  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.
