Phase stability of cation-doped LiMnO$_{2}$]{Phase stability of   cation-doped LiMnO$_{2}$ within the GGA+U approximation
  First principles density functional theory calculations within the GGA+U approximation were performed for LiMn$_{1-x}$M$_x$O$_{2}$, a candidate cathode material for lithium-ion batteries, with ($x=0.25$, M=Ni, Fe, Co, Mg), to investigate the effect of doping on the destabilization of the monoclinic structure relative to the layered rhombohedral structure. A primary motivation of this work was to determine to what extent the predictions of the electronically more realistic GGA+U treatment would differ from those obtained within the GGA. Several significant qualitative changes are found. For the pristine system in the rhombohedral structure, Mn ions show a high-spin state within GGA+U, rather than the low spin (metallic) state found in GGA. The doped rhombohedral structure is unstable within GGA+U, rather than metastable, as in GGA. In the monoclinic structure, the dopant oxidation states are the same (trivalent Fe, divalent Co, Ni) in GGA+U and GGA. Co and Ni ions show a higher spin state in GGA+U than in GGA. The divalent dopants destabilized the monoclinic structure to a greater extent than trivalent dopants within the GGA+U, as expected from previous GGA calculations. Overall, our results suggest that the relatively close agreement sometimes found between properties calculated within the GGA and GGA+U may be misleading, because the underlying electronic behaviors may be profoundly different. 
N. N. Shukla, S. Shukla, R. Prasad, R. Benedek