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. 
P. Nov\'ak, J. Kune\v{s}, K. Kn\'i\v{z}ek
cond-mat.str-el