Kohn–Sham equations
E645115
equations
formalism in density functional theory
self-consistent field equations
single-particle equations
The Kohn–Sham equations are a set of self-consistent single-particle equations in density functional theory that map an interacting many-electron system onto a fictitious non-interacting system with the same electron density.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
equations
ⓘ
formalism in density functional theory ⓘ self-consistent field equations ⓘ single-particle equations ⓘ |
| aimsToReproduce | exact ground-state electron density ⓘ |
| approximates | exchange–correlation energy functional ⓘ |
| assumes | existence of non-interacting reference system ⓘ |
| basedOn | density functional theory ⓘ |
| centralConcept |
effective single-particle orbitals
ⓘ
self-consistent electron density ⓘ |
| commonlyUses |
generalized gradient approximation
ⓘ
hybrid exchange–correlation functionals ⓘ local density approximation ⓘ |
| describes | fictitious non-interacting electron system ⓘ |
| field |
computational materials science
ⓘ
condensed matter physics ⓘ quantum chemistry ⓘ |
| generalizedTo | time-dependent Kohn–Sham equations NERFINISHED ⓘ |
| implementedIn |
ABINIT
NERFINISHED
ⓘ
CP2K NERFINISHED ⓘ Gaussian NERFINISHED ⓘ Quantum ESPRESSO NERFINISHED ⓘ VASP NERFINISHED ⓘ |
| includesTerm |
Hartree potential
NERFINISHED
ⓘ
exchange–correlation potential ⓘ external potential ⓘ |
| introducedBy |
Lu Jeu Sham
NERFINISHED
ⓘ
Walter Kohn NERFINISHED ⓘ |
| maps |
interacting many-electron system
ⓘ
non-interacting reference system ⓘ |
| neglectsExplicit | explicit electron–electron interaction in reference system ⓘ |
| preserves | ground-state electron density of interacting system ⓘ |
| publishedIn | Physical Review NERFINISHED ⓘ |
| relatedTo | Hohenberg–Kohn theorems NERFINISHED ⓘ |
| replaces | many-body Schrödinger equation ⓘ |
| requires | exchange–correlation functional ⓘ |
| solvedBy | self-consistent field method ⓘ |
| solvedWith |
localized atomic orbitals
ⓘ
plane-wave basis sets ⓘ real-space grids ⓘ |
| titleOfOriginalPaper | Self-Consistent Equations Including Exchange and Correlation Effects NERFINISHED ⓘ |
| usedFor |
band structure calculations
ⓘ
electronic structure calculations ⓘ materials property predictions ⓘ molecular property calculations ⓘ |
| usesPotential | Kohn–Sham effective potential NERFINISHED ⓘ |
| validFor | ground-state properties ⓘ |
| yearProposed | 1965 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.