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, will have lower zero-point energy. With a lower zero-point energy, 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). Classification Primary kinetic isotope effects A primary kinetic isotope effect may be found when a bond to the isotopically labeled atom is being formed or broken. Depending on the way a kinetic isotope effect is probed (parallel measurement of rates vs. intermolecular competition vs. intramolecular competition), the observation of a primary kinetic isotope effect 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 primary kinetic isotope effect must reflect bond cleavage/formation to the isotope at the rate-limiting step is frequently repeated in textbooks and the primary literature: see the section on experiments below.) For the previously mentioned nucleophilic substitution reactions, primary kinetic isotope effects have been investigated for both the leaving groups, the nucleophiles, and the α-carbon at which the substitution occurs. Interpretation of the leaving group kinetic isotope effects had been difficult at first due to significant contributions from temperature independent factors. Kinetic isotope effects at the α-carbon can be used to develop some understanding into the symmetry of the transition state in SN2 reactions, although this kinetic isotope effect is less sensitive than what would be ideal, also due to contribution from non-vibrational factors. Secondary kinetic isotope effects A secondary kinetic isotope effect is observed when no bond to the isotopically labeled atom in the reactant is broken or formed. Secondary kinetic isotope effects tend to be much smaller than primary kinetic isotope effects; however, secondary deuterium isotope effects can be as large as 1.4 per deuterium atom, and techniques have been developed to measure heavy-element isotope effects to very high precision, so secondary kinetic isotope effects are still very useful for elucidating reaction mechanisms. For the aforementioned nucleophilic substitution reactions, secondary hydrogen kinetic isotope effects at the α-carbon provide a direct means to distinguish between SN1 and SN2 reactions. It has been found that SN1 reactions typically lead to large secondary kinetic isotope effects, approaching to their theoretical maximum