Semiclassical Spin Exchange via Temperature-Dependent Transition States

Abstract: Spin-exchange collisions have been widely studied in recent years, and various quantum-mechanical scattering approaches have been developed to calculate the rates. However, these methods based on global knowledge of wavefunctions can be computationally demanding and do not offer a simple mechanistic interpretation. Here, we present a new semiclassical transition-state theory (SCTST) derived from first principles to describe the nonadiabatic transition between two states which differ only in their spins, where classical TST and Landau--Zener theory fail. We apply our theory to describe the spin-exchange collision between the nuclear spin of 3He and the electronic spin of 23Na. SCTST reveals that the reaction proceeds via a temperature-dependent transition state, determined by an intricate compromise between minimizing the activation energy and maximizing the hyperfine coupling. It further demonstrates the importance of quantum delocalization effects prevalent in spin exchange even when tunneling is suppressed and successfully explains the weak temperature dependence of the rate. Moreover, since it depends only on local information at a single point, the computational cost is significantly reduced.