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75-707: LPO may refer to: Lipid peroxidation LPO-50 , a flamethrower built by the Soviet Union Law practice optimization Landing Page Optimization Leading Petty Officer Legal Process Outsourcing Lexicographic path ordering , a well-ordering in term rewriting (computer science) Libertarian Party of Ohio Libration point orbit Licensed Post Office Limited principle of omniscience London Philharmonic Orchestra Louisiana Philharmonic Orchestra Lactoperoxidase , an antibacterial protein present in milk and saliva Topics referred to by

150-406: A kinetic isotope effect ( KIE ) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes . Formally, it is the ratio of rate constants for the reactions involving the light ( k L ) and the heavy ( k H ) isotopically substituted reactants ( isotopologues ): KIE = k L /k H . This change in reaction rate

225-496: A unimolecular (S N 1) or bimolecular (S N 2) pathway. In the reaction of methyl bromide and cyanide (shown in the introduction), the observed methyl carbon KIE indicates an S N 2 mechanism. Depending on the pathway, different strategies may be used to stabilize the transition state of the rate-determining step of the reaction and improve the reaction rate and selectivity, which are important for industrial applications. Isotopic rate changes are most pronounced when

300-424: 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

375-468: A correction factor. 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. In many cases and especially for hydrogen-transfer reactions, contributions to KIEs from tunneling are significant (see below). In some cases,

450-470: A few criteria are considered: Also for reactions where isotopes include H, D and T, a criterion of tunneling is the Swain-Schaad relations which compare the rate constants ( k ) of the reactions where H, D or T are exchanged: In organic reactions, this proton tunneling effect has been observed in such reactions as the deprotonation and iodination of nitropropane with hindered pyridine base with

525-497: A further rate enhancement is seen for the lighter isotope, possibly due to quantum tunneling . 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 classical mechanics , particles can pass through classically forbidden regions of space in quantum mechanics based on wave–particle duality . Tunneling can be analyzed using Bell's modification of

600-417: 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 [A···H···B] 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. To calculate

675-419: A lipid hydroperoxyl radical ( LOO• ). The lipid hydroperoxyl radical ( LOO• ) can further abstract hydrogen from a new PUFA substrate, forming another lipid radical ( L• ) and now finally a lipid hydroperoxide (LOOH). The lipid hydroperoxyl radical ( LOO• ) can also undergo a variety of reactions to produce new radicals. The additional lipid radical ( L• ) continues the chain reaction , whilst

750-526: A pre-equilibrium, so that the C-H bond cleavage occurs somewhere before the rate-determining step.) 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 inferred from

825-435: A reported KIE of 25 at 25°C: and in a 1,5-sigmatropic hydrogen shift , though it is observed that it is hard to extrapolate experimental values obtained at high temperature to lower temperatures: 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

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900-400: Is a quantum effect that occurs mainly because heavier isotopologues have lower vibrational frequencies than their lighter counterparts. In most cases, this implies a greater energy input needed for heavier isotopologues to reach the transition state (or, in rare cases, dissociation limit ), and therefore, a slower reaction rate. The study of KIEs can help elucidate reaction mechanisms , and

975-423: Is a substrate, isomers of hydroperoxyeicosatetraenoic acid (HPETEs) and hydroxyeicosatetraenoic acids (HETEs) are formed. Antioxidants play a crucial role in mitigating lipid peroxidation by neutralizing free radicals, thereby halting radical chain reactions. Key antioxidants include vitamin C and vitamin E . Additionally, enzymes including superoxide dismutase , catalase , and peroxidase contribute to

1050-510: 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 k H and k D . 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

1125-593: Is being generated one carbon atom away (a β SKIE). These isotope effects have a theoretical maximum of k H / k D = 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 k H / k D = 2 ≈ 0.7. In practice, k H / k D ~ 1.1-1.2 and k H /k D ~ 0.8-0.9 are typical for α SKIEs, while k H / k D ~ 1.15-1.3 are typical for β SKIE. For reactants containing several isotopically substituted β-hydrogens,

1200-452: Is best illustrated by the lethal phenotype of glutathione peroxidase 4 ( GPX4 ) knockout mice. These animals do not survive past embryonic day 8, indicating that the removal of lipid hydroperoxides is essential for mammalian life. It is unclear whether dietary lipid peroxides are bioavailable and play a role in disease, as a healthy human body has protective mechanisms in place against such hazards. Certain diagnostic tests are available for

