The previous post mapped Δ and d-electron count onto expected band gap regimes. But Δ itself is derived from bond length — and bond length isn't the only structural lever. Coordination number changes the picture entirely: a six-coordinate octahedral site and a four-coordinate tetrahedral site split the d-orbitals into different patterns altogether, with different gap-determining transitions. This post looks at bond length and coordination number directly as inputs to the metal-insulator transition (MIT).
Two distinct levers
Bond length acts continuously: as M–X stretches, Δ shrinks roughly as 1/d⁵, narrowing the t₂g/eg-derived gap until bands overlap and the compound crosses into a metallic regime. This is the kind of transition that can in principle be tuned smoothly — by pressure, by chemical substitution that changes lattice parameters slightly, or across a solid-solution series.
Coordination number acts discretely. Octahedral coordination splits d-orbitals into t₂g (lower, 3-fold) and eg (upper, 2-fold). Tetrahedral coordination inverts this: e (lower, 2-fold) and t₂ (upper, 3-fold), with a smaller overall splitting for the same bond length — roughly Δ_tet ≈ (4/9)Δ_oct. So a compound that's a moderate-gap insulator in octahedral coordination can become metallic simply by adopting a tetrahedral motif at the same bond length, because the splitting itself is smaller.
Application: MIT phase map
The widget below combines both levers. Set the coordination geometry and sweep the M–X bond length — the indicator shows where the compound sits relative to the metal-insulator boundary, using the same Δ-vs-bandwidth logic as the previous post but now with the coordination-dependent splitting factor included.
Metal-insulator transition map
Coordination geometry sets the splitting factor; bond length sets its magnitude. Together they determine which side of the MIT a compound falls on.
Effective Δ
– eV
Regime
–
Tetrahedral splitting taken as 4/9 of octahedral for the same bond length — same compound, different coordination, different side of the MIT.
Why this matters for the dataset
This is the first descriptor pair where I expect the dataset to actively contradict the simple picture — and that's the point. If a tetrahedral d⁵ compound with a moderate bond length shows up as a wide-gap insulator despite the smaller nominal splitting, that's a signal that the ZSA charge-transfer mechanism (not the crystal-field-driven Mott picture) is dominant for that compound, and the coordination-number-based Δ scaling alone isn't the right descriptor for it. Flagging these cases is more useful than smoothing over them.
Next
This closes out the electronic-side posts for now. The next post shifts to the magnetic side: Goodenough-Kanamori-Anderson rules as explicit ML features, building on the exchange-sign estimator from the descriptors post but applied across the dataset's actual M–X–M angle distribution.
My name is Dr Abderrahmane Reggad. I'm a 54 year old and I am a researcher in materials' sciences. 
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