• Kinetic isotope effects at the α-carbon can be used to develop some understanding into the symmetry of the transition state in SN2 reactions, although this kinetic isotope
  effect is less sensitive than what would be ideal, also due to contribution from non-vibrational factors.

• Depending on the mass of the atom that moves along the reaction coordinate and nature (width and height) of the energy barrier, quantum mechanical tunneling may also make
  a large contribution to an observed kinetic isotope effect and may need to be separately considered, in addition to the “semi-classical” transition state theory model.

• For a reaction with this profile, all three experiments (A, B, and C) will yield a significant primary kinetic isotope effect: Reaction energy profile for when C-H cleavage
  occurs at the RDS On the other hand, if a reaction follows the following energy profile, in which the C-H or C-D bond cleavage is irreversible but occurs after the rate-determining step (RDS), no significant kinetic isotope effect will be
  observed with Experiment A, since the overall rate is not affected by the isotopic substitution.

• [8][9] The kinetic isotope effect arises largely from the changes to vibrational ground states produced by the isotopic perturbation along the minimum energy pathway of the
  potential energy surface, which may only be accounted for with quantum mechanical treatments of the system.

• A value of is thought to be maximal for a semi-classical primary kinetic isotope effect (no tunneling) for reactions taking place around 298 K. (The formula for kH/kD has
  a temperature dependence, so larger isotope effects are possible at lower temperatures).

• The ratio between the amounts of the two species in the reactants and the products will thus change gradually over the course of the reaction, and this gradual change can
  be treated in the following manner:[8] Assume that two isotopic molecules, A1 and A2, undergo irreversible competition reactions in the following manner: The kinetic isotope effect for this scenario is found to be: Where F1 and F2 refer to
  the fraction of conversions for the isotopic species A1 and A2, respectively.

• In many cases, the rate difference can be rationalized by noting that the mass of an atom affects the vibrational frequency of the chemical bond that it forms, even if the
  potential energy surface for the reaction is nearly identical.

• Hence, the lower zero-point energy of the deuterated species translates into a larger activation energy for its reaction, as shown in the following figure, leading to a normal
  kinetic isotope effect.

• [13] As mentioned, especially for hydrogen/deuterium substitution, most kinetic isotope effects arise from the difference in zero-point energy (ZPE) between the reactants
  and the transition state of the isotopologues in question, and this difference can be understood qualitatively with the following description: within the Born–Oppenheimer approximation, the potential energy surface is the same for both isotopic
  species.

• Hence, for hydrogen/deuterium kinetic isotope effects, the observed values are typically dominated by the last factor, ZPE (an exponential function of vibrational zero-point
  energy differences), consisting of contributions from the zero-point energy differences for each of the vibrational modes of the reactants and transition state, which can be represented as follows:[7], where we define and .The sums in the
  exponent of the second expression can be interpreted as running over all vibrational modes of the reactant ground state and the transition state.

• [35] Experiments Simmons and Hartwig refer to the following three cases as the main types of kinetic isotope effect experiments involving C-H bond functionalization:[5] A)
  KIE determined from absolute rates of two parallel reactions In this experiment, the rate constants for the normal substrate and its isotopically labeled analogue are determined independently, and the KIE is obtained as a ratio of the two.

• Moreover, as noted in the paragraph above, the experiments provide kinetic isotope effect data for different steps of a multi-step reaction, depending on the relative locations
  of the rate-limiting step, product-determining steps, and/or C-H/D cleavage step.

• It has been found that SN1 reactions typically lead to large secondary kinetic isotope effects, approaching to their theoretical maximum at about 1.22, while SN2 reactions
  typically yield secondary kinetic isotope effects that are very close to or less than unity.

• For an SN1 reaction, since the carbon atom is converted into an sp2 hybridized carbenium ion during the transition state for the rate-determining step with an increase in
  Cα-H(D) bond order, an inverse kinetic isotope effect would be expected if only the stretching vibrations were important.

• Reaction energy profile for when the C-H bond cleavage occurs at a product-determining step after the RDS show Evaluation of Kinetic Isotope Effects in a Hypothetical Multi-Step
  Reaction Evaluation of rate constant ratios from intermolecular competition reactions[edit] In competition reactions, the kinetic isotope effect is calculated from isotopic product or remaining reactant ratios after the reaction, but these
  ratios depend strongly on the extent of completion of the reaction.