1275-539: Is different from Wikidata All article disambiguation pages All disambiguation pages Lipid peroxidation In pathology and medicine , lipid peroxidation plays a role in cell damage which has broadly been implicated in the pathogenesis of various diseases and disease states, including ageing , whereas in food science lipid peroxidation is one of many pathways to rancidity . The chemical reaction of lipid peroxidation consists of three phases: initiation , propagation , and termination . In

1350-432: Is greatest for small barrier widths. Optimal tunneling distances of protons between donor and acceptor atom is 40 pm. Tunneling is a quantum effect tied to the laws of wave mechanics, not kinetics . 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. Peter S. Zuev et al. reported rate constants for

1425-469: 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 possibilities. Starting materials containing H are often commercially available, making the synthesis of isotopically enriched starting materials relatively straightforward. Also, due to

1500-420: Is occasionally exploited in drug development to improve unfavorable pharmacokinetics by protecting metabolically vulnerable C-H bonds. 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 nucleophilic substitution reaction follows

1575-451: Is often found that tunneling is a major factor when they do exceed such values. A value of k H / k D ~ 10 is thought to be maximal for a semi-classical PKIE (no tunneling) for reactions at ≈298 K. (The formula for k H / k D 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);

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1650-427: Is only 4% faster than the corresponding C reaction; even though, in both cases, the isotope is one atomic mass unit (amu) ( dalton ) heavier. 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 vibrational frequency of the chemical bond that it forms, even if the potential energy surface for

1725-417: Is the reaction carried out by alcohol dehydrogenase . Competitive KIEs for the hydrogen transfer step at 25°C resulted in 3.6 and 10.2 for primary and secondary KIEs, respectively. Isotopic effect expressed with the equations given above only refer to reactions that can be described with first-order kinetics . In all instances in which this is not possible, transient KIEs should be taken into account using

1800-446: Is unique to the transition state). The simplified formula above, predicts a maximum for k H / k D as 6.9. If the complete disappearance of two bending vibrations is also included, k H / k D 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 k H / k D values exceed 7-8 near room temperature. Furthermore, it

1875-599: The Arrhenius equation , which includes the addition of a tunneling factor, Q: where A is the Arrhenius parameter, E is the barrier height and where α = E R T {\displaystyle \alpha ={\frac {E}{RT}}} and β = 2 a π 2 ( 2 m E ) 1 / 2 h {\displaystyle \beta ={\frac {2a\pi ^{2}(2mE)^{1/2}}{h}}} Examination of

1950-474: The Born–Oppenheimer approximation , 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

2025-415: The initiation phase, a pro-oxidant hydroxyl radical ( OH• ) abstracts the hydrogen at the allylic position (–CH 2 –CH=CH 2 ) or methine bridge (=CH−) on the stable lipid substrate, typically a polyunsaturated fatty acid (PUFA), to form the lipid radical ( L• ) and water (H 2 O). In the propagation phase, the lipid radical ( L• ) reacts with molecular oxygen ( O 2 ) to form

2100-429: The oxidation response by reducing the presence of hydrogen peroxide , which is a prevalent precursor of the hydroxyl radical ( OH• ). As an example, vitamin E can donate a hydrogen atom to the lipid hydroperoxyl radical ( LOO• ) to form a vitamin E radical, which further reacts with another lipid hydroperoxyl radical ( LOO• ) forming non-radical products. Phototherapy may cause lipid peroxidation, leading to

2175-509: The β 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 observed that can not be accounted for by differences in ZPEs. Also, the β term depends linearly with barrier width, 2a. As with mass, tunneling

2250-504: The GEBIK and GEBIF equations. Simmons and Hartwig refer to the following three cases as the main types of KIE experiments involving C-H bond functionalization: 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

2325-458: 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(- u i ) = exp(- hν i / k B T ) < 0.01 at 298 K, resulting in negligible contributions from the 1–exp(- u i ) factors). Hence, for hydrogen/deuterium KIEs,

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2400-401: 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. The theoretical treatment of isotope effects relies heavily on transition state theory , which assumes a single potential energy surface for the reaction, and a barrier between the reactants and

2475-449: 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

2550-407: The accuracy with which each of these rate constants can be 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

