Kinetic isotope effects

What are KIEs?

A kinetic isotope effect (KIE) is a measurement of how much a reaction rate changes upon isotopically labeling the reactant. It is the ratio of reaction rate constants for reactant molecules containing the light and heavy isotopes:

KIE = ^lightk/^heavyk

Primary KIEs are where the labeled atom is directly involved in the bond making and bond breaking steps.

Secondary KIEs involve isotopic labels remote from the where the chemistry is occurring.

Both types of KIE are used to determine TS structures. For example, in dAMP hydrolysis, the primary 9-¹⁵N KIE reported on the extent of C-N bond breakage at the TS, while the secondary 2'-²H KIE gave the conformation of the ribose ring.

What Do KIEs Tell Us?

KIEs tell us about the change in "vibrational environment" of an isotopically labeled atom between the reactant and the TS. By "vibrational environment" we mean the strengths of the bonds (e.g., the stretching and bending force constants) between atoms in a molecule.

When discussing KIEs, we think of molecules as spheres connected together with springs. The strength of each spring reflects the strength of the bond. We treat each spring as a "harmonic oscillator", which means that is vibrates with a frequency that depends on the spring strength and the mass of the sphere (i.e., the isotopic label).

KIEs depend (mostly) on zero point energies (ZPEs). ZPE is the vibrational energy in a bond at 0 K. Atoms cannot be at rest, even at absolute zero, because this would violate the Heisenberg Uncertainty Principle. The ZPE is a function of vibrational frequency, which is in turn a function of the strength of a bond, and the mass of the vibrating atoms.

Strong bonds, light atoms → high ZPE

Weak bonds, heavy atoms → low ZPE

If a bond becomes weaker in the transition state, its ZPE decreases more for the light isotope than the heavy isotope. This means that the activation energy for the light isotope is less than for the heavy isotope and therefore it reacts faster - a KIE.

Once we have measured the experimental KIEs, we use quantum chemical calculations to interpret what they tell us about atoms' vibrational environments and to determine the TS structure with sub-Angstrom accuracy.

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