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Kinetic isotope effect
In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for the reactions involving the light (kL) and the heavy (kH) isotopically substituted reactants (isotopologues): KIE = kL/kH.
This change in reaction rate 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 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 a unimolecular (SN1) or bimolecular (SN2) pathway.
In the reaction of methyl bromide and cyanide (shown in the introduction), the observed methyl carbon KIE is 1.082, a small effect which indicates an SN2 mechanism in which the C-Br bond is formed as the C-CN bond is broken. For SN1 reactions in which the leaving group leaves first to form a trivalent carbon transition state, the KIE is close to the maximum observed value for a secondary KIE (SKIE, see below) of 1.22. 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 the relative mass change is greatest, since the effect is related to vibrational frequencies of the affected bonds. Thus, replacing normal hydrogen (1H) with its isotope deuterium (D or 2H), 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–1H bond is typically 6–10x faster than with a C–2H bond, whereas a 12C reaction is only 4% faster than the corresponding 13C 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 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 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: 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 the α-carbon can be used to develop some understanding into the symmetry of the transition state in SN2 reactions, though this KIE is less sensitive than what would be ideal, also due to contribution from non-vibrational factors.
Kinetic isotope effect
In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for the reactions involving the light (kL) and the heavy (kH) isotopically substituted reactants (isotopologues): KIE = kL/kH.
This change in reaction rate 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 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 a unimolecular (SN1) or bimolecular (SN2) pathway.
In the reaction of methyl bromide and cyanide (shown in the introduction), the observed methyl carbon KIE is 1.082, a small effect which indicates an SN2 mechanism in which the C-Br bond is formed as the C-CN bond is broken. For SN1 reactions in which the leaving group leaves first to form a trivalent carbon transition state, the KIE is close to the maximum observed value for a secondary KIE (SKIE, see below) of 1.22. 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 the relative mass change is greatest, since the effect is related to vibrational frequencies of the affected bonds. Thus, replacing normal hydrogen (1H) with its isotope deuterium (D or 2H), 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–1H bond is typically 6–10x faster than with a C–2H bond, whereas a 12C reaction is only 4% faster than the corresponding 13C 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 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 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: 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 the α-carbon can be used to develop some understanding into the symmetry of the transition state in SN2 reactions, though this KIE is less sensitive than what would be ideal, also due to contribution from non-vibrational factors.