• Since hydrogen and deuterium tend to be much lighter compared to most reactants and transition states, there is little difference in the molecular masses and moments of inertia
  between H and D containing molecules, so the MMI factor is usually also approximated as unity.

• [8] It is also possible in case of 13C kinetic isotope effects, as well as similar cases, to simply rely on the natural abundance of the isotopic carbon for the kinetic isotope
  effect experiments, eliminating the need for isotopic labeling.

• For SN2 reactions, bending vibrations still play an important role for the kinetic isotope effect, but stretching vibrational contributions are of more comparable magnitude,
  and the resulting kinetic isotope effect may be normal or inverse depending on the specific contributions of the respective vibrations.

• These changes are attributed to a change in steric environment when the carbon bound to the H/D undergoes rehybridization from sp3 to sp2 or vice versa (an α secondary kinetic
  isotope effect), or bond weakening due to hyperconjugation in cases where a carbocation is being generated one carbon atom away (a β secondary kinetic isotope effect).

• Nevertheless, a measurement of a large kinetic isotope effect through direct comparison of rate constants is indicative that C-H bond cleavage occurs at the rate-determining
  step.

• However, an observed kinetic isotope effect from this experiment is more difficult to interpret, since it may either mean that C-H bond cleavage occurs during the rate-determining
  step or at a product-determining step ensuing the rate-determining step.

• To calculate the maximum possible value for a non-tunneling deuterium KIE, we consider the case in which the zero-point energy difference between the stretching vibrations
  of a typical carbon-hydrogen bond and carbon-deuterium bond disappears in the transition state (an energy difference of, or about), without any compensation from a zero-point energy difference at the transition state (e.g., from the symmetric
  stretch, which is unique to the transition state).

• (The misconception that a primary kinetic isotope effect must reflect bond cleavage/formation to the isotope at the rate-limiting step is frequently repeated in textbooks
  and the primary literature: see the section on experiments below.

• [3][4]: 427  Depending on the way a kinetic isotope effect is probed (parallel measurement of rates vs. intermolecular competition vs. intramolecular competition), the observation
  of a primary kinetic isotope effect is indicative of breaking/forming a bond to the isotope at the rate-limiting step, or subsequent product-determining step(s).

• Nevertheless, it is still generally true that cleavage of a bond with a higher vibrational frequency will give a larger isotope effect.

• [1][6][7] Theory The theoretical treatment of isotope effects relies heavily on transition state theory, which assumes a single potential energy surface for the reaction,
  and a barrier between the reactants and the products on this surface, on top of which resides the transition state.

• The observed large normal kinetic isotope effects 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.

• Also, due to the large relative difference in the mass of deuterium and protium and the attendant differences in vibrational frequencies, the magnitude of the isotope effect
  is larger than any other pair of isotopes except protium and tritium,[10] allowing both primary and secondary isotope effects to be easily measured and interpreted.

• Interpretation of the leaving group kinetic isotope effects had been difficult at first due to significant contributions from temperature independent factors.

• (A smaller value could indicate an isotope effect due to a pre-equilibrium, so that the C-H bond cleavage occurs somewhere before the rate-determining step.)

• As a result, very large kinetic isotope effects are observed that can not be accounted for by differences in zero point energies.

• Because of the exponential dependence, even very low kinetic isotope effects lead to large changes in isotopic composition of the starting material at high conversions.

• When the products are followed, the kinetic isotope effect can be calculated using the products ratio RP along with R0 as follows: Kinetic isotope effect measurement at natural
  abundance[edit] Kinetic isotope effect measurement at natural abundance is a simple general method for measuring kinetic isotope effects (KIE) for chemical reactions performed with materials of natural abundance.

• Nevertheless, the irreversible C-H bond cleavage step will give a primary kinetic isotope effect with the other two experiments, since the second step would still affect the
  product distribution.

