Note that 𝐄 = (𝐑 = ) is not the final adiabatic potential energy vector of Z because the elements are not sorted in energetic order. In practice, our preferred choice of diabatic representation usually satisfies the constraint that at any dissociation geometry (where 𝐑 = equals 𝐑 =,G ), the diabatic potentials equal the adiabatic ones, although they might be in a different order. We will assume this usual constraint in the present article. However, we will also require the following constraints that include state ordering: