Foundation 1: What is Kohn–Sham DFT?
Short answer: Kohn-Sham density functional theory (KS-DFT) is the theoretical framework at the foundation of the majority of modern, practical applications of density functional theory in chemistry.
Long(er) answer: DFT is an exact theory based on the idea that the electron density can be used as the basic quantity to calculate all components of the electronic structure of a system, including its total electronic energy. A first attempt at using the density as a basic variable dates back to the 1920s, when Thomas, Fermi, and later Dirac proposed the first density functional.2–5Unfortunately, the Thomas–Fermi–Dirac functional has very limited practical utility for chemistry because it predicts molecules to be less stable than their separated constituent atoms.6 In 1964, Hohenberg and Kohn established the existence of a universal, exact energy functional of the density.7 One year later, Kohn and Sham introduced a useful framework to circumvent the difficulties of calculating the kinetic energy of the electrons as a functional of the electron density by means of a basis set expansion.8 Their KS-DFT framework uses orbitals to describe a fictitious system of non‑interacting electrons with the same density as the real, interacting one, and reorganizes all the differences between the two systems, together with all the other effects that are non-trivial to calculate, into the unknownexchange–correlation (xc ) functional.
For further details on the mathematical foundations we refer the interested readers to “DFT in a Nutshell”,1 as well as to some of the main textbooks in the field,9–15while for research challenges we point them to recent reviews16–23 and references therein.