• [3] Formally, it is the ratio of rate constants for the reactions involving the light (kL) and the heavy (kH) isotopically substituted reactants (isotopologues): This change
  in reaction rate is a quantum mechanical effect that primarily results from heavier isotopologues having lower vibrational frequencies compared to their lighter counterparts.

• Evaluation Measurement of F1 in terms of weights per unit volume or molarities of the reactants Isotopic enrichment of the starting material can be calculated from the dependence
  of R/R0 on F1 for various kinetic isotope effects, yielding the following figure.

• Therefore, with Experiments B and C, it is possible to observe the kinetic isotope effect even if C-H or C-D bond cleavage occurs not in the rate-determining step, but in
  the product-determining step.

• [3][4]: 427  Secondary kinetic isotope effects tend to be much smaller than primary kinetic isotope effects; however, secondary deuterium isotope effects can be as large as
  1.4 per deuterium atom, and techniques have been developed to measure heavy-element isotope effects to very high precision, so secondary kinetic isotope effects are still very useful for elucidating reaction mechanisms.

• The kinetic isotope effect from this experiment is determined by the relative amount of products formed from C-H versus C-D functionalization (or it can be inferred from the
  relative amounts of unreacted starting materials).

• One non-C-H activation example of different isotope effects being observed in the case of intermolecular (Experiment B) and intramolecular (Experiment C) competition is the
  photolysis of diphenyldiazomethane in the presence of t-butylamine.

• [16] Depending on the nature of the transition state of H-transfer (symmetrical vs. “early” or “late” and linear vs. bent), the extent to which a primary deuterium isotope
  effect approaches this maximum varies.

• [8] The deuterium kinetic isotope effect (2H KIE) is by far the most common, useful, and well-understood type of kinetic isotope effect.

• In many cases and especially for hydrogen-transfer reactions, contributions to kinetic isotope effects from tunneling are significant (see below).

• The fraction of molecules with enough energy to have excited state A–H/D bond vibrations is generally small for reactions at or near room temperature (bonds to hydrogen usually
  vibrate at or higher, so, resulting in negligible contributions from the 1–exp(-ui) factors).

• In the case of a homolytic C–H/D bond dissociation, the transition state term disappears, and neglecting other vibrational modes, Thus, a larger isotope effect is observed
  for a stiffer (“stronger”) C–H/D bond.

• Background The kinetic isotope effect is considered to be one of the most essential and sensitive tools for the study of reaction mechanisms, the knowledge of which allows
  the improvement of the desirable qualities of the corresponding reactions.

• In general, smaller force constants in the transition state are expected to yield a normal kinetic isotope effect, and larger force constants in the transition state are expected
  to yield an inverse kinetic isotope effect when stretching vibrational contributions dominate the kinetic isotope effect.

• [17] For secondary deuterium isotope effects, Streitwieser proposed that weakening (or strengthening, in the case of an inverse isotope effect) of bending modes from the reactant
  ground state to the transition state are largely responsible for observed isotope effects.

• In contrast to Experiment B, the reaction does not need to be halted at low consumption of isotopic starting material to obtain an accurate kH/kD, since the ratio of H and
  D in the starting material is 1:1, regardless of the extent of conversion.

• Since the heavier (in this case the deuterated) species behaves more “classically,” its vibrational energy levels are closer to the classical potential energy curve, and it
  has a lower zero-point energy.

• Isotopic rate changes are most pronounced when the relative mass change is greatest, since the effect is related to vibrational frequencies of the affected bonds.

• For isotope effects involving elements other than hydrogen, many of these simplifications are not valid, and the magnitude of the isotope effect may depend strongly on some
  or all of the neglected factors.

• [15] This effect should, in principle, be taken into account all 3N−6 vibrational modes for the starting material and 3N‡−7 vibrational modes at the transition state (one
  mode, the one corresponding to the reaction coordinate, is missing at the transition state, since a bond breaks and there is no restorative force against the motion).

• [12][4]: 427  Bigeleisen’s general formula for deuterium kinetic isotope effects (which is also applicable to heavier elements) is given below.

• The absence of a kinetic isotope effect, at least according to Simmons and Hartwig, is nonetheless indicative of the C-H bond cleavage not occurring during the rate-determining
  step.

• In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced
  by one of its isotopes.

