S outer is the set of atoms belonging to the outer shell, obtained by computing the alpha shape of the nanoparticle, and R(S outer ) represents the distances from each atom in S outer to the centroid. The obtained scores are then normalized between 0 and 1 within the dataset, with 0 being the least spherical and 1 being the most spherical nanoparticle. Figure shows the sphericity scores for the entire dataset. Generally, ReaxFF produces geometries with lower sphericity scores, while the geometries optimized using MACE-MP-0 are consistently more spherical. In addition, our sphericity concept is a good measure of the geometrical deformation of the nanoparticle against oxygen ratio. This tendency towards more spherical geometries suggests that MACE-MP-0 favors more compact and densely packed structures, compared to the more irregular structures predicted by ReaxFF.