X-ray diffraction analysis for ReO 3 -type TiOF 2 ; Pair Distribution Function data for TiOF 4 between 8 Å to 40 Å; Additional details of the cluster expansion model fitting and model ECIs; Details of the Genetic Algorithm structure prediction scheme; Structural analysis of the GA-predicted structures; Correlation between calculated σ iso and experimental δ iso values for 19 F in titanium (oxy)-fluorides; Haeberlen convention used to define the shielding and chemical shift NMR parameters; Details about calculations using the NMR-CASTEP code; Previously reported relationships between calculated σ iso and experimental δ iso values for 19 F in inorganic fluorides; Derivation of an empirical linear relation between calculated σ iso and experimental δ iso values for 19 F in titanium (oxy)-fluorides; Effect of DFT calculation method on atomic positions for TiF 4 ; Simulated 19 F MAS NMR spectra for all four 4 × 4 × 4 GA-predicted structural models.