Theory of classical kinetic isotope effects in evaporation

Isotopic fractionation resulting from kinetic isotope effects (KIEs) in evaporation is a key to investigating high-temperature evaporation events in the early Solar System. The magnitude of the KIEs is represented by the kinetic isotope fractionation factor $\alpha$, which is predicted as $\alpha ={\left(m_H/m_L\right)}^{1/2}$ ($m_L/m_H$: the mass ratio of the isotopic evaporated gas species) to a first approximation based on the Hertz-Knudsen equation. However, the experimentally measured $\alpha$ are often closer to 1 than this prediction to various degrees. In this study, we investigated the reason for this observation based on the transition state theory. To evaluate the classical (high-temperature) limit of $\alpha$, which is given by the isotopic ratio of the imaginary frequencies representing the evaporative motion at the transition state, we constructed a simple model for the vibrational normal mode analysis. In this model, we included the interaction of the evaporating species with the condensed phase surface and the degrees of freedom of atoms in the condensed phase. The present theory clarified the relationship between the magnitude of the evaporative KIEs and the properties of the potential energy surface: the classical limit of $\alpha$ becomes closer to 1 than ${\left(m_H/m_L\right)}^{1/2}$ due to the effect of the condensed-phase degrees of freedom when there exists a potential energy barrier, which is related to unstable interaction between the evaporating species and the condensed phase surface. This result is consistent with the previous experimental data and provides general insights into classical KIEs in chemical reactions.