2625-565: The aforementioned nucleophilic substitution reactions, secondary hydrogen KIEs at the α-carbon provide a direct means to distinguish between S N 1 and S N 2 reactions. It has been found that S N 1 reactions typically lead to large SKIEs, approaching to their theoretical maximum at about 1.22, while S N 2 reactions typically yield SKIEs that are very close to or less than 1. KIEs greater than 1 are called normal kinetic isotope effects , while KIEs less than 1 are called inverse kinetic isotope effects (IKIE). In general, smaller force constants in

2700-449: 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 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

2775-412: The context of isotope effects, hydrogen often means the light isotope, protium ( H), specifically. In the rest of this article, reference to hydrogen and deuterium in parallel grammatical constructions or direct comparisons between them should be interpreted as meaning H and H. The theory of KIEs was first formulated by Jacob Bigeleisen in 1949. Bigeleisen's general formula for H KIEs (which

2850-418: The donor and acceptor atom close to the optimal tunneling distance, 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

2925-445: The energy barrier, quantum tunnelling 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. 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 density functional theory calculations

3000-567: The energy surface of a reaction but can "leak out" into the next energy minimum. In light of this, tunneling should be temperature independent. 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 preexponential factor ratios A H / A D ranging from 0.43 to 0.54 and large activation energy differences from 9.0 to 9.7 kJ/mol. Basing their arguments on transition state theory ,

3075-507: 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. 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. Another example of tunneling contribution to proton transfer in enzymatic reactions

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3150-571: The extent to which a primary H isotope effect approaches this maximum, varies. A model developed by Westheimer predicted that symmetrical (thermoneutral, by Hammond's postulate ), 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. For secondary H isotope effects, Streitwieser proposed that weakening (or strengthening, in

3225-410: The factor of ⁠ 1 / 2 ⁠ and the sums of u i = h ν i / k B T {\displaystyle u_{i}=h\nu _{i}/k_{\mathrm {B} }T} 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

3300-756: The general expression given above using some simplifications: i.e., 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 u i X ∝ μ X − 1 / 2 ≅ m X − 1 / 2 {\displaystyle u_{i\mathrm {X} }\propto \mu _{\mathrm {X} }^{-1/2}\cong m_{\mathrm {X} }^{-1/2}} ; X = H. The subscript " s " refers to these "semi-classical" KIEs, which disregard quantum tunneling. Tunneling contributions must be treated separately as

3375-472: The isotope at the rate-limiting step is often repeated in textbooks and the primary literature: see the section on experiments below. ) 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 independent factors. KIEs at

3450-486: 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

3525-405: The lipid hydroperoxide (LOOH) is the primary end product. The formation of lipid radicals is sensitive to the kinetic isotope effect . Reinforced lipids in the membrane can suppress the chain reaction of lipid peroxidation. The termination step can vary, in both its actual chemical reaction and when it will occur. Lipid peroxidation is a self-propagating chain reaction and will proceed until

3600-422: The lipid substrate is consumed and the last two remaining radicals combine, or a reaction which terminates it occurs. Termination can occur when two lipid hydroperoxyl radicals ( LOO• ) react to form peroxide and oxygen (O 2 ). Termination can also occur when the concentration of radical species is high. The primary products of lipid peroxidation are lipid hydroperoxides (LOOH). When arachidonic acid

3675-435: 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 [3000 – 2200 cm ]/2 = 400 cm ≈ 1.15 kcal/mol), without any compensation from a ZPE difference at the transition state (e.g., from the symmetric A···H···B stretch, which

3750-405: 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: 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 S (containing σ X ) is the ratio of the symmetry numbers for

3825-530: 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 k H / k D > 2 are not uncommon. The following simple expressions relating H and H KIEs, which are also known as the Swain equation (or the Swain-Schaad-Stivers equations), can be derived from

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3900-421: The observed values are typically dominated by the last factor, ZPE (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: where we define The sums in the exponent of the second expression can be interpreted as running over all vibrational modes of

3975-538: 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 harmonic oscillator is a good approximation for a vibrating bond, at least for low-energy vibrational states. Quantum mechanics gives the vibrational ZPE as ϵ i ( 0 ) = 1 2 h ν i {\displaystyle \epsilon _{i}^{(0)}={\frac {1}{2}}h\nu _{i}} . Thus, we can readily interpret

4050-440: 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

4125-476: The quantification of the end-products of lipid peroxidation, to be specific, malondialdehyde (MDA). The most commonly used test is called a TBARS Assay ( thiobarbituric acid reactive substances assay). Thiobarbituric acid reacts with malondialdehyde to yield a fluorescent product. However, there are other sources of malondialdehyde, so this test is not completely specific for lipid peroxidation. Kinetic isotope effect In physical organic chemistry ,

