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In recent years, was synthesized a new class of transition metal oxide based on the elements with unfilled 5d electron shell. Unlike traditional systems with unfilled 3d shell in 5d electron systems 5d shell feel a strong spin-orbit interaction, which leads to a significant change in their physical properties. In this paper, a theoretical description of the local electronic and magnetic properties of one of the representatives 5d systems - iridium oxides. These systems have a tetragonal lattice structure and therefore the quantum - mechanical analysis of local electronic states, taking into account the effects of the crystal field, Coulomb interactions and strong spin - orbit coupling can be done analytically. The results of such an analysis, in particular, found the wave functions and energy for their electronic states ion Ir4 +, placed in an octahedral environment of oxygen ions. Results of the analysis of the magnetic interaction of ions of iridium at the nearest lattice derived from the generalized theory superexchange. On the electrons partially filled d - skins the electric field, which has not spherically symmetric, but only symmetry corresponding node position of the crystal lattice, which is the ion. For transition metal ions of five and large periods of the periodic table (with partially filled 4d - or 5d - shell ions in heavy elements) spin - orbit interaction is large. Multiplet splitting due to the spin - orbit interaction can be compared with splitting in the crystal field (or even more of it).