Post 9 ended on a question: does ZSA electronic character — Mott-Hubbard vs charge-transfer — predict which GKA exchange pathway actually wins? This post tests the coupling step from post 1's original roadmap.
Posts 5 and 6 treated the electronic side — Δ, bond length, coordination number against band gap — and post 9 treated the magnetic side — M–X–M angle and d-electron count against ordering type, via GKA reasoning. Both posts used the same underlying quantities (bond length, angle, d-filling) but never crossed over. Post 1's roadmap explicitly listed coupling as its own step, separate from either side alone, on the bet that electronic character changes how reliably the magnetic rules apply — not just what the band gap looks like.
Why coupling might exist
The GKA rules assume a clean superexchange pathway through the anion p-orbital. But how much that pathway is mediated by the anion versus gated by on-site correlation on the metal depends on exactly the quantity post 4 introduced for the electronic side: the ZSA charge-transfer energy ΔCT = εd − εp − U/2. In a charge-transfer compound (ΔCT clearly negative, anion p-states close to or above the metal d-states), the exchange pathway runs mostly through the anion and should track the simple GKA angle picture closely. In a Mott-Hubbard compound (ΔCT clearly positive, large U dominating), the same nominal pathway is gated by U in a way that can suppress, strengthen, or even invert the naive angle-based prediction depending on filling. If that's right, GKA-based predictions should be systematically more reliable for charge-transfer compounds than for Mott-Hubbard ones — a testable, falsifiable claim rather than a vague intuition.
Application: electronic–magnetic coupling map
The widget below crosses ΔCT (x-axis) against M–X–M angle (y-axis). Two regions are where GKA should apply cleanly; two are flags — either a U-gated pathway where the simple angle rule is expected to be unreliable, or the ΔCT ≈ 0 boundary zone where the dominant mechanism itself is ambiguous. Click a region for the reasoning.
Electronic–magnetic coupling map
ΔCT (x-axis) vs M–X–M angle (y-axis). Click a region to see the reasoning.
Reasoning
Click a region above for the reasoning behind that combination.
Schematic boundaries from the coupling hypothesis above — the dataset test is whether the “flag” regions actually show more scatter in observed ordering than the “clean” regions.
What counts as a successful coupling, and what counts as a flag
This hypothesis is falsifiable in a specific way: pull the real dataset, split it into the four regions above, and check whether observed ordering types actually cluster tightly with GKA predictions in the “clean” regions and scatter more in the “gated” and “boundary” regions. If they do, electronic character is adding real information beyond geometry alone, and any later formula (post 11) should include cross-terms between ΔCT/U and the angle-based descriptors, not just treat them additively. If the scatter is roughly the same everywhere, that's still a useful result — it would mean the angle-only GKA picture is doing most of the work on its own, and the electronic descriptors are redundant for predicting ordering type specifically, even though they remain essential for the band gap side.
Where this leads
Either outcome feeds directly into the next post: a symbolic regression pass over the full 27-feature set from the v6.0 pipeline, looking for an explicit formula rather than a feature-importance ranking. If the coupling tested here is real, that search should be told to consider interaction terms between the electronic and magnetic descriptor groups; if it isn't, the search can stay additive and the descriptor list gets simpler.
My name is Dr Abderrahmane Reggad. I'm a 54 year old and I am a researcher in materials' sciences.
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