Recall that the lower-dimensional DPEM is not the final DPEM. The final DPEM is the sum of the lower-dimensional DPEM (𝚵 % ) and a many-body DPEM. The first 𝑁 !"#"$! elements of 𝚵 % 23 are nonzero and are the same as the 𝑁 !"#"$! adiabatic potential energies except they might be ordered differently. For O3, we use