Can a Secondary Isotope Effect Be Larger than a Primary?

Primary and secondary ¹⁸O equilibrium isotope effects on the acidities of a variety of Brønsted and Lewis acids centered on carbon, boron, nitrogen, and phosphorus were computed by density-functional theory. For many of these acids, the secondary isotope effect was found to be larger than the primary isotope effect. This is a counterintuitive result, because the H atom that is lost is closer to the ¹⁸O atom that is responsible for the primary isotope effect. The relative magnitudes of the isotope effects can be associated with the vibrational frequency and zero-point energy of the XO vibrations, which are greater than those of the XO vibrations. However, the difference between these contributions is small, and the major responsibility for the larger secondary isotope effect comes from the moment-of-inertia factor, which depends on the position of the ¹⁸O atom relative to the principal axes of rotation