However, the experimental synthesis of those compounds may be challenging (e.g. require out-ofequilibrium conditions) or impossible. It is likely that the predicted phases exist in the disordered forms due to the cation mixing behaviors of Li/Ni. The predicted phase stability at 0 K does not account for the temperature effect which also encourages disordering. The challenges of getting a precise control of the known compositions/structures in the Li-Ni-O phase space have also been discussed in previous works. We tried to incorporate finite temperature effects in our PBEsol+U convex hull analysis. This includes computing the constant volume Helmholtz free energies from phonon calculations (see Figure ), where the entropy term of O 2 gas was taken from the Thermochemical Tables. Additionally we estimated the Gibbs free energies using the machinelearned descriptor (see Figure ). Unfortunately, neither approaches correctly capture the stability of known phases. The DFT+U method, with U calibrated to materials properties (e.g. band gaps, oxidation enthalpies) are limited known experimental phases such as NiO and NiO 2 .