Editing Kinetic isotope effect (section)

=== 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]]