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.

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All labels observed (7)

Label	Occurrences
Kohn–Sham density functional theory	4
Kohn–Sham equations canonical	4
Self-Consistent Equations Including Exchange and Correlation Effects	2
Kohn–Sham effective potential	1
Kohn–Sham matrix	1
Kohn–Sham operator	1
time-dependent Kohn–Sham equations	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.
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
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 ⓘ linked to: Kohn–Sham equations
implementedIn	ABINIT ⓘ CP2K ⓘ Gaussian ⓘ Quantum ESPRESSO ⓘ VASP ⓘ
includesTerm	Hartree potential ⓘ linked to: Coulomb potential exchange–correlation potential ⓘ external potential ⓘ
introducedBy	Lu Jeu Sham ⓘ Walter Kohn ⓘ
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 ⓘ
relatedTo	Hohenberg–Kohn theorems ⓘ linked to: Hohenberg–Kohn theorem
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 ⓘ linked to: Kohn–Sham equations
usedFor	band structure calculations ⓘ electronic structure calculations ⓘ materials property predictions ⓘ molecular property calculations ⓘ
usesPotential	Kohn–Sham effective potential ⓘ linked to: Kohn–Sham equations
validFor	ground-state properties ⓘ
yearProposed	1965 ⓘ

How these facts were elicited