• [36] Thus, Experiments A, B, and C will give results of differing levels of precision and require different experimental setup and ways of analyzing data.

• [1] Depending on the pathway, different strategies may be used to stabilize the transition state of the rate-determining step of the reaction and improve the reaction rate
  and selectivity, which are important for industrial applications.

• [7][13] (Strictly speaking, a term resulting from an isotopic difference in transmission coefficients should also be included.

• [7] The complicated expression given above can be represented as the product of four separate factors:[7] For the special case of deuterium isotope effects, we will argue
  that the first three terms can be treated as equal to or well approximated by unity.

• As a result, the feasibility of each type of experiment will depend on the kinetic and stoichiometric profile of the reaction, as well as the physical characteristics of the
  reaction mixture (e.g., homogeneous vs. heterogeneous).

• However, a quantum-mechanical treatment of the energy introduces discrete vibrational levels onto this curve, and the lowest possible energy state of a molecule corresponds
  to the lowest vibrational energy level, which is slightly higher in energy than the minimum of the potential energy curve.

• In most cases, this implies a greater energetic input needed for heavier isotopologues to reach the transition state (or, in rare cases, the dissociation limit), and consequently,
  a slower reaction rate.

• Alternatively, one may interpret them as running over those modes unique to the reactant or the transition state or whose vibrational frequencies change substantially upon
  advancing along the reaction coordinate.

• For reactants containing several isotopically substituted β-hydrogen atoms, the observed isotope effect is often the result of several H/D’s at the β position acting in concert.

• In such a scenario, an isotope effect may be observed in Experiment C (where choice of the isotope can take place even after substrate binding) but not in Experiment B (since
  the choice of whether C-H or C-D bond cleaves is already made as soon as the substrate binds irreversibly).

• In contrast, secondary effects are generally very small for heavier elements and close in magnitude to the experimental uncertainty, which complicates their interpretation
  and limits their utility.

• The zero-point energy differences between the two isotopic species, at least in most cases, diminish in the transition state, since the bond force constant decreases during
  bond breaking.

 

