Brillouin theorem

E675971

result in Hartree–Fock theory result in quantum chemistry theorem

Brillouin theorem is a fundamental result in quantum chemistry and Hartree–Fock theory stating that single excitations from a Hartree–Fock ground state do not mix with the ground state and therefore do not lower its energy to first order.

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All labels observed (2)

Label	Occurrences
Brillouin condition	2
Brillouin theorem canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T7603296 — 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: Brillouin theorem
Context triple: [Léon Brillouin, notableConcept, Brillouin theorem]

A. 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.
B. Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
C. de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
D. Hohenberg–Kohn 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.
E. 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.
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: Brillouin theorem
Target entity description: Brillouin theorem is a fundamental result in quantum chemistry and Hartree–Fock theory stating that single excitations from a Hartree–Fock ground state do not mix with the ground state and therefore do not lower its energy to first order.

A. 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.
B. Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
C. de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
D. Hohenberg–Kohn 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.
E. 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.
F. None of above. chosen

Statements (43)

Predicate	Object
instanceOf	result in Hartree–Fock theory ⓘ result in quantum chemistry ⓘ theorem ⓘ
alsoKnownAs	Brillouin condition ⓘ linked to: Brillouin theorem
appliesTo	Hartree–Fock ground state ⓘ linked to: Hartree–Fock method closed-shell Hartree–Fock solutions ⓘ single-determinant wavefunctions ⓘ
assumes	Hartree–Fock orbitals are variationally optimized ⓘ the Hartree–Fock determinant is a stationary point of the energy ⓘ linked to: Slater determinant
category	Hartree–Fock method concept ⓘ electronic structure theory concept ⓘ quantum chemistry theorem ⓘ
concerns	configuration interaction ⓘ first-order energy corrections ⓘ single excitations ⓘ stationary conditions of the Hartree–Fock energy ⓘ
doesNotHoldIf	orbitals are not fully optimized ⓘ reference state is not a Hartree–Fock stationary point ⓘ
energyImplication	ground-state energy corrections start from double excitations in many-body expansions ⓘ
field	quantum chemistry ⓘ quantum mechanics ⓘ theoretical chemistry ⓘ
holdsFor	restricted Hartree–Fock ⓘ linked to: Hartree–Fock method unrestricted Hartree–Fock ⓘ
implies	configuration interaction singles (CIS) does not change the Hartree–Fock ground-state energy ⓘ correlation energy cannot be recovered from single excitations alone ⓘ first-order correction to the Hartree–Fock energy from single excitations is zero ⓘ matrix elements between the Hartree–Fock determinant and singly excited determinants vanish ⓘ the Hartree–Fock determinant is an eigenfunction of the Fock operator within the space of single excitations ⓘ linked to: Hartree–Fock method