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Dominant role of orbital splitting in determining cathode potential in $O3$ $NaTMO_2$ compounds

Designing high potential cathodes for Na-ion batteries, which are comparable in performance to Li-ion cathodes, remains a challenging task. Through comprehensive density functional calculations, we disentangle the relationship between the cathode potential and the ionicity of $TM-O$ bonds in $O3$ $NaTMO_2$ compounds in which TM ions is a fourth- or fifth-row transition metal. We demonstrate that the magnetic exchange interaction and the local distortions in the coordination environment of TM ions play more significant roles in determining the cathode potential of the $TM^{3+}$ $\to$ $TM^{4+}+ e^-$ reaction than the ionicity of the $TM-O$ bonds in these compounds. These results indicate that designing cathode materials solely based on empirical electronegativity values to achieve high potential may not be a feasible strategy without taking into account a detailed structural assessment.