Kinetic Isotope Effects (CHEM 2087)

This set covers vocabulary and concepts related to primary, secondary, and solvent kinetic isotope effects, including mathematical models, transition state theory, and specific chemical examples.

Kinetic Isotope Effects (KIE)

Kinetic effects resulting from an isotope change at the bond being broken, elsewhere in the reacting molecule, or in the solvent.

Primary Isotope Effect ($1^\circ$)

A kinetic isotope effect that occurs specifically at the bond being broken during the rate-determining step.

Secondary Isotope Effect ($2^\circ$)

A kinetic isotope effect that occurs due to an isotopic change made elsewhere in the reacting molecule (not at the bond being broken).

Solvent Isotope Effect

A kinetic isotope effect resulting from changing the hydrogen atoms of the solvent to deuterium, such as using $D_2O$ instead of $H_2O$.

Reduced Mass ($\mu$)

A physical quantity altered by a change in isotope, calculated for two atoms X and Y as $\mu = \frac{m_Xm_Y}{m_X + m_Y}$, which determines the vibrational frequency in the Harmonic Oscillator Model.

Harmonic Oscillator Model of Bond Vibration

A model defined by the equation \nu = \frac{1}{2\pi} \sqrt{rac{k}{\mu}} where vibrational frequency ($\nu$) depends on the force constant ($k$) and reduced mass ($\mu$).

Zero Point Energy ($E_0$)

The lowest possible energy that a quantum mechanical physical system may have, defined as $E_0 = \frac{1}{2} h\nu$. The difference in these energies for C–H and C–D bonds originates the kinetic isotope effect.

C–D vs. C–H Bond Dissociation Energy

The bond dissociation energy for C–D is approximately $5\,kJ\,mol^{-1}$ more than for C–H, meaning the heavier isotope bond is harder to break.

Symmetric Stretch

The specific type of vibration at the transition state that is the primary consideration for deciding the magnitude of a kinetic isotope effect.

Maximum Primary Isotope Effect

An effect of $k_H/k_D \approx 5-7$ observed when the hydrogen atom is half-transferred in the transition state.

Early Transition State (KIE)

A state where the hydrogen atom is still strongly bonded to the reactant site, resulting in no observed primary isotope effect.

Late Transition State (KIE)

A state where the hydrogen atom is almost completely transferred to the product site, resulting in no observed primary isotope effect.

Acetate ion catalysed enolisation of acetone

An example of rate-determining C–H bond breaking showing a primary isotope effect with a $k_H/k_D \approx 5$.

$\alpha$-Secondary Isotope Effect

A small kinetic isotope effect observed when a hydrogen atom attached to one of the reacting atoms is changed for deuterium, often due to hybridisation changes.

Normal $\alpha$-Secondary KIE

A $k_H/k_D$ value between 1 and 1.4, observed when the rate-determining step involves a decrease in p-orbital character (e.g., $sp^3$ to $sp^2$).

Inverse $\alpha$-Secondary KIE

A $k_H/k_D$ value between 0.7 and 1.0, observed when the rate-determining step involves an increase in p-orbital character (e.g., $sp^2$ to $sp^3$).

$\beta$-Secondary Isotope Effect

A kinetic isotope effect observed mainly for carbocation-forming reactions when a $\beta$-hydrogen to the developing cationic carbon is changed for deuterium.

Hyperconjugation (KIE Origin)

The overlap of a bonding $\beta$-C–H $\sigma$-orbital with an empty p-orbital; it stabilizes a carbocation centre more effectively than a $\beta$-C–D $\sigma$-orbital, leading to a normal $2^\circ$ KIE.

Autoprotolysis Constant of $D_2O$ ($K_D$)

The equilibrium constant for the self-ionization of heavy water, which is $10^{-14.87}$, compared to $10^{-14}$ for $H_2O$, making $H_2O$ more acidic.

Primary Solvent Isotope Effect

Occurs when a proton comes from the solvent in the rate-determining step, such as the acetate anion catalysed hydrolysis of phenyl acetate.