Editing Kinetic isotope effect (section)

=== Secondary kinetic isotope effects ===
A '''secondary kinetic isotope effect''' (SKIE) is observed when no bond to the isotopically labeled atom in the reactant is broken or formed.<ref name="Atkins" /><ref name="Laidler_1987" />{{rp|427}} SKIEs tend to be much smaller than PKIEs; however, secondary deuterium isotope effects can be as large as 1.4 per {{sup|2}}H atom, and techniques have been developed to measure heavy-element isotope effects to very high precision, so SKIEs are still very useful for elucidating reaction mechanisms.

For the aforementioned nucleophilic substitution reactions, secondary hydrogen KIEs at the α-carbon provide a direct means to distinguish between S{{sub|N}}1 and S{{sub|N}}2 reactions. It has been found that S{{sub|N}}1 reactions typically lead to large SKIEs, approaching to their theoretical maximum at about 1.22, while S{{sub|N}}2 reactions typically yield SKIEs that are very close to or less than 1. KIEs greater than 1 are called '''normal kinetic isotope effects''', while KIEs less than 1 are called '''inverse kinetic isotope effects''' (IKIE). In general, smaller force constants in the transition state are expected to yield a normal KIE, and larger force constants in the transition state are expected to yield an IKIE when stretching vibrational contributions dominate the KIE.<ref name="Westaway1" />

[[File:SN1 vs SN2.png|center]]

The magnitudes of such SKIEs at the α-carbon atom are largely determined by the C{{sub|α}}-H({{sup|2}}H) vibrations. For an S{{sub|N}}1 reaction, since the carbon atom is converted into an sp{{sup|2}} hybridized carbenium ion during the transition state for the rate-determining step with an increase in C{{sub|α}}-H({{sup|2}}H) bond order, an IKIE would be expected if only the stretching vibrations were important. The observed large normal KIEs are found to be caused by significant out-of-plane bending vibrational contributions when going from the reactants to the transition state of carbenium ion formation. For S{{sub|N}}2 reactions, bending vibrations still play an important role for the KIE, but stretching vibrational contributions are of more comparable magnitude, and the resulting KIE may be normal or inverse depending on the specific contributions of the respective vibrations.<ref name="Westaway1" /><ref>{{cite journal| vauthors = Poirier RA, Wang Y, Westaway KC |title=A Theoretical Study of the Relationship between Secondary .alpha.-Deuterium Kinetic Isotope Effects and the Structure of S{{sub|N}}2 Transition States|journal=Journal of the American Chemical Society|date=March 1994|volume=116|issue=6|pages=2526–2533|doi=10.1021/ja00085a037|bibcode=1994JAChS.116.2526P }}</ref><ref name=Buncel5>{{cite book | vauthors = Buncel E, Lee CC | series = Isotopes in Organic Chemistry | title = Isotopes in cationic reactions | publisher = Elsevier | location = Amsterdam | year = 1977 | volume = 5 | isbn = 978-0-444-41927-9 | oclc = 867217247 | url-access = registration | url = https://archive.org/details/isotopesincation0005unse }}</ref>