Coordination-Resolved Surrogate Models for Thermodynamic Stability, Band Gaps, and Magnetic Moments of Spinel Oxides, Sulfides, and Selenides

Abstract

We curated 320 cubic ($Fd\bar{3}m$) spinel entries from the Materials Project-nitrides, oxides, sulfides, and selenides, including single-cation mixed-valence $A_3X_4$ compounds-and trained tree-ensemble surrogates for the formation energy, energy above the convex hull, band gap, total magnetization, and metallicity. Cations were assigned to tetrahedral-like and octahedral-like groups from CrystalNN coordination numbers rather than from element identity, and the evaluation was group-aware throughout: splits were grouped by reduced formula, every transform was fit on training folds only, and champion models were selected on cross-validated scores before the holdout was examined. Over twenty repeated grouped holdouts (single-seed refits that reuse the tuned hyperparameters, and are therefore mildly optimistic) the champions reach mean absolute errors of $0.121\pm0.030$ eV/atom for the formation energy, $0.048\pm0.013$ eV/atom for the hull distance, and $1.27\pm0.19$~\muBfu{} for the magnetization, with a metallicity accuracy of $0.85\pm0.06$. Band-gap regression does not beat a trivial baseline on the 19-member non-metal holdout under paired bootstrap testing, we report this negative result and trace it to sample scarcity and to the semi-local DFT labels. On the identical grouped split, the tabular champion is more accurate than an untuned MEGNet trained from scratch (0.087 versus 0.209 eV/atom formation-energy MAE on the primary holdout), a comparison that bounds, rather than settles, the descriptor-versus-graph question at this data scale. SHAP attribution ties the magnetization model to octahedral $d$-occupancy and the formation-energy and band-gap models to electronegativity descriptors, and grouped conformal intervals, permutation nulls, and leave-one-chemistry-out tests bound a domain of applicability that is uneven across anions and cations.