Crystal field of rare earth impurities in LaF3

•Crystal field of all trivalent lanthanide impurities in LaF3 is calculated ab initio.•Hybridization of 4f states with valence states of ligands is important.•Atomic-like calculation is used to determine multiplet splitting.•Theory is in good agreement with available absorption and luminescence results.

The crystal field parameters of 13 trivalent lanthanide ions substituted for La in LaF3 were calculated using the combination of the band structure and Wannier function calculations. Performing an atomic exact diagonalization with thus obtained crystal-field parameters we compute the crystal-field splitting of atomic multiplets. The calculation is compared with the available experimental results and a good agreement is found.