Density functional theory

Not to be confused with Discrete Fourier transform.
Electronic structure methods
Valence bond theory
Coulson–Fischer theory
Generalized valence bond
Modern valence bond theory
Molecular orbital theory
Hartree–Fock method
Semi-empirical quantum chemistry methods
Møller–Plesset perturbation theory
Configuration interaction
Coupled cluster
Multi-configurational self-consistent field
Quantum chemistry composite methods
Quantum Monte Carlo
Density functional theory
Time-dependent density functional theory
Thomas–Fermi model
Orbital-free density functional theory
Linearized augmented-plane-wave method
Projector augmented wave method
Electronic band structure
Nearly free electron model
Tight binding
Muffin-tin approximation
k·p perturbation theory
Empty lattice approximation
GW approximation
Korringa–Kohn–Rostoker method

Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals - that is, functions that accept a function as input and output a single real number.[1] In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.

DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. Computational costs are relatively low when compared to traditional methods, such as exchange only Hartree–Fock theory and its descendants that include electron correlation. Since, DFT has become an important tool for methods of nuclear spectroscopy such as Mössbauer spectroscopy or perturbed angular correlation, in order to understand the origin of specific electric field gradients in crystals.

Despite recent improvements, there are still difficulties in using density functional theory to properly describe: intermolecular interactions (of critical importance to understanding chemical reactions), especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces, dopant interactions and some strongly correlated systems; and in calculations of the band gap and ferromagnetism in semiconductors.[2] The incomplete treatment of dispersion can adversely affect the accuracy of DFT (at least when used alone and uncorrected) in the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms)[3] or where dispersion competes significantly with other effects (e.g. in biomolecules).[4] The development of new DFT methods designed to overcome this problem, by alterations to the functional[5] or by the inclusion of additive terms,[6][7][8][9][10] is a current research topic. Classical density functional theory uses a similar formalism to calculate the properties of non-uniform classical fluids.

Despite the current popularity of these alterations or of the inclusion of additional terms, they are reported[11] to stray away from the search for the exact functional. Further, DFT potentials obtained with adjustable parameters are no longer true DFT potentials,[12] given that they are not functional derivatives of the exchange correlation energy with respect to the charge density. Consequently, it is not clear if the second theorem of DFT holds[12][13] in such conditions.

  1. ^ Weisstein, Eric W. "Functional". mathworld.wolfram.com. Retrieved 2024-10-05.
  2. ^ Assadi, M. H. N.; et al. (2013). "Theoretical study on copper's energetics and magnetism in TiO2 polymorphs". Journal of Applied Physics. 113 (23): 233913–233913–5. arXiv:1304.1854. Bibcode:2013JAP...113w3913A. doi:10.1063/1.4811539. S2CID 94599250.
  3. ^ Van Mourik, Tanja; Gdanitz, Robert J. (2002). "A critical note on density functional theory studies on rare-gas dimers". Journal of Chemical Physics. 116 (22): 9620–9623. Bibcode:2002JChPh.116.9620V. doi:10.1063/1.1476010.
  4. ^ Vondrášek, Jiří; Bendová, Lada; Klusák, Vojtěch; Hobza, Pavel (2005). "Unexpectedly strong energy stabilization inside the hydrophobic core of small protein rubredoxin mediated by aromatic residues: correlated ab initio quantum chemical calculations". Journal of the American Chemical Society. 127 (8): 2615–2619. doi:10.1021/ja044607h. PMID 15725017.
  5. ^ Grimme, Stefan (2006). "Semiempirical hybrid density functional with perturbative second-order correlation". Journal of Chemical Physics. 124 (3): 034108. Bibcode:2006JChPh.124c4108G. doi:10.1063/1.2148954. PMID 16438568. S2CID 28234414.
  6. ^ Zimmerli, Urs; Parrinello, Michele; Koumoutsakos, Petros (2004). "Dispersion corrections to density functionals for water aromatic interactions". Journal of Chemical Physics. 120 (6): 2693–2699. Bibcode:2004JChPh.120.2693Z. doi:10.1063/1.1637034. PMID 15268413. S2CID 20826940.
  7. ^ Grimme, Stefan (2004). "Accurate description of van der Waals complexes by density functional theory including empirical corrections". Journal of Computational Chemistry. 25 (12): 1463–1473. doi:10.1002/jcc.20078. PMID 15224390. S2CID 6968902.
  8. ^ Jurečka, P.; Černý, J.; Hobza, P.; Salahub, D. R. (2006). "Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations". Journal of Computational Chemistry. 28 (2): 555–569. doi:10.1002/jcc.20570. PMID 17186489. S2CID 7837488.
  9. ^ Von Lilienfeld, O. Anatole; Tavernelli, Ivano; Rothlisberger, Ursula; Sebastiani, Daniel (2004). "Optimization of effective atom centered potentials for London dispersion forces in density functional theory" (PDF). Physical Review Letters. 93 (15): 153004. Bibcode:2004PhRvL..93o3004V. doi:10.1103/PhysRevLett.93.153004. PMID 15524874.
  10. ^ Tkatchenko, Alexandre; Scheffler, Matthias (2009). "Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data". Physical Review Letters. 102 (7): 073005. Bibcode:2009PhRvL.102g3005T. doi:10.1103/PhysRevLett.102.073005. hdl:11858/00-001M-0000-0010-F9F2-D. PMID 19257665.
  11. ^ Medvedev, Michael G.; Bushmarinov, Ivan S.; Sun, Jianwei; Perdew, John P.; Lyssenko, Konstantin A. (2017-01-05). "Density functional theory is straying from the path toward the exact functional". Science. 355 (6320): 49–52. Bibcode:2017Sci...355...49M. doi:10.1126/science.aah5975. ISSN 0036-8075. PMID 28059761. S2CID 206652408.
  12. ^ a b Jiang, Hong (2013-04-07). "Band gaps from the Tran-Blaha modified Becke-Johnson approach: A systematic investigation". The Journal of Chemical Physics. 138 (13): 134115. Bibcode:2013JChPh.138m4115J. doi:10.1063/1.4798706. ISSN 0021-9606. PMID 23574216.
  13. ^ Bagayoko, Diola (December 2014). "Understanding density functional theory (DFT) and completing it in practice". AIP Advances. 4 (12): 127104. Bibcode:2014AIPA....4l7104B. doi:10.1063/1.4903408. ISSN 2158-3226.