Two words of caution are in order regarding the generation of exact-energy unperturbed Hamiltonians: First, the unperturbed Hamiltonian, which generates the exact ground state energy, obeys no variational principle. Additionally, due to the dependence of Ĥ(0) on the density, an incorrect choice might lead to a violation of variationality with respect to ρ. Second, while there always exists an unperturbed Hamiltonian that recreates the exact correlation energy, the same cannot be said about the exact wavefunction, since the second order wavefunction can only include up to quadruply excited determinants.