TM Chalcogenides · Research Series

Raw structural fields become ML-ready descriptors: crystal field splitting Δ, GKA exchange indicators, Mott criterion, ZSA classification, and electronegativity difference — each grounded in a physical mechanism.

Research

The unified table now has raw fields: lattice parameters, bond lengths, bond angles, d-electron count, the property block, provenance. None of that is directly useful to a regression model yet — what matters is the combinations that map onto known physics. This post is the list of descriptors I'm computing, and the reasoning behind each one.

Electronic-side descriptors

  • Crystal field splitting Δ — estimated from M–X bond length via Δ ∝ 1/d⁵ for octahedral coordination, scaled to a reference value per transition metal series. Sets the t₂g/eg energy separation.
  • d-electron count — from the formal oxidation state of M. Combined with Δ, determines high-spin vs low-spin configuration.
  • Electronegativity difference (M − X) — a proxy for ionic vs covalent bonding character, which shifts where the chalcogen p-band sits relative to the metal d-band.
  • Zaanen-Sawatzky-Allen indicator — a derived flag comparing the charge-transfer energy Δ_CT (M d-level to X p-level) against the Hubbard U, classifying the compound as Mott-Hubbard-like or charge-transfer-like.

Magnetic-side descriptors

  • M–X–M superexchange angle — directly from structure. Central to Goodenough-Kanamori-Anderson: near-180° favors strong antiferromagnetic superexchange for half-filled orbitals, near-90° often favors ferromagnetic coupling.
  • GKA rule indicator — a categorical feature encoding the expected sign of the exchange interaction given the d-electron count, orbital occupation, and the M–X–M angle bucket (≈90° vs ≈180° vs intermediate).
  • Mott criterion value — ratio of the M–M distance to a critical radius for that d-electron configuration; used as a rough indicator of localized vs itinerant magnetic moments.
  • Ionic radius ratio — M/X radius ratio, which affects the coordination geometry and therefore which superexchange pathway dominates.

Application: descriptor calculator

The widget below computes the GKA indicator and a rough exchange-sign expectation from the M–X–M angle and d-electron count — the two inputs that, in my experience, carry most of the signal for magnetic ordering type.

GKA exchange-sign estimator

Adjust the M–X–M superexchange angle and d-electron count to see the expected exchange sign under Goodenough-Kanamori-Anderson reasoning.

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Geometry regime

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Expected exchange sign

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GKA reasoning

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A simplified, single-pathway view — real compounds often have competing pathways, which is exactly why this becomes a feature rather than a final answer.

Why these and not raw lattice parameters

A regression model could in principle be handed raw lattice constants a, b, c and figure out the rest itself — but that's exactly the black-box outcome I want to avoid. If a model finds that band gap correlates with lattice parameter c, that's not a result I can act on; it's not clear what physically changes when c changes. If instead it correlates with Δ or the GKA indicator, that's a statement I can check against established theory, and one that should generalize to compounds with different lattice parameters but the same underlying crystal field or exchange geometry.

Feature EngineeringGKA RulesCrystal Field TheoryZSAMott CriterionDescriptors