The electronic states of lanthanide (Ln) atoms doped into the ternary thiogallate CaGa 2 S 4 are investigated from the relativistic first principle calculations by the discrete variational Xα method (relativistic DV-Xα) on LnCa 8 Ga 12 S 24 spherical clusters. In view of the self-consistent charge (SCC) convergence, atomic coordinates in the cluster are optimized. As the result, a certain lattice contraction is locally induced around the Ln Ca substitution by more than 30% in maximum. The 4f orbitals of the Ln atom are not electronically isolated but form many molecular orbitals mainly hybridized with valence orbitals of the surrounding S and the second nearest Ga atoms. The LS coupling of the 4f orbitals does not always result in the discrete level splitting as the j = 5/2 and 7/2 states. Both of these states are partially degenerated to make some molecular orbitals.1 Introduction The ternary thiogallate CaGa 2 S 4 doped with lanthanide elements (CaGa 2 S 4 :Ln) are promising for optoelectronic devices such as wavelength-tuneable light emitters with the laser oscillation [1][2][3][4]. However, the detailed optoelectronic mechanism has been little known especially on the spin properties of 4f electrons of the Ln atoms. The aim of this work is to clarify the electronic states of the Ln atoms when doped in CaGa 2 S 4 , by the first principle electronic state calculation. Recent progress and success of the first principle calculations have been worthwhile noticing in the field of materials design [5,6]. We have adopted the discrete variational Xα (DV-Xα) method, one of the cluster methods, which is suitable for evaluating local electronic states of atoms. We have reported the nonrelativistic feature of the electronic system of CaGa 2 S 4 :Ln as the first step of our investigation [7]. Optical processes in CaGa 2 S 4 :Ln are regarded as mostly relating to the 4f-5d and 4f-4f transitions in the Ln atoms, where the 4f states have been treated generally as electronically isolated in the host crystals. Our previous work revealed that the 4f orbitals also hybridized with their environmental valence orbitals such as the 3p orbitals of the surrounding S atoms to form molecular orbitals. The relativistic quantum effects would promote the hybridization character furthermore. In this work, the electronic states of the Ln atoms are investigated using the relativistic DV-Xα method (rel.) in comparison with the nonrelativistic one (nonrel.).