Editing Kinetic isotope effect (section)

=== 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}}