Semiclassical spin exchange via temperature-dependent transition states

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 wave functions can be computationally demanding, are limited to small systems, and do not offer a mechanistic interpretation. Here, we present a semiclassical transition-state theory (SCTST) derived from first principles to describe the nonadiabatic transition between two states that 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>He</a:mi> <a:mprescripts/> <a:none/> <a:mn>3</a:mn> </a:mmultiscripts> </a:math> and the electronic spin of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Na</b:mi> <b:mprescripts/> <b:none/> <b:mn>23</b:mn> </b:mmultiscripts> </b:math> . SCTST reveals that the reaction proceeds via temperature-dependent transition states, 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 observed weak temperature dependence of the rate. Finally, we showcase the power of SCTST by making predictions for the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mmultiscripts> <c:mi>He</c:mi> <c:mprescripts/> <c:none/> <c:mrow> <c:mn>3</c:mn> </c:mrow> </c:mmultiscripts> <c:mo>+</c:mo> <c:msub> <c:mi>CH</c:mi> <c:mn>3</c:mn> </c:msub> </c:mrow> </c:math> spin-exchange collision in full dimensionality, where we find that the internal degrees of freedom induce symmetry-broken transition states.