(3.5.4) Xu : The electron density and the electronic energy are two quantities of fundamental importance. While an accurate description of the density allows for correct physical insight from the charge distribution, accurate determination of energies and their changes allows for precise quantification of the properties of a system of interest. The Hohenberg-Kohn theorems , which state that there exists a mapping from the ground-state electron density of a many-body system to its total energy, lay the foundation of modern DFT. To put DFT in practical use, the central questions are then (Q1) how to find the ground-state density of a physical system, and (Q2) how to set up a mapping from the density to the total energy. The Kohn-Sham scheme answers Q1 and Q2 simultaneously in a self-consistent way, using a local exchange-correlation potential, obtained by taking the derivative directly from a given DFA.