The comparative study of structural, electronic properties, topology of the Fermi surface, and the features of chemical bonding in layered 1111-oxyarsenides LaRhAsO and LaIrAsO has been performed based on the results of ab initio modeling of their electronic structure. It was established that only weak sensitivity with respect both to electron and hole doping is expected for LaIrAsO being non-magnetic metal, however, the Rh-containing compound should be characterized with weak band magnetism, and the hole doping is expected to be able to move its ground state away from the boundary of magnetic instability. The mentioned feature allows to consider LaRhAsO oxyarsenide as a possible electron analogue of LaFeAsO compound being the initial phase for the layered FeAs-superconductors.
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