Kinetic isotope effect

4749:

inferred from the relative amounts of unreacted starting materials). One must quench the reaction before it goes to completion to observe the KIE (see the Evaluation section below). Generally, the reaction is halted at low conversion (~5 to 10% conversion) or a large excess (> 5 equiv.) of the isotopic mixture is used. This experiment type ensures that both C-H and C-D bond functionalizations occur under exactly the same conditions, and the ratio of products from C-H and C-D bond functionalizations can be measured with much greater precision than the rate constants in Experiment A. Moreover, only a single measurement of product concentrations from a single sample is required. 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. The absence of a KIE, at least according to Simmons and Hartwig, is nonetheless indicative of the C-H bond cleavage not occurring during the rate-determining step.

2871:, the potential energy surface is the same for both isotopic species. However, a quantum 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. This difference, known as the ZPE, is a manifestation of the uncertainty principle that necessitates an uncertainty in the C-H or C-D bond length. 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 ZPE. The ZPE 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. Hence, the lower ZPE of the deuterated species translates into a larger activation energy for its reaction, as shown in the following figure, leading to a normal KIE. This effect should, in principle, be taken into account all 3 1615: 7738: 743: 4833: 1610:{\displaystyle {\frac {k_{{\ce {H}}}}{k_{{\ce {D}}}}}=\left({\frac {\sigma _{{\ce {H}}}\sigma _{{\ce {D}}}^{\ddagger }}{\sigma _{{\ce {D}}}\sigma _{{\ce {H}}}^{\ddagger }}}\right)\left({\frac {M_{{\ce {H}}}^{\ddagger }M_{{\ce {D}}}}{M_{{\ce {D}}}^{\ddagger }M_{{\ce {H}}}}}\right)^{\frac {3}{2}}\left({\frac {I_{x{\ce {H}}}^{\ddagger }I_{y{\ce {H}}}^{\ddagger }I_{z{\ce {H}}}^{\ddagger }}{I_{x{\ce {D}}}^{\ddagger }I_{y{\ce {D}}}^{\ddagger }I_{z{\ce {D}}}^{\ddagger }}}{\frac {I_{x{\ce {D}}}I_{y{\ce {D}}}I_{z{\ce {D}}}}{I_{x{\ce {H}}}I_{y{\ce {H}}}I_{z{\ce {H}}}}}\right)^{\frac {1}{2}}\left({\frac {\prod \limits _{i=1}^{3N^{\ddagger }-7}{\frac {1-e^{-u_{i{\ce {D}}}^{\ddagger }}}{1-e^{-u_{i{\ce {H}}}^{\ddagger }}}}}{\prod \limits _{i=1}^{3N-6}{\frac {1-e^{-u_{i{\ce {D}}}}}{1-e^{-u_{i{\ce {H}}}}}}}}\right)e^{-{\frac {1}{2}}\left}} 7730: 7665: 4821: 657:

possibilities. Starting materials containing H are often commercially available, making the synthesis of isotopically enriched starting materials relatively straightforward. Also, due to the large relative difference in the mass of H and H and the attendant differences in vibrational frequency, the isotope effect is larger than for any other pair of isotopes except H and H, allowing both primary and secondary isotope effects to be easily measured and interpreted. 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. In the context of isotope effects,

7657: 8489:. This notation is consistent with the fact that, experimentally, H KIEs 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 usually 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. 7607: 8415: 7893: 4637: 4806: 645:, 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 KIE 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. Depending on the mass of the atom that moves along the reaction coordinate and nature (width and height) of the energy barrier, 8368: 7623: 7615: 551:(PKIE) may be found when a bond to the isotopically labeled atom is being formed or broken. Depending on the way a KIE is probed (parallel measurement of rates vs. intermolecular competition vs. intramolecular competition), the observation of a PKIE is indicative of breaking/forming a bond to the isotope at the rate-limiting step, or subsequent product-determining step(s). (The misconception that a PKIE must reflect bond cleavage/formation to the isotope at the rate-limiting step is often repeated in textbooks and the primary literature: 691:. However, this formula is "semi-classical" in that it neglects the contribution from quantum tunneling, which is often introduced as a separate correction factor. Bigeleisen's formula also does not deal with differences in non-bonded repulsive interactions caused by the slightly shorter C–D bond compared to a C–H bond. In the equation, subscript H or D refer to the species with H or H, respectively; quantities with or without the double-dagger, ‡, refer to transition state or reactant ground state, respectively. (Strictly speaking, a 5298:

ordinary counterparts. One can also, in case of C KIEs, as well as similar cases, simply rely on the natural abundance of the isotopic carbon for the KIE experiments, eliminating the need for isotopic labeling. The two isotopic substrates will react through the same mechanism, but at different rates. 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 as follows: Assume that two isotopic molecules, A

4644:

where the amino acid side chains can "force" the donor and acceptor atom closer together by electrostatic and noncovalent interactions. It is also possible that the enzyme and its unusual hydrophobic environment inside a reaction site provides tunneling-promoting vibration. Studies on ketosteroid isomerase have provided experimental evidence that the enzyme actually enhances the coupled motion/hydrogen tunneling by comparing primary and secondary KIEs of the reaction under enzyme-catalyzed and non-enzyme-catalyzed conditions.

4621: 8442: 7907: 4356: 7544: 7518: 4730:

measured. Furthermore, reproducing the exact conditions in the two parallel reactions can be very challenging. 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. (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.)

3813: 8033: 4064: 7782: 7572: 7865:

in frequency due to the symmetry of an sp hybridized carbon. In an sp 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). The theoretical maximum change caused by the bending frequency difference has been calculated as 1.4.

7927: 7594:, measured 90° flip angle, a digital resolution of at least 5 points across a peak, and a signal:noise greater than 250. The raw FID is zero-filled to at least 256K points before the Fourier transform. NMR spectra are phased and then treated with a zeroth order baseline correction without any tilt correction. Signal integrations are determined numerically with a minimal tolerance for each integrated signal. 4846:

is of simpler order that involves the investigation of whether particular isotopic substitutions produce a detectable KIE or not. Vibrational changes from isotopic substitution at atoms away from the site where the reaction occurs tend to cancel between the reactant and the transition state. Therefore, the presence of a KIE indicates that the isotopically labeled atom is at or very near the reaction site.

4850:

the transition state ZPEs may be identical between the normal reactant and its isotopically labeled version. Alternatively, it may mean that the isotopic substitution is at the reaction site, but vibrational changes associated with bonds to this atom occur after the rate-determining step. Such a case is illustrated in the following example, in which ABCD represents the atomic skeleton of a molecule.

3334:). Thus, a larger isotope effect is observed for a stiffer ("stronger") C–H/D bond. For most reactions of interest, a hydrogen atom is transferred between two atoms, with a transition-state and vibrational modes at the transition state need to be accounted for. Nevertheless, it is still generally true that cleavage of a bond with a higher vibrational frequency will give a larger isotope effect. 579:(SKIE) is observed when no bond to the isotopically labeled atom in the reactant is broken or formed. SKIEs tend to be much smaller than PKIEs; however, secondary deuterium isotope effects can be as large as 1.4 per 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. 7861:. 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. 7265: 3546: 297: 7888:(FAD), while path B involves a free-radical intermediate. As path A results in the intermediate carbon changing hybridization from sp to sp 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. 8255:

For instance, determining nitrogen isotope effect along with hydrogen isotope effect was used to show that the reaction of 2-phenylethyltrimethylammonium ion with ethoxide in ethanol at 40°C follows an E2 mechanism, as opposed to alternative non-concerted mechanisms. This conclusion was reached upon showing that this reaction yields a nitrogen isotope effect,

6610: 4829:

Nevertheless, the irreversible C-H bond cleavage step will give a primary KIE with the other two experiments, since the second step would still affect the product distribution. Therefore, with Experiments B and C, it is possible to observe the KIE even if C-H or C-D bond cleavage occurs not in the rate-determining step, but in the product-determining step.

5208:. Hence, if the first step is rate-determining, there will not be an observable kinetic isotope effect in the overall reaction with isotopic labeling of A, but there will be one if the second step is rate-determining. For intermediate cases where both steps have comparable rates, the magnitude of the kinetic isotope effect will depend on the ratio of 8020:

the other this may be manifested by a steric effect on the rate constant. For the example above, H racemizes faster than H resulting in a SIE. A model for the SIE was developed by Bartell. A SIE is usually small, unless the transformations passes through a transition state with severe steric encumbrance, as in the racemization process shown above.

4802:-butylamine was proposed. Because there is little isotopic difference in the rate of nucleophilic attack, the intermolecular experiment resulted in a KIE close to 1. In the intramolecular case, however, the product ratio is determined by the proton transfer that occurs after the nucleophilic attack, a process which has a substantial KIE of 2.6. 8194:

hydrogen. Detectable KIEs occur only when solutes exchange hydrogen with the solvent or when there is a specific solute-solvent interaction near the reaction site. Both such phenomena are common for protic solvents, in which the hydrogen is exchangeable, and they may form dipole-dipole interactions or hydrogen bonds with polar molecules.

3157: 7461:. This technique for measuring KIEs overcomes many limitations of previous KIE measurement methods. KIE measurements from isotopically labeled materials require a new synthesis for each isotopically labeled material (a process often prohibitively difficult), a competition reaction, and an analysis. The KIE measurement at 3338: 4813:

characteristics of the reaction mixture (e.g. homogeneous vs. heterogeneous). Moreover, as noted in the paragraph above, the experiments provide KIE 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.

2145:) is the ratio of the symmetry numbers for the various species. This will be a rational number (a ratio of integers) that depends on the number of molecular and bond rotations leading to the permutation of identical atoms or groups in the reactants and the transition state. For systems of low symmetry, all σ 3808:{\displaystyle \left({\frac {\ln \left({\frac {k_{{\ce {H}}}}{k_{{\ce {T}}}}}\right)}{\ln \left({\frac {k_{{\ce {H}}}}{k_{{\ce {D}}}}}\right)}}\right)_{s}\cong {\frac {1-{\sqrt {m_{{\ce {H}}}/m_{{\ce {T}}}}}}{1-{\sqrt {m_{{\ce {H}}}/m_{{\ce {D}}}}}}}={\frac {1-{\sqrt {1/3}}}{1-{\sqrt {1/2}}}}\cong 1.44} 3519:~ 1.15-1.3 are typical for β SKIE. For reactants containing several isotopically substituted β-hydrogens, the observed isotope effect is often the result of several H/D's at the β position acting in concert. In these cases, the effect of each isotopically labeled atom is multiplicative, and cases where 2186:) corrects for the KIE caused by the reactions of vibrationally excited molecules. 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 1000 cm or higher, so exp(- 8287:

at 60°C. Though the reaction of the trans isomer, which follows syn elimination, has a smaller nitrogen KIE (1.0064) than the cis isomer which undergoes anti elimination (1.0108); both results are large enough to be indicative of weakening of the C-N bond in the transition state that would occur in a

5297:

In competition reactions, KIE 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. Most often, the isotopic substrate consists of molecules labeled in a specific position and their unlabeled,

4849:

The absence of an isotope effect is more difficult to interpret: It may mean that the isotopically labeled atom is away from the reaction site, but it may also mean there are certain compensating effects that lead to the lack of an observable KIE. For example, the differences between the reactant and

4845:

A large part of the KIE arises from vibrational ZPE differences between the reactant ground state and the transition state that vary between the reactant and its isotopically substituted analog. While one can carry out involved calculations of KIEs using computational chemistry, much of the work done

4772:

to the cleavage of the C-H or C-D bond. 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

4748:

This type of experiment, uses the same substrates as used in Experiment A, but they are allowed in to react in the same container, instead of two separate containers. The KIE in this experiment is determined by the relative amount of products formed from C-H versus C-D functionalization (or it can be

4351:

term shows exponential dependence on the particle's mass. As a result, tunneling is much more likely for a lighter particle such as hydrogen. Simply doubling the mass of a tunneling proton by replacing it with a deuteron drastically reduces the rate of such reactions. As a result, very large KIEs are

8303:

Since KIEs arise from differences in isotopic mass, the largest observable KIEs are associated with isotopic substitution of H with H (2x increase in mass) or H (3x increase in mass). KIEs from isotopic mass ratios can be as large as 36.4 using muons. They have produced the lightest "hydrogen" atom,

8272:

Similarly, combining nitrogen and hydrogen isotope effects was used to show that syn eliminations of simple ammonium salts also follow a concerted mechanism, which was a question of debate before. In the following two reactions of 2-phenylcyclopentyltrimethylammonium ion with ethoxide, both of which

8202:

Most organic reactions involve breaking and making bonds to carbon; thus, it is reasonable to expect detectable carbon isotope effects. When C is used as the label, the change in mass of the isotope is only ~8%, though, which limits the observable KIEs to much smaller values than the ones observable

8019:

of 9,10-dihydro-4,5-dimethylphenanthrene. The smaller amplitude of vibration for H than for H in C–H, C–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

7868:

When carbon undergoes a reaction that changes its hybridization from sp to sp, the out-of-plane bending force constant at the transition state is weaker as it is developing sp character and a "normal" SKIE is observed with typical values of 1.1 to 1.2. Conversely, when carbon's hybridization changes

7505:

for natural abundance KIE measurements. Pascal et al. were inspired by studies demonstrating dramatic variations of deuterium within identical compounds from different sources and hypothesized that NMR could be used to measure H KIEs at natural abundance. Pascal and coworkers tested their hypothesis

4430:

The observation that tunneling is not entirely temperature independent can be explained by the fact that not all molecules of a given species occupy their vibrational ground state at varying temperatures. Adding thermal energy to a potential energy well could cause higher vibrational levels than the

4039:

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. Thus, KIEs for elements other than hydrogen are often much harder to rationalize or interpret.

2623: 562:

For the aforementioned nucleophilic substitution reactions, PKIEs have been investigated for both the leaving groups, the nucleophiles, and the α-carbon at which the substitution occurs. Interpretation of the leaving group KIEs was difficult at first due to significant contributions from temperature

8211:

Often, the largest source of error in a study that depends on the natural abundance of carbon is the slight variation in natural C abundance itself. Such variations arise; because the starting materials in the reaction, are themselves products of other reactions that have KIEs and thus isotopically

7898:

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

7872:

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

7864:

SKIEs can be explained in terms of changes in orbital hybridization. When the hybridization of a carbon atom changes from sp to sp, 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 hybridized carbon are similar

7803:

Primary hydrogen KIEs refer to cases in which a bond to the isotopically labeled hydrogen is formed or broken at a rate- and/or product-determining step of a reaction. These are the most commonly measured KIEs, and much of the previously covered theory refers to primary KIEs. When there is adequate

4643:

It has long been speculated that high efficiency of enzyme catalysis in proton or hydride ion transfer reactions could be due partly to the quantum mechanical tunneling effect. Environment at the active site of an enzyme positions the donor and acceptor atom close to the optimal tunneling distance,

8460:

This convention exists for both convenience in nomenclature and as a reflection of how deuterium KIEs are generally studied experimentally: Though deuterium (H) has the IUPAC-sanctioned symbol D, there is no common symbol that specifically refers to protium (H). Still, it has proven useful to have

8254:

Owing to experimental uncertainties, measurement of isotope effect may entail significant uncertainty. Often isotope effects are determined through complementary studies on a series of isotopomers. Accordingly, it is quite useful to combine hydrogen isotope effects with heavy-atom isotope effects.

7820:

about 10–13 at room temperature, it is quite likely that the hydrogen transfer is linear and that the hydrogen is fairly symmetrically located in the transition state. It is usually not possible to make comments about tunneling contributions to the observed isotope effect unless the effect is very

7705:

of H over C, to theoretically improve measurement sensitivity by a factor of 4 or decrease experiment time by a factor of 16. This method for natural abundance kinetic isotope measurement is favorable for analysis for reactions containing unstable starting materials, and catalysts or products that

7696:

Though KIE measurements at natural abundance are a powerful tool for understanding reaction mechanisms, the amounts of material needed for analysis can make this technique inaccessible for reactions that use expensive reagents or unstable starting materials. To mitigate these limitations, Jacobsen

7550:

This work by Singleton et al. established the measurement of multiple C KIEs within the design of a single experiment. These H and C KIE measurements determined at natural abundance found the "inside" hydrogens of the diene experience a more pronounced H KIE than the "outside" hydrogens and the C1

4828:

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 KIE will be observed with Experiment A, since the overall rate is not affected by the isotopic substitution.

4385:

Peter S. Zuev et al. reported rate constants for the ring expansion of 1-methylcyclobutylfluorocarbene to be 4.0 × 10/s in nitrogen and 4.0 × 10/s in argon at 8 kelvin. They calculated that at 8 kelvin, the reaction would proceed via a single quantum state of the reactant so that the reported rate

3449:

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. These changes are attributed to a change in steric environment when the carbon bound to

3362:

To calculate the maximum possible value for a non-tunneling H KIE, we consider the case where the ZPE difference between the stretching vibrations of a C-H bond (3000 cm) and C-H bond (2200 cm) disappears in the transition state (an energy difference of /2 = 400 cm ≈ 1.15 kcal/mol),

8250:

acts as a leaving group are convenient to interpret, especially since chlorine acts as a monatomic species with no internal bonding to complicate the reaction coordinate, and it has two stable isotopes, Cl and Cl, both with high abundance. The major challenge to the interpretation of such isotope

4767:

This type of experiment is analogous to Experiment B, except this time there is an intramolecular competition for the C-H or C-D bond functionalization. In most cases, the substrate possesses a directing group (DG) between the C-H and C-D bonds. Calculation of the KIE from this experiment and its

4389:

So even though conventional chemical reactions tend to slow down dramatically as the temperature is lowered, tunneling reactions rarely change at all. Particles that tunnel through an activation barrier are a direct result of the fact that the wave function of an intermediate species, reactant or

3433:

has a temperature dependence, so larger isotope effects are possible at lower temperatures.) Depending on the nature of the transition state of H-transfer (symmetric vs. "early" or "late" and linear vs. bent); the extent to which a primary H isotope effect approaches this maximum, varies. A model

7902:

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

4812:

Thus, Experiments A, B, and C will give results of differing levels of precision and require different experimental setup and ways of analyzing data. As a result, the feasibility of each type of experiment depends on the kinetic and stoichiometric profile of the reaction, as well as the physical

2783:

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. Or, one may interpret them as running over those modes unique to the reactant or the transition state or whose vibrational frequencies

628:-H(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 7713:-catalyzed glycosylation of galactose as a reaction that met both of the aforementioned criteria (expensive materials and unstable substrates) and was a reaction with a poorly understood mechanism. Glycosylation is a special case of nucleophilic substitution that lacks clear definition between S 5287:

This hypothetical consideration reveals how observing KIEs may be used to investigate reaction mechanisms. The existence of a KIE is indicative of a change to the vibrational force constant of a bond associated with the isotopically labeled atom at or before the rate-controlling step. Intricate

4729:

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. The accuracy of the measured KIE is severely limited by the accuracy with which each of these rate constants can be

4431:

ground state to become populated. For a conventional kinetically driven reaction, this excitation would only have a small influence on the rate. However, for a tunneling reaction, the difference between the ZPE and the first vibrational energy level could be huge. The tunneling correction term

656:

calculations is now fairly routine. Moreover, several qualitative and semi-quantitative models allow rough estimates of deuterium isotope effects to be made without calculations, often providing enough information to rationalize experimental data or even support or refute different mechanistic

8193:

For the solvent isotope effects to be measurable, a fraction of the solvent must have a different isotopic composition than the rest. Therefore, large amounts of the less common isotopic species must be available, limiting observable solvent isotope effects to isotopic substitutions involving

6276: 3442:), linear transition states have the largest isotope effects, while transition states that are "early" or "late" (for exothermic or endothermic reactions, respectively), or nonlinear (e.g. cyclic) exhibit smaller effects. These predictions have since received extensive experimental support. 1877: 5492: 25: 2174:) refers to the ratio of the molecular masses and the moments of inertia. Since hydrogen and deuterium tend to be much lighter than 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 7913:

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.

7721:

2 mechanistic character. The presence of the oxygen adjacent to the site of displacement (i.e., C1) can stabilize positive charge. This charge stabilization can cause any potential concerted pathway to become asynchronous and approaches intermediates with oxocarbenium character of the

8436:

In asymmetric catalysis, there are rare cases where a KIE manifests as a significant difference in the enantioselectivity observed for a deuterated substrate compared to a non-deuterated one. One example was reported by Toste and coworkers, in which a deuterated substrate produced an

5288:

calculations may be used to learn a great amount of detail about the transition state from observed kinetic isotope effects. More commonly, though, the mere qualitative knowledge that a bond associated with the isotopically labeled atom is altered in a certain way can be very useful.