Works Cited

[‘1. Westaway KC (2006). “Using kinetic isotope effects to determine the structure of the transition states of SN2 reactions”. Advances in Physical Organic Chemistry. 41: 217–273. doi:10.1016/S0065-3160(06)41004-2. ISBN 978-0-12-033541-1.
2. ^ Lynn
KR, Yankwich PE (5 August 1961). “Isotope Fractionation at the Methyl Carbon in the Reactions of Cyanide Ion with Methyl Chloride and Methyl Bromide”. Journal of the American Chemical Society. 83 (15): 3220–3223. doi:10.1021/ja01476a012.
3. ^ Jump
up to:a b c d e f Atkins P, de Paula J (2006). Atkins’ Physical Chemistry (8th ed.). Oxford University Press. pp. 286–288, 816–818. ISBN 978-0-19-870072-2.
4. ^ Jump up to:a b c d e f g h Laidler KJ (1987). Chemical Kinetics (3rd ed.). Harper &
Row. ISBN 978-0-06-043862-3.
5. ^ Jump up to:a b c d Simmons EM, Hartwig JF (March 2012). “On the Interpretation of Deuterium Kinetic Isotope Effects in C–H Bond Functionalizations by Transition‐Metal Complexes”. Angewandte Chemie International
Edition. 51 (1): 3066–72. doi:10.1002/anie.201107334. PMID 22392731.
6. ^ Poirier RA, Wang Y, Westaway KC (March 1994). “A Theoretical Study of the Relationship between Secondary .alpha.-Deuterium Kinetic Isotope Effects and the Structure of SN2
Transition States”. Journal of the American Chemical Society. 116 (6): 2526–2533. doi:10.1021/ja00085a037.
7. ^ Jump up to:a b c d e Buncel E, Lee CC (1977). Isotopes in cationic reactions. Isotopes in Organic Chemistry. Vol. 5. Amsterdam: Elsevier.
ISBN 978-0-444-41927-9. OCLC 867217247.
8. ^ Jump up to:a b c d e f g h i Melander L, Saunders WH (1980). Reaction Rates of Isotopic Molecules. New York: Wiley.
9. ^ Bigeleisen J, Wolfsberg M (January 1957). “Theoretical and experimental aspects
of isotope effects in chemical kinetics”. Advances in Chemical Physics. 1: 15–76.
10. ^ If muonium (μ+e–) is treated as an isotope of hydrogen, then even larger KIEs are possible, in principle. However, studies involving muonium are limited by the
short half-life of the muon (22 microseconds) (see Villà J, Corchado JC, González-Lafont A, Lluch JM, Truhlar DG (November 1998). “Explanation of deuterium and muonium kinetic isotope effects for hydrogen atom addition to an olefin”. Journal of the
American Chemical Society. 120 (46): 12141–2. doi:10.1021/ja982616i. for an example of a kMu/kH isotope effect.)
11. ^ This convention exists for both convenience in nomenclature and as a reflection of how deuterium kinetic isotope effects are generally
studied experimentally: Although deuterium has the IUPAC-sanctioned symbol D = 2H, there is no common symbol that specifically refers to protium (1H). Nevertheless, it has proven useful to have labels to refer to the respective rate constants of protium-
or deuterium-containing isotopologues, so kH and kD, respectively, have typically been used. Moreover, the magnitude of a kinetic isotope effect could then be expressed as kH/kD. This notation is consistent with the fact that, experimentally, deuterium
kinetic isotope effects are measured by comparing the reaction rate of a deuterium-enriched starting material to that of an unenriched starting material containing hydrogen at natural abundance. This is almost always valid, since protium accounts
for 99.9885% of natural hydrogen, so there is generally no need to further deplete the deuterium in the starting material to obtain a “protium-enriched” sample. Combined, the notation and experimental setup led to the common conceptualization of deuterium
as a “substituent” that takes the place of “regular” hydrogen in an isotope effect study.
12. ^ Bigeleisen J (August 1949). “The Relative Reaction Velocities of Isotopic Molecules”. Journal of Chemical Physics. 17 (8): 675–678. Bibcode:1949JChPh..17..675B.
doi:10.1063/1.1747368.
