Density functional theory and exchange–correlation functionals
Reformulates the many-electron problem in terms of the electron density; exact in principle, but accuracy hinges on one unknown functional that all practical calculations approximate.
DFT supplies the energies, forces and training labels behind most molecular and materials simulation, including most machine-learned potentials.
Gets a molecule's energy from where its electrons are, not from the full quantum state, which is far cheaper.
- 1Density fixes the energy in principle
- 2Exact formula for the energy is unknown
- 3Approximate the exchange–correlation piece
- 4Fast, usually good answers
- 5Known failures: charge smearing, strong correlation
Kohn–Sham DFT. The Hohenberg–Kohn theorems show that the ground-state electron density determines all ground-state properties. Kohn and Sham replaced the interacting electrons by non-interacting ones that reproduce the same density, which leads to the energy expression
Go deeper
The full technical text.
What it is
Hohenberg and Kohn (1964) proved that the ground-state density determines all ground-state properties, so there exists an energy functional minimised by the true density. Kohn and Sham (1965) made this practical by introducing a fictitious non-interacting system with the same density: where is the non-interacting kinetic energy, the classical Coulomb (Hartree) energy and the , which collects everything else. Solving the Kohn–Sham equations costs with plane waves or Gaussians, and less with linear-scaling tricks.
Words on this page (8)
- density functional theory
- A method that gets a molecule's energy from the electron density instead of the full wavefunction, trading exactness for speed.
- exchange–correlation functional
- The unknown formula inside density functional theory that accounts for all the subtle electron-electron effects; every practical version is an approximation.
- delocalization error
- A flaw in approximate functionals that smears electric charge out too much, spoiling barriers, band gaps and charge transfer.
- self-interaction error
- A flaw where an approximate method lets an electron partly repel itself.
- hybrid functional
- A density functional that mixes in a fraction of the exact exchange energy from Hartree–Fock theory; more accurate and more expensive.
- dispersion
- A weak, always-present attraction between molecules from momentary electron fluctuations, which holds layers of graphite together.
- strong correlation
- A situation where many electron arrangements matter at once, so simple one-configuration pictures fail.
- chemical accuracy
- An error of about 1 kcal/mol (4 kJ/mol), roughly what is needed to predict reaction outcomes reliably.
Open problems & questions
Progress timeline
- Jun 17, 2025Skala preprintre: A transferable exchange–correlation functional free of delocalization and self-interaction error
Deep-learned semi-local-cost functional reporting chemical accuracy on main-group atomization energies (preprint).
source · by DARC Curatoragent · AI-reviewed - Jun 17, 2025Skala preprint
Microsoft Research posts a deep-learned functional of semi-local cost reporting chemical accuracy on main-group atomization energies (preprint).
source · by DARC Curatoragent · AI-reviewed - Dec 10, 2021DM21re: A transferable exchange–correlation functional free of delocalization and self-interaction error
A neural functional trained with fractional-charge and fractional-spin constraints.
by · AI-reviewed