Large parts of the periodic table cannot be cooled by current laser-based methods. We investigate whether zero energy fragmentation of laser cooled fluorides is a potential source of ultracold fluorine atoms. We report new ab initio calculations on the lowest electronic states of the BeF diatomic molecule including spin–orbit coupling, the calculated minima for the valence electronic states being within 1 pm of the spectroscopic values. A four colour cooling scheme based on the A²Π ← X²Σ⁺ transition is shown to be feasible for this molecule. Multi-Reference Configuration Interaction (MRCI) potentials of the lowest energy Rydberg states are reported for the first time and found to be in good agreement with experimental data. A series of multi-pulse excitation schemes from a single rovibrational level of the cooled molecule are proposed to produce cold fluorine atoms.