7206: 3931: 676:

in 1949. Bigeleisen's general formula for H KIEs (which is also applicable to heavier elements) is given below. It employs transition state theory and a statistical mechanical treatment of translational, rotational, and vibrational levels for the calculation of rate constants

7577:

The limitations for determining KIEs at natural abundance using NMR are that the recovered material must have a suitable amount and purity for NMR analysis (the signal of interest should be distinct from other signals), the reaction of interest must be irreversible, and the

2131: 495:, the mass increases by only 8%. The rate of a reaction involving a C–H bond is typically 6–10x faster than with a C–H bond, whereas a C reaction is only 4% faster than the corresponding C reaction; even though, in both cases, the isotope is one atomic mass unit (amu) ( 632:

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.

3291: 10047:

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".

7602:

Colletto et al. developed a regioselective β-arylation of benzothiophenes at room temperature with aryl iodides as coupling partners and sought to understand the mechanism of this reaction by performing natural abundance KIE measurements via single pulse NMR.

5991: 1742: 3037: 5807: 3030:

terms over ground state and transition state vibrational modes in the exponent of the simplified formula above. For a harmonic oscillator, vibrational frequency is inversely proportional to the square root of the reduced mass of the vibrating system:

3450:

the H/D undergoes rehybridization from sp to sp or vice versa (an α SKIE), or bond weakening due to hyperconjugation in cases where a carbocation is being generated one carbon atom away (a β SKIE). These isotope effects have a theoretical maximum of

8437:

enantioselectivity of 83% ee, compared to 93% ee for the undeuterated substrate. The effect was taken to corroborate additional inter- and intramolecular competition KIE data that suggested cleavage of the C-H/D bond in the enantiodetermining step.

5643:

In this treatment, all other reactants are assumed to be non-isotopic. Assuming further that the reaction is of first order with respect to the isotopic substrate A, the following general rate expression for both these reactions can be written:

606:(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. 8164:

O is usually a stronger acid than RH. Deuteration shifts the equilibrium toward the more strongly bound acid species RD in which the effect of deuteration on zero-point vibrational energy is greater, so that the deuterated equilibrium constant

7821:

large. If the primary KIE is not as large, it is generally considered to be indicative of a significant contribution from heavy-atom motion to the reaction coordinate, though it may also mean that hydrogen transfer follows a nonlinear pathway.

2777: 7829:

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

4030: 4224: 417:

KIE is considered one of the most essential and sensitive tools for studying reaction mechanisms, the knowledge of which allows improvement of the desirable qualities of said reactions. For example, KIEs can be used to reveal whether a

8292: 4647:

Many examples exist for proton tunneling in enzyme-catalyzed reactions that were discovered by KIE. A well-studied example is methylamine dehydrogenase, where large primary KIEs of 5–55 have been observed for the proton transfer step.

7834:(ZPE) affect the rates of chemical reactions. 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. SKIEs are defined as 5614: 2227: 4723: 2866:

As mentioned, especially for H/H substitution, most KIEs arise from the difference in ZPE between the reactants and the transition state of the isotopologues; this difference can be understood qualitatively as follows: in the

9849:

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".

3937:

In deriving these expressions, the reasonable approximation that reduced mass roughly equals the mass of the H, H, or H, was used. Also, the vibrational motion was assumed to be approximated by a harmonic oscillator, so that

2849:, and cancellations occur when the sums in the exponent are calculated. Thus, in practice, H KIEs are often largely dependent on a handful of key vibrational modes because of this cancellation, making qualitative analyses of 7745:

Jacobsen and coworkers observed small normal KIEs at C1, C2, and C5 which suggests significant oxocarbenium character in the transition state and an asynchronous reaction mechanism with a large degree of charge separation.

6478: 10670:"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" 8338:

The KIE leads to a specific distribution of H in natural products, depending on the route they were synthesized in nature. By NMR spectroscopy, it is therefore easy to detect whether the alcohol in wine was fermented from

6796: 8023:

Another example of the SIE is in the deslipping reaction of rotaxanes. H, due to its smaller effective size, allows easier passage of the stoppers through the macrocycle, resulting in faster deslipping for the deuterated

4816:

The hypothetical examples below illustrate common scenarios. Consider the following reaction coordinate diagram. For a reaction with this profile, all three experiments (A, B, and C) will yield a significant primary KIE:

2882:

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). The

2221:(an exponential function of vibrational ZPE differences), consisting of contributions from the ZPE differences for each of the vibrational modes of the reactants and transition state, which can be represented as follows: 469: 292:{\displaystyle {\begin{matrix}\\{\ce {{CN^{-}}+{^{12}CH3-Br}->{^{12}CH3-CN}+Br^{-}}}\\{\ce {{CN^{-}}+{^{13}CH3-Br}->{^{13}CH3-CN}+Br^{-}}}\\{}\end{matrix}}\qquad {\text{KIE}}={\frac {k_{12}}{k_{13}}}=1.082\pm 0.008} 5999: 4768:

interpretation follow the same considerations as that of Experiment B. However, the results of Experiments B and C will differ if the irreversible binding of the isotope-containing substrate takes place in Experiment B

4423:

factor ratios associated with the large activation energy differences (usually about 4.5 kJ/mol for C–H(D) bonds) provided strong evidence for tunneling. For the purpose of this discussion, it is important is that the

3353:

the same one as the reaction coordinate. The reaction coordinate represents a vibration with a negative force constant (and imaginary vibrational frequency) for the transition state. The ZPE shown for the ground state

1747: 8335:, in which there is a 36.4x difference in isotopic mass. For this reaction, isotopic substitution happens to produce an IKIE, and the authors report a KIE as low as 1.74 × 10, which is the smallest KIE ever reported. 5312: 8245:

1 reactions, involve strengthening of the remaining bonds to carbon. In many such reactions, leaving group isotope effects tend to be easier to interpret. For example, substitution and elimination reactions in which

6604: 4761: 4742: 5253:

appears in the simplified rate expression regardless of which step is rate-determining, but it will be less pronounced if the second step is rate-determining due to some cancellation between the isotope effects on

3363:

without any compensation from a ZPE difference at the transition state (e.g., from the symmetric A···H···B stretch, which is unique to the transition state). The simplified formula above, predicts a maximum for

6640:). When one of the species, e.g. 2, is a radioisotope, its mixture with the other species can also be analyzed by its radioactivity, which is measured in molar activities that are proportional to / (+) ≈ / = R 4854: 8173:. 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 7589:

Experimental details for using quantitative single pulse NMR to measure KIE at natural abundance as follows: the experiment needs to be performed under quantitative conditions including a relaxation time of 5

6826: 6631:

As for finding the KIEs, mixtures of substrates containing stable isotopes may be analyzed with a mass spectrometer, which yields the ratios of the isotopic molecules in the initial substrate (defined here as

4985: 3464:= 2 ≈ 1.4. For a SKIE at the α position, rehybridization from sp to sp produces a normal isotope effect, while rehybridization from sp to sp results in an inverse isotope effect with a theoretical minimum of 2696: 10699:

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".

7440: 7536:. Previous studies by Gajewski on isotopically enrich materials observed KIE results that suggested an asynchronous transition state, but were always consistent, within error, for a perfectly synchronous 735: 7789:

The major limitation for determining KIEs at natural abundance using IRMS is the required site selective degradation without isotopic fractionation into an analyzable small molecule, a non-trivial task.

3825: 8308:

with a negative muon μ to form Heμ (mass 4.116 amu). Since μ is much heavier than an electron, it orbits much closer to the nucleus, effectively shielding one proton, making Heμ behave as H. With these

5182: 2949: 4343: 10486:

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".

4052:. This is typically only observed for reactions involving bonds to hydrogen. Tunneling occurs when a molecule penetrates through a potential energy barrier rather than over it. Though not allowed by 2041: 8950:(μe) 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 10457:

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".

9606:

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-methylenebicyclodec-1-ene: evidence for tunneling?".

7261:

for various KIEs, yielding the following figure. Due to the exponential dependence, even very low KIEs lead to large changes in isotopic composition of the starting material at high conversions.

8003: 5317: 4367:

term depends linearly with barrier width, 2a. As with mass, tunneling is greatest for small barrier widths. Optimal tunneling distances of protons between donor and acceptor atom is 40 pm.

2232: 9246:

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".

8241:

Interpretation of carbon isotope effects is usually complicated by simultaneously forming and breaking bonds to carbon. Even reactions that involve only bond cleavage from the carbon, such as S

3028: 4652: 3194: 4386:

constant is temperature independent and the tunneling contribution to the rate was 152 orders of magnitude greater than the contribution of passage over the transition state energy barrier.

8304:

H (0.113 amu), in which an electron orbits a positive muon (μ) "nucleus" that has a mass of 206 electrons. They have also prepared the heaviest "hydrogen" atom by replacing one electron in

7688:

causes a relative decrease in the observed C KIE which led Frost et al. to suggest a change in the rate limiting step from cis oxidation to coordination of palladium to the cyanoformamide.

5285:

to a lesser extent if the B-C bond vibrations are affected in the transition state of the first step. There may thus be a small isotope effect even if the first step is rate-determining.

4671: 5826: 3152:{\displaystyle \nu _{\mathrm {X} }={\frac {1}{2\pi }}{\sqrt {\frac {k_{\mathrm {f} }}{\mu _{\mathrm {X} }}}}\cong {\frac {1}{2\pi }}{\sqrt {\frac {k_{\mathrm {f} }}{m_{\mathrm {X} }}}}} 10020:

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".

9519:

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".

8952:

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".

2847: 4390:

product is not confined to the energy well of a particular trough along the energy surface of a reaction but can "leak out" into the next energy minimum. In light of this, tunneling

4265: 1627: 649:

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.

4443:

increase. The decrease of the barrier width can have such a huge impact on the tunneling rate that even a small population of excited vibrational states would dominate this process.

2035:

are the number of atoms in the reactants and the transition states, respectively. The complicated expression given above can be represented as the product of four separate factors:

6648:, so that the same ratios as in the other case can be measured as long as the radioisotope is present in tracer amounts. Such ratios may also be determined using NMR spectroscopy. 5065: 10518:

Houk KN, Gustafson SM, Black KA (October 1992). "Theoretical secondary kinetic isotope effects and the interpretation of transition state geometries. 1. The Cope rearrangement".

1936: 5650: 652:

The deuterium kinetic isotope effect (H KIE) is by far the most common, useful, and well-understood type of KIE. The accurate prediction of the numerical value of a H KIE using

10577:, 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". 610: 7268:

The isotopic enrichment of the relative amount of species 2 with respect to species 1 in the starting material as a function of conversion of species 1. The value of the KIE (

502:

Isotopic substitution can modify the reaction rate in a variety of ways. In many cases, the rate difference can be rationalized by noting that the mass of an atom affects the

7630:

The observation of a primary C isotope effect at C3, an inverse H isotope effect, a secondary C isotope effect at C2, and the lack of a H isotope effect at C2; led Colletto

4790:

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

10780:

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".

7876:

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

4382:. Therefore, tunneling tends to become more important at low temperatures, where even the smallest kinetic energy barriers may not be overcome but can be tunneled through. 4129: 2812: 2701: 7899:

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.

4397:

For the hydrogen abstraction from gaseous n-alkanes and cycloalkanes by hydrogen atoms over the temperature range 363–463 K, the H/D KIE data were characterized by small

3341:

Differences in ZPE and corresponding differences in activation energy for the breaking of analogous C-H and C-D bonds. In this schematic, the curves actually represent (3

8819:

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 S

9695:

Wilde TC, Blotny G, Pollack RM (May 2008). "Experimental evidence for enzyme-enhanced coupled motion/quantum mechanical hydrogen tunneling by ketosteroid isomerase".

3941: 3391:

values as large as 15-20 can be predicted. Bending frequencies are very unlikely to vanish in the transition state, however, and there are only a few cases in which

4140: 10285:

Burlingham BT, Pratt LM, Davidson ER, Shiner VJ, Fong J, Widlanski TS (October 2003). "34S isotope effect on sulfate ester hydrolysis: mechanistic implications".

624:

1 reaction, since the carbon atom is converted into an sp hybridized carbenium ion during the transition state for the rate-determining step with an increase in C

8011:

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

8784:

Simmons EM, Hartwig JF (March 2012). "On the Interpretation of Deuterium Kinetic Isotope Effects in C–H Bond Functionalizations by Transition-Metal Complexes".

4067:

The potential energy well of a tunneling reaction. The dash-red arrow shows the classical activated process, while the solid-red arrow shows the tunneling path.

2137:

For the special case of H isotope effects, we will argue that the first three terms can be treated as equal to or well approximated by unity. The first factor

2618:{\displaystyle {\begin{aligned}{\frac {k_{{\ce {H}}}}{k_{{\ce {D}}}}}&\cong \exp \left\{-{\frac {1}{2}}\left\right\}\\&\cong \exp \left\end{aligned}}} 8662:

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".

7869:

from sp to sp, 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.

4832: 2784:

change substantially upon advancing along the reaction coordinate. The remaining pairs of reactant and transition state vibrational modes have very similar

9730:

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".

5503: 8219:

In the starting material that has not undergone any reaction, determine the ratios of the other carbon NMR peak integrals to that of the reference carbon.

7698: 4773:

binds irreversibly). In contrast to Experiment B, the reaction need not be halted at low consumption of isotopic starting material to obtain an accurate

7697:

and coworkers developed H to C polarization transfer as a means to reduce the time and material required for KIE measurements at natural abundance. The

6271:{\displaystyle {1 \over k_{1}}\times \int \limits _{\ce {^{0}}}^{\ce {}}{d \over }={1 \over k_{2}}\times \int \limits _{\ce {^{0}}}^{\ce {}}{d \over }} 4036:" refers to these "semi-classical" KIEs, which disregard quantum tunneling. Tunneling contributions must be treated separately as a correction factor. 9921:

Singleton DA, Thomas AA (September 1995). "High-Precision Simultaneous Determination of Multiple Small Kinetic Isotope Effects at Natural Abundance".

10544: 10409: 6661: 6295: 3405:

values exceed 7-8 near room temperature. Furthermore, it is often found that tunneling is a major factor when they do exceed such values. A value of

1872:{\displaystyle u_{i}^{\ddagger }:={\frac {h\nu _{i}^{\ddagger }}{k_{\mathrm {B} }T}}={\frac {hcN_{\mathrm {A} }{\tilde {\nu }}_{i}^{\ddagger }}{RT}}} 5487:{\displaystyle {\begin{aligned}{\ce {{A1}+{B}+{C}+\cdots }}\ &{\ce {->P1}}\\{\ce {{A2}+{B}+{C}+\cdots }}\ &{\ce {->P2}}\end{aligned}}} 8212:

enrich the products. To compensate for this error when NMR spectroscopy is used to determine the KIE, the following guidelines have been proposed:

7681: 582:

For the aforementioned nucleophilic substitution reactions, secondary hydrogen KIEs at the α-carbon provide a direct means to distinguish between S

10633:

Felder T, Schalley CA (May 2003). "Secondary isotope effects on the deslipping reaction of rotaxanes: high-precision measurement of steric size".

7210:

This relation can be solved in terms of the KIE to obtain the KIE expression given above. When the uncommon isotope has very low abundance, both R

8414: 4523:

Also for reactions where isotopes include H, D and T, a criterion of tunneling is the Swain-Schaad relations which compare the rate constants (

9219:

Streitwieser A, Jagow RH, Fahey RC, Suzuki S (May 1958). "Kinetic isotope effects in the acetolyses of deuterated cyclopentyl tosylates1, 2".

393:

frequencies than their lighter counterparts. In most cases, this implies a greater energy input needed for heavier isotopologues to reach the

10320:

Hennig C, Oswald RB, Schmatz S (March 2006). "Secondary kinetic isotope effect in nucleophilic substitution: a quantum-mechanical approach".

7838:(etc.) secondary isotope effects where such prefixes refer to the position of the isotopic substitution relative to the reaction center (see 6501: 7201:{\displaystyle {R \over R_{0}}={\ce {{\frac {/}{^0/^0}}}}={\ce {{\frac {/^0}{/^0}}}}={\frac {1-F_{2}}{1-F_{1}}}=(1-F_{1})^{(k_{2}/k_{1})-1}} 10606:

Bartell LS (1 September 1961). "The Role of Non-bonded Repulsions in Secondary Isotope Effects. I. Alpha and Beta Substitution Effects.1".

8233:

If these as well as some other precautions listed by Jankowski are followed, KIEs with precisions of three decimal places can be achieved.

7804:

evidence that transfer of the labeled hydrogen occurs in the rate-determining step of a reaction, if a fairly large KIE is observed, e.g. k

8216:

Choose a carbon that is remote from the reaction center that will serve as a reference and assume it does not have a KIE in the reaction.

2887:

is a good approximation for a vibrating bond, at least for low-energy vibrational states. Quantum mechanics gives the vibrational ZPE as

7737: 7524:

Singleton and coworkers demonstrated the capacity of C NMR based natural abundance KIE measurements for studying the mechanism of the

4866: 2635: 2183: 3926:{\displaystyle \left({\frac {k_{{\ce {H}}}}{k_{{\ce {T}}}}}\right)_{s}=\left({\frac {k_{{\ce {H}}}}{k_{{\ce {D}}}}}\right)_{s}^{1.44}} 7664: 7306: 10782: 10753: 10579: 10459: 9579: 9550: 694: 2126:{\displaystyle {\frac {k_{{\ce {H}}}}{k_{{\ce {D}}}}}=\mathbf {S} \times \mathbf {MMI} \times \mathbf {EXC} \times \mathbf {ZPE} } 563:

independent factors. KIEs at the α-carbon can be used to develop some understanding into the symmetry of the transition state in S

9468:

Zuev PS, Sheridan RS, Albu TV, Truhlar DG, Hrovat DA, Borden WT (February 2003). "Carbon tunneling from a single quantum state".

8587: 7494: 7466: 5076: 4696: 4686: 4667:. Competitive KIEs for the hydrogen transfer step at 25°C resulted in 3.6 and 10.2 for primary and secondary KIEs, respectively. 2890: 9990:

Martin GJ, Martin ML (1984). "Deuterium labelling at the natural abundance level as studied by high field quantitative 2H NMR".

4040:

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

3297:

In the case of homolytic C–H/D bond dissociation, the transition state term disappears; and neglecting other vibrational modes,

567:

2 reactions, though this KIE is less sensitive than what would be ideal, also due to contribution from non-vibrational factors.

10080:"Room-Temperature Direct β-Arylation of Thiophenes and Benzo[b]thiophenes and Kinetic Evidence for a Heck-type Pathway" 9184:

Kwart H (1 December 1982). "Temperature dependence of the primary kinetic hydrogen isotope effect as a mechanistic criterion".

8592: 6613:

Relation between the fractions of conversion for the two competing reactions with isotopic substrates. The rate constant ratio

4631:, though it is observed that it is hard to extrapolate experimental values obtained at high temperature to lower temperatures: 4270: 7774:

monoesters. Their observation of a large KIE suggests S-O bond cleavage is rate controlling and likely rules out an associate

4636: 4594:

Experimental values of X exceeding 3.26 and Y lower than 1.44 are evidence of a certain amount of contribution from tunneling.

9974: 9890: 9371: 9342: 9309: 9160: 9084: 9051: 8872: 8761: 8721: 8646: 7766:

for natural abundance KIE measurements. Widlanski and coworkers demonstrated S KIE at natural abundance measurements for the

3540:(or the Swain-Schaad-Stivers equations), can be derived from the general expression given above using some simplifications: 8566: 8561: 8082: 10132:"Mechanistic Model for Enantioselective Intramolecular Alkene Cyanoamidation via Palladium-Catalyzed C-CN Bond Activation" 9548:

Lewis ES, Funderburk L (1967). "Rates and isotope effects in the proton transfers from 2-nitropropane to pyridine bases".

8928:

Bigeleisen J, Wolfsberg M (January 1957). "Theoretical and experimental aspects of isotope effects in chemical kinetics".

8367: 10915: 8074: 7937: 3286:{\displaystyle \Delta u_{i}\cong \left(1-{\frac {1}{\sqrt {2}}}\right){\frac {h\nu _{i\mathrm {H} }}{k_{\mathrm {B} }T}}} 479:

change is greatest, since the effect is related to vibrational frequencies of the affected bonds. Thus, replacing normal

8291: 7656: 8571: 4798:-butylamine. To explain this result, the formation of diphenylcarbene, followed by irreversible nucleophilic attack by 2970: 2868: 5986:{\displaystyle {1 \over k_{1}}\times {\ce {{\mathit {d}} \over }}={1 \over k_{2}}\times {\ce {{\mathit {d}} \over }}} 5812:

Since f(,,...) does not depend on the isotopic composition of A, it can be solved for in both rate expressions with A

10863:

Bell RP, Crooks JE (20 July 1965). "Kinetic Hydrogen Isotope Effects in the Ionization of Some Ketonic Substances".

