Electronic Spin-Dependent Dynamics through the Lens of Angular Momentum Exchange. II. Insights from a Model System

This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we highlighted how spin- orbit coupling introduces electronic spin-dependence in the dynamics. Electronic spin- dependence emerges in the nuclear equations of motion through the non-adiabatic couplings, which serve as conduits for angular momentum transfer between electrons and nuclei. In addition, the non-adiabatic couplings are shaped by the topology of the electronic Hilbert space. Here in Part II, we illustrate these concepts through the analysis of a one-electron triatomic E′ ⊗e′ Jahn–Teller model. In the spin-independent case, this system represents a prototype cylindrically symmetric model featuring a con- ical intersection, which disappears once spin-orbit coupling is included. Starting from total angular momentum conservation, we find that in the body-fixed frame of our model, angular momentum transfer occurs between the electron and nuclear vibra- tions. In the spin-dependent dynamics, this manifests as an asymmetric dispersion of an angular-momentum-free initial wave packet, contrasting the symmetric evolution in the spin-independent case. This asymmetry is mirrored for the two spin direc- tions, providing a mechanism to differentiate spin states. The full implications of this mechanism in more realistic systems remains an open question.