The second theorem is the DFT variant of the variational principle (see section 2.2.1). It states that only the exact ground state density 𝜌 0 results in the ground state energy 𝐸 0 and every other density delivers higher energies. This gives an idea of how to search for the ground state density: just check if the energy lowers upon changing a test density. These theorems however do not lead to a practically useful method since there is no systematic way to vary a density. This goal was achieved a few years later by Kohn and Sham (KS). They formulated the energy functional as in eq. 2.2.