Hohenberg–Kohn theorem

E645114

foundational result of density functional theory result in quantum mechanics theorem

The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.

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All labels observed (4)

Label	Occurrences
Hohenberg–Kohn theorems	2
Hohenberg–Kohn theorem canonical	1
first Hohenberg–Kohn theorem	1
second Hohenberg–Kohn theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T7150595 — 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: Hohenberg–Kohn theorem
Context triple: [density functional theory, hasTheorem, Hohenberg–Kohn theorem]

A. Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
B. Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
C. Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
D. 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.
E. Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
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: Hohenberg–Kohn theorem
Target entity description: The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.

A. Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
B. Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
C. Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
D. 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.
E. Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
F. None of above. chosen

Statements (42)

Predicate	Object
instanceOf	foundational result of density functional theory ⓘ result in quantum mechanics ⓘ theorem ⓘ
addresses	many-body problem in quantum mechanics ⓘ
appliesTo	systems of interacting electrons in an external potential ⓘ
assumes	non-degenerate ground state ⓘ
basisOf	density functional theory ⓘ
category	theorems in mathematical physics ⓘ theorems in quantum mechanics ⓘ
concerns	electron density ⓘ ground state of quantum systems ⓘ many-electron systems ⓘ
contrastWith	wavefunction methods depending on 3N variables for N electrons ⓘ
dimensionOfBasicVariable	three-dimensional spatial function ⓘ
field	condensed matter physics ⓘ quantum chemistry ⓘ quantum mechanics ⓘ
firstTheoremStates	the external potential is a unique functional of the ground-state density ⓘ
hasPart	first Hohenberg–Kohn theorem ⓘ linked to: Hohenberg–Kohn theorem second Hohenberg–Kohn theorem ⓘ linked to: Hohenberg–Kohn theorem
implies	existence of a universal energy functional of the electron density ⓘ one-to-one correspondence between ground-state density and external potential ⓘ
motivates	search for approximate exchange–correlation functionals ⓘ
namedAfter	Pierre Hohenberg ⓘ Walter Kohn ⓘ
originalAuthors	Pierre Hohenberg ⓘ Walter Kohn ⓘ
originalPaperTitle	Inhomogeneous Electron Gas ⓘ
provides	variational principle for the electron density ⓘ
publishedIn	Physical Review ⓘ
relatedTo	Kohn–Sham equations ⓘ Schrödinger equation ⓘ variational principle ⓘ
replaces	wavefunction as basic variable with electron density ⓘ
secondTheoremStates	the correct ground-state density minimizes the energy functional ⓘ
states	all ground-state properties of a many-electron system are functionals of the ground-state electron density ⓘ the ground-state electron density uniquely determines the external potential up to an additive constant ⓘ
underpins	Kohn–Sham density functional theory ⓘ linked to: Kohn–Sham equations
usedIn	computational chemistry ⓘ electronic structure calculations ⓘ materials science ⓘ
yearProposed	1964 ⓘ

How these facts were elicited

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

density functional theory → hasTheorem → Hohenberg–Kohn theorem ⓘ

Hohenberg–Kohn theorem → hasPart → first Hohenberg–Kohn theorem ⓘ

linked to: Hohenberg–Kohn theorem

Hohenberg–Kohn theorem → hasPart → second Hohenberg–Kohn theorem ⓘ

linked to: Hohenberg–Kohn theorem

Kohn–Sham equations → relatedTo → Hohenberg–Kohn theorems ⓘ

linked to: Hohenberg–Kohn theorem

Pierre Hohenberg → knownFor → Hohenberg–Kohn theorems ⓘ

linked to: Hohenberg–Kohn theorem

All labels observed (4)

How this entity was disambiguated Show

Statements (42)

How these facts were elicited Show

Referenced by (5)

How this entity was disambiguated

How these facts were elicited