Density functional theory

Each electron in an atom, molecule, or solid interacts with all the other electrons through electrostatic Coulomb forces. In addition, electrons interact with atomic nuclei through similar Coulomb forces. ……the nuclear coordinates Ri are then parameters which appear in the quantum state of the electrons. This quantum state is described as a many-body state because the mutual interactions between the electrons do not allow us to discuss the motion of anyone electron independently of the others.

In a solid with 10^23 electrons per cubic centimetre the determination of the many electron wavefunction is a hopeless task. …in 1964 proved a fundamental theorem: all aspects of the electronic structure of a system of interacting electrons, in an external potential v(r) and a non-degenerate ground state, are completely determined by the electronic charge density p(r). The external potential in the present context is the potential due to the atomic nuclei. This theorem immediately leads to a major simplification: rather than working with the many electron wavefunction we work with a function of just three variables, p(r).
….they derived a system of self consistent one particle equations for the description of electronic ground states. The interacting N electron problem is thus mapped rigorously onto N single electron equations, in which each electron is moving independently of the other electrons, but it experiences and effective potential which emulates all the interactions with the other particles. In other words, the electrostatic interactions between the electrons have effectively been switched off so that the motion of each electron is independent of the other electrons. In place of these electrostatic interactions each independent electron is now moving in an effective single particle potential which simulates exactly the interactions with all the other electrons. Moreover, the effective single particle potential is a unique functional of the electron density.


Sutton A P, Balluffi R W, (1996), Interfaces in Crystalline Materials, Clarendon Press Oxford

A functional is a function of a function.
Coulomb repulsion energy lowering = correlation energy
Exclusion principle = exchange energy

sol= a liquid colloidal solution
micelle= electrically charged group of molecules; an electrically charge particle formed by an aggregate of ions or molecules in soaps, detergents, and other suspensions