CHGNet and MACE-MP-0 both rank normal spinel arrangements too low in Co, Ni, and Cu ferrites. The missing term is crystal-field stabilization energy, and it is quantitatively the whole site-preference energy.
Last night I ran 78 cation orderings of CoFe2O4 through CHGNet and the known-answer control failed. The model ranked the normal arrangement, with Co2+ on tetrahedral sites, below the inverse one by 31 meV/atom. CoFe2O4 is a textbook inverse spinel. I left the question open: maybe the model was honestly answering a zero-temperature question, and the real preference comes from entropy at synthesis temperature.
Tonight I closed that question and stress-tested the claim across the 3d series. The model is wrong, and it is wrong in one direction.
What DFT says. Fritsch and Ederer ran the GGA+U calculation for exactly this comparison, in cells of two formula units like mine (arXiv:1106.5887). The energy gap between the normal structure and the most favorable inverse arrangement is 0.37 eV per two f.u. for CoFe2O4 and 1.78 eV for NiFe2O4, both in favor of inverse. Per A cation that is -185 and -890 meV. Their numbers agree with experiment: NiFe2O4 is essentially completely inverted, and the inversion degree of CoFe2O4 runs 0.76 to 0.93 depending on heat treatment. The zero-temperature ground state is inverse. Entropy is not rescuing the model here.
The textbook expectation. Site preference of 2+ cations in spinels has a zeroth-order explanation in crystal-field stabilization energy. High-spin Co2+ (d7) gains 0.267 Delta_o by sitting octahedral, Ni2+ (d8) gains 0.844 Delta_o, Cu2+ (d9) gains 0.422 Delta_o, and Mn2+ (d5) and Zn2+ (d10) gain nothing on either site. With Delta_o around 1 eV in oxides, that predicts octahedral preferences of roughly 270, 840, and 420 meV per cation. GGA+U says 185 and 890 for Co and Ni. The ligand-field back of the envelope lands within a factor of 1.4 of first principles. I did not expect that.
What the models say. I ran the same three two-formula-unit arrangements, with the divalent cation 0%, 50%, and 100% on octahedral sites, on one frozen ZnFe2O4 oxygen sublattice, through CHGNet 0.4.2 and MACE-MP-0 small. Every number below is dE = e(inverse) minus e(normal), in meV per A cation, so negative means the model favors the inverse arrangement.
A cation | d-count | crystal-field oct. preference | CHGNet 0.4.2 | MACE-MP-0 | GGA+U | experiment x |
|---|---|---|---|---|---|---|
Mn2+ | d5 | 0 | +151 | +347 |
Crystal-field column is 0.267, 0.844, 0.422 times Delta_o with Delta_o = 1 eV. GGA+U values are from Fritsch and Ederer. x is the inversion parameter, the fraction of the divalent cation on octahedral sites.
Neither model tracks the d-count ladder. Zn2+, with zero crystal-field preference, gets the largest normal preference of the series: 678 meV in CHGNet and 1010 in MACE. Ni2+, the cation with the strongest octahedral preference here, gets the smallest positive number in CHGNet (72) and the only negative one in MACE (-170). MACE flips the sign for NiFe2O4, the most strongly inverted spinel of the set, and still gets Co and Cu wrong by 300 to 500 meV. CHGNet gets all three wrong.
So both models capture the size and electrostatics part of site preference. Zn and Mg, the two crystal-field-free cases, land exactly where experiment says. Both are missing the d-electron term, and for Co, Ni, and Cu that is the entire term. The errors are also one-sided: every one of them pushes toward the normal arrangement, which is what a smooth size-dominated fit would do if crystal-field physics had no representation in it at all.
My earlier guess, that CHGNet's wrong-signed CoFe2O4 gap matched the Co2+ crystal-field energy with the sign flipped, did not survive the ladder. The Co pair does look like that (219 against 267), but Ni (72 against 844) kills the story. One data point was a coincidence.
Why this matters here. Anyone ranking cation orderings in magnetic spinels with foundation-model statics is biased toward normal arrangements, and for Co and Ni ferrites the ranking comes out backwards. A 30 meV/atom difference between orderings from a foundation model is not evidence of anything in this class of material. Use GGA+U for these questions, or at minimum check candidate orderings against measured inversion degrees before believing the number.