13. ^ Jump up to:a b c Lowry TH, Richardson KS (1987). Mechanism and theory in organic chemistry (3rd ed.). New York: Harper & Row. pp. 256. ISBN 978-0-06-044084-8. OCLC 14214254.
14. ^ Carpenter BK (1984). Determination
of organic reaction mechanisms. New York: Wiley. p. 86. ISBN 978-0-471-89369-1. OCLC 9894996.
15. ^ Carpenter BK (February 2010). “Kinetic isotope effects: unearthing the unconventional”. Nature Chemistry. 2 (2): 80–2. Bibcode:2010NatCh…2…80C.
doi:10.1038/nchem.531. PMID 21124393.
16. ^ Carroll FA (2010). Perspectives on structure and mechanism in organic chemistry (2nd ed.). Hoboken, N.J.: John Wiley. ISBN 978-0-470-27610-5. OCLC 286483846.
17. ^ Kwart H (1 December 1982). “Temperature
dependence of the primary kinetic hydrogen isotope effect as a mechanistic criterion”. Accounts of Chemical Research. 15 (12): 401–408. doi:10.1021/ar00084a004. ISSN 0001-4842.
18. ^ Streitwieser A, Jagow RH, Fahey RC, Suzuki S (May 1958). “Kinetic
isotope effects in the acetolyses of deuterated cyclopentyl tosylates1, 2”. Journal of the American Chemical Society. 80 (9): 2326–32. doi:10.1021/ja01542a075.
19. ^ Swain CG, Stivers EC, Reuwer Jr JF, Schaad LJ (1 November 1958). “Use of Hydrogen
Isotope Effects to Identify the Attacking Nucleophile in the Enolization of Ketones Catalyzed by Acetic Acid”. Journal of the American Chemical Society. 80 (21): 5885–5893. doi:10.1021/ja01554a077.
20. ^ Jump up to:a b c d e f g h i j Anslyn EV,
Dougherty DA (2006). Modern Physical Organic Chemistry. University Science Books. pp. 428–437. ISBN 978-1-891389-31-3.
21. ^ Razauy M (2003). Quantum Theory of Tunneling. World Scientific. ISBN 978-981-238-019-7.
22. ^ Silbey RJ, Alberty RA, Bawendi
MG (2005). Physical Chemistry. John Wiley & Sons. pp. 326–338. ISBN 978-0-471-21504-2.
23. ^ Borgis D, Hynes JT (1993). “Dynamical theory of proton tunneling transfer rates in solution: General formulation”. Chemical Physics. 170 (3): 315–346. Bibcode:1993CP….170..315B.
doi:10.1016/0301-0104(93)85117-Q.
24. ^ Jump up to:a b Krishtalik LI (May 2000). “The mechanism of the proton transfer: an outline”. Biochimica et Biophysica Acta (BBA) – Bioenergetics. 1458 (1): 6–27. doi:10.1016/S0005-2728(00)00057-8. PMID 10812022.
25. ^
Zuev PS, Sheridan RS, Albu TV, Truhlar DG, Hrovat DA, Borden WT (February 2003). “Carbon tunneling from a single quantum state”. Science. 299 (5608): 867–70. Bibcode:2003Sci…299..867Z. doi:10.1126/science.1079294. PMID 12574623. S2CID 20959068.
26. ^
Fujisaki N, Ruf A, Gaeumann T (1987). “Tunnel effects in hydrogen-atom-transfer reactions as studied by the temperature dependence of the hydrogen deuterium kinetic isotope effects”. Journal of Physical Chemistry. 91 (6): 1602–1606. doi:10.1021/j100290a062.
27. ^
Lewis ES, Funderburk L (1967). “Rates and isotope effects in the proton transfers from 2-nitropropane to pyridine bases”. Journal of the American Chemical Society. 89 (10): 2322–2327. doi:10.1021/ja00986a013.
28. ^ Dewar MJ, Healy EF, Ruiz JM (1988).
“Mechanism of the 1,5-sigmatropic hydrogen shift in 1,3-pentadiene”. Journal of the American Chemical Society. 110 (8): 2666–2667. doi:10.1021/ja00216a060.
29. ^ von Doering W, Zhao X (July 2006). “Effect on kinetics by deuterium in the 1,5-hydrogen
shift of a cisoid-locked 1,3(Z)-pentadiene, 2-methyl-10-methylenebicyclo[4.4.0]dec-1-ene: evidence for tunneling?”. Journal of the American Chemical Society. 128 (28): 9080–5. doi:10.1021/ja057377v. PMID 16834382.
30. ^ 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
31. ^ Kohen A, Klinman JP (July 1999). “Hydrogen tunneling in biology”. Chemistry & Biology. 6 (7): R191-8. doi:10.1016/S1074-5521(99)80058-1.
PMID 10381408.
32. ^ Wilde TC, Blotny G, Pollack RM (May 2008). “Experimental evidence for enzyme-enhanced coupled motion/quantum mechanical hydrogen tunneling by ketosteroid isomerase”. Journal of the American Chemical Society. 130 (20): 6577–85.
