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We have evaluated the successes and failures of the Hubbard-corrected densityfunctional theory (DFT+U) approach to study Mg doping of LiCoO$_2$. We computedthe effect of the U parameter on the energetic, geometric and electronicproperties of two possible doping mechanisms: (1) substitution of Mg onto a Co(or Li) site with an associated impurity state and, (2) formation ofimpurity-state-free complexes of substitutional Mg and point defects inLiCoO$_2$. We find that formation of impurity states results in changes on thevalency of Co in LiCoO$_2$. Variation of the Co U shifts the energy of theimpurity state, resulting in energetic, geometric and electronic propertiesthat depend significantly on the specific value of U. In contrast, theproperties of the impurity-state-free complexes are insensitive to U. Theseresults identify reasons for the strong dependence on the doping properties onthe chosen value of U and for the overall difficulty of achieving agreementwith the experimentally known energetic and electronic properties of dopedtransition metal oxides such as LiCoO$_2$.

Successes and failures of Hubbard-corrected density functional theory: The case of Mg doped LiCoO$_2$