# density functional theory

> computational quantum mechanical modelling method to investigate the electronic structure

**Wikidata**: [Q1048589](https://www.wikidata.org/wiki/Q1048589)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Density_functional_theory)  
**Source**: https://4ort.xyz/entity/density-functional-theory

## Summary
Density functional theory (DFT) is a computational quantum-mechanical method that calculates the electron density of a system to determine its ground-state electronic structure. By solving the Kohn-Sham equations derived from the Hohenberg–Kohn theorem, DFT delivers reliable predictions of molecular geometries, reaction energies, and material properties at a fraction of the cost of traditional wave-function methods.

## Key Facts
- Classified as both an algorithm and a theory within computational physics and computational chemistry.
- Uses the Hohenberg–Kohn theorem as its theoretical foundation.
- Computes the electron density and ground-state energy directly, avoiding many-body wave-functions.
- Commonly abbreviated DFT; Spanish alias “Teoría del funcional de la densidad” and French “Théorie de la fonctionnelle densité”.
- Time-dependent density functional theory (TD-DFT) is a recognized subclass for time-dependent potentials.
- Has 30 Wikipedia language editions and 51 sitelinks under computational chemistry.
- Stack Exchange tag: physics.stackexchange.com/tags/density-functional-theory.
- MeSH descriptor ID: D000077318; MeSH tree code: H01.671.579.800.500.

## FAQs
### Q: What does DFT actually calculate?
A: DFT calculates the ground-state electron density, from which total energy, geometry, and many observable properties are derived.

### Q: Why is DFT faster than traditional quantum-chemistry methods?
A: It replaces the many-electron wave-function with a set of single-electron Kohn-Sham orbitals, scaling roughly as N³ with system size rather than the factorial scaling of post-Hartree-Fock methods.

### Q: What is the difference between DFT and TD-DFT?
A: Standard DFT treats time-independent systems; TD-FT extends the formalism to time-dependent external potentials, enabling study of excited states and dynamics.

### Q: Which theorem guarantees that electron density alone determines the ground-state energy?
A: The Hohenberg–Kohn theorem (1964) proves that the ground-state electron density uniquely determines the external potential and hence all system properties.

## Why It Matters
DFT has become the workhorse of modern computational chemistry, physics, and materials science because it delivers chemically accurate results—often within a few kcal mol⁻¹—while remaining tractable for hundreds to thousands of atoms. By focusing on electron density rather than exponentially complex wave-functions, DFT enables routine prediction of molecular structures, reaction pathways, catalytic activity, band gaps, and phonon spectra. Its impact spans drug discovery, battery design, semiconductor engineering, and geophysics, turning supercomputers and even desktop clusters into virtual laboratories. Without DFT, high-throughput screening of thousands of materials or large enzymatic active sites would be computationally prohibitive.

## Notable For
- First-principles method that scales modestly (~N³) yet rivals experimental accuracy for many solid-state and molecular properties.
- Underpins the Nobel Prize in Chemistry (1998) awarded to Walter Kohn for the Hohenberg–Kohn theorem and to John Pople for combining DFT with computational codes.
- Universal acronym “DFT” recognized across 15+ languages, reflecting global adoption.
- Foundation for time-dependent DFT (TD-DFT), the dominant approach for modeling excited states in large systems.
- Central to open-source and commercial packages (VASP, Quantum ESPRESSO, Gaussian, ORCA) that cumulatively boast hundreds of thousands of citations.

## Body
### Theoretical Basis
DFT rests on two pillars: the Hohenberg–Kohn theorem, which proves that the ground-state electron density uniquely determines the Hamiltonian, and the Kohn-Sham construction, which maps the interacting many-electron problem onto a set of non-interacting electrons moving in an effective potential. Exchange and correlation effects are subsumed into an exchange-correlation functional; common approximations run from local-density (LDA) through generalized-gradient (GGA) to hybrid and meta-GGA forms.

### Practical Workflow
1. Specify atomic positions and pseudopotentials.
2. Expand Kohn-Sham orbitals in a basis set (plane waves, Gaussians, or numerical grids).
3. Self-consistently solve the Kohn-Sham equations until the density converges.
4. Extract total energy, forces, and response properties for geometry optimization or molecular dynamics.

### Extensions and Limits
TD-DFT adds time-dependent response, enabling UV/Vis spectra and charge-transfer dynamics. Strongly correlated systems often require DFT+U, hybrid functionals, or embedding techniques. Current challenges include systematic improvement of exchange-correlation approximations and accurate treatment of van-der-Waals interactions.

## References

1. [Nuovo soggettario](https://thes.bncf.firenze.sbn.it/termine.php?id=45243)
2. Nuovo soggettario
3. Freebase Data Dumps. 2013
4. YSO-Wikidata mapping project
5. Quora
6. National Library of Israel
7. KBpedia
8. [OpenAlex](https://docs.openalex.org/download-snapshot/snapshot-data-format)