doi:10.1021/ja0732330. PMID 18426205.
33. ^ Truhlar DG, Gao J, Alhambra C, Garcia-Viloca M, Corchado J, Sánchez M, Villà J (2002). “The Incorporation of Quantum Effects in Enzyme Kinetics Modeling”. Accounts of Chemical Research. 35 (6): 341–349.
doi:10.1021/ar0100226. PMID 12069618.
34. ^ Kohen, A; Klinman, J. P (1998). “Enzyme Catalysis: Beyond Classical Paradigms”. Accounts of Chemical Research. 31 (7): 397–404. doi:10.1021/ar9701225.
35. ^ Maggi F, Riley WJ (2010). “Mathematical treatment
of isotopologue and isotopomer speciation and fractionation in biochemical kinetics”. Geochimica et Cosmochimica Acta. 74 (6): 1823. Bibcode:2010GeCoA..74.1823M. doi:10.1016/j.gca.2009.12.021. S2CID 55422661.
36. ^ Newall, A. Raymond; Hayes, John;
Bethell, Donald (1 January 1974). “Intermediates in the decomposition of aliphatic diazo-compounds. Part XI. Mechanistic studies on the reaction of diphenylmethylene with amines in solution”. Journal of the Chemical Society, Perkin Transactions 2
(11): 1307–1312. doi:10.1039/P29740001307. ISSN 1364-5471.
37. ^ Buncel E, Lee CC (1977). Carbon-13 in Organic Chemistry. Isotopes in Organic Chemistry. Vol. 3. Amsterdam: Elsevier. ISBN 978-0-444-41472-4. OCLC 606113159.
38. ^ Jump up to:a b
c d Singleton DA, Thomas AA (September 1995). “High-Precision Simultaneous Determination of Multiple Small Kinetic Isotope Effects at Natural Abundance”. Journal of the American Chemical Society. 117 (36): 9357–9358. doi:10.1021/ja00141a030.
39. ^
Jump up to:a b c Jankowski S (January 2009). “Application of NMR spectroscopy in isotope effects studies”. Annual Reports on NMR Spectroscopy. 68: 149–191. doi:10.1016/S0066-4103(09)06803-3. ISBN 978-0-12-381041-0.
40. ^ Martin GJ, Martin ML (1984).
“Deuterium labelling at the natural abundance level as studied by high field quantitative 2H NMR”. Tetrahedron Letters. 22 (36): 3525–3528. doi:10.1016/s0040-4039(01)81948-1.
41. ^ Jump up to:a b Pascal Jr RA, Baum MW, Wagner CK, Rodgers LR (September
1984). “Measurement of deuterium kinetic isotope effects in organic reactions by natural-abundance deuterium NMR spectroscopy”. Journal of the American Chemical Society. 106 (18): 5377–5378. doi:10.1021/ja00330a071.
42. ^ Gajewski JJ, Peterson KB,
Kagel JR, Huang YJ (December 1989). “Transition-state structure variation in the Diels-Alder reaction from secondary deuterium kinetic isotope effects. The reaction of nearly symmetrical dienes and dienophiles is nearly synchronous”. Journal of the
American Chemical Society. 111 (25): 9078–9081. doi:10.1021/ja00207a013.
43. ^ Jump up to:a b Colletto C, Islam S, Juliá-Hernández F, Larrosa I (February 2016). “Room-Temperature Direct β-Arylation of Thiophenes and Benzo[b]thiophenes and Kinetic
Evidence for a Heck-type Pathway”. Journal of the American Chemical Society. 138 (5): 1677–83. doi:10.1021/jacs.5b12242. PMC 4774971. PMID 26788885.
44. ^ Jump up to:a b Frost GB, Serratore NA, Ogilvie JM, Douglas CJ (April 2017). “Mechanistic Model
for Enantioselective Intramolecular Alkene Cyanoamidation via Palladium-Catalyzed C-CN Bond Activation”. The Journal of Organic Chemistry. 82 (7): 3721–3726. doi:10.1021/acs.joc.7b00196. PMC 5535300. PMID 28294618.
45. ^ Kwan EE, Park Y, Besser
HA, Anderson TL, Jacobsen EN (January 2017). “13C Kinetic Isotope Effect Measurements Enabled by Polarization Transfer”. Journal of the American Chemical Society. 139 (1): 43–46. doi:10.1021/jacs.6b10621. PMC 5674980. PMID 28005341.
46. ^ Park Y,
Harper KC, Kuhl N, Kwan EE, Liu RY, Jacobsen EN (January 2017). “Macrocyclic bis-thioureas catalyze stereospecific glycosylation reactions”. Science. 355 (6321): 162–166. Bibcode:2017Sci…355..162P. doi:10.1126/science.aal1875. PMC 5671764. PMID
28082586.
47. ^ Burlingham BT, Pratt LM, Davidson ER, Shiner VJ, Fong J, Widlanski TS (October 2003). “34S isotope effect on sulfate ester hydrolysis: mechanistic implications”. Journal of the American Chemical Society. 125 (43): 13036–7. doi:10.1021/ja0279747.
