Extended DFT+U method: application to analysis of complex doping effects, methodological developments and materials design.

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During the last year the newly proposed extension of DFT+U method with corrections for interactions between the electrons with opposite spins (absent in standard DFT+U) has been applied for the study of energies of formation of transition metal oxides and voltage profiles of complex battery cathodes that contain two types of active redox centers.Detailed tests revealed that energies of formation could be calculated by setting of magnetic moments close to experimental values by the newly introduced correction term. Linear response method was found not accurate for this task. Moreover tests have shown superiority of SCAN functional over PBE. Thus the methodology for evaluation of formation energies of transition metal oxides has been formulated. Tests have been performed for Mn, Fe, V and Cr oxides, yielding a good agreement with experiment for energies of formation and magnetic moments.The extended DFT+U method has been also applied for the study of electrochemical properties of a layered oxide structure, which contains two types of transition metals (Ni and Mn). This method provided very promising and accurate prediction of the voltage profile in a good agreement with experimental measurements. A robust form of evaluation of the U parameters has been proposed for the standard DFT+U method as well.