Representation, Transferability, and Trustworthy Uncertainty in Machine‐Learning Prediction of the HOMO – LUMO Gap of Transition‐Metal Complexes

ABSTRACT

The frontier–orbital (HOMO–LUMO) gap is a compact descriptor of the electronic structure of transition–metal complexes (TMCs) and a recurrent screening target for catalysis, photophysics, and functional material design; however, its evaluation by density functional theory (DFT) is costly at the library scale. Working entirely from the public tmQM database, with no additional DFT calculations and no experiments, we examine three questions that are seldom treated together: how much structural detail a model requires, whether it generalizes across the periodic table, and how far its uncertainty estimates can be trusted. For 108,541 mononuclear TMCs, we construct a hierarchy of representations of increasing cost: composition‐and‐coordination descriptors; the same descriptors augmented with inexpensive cheminformatics (RDKit) features; and a SchNet graph neural network that operates directly on the three‐dimensional geometry. The predictive accuracy increases monotonically across the hierarchy (test R ²  ≈ 0.57 → 0.63 → 0.77; mean absolute error 0.44 → 0.30 eV), and Shapley value analysis attributes the predictions to chemically reasonable factors. We then show that this in‐domain accuracy is a poor proxy for reliability. Leave‐one‐series‐out and leave‐one‐metal‐out evaluations reveal a sharp loss of accuracy on unseen chemistry (median leave‐one‐metal‐out R ²  ≈ 0.34; worst case d ¹⁰ zinc, R ²  < 0), and, contrary to a natural expectation, neither of two geometry networks (SchNet, DimeNet++) extrapolates better than the simpler tabular model across metal series—both are often worse—although the directional architecture alone extrapolates with positive skill to a single withheld metal. Finally, although standard split‐conformal intervals are well calibrated in the domain (≈90% coverage), they undercover (81%) for an unseen series; we demonstrate that series‐conditional (Mondrian) calibration restores per‐series coverage and that a distance‐based applicability‐domain filter flags essentially all out‐of‐domain complexes, recovering calibrated coverage on the retained subset. The study offers a transparent, reproducible recipe for deciding when and how confidently such models may be applied.