PMID 14570471.
48. ^ Hennig C, Oswald RB, Schmatz S (March 2006). “Secondary kinetic isotope effect in nucleophilic substitution: a quantum-mechanical approach”. The Journal of Physical Chemistry A. 110 (9): 3071–9. Bibcode:2006JPCA..110.3071H.
doi:10.1021/jp0540151. PMID 16509628.
49. ^ Jump up to:a b Cleland WW (December 2003). “The use of isotope effects to determine enzyme mechanisms”. The Journal of Biological Chemistry. 278 (52): 51975–84. doi:10.1074/jbc.X300005200. PMID 14583616.
50. ^
Jump up to:a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the “Gold Book”) (1997). Online corrected version: (2006–) “Secondary isotope effect”. doi:10.1351/goldbook.S05523
51. ^ “Definition of isotope effect, secondary”. Chemistry Dictionary.
Chemitool.
52. ^ Kurtz KA, Fitzpatrick PF (1997). “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 of the American Chemical
Society. 119 (5): 1155–1156. doi:10.1021/ja962783n.
53. ^ Angelis YS, Hatzakis NS, Smonou I, Orfanopoulos M (2006). “Oxidation of benzyl alcohols by dimethyldioxirane. The question of concerted versus stepwise mechanisms probed by kinetic isotope
effects”. Tetrahedron Letters. 42 (22): 3753–3756. doi:10.1016/S0040-4039(01)00539-1.
54. ^ Jump up to:a b Houk KN, Gustafson SM, Black KA (October 1992). “Theoretical secondary kinetic isotope effects and the interpretation of transition state
geometries. 1. The Cope rearrangement”. Journal of the American Chemical Society. 114 (22): 8565–72. doi:10.1021/ja00048a032.
55. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the “Gold Book”) (1997). Online corrected version: (2006–) “steric
isotope effect”. doi:10.1351/goldbook.S06001
56. ^ Mislow K, Graeve R, Gordon AJ, Wahl GH (1963). “A Note on Steric Isotope Effects. Conformational Kinetic Isotope Effects in The Racemization of 9,10-Dihydro-4,5-Dimethylphenanthrene”. Journal of
the American Chemical Society. 85 (8): 1199–1200. doi:10.1021/ja00891a038.
57. ^ Bartell LS (1 September 1961). “The Role of Non-bonded Repulsions in Secondary Isotope Effects. I. Alpha and Beta Substitution Effects.1”. Journal of the American Chemical
Society. 83 (17): 3567–3571. doi:10.1021/ja01478a006.
58. ^ Felder T, Schalley CA (May 2003). “Secondary isotope effects on the deslipping reaction of rotaxanes: high-precision measurement of steric size”. Angewandte Chemie. 42 (20): 2258–60. doi:10.1002/anie.200350903.
PMID 12772156.
59. ^ Churchill, David G.; Janak, Kevin E.; Wittenberg, Joshua S.; Parkin, Gerard (11 January 2003). “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”. J. Am. Chem. Soc. 125 (5): 1403–1420. Retrieved 26 January 2023.
60. ^ Fleming DG, Arseneau DJ, Sukhorukov O, Brewer JH, Mielke SL, Schatz GC, Garrett
BC, Peterson KA, Truhlar DG (January 2011). “Kinetic isotope effects for the reactions of muonic helium and muonium with H2”. Science. 331 (6016): 448–50. Bibcode:2011Sci…331..448F. doi:10.1126/science.1199421. PMID 21273484. S2CID 206530683.
61. ^
Wiberg KB, Slaugh LH (1958). “The Deuterium Isotope Effect in the Side Chain Halogenation of Toluene”. Journal of the American Chemical Society. 80 (12): 3033–3039. doi:10.1021/ja01545a034.
62. ^ Lynch RA, Vincenti SP, Lin YT, Smucker LD, Subba
Rao SC (1972). “Anomalous kinetic hydrogen isotope effects on the rate of ionization of some dialkyl substituted ketones”. Journal of the American Chemical Society. 94 (24): 8351–8356. doi:10.1021/ja00779a012.
63. ^ Zi W, Wang YM, Toste FD (September
2014). “An in situ directing group strategy for chiral anion phase-transfer fluorination of allylic alcohols”. Journal of the American Chemical Society. 136 (37): 12864–7. doi:10.1021/ja507468u. PMC 4183625. PMID 25203796.
Photo credit: https://www.flickr.com/photos/enerva/10503217854/’]