#Functional equivalence theory wiki code

To answer your questions in this context:ДЎ) The initial density depends on the guess, which is a whole different can of worms, but the same is true for HF calculations. JA Pople, PMW Gill, BG Johnson Chem Phys Lett 199, 557 (1992). Thus one obtains the energy and the KS operator (the equivalent of the Fock operator) and can perform a SCF procedure in a given basis set. The potential needs to evaluated numerically on a grid, a procedure that yields the XC energy for almost all choices of density functionals.

#Functional equivalence theory wiki code

When implementing this idea, one learns that one can basically use a HF code and replace the exchange term by the exchange-correlation (XC) potential (which is projected back on to the AO basis set). See this question for pointers on where to read more: Equivalent of Szabo and Ostlund book for DFT.ДЄs often in DFT, practicality showed a way that was justified later. This wave-function works just like a Slater determinant and is called the Kohn-Sham determinant. Kohn and Sham proposed to make use of what is typically called a 'fictitious, non-interacting reference', that is, a wave-function whose main purpose would be to yield a density to be used in all other (nucleus-electron attraction, Coulomb, exchange, and correlation energy/potential) and whose secondary function is to provide the kinetic energy, which is accurate from wave-function theory.

Kohn-Sham DFT was created to solve a historical problem of DFT: The electronic kinetic energy term (as used in the Thomas-Fermi model) was not accurate enough. This is what most people mean by 'DFT', but, as noted in the comments, things such as orbital-free DFT exist. This answer only deals with the most common variety of Density Functional Theory, namely, Kohn-Sham DFT.