8047:

than the undeuterated one, and these cases are said to exhibit inverse KIEs (IKIE). IKIEs are often observed in the

7729: 4415:

ranging from 0.43 to 0.54 and large activation energy differences from 9.0 to 9.7 kJ/mol. Basing their arguments on

9387:

Borgis D, Hynes JT (1993). "Dynamical theory of proton tunneling transfer rates in solution: General formulation".

8556: 4663:

Another example of tunneling contribution to proton transfer in enzymatic reactions is the reaction carried out by

669:

in parallel grammatical constructions or direct comparisons between them should be interpreted as meaning H and H.

4820: 9806: 8222:

Obtain the same ratios for the carbons in a sample of the starting material after it has undergone some reaction.

7781: 7755: 7470: 3419:~ 10 is thought to be maximal for a semi-classical PKIE (no tunneling) for reactions at ≈298 K. (The formula for 1737:{\displaystyle u_{i}:={\frac {h\nu _{i}}{k_{\mathrm {B} }T}}={\frac {hcN_{\mathrm {A} }{\tilde {\nu }}_{i}}{RT}}} 2217:) factors). Hence, for hydrogen/deuterium KIEs, the observed values are typically dominated by the last factor, 7606: 4722: 523: 4711:

refer to the following three cases as the main types of KIE experiments involving C-H bond functionalization:

3174:. Moreover, the reduced mass is approximated by the mass of the light atom of the system, X = H or D. Because 2817: 9773: 9732: 9521: 4232: 389:

This change in reaction rate is a quantum effect that occurs mainly because heavier isotopologues have lower

9802:"Mathematical treatment of isotopologue and isotopomer speciation and fractionation in biochemical kinetics" 5802:{\displaystyle {\text{rate}}={-d \over dt}=k_{n}\times \times f(,,\cdots ){\text{ where }}n=1{\text{ or }}2} 4691:

Isotopic effect expressed with the equations given above only refer to reactions that can be described with

3349:-7)-dimensional hypersurfaces, and the vibrational mode whose ZPE is illustrated at the transition state is 10930: 8621:

Westaway KC (2006). "Using kinetic isotope effects to determine the structure of the transition states of S

4996: 7668:

C KIEs for enantioselective intramolecular alkene cyanoamidation reaction (left no additive, right add BPh

4860:

Assuming steady state conditions for the intermediate ABC, the overall rate of reaction is the following:

594:

1 reactions typically lead to large SKIEs, approaching to their theoretical maximum at about 1.22, while S

9577:

Dewar MJ, Healy EF, Ruiz JM (1988). "Mechanism of the 1,5-sigmatropic hydrogen shift in 1,3-pentadiene".

7885: 4836:

Reaction energy profile for when the C-H bond cleavage occurs at a product-determining step after the RDS

1905: 4428:

factor ratio for the various paraffins they used was roughly constant throughout the temperature range.

598:

2 reactions typically yield SKIEs that are very close to or less than 1. KIEs greater than 1 are called

10925: 10910: 10751:

Wiberg KB, Slaugh LH (1958). "The Deuterium Isotope Effect in the Side Chain Halogenation of Toluene".

8461:

labels to refer to the respective rate constants of protium- or deuterium-containing isotopologues, so

4452:

To determine if tunneling is involved in KIE of a reaction with H or D, a few criteria are considered:

322: 10811:"An in situ directing group strategy for chiral anion phase-transfer fluorination of allylic alcohols" 5268:. This outcome is related to the fact that equilibrium isotope effects are usually smaller than KIEs. 4787:, since the ratio of H and D in the starting material is 1:1, regardless of the extent of conversion. 4620: 4057: 2772:{\displaystyle \Delta u_{i}^{\ddagger }:=u_{i\mathrm {H} }^{\ddagger }-u_{i\mathrm {D} }^{\ddagger }} 653: 419: 10439: 8475:, respectively, have typically been used. Moreover, the magnitude of a KIE can then be expressed as 8317:

was investigated. Rate constants from reacting the lightest and the heaviest hydrogen analogs with H

7622: 6644:

in the initial substrate, / (+) ≈ / = R in the substrate after some conversion, and / (+) ≈ / = R

4760: 4741: 661:

often means the light isotope, protium (H), specifically. In the rest of this article, reference to

8073:

An inverse effect can also occur in a multistep reaction if the overall rate constant depends on a

7614: 4081: 511: 398: 8106: 4056:, particles can pass through classically forbidden regions of space in quantum mechanics based on 2787: 737:

term resulting from an isotopic difference in transmission coefficients should also be included.)

468: 8709: 8577: 4416: 642: 4435:

is linearly dependent on barrier width and this width is significantly diminished as the number

4025:{\displaystyle u_{i\mathrm {X} }\propto \mu _{\mathrm {X} }^{-1/2}\cong m_{\mathrm {X} }^{-1/2}} 10668:

Churchill, David G.; Janak, Kevin E.; Wittenberg, Joshua S.; Parkin, Gerard (11 January 2003).

9301: 8713: 8426: 5292: 4853: 3439: 1966: 526:(ZPE). With a lower ZPE, more energy must be supplied to break the bond, resulting in a higher 9043: 9036: 7653:-catalyzed C-N bond activation using natural abundance KIE measurements via single pulse NMR. 7264: 6483:

Which can also be expressed in terms of fraction amounts of conversion of the two reactions, F

4603:

In organic reactions, this proton tunneling effect has been observed in such reactions as the

4219:{\displaystyle Q={\frac {e^{\alpha }}{\beta -\alpha }}(\beta e^{-\alpha }-\alpha e^{-\beta })} 8078: 8048: 7892: 7839: 7759: 7498: 7474: 4664: 4398: 3358:

refer to the vibration corresponding to the reaction coordinate in the case of a primary KIE.

458: 9293: 8701: 5187:

In most cases, isotopic substitution at A, especially if it is a heavy atom, will not alter

10872: 10709: 10329: 10241: 9815: 9477: 9398: 9363: 9117: 9003: 8375: 7877: 4692: 4628: 4048:

In some cases, a further rate enhancement is seen for the lighter isotope, possibly due to

9953:

Jankowski S (January 2009). "Application of NMR spectroscopy in isotope effects studies".

7638:-arylation of benzothiophenes at room temperature with aryl iodides as coupling partners. 4805: 8: 10488: 7850:

refers to the isotope associated with an atom neighboring the reaction center and so on.

7680:

suggests a reaction mechanism with rate limiting cis oxidation into the C–CN bond of the

6609: 4053: 3446: 2884: 503: 453:

2 mechanism. Depending on the pathway, different strategies may be used to stabilize the

390: 10876: 10713: 10333: 10245: 9819: 9481: 9402: 9121: 9108:

Carpenter BK (February 2010). "Kinetic isotope effects: unearthing the unconventional".

9007: 10920: 10888: 10835: 10810: 10733: 10262: 10229: 10205: 10180: 10156: 10131: 10104: 10079: 9831: 9501: 9327: 8861: 8582: 8379: 8351: 7775: 7741:

C kinetic isotope effect measurements for thiourea catalyzed glycosylation of galactose

7702: 7579: 7552: 7537: 7507: 4492: 4379: 4072: 1899: 646: 531: 402: 10501: 10003: 9966: 9672: 9655: 9445: 9428: 8994:

Bigeleisen J (August 1949). "The Relative Reaction Velocities of Isotopic Molecules".

8638: 7514:. Pascal et al. measured a KIE of 2.2 using H NMR for materials of natural abundance. 7247:

Isotopic enrichment of the starting material can be calculated from the dependence of

6651:

When the substrate composition is followed, the following KIE expression in terms of R

10840: 10737: 10725: 10650: 10389: 10345: 10302: 10267: 10210: 10161: 10109: 9970: 9896: 9886: 9863: 9749: 9712: 9677: 9623: 9493: 9450: 9410: 9367: 9338: 9305: 9294: 9201: 9166: 9156: 9133: 9090: 9080: 9057: 9047: 8878: 8868: 8801: 8757: 8717: 8702: 8642: 7854: 7831: 7583: 7482: 7462: 7458: 7454: 5609:{\displaystyle {\text{KIE}}={k_{1} \over k_{2}}={\frac {\ln(1-F_{1})}{\ln(1-F_{2})}}} 4791: 4436: 4375: 4049: 2024: 1958: 527: 519: 515: 338: 10892: 10554: 10419: 9835: 9505: 7551:

and C4 experience a significant KIE. These key observations suggest an asynchronous

3536:

The following simple expressions relating H and H KIEs, which are also known as the

10880: 10830: 10822: 10791: 10762: 10717: 10642: 10615: 10588: 10558: 10549: 10527: 10497: 10468: 10423: 10414: 10379: 10337: 10294: 10257: 10249: 10200: 10192: 10151: 10143: 10099: 10091: 10057: 10029: 9999: 9962: 9930: 9855: 9823: 9782: 9741: 9704: 9667: 9615: 9588: 9559: 9530: 9485: 9440: 9406: 9389: 9334: 9255: 9228: 9193: 9125: 9011: 8961: 8832: 8793: 8671: 8634: 8406: 7858: 7564: 7533: 7465:

avoids these issues by taking advantage of high precision quantitative techniques (

7286:

When the products are followed, the KIE can be calculated using the products ratio

3435: 1973:(X = H or D) are the symmetry numbers for the reactants and transition states. The 673: 454: 406: 394: 7214:

and R are very small and not significantly different from each other, such that 1-

4674:

Mechanism of alcohol dehydrogenase. The rate-limiting step is the proton transfer.

3377:

as 6.9. If the complete disappearance of two bending vibrations is also included,

10669: 8430: 4708: 4440: 1888: 616:

The magnitudes of such SKIEs at the α-carbon atom are largely determined by the C

530:

for bond cleavage, which in turn lowers the measured rate (see, for example, the

7906: 6473:{\displaystyle {k_{1} \over k_{2}}={\frac {\ce {\ln(/^{0})}}{\ce {\ln(/^{0})}}}} 9801: 9768: 8086: 6791:{\displaystyle {\text{KIE}}={\frac {k_{1}}{k_{2}}}={\frac {\ln(1-F_{1})}{\ln}}} 3537: 3171: 1947: 442: 401:), and therefore, a slower reaction rate. The study of KIEs can help elucidate 305: 9827: 10904: 10553:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " 10418:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " 9900: 9867: 9205: 9170: 8882: 8516: 8425:

by deprotonation of the ketone. In this study the KIE is calculated from the

8374:

In this particular "intramolecular KIE" study, a benzylic hydrogen undergoes

8273:

yield 1-phenylcyclopentene, both isomers exhibited a nitrogen isotope effect

8269:, of 1.0133±0.0002 along with a hydrogen KIE of 3.2 at the leaving hydrogen. 7556: 7525: 4604: 507: 496: 462: 354: 334: 10721: 10562: 10427: 10253: 10147: 9489: 9061: 5293:

Evaluation of rate constant ratios from intermolecular competition reactions

4651: 3337: 2210:) < 0.01 at 298 K, resulting in negligible contributions from the 1–exp(- 10884: 10844: 10729: 10654: 10646: 10393: 10384: 10367: 10349: 10306: 10271: 10230:"Macrocyclic bis-thioureas catalyze stereospecific glycosylation reactions" 10214: 10165: 10113: 9753: 9716: 9681: 9627: 9497: 9454: 9137: 9094: 8805: 8797: 8499: 8355: 8016: 8012: 4656: 4608: 423: 405:, and is occasionally exploited in drug development to improve unfavorable 372: 313: 10181:"13C Kinetic Isotope Effect Measurements Enabled by Polarization Transfer" 7445: 449:(shown in the introduction), the observed methyl carbon KIE indicates an S 10574: 10196: 10095: 9859: 8310: 7881: 7846:

refers to the isotope associated with the reaction center and the prefix

7597: 7511: 431: 10795: 10766: 10619: 10592: 10531: 10228:

Park Y, Harper KC, Kuhl N, Kwan EE, Liu RY, Jacobsen EN (January 2017).

10061: 10033: 9934: 9592: 9563: 9534: 9259: 9232: 9197: 8836: 8675: 8441: 6599:{\displaystyle {k_{1} \over k_{2}}={\frac {\ln(1-F_{1})}{\ln(1-F_{2})}}} 4670: 2016:

are directly proportional to the corresponding vibrational frequencies,

9641: 8344: 8206: 7767: 7646: 6636:), in the substrate after some conversion (/=R), or in the product (/=R 4355: 2006:) terms are the moments of inertia about the three principal axes. The 1939: 10826: 10472: 10341: 10298: 9786: 9745: 9708: 9644:. The extrapolated KIE at 25°C is 16.6 but the margin of error is high 9619: 9129: 9015: 8965: 7543: 7517: 4519:

The geometries of the reactants and products are usually very similar.

10179:

Kwan EE, Park Y, Besser HA, Anderson TL, Jacobsen EN (January 2017).

7650: 492: 488: 484: 8236: 5452: 5370: 5070:

Or if the second step is rate-determining, the equation reduces to:

4063: 182: 81: 10078:

Colletto C, Islam S, Juliá-Hernández F, Larrosa I (February 2016).

10077: 9885:. Isotopes in Organic Chemistry. Vol. 3. Amsterdam: Elsevier. 8867:. Isotopes in Organic Chemistry. Vol. 5. Amsterdam: Elsevier. 8247: 8032: 8025: 7710: 7571: 7560: 7529: 4612: 480: 346: 8429:

for regular 2,4-dimethyl-3-pentanone and its deuterated isomer by

6808:

in terms of weights per unit volume or molarities of the reactants

4699:

should be taken into account using the GEBIK and GEBIF equations.

465:

and selectivity, which are important for industrial applications.

10485: 8951: 8947: 8422: 8402: 8359: 8340: 8067: 8066:)PtMe(H). In such cases the C-D bond in the transition state, an 7771: 7763: 7733:

Reaction scheme for thiourea catalyzed glycosylation of galactose

7634:

to suggest a Heck-type reaction mechanism for the regioselective

7502: 7478: 5246:. The KIE will always be observable with this substitution since 4990:

If the first step is rate-determining, this equation reduces to:

4980:{\displaystyle {\frac {d}{dt}}={\frac {k_{1}k_{3}}{k_{2}+k_{3}}}} 4513: 2691:{\displaystyle \Delta u_{i}:=u_{i\mathrm {H} }-u_{i\mathrm {D} }} 446: 350: 309: 5820:, and the two can be equated to derive the following relations: 4134:

where A is the Arrhenius parameter, E is the barrier height and

10698: 9729: 8528: 8398: 8305: 8225:

The ratios of the latter ratios to the former ratios yields R/R

7926: 7435:{\displaystyle {k_{1} \over k_{2}}={\frac {\ln(1-F_{1})}{\ln}}} 5627:

refer to the fraction of conversions for the isotopic species A

4824:

Reaction energy profile for when C-H cleavage occurs at the RDS

4352:

observed that can not be accounted for by differences in ZPEs.

1980:

are the molecular masses of the corresponding species, and the

641:

The theoretical treatment of isotope effects relies heavily on

10667: 7884:

anions. Path A involved a nucleophilic attack on the coenzyme

10284: 10130:

Frost GB, Serratore NA, Ogilvie JM, Douglas CJ (April 2017).

8052: 7873:

is stronger in the transition state than in either reactant.

7853:

In physical organic chemistry, SKIE is discussed in terms of

730:{\displaystyle \kappa _{\mathrm {H} }/\kappa _{\mathrm {D} }} 609: 514:

for the reaction is nearly identical. Heavier isotopes will (

16:

Change in chemical reaction rate due to isotopic substitution

10129: 9218: 9153:

Perspectives on structure and mechanism in organic chemistry

8421:

In this reaction the rate-limiting step is formation of the

6289:, respectively. This leads to the following KIE expression: 4718:

KIE determined from absolute rates of two parallel reactions

4378:

is a quantum effect tied to the laws of wave mechanics, not

475:

Isotopic rate changes are most pronounced when the relative

10368:"The use of isotope effects to determine enzyme mechanisms" 9245: 8188: 5177:{\displaystyle {\frac {d}{dt}}={\frac {k_{1}k_{3}}{k_{2}}}} 4071:

Tunneling can be analyzed using Bell's modification of the

2944:{\displaystyle \epsilon _{i}^{(0)}={\frac {1}{2}}h\nu _{i}} 476: 342: 10046: 10019: 8397:). A large KIE of 5.56 is associated with the reaction of 8089:

reactions are usually 2-3 times greater for reactions in D

8540: 7072: 7045: 7016: 6989: 6951: 6918: 6894: 6868: 6450: 6423: 6380: 6353: 6206: 6177: 6072: 6043: 5974: 5952: 5896: 5874: 5476: 5414: 5394: 5332: 4338:{\displaystyle \beta ={\frac {2a\pi ^{2}(2mE)^{1/2}}{h}}} 204: 161: 103: 60: 9771:(1998). "Enzyme Catalysis: Beyond Classical Paradigms". 8070:

species, is highly stabilized relative to the C–H bond.

8043:

Reactions are known where the deuterated species reacts

4841:

Evaluation of KIEs in a Hypothetical Multi-Step Reaction

4075:, which includes the addition of a tunneling factor, Q: 10779: 9467: 7785:

34S isotope effect on sulfate ester hydrolysis reaction

7446:

Kinetic isotope effect measurement at natural abundance

10573: 10178: 9852:

Journal of the Chemical Society, Perkin Transactions 2

7598:

Organometallic reaction mechanism elucidation examples

30: 9042:(3rd ed.). New York: Harper & Row. pp. 7940: 7824: 7660:

Enantioselective intramolecular alkene cyanoamidation

7481:, in either product or starting material for a given 7309: 6829: 6664: 6504: 6298: 6002: 5829: 5653: 5506: 5315: 5079: 4999: 4869: 4273: 4235: 4143: 4084: 3944: 3828: 3549: 3197: 3040: 2973: 2893: 2820: 2790: 2704: 2638: 2230: 2044: 1908: 1750: 1630: 746: 697: 28: 9357: 8562:

Equilibrium constant#Effect of isotopic substitution

2149:(reactant and transition state) will be unity; thus 570: 10319: 9518: 9433:

Biochimica et Biophysica Acta (BBA) - Bioenergetics

8927: 8818: 7998:{\displaystyle {\frac {k_{(X=D)}}{k_{(X=H)}}}=1.15} 7798: 7699:

distortionless enhancement by polarization transfer

4680: 2875:

