Conceptual Shift in Our Understanding of Degenerate Radical Spin Systems: Spin-Rotation Coupling Turned on Its Head

Abstract

For most chemists, Kramers’ degeneracy refers to the fact that for any radical system, every potential energy surface is at least doubly degenerate (with spin up and spin down, time-reversed solutions) for all nuclear positions X. Yet, as is well-known to the community of spin chemists, one can experimentally detect a splitting of most rotational levels for a doublet system, highlighting that nuclear motion breaks the spin degeneracy of such Born–Oppenheimer (BO) electronic states. Thus, the implications of BO degeneracy are very limited for spectroscopy unless one further includes nuclear-electronic entanglement in a robust fashion; indeed, understanding radical molecules (and the degeneracy of their stationary states) can be quite nonintuitive within the paradigm of BO potential energy surfaces. As an alternative to BO theory, recent developments have suggested characterizing radical potential energy surfaces as functions of both nuclear position X and nuclear momentum P, an approach which has been shown to recover a host of observables outside of BO theory, e.g., vibrational circular dichroism, Raman optical activity, and lambda-doubling. Here, we show that such a technique predicts that different spin states will follow different (nondegenerate) potential energy surfaces and that the differences in these spin-dependent surfaces are quantitatively consistent with experimental spin-rotation couplings─all without contradiction to overall Kramers’ degeneracy. Thus, the present finding suggests that there is still much to learn about spin-resolved molecular reactivity, demanding a conceptual shift in our understanding of coupled spin-nuclear motion, especially in chiral molecules and materials where spin-separation is known to arise.