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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kohn–Sham equations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7150596 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Kohn–Sham equations Context triple: [density functional theory, hasTheorem, Kohn–Sham equations]
-
A.
Hartree–Fock method
The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
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B.
density functional theory
Density functional theory is a quantum mechanical method for calculating the electronic structure and properties of many-body systems, widely used in physics, chemistry, and materials science.
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C.
Electronic Structures of Molecules
Electronic Structures of Molecules is a foundational scientific work by Robert S. Mulliken that systematically develops molecular orbital theory and its application to understanding the electronic properties and bonding of molecules.
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D.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
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E.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Kohn–Sham equations Target entity description: 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.
-
A.
Hartree–Fock method
The Hartree–Fock method is an approximate quantum mechanical approach for determining the electronic structure of atoms, molecules, and solids by modeling electrons as occupying self-consistent single-particle orbitals.
-
B.
density functional theory
Density functional theory is a quantum mechanical method for calculating the electronic structure and properties of many-body systems, widely used in physics, chemistry, and materials science.
-
C.
Electronic Structures of Molecules
Electronic Structures of Molecules is a foundational scientific work by Robert S. Mulliken that systematically develops molecular orbital theory and its application to understanding the electronic properties and bonding of molecules.
-
D.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
E.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
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Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Kohn–Sham equations Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.