6 vibrational modes for the starting material and 3

10517: 10227: 9848: 9694: 9429:"The mechanism of the proton transfer: an outline" 9422: 9420: 9326: 9035: 8860: 8207:Compensating for variations in C natural abundance 8144:The rate of formation of products is then d/dt = k 8038: 7997: 7749: 7453:is a simple general method for measuring KIEs for 7434: 7200: 6790: 6598: 6472: 6270: 5985: 5801: 5608: 5486: 5176: 5059: 4979: 4695:. In all instances in which this is not possible, 4527:) of the reactions where H, D or T are exchanged: 4337: 4259: 4218: 4123: 4024: 3925: 3807: 3285: 3151: 3022: 2943: 2841: 2806: 2771: 2690: 2617: 2178:factor is usually also approximated as unity. The 2125: 1930: 1871: 1736: 1609: 729: 542: 518:) lead to lower vibration frequencies, or, viewed 409:by protecting metabolically vulnerable C-H bonds. 291: 9916: 9914: 9912: 9910: 8574:(ribulose-1,5-bisphosphate carboxylase oxygenase) 8237:Isotope effects with elements heavier than carbon 4756:KIE determined from an intramolecular competition 4737:KIE determined from an intermolecular competition 3023:{\displaystyle u_{i}=h\nu _{i}/k_{\mathrm {B} }T} 487:(D or H), doubles the mass; whereas in replacing 10902: 10456: 8912: 8385:as the brominating agent. It was found that PhCH 7676:The primary C KIE observed in the absence of BPh 4659:converts primary amines to aldehyde and ammonia. 10405: 10403: 9920: 9640:In this study the KIE is measured by sensitive 9605: 9547: 9417: 9291: 9033: 8539:. Phenyl has also been called by the symbol Φ ( 8251:affects is the solvation of the leaving group. 7649:additives on the mechanism of enantioselective 6281:Where and are the initial concentrations of A 2951:. Thus, we can readily interpret the factor of 10632: 9907: 9576: 8783: 8779: 8777: 8775: 8773: 8747: 8745: 8743: 8741: 8739: 8737: 8735: 8733: 8699: 5306:, undergo irreversible competition reactions: 5271:Isotopic substitution of B will clearly alter 4488:Reaction still proceeds at lower temperatures. 3438:predicted that symmetrical (thermoneutral, by 2182:factor (containing the product of vibrational 7610:Regioselective β-arylation of benzothiophenes 6816:using the previously derived expression for F 10865:Proceedings of the Royal Society of London A 10750: 10400: 9989: 9948: 9946: 9944: 9766: 9760: 9653: 9101: 9077:Determination of organic reaction mechanisms 8661: 8197: 7542: 7516: 4804: 4655:Mechanism of methylamine dehydrogenase, the 10808: 9386: 9155:(2nd ed.). Hoboken, N.J.: John Wiley. 8770: 8730: 8616: 8614: 8612: 8610: 8608: 8105:O This can be explained for a mechanism of 4794:of diphenyldiazomethane in the presence of 672:The theory of KIEs was first formulated by 10862: 10809:Zi W, Wang YM, Toste FD (September 2014). 10361: 10359: 9799: 9426: 9358:Silbey RJ, Alberty RA, Bawendi MG (2005). 8993: 8908: 8906: 8904: 8902: 8900: 8898: 8896: 8894: 8892: 8440: 7857:such as induction, bond hybridization, or 7570: 5497:The KIE for this scenario is found to be: 4485:=activation energy; ZPE=zero point energy) 4359:Donor-acceptor model of a proton transfer. 10834: 10440:"Definition of isotope effect, secondary" 10383: 10261: 10204: 10155: 10103: 9952: 9941: 9880: 9671: 9444: 9287: 9285: 9283: 9281: 9279: 9277: 9275: 9273: 9271: 9269: 9107: 9074: 9038:Mechanism and theory in organic chemistry 8858: 8854: 8852: 8850: 8848: 8846: 7917: 7497:(NMR) is a method amenable for measuring 3505:~ 0.8-0.9 are typical for α SKIEs, while 10815:Journal of the American Chemical Society 10783:Journal of the American Chemical Society 10754:Journal of the American Chemical Society 10608:Journal of the American Chemical Society 10580:Journal of the American Chemical Society 10520:Journal of the American Chemical Society 10460:Journal of the American Chemical Society 10287:Journal of the American Chemical Society 10185:Journal of the American Chemical Society 10084:Journal of the American Chemical Society 10050:Journal of the American Chemical Society 10022:Journal of the American Chemical Society 9923:Journal of the American Chemical Society 9697:Journal of the American Chemical Society 9608:Journal of the American Chemical Society 9580:Journal of the American Chemical Society 9551:Journal of the American Chemical Society 9512: 9248:Journal of the American Chemical Society 9221:Journal of the American Chemical Society 8954:Journal of the American Chemical Society 8825:Journal of the American Chemical Society 8695: 8693: 8691: 8689: 8687: 8685: 8664:Journal of the American Chemical Society 8620: 8605: 8189:Solvent hydrogen kinetic isotope effects 7780: 7736: 7728: 7663: 7655: 7621: 7613: 7605: 7582:must not change for the duration of the 7263: 6608: 4831: 4819: 4669: 4650: 4615:base with a reported KIE of 25 at 25°C: 4354: 4062: 3336: 2842:{\displaystyle \Delta u_{i}^{\ddagger }} 10605: 10513: 10511: 10365: 10356: 9874: 9688: 9150: 8889: 8786:Angewandte Chemie International Edition 8751: 8588:Transient kinetic isotope fractionation 8097:O than for the analogous reactions in H 7758:(IRMS) is another method for measuring 7495:nuclear magnetic resonance spectroscopy 7467:nuclear magnetic resonance spectroscopy 4687:Transient kinetic isotope fractionation 4260:{\displaystyle \alpha ={\frac {E}{RT}}} 1938:= frequency of vibration, expressed in 357:for the reactions involving the light ( 10903: 9380: 9351: 9324: 9318: 9266: 8843: 8627:Advances in Physical Organic Chemistry 8015:. An example of such an effect is the 7709:Jacobsen and coworkers identified the 5225:Isotopic substitution of D will alter 371:) isotopically substituted reactants ( 10125: 10123: 10073: 10071: 10015: 10013: 9793: 9723: 9647: 9300:. University Science Books. pp. 9183: 9029: 9027: 9025: 8682: 8354:that was elucidated using the KIE is 7701:(DEPT) takes advantage of the larger 5933: 5855: 5060:{\displaystyle {\frac {d}{dt}}=k_{1}} 590:2 reactions. It has been found that S 10508: 9461: 8915:Reaction Rates of Isotopic Molecules 8567:Isotope effect on lipid peroxidation 7645:sought to understand the effects of 7626:C KIEs measured at natural abundance 7618:H KIEs measured at natural abundance 7451:KIE measurement at natural abundance 602:, while KIEs less than 1 are called 10372:The Journal of Biological Chemistry 10322:The Journal of Physical Chemistry A 7488: 4371:Temperature dependence in tunneling 2389: 2300: 1931:{\displaystyle {\tilde {\nu }}_{i}} 1532: 1443: 1313: 1194: 13: 10855: 10550:Compendium of Chemical Terminology 10415:Compendium of Chemical Terminology 10120: 10068: 10010: 9955:Annual Reports on NMR Spectroscopy 9022: 8756:(3rd ed.). Harper & Row. 8572:Kinetic isotope effects of RuBisCO 8515:In the diagrams below, "Et" means 8290: 7905: 7825:Secondary hydrogen isotope effects 5201:, but it will most probably alter 4852: 4759: 4740: 4721: 4000: 3969: 3954: 3271: 3257: 3198: 3140: 3128: 3092: 3080: 3047: 3011: 2821: 2791: 2758: 2735: 2705: 2682: 2664: 2639: 2588: 2569: 2566: 2536: 2514: 2511: 2508: 2505: 2502: 1828: 1798: 1698: 1668: 721: 704: 608: 467: 14: 10942: 9654:Kohen A, Klinman JP (July 1999). 9296:Modern Physical Organic Chemistry 8389:brominates 4.86x faster than PhCD 8298: 3445:For secondary H isotope effects, 571:Secondary kinetic isotope effects 537: 10136:The Journal of Organic Chemistry 9292:Anslyn EV, Dougherty DA (2006). 9034:Lowry TH, Richardson KS (1987). 8913:Melander L, Saunders WH (1980). 8557:Crossover experiment (chemistry) 8413: 8366: 8031: 7925: 7891: 7799:Primary hydrogen isotope effects 4681:Transient kinetic isotope effect 4635: 4619: 2119: 2116: 2113: 2105: 2102: 2099: 2091: 2088: 2085: 2077: 2027:(ZPE) (see below). The integers 577:secondary kinetic isotope effect 554: 461:of the reaction and improve the 10802: 10773: 10744: 10692: 10661: 10626: 10599: 10567: 10538: 10479: 10450: 10432: 10313: 10278: 10221: 10172: 10040: 9983: 9842: 9807:Geochimica et Cosmochimica Acta 9656:"Hydrogen tunneling in biology" 9634: 9599: 9570: 9541: 9239: 9212: 9177: 9144: 9079:. New York: Wiley. p. 86. 9068: 8987: 8940: 8509: 8492: 8454: 8203:with hydrogen isotope effects. 8107:specific hydrogen-ion catalysis 8051:of alkyl metal hydrides, e.g. ( 8039:Inverse kinetic isotope effects 7793: 7756:isotope-ratio mass spectrometry 7750:Isotope-ratio mass spectrometry 7726:1 mechanism for glycosylation. 7510:of dimethyl diazomalonate into 7471:isotope-ratio mass spectrometry 6627:(KIE) is varied for each curve. 6495:=/ for n = 1 or 2, as follows: 604:inverse kinetic isotope effects 543:Primary kinetic isotope effects 353:. Formally, it is the ratio of 312:, the KIE of the carbon in the 244: 9883:Carbon-13 in Organic Chemistry 8921: 8863:Isotopes in cationic reactions 8812: 8655: 8593:Urey–Bigeleisen–Mayer equation 7982: 7970: 7960: 7948: 7691: 7473:) to site selectively measure 7426: 7423: 7385: 7376: 7365: 7346: 7187: 7159: 7155: 7135: 7075: 7059: 7048: 7032: 7019: 7003: 6992: 6976: 6954: 6938: 6921: 6905: 6897: 6881: 6871: 6855: 6782: 6761: 6742: 6739: 6728: 6709: 6590: 6571: 6560: 6541: 6463: 6453: 6437: 6426: 6410: 6406: 6393: 6383: 6367: 6356: 6340: 6336: 6262: 6244: 6239: 6221: 6209: 6193: 6180: 6164: 6128: 6110: 6105: 6087: 6075: 6059: 6046: 6030: 5977: 5961: 5955: 5939: 5899: 5883: 5877: 5861: 5774: 5765: 5757: 5751: 5743: 5740: 5731: 5716: 5686: 5671: 5600: 5581: 5570: 5551: 5168: 5162: 5147: 5132: 5092: 5086: 5054: 5039: 5012: 5006: 4958: 4952: 4937: 4922: 4882: 4876: 4702: 4629:1,5-sigmatropic hydrogen shift 4312: 4299: 4213: 4175: 2910: 2904: 2869:Born–Oppenheimer approximation 2572: 2563: 2520: 2499: 2454: 2418: 2382: 2336: 1916: 1841: 1711: 1597: 1561: 1525: 1479: 600:normal kinetic isotope effects 549:primary kinetic isotope effect 316:was found to be 1.082 ± 0.008. 1: 10502:10.1016/S0040-4039(01)00539-1 10004:10.1016/s0040-4039(01)81948-1 9967:10.1016/S0066-4103(09)06803-3 9774:Accounts of Chemical Research 9733:Accounts of Chemical Research 9673:10.1016/S1074-5521(99)80058-1 9522:Journal of Physical Chemistry 9446:10.1016/S0005-2728(00)00057-8 9186:Accounts of Chemical Research 8700:Atkins P, de Paula J (2006). 8639:10.1016/S0065-3160(06)41004-2 8598: 7282:) is indicated at each curve. 4599:Examples for tunneling in KIE 4124:{\displaystyle k=QAe^{-E/RT}} 412: 10366:Cleland WW (December 2003). 9411:10.1016/0301-0104(93)85117-Q 8930:Advances in Chemical Physics 8321:were then used to calculate 8085:. For example, the rates of 7457:performed with materials of 4394:be temperature independent. 4043: 2807:{\displaystyle \Delta u_{i}} 2153:can often be neglected. The 7: 9329:Quantum Theory of Tunneling 8996:Journal of Chemical Physics 8550: 7886:flavin adenine dinucleotide 6812:Taking the ratio of R and R 510:that it forms, even if the 10: 10947: 10916:Physical organic chemistry 9800:Maggi F, Riley WJ (2010). 9427:Krishtalik LI (May 2000). 8704:Atkins' Physical Chemistry 8343:, or from illicitly added 8313:, the reaction of H with H 8083:equilibrium isotope effect 7493:Quantitative single-pulse 4684: 4448:Criteria for KIE tunneling 620:-H(H) vibrations. For an S 349:is replaced by one of its 323:physical organic chemistry 9881:Buncel E, Lee CC (1977). 9828:10.1016/j.gca.2009.12.021 8859:Buncel E, Lee CC (1977). 8198:Carbon-13 isotope effects 7221:can be approximated with 3533:> 2 are not uncommon. 3478:= 2 ≈ 0.7. In practice, 654:density functional theory 636: 420:nucleophilic substitution 210: 167: 109: 66: 10420:Secondary isotope effect 8447: 5278:, but it may also alter 4495:pre-exponential factors 4032:; X = H. The subscript " 512:potential energy surface 205: 197: 162: 154: 104: 96: 61: 53: 10722:10.1126/science.1199421 10563:10.1351/goldbook.S06001 10428:10.1351/goldbook.S05523 10254:10.1126/science.aal1875 10148:10.1021/acs.joc.7b00196 9660:Chemistry & Biology 9490:10.1126/science.1079294 8710:Oxford University Press 8578:Magnetic isotope effect 8427:reaction rate constants 7706:are relatively costly. 4417:transition state theory 2157:factor (containing the 643:transition state theory 333:) is the change in the 10885:10.1098/rspa.1965.0144 10647:10.1002/anie.200350903 10385:10.1074/jbc.X300005200 8823:2 Transition States". 8798:10.1002/anie.201107334 8295: 8160:. In the first step, H 7999: 7918:Steric isotope effects 7910: 7786: 7742: 7734: 7673: 7661: 7627: 7619: 7611: 7547: 7521: 7436: 7283: 7202: 6792: 6655:and R can be derived: 6628: 6600: 6474: 6272: 6214: 6080: 5987: 5803: 5610: 5488: 5178: 5061: 4981: 4857: 4837: 4825: 4809: 4764: 4745: 4726: 4675: 4660: 4360: 4339: 4261: 4220: 4125: 4068: 4026: 3927: 3809: 3359: 3287: 3153: 3024: 2945: 2843: 2808: 2773: 2692: 2619: 2577: 2525: 2417: 2335: 2127: 2023:, and the vibrational 1967:universal gas constant 1932: 1873: 1738: 1611: 1560: 1478: 1341: 1229: 731: 613: 472: 327:kinetic isotope effect 293: 10555:steric isotope effect 9364:John Wiley & Sons 9075:Carpenter BK (1984). 8294: 8081:which has an inverse 8079:rate-determining step 8049:reductive elimination 8000: 7909: 7840:alpha and beta carbon 7784: 7760:kinetic fractionation 7740: 7732: 7684:. The addition of BPh 7667: 7659: 7625: 7617: 7609: 7546: 7520: 7499:kinetic fractionation 7475:kinetic fractionation 7437: 7267: 7203: 6793: 6612: 6601: 6475: 6273: 6157: 6023: 5988: 5804: 5611: 5489: 5179: 5062: 4982: 4856: 4835: 4823: 4808: 4763: 4744: 4725: 4673: 4665:alcohol dehydrogenase 4654: 4399:preexponential factor 4358: 4340: 4262: 4221: 4126: 4066: 4058:wave–particle duality 4027: 3928: 3810: 3340: 3288: 3154: 3025: 2946: 2844: 2809: 2774: 2693: 2620: 2552: 2488: 2388: 2299: 2128: 1933: 1874: 1739: 1612: 1531: 1442: 1312: 1193: 732: 612: 504:vibrational frequency 483:(H) with its isotope 471: 459:rate-determining step 294: 10444:Chemistry Dictionary 10197:10.1021/jacs.6b10621 10096:10.1021/jacs.5b12242 9860:10.1039/P29740001307 9366:. pp. 326–338. 