 | pages = 9080–9085 | doi = 10.1021/ja057377v}}</ref><ref>In this study the KIE is measured by sensitive [[proton NMR]]. The extrapolated KIE at 25 °C is 16.6 but the margin of error is high</ref>
:[[Image:KIE effect sigmatropicReaction 2006.png|400px|KIE effect sigmatropic Reaction]]
==See also==
* A pioneer in KIE research: [[Barton Hawkins]]
* A KIE researcher: [[Michael Kearney]]
* KIE is part of the wider field of [[Chemical kinetics]]
==External links==
* [http://clem.mscd.edu/~wiederm/401chp/unit1chp/kiechp/Welcome.htm Testing a Mechanism: Kinetic Isotope Effects]
* [http://www.orgchem.iisc.ernet.in/faculty/um/cd213/isotope2.html Primary Kinetic Isotope Effect]
* [http://www.scs.uiuc.edu/chem/gradprogram/chem435/Abstract%20Baird1.pdf Measuring Kinetic Isotope Effect of Carbon at Natural Abundance]
* [http://www.ca.sandia.gov/crf/viewArticle.php?cid=300011 Kinetic Isotope Effects in Barrierless Reactions of CH Radicals]
* [http://www.chem.tamu.edu/rgroup/singleton/SingletonRes.html Singleton Research Group]
* [http://mch3w.ch.man.ac.uk/theory/posters/mn/poster.htm Kinetic Isotope Effects in the Hydride Transfer Reaction of Xylose Isomerase]
* [http://www.whoi.edu/hpb/viewPage.do?id=3657&cl=13 Stable chlorine intramolecular kinetic isotope effects from the abiotic dehydrochlorination of DDT]
==References==
<div class="references-small"><references/></div>
[[Category:Chemical kinetics]]
[[Category:Physical organic chemistry]]
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