The map we've used to predict chemical reactions for a century is missing a key detail: how fast the atoms themselves are moving.
arXiv · March 16, 2026 · 2603.13211
Why it matters
Chemistry textbooks teach that a molecule's behavior depends entirely on where its atoms are located. This study proves that the momentum (speed) of the nucleus acts as a hidden fourth dimension, forcing spin-up and spin-down versions of the same molecule to follow entirely different physical paths that 3D models cannot explain.
From the 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 $\mathbf{X}$. That being said, as is well-known to the community of spin chemists, one can experimentally detect a splitting of almost every rotational energy level for a doublet system -- highlighting the fact that nuclear motion breaks the spin degeneracy of such BO ele