Electrostatic Dominance of Frontier Orbital Energies in Lanthanide Complexes

<jats:p> The 4f orbitals of lanthanides are shielded by filled 5s <jats:sup>2</jats:sup> 5p <jats:sup>6</jats:sup> subshells, so that lanthanide–ligand bonding is often dominated by electrostatic interactions. Random forest models built from 31 composition-based descriptors, without any three-dimensional coordinates, predict the HOMO energies of 17,269 lanthanide complexes (LnQM, ωB97M-V/def2-SVPD) with a 5-fold cross-validation MAE of 0.159 eV (R <jats:sup>2</jats:sup> = 0.991), and total charge dominates feature importance (∼95%) in leave-one-element-out validation. A controlled comparison on 41,374 3d complexes (tmQM) shows markedly weaker charge dependence, consistent with a larger role of covalent interactions in 3d systems. Standard equivariant graph neural networks, untuned for this task, perform far worse than the composition-based model. The spin-resolved HOMO-LUMO gap reaches a minimum at Gd <jats:sup>3+</jats:sup> (f <jats:sup>7</jats:sup> ), a configuration-based analog of the gadolinium break, while absolute orbital energies remain electrostatically dominated. </jats:p>