8970:for an example of a 8376:radical substitution 8109:of a reactant R by H 7938: 7878:d-amino acid oxidase 7812:of at least 5-6 or k 7307: 6827: 6662: 6502: 6296: 6000: 5827: 5651: 5504: 5313: 5239:while not affecting 5077: 4997: 4867: 4693:first-order kinetics 4271: 4233: 4141: 4082: 3942: 3826: 3547: 3195: 3038: 2971: 2891: 2818: 2788: 2702: 2636: 2228: 2042: 1906: 1748: 1628: 744: 695: 520:quantum mechanically 397:(or, in rare cases, 26: 10931:Reaction mechanisms 10877:1965RSPSA.286..285B 10796:10.1021/ja00779a012 10767:10.1021/ja01545a034 10714:2011Sci...331..448F 10620:10.1021/ja01478a006 10593:10.1021/ja00891a038 10532:10.1021/ja00048a032 10489:Tetrahedron Letters 10334:2006JPCA..110.3071H 10246:2017Sci...355..162P 10062:10.1021/ja00207a013 10034:10.1021/ja00330a071 9992:Tetrahedron Letters 9935:10.1021/ja00141a030 9820:2010GeCoA..74.1823M 9593:10.1021/ja00216a060 9564:10.1021/ja00986a013 9535:10.1021/j100290a062 9482:2003Sci...299..867Z 9403:1993CP....170..315B 9260:10.1021/ja01554a077 9233:10.1021/ja01542a075 9198:10.1021/ar00084a004 9151:Carroll FA (2010). 9122:2010NatCh...2...80C 9008:1949JChPh..17..675B 8837:10.1021/ja00085a037 8752:Laidler KJ (1987). 8676:10.1021/ja01476a012 8527:; while "Ph" means 8288:concerted process. 7074: 7047: 7018: 6991: 6953: 6920: 6896: 6870: 6452: 6425: 6382: 6355: 6261: 6238: 6208: 6179: 6127: 6104: 6074: 6045: 5976: 5954: 5898: 5876: 5478: 5463: 5416: 5396: 5381: 5334: 4347:Examination of the 4054:classical mechanics 4021: 3990: 3922: 3440:Hammond's postulate 2914: 2885:harmonic oscillator 2838: 2768: 2745: 2722: 2605: 2381: 2358: 2184:partition functions 1857: 1789: 1765: 1524: 1501: 1304: 1266: 1068: 1048: 1028: 1006: 986: 966: 907: 876: 844: 813: 553:see the section on 441:In the reaction of 422:reaction follows a 403:reaction mechanisms 304:In the reaction of 193: 92: 9360:Physical Chemistry 8917:. New York: Wiley. 8583:Reaction mechanism 8352:reaction mechanism 8296: 7995: 7911: 7855:electronic effects 7787: 7776:reaction mechanism 7743: 7735: 7703:gyromagnetic ratio 7674: 7662: 7628: 7620: 7612: 7580:reaction mechanism 7553:reaction mechanism 7548: 7538:reaction mechanism 7522: 7508:insertion reaction 7455:chemical reactions 7432: 7284: 7198: 7062: 7035: 7006: 6979: 6941: 6908: 6884: 6858: 6788: 6629: 6596: 6470: 6440: 6413: 6370: 6343: 6268: 6247: 6224: 6196: 6167: 6113: 6090: 6062: 6033: 5983: 5964: 5942: 5886: 5864: 5799: 5606: 5484: 5482: 5466: 5404: 5384: 5322: 5174: 5057: 4977: 4858: 4838: 4826: 4810: 4765: 4746: 4727: 4676: 4661: 4607:and iodination of 4509:is not equal to 1. 4361: 4335: 4257: 4216: 4121: 4073:Arrhenius equation 4069: 4022: 3994: 3963: 3923: 3875: 3805: 3360: 3283: 3149: 3020: 2941: 2894: 2839: 2824: 2804: 2769: 2749: 2726: 2708: 2688: 2615: 2613: 2591: 2362: 2339: 2123: 1928: 1900:Boltzmann constant 1869: 1834: 1775: 1751: 1734: 1607: 1505: 1482: 1285: 1247: 1049: 1029: 1009: 987: 967: 947: 891: 860: 828: 797: 727: 647:quantum tunnelling 614: 532:Arrhenius equation 473: 399:dissociation limit 302:An example of KIE. 289: 242: 10926:Chemical kinetics 10911:Organic chemistry 10871:(1406): 285–299. 10827:10.1021/ja507468u 10790:(24): 8351–8356. 10761:(12): 3033–3039. 10635:Angewandte Chemie 10614:(17): 3567–3571. 10496:(22): 3753–3756. 10473:10.1021/ja962783n 10342:10.1021/jp0540151 10299:10.1021/ja0279747 10240:(6321): 162–166. 10056:(25): 9078–9081. 10028:(18): 5377–5378. 9998:(36): 3525–3528. 9976:978-0-12-381041-0 9929:(36): 9357–9358. 9892:978-0-444-41472-4 9854:(11): 1307–1312. 9787:10.1021/ar9701225 9746:10.1021/ar0100226 9709:10.1021/ja0732330 9620:10.1021/ja057377v 9558:(10): 2322–2327. 9373:978-0-471-21504-2 9344:978-981-238-019-7 9325:Razauy M (2003). 9311:978-1-891389-31-3 9254:(21): 5885–5893. 9162:978-0-470-27610-5 9130:10.1038/nchem.531 9086:978-0-471-89369-1 9053:978-0-06-044084-8 9016:10.1063/1.1747368 8966:10.1021/ja982616i 8874:978-0-444-41927-9 8763:978-0-06-043862-3 8754:Chemical Kinetics 8723:978-0-19-870072-2 8670:(15): 3220–3223. 8648:978-0-12-033541-1 8383:-bromosuccinimide 8378:by bromine using 8169:is greater than K 8009: 8008: 7987: 7832:zero-point energy 7584:chemical reaction 7483:chemical reaction 7463:natural abundance 7459:natural abundance 7430: 7332: 7130: 7086: 7065: 7038: 7009: 6982: 6965: 6944: 6911: 6887: 6861: 6845: 6786: 6695: 6668: 6594: 6527: 6468: 6443: 6416: 6373: 6346: 6321: 6266: 6251: 6228: 6199: 6170: 6152: 6132: 6117: 6094: 6065: 6036: 6018: 5981: 5967: 5945: 5935: 5923: 5903: 5889: 5867: 5857: 5845: 5794: 5780: 5779: where 5763: 5749: 5723: 5698: 5678: 5657: 5604: 5537: 5510: 5469: 5464: 5443: 5432: 5424: 5407: 5387: 5382: 5361: 5350: 5342: 5325: 5172: 5104: 5024: 4975: 4894: 4512:A large negative 4437:vibrational modes 4333: 4255: 4173: 4050:quantum tunneling 3906: 3902: 3890: 3860: 3856: 3844: 3797: 3794: 3771: 3744: 3741: 3737: 3720: 3700: 3696: 3679: 3645: 3638: 3634: 3622: 3594: 3590: 3578: 3281: 3235: 3234: 3147: 3146: 3117: 3099: 3098: 3069: 2926: 2586: 2534: 2450: 2432: 2373: 2350: 2292: 2261: 2257: 2245: 2071: 2067: 2055: 2025:zero-point energy 1959:Avogadro constant 1919: 1867: 1844: 1808: 1732: 1714: 1678: 1593: 1575: 1516: 1493: 1435: 1413: 1410: 1403: 1370: 1308: 1296: 1258: 1183: 1168: 1163: 1148: 1133: 1116: 1101: 1086: 1070: 1060: 1040: 1020: 998: 978: 958: 935: 921: 916: 899: 885: 868: 846: 836: 824: 805: 793: 773: 769: 757: 528:activation energy 524:zero-point energy 364:) and the heavy ( 339:chemical reaction 275: 248: 226: 218: 206: 200: 194: 175: 163: 157: 142: 125: 117: 105: 99: 93: 74: 62: 56: 41: 10938: 10896: 10849: 10848: 10838: 10806: 10800: 10799: 10777: 10771: 10770: 10748: 10742: 10741: 10708:(6016): 448–50. 10696: 10690: 10689: 10687: 10685: 10674:J. Am. Chem. Soc 10665: 10659: 10658: 10630: 10624: 10623: 10603: 10597: 10596: 10587:(8): 1199–1200. 10571: 10565: 10542: 10536: 10535: 10515: 10506: 10505: 10483: 10477: 10476: 10467:(5): 1155–1156. 10454: 10448: 10447: 10436: 10430: 10407: 10398: 10397: 10387: 10378:(52): 51975–84. 10363: 10354: 10353: 10317: 10311: 10310: 10282: 10276: 10275: 10265: 10225: 10219: 10218: 10208: 10176: 10170: 10169: 10159: 10142:(7): 3721–3726. 10127: 10118: 10117: 10107: 10075: 10066: 10065: 10044: 10038: 10037: 10017: 10008: 10007: 9987: 9981: 9980: 9950: 9939: 9938: 9918: 9905: 9904: 9878: 9872: 9871: 9846: 9840: 9839: 9797: 9791: 9790: 9764: 9758: 9757: 9727: 9721: 9720: 9692: 9686: 9685: 9675: 9651: 9645: 9638: 9632: 9631: 9603: 9597: 9596: 9587:(8): 2666–2667. 9574: 9568: 9567: 9545: 9539: 9538: 9529:(6): 1602–1606. 9516: 9510: 9509: 9476:(5608): 867–70. 9465: 9459: 9458: 9448: 9424: 9415: 9414: 9390:Chemical Physics 9384: 9378: 9377: 9355: 9349: 9348: 9335:World Scientific 9332: 9322: 9316: 9315: 9299: 9289: 9264: 9263: 9243: 9237: 9236: 9216: 9210: 9209: 9181: 9175: 9174: 9148: 9142: 9141: 9110:Nature Chemistry 9105: 9099: 9098: 9072: 9066: 9065: 9041: 9031: 9020: 9019: 8991: 8985: 8984:isotope effect.) 8969: 8944: 8938: 8937: 8925: 8919: 8918: 8910: 8887: 8886: 8866: 8856: 8841: 8840: 8831:(6): 2526–2533. 8816: 8810: 8809: 8781: 8768: 8767: 8749: 8728: 8727: 8708:(8th ed.). 8707: 8697: 8680: 8679: 8659: 8653: 8652: 8618: 8544: 8513: 8507: 8496: 8490: 8458: 8444: 8417: 8407:sodium hydroxide 8370: 8101:O catalyzed by H 8093:O catalyzed by D 8035: 8004: 8002: 8001: 7996: 7988: 7986: 7985: 7964: 7963: 7942: 7929: 7922: 7921: 7895: 7859:hyperconjugation 7637: 7574: 7565:maleic anhydride 7534:maleic anhydride 7506:by studying the 7489:Single-pulse NMR 7441: 7439: 7438: 7433: 7431: 7429: 7422: 7421: 7412: 7407: 7406: 7397: 7396: 7368: 7364: 7363: 7338: 7333: 7331: 7330: 7321: 7320: 7311: 7207: 7205: 7204: 7199: 7197: 7196: 7186: 7185: 7176: 7171: 7170: 7153: 7152: 7131: 7129: 7128: 7127: 7111: 7110: 7109: 7093: 7088: 7087: 7085: 7084: 7083: 7078: 7073: 7070: 7063: 7056: 7051: 7046: 7043: 7036: 7029: 7028: 7027: 7022: 7017: 7014: 7007: 7000: 6995: 6990: 6987: 6980: 6973: 6967: 6966: 6964: 6963: 6962: 6957: 6952: 6949: 6942: 6935: 6930: 6929: 6924: 6919: 6916: 6909: 6901: 6900: 6895: 6892: 6885: 6879: 6874: 6869: 6866: 6859: 6852: 6846: 6844: 6843: 6831: 6804:Measurement of F 6797: 6795: 6794: 6789: 6787: 6785: 6781: 6780: 6771: 6760: 6759: 6731: 6727: 6726: 6701: 6696: 6694: 6693: 6684: 6683: 6674: 6669: 6666: 6605: 6603: 6602: 6597: 6595: 6593: 6589: 6588: 6563: 6559: 6558: 6533: 6528: 6526: 6525: 6516: 6515: 6506: 6479: 6477: 6476: 6471: 6469: 6467: 6466: 6462: 6461: 6456: 6451: 6448: 6441: 6434: 6429: 6424: 6421: 6414: 6397: 6396: 6392: 6391: 6386: 6381: 6378: 6371: 6364: 6359: 6354: 6351: 6344: 6327: 6322: 6320: 6319: 6310: 6309: 6300: 6277: 6275: 6274: 6269: 6267: 6265: 6257: 6252: 6249: 6242: 6234: 6229: 6226: 6216: 6213: 6212: 6207: 6204: 6197: 6190: 6189: 6188: 6183: 6178: 6175: 6168: 6153: 6151: 6150: 6138: 6133: 6131: 6123: 6118: 6115: 6108: 6100: 6095: 6092: 6082: 6079: 6078: 6073: 6070: 6063: 6056: 6055: 6054: 6049: 6044: 6041: 6034: 6019: 6017: 6016: 6004: 5992: 5990: 5989: 5984: 5982: 5980: 5975: 5972: 5965: 5959: 5958: 5953: 5950: 5943: 5937: 5936: 5929: 5924: 5922: 5921: 5909: 5904: 5902: 5897: 5894: 5887: 5881: 5880: 5875: 5872: 5865: 5859: 5858: 5851: 5846: 5844: 5843: 5831: 5808: 5806: 5805: 5800: 5795: 5792: 5781: 5778: 5764: 5761: 5750: 5747: 5730: 5729: 5724: 5721: 5712: 5711: 5699: 5697: 5689: 5685: 5684: 5679: 5676: 5663: 5658: 5655: 5635:, respectively. 5615: 5613: 5612: 5607: 5605: 5603: 5599: 5598: 5573: 5569: 5568: 5543: 5538: 5536: 5535: 5526: 5525: 5516: 5511: 5508: 5493: 5491: 5490: 5485: 5483: 5479: 5477: 5474: 5467: 5465: 5462: 5461: 5448: 5441: 5440: 5433: 5430: 5425: 5422: 5417: 5415: 5412: 5405: 5397: 5395: 5392: 5385: 5383: 5380: 5379: 5366: 5359: 5358: 5351: 5348: 5343: 5340: 5335: 5333: 5330: 5323: 5183: 5181: 5180: 5175: 5173: 5171: 5161: 5160: 5150: 5131: 5130: 5121: 5120: 5110: 5105: 5103: 5095: 5081: 5066: 5064: 5063: 5058: 5038: 5037: 5025: 5023: 5015: 5001: 4986: 4984: 4983: 4978: 4976: 4974: 4973: 4972: 4951: 4950: 4940: 4921: 4920: 4911: 4910: 4900: 4895: 4893: 4885: 4871: 4639: 4623: 4344: 4342: 4341: 4336: 4334: 4329: 4328: 4327: 4323: 4298: 4297: 4281: 4266: 4264: 4263: 4258: 4256: 4254: 4243: 4225: 4223: 4222: 4217: 4212: 4211: 4193: 4192: 4174: 4172: 4161: 4160: 4151: 4130: 4128: 4127: 4122: 4120: 4119: 4112: 4031: 4029: 4028: 4023: 4020: 4016: 4004: 4003: 3989: 3985: 3973: 3972: 3959: 3958: 3957: 3932: 3930: 3929: 3924: 3921: 3916: 3911: 3907: 3905: 3904: 3903: 3900: 3893: 3892: 3891: 3888: 3881: 3871: 3870: 3865: 3861: 3859: 3858: 3857: 3854: 3847: 3846: 3845: 3842: 3835: 3814: 3812: 3811: 3806: 3798: 3796: 3795: 3790: 3782: 3773: 3772: 3767: 3759: 3750: 3745: 3743: 3742: 3740: 3739: 3738: 3735: 3728: 3723: 3722: 3721: 3718: 3711: 3702: 3701: 3699: 3698: 3697: 3694: 3687: 3682: 3681: 3680: 3677: 3670: 3661: 3656: 3655: 3650: 3646: 3644: 3643: 3639: 3637: 3636: 3635: 3632: 3625: 3624: 3623: 3620: 3613: 3600: 3599: 3595: 3593: 3592: 3591: 3588: 3581: 3580: 3579: 3576: 3569: 3556: 3326: 3324: 3323: 3320: 3317: 3292: 3290: 3289: 3284: 3282: 3280: 3276: 3275: 3274: 3263: 3262: 3261: 3260: 3243: 3241: 3237: 3236: 3230: 3226: 3210: 3209: 3158: 3156: 3155: 3150: 3148: 3145: 3144: 3143: 3133: 3132: 3131: 3121: 3120: 3118: 3116: 3105: 3100: 3097: 3096: 3095: 3085: 3084: 3083: 3073: 3072: 3070: 3068: 3057: 3052: 3051: 3050: 3029: 3027: 3026: 3021: 3016: 3015: 3014: 3004: 2999: 2998: 2983: 2982: 2967:and the sums of 2966: 2964: 2963: 2960: 2957: 2950: 2948: 2947: 2942: 2940: 2939: 2927: 2919: 2913: 2902: 2848: 2846: 2845: 2840: 2837: 2832: 2813: 2811: 2810: 2805: 2803: 2802: 2778: 2776: 2775: 2770: 2767: 2762: 2761: 2744: 2739: 2738: 2721: 2716: 2697: 2695: 2694: 2689: 2687: 2686: 2685: 2669: 2668: 2667: 2651: 2650: 2629:where we define 2624: 2622: 2621: 2616: 2614: 2610: 2606: 2604: 2599: 2587: 2579: 2576: 2575: 2560: 2548: 2547: 2535: 2527: 2524: 2523: 2496: 2470: 2466: 2462: 2461: 2457: 2453: 2452: 2451: 2448: 2435: 2434: 2433: 2430: 2416: 2402: 2380: 2375: 2374: 2371: 2357: 2352: 2351: 2348: 2334: 2327: 2326: 2313: 2293: 2285: 2262: 2260: 2259: 2258: 2255: 2248: 2247: 2246: 2243: 2236: 2132: 2130: 2129: 2124: 2122: 2108: 2094: 2080: 2072: 2070: 2069: 2068: 2065: 2058: 2057: 2056: 2053: 2046: 1937: 1935: 1934: 1929: 1927: 1926: 1921: 1920: 1912: 1878: 1876: 1875: 1870: 1868: 1866: 1858: 1856: 1851: 1846: 1845: 1837: 1833: 1832: 1831: 1814: 1809: 1807: 1803: 1802: 1801: 1790: 1788: 1783: 1770: 1764: 1759: 1743: 1741: 1740: 1735: 1733: 1731: 1723: 1722: 1721: 1716: 1715: 1707: 1703: 1702: 1701: 1684: 1679: 1677: 1673: 1672: 1671: 1660: 1659: 1658: 1645: 1640: 1639: 1621:where we define 1616: 1614: 1613: 1608: 1606: 1605: 1604: 1600: 1596: 1595: 1594: 1591: 1578: 1577: 1576: 1573: 1559: 1545: 1523: 1518: 1517: 1514: 1500: 1495: 1494: 1491: 1477: 1470: 1469: 1456: 1436: 1428: 1418: 1414: 1412: 1411: 1409: 1408: 1407: 1406: 1405: 1404: 1401: 1376: 1375: 1374: 1373: 1372: 1371: 1368: 1343: 1340: 1326: 1310: 1309: 1307: 1306: 1305: 1303: 1298: 1297: 1294: 1269: 1268: 1267: 1265: 1260: 1259: 1256: 1231: 1228: 1221: 1220: 1207: 1191: 1185: 1184: 1176: 1174: 1170: 1169: 1167: 1166: 1165: 1164: 1161: 1151: 1150: 1149: 1146: 1136: 1135: 1134: 1131: 1120: 1119: 1118: 1117: 1114: 1104: 1103: 1102: 1099: 1089: 1088: 1087: 1084: 1073: 1071: 1069: 1067: 1062: 1061: 1058: 1047: 1042: 1041: 1038: 1027: 1022: 1021: 1018: 1007: 1005: 1000: 999: 996: 985: 980: 979: 976: 965: 960: 959: 956: 945: 937: 936: 928: 926: 922: 920: 919: 918: 917: 914: 906: 901: 900: 897: 889: 888: 887: 886: 883: 875: 870: 869: 866: 858: 851: 847: 845: 843: 838: 837: 834: 827: 826: 825: 822: 814: 812: 807: 806: 803: 796: 795: 794: 791: 783: 774: 772: 771: 770: 767: 760: 759: 758: 755: 748: 736: 734: 733: 728: 726: 725: 724: 714: 709: 708: 707: 674:Jacob Bigeleisen 455:transition state 407:pharmacokinetics 395:transition state 341:when one of the 298: 296: 295: 290: 276: 274: 273: 264: 263: 254: 249: 246: 243: 239: 233: 232: 231: 224: 219: 216: 215: 198: 195: 192: 191: 178: 176: 173: 172: 155: 149: 148: 147: 140: 132: 131: 130: 123: 118: 115: 114: 97: 94: 91: 90: 77: 75: 72: 71: 54: 48: 47: 46: 39: 32: 10946: 10945: 10941: 10940: 10939: 10937: 10936: 10935: 10901: 10900: 10899: 10858: 10856:Further reading 10853: 10852: 10821:(37): 12864–7. 10807: 10803: 10778: 10774: 10749: 10745: 10697: 10693: 10683: 10681: 10666: 10662: 10641:(20): 2258–60. 