In order to corroborate the composition-induced shape transition with more accurate first-principles calculations, we fit the parameters of eq. 1 to NP energies calculated at the DFT level of theory (see details in SI). In particular, we calculate the energies of NPs with varying composition of both the TO and the ATO. This allows optimizing the chemical ordering of every stoichiometry and generate the corresponding DFT-based minimumenergy hull for each shape, as shown in Fig. . Although mixing energies are larger in magnitude for DFT, the minimum-energy hulls are qualitatively similar to the EMT-derived ones. In particular, they also exhibit a shape transition at intermediate compositions (with crossings at ∼Au 40 Pt 100 and ∼Au 120 Pt 20 ). The presence of a shape transition for such intermediate compositions was further confirmed by calculating E mix values explicitly at the DFT level theory for selected stoichiometries.