To model the relative energies of competing O/F anion configurations within the ReO 3 -type TiOF 2 structure, we fitted a cluster expansion model to DFT-calculated energies of 65 symmetry inequivalent 2 × 2 × 2 supercells. These 65 supercells were sampled from the complete set of 2664 symmetry inequivalent 2 × 2 × 2 supercells of ReO 3 -type TiOF 2 , which we enumerated using bsym . These DFT calculations were performed using the VASP code , with a plane-wave cutoff energy of 700 eV and a 4 × 4 × 4 Monkhorst-Pack k-point grid. The interactions between core and valence electrons were described using the projector augmented wave method , with cores configurations of [Mg] for Ti, [He] for O, and [He] for F; for Li, all electrons were treated as valence. These calculations used the revised Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) functional (PBEsol) , with a Dudarev +U correction applied to the Ti d states (GGA+U ) . A value of U Ti,d = 4.2 eV was used, as for previous calculations on TiO 2 , Liintercalated TiO 2 , and Ti-deficient hydroxyfluorinated anatase TiO 2 .