Challenges in computational evaluation of redox and magnetic properties of Fe-based sulfate cathode materials of Li- and Na-ion batteries

Several Fe-based sulfates have been proposed recently as cathode materials characterized by a high average operating voltage (i.e. Li2Fe(SO4)2 and Na2Fe2(SO4)3) or low fabrication temperature (e.g. Na2Fe(SO4)2·2H2O)). In this work, we apply three methods to evaluate the redox potentials and magnetic properties of these materials: (1) local density functional theory (DFT) in Perdew-Burke-Ernzerhof parametrization; (2) rotationally invariant DFT + U; and (3) DFT + U with magnetic exchange, suggested herein. The U parameters used for DFT + U calculations have been evaluated by using a linear response method (this applies to DFT + U as well as DFT + U calculations with a magnetic exchange term). Moreover, we have performed adjustments of U and, for the case of magnetic exchange, J parameters, to find better agreement with experimental measurements of redox and magnetic properties. We find that a self-consistent DFT + U/linear response approach yields quite overestimated redox potentials as compared to experiment. On the other hand, we also show that DFT + U calculations are not capable of providing a reasonably accurate description of both redox and magnetic properties for the case of Li2Fe(SO4)2, even when adjusted U parameters are employed. As a solution, we demonstrate that a DFT + U methodology augmented by a magnetic exchange term potentially provides more precise values for both the redox potentials and the magnetic moments of the Fe ions in the studied materials. Thus our work shows that for a more accurate description of redox and magnetic properties, further extensions of the DFT + U method, such as inclusion of the contribution of magnetic exchange, should be considered.