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Effect of disorder and doping on electronic structure and diffusion properties of Li$_{3}$V$_{2}$O$_{5}$

V$_{2}$O$_{5}$ in its $ω$ phase (Li$_{3}$V$_{2}$O$_{5}$) with excess lithium is a potential alternative to the graphite anode for lithium-ion batteries at low temperature and fast charging conditions due to its safer voltage (0.6 V vs Li$^{+}$/Li(s)) and high lithium transport rate. In-operando cationic disorder, as observed in most ordered materials, can produce significant changes in charge compensation mechanisms, anionic activity, lithium diffusion and operational voltages. In this work, we report the variation in structural distortion, electronic structure and migration barrier accompanied by disorder using first-principles calculations. Due to segregation of lithium atoms in the disordered state, we observe greater distortion, emergence of metallic behaviour and potential anionic activity from non-bonding oxygen states near the Fermi level. Redox capacity can be tuned by doping with 3d metals which can adjust the participating cationic states, and by fluorine substitution which can stabilize or suppress anionic states. Moreover, suppression of anionic activity is found to decrease structural distortion, crucial for mitigating voltage fade and hysteresis. Diffusion barrier calculations in the presence of disorder indicate the activation of the remaining 3D-paths for lithium hopping which are unavailable in the ordered configuration, explaining its fast-charging ability observed in experiments.