4200-468: 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 MMI factor is usually also approximated as unity. The EXC factor (containing the product of vibrational partition functions ) corrects for

4275-571: 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 change substantially upon advancing along the reaction coordinate. The remaining pairs of reactant and transition state vibrational modes have very similar Δ u i {\displaystyle \Delta u_{i}} and Δ u i ‡ {\displaystyle \Delta u_{i}^{\ddagger }} , and cancellations occur when

4350-458: The reaction is nearly identical. Heavier isotopes will ( classically ) lead to lower vibration frequencies, or, viewed quantum mechanically , have lower zero-point energy (ZPE). With a lower ZPE, more energy must be supplied to break the bond, resulting in a higher activation energy for bond cleavage, which in turn lowers the measured rate (see, for example, the Arrhenius equation ). A primary kinetic isotope effect (PKIE) may be found when

4425-412: The relative mass change is greatest, since the effect is related to vibrational frequencies of the affected bonds. Thus, replacing normal hydrogen ( H) with its isotope deuterium (D or H), doubles the mass; whereas in replacing carbon-12 with carbon-13 , 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

4500-463: 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

4575-404: 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 constant is temperature independent and the tunneling contribution to the rate was 152 orders of magnitude greater than the contribution of passage over

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4650-584: The rupture of red blood cell cell membranes. End-products of lipid peroxidation may be mutagenic and carcinogenic . For instance, the end-product MDA reacts with deoxyadenosine and deoxyguanosine in DNA, forming DNA adducts to them, primarily M 1 G . Reactive aldehydes can also form Michael adducts or Schiff bases with thiol or amine groups in amino acid side chains. Thus, they are able to inactivate sensitive proteins through electrophilic stress. The toxicity of lipid hydroperoxides to animals

4725-427: 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

4800-403: The same term [REDACTED] This disambiguation page lists articles associated with the title LPO . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=LPO&oldid=1116235200 " Category : Disambiguation pages Hidden categories: Short description

4875-896: 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 κ H / κ D {\displaystyle \kappa _{\mathrm {H} }/\kappa _{\mathrm {D} }} term resulting from an isotopic difference in transmission coefficients should also be included. ) where we define Here, h = Planck constant ; k B = Boltzmann constant ; ν ~ i {\displaystyle {\tilde {\nu }}_{i}} = frequency of vibration, expressed in wavenumber ; c = speed of light ; N A = Avogadro constant ; and R = universal gas constant . The σ X (X = H or D) are

4950-414: The small A 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 A factor ratio for the various paraffins they used was roughly constant throughout the temperature range. To determine if tunneling is involved in KIE of a reaction with H or D,

5025-433: The square root of the reduced mass of the vibrating system: where k f is the force constant . Moreover, the reduced mass is approximated by the mass of the light atom of the system, X = H or D. Because m D ≈ 2 m H , In the case of homolytic C–H/D bond dissociation, the transition state term disappears; and neglecting other vibrational modes, k H / k D = exp( ⁠ 1 / 2 ⁠ Δ u i ). Thus,

5100-449: 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 k H / k D possible. 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

5175-430: The symmetry numbers for the reactants and transition states. The M X are the molecular masses of the corresponding species, and the I q X ( q = x , y , or z ) terms are the moments of inertia about the three principal axes. The u i X are directly proportional to the corresponding vibrational frequencies, ν i , and the vibrational zero-point energy (ZPE) (see below). The integers N and N are

5250-409: 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. The magnitudes of such SKIEs at the α-carbon atom are largely determined by the C α -H( H) vibrations. For an S N 1 reaction, since the carbon atom is converted into an sp hybridized carbenium ion during

5325-409: The transition state energy barrier. 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 product is not confined to the energy well of a particular trough along

5400-444: The transition state for the rate-determining step with an increase in C α -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 N 2 reactions, bending vibrations still play an important role for

5475-429: 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 N− 6 vibrational modes for the starting material and 3 N − 7 vibrational modes at the transition state (one mode,

5550-423: 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 X (reactant and transition state) will be unity; thus S can often be neglected. The MMI factor (containing the M X and I q X ) refers to

5625-675: The α-carbon can be used to develop some understanding into the symmetry of the transition state in S N 2 reactions, though this KIE is less sensitive than what would be ideal, also due to contribution from non-vibrational factors. A secondary kinetic isotope effect (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. For

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