This energy difference gives a measure of how well Ψ approximates the ground state Φ v of the effective Hamiltonian H v . The smaller the energy difference, the better the approximation of Ψ to Φ v . It is elementary to confirm that the energy difference is minimized by the exact Kohn-Sham Hamiltonian H v s . Interestingly, the exact density property of the Kohn-Sham state is the result of the Rayleigh-Ritz optimization and the density is not a priori fixed. Hence, the Kohn-Sham Slater determinant, on top of being "density optimal", it is also "energetically optimal" in a Rayleigh-Ritz optimization, which physically is equivalent to the total energy minimization of Hartree-Fock theory. I note that the variational principle in eqn ( ) can be used to construct optimally converging power series expansions for the Kohn-Sham potential, without using the adiabatic connection path formalism 85 .