The permuted database has 𝑆 = 𝑁 _ 𝑁 ,-./"! geometries, where 𝑁 _ is the number of nonidentity permutations of the O3 molecule, which is 5. All the geometries in database 𝑆 are generated by permuting identical nuclei for each geometry in the adiabatic database such that the permuted geometries have the same adiabatic potential energies.