Currently, LiCoO2 is widely used as cathode in lithium ion batteries for "small" applications (e.g., laptops and cell phones). However, the relatively high cost and safety problems limit its applications in electric vehicles. Partial substitution of Co with other transition metals, such as Ni and Mn, can lower costs and improve battery performance and safety. The present dissertation aims at studying the Li-(Co,Ni)-O system using CALPHAD (calculation of phase diagrams) modeling and ab initio calculations. It is found that DFT (density functional theory) cannot be used to obtain accurate enthalpies of formation for transition metal-containing oxides. By probing a series of metal oxides using ab initio calculations, it is proposed that one needs to correct the GGA data with -0.8 and +0.8 eV shifts for oxides of transition metals with valence state of +2 and +4, respectively. This modifies strong correlations of localized and hybridized d transition metal states and provides an alternative to the Hubbard approach or the GW approximation, which enables the prediction of enthalpies of formation for transition metalcontaining oxides.