The electronic structure, Fermi surface, angle dependence of the cyclotron masses and extremal cross sections of the Fermi surface as well as x-ray magnetic circular dichroism (XMCD) in the CeAgSb2 compound were investigated from first principles using the fully relativistic Dirac linear muffin-tin orbital method. In our calculations Ce 4f states have been considered as: 1) itinerant using the generalized gradient approximation (GGA), 2) fully localized, treating them as core states, and 3) partly localized using the GGA + U approximation. The effect of the spin-orbit (SO) interaction and Coulomb repulsion U in a frame of the GGA + U method on the Fermi surface, orbital dependence of the cyclotron masses, and extremal cross sections of the Fermi surface are examined in details. We show that the conventional GGA band calculations fail to describe the Fermi surface of the CeAgSb2 due to wrong position of Ce 4f states (too close to the EF). On the other hand, fully localized (4f states in core) and the GGA + U approach produce similar Fermi surfaces and dHvA frequencies in the CeAgSb2. A good agreement with the experimental data of XMCD spectra at the Ce M4.5 edges was achieved using the GGA + U approximation. The origin of the XMCD spectra in the compound is examined. The core hole effect in the final states has been investigated using a supercell approximation. It improves the agreement be-tween the theory and the experiment of the XAS and the XMCD spectra at the Ce M4.5 edges.
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