Crystal field of rare earth impurities in LaF${}_3$

The crystal field parameters of 13 trivalent lanthanide ions substituted for La in LaF${}_3$ 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.