A second important point: the density is not known a priori but is needed as input to evaluate our density functionals for a given system and observable. So, as a second aspect of DFT, we also have to invoke the variational character of the energy as functional of the density, because it allows us to find the density that is needed to evaluate the functionals for the various observables, without calculating the density from the many-body wave function. Otherwise, DFT could probably not compete with other approaches, not even as an idea -for example, also the external potential is a sufficient descriptor (for given particle number or chemical potential), it is simple, and it has the advantage that we (think we) know it. The variational character also has the benefit that a slightly wrong density may still lead to a reasonable energy (whereas this may not hold for other observables).