10631: 10627: 10604: 10600: 10572: 10568: 10543: 10539: 10526:(22): 8565–72. 10516: 10509: 10484: 10480: 10455: 10451: 10438: 10437: 10433: 10408: 10401: 10364: 10357: 10318: 10314: 10293:(43): 13036–7. 10283: 10279: 10226: 10222: 10177: 10173: 10128: 10121: 10076: 10069: 10045: 10041: 10018: 10011: 9988: 9984: 9977: 9951: 9942: 9919: 9908: 9893: 9879: 9875: 9847: 9843: 9798: 9794: 9765: 9761: 9728: 9724: 9703:(20): 6577–85. 9693: 9689: 9652: 9648: 9639: 9635: 9604: 9600: 9575: 9571: 9546: 9542: 9517: 9513: 9466: 9462: 9425: 9418: 9385: 9381: 9374: 9356: 9352: 9345: 9323: 9319: 9312: 9290: 9267: 9244: 9240: 9217: 9213: 9192:(12): 401–408. 9182: 9178: 9163: 9149: 9145: 9106: 9102: 9087: 9073: 9069: 9054: 9032: 9023: 8992: 8988: 8983: 8976: 8960:(46): 12141–2. 8945: 8941: 8926: 8922: 8911: 8890: 8875: 8857: 8844: 8822: 8817: 8813: 8782: 8771: 8764: 8750: 8731: 8724: 8716:–288, 816–818. 8698: 8683: 8660: 8656: 8649: 8624: 8619: 8606: 8601: 8553: 8548: 8547: 8538: 8534: 8526: 8522: 8514: 8510: 8505: 8497: 8493: 8488: 8481: 8474: 8467: 8459: 8455: 8450: 8431:optical density 8396: 8392: 8388: 8334: 8327: 8320: 8316: 8301: 8286: 8279: 8268: 8261: 8244: 8239: 8228: 8209: 8200: 8191: 8184: 8180: 8176: 8172: 8168: 8163: 8159: 8155: 8151: 8147: 8139: 8135: 8128: 8124: 8116: 8112: 8104: 8100: 8096: 8092: 8075:pre-equilibrium 8064: 8060: 8056: 8041: 8005: 7969: 7965: 7947: 7943: 7941: 7939: 7936: 7935: 7920: 7827: 7819: 7815: 7811: 7807: 7801: 7796: 7754:High precision 7752: 7725: 7720: 7716: 7694: 7687: 7679: 7671: 7635: 7600: 7593: 7491: 7448: 7417: 7413: 7408: 7402: 7398: 7392: 7388: 7369: 7359: 7355: 7339: 7337: 7326: 7322: 7316: 7312: 7310: 7308: 7305: 7304: 7299: 7291: 7281: 7274: 7260: 7253: 7245: 7244: 7242: 7231: 7220: 7213: 7181: 7177: 7172: 7166: 7162: 7158: 7154: 7148: 7144: 7123: 7119: 7112: 7105: 7101: 7094: 7092: 7079: 7071: 7066: 7058: 7057: 7052: 7044: 7039: 7031: 7030: 7023: 7015: 7010: 7002: 7001: 6996: 6988: 6983: 6975: 6974: 6972: 6971: 6958: 6950: 6945: 6937: 6936: 6931: 6925: 6917: 6912: 6904: 6903: 6902: 6893: 6888: 6880: 6875: 6867: 6862: 6854: 6853: 6851: 6850: 6839: 6835: 6830: 6828: 6825: 6824: 6819: 6815: 6809: 6807: 6801: 6800: 6776: 6772: 6767: 6755: 6751: 6732: 6722: 6718: 6702: 6700: 6689: 6685: 6679: 6675: 6673: 6665: 6663: 6660: 6659: 6654: 6647: 6643: 6639: 6635: 6626: 6619: 6584: 6580: 6564: 6554: 6550: 6534: 6532: 6521: 6517: 6511: 6507: 6505: 6503: 6500: 6499: 6494: 6490: 6486: 6457: 6449: 6444: 6436: 6435: 6430: 6422: 6417: 6409: 6405: 6398: 6387: 6379: 6374: 6366: 6365: 6360: 6352: 6347: 6339: 6335: 6328: 6326: 6315: 6311: 6305: 6301: 6299: 6297: 6294: 6293: 6288: 6284: 6253: 6248: 6243: 6230: 6225: 6217: 6215: 6205: 6200: 6192: 6191: 6184: 6176: 6171: 6163: 6162: 6161: 6146: 6142: 6137: 6119: 6114: 6109: 6096: 6091: 6083: 6081: 6071: 6066: 6058: 6057: 6050: 6042: 6037: 6029: 6028: 6027: 6012: 6008: 6003: 6001: 5998: 5997: 5973: 5968: 5960: 5951: 5946: 5938: 5932: 5931: 5930: 5928: 5917: 5913: 5908: 5895: 5890: 5882: 5873: 5868: 5860: 5854: 5853: 5852: 5850: 5839: 5835: 5830: 5828: 5825: 5824: 5819: 5815: 5791: 5777: 5760: 5746: 5725: 5720: 5719: 5707: 5703: 5690: 5680: 5675: 5674: 5664: 5662: 5654: 5652: 5649: 5648: 5640: 5634: 5630: 5626: 5622: 5594: 5590: 5574: 5564: 5560: 5544: 5542: 5531: 5527: 5521: 5517: 5515: 5507: 5505: 5502: 5501: 5481: 5480: 5475: 5470: 5457: 5453: 5447: 5446: 5444: 5429: 5421: 5413: 5408: 5403: 5402: 5399: 5398: 5393: 5388: 5375: 5371: 5365: 5364: 5362: 5347: 5339: 5331: 5326: 5321: 5320: 5316: 5314: 5311: 5310: 5305: 5301: 5295: 5290: 5289: 5284: 5277: 5267: 5260: 5252: 5245: 5238: 5231: 5221: 5214: 5207: 5200: 5193: 5156: 5152: 5151: 5126: 5122: 5116: 5112: 5111: 5109: 5096: 5082: 5080: 5078: 5075: 5074: 5033: 5029: 5016: 5002: 5000: 4998: 4995: 4994: 4968: 4964: 4946: 4942: 4941: 4916: 4912: 4906: 4902: 4901: 4899: 4886: 4872: 4870: 4868: 4865: 4864: 4842: 4786: 4779: 4705: 4689: 4683: 4678: 4677: 4600: 4596: 4595: 4588: 4581: 4574: 4567: 4557: 4550: 4543: 4536: 4508: 4501: 4483: 4468: 4461: 4449: 4445: 4444: 4441:Morse potential 4414: 4407: 4372: 4319: 4315: 4311: 4293: 4289: 4282: 4280: 4272: 4269: 4268: 4247: 4242: 4234: 4231: 4230: 4204: 4200: 4185: 4181: 4162: 4156: 4152: 4150: 4142: 4139: 4138: 4108: 4101: 4097: 4083: 4080: 4079: 4046: 4012: 4005: 3999: 3998: 3981: 3974: 3968: 3967: 3953: 3949: 3945: 3943: 3940: 3939: 3917: 3912: 3899: 3898: 3894: 3887: 3886: 3882: 3880: 3876: 3866: 3853: 3852: 3848: 3841: 3840: 3836: 3834: 3830: 3829: 3827: 3824: 3823: 3786: 3781: 3774: 3763: 3758: 3751: 3749: 3734: 3733: 3729: 3724: 3717: 3716: 3712: 3710: 3703: 3693: 3692: 3688: 3683: 3676: 3675: 3671: 3669: 3662: 3660: 3651: 3631: 3630: 3626: 3619: 3618: 3614: 3612: 3608: 3601: 3587: 3586: 3582: 3575: 3574: 3570: 3568: 3564: 3557: 3555: 3551: 3550: 3548: 3545: 3544: 3532: 3525: 3518: 3511: 3504: 3498: 3491: 3484: 3477: 3470: 3463: 3456: 3432: 3425: 3418: 3411: 3404: 3397: 3390: 3383: 3376: 3369: 3332: 3321: 3318: 3315: 3314: 3312: 3310: 3303: 3270: 3269: 3265: 3264: 3256: 3252: 3248: 3244: 3242: 3225: 3218: 3214: 3205: 3201: 3196: 3193: 3192: 3187: 3180: 3169: 3139: 3138: 3134: 3127: 3126: 3122: 3119: 3109: 3104: 3091: 3090: 3086: 3079: 3078: 3074: 3071: 3061: 3056: 3046: 3045: 3041: 3039: 3036: 3035: 3010: 3009: 3005: 3000: 2994: 2990: 2978: 2974: 2972: 2969: 2968: 2961: 2958: 2955: 2954: 2952: 2935: 2931: 2918: 2903: 2898: 2892: 2889: 2888: 2862: 2855: 2833: 2828: 2819: 2816: 2815: 2798: 2794: 2789: 2786: 2785: 2763: 2757: 2753: 2740: 2734: 2730: 2717: 2712: 2703: 2700: 2699: 2681: 2677: 2673: 2663: 2659: 2655: 2646: 2642: 2637: 2634: 2633: 2612: 2611: 2600: 2595: 2578: 2562: 2561: 2556: 2543: 2539: 2526: 2498: 2497: 2492: 2487: 2483: 2468: 2467: 2447: 2443: 2439: 2429: 2425: 2421: 2403: 2392: 2376: 2370: 2366: 2353: 2347: 2343: 2322: 2318: 2314: 2303: 2298: 2294: 2284: 2280: 2276: 2263: 2254: 2253: 2249: 2242: 2241: 2237: 2235: 2231: 2229: 2226: 2225: 2215: 2206: 2198: 2191: 2173: 2169: 2163: 2148: 2144: 2112: 2098: 2084: 2076: 2064: 2063: 2059: 2052: 2051: 2047: 2045: 2043: 2040: 2039: 2021: 2015: 2011: 1989: 1985: 1979: 1972: 1956: 1922: 1911: 1910: 1909: 1907: 1904: 1903: 1897: 1889:Planck constant 1859: 1852: 1847: 1836: 1835: 1827: 1826: 1822: 1815: 1813: 1797: 1796: 1792: 1791: 1784: 1779: 1771: 1769: 1760: 1755: 1749: 1746: 1745: 1724: 1717: 1706: 1705: 1704: 1697: 1696: 1692: 1685: 1683: 1667: 1666: 1662: 1661: 1654: 1650: 1646: 1644: 1635: 1631: 1629: 1626: 1625: 1590: 1586: 1582: 1572: 1568: 1564: 1546: 1535: 1519: 1513: 1509: 1496: 1490: 1486: 1465: 1461: 1457: 1446: 1441: 1437: 1427: 1423: 1419: 1400: 1396: 1392: 1388: 1384: 1377: 1367: 1363: 1359: 1355: 1351: 1344: 1342: 1327: 1316: 1311: 1299: 1293: 1289: 1281: 1277: 1270: 1261: 1255: 1251: 1243: 1239: 1232: 1230: 1216: 1212: 1208: 1197: 1192: 1190: 1186: 1175: 1160: 1156: 1152: 1145: 1141: 1137: 1130: 1126: 1122: 1121: 1113: 1109: 1105: 1098: 1094: 1090: 1083: 1079: 1075: 1074: 1072: 1063: 1057: 1053: 1043: 1037: 1033: 1023: 1017: 1013: 1008: 1001: 995: 991: 981: 975: 971: 961: 955: 951: 946: 944: 943: 939: 938: 927: 913: 912: 908: 902: 896: 895: 890: 882: 881: 877: 871: 865: 864: 859: 857: 853: 852: 839: 833: 832: 821: 820: 816: 815: 808: 802: 801: 790: 789: 785: 784: 782: 778: 766: 765: 761: 754: 753: 749: 747: 745: 742: 741: 720: 719: 715: 710: 703: 702: 698: 696: 693: 692: 690: 683: 639: 631: 627: 623: 619: 597: 593: 589: 585: 573: 566: 545: 540: 452: 437: 429: 415: 384: 380: 369: 362: 319: 318: 317: 299: 269: 265: 259: 255: 253: 245: 241: 240: 238: 235: 234: 227: 223: 211: 196: 187: 183: 177: 168: 153: 143: 139: 138: 137: 134: 133: 126: 122: 110: 95: 86: 82: 76: 67: 52: 42: 38: 37: 36: 33: 29: 27: 24: 23: 17: 12: 11: 5: 10944: 10934: 10933: 10928: 10923: 10918: 10913: 10898: 10897: 10859: 10857: 10854: 10851: 10850: 10801: 10772: 10743: 10691: 10680:(5): 1403–1420 10660: 10625: 10598: 10566: 10537: 10507: 10478: 10449: 10431: 10399: 10355: 10312: 10277: 10220: 10171: 10119: 10090:(5): 1677–83. 10067: 10039: 10009: 9982: 9975: 9940: 9906: 9891: 9873: 9841: 9792: 9781:(7): 397–404. 9759: 9740:(6): 341–349. 9722: 9687: 9646: 9633: 9614:(28): 9080–5. 9598: 9569: 9540: 9511: 9460: 9416: 9397:(3): 315–346. 9379: 9372: 9350: 9343: 9317: 9310: 9265: 9238: 9227:(9): 2326–32. 9211: 9176: 9161: 9143: 9100: 9085: 9067: 9052: 9021: 9002:(8): 675–678. 8986: 8981: 8974: 8939: 8920: 8888: 8873: 8842: 8820: 8811: 8792:(1): 3066–72. 8769: 8762: 8729: 8722: 8681: 8654: 8647: 8625:2 reactions". 8622: 8603: 8602: 8600: 8597: 8596: 8595: 8590: 8585: 8580: 8575: 8569: 8564: 8559: 8552: 8549: 8546: 8545: 8536: 8532: 8524: 8520: 8508: 8503: 8491: 8486: 8479: 8472: 8465: 8452: 8451: 8449: 8446: 8433:measurements. 8419: 8418: 8394: 8390: 8386: 8372: 8371: 8332: 8325: 8318: 8314: 8300: 8299:Other examples 8297: 8284: 8277: 8266: 8259: 8242: 8238: 8235: 8231: 8230: 8226: 8223: 8220: 8217: 8208: 8205: 8199: 8196: 8190: 8187: 8182: 8178: 8174: 8170: 8166: 8161: 8157: 8153: 8149: 8145: 8142: 8141: 8137: 8133: 8130: 8126: 8125:O + R ⇌ RH + H 8122: 8114: 8110: 8102: 8098: 8094: 8090: 8087:acid-catalyzed 8062: 8058: 8054: 8040: 8037: 8007: 8006: 7994: 7991: 7984: 7981: 7978: 7975: 7972: 7968: 7962: 7959: 7956: 7953: 7950: 7946: 7934: 7931: 7930: 7919: 7916: 7842:). The prefix 7826: 7823: 7817: 7813: 7809: 7805: 7800: 7797: 7795: 7792: 7751: 7748: 7723: 7718: 7714: 7693: 7690: 7685: 7682:cyanoformamide 7677: 7669: 7599: 7596: 7591: 7490: 7487: 7447: 7444: 7443: 7442: 7428: 7425: 7420: 7416: 7411: 7405: 7401: 7395: 7391: 7387: 7384: 7381: 7378: 7375: 7372: 7367: 7362: 7358: 7354: 7351: 7348: 7345: 7342: 7336: 7329: 7325: 7319: 7315: 7297: 7289: 7279: 7272: 7258: 7251: 7240: 7229: 7218: 7211: 7209: 7208: 7195: 7192: 7189: 7184: 7180: 7175: 7169: 7165: 7161: 7157: 7151: 7147: 7143: 7140: 7137: 7134: 7126: 7122: 7118: 7115: 7108: 7104: 7100: 7097: 7091: 7082: 7077: 7069: 7061: 7055: 7050: 7042: 7034: 7026: 7021: 7013: 7005: 6999: 6994: 6986: 6978: 6970: 6961: 6956: 6948: 6940: 6934: 6928: 6923: 6915: 6907: 6899: 6891: 6883: 6878: 6873: 6865: 6857: 6849: 6842: 6838: 6834: 6817: 6813: 6810: 6805: 6803: 6802: 6799: 6798: 6784: 6779: 6775: 6770: 6766: 6763: 6758: 6754: 6750: 6747: 6744: 6741: 6738: 6735: 6730: 6725: 6721: 6717: 6714: 6711: 6708: 6705: 6699: 6692: 6688: 6682: 6678: 6672: 6652: 6645: 6641: 6637: 6633: 6624: 6617: 6607: 6606: 6592: 6587: 6583: 6579: 6576: 6573: 6570: 6567: 6562: 6557: 6553: 6549: 6546: 6543: 6540: 6537: 6531: 6524: 6520: 6514: 6510: 6492: 6488: 6484: 6481: 6480: 6465: 6460: 6455: 6447: 6439: 6433: 6428: 6420: 6412: 6408: 6404: 6401: 6395: 6390: 6385: 6377: 6369: 6363: 6358: 6350: 6342: 6338: 6334: 6331: 6325: 6318: 6314: 6308: 6304: 6286: 6282: 6279: 6278: 6264: 6260: 6256: 6246: 6241: 6237: 6233: 6223: 6220: 6211: 6203: 6195: 6187: 6182: 6174: 6166: 6160: 6156: 6149: 6145: 6141: 6136: 6130: 6126: 6122: 6112: 6107: 6103: 6099: 6089: 6086: 6077: 6069: 6061: 6053: 6048: 6040: 6032: 6026: 6022: 6015: 6011: 6007: 5994: 5993: 5979: 5971: 5963: 5957: 5949: 5941: 5927: 5920: 5916: 5912: 5907: 5901: 5893: 5885: 5879: 5871: 5863: 5849: 5842: 5838: 5834: 5817: 5813: 5810: 5809: 5798: 5793: or 5790: 5787: 5784: 5776: 5773: 5770: 5767: 5759: 5756: 5753: 5745: 5742: 5739: 5736: 5733: 5728: 5718: 5715: 5710: 5706: 5702: 5696: 5693: 5688: 5683: 5673: 5670: 5667: 5661: 5641: 5638: 5637: 5632: 5628: 5624: 5620: 5617: 5616: 5602: 5597: 5593: 5589: 5586: 5583: 5580: 5577: 5572: 5567: 5563: 5559: 5556: 5553: 5550: 5547: 5541: 5534: 5530: 5524: 5520: 5514: 5495: 5494: 5473: 5460: 5456: 5451: 5445: 5439: 5436: 5428: 5420: 5411: 5401: 5400: 5391: 5378: 5374: 5369: 5363: 5357: 5354: 5346: 5338: 5329: 5319: 5318: 5303: 5299: 5294: 5291: 5282: 5275: 5265: 5258: 5250: 5243: 5236: 5229: 5219: 5212: 5205: 5198: 5191: 5185: 5184: 5170: 5167: 5164: 5159: 5155: 5149: 5146: 5143: 5140: 5137: 5134: 5129: 5125: 5119: 5115: 5108: 5102: 5099: 5094: 5091: 5088: 5085: 5068: 5067: 5056: 5053: 5050: 5047: 5044: 5041: 5036: 5032: 5028: 5022: 5019: 5014: 5011: 5008: 5005: 4988: 4987: 4971: 4967: 4963: 4960: 4957: 4954: 4949: 4945: 4939: 4936: 4933: 4930: 4927: 4924: 4919: 4915: 4909: 4905: 4898: 4892: 4889: 4884: 4881: 4878: 4875: 4843: 4840: 4839: 4784: 4777: 4758: 4757: 4739: 4738: 4720: 4719: 4704: 4701: 4697:transient KIEs 4685:Main article: 4682: 4679: 4641: 4640: 4625: 4624: 4611:with hindered 4601: 4598: 4597: 4593: 4592: 4586: 4579: 4572: 4565: 4555: 4548: 4541: 4534: 4521: 4520: 4517: 4516:of activation. 