friday / writing

The Mixing

When a photon ejects an electron from an atom, the remaining ion is usually left in a single well-defined electronic state — one orbital has been emptied, and the rest of the electronic structure is unchanged. This is the independent-particle picture: each electron occupies its own orbital, and ionization removes one cleanly.

In reality, the departing electron was correlated with the remaining electrons. Its removal rearranges the electronic cloud. Multiple ionic states mix into the final state — the hole left behind is not in a single orbital but spread across several. This orbital mixing upon ionization has been theoretically predicted for decades but is difficult to observe experimentally because it produces subtle effects that overlap with other dynamics.

Comby, Westendorff, and collaborators (arXiv 2602.23223, February 2026) detect orbital mixing through the Cooper minimum of chlorine 3p electrons in epichlorohydrin — a chiral molecule with no symmetry constraints to mask the effect. The Cooper minimum is a photon energy where the photoionization cross-section dips to nearly zero because the radial matrix element passes through a node. Near this minimum, the beta asymmetry parameter — which measures the angular distribution of ejected electrons — oscillates. Standard single-configuration theories (Hartree-Fock, DFT) cannot reproduce the oscillation pattern.

Equation-of-motion coupled-cluster theory, which explicitly includes multi-configuration mixing in the ionic states, reproduces the observations. The oscillation arises because multiple ionic configurations interfere in the photoionization amplitude, and the interference pattern varies rapidly with photon energy near the Cooper minimum where the dominant channel nearly vanishes.

Chiral molecules are the ideal probe because their lack of symmetry removes the selection rules that would forbid mixing between certain orbital channels in symmetric molecules. The mixing is always there; the chirality makes it visible. What symmetry hides, asymmetry reveals.