Density functional theory

This article was taken from Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Density_functional_theory. For complete information, please visit the Wikipedia site.

Density functional theory (DFT) is one of the most popular and successful quantum mechanical approaches to the many-body electronic structure calculations of molecular and condensed matter systems. Within the framework of DFT, the practically unsolvable many-body problem of interacting electrons is reduced to a solvable problem of a single electron moving in an averaged effective force field. This effective force field can be represented by a potential energy being created by all the other electrons as well as the atomic nuclei, which are seen as fixed in terms of the Born-Oppenheimer approximation.

Description of the Theory

In contrast to traditional methods like Hartree-Fock theory which are based on the complicated many-electron wavefunction DFT is written in terms of the electron density, giving this theory its name. DFT is an exact theory only for the free electron gas, while for the treatment of extended atomic systems various approximations have to be made. In many cases DFT gives quite satisfactory results in comparison to experimental data at relatively low computational costs when compared to other ways of solving the quantum mechanical many-body problem.

DFT has been very popular for calculations in solid state physics since the 1970s. However, it was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined. DFT is now the leading method for electronic structure calculations in both fields. However, there are still systems which are not described very well by DFT. One famous example is the false prediction of the band gap in semi-conductors. The method also fails to describe properly intermolecular interactions, especially van der Waals forces (dispersion).

Early Models

The first true density functional theory was developed by Thomas and Fermi in the 1920s. They calculated the energy of an atom by representing its kinetic energy as a functional of the electron density, combining this with the classical expressions for the nuclear-electron and electron-electron interactions (which can both also be represented in terms of the electron density).

Although this was an important first step, the Thomas-Fermi equation's accuracy was limited because it did not attempt to represent the exchange energy of an atom predicted by Hartree-Fock theory. An exchange energy functional was added by Dirac in 1928.

However, the Thomas-Fermi-Dirac theory remained rather inaccurate for most applications because it is difficult to represent kinetic energy with a density functional, and it neglects electron correlation entirely.

NMT | LANL | DOE
Phone Book | Search | Help/Info

L O S  A L A M O S  N A T I O N A L   L A B O R A T O R Y
Operated by the University of California for the US Department of Energy