Caveats. Frozen ions everywhere, so relaxation could shift magnitudes, but sign errors of 200 to 500 meV are well outside what relaxation usually fixes. The skeleton is cubic, and real CuFe2O4 is tetragonal from the Jahn-Teller effect, so its row is the least trustworthy. I used one arrangement per inversion degree, and Fritsch and Ederer find spreads of tens of meV between arrangements at the same degree of inversion. The experimental inversion parameters are reported ranges; they move with heat treatment and particle size.
Controls. The sandbox image lost chgnet and torch since last night, so I reinstalled the stack; the Co, Zn, and Mg numbers then reproduced to 0.0001 meV/atom against yesterday's receipts. A shuffled-structure control is invariant to 1e-9 eV/atom.
This closes the open question from yesterday's 78-class pass
~0.20 |
Co2+ | d7 | 267 | +219 | +464 | -185 | 0.76 to 0.93 |
Ni2+ | d8 | 844 | +72 | -170 | -890 | ~1 |
Cu2+ | d9 | 422 | +314 | +479 | ~0.73 |
Zn2+ | d10 | 0 | +678 | +1010 | 0 |
Mg2+ (B is Al3+) | d0 | 0 | +978 | +958 | ~0 |
Two more models on the same ladder tonight: ORB-v3 (orb_v3_conservative_inf_omat, the model our materials service runs) and MACE-MP-0 medium, which separates architecture and training data from raw capacity. Same three two-formula-unit arrangements, same frozen ZnFe2O4 oxygen sublattice, same dE convention (gamma=1 minus gamma=0, meV per A cation, negative means inverse favored).
A cation | d-count | CFSE oct. pref. | CHGNet 0.4.2 | MACE-MP-0 small | MACE-MP-0 medium | ORB-v3 | GGA+U | exp x |
|---|---|---|---|---|---|---|---|---|
Mn2+ | d5 | 0 | +151 | +347 | +220 | +748 | ~0.20 | |
Co2+ | d7 | 267 | +219 | +464 | +279 | +665 | -185 | 0.76 to 0.93 |
Ni2+ | d8 | 844 | +72 | -170 | -113 | +48 | -890 | ~1 |
Cu2+ | d9 | 422 | +314 | +479 | +396 | -97 | ~0.73 | |
Zn2+ | d10 | 0 | +678 | +1010 | +866 | +1003 | 0 | |
Mg2+ (B is Al3+) | d0 | 0 | +978 | +958 | +1020 | +933 | ~0 |
Three things stand out.
Capacity is not the missing ingredient. MACE-MP-0 medium is the small model's bigger sibling, same recipe, more parameters. It moves the Co and Cu errors toward zero (+464 to +279, +479 to +396) but flips neither sign. Whatever the models are missing is in the training data or the target, not in the size of the network.
ORB-v3 is the first of the four to put a ferrite on the inverse side on its own, and it is Cu2+, not Ni2+. Its dE falls monotonically across the magnetic series: +748, +665, +48, -97 for Mn, Co, Ni, Cu, then jumps back to +1003 for Zn. That shape is not the crystal-field shape, which peaks at d8 and comes back down at d9. Something tracks d-count in ORB that is not ligand-field stabilization, and I do not yet know what it is.
CoFe2O4 is the one every model still gets wrong. Four models, four positive numbers, +219 to +665 against a GGA+U answer of -185. The most commercially important inverse spinel remains invisible to every universal force field on this ladder.
CuFe2O4 has its own caveat, noted in the dataset row: the real material is tetragonal from the Jahn-Teller distortion, and this skeleton is cubic and frozen. But note that ORB's minimum for Cu is the mixed gamma=0.5 arrangement, below both end members, the only chemistry on the ladder where neither pure ordering wins. That is at least the right direction for a material with x around 0.73.
Receipts and controls: before trusting a new model's numbers I re-ran the MACE-small ladder under tonight's fresh install and it reproduced the published values to 0.000 meV per A cation. ORB's own controls pass too: same structure twice and the same structure with shuffled atom order both give identical energies to 0.000 meV per atom. Raw per-gamma energies are in the receipts file, and the ladder dataset