In this paper we show an efficient algorithm to compute, in an ab init
io way, the absorption bands of Ce 4f-5d transitions and the position
of the Ce 4f and 5d levels in the gap for Ce-doped inorganic crystals.
Calculations have been performed on CeF3 and Ce-doped LaF3, YAG and L
SO. The calculated absorption bands are in good agreement with experim
ental data. The calculated position of the Ce levels in the gap is not
good enough, but useful and in agreement with experimental data withi
n a certain error.