second Hohenberg-Kohn theorem

the first theorem tells us that the ground-state density contains the information needed to describe the system, whereas the second provides a way to identify that density through energy minimization. So i partially agree with the statement. The second Hohenberg–Kohn theorem can be understood as a natural extension of the first, although it does not follow from the first theorem alone. The first theorem establishes the relationship between the ground-state electron density and the external potential, while the second introduces the variational property of the energy functional.