The groundstate energy can be obtained variationally: the density that minimises the total energy is the exact groundstate density.
Although the Hohenberg-Kohn theorems are extremely powerful, they do not offer a way of computing the ground-state density of a system in practice. About one year after the seminal DFT paper by Hohenberg and Kohn, Kohn and Sham devised a simple method for carrying-out DFT calculations, that retains the exact nature of DFT. This method is described next.