The electronic structures of LiYF4:Ce3+ and LiYF4 crystal simulated by an embedded （in a microcrystal containing 1938 ions） cluster CeY4Li8F24, and Y5Li8F24 respectively, were computed by the ab initio self-consistent relativistic DV-Xa（discrete variational Xa） method. The ground-state calculation showed that only the lowest 5d level Ed of Ce3+ ion lies around the BCB （bottom of the conduction band） while the lowest 4f levels is 2.5 eV lower than BCB. The CB states consist of 4d of Y mixed with 5d of Ce, even for the wavefunctions （WFS） with energy Ed under BCB there are still 24% of Y-4d and 9% of F-2p as components. So, they are not pure crystal-field states at all. Furthermore, transition state （TS） calculation was performed to obtain the 4f→5d transition energies Efd, to improve the previous calculation performed by Andriessen et al, in which a small CeF8 cluster embedded in an array of point charge was used and the results of ground-state calculation were roughly used to compare with the observed 4f→5d transition energies. The ionic radius of Ce3+ is larger than that of Y3+, so we had also modeled approximately the lattice relaxation. As results, the CeY4Li8F24 cluster with 4.56% outward relaxation （of the nearest-neighbor and next nearest-neighbor eight fluorines） has the lowest total energy and gave satisfactory 4f→5d energies Efd, but the ground-state calculated Ed is 0.68 eV higher than BCB. For another cluster with 7.36% outward relaxation the Ed is 0.43 eV lower than BCB, which makes the observation of fine structure （including zero-phonon line） of the lowest 5d band understandable easier, but the splits between the transition energies Efd were not as good as the former. Therefore, we consider the relaxation is some how around 4.56%～7.36% outward, not as large as 10% proposed by Andriessen et al.
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