4510: 4506: 4499: 4489: 4486: 4481: 4466: 4459: 4450: 4447: 4446: 4412: 4405: 4373: 4370: 4369: 4332: 4326: 4322: 4318: 4314: 4310: 4307: 4304: 4301: 4296: 4292: 4288: 4285: 4279: 4276: 4253: 4250: 4246: 4241: 4238: 4227: 4226: 4215: 4210: 4207: 4203: 4199: 4196: 4191: 4188: 4184: 4180: 4177: 4171: 4168: 4165: 4159: 4155: 4149: 4146: 4132: 4131: 4118: 4115: 4111: 4107: 4104: 4100: 4096: 4093: 4090: 4087: 4045: 4042: 4019: 4015: 4011: 4008: 4002: 3997: 3993: 3988: 3984: 3980: 3977: 3971: 3966: 3962: 3956: 3952: 3948: 3935: 3934: 3920: 3915: 3910: 3897: 3885: 3879: 3874: 3869: 3864: 3851: 3839: 3833: 3817: 3816: 3804: 3801: 3793: 3789: 3785: 3780: 3777: 3770: 3766: 3762: 3757: 3754: 3748: 3732: 3727: 3715: 3709: 3706: 3691: 3686: 3674: 3668: 3665: 3659: 3654: 3649: 3642: 3629: 3617: 3611: 3607: 3604: 3598: 3585: 3573: 3567: 3563: 3560: 3554: 3538:Swain equation 3530: 3523: 3516: 3509: 3502: 3496: 3492:~ 1.1-1.2 and 3489: 3482: 3475: 3468: 3461: 3454: 3430: 3423: 3416: 3409: 3402: 3395: 3388: 3381: 3374: 3367: 3330: 3308: 3301: 3295: 3294: 3279: 3273: 3268: 3259: 3255: 3251: 3247: 3240: 3233: 3229: 3224: 3221: 3217: 3213: 3208: 3204: 3200: 3185: 3178: 3172:force constant 3167: 3161: 3160: 3142: 3137: 3130: 3125: 3115: 3112: 3108: 3103: 3094: 3089: 3082: 3077: 3067: 3064: 3060: 3055: 3049: 3044: 3019: 3013: 3008: 3003: 2997: 2993: 2989: 2986: 2981: 2977: 2938: 2934: 2930: 2925: 2922: 2917: 2912: 2909: 2906: 2901: 2897: 2860: 2853: 2836: 2831: 2827: 2823: 2801: 2797: 2793: 2781: 2780: 2766: 2760: 2756: 2752: 2748: 2743: 2737: 2733: 2729: 2725: 2720: 2715: 2711: 2707: 2684: 2680: 2676: 2672: 2666: 2662: 2658: 2654: 2649: 2645: 2641: 2627: 2626: 2609: 2603: 2598: 2594: 2590: 2585: 2582: 2574: 2571: 2568: 2565: 2559: 2555: 2551: 2546: 2542: 2538: 2533: 2530: 2522: 2519: 2516: 2513: 2510: 2507: 2504: 2501: 2495: 2491: 2486: 2482: 2479: 2476: 2473: 2471: 2469: 2465: 2460: 2456: 2446: 2442: 2438: 2428: 2424: 2420: 2415: 2412: 2409: 2406: 2401: 2398: 2395: 2391: 2387: 2384: 2379: 2369: 2365: 2361: 2356: 2346: 2342: 2338: 2333: 2330: 2325: 2321: 2317: 2312: 2309: 2306: 2302: 2297: 2291: 2288: 2283: 2279: 2275: 2272: 2269: 2266: 2264: 2252: 2240: 2234: 2233: 2213: 2204: 2196: 2189: 2171: 2167: 2161: 2146: 2142: 2135: 2134: 2121: 2118: 2115: 2111: 2107: 2104: 2101: 2097: 2093: 2090: 2087: 2083: 2079: 2075: 2062: 2050: 2019: 2013: 2009: 1987: 1983: 1977: 1970: 1954: 1948:speed of light 1925: 1918: 1915: 1895: 1881: 1880: 1865: 1862: 1855: 1850: 1843: 1840: 1830: 1825: 1821: 1818: 1812: 1806: 1800: 1795: 1787: 1782: 1778: 1774: 1768: 1763: 1758: 1754: 1730: 1727: 1720: 1713: 1710: 1700: 1695: 1691: 1688: 1682: 1676: 1670: 1665: 1657: 1653: 1649: 1643: 1638: 1634: 1619: 1618: 1603: 1599: 1589: 1585: 1581: 1571: 1567: 1563: 1558: 1555: 1552: 1549: 1544: 1541: 1538: 1534: 1530: 1527: 1522: 1512: 1508: 1504: 1499: 1489: 1485: 1481: 1476: 1473: 1468: 1464: 1460: 1455: 1452: 1449: 1445: 1440: 1434: 1431: 1426: 1422: 1417: 1399: 1395: 1391: 1387: 1383: 1380: 1366: 1362: 1358: 1354: 1350: 1347: 1339: 1336: 1333: 1330: 1325: 1322: 1319: 1315: 1302: 1292: 1288: 1284: 1280: 1276: 1273: 1264: 1254: 1250: 1246: 1242: 1238: 1235: 1227: 1224: 1219: 1215: 1211: 1206: 1203: 1200: 1196: 1189: 1182: 1179: 1173: 1159: 1155: 1144: 1140: 1129: 1125: 1112: 1108: 1097: 1093: 1082: 1078: 1066: 1056: 1052: 1046: 1036: 1032: 1026: 1016: 1012: 1004: 994: 990: 984: 974: 970: 964: 954: 950: 942: 934: 931: 925: 911: 905: 894: 880: 874: 863: 856: 850: 842: 831: 819: 811: 800: 788: 781: 777: 764: 752: 723: 718: 713: 706: 701: 688: 681: 638: 635: 629: 625: 621: 617: 595: 591: 587: 583: 572: 569: 564: 544: 541: 539: 538:Classification 536: 450: 443:methyl bromide 435: 427: 414: 411: 382: 378: 367: 360: 355:rate constants 306:methyl bromide 300: 288: 285: 282: 279: 272: 268: 262: 258: 252: 237: 236: 230: 222: 214: 209: 203: 190: 186: 181: 171: 166: 160: 152: 146: 136: 135: 129: 121: 113: 108: 102: 89: 85: 80: 70: 65: 59: 51: 45: 35: 34: 31: 22: 21: 20: 15: 9: 6: 4: 3: 2: 10943: 10932: 10929: 10927: 10924: 10922: 10919: 10917: 10914: 10912: 10909: 10908: 10906: 10894: 10890: 10886: 10882: 10878: 10874: 10870: 10866: 10861: 10860: 10846: 10842: 10837: 10832: 10828: 10824: 10820: 10816: 10812: 10805: 10797: 10793: 10789: 10785: 10784: 10776: 10768: 10764: 10760: 10756: 10755: 10747: 10739: 10735: 10731: 10727: 10723: 10719: 10715: 10711: 10707: 10703: 10695: 10679: 10675: 10671: 10664: 10656: 10652: 10648: 10644: 10640: 10636: 10629: 10621: 10617: 10613: 10609: 10602: 10594: 10590: 10586: 10582: 10581: 10576: 10570: 10564: 10560: 10556: 10552: 10551: 10546: 10541: 10533: 10529: 10525: 10521: 10514: 10512: 10503: 10499: 10495: 10491: 10490: 10482: 10474: 10470: 10466: 10462: 10461: 10453: 10445: 10441: 10435: 10429: 10425: 10421: 10417: 10416: 10411: 10406: 10404: 10395: 10391: 10386: 10381: 10377: 10373: 10369: 10362: 10360: 10351: 10347: 10343: 10339: 10335: 10331: 10328:(9): 3071–9. 10327: 10323: 10316: 10308: 10304: 10300: 10296: 10292: 10288: 10281: 10273: 10269: 10264: 10259: 10255: 10251: 10247: 10243: 10239: 10235: 10231: 10224: 10216: 10212: 10207: 10202: 10198: 10194: 10190: 10186: 10182: 10175: 10167: 10163: 10158: 10153: 10149: 10145: 10141: 10137: 10133: 10126: 10124: 10115: 10111: 10106: 10101: 10097: 10093: 10089: 10085: 10081: 10074: 10072: 10063: 10059: 10055: 10051: 10043: 10035: 10031: 10027: 10023: 10016: 10014: 10005: 10001: 9997: 9993: 9986: 9978: 9972: 9968: 9964: 9960: 9956: 9949: 9947: 9945: 9936: 9932: 9928: 9924: 9917: 9915: 9913: 9911: 9902: 9898: 9894: 9888: 9884: 9877: 9869: 9865: 9861: 9857: 9853: 9845: 9837: 9833: 9829: 9825: 9821: 9817: 9813: 9809: 9808: 9803: 9796: 9788: 9784: 9780: 9776: 9775: 9770: 9769:Klinman, J. P 9763: 9755: 9751: 9747: 9743: 9739: 9735: 9734: 9726: 9718: 9714: 9710: 9706: 9702: 9698: 9691: 9683: 9679: 9674: 9669: 9666:(7): R191-8. 9665: 9661: 9657: 9650: 9643: 9637: 9629: 9625: 9621: 9617: 9613: 9609: 9602: 9594: 9590: 9586: 9582: 9581: 9573: 9565: 9561: 9557: 9553: 9552: 9544: 9536: 9532: 9528: 9524: 9523: 9515: 9507: 9503: 9499: 9495: 9491: 9487: 9483: 9479: 9475: 9471: 9464: 9456: 9452: 9447: 9442: 9438: 9434: 9430: 9423: 9421: 9412: 9408: 9404: 9400: 9396: 9392: 9391: 9383: 9375: 9369: 9365: 9361: 9354: 9346: 9340: 9336: 9331: 9330: 9321: 9313: 9307: 9303: 9298: 9297: 9288: 9286: 9284: 9282: 9280: 9278: 9276: 9274: 9272: 9270: 9261: 9257: 9253: 9249: 9242: 9234: 9230: 9226: 9222: 9215: 9207: 9203: 9199: 9195: 9191: 9187: 9180: 9172: 9168: 9164: 9158: 9154: 9147: 9139: 9135: 9131: 9127: 9123: 9119: 9115: 9111: 9104: 9096: 9092: 9088: 9082: 9078: 9071: 9063: 9059: 9055: 9049: 9045: 9040: 9039: 9030: 9028: 9026: 9017: 9013: 9009: 9005: 9001: 8997: 8990: 8980: 8973: 8967: 8963: 8959: 8955: 8949: 8943: 8935: 8931: 8924: 8916: 8909: 8907: 8905: 8903: 8901: 8899: 8897: 8895: 8893: 8884: 8880: 8876: 8870: 8865: 8864: 8855: 8853: 8851: 8849: 8847: 8838: 8834: 8830: 8826: 8815: 8807: 8803: 8799: 8795: 8791: 8787: 8780: 8778: 8776: 8774: 8765: 8759: 8755: 8748: 8746: 8744: 8742: 8740: 8738: 8736: 8734: 8725: 8719: 8715: 8711: 8706: 8705: 8696: 8694: 8692: 8690: 8688: 8686: 8677: 8673: 8669: 8665: 8658: 8650: 8644: 8640: 8636: 8632: 8628: 8617: 8615: 8613: 8611: 8609: 8604: 8594: 8591: 8589: 8586: 8584: 8581: 8579: 8576: 8573: 8570: 8568: 8565: 8563: 8560: 8558: 8555: 8554: 8542: 8530: 8518: 8512: 8501: 8495: 8485: 8478: 8471: 8464: 8457: 8453: 8445: 8443: 8438: 8434: 8432: 8428: 8424: 8416: 8412: 8411: 8410: 8408: 8404: 8400: 8384: 8382: 8377: 8369: 8365: 8364: 8363: 8361: 8357: 8353: 8348: 8346: 8342: 8336: 8331: 8324: 8312: 8307: 8293: 8289: 8283: 8276: 8270: 8265: 8258: 8252: 8249: 8234: 8224: 8221: 8218: 8215: 8214: 8213: 8204: 8195: 8186: 8131: 8120: 8119: 8118: 8108: 8088: 8084: 8080: 8077:prior to the 8076: 8071: 8069: 8065: 8050: 8046: 8036: 8034: 8029: 8027: 8021: 8018: 8014: 8013:isotopologues 7992: 7989: 7979: 7976: 7973: 7966: 7957: 7954: 7951: 7944: 7933: 7932: 7928: 7924: 7923: 7915: 7908: 7904: 7900: 7896: 7894: 7889: 7887: 7883: 7879: 7874: 7870: 7866: 7862: 7860: 7856: 7851: 7849: 7845: 7841: 7837: 7833: 7822: 7791: 7783: 7779: 7777: 7773: 7769: 7765: 7761: 7757: 7747: 7739: 7731: 7727: 7712: 7707: 7704: 7700: 7689: 7683: 7666: 7658: 7654: 7652: 7648: 7644: 7639: 7633: 7624: 7616: 7608: 7604: 7595: 7587: 7585: 7581: 7575: 7573: 7568: 7566: 7562: 7558: 7557:cycloaddition 7554: 7545: 7541: 7539: 7535: 7531: 7527: 7526:cycloaddition 7519: 7515: 7513: 7509: 7504: 7500: 7496: 7486: 7484: 7480: 7476: 7472: 7468: 7464: 7460: 7456: 7452: 7418: 7414: 7409: 7403: 7399: 7393: 7389: 7382: 7379: 7373: 7370: 7360: 7356: 7352: 7349: 7343: 7340: 7334: 7327: 7323: 7317: 7313: 7303: 7302: 7301: 7296: 7292: 7278: 7271: 7266: 7262: 7257: 7250: 7239: 7235: 7228: 7224: 7217: 7193: 7190: 7182: 7178: 7173: 7167: 7163: 7149: 7145: 7141: 7138: 7132: 7124: 7120: 7116: 7113: 7106: 7102: 7098: 7095: 7089: 7080: 7067: 7053: 7040: 7024: 7011: 6997: 6984: 6968: 6959: 6946: 6932: 6926: 6913: 6889: 6876: 6863: 6847: 6840: 6836: 6832: 6823: 6822: 6821: 6777: 6773: 6768: 6764: 6756: 6752: 6748: 6745: 6736: 6733: 6723: 6719: 6715: 6712: 6706: 6703: 6697: 6690: 6686: 6680: 6676: 6670: 6658: 6657: 6656: 6649: 6623: 6616: 6611: 6585: 6581: 6577: 6574: 6568: 6565: 6555: 6551: 6547: 6544: 6538: 6535: 6529: 6522: 6518: 6512: 6508: 6498: 6497: 6496: 6458: 6445: 6431: 6418: 6402: 6399: 6388: 6375: 6361: 6348: 6332: 6329: 6323: 6316: 6312: 6306: 6302: 6292: 6291: 6290: 6258: 6254: 6235: 6231: 6218: 6201: 6185: 6172: 6158: 6154: 6147: 6143: 6139: 6134: 6124: 6120: 6101: 6097: 6084: 6067: 6051: 6038: 6024: 6020: 6013: 6009: 6005: 5996: 5995: 5969: 5947: 5925: 5918: 5914: 5910: 5905: 5891: 5869: 5847: 5840: 5836: 5832: 5823: 5822: 5821: 5796: 5788: 5785: 5782: 5771: 5768: 5754: 5737: 5734: 5726: 5713: 5708: 5704: 5700: 5694: 5691: 5681: 5668: 5665: 5659: 5647: 5646: 5645: 5636: 5595: 5591: 5587: 5584: 5578: 5575: 5565: 5561: 5557: 5554: 5548: 5545: 5539: 5532: 5528: 5522: 5518: 5512: 5500: 5499: 5498: 5471: 5458: 5454: 5449: 5437: 5434: 5426: 5418: 5409: 5389: 5376: 5372: 5367: 5355: 5352: 5344: 5336: 5327: 5309: 5308: 5307: 5286: 5281: 5274: 5269: 5264: 5257: 5249: 5242: 5235: 5228: 5223: 5218: 5211: 5204: 5197: 5190: 5165: 5157: 5153: 5144: 5141: 5138: 5135: 5127: 5123: 5117: 5113: 5106: 5100: 5097: 5089: 5083: 5073: 5072: 5071: 5051: 5048: 5045: 5042: 5034: 5030: 5026: 5020: 5017: 5009: 5003: 4993: 4992: 4991: 4969: 4965: 4961: 4955: 4947: 4943: 4934: 4931: 4928: 4925: 4917: 4913: 4907: 4903: 4896: 4890: 4887: 4879: 4873: 4863: 4862: 4861: 4855: 4851: 4847: 4834: 4830: 4822: 4818: 4814: 4807: 4803: 4801: 4797: 4793: 4788: 4783: 4776: 4771: 4762: 4755: 4752: 4751: 4750: 4743: 4736: 4733: 4732: 4731: 4724: 4717: 4714: 4713: 4712: 4710: 4700: 4698: 4694: 4688: 4672: 4668: 4666: 4658: 4653: 4649: 4645: 4638: 4634: 4633: 4632: 4630: 4622: 4618: 4617: 4616: 4614: 4610: 4606: 4605:deprotonation 4591: 4585: 4578: 4571: 4564: 4560: 4554: 4547: 4540: 4533: 4530: 4529: 4528: 4526: 4518: 4515: 4511: 4505: 4498: 4494: 4490: 4487: 4484: 4477: 4473: 4469: 4462: 4455: 4454: 4453: 4442: 4438: 4434: 4429: 4427: 4422: 4418: 4411: 4404: 4400: 4395: 4393: 4387: 4383: 4381: 4377: 4368: 4366: 4357: 4353: 4350: 4345: 4330: 4324: 4320: 4316: 4308: 4305: 4302: 4294: 4290: 4286: 4283: 4277: 4274: 4251: 4248: 4244: 4239: 4236: 4208: 4205: 4201: 4197: 4194: 4189: 4186: 4182: 4178: 4169: 4166: 4163: 4157: 4153: 4147: 4144: 4137: 4136: 4135: 4116: 4113: 4109: 4105: 4102: 4098: 4094: 4091: 4088: 4085: 4078: 4077: 4076: 4074: 4065: 4061: 4059: 4055: 4051: 4041: 4037: 4035: 4017: 4013: 4009: 4006: 3995: 3991: 3986: 3982: 3978: 3975: 3964: 3960: 3950: 3946: 3918: 3913: 3908: 3895: 3883: 3877: 3872: 3867: 3862: 3849: 3837: 3831: 3822: 3821: 3820: 3802: 3799: 3791: 3787: 3783: 3778: 3775: 3768: 3764: 3760: 3755: 3752: 3746: 3730: 3725: 3713: 3707: 3704: 3689: 3684: 3672: 3666: 3663: 3657: 3652: 3647: 3640: 3627: 3615: 3609: 3605: 3602: 3596: 3583: 3571: 3565: 3561: 3558: 3552: 3543: 3542: 3541: 3539: 3534: 3529: 3522: 3515: 3508: 3501: 3495: 3488: 3481: 3474: 3467: 3460: 3453: 3448: 3443: 3441: 3437: 3434:developed by 3429: 3422: 3415: 3408: 3401: 3394: 3387: 3380: 3373: 3366: 3357: 3352: 3348: 3344: 3339: 3335: 3333: 3307: 3300: 3277: 3266: 3253: 3249: 3245: 3238: 3231: 3227: 3222: 3219: 3215: 3211: 3206: 3202: 3191: 3190: 3189: 3184: 3177: 3173: 3166: 3135: 3123: 3113: 3110: 3106: 3101: 3087: 3075: 3065: 3062: 3058: 3053: 3042: 3034: 3033: 3032: 3017: 3006: 3001: 2995: 2991: 2987: 2984: 2979: 2975: 2936: 2932: 2928: 2923: 2920: 2915: 2907: 2899: 2895: 2886: 2881: 2878: 2874: 2870: 2864: 2859: 2852: 2834: 2829: 2825: 2799: 2795: 2764: 2754: 2750: 2746: 2741: 2731: 2727: 2723: 2718: 2713: 2709: 2678: 2674: 2670: 2660: 2656: 2652: 2647: 2643: 2632: 2631: 2630: 2607: 2601: 2596: 2592: 2583: 2580: 2557: 2553: 2549: 2544: 2540: 2531: 2528: 2517: 2493: 2489: 2484: 2480: 2477: 2474: 2472: 2463: 2458: 2444: 2440: 2436: 2426: 2422: 2413: 2410: 2407: 2404: 2399: 2396: 2393: 2385: 2377: 2367: 2363: 2359: 2354: 2344: 2340: 2331: 2328: 2323: 2319: 2315: 2310: 2307: 2304: 2295: 2289: 2286: 2281: 2277: 2273: 2270: 2267: 2265: 2250: 2238: 2224: 2223: 2222: 2220: 2216: 2209: 2203: 2199: 2192: 2185: 2181: 2177: 2170: 2160: 2156: 2152: 2141:(containing σ 2140: 2109: 2095: 2081: 2073: 2060: 2048: 2038: 2037: 2036: 2034: 2030: 2026: 2022: 2012: 2005: 2001: 1997: 1993: 1986: 1976: 1968: 1964: 1960: 1953: 1949: 1945: 1941: 1923: 1913: 1901: 1894: 1890: 1886: 1863: 1860: 1853: 1848: 1838: 1823: 1819: 1816: 1810: 1804: 1793: 1785: 1780: 1776: 1772: 1766: 1761: 1756: 1752: 1728: 1725: 1718: 1708: 1693: 1689: 1686: 1680: 1674: 1663: 1655: 1651: 1647: 1641: 1636: 1632: 1624: 1623: 1622: 1601: 1587: 1583: 1579: 1569: 1565: 1556: 1553: 1550: 1547: 1542: 1539: 1536: 1528: 1520: 1510: 1506: 1502: 1497: 1487: 1483: 1474: 1471: 1466: 1462: 1458: 1453: 1450: 1447: 1438: 1432: 1429: 1424: 1420: 1415: 1397: 1393: 1389: 1385: 1381: 1378: 1364: 1360: 1356: 1352: 1348: 1345: 1337: 1334: 1331: 1328: 1323: 1320: 1317: 1300: 1290: 1286: 1282: 1278: 1274: 1271: 1262: 1252: 1248: 1244: 1240: 1236: 1233: 1225: 1222: 1217: 1213: 1209: 1204: 1201: 1198: 1187: 1180: 1177: 1171: 1157: 1153: 1142: 1138: 1127: 1123: 1110: 1106: 1095: 1091: 1080: 1076: 1064: 1054: 1050: 1044: 1034: 1030: 1024: 1014: 1010: 1002: 992: 988: 982: 972: 968: 962: 952: 948: 940: 932: 929: 923: 909: 903: 892: 878: 872: 861: 854: 848: 840: 829: 817: 809: 798: 786: 779: 775: 762: 750: 740: 739: 738: 716: 711: 699: 687: 680: 675: 670: 668: 664: 660: 655: 650: 648: 644: 634: 611: 607: 605: 601: 580: 578: 568: 560: 558: 556: 550: 535: 533: 529: 525: 522:, have lower 521: 517: 513: 509: 508:chemical bond 505: 500: 498: 494: 490: 486: 482: 478: 470: 466: 464: 463:reaction rate 460: 456: 448: 444: 439: 433: 425: 421: 410: 408: 404: 400: 396: 392: 387: 385: 374: 373:isotopologues 370: 363: 356: 352: 348: 344: 340: 336: 335:reaction rate 332: 328: 324: 315: 311: 307: 303: 286: 283: 280: 277: 270: 266: 260: 256: 250: 228: 220: 212: 207: 201: 188: 184: 179: 169: 164: 158: 150: 144: 127: 119: 111: 106: 100: 87: 83: 78: 68: 63: 57: 49: 43: 19: 10868: 10864: 10818: 10814: 10804: 10787: 10781: 10775: 10758: 10752: 10746: 10705: 10701: 10694: 10682:. Retrieved 10677: 10673: 10663: 10638: 10634: 10628: 10611: 10607: 10601: 10584: 10578: 10569: 10548: 10540: 10523: 10519: 10493: 10487: 10481: 10464: 10458: 10452: 10446:. Chemitool. 10443: 10434: 10413: 10375: 10371: 10325: 10321: 10315: 10290: 10286: 10280: 10237: 10233: 10223: 10191:(1): 43–46. 10188: 10184: 10174: 10139: 10135: 10087: 10083: 10053: 10049: 10042: 10025: 10021: 9995: 9991: 9985: 9958: 9954: 9926: 9922: 9882: 9876: 9851: 9844: 9811: 9805: 9795: 9778: 9772: 9762: 9737: 9731: 9725: 9700: 9696: 9690: 9663: 9659: 9649: 9636: 9611: 9607: 9601: 9584: 9578: 9572: 9555: 9549: 9543: 9526: 9520: 9514: 9473: 9469: 9463: 9436: 9432: 9394: 9388: 9382: 9359: 9353: 9328: 9320: 9295: 9251: 9247: 9241: 9224: 9220: 9214: 9189: 9185: 9179: 9152: 9146: 9113: 9109: 9103: 9076: 9070: 9037: 8999: 8995: 8989: 8978: 8971: 8957: 8953: 8942: 8933: 8929: 8923: 8914: 8862: 8828: 8824: 8814: 8789: 8785: 8753: 8703: 8667: 8663: 8657: 8630: 8626: 8511: 8494: 8483: 8476: 8469: 8462: 8456: 8439: 8435: 8420: 8380: 8373: 8356:halogenation 8349: 8337: 8329: 8322: 8311:exotic atoms 8302: 8281: 8274: 8271: 8263: 8256: 8253: 8240: 8232: 8210: 8201: 8192: 8143: 8072: 8044: 8042: 8030: 8022: 8017:racemization 8010: 7912: 7901: 7897: 7890: 7875: 7871: 7867: 7863: 7852: 7847: 7843: 7835: 7828: 7802: 7794:Case studies 7788: 7753: 7744: 7708: 7695: 7675: 7642: 7640: 7631: 7629: 7601: 7588: 7576: 7569: 7549: 7523: 7492: 7450: 7449: 7300:as follows: 7294: 7287: 7285: 7276: 7269: 7255: 7248: 7246: 7237: 7233: 7226: 7222: 7215: 6820:, one gets: 6811: 6650: 6630: 6621: 6614: 6482: 6280: 5811: 5642: 5618: 5496: 5296: 5279: 5272: 5270: 5262: 5255: 5247: 5240: 5233: 5226: 5224: 5216: 5209: 5202: 5195: 5188: 5186: 5069: 4989: 4859: 4848: 4844: 4827: 4815: 4811: 4799: 4795: 4789: 4781: 4774: 4769: 4766: 4753: 4747: 4734: 4728: 4715: 4707:Simmons and 4706: 4690: 4662: 4657:quinoprotein 4646: 4642: 4626: 4609:nitropropane 4602: 4590: 4583: 4576: 4569: 4562: 4559: 4552: 4545: 4538: 4531: 4524: 4522: 4503: 4496: 4479: 4475: 4471: 4464: 4457: 4451: 4432: 4425: 4420: 4419:, the small 4409: 4402: 4396: 4391: 4388: 4384: 4374: 4364: 4362: 4348: 4346: 4228: 4133: 4070: 4047: 4038: 4033: 3936: 3818: 3535: 3527: 3520: 3513: 3506: 3499: 3493: 3486: 3479: 3472: 3465: 3458: 3451: 3447:Streitwieser 3444: 3427: 3420: 3413: 3406: 3399: 3392: 3385: 3378: 3371: 3364: 3361: 3355: 3350: 3346: 3342: 3328: 3305: 3298: 3296: 3182: 3175: 3164: 3162: 2879: 2876: 2872: 2865: 2857: 2850: 2782: 2628: 2218: 2211: 2207: 2201: 2194: 2187: 2179: 2175: 2165: 2158: 2154: 2150: 2138: 2136: 2032: 2028: 2017: 2007: 2003: 1999: 1995: 1991: 1981: 1974: 1962: 1951: 1943: 1892: 1884: 1882: 1620: 685: 678: 671: 666: 662: 658: 651: 640: 615: 603: 599: 581: 576: 574: 561: 552: 548: 546: 501: 474: 440: 438:2) pathway. 424:unimolecular 416: 388: 376: 365: 358: 330: 326: 320: 314:methyl group 301: 18: 9961:: 149–191. 9814:(6): 1823. 9439:(1): 6–27. 9116:(2): 80–2. 8712:. pp. 8633:: 217–273. 8498:"Me" means 8185:decreases. 7882:nitroalkane 7692:DEPT-55 NMR 7512:cyclohexane 7293:along with 6491:, where 1-F 4703:Experiments 555:experiments 516:classically 499:) heavier. 432:bimolecular 391:vibrational 10905:Categories 10684:26 January 9767:Kohen, A; 9642:proton NMR 8599:References 8345:saccharose 7768:hydrolysis 7647:Lewis acid 5639:Evaluation 4792:photolysis 4363:Also, the 3436:Westheimer 3345:6)- and (3 2863:possible. 1940:wavenumber 413:Background 10921:Deuterium 10738:206530683 9901:606113159 9868:1364-5471 9206:0001-4842 9171:286483846 8883:867217247 8026:rotaxanes 7651:palladium 7383:− 7374:⁡ 7353:− 7344:⁡ 7191:− 7142:− 7117:− 7099:− 6749:− 6737:⁡ 6716:− 6707:⁡ 6578:− 6569:⁡ 6548:− 6539:⁡ 6403:⁡ 6333:⁡ 6159:∫ 6155:× 6025:∫ 6021:× 5926:× 5848:× 5772:⋯ 5735:× 5714:× 5666:− 5588:− 5579:⁡ 5558:− 5549:⁡ 5438:⋯ 5356:⋯ 4627:and in a 4493:Arrhenius 4470:) > Δ( 4376:Tunneling 4291:π 4275:β 4237:α 4209:β 4206:− 4198:α 4195:− 4190:α 4187:− 4179:β 4170:α 4167:− 4164:β 4158:α 4103:− 4044:Tunneling 4007:− 3992:≅ 3976:− 3965:μ 3961:∝ 3800:≅ 3779:− 3756:− 3708:− 3667:− 3658:≅ 3606:⁡ 3562:⁡ 3250:ν 3223:− 3212:≅ 3199:Δ 3114:π 3102:≅ 3088:μ 3066:π 3043:ν 2992:ν 2933:ν 2896:ϵ 2835:‡ 2822:Δ 2792:Δ 2765:‡ 2747:− 2742:‡ 2719:‡ 2706:Δ 2671:− 2640:Δ 2602:‡ 2589:Δ 2554:∑ 2550:− 2537:Δ 2490:∑ 2481:⁡ 2475:≅ 2437:− 2411:− 2390:∑ 2386:− 2378:‡ 2360:− 2355:‡ 2329:− 2324:‡ 2301:∑ 2282:− 2274:⁡ 2268:≅ 2193:) = exp(- 2110:× 2096:× 2082:× 1917:~ 1914:ν 1854:‡ 1842:~ 1839:ν 1786:‡ 1777:ν 1762:‡ 1712:~ 1709:ν 1652:ν 1580:− 1554:− 1533:∑ 1529:− 1521:‡ 1503:− 1498:‡ 1472:− 1467:‡ 1444:∑ 1425:− 1390:− 1382:− 1357:− 1349:− 1335:− 1314:∏ 1301:‡ 1283:− 1275:− 1263:‡ 1245:− 1237:− 1223:− 1218:‡ 1195:∏ 1065:‡ 1045:‡ 1025:‡ 1003:‡ 983:‡ 963:‡ 904:‡ 873:‡ 841:‡ 830:σ 818:σ 810:‡ 799:σ 787:σ 717:κ 700:κ 667:deuterium 493:carbon-13 489:carbon-12 485:deuterium 375:): KIE = 347:reactants 284:± 229:− 213:− 170:− 145:− 128:− 112:− 69:− 44:− 10893:96761478 10845:25203796 10730:21273484 10655:12772156 10575:Mislow K 10394:14583616 10350:16509628 10307:14570471 10272:28082586 10215:28005341 10166:28294618 10114:26788885 9836:55422661 9754:12069618 9717:18426205 9682:10381408 9628:16834382 9506:20959068 9498:12574623 9455:10812022 9138:21124393 9062:14214254 8936:: 15–76. 8806:22392731 8551:See also 8350:Another 8248:chlorine 7903:scheme. 7764:isotopes 7711:thiourea 7561:isoprene 7555:for the 7530:isoprene 7503:isotopes 7479:isotopes 6259:′ 6236:′ 6125:′ 6102:′ 5450:→ 5368:→ 4613:pyridine 4380:kinetics 663:hydrogen 659:hydrogen 481:hydrogen 351:isotopes 180:→ 79:→ 10873:Bibcode 10836:4183625 10710:Bibcode 10702:Science 10330:Bibcode 10263:5671764 10242:Bibcode 10234:Science 10206:5674980 10157:5535300 10105:4774971 9816:Bibcode 9478:Bibcode 9470:Science 9399:Bibcode 9118:Bibcode 9095:9894996 9004:Bibcode 8948:muonium 8423:enolate 8403:bromine 8399:ketones 8360:toluene 8341:glucose 8113:O (or D 8068:agostic 7772:sulfate 7717:1 and S 5619:Where F 4709:Hartwig 4514:entropy 4439:on the 4401:ratios 3325:⁠ 3313:⁠ 3170:is the 2965:⁠ 2953:⁠ 1969:. The σ 586:1 and S 506:of the 457:of the 447:cyanide 345:in the 310:cyanide 10891: 10843: 10833: 10736: 10728: 10653: 10392: 10348: 10305: 10270: 10260: 10213: 10203: 10164: 10154: 10112: 10102: 9973: 9899: 9889: 9866: 9834: 9752: 9715: 9680: 9626: 9504: 9496: 9453: 9370: 9341: 9308: 9304:–437. 9204: 9169: 9159: 9136: 9093: 9083: 9060: 9050: 8881: 8871: 8804: 8760: 8720: 8645: 8529:phenyl 8500:methyl 8306:helium 8132:RH + H 8045:faster 7643:et al. 7641:Frost 7632:et al. 5442: 5360: 4392:should 4229:where 3819:i.e., 3311:= exp( 3163:where 1961:; and 1883:Here, 637:Theory 557:below. 497:dalton 430:1) or 10889:S2CID 10734:S2CID 10545:IUPAC 10410:IUPAC 9832:S2CID 9502:S2CID 8517:ethyl 8448:Notes 8401:with 8393:(PhCH 8140:O + P 8136:O → H 7880:with 7563:with 7532:with 6487:and F 6285:and A 5816:and A 5631:and A 5623:and F 5302:and A 4770:prior 4561:and 2002:, or 491:with 343:atoms 337:of a 308:with 287:0.008 281:1.082 10841:PMID 10726:PMID 10686:2023 10651:PMID 10390:PMID 10346:PMID 10303:PMID 10268:PMID 10211:PMID 10162:PMID 10110:PMID 9971:ISBN 9897:OCLC 9887:ISBN 9864:ISSN 9750:PMID 9713:PMID 9678:PMID 9624:PMID 9494:PMID 9451:PMID 9437:1458 9368:ISBN 9339:ISBN 9306:ISBN 9202:ISSN 9167:OCLC 9157:ISBN 9134:PMID 9091:OCLC 9081:ISBN 9058:OCLC 9048:ISBN 8879:OCLC 8869:ISBN 8802:PMID 8758:ISBN 8718:ISBN 8643:ISBN 8502:, CH 8468:and 8405:and 8326:0.11 8117:O). 7993:1.15 5656:rate 5261:and 5232:and 5215:and 4491:The 4267:and 3919:1.44 3803:1.44 2814:and 2698:and 2164:and 2031:and 1744:and 684:and 665:and 477:mass 445:and 325:, a 10881:doi 10869:286 10831:PMC 10823:doi 10819:136 10792:doi 10763:doi 10718:doi 10706:331 10678:125 10643:doi 10616:doi 10589:doi 10559:doi 10557:". 10528:doi 10524:114 10498:doi 10469:doi 10465:119 10424:doi 10422:". 10380:doi 10376:278 10338:doi 10326:110 10295:doi 10291:125 10258:PMC 10250:doi 10238:355 10201:PMC 10193:doi 10189:139 10152:PMC 10144:doi 10100:PMC 10092:doi 10088:138 10058:doi 10054:111 10030:doi 10026:106 10000:doi 9963:doi 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7424:) 7419:0 7415:R 7410:/ 7404:P 7400:R 7394:1 7390:F 7386:( 7380:1 7377:[ 7366:) 7361:1 7357:F 7350:1 7347:( 7335:= 7328:2 7324:k 7318:1 7314:k 7298:0 7295:R 7290:P 7288:R 7280:2 7277:k 7275:/ 7273:1 7270:k 7259:1 7256:F 7252:0 7243:. 7241:0 7238:c 7236:/ 7234:c 7230:0 7227:m 7225:/ 7223:m 7219:1 7216:F 7212:0 7194:1 7188:) 7183:1 7179:k 7174:/ 7168:2 7164:k 7160:( 7156:) 7150:1 7146:F 7139:1 7136:( 7133:= 7125:1 7121:F 7114:1 7107:2 7103:F 7096:1 7090:= 7081:0 7076:] 7068:1 7064:A 7060:[ 7054:/ 7049:] 7041:1 7037:A 7033:[ 7025:0 7020:] 7012:2 7008:A 7004:[ 6998:/ 6993:] 6985:2 6981:A 6977:[ 6969:= 6960:0 6955:] 6947:1 6943:A 6939:[ 6933:/ 6927:0 6922:] 6914:2 6910:A 6906:[ 6898:] 6890:1 6886:A 6882:[ 6877:/ 6872:] 6864:2 6860:A 6856:[ 6848:= 6841:0 6837:R 6833:R 6818:2 6814:0 6806:1 6783:] 6778:0 6774:R 6769:/ 6765:R 6762:) 6757:1 6753:F 6746:1 6743:( 6740:[ 6729:) 6724:1 6720:F 6713:1 6710:( 6698:= 6691:2 6687:k 6681:1 6677:k 6671:= 6653:0 6646:P 6642:0 6638:P 6634:0 6625:2 6622:k 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5701:= 5695:t 5692:d 5687:] 5682:n 5677:A 5672:[ 5669:d 5660:= 5633:2 5629:1 5625:2 5621:1 5601:) 5596:2 5592:F 5585:1 5582:( 5571:) 5566:1 5562:F 5555:1 5552:( 5540:= 5533:2 5529:k 5523:1 5519:k 5513:= 5472:2 5468:P 5459:2 5455:k 5435:+ 5431:C 5427:+ 5423:B 5419:+ 5410:2 5406:A 5390:1 5386:P 5377:1 5373:k 5353:+ 5349:C 5345:+ 5341:B 5337:+ 5328:1 5324:A 5304:2 5300:1 5283:1 5280:k 5276:3 5273:k 5266:2 5263:k 5259:1 5256:k 5251:1 5248:k 5244:3 5241:k 5237:2 5234:k 5230:1 5227:k 5220:2 5217:k 5213:3 5210:k 5206:3 5203:k 5199:2 5196:k 5192:1 5189:k 5169:] 5166:D 5163:[ 5158:2 5154:k 5148:] 5145:D 5142:C 5139:B 5136:A 5133:[ 5128:3 5124:k 5118:1 5114:k 5107:= 5101:t 5098:d 5093:] 5090:A 5087:[ 5084:d 5055:] 5052:D 5049:C 5046:B 5043:A 5040:[ 5035:1 5031:k 5027:= 5021:t 5018:d 5013:] 5010:A 5007:[ 5004:d 4970:3 4966:k 4962:+ 4959:] 4956:D 4953:[ 4948:2 4944:k 4938:] 4935:D 4932:C 4929:B 4926:A 4923:[ 4918:3 4914:k 4908:1 4904:k 4897:= 4891:t 4888:d 4883:] 4880:A 4877:[ 4874:d 4800:t 4796:t 4785:D 4782:k 4780:/ 4778:H 4775:k 4589:) 4587:D 4584:k 4582:/ 4580:H 4577:k 4573:T 4570:k 4568:/ 4566:H 4563:k 4558:) 4556:T 4553:k 4551:/ 4549:D 4546:k 4542:T 4539:k 4537:/ 4535:H 4532:k 4525:k 4507:H 4504:A 4502:/ 4500:D 4497:A 4482:a 4480:E 4474:- 4467:a 4465:E 4463:- 4460:a 4458:E 4433:Q 4426:A 4421:A 4413:D 4410:A 4408:/ 4406:H 4403:A 4365:β 4349:β 4331:h 4325:2 4321:/ 4317:1 4313:) 4309:E 4306:m 4303:2 4300:( 4295:2 4287:a 4284:2 4278:= 4252:T 4249:R 4245:E 4240:= 4214:) 4202:e 4183:e 4176:( 4154:e 4148:= 4145:Q 4117:T 4114:R 4110:/ 4106:E 4099:e 4095:A 4092:Q 4089:= 4086:k 4034:s 4018:2 4014:/ 4010:1 4001:X 3996:m 3987:2 3983:/ 3979:1 3970:X 3955:X 3951:i 3947:u 3933:. 3914:s 3909:) 3901:D 3896:k 3889:H 3884:k 3878:( 3873:= 3868:s 3863:) 3855:T 3850:k 3843:H 3838:k 3832:( 3815:; 3792:2 3788:/ 3784:1 3776:1 3769:3 3765:/ 3761:1 3753:1 3747:= 3736:D 3731:m 3726:/ 3719:H 3714:m 3705:1 3695:T 3690:m 3685:/ 3678:H 3673:m 3664:1 3653:s 3648:) 3641:) 3633:D 3628:k 3621:H 3616:k 3610:( 3597:) 3589:T 3584:k 3577:H 3572:k 3566:( 3553:( 3531:D 3528:k 3526:/ 3524:H 3521:k 3517:D 3514:k 3512:/ 3510:H 3507:k 3503:D 3497:H 3494:k 3490:D 3487:k 3485:/ 3483:H 3480:k 3476:D 3473:k 3471:/ 3469:H 3466:k 3462:D 3459:k 3457:/ 3455:H 3452:k 3431:D 3428:k 3426:/ 3424:H 3421:k 3417:D 3414:k 3412:/ 3410:H 3407:k 3403:D 3400:k 3398:/ 3396:H 3393:k 3389:D 3386:k 3384:/ 3382:H 3379:k 3375:D 3372:k 3370:/ 3368:H 3365:k 3347:N 3331:i 3329:u 3327:Δ 3322:2 3319:/ 3316:1 3309:D 3306:k 3304:/ 3302:H 3299:k 3293:. 3278:T 3272:B 3267:k 3258:H 3254:i 3246:h 3239:) 3232:2 3228:1 3220:1 3216:( 3207:i 3203:u 3186:H 3183:m 3179:D 3176:m 3168:f 3165:k 3159:, 3141:X 3136:m 3129:f 3124:k 3111:2 3107:1 3093:X 3081:f 3076:k 3063:2 3059:1 3054:= 3048:X 3018:T 3012:B 3007:k 3002:/ 2996:i 2988:h 2985:= 2980:i 2976:u 2962:2 2959:/ 2956:1 2937:i 2929:h 2924:2 2921:1 2916:= 2911:) 2908:0 2905:( 2900:i 2880:− 2877:N 2861:D 2858:k 2856:/ 2854:H 2851:k 2830:i 2826:u 2800:i 2796:u 2779:. 2759:D 2755:i 2751:u 2736:H 2732:i 2728:u 2714:i 2710:u 2683:D 2679:i 2675:u 2665:H 2661:i 2657:u 2648:i 2644:u 2625:, 2608:] 2597:i 2593:u 2584:2 2581:1 2573:) 2570:S 2567:T 2564:( 2558:i 2545:i 2541:u 2532:2 2529:1 2521:) 2518:. 2515:t 2512:c 2509:a 2506:e 2503:r 2500:( 2494:i 2485:[ 2464:} 2459:] 2455:) 2449:D 2445:i 2441:u 2431:H 2427:i 2423:u 2419:( 2414:6 2408:N 2405:3 2400:1 2397:= 2394:i 2383:) 2372:D 2368:i 2364:u 2349:H 2345:i 2341:u 2337:( 2332:7 2320:N 2316:3 2311:1 2308:= 2305:i 2296:[ 2290:2 2287:1 2278:{ 2256:D 2251:k 2244:H 2239:k 2214:i 2212:u 2208:T 2205:B 2202:k 2200:/ 2197:i 2190:i 2188:u 2172:X 2168:q 2166:I 2162:X 2159:M 2151:S 2147:X 2143:X 2139:S 2133:. 2120:E 2117:P 2114:Z 2106:C 2103:X 2100:E 2092:I 2089:M 2086:M 2078:S 2074:= 2066:D 2061:k 2054:H 2049:k 2033:N 2029:N 2020:i 2018:ν 2014:X 2010:i 2008:u 2004:z 2000:y 1996:x 1992:q 1990:( 1988:X 1984:q 1982:I 1978:X 1975:M 1971:X 1963:R 1955:A 1952:N 1944:c 1924:i 1896:B 1893:k 1885:h 1879:. 1864:T 1861:R 1849:i 1829:A 1824:N 1820:c 1817:h 1811:= 1805:T 1799:B 1794:k 1781:i 1773:h 1757:i 1753:u 1729:T 1726:R 1719:i 1699:A 1694:N 1690:c 1687:h 1681:= 1675:T 1669:B 1664:k 1656:i 1648:h 1637:i 1633:u 1617:, 1602:] 1598:) 1592:D 1588:i 1584:u 1574:H 1570:i 1566:u 1562:( 1557:6 1551:N 1548:3 1543:1 1540:= 1537:i 1526:) 1515:D 1511:i 1507:u 1492:H 1488:i 1484:u 1480:( 1475:7 1463:N 1459:3 1454:1 1451:= 1448:i 1439:[ 1433:2 1430:1 1421:e 1416:) 1402:H 1398:i 1394:u 1386:e 1379:1 1369:D 1365:i 1361:u 1353:e 1346:1 1338:6 1332:N 1329:3 1324:1 1321:= 1318:i 1295:H 1291:i 1287:u 1279:e 1272:1 1257:D 1253:i 1249:u 1241:e 1234:1 1226:7 1214:N 1210:3 1205:1 1202:= 1199:i 1188:( 1181:2 1178:1 1172:) 1162:H 1158:z 1154:I 1147:H 1143:y 1139:I 1132:H 1128:x 1124:I 1115:D 1111:z 1107:I 1100:D 1096:y 1092:I 1085:D 1081:x 1077:I 1059:D 1055:z 1051:I 1039:D 1035:y 1031:I 1019:D 1015:x 1011:I 997:H 993:z 989:I 977:H 973:y 969:I 957:H 953:x 949:I 941:( 933:2 930:3 924:) 915:H 910:M 898:D 893:M 884:D 879:M 867:H 862:M 855:( 849:) 835:H 823:D 804:D 792:H 780:( 776:= 768:D 763:k 756:H 751:k 722:D 712:/ 705:H 689:D 686:k 682:H 679:k 630:N 626:α 622:N 618:α 596:N 592:N 588:N 584:N 565:N 451:N 436:N 428:N 383:H 379:L 377:k 368:H 366:k 361:L 359:k 329:( 278:= 267:k 257:k 251:= 221:+ 202:3 185:k 159:3 151:+ 120:+ 101:3 84:k 58:3 50:+

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Knowledge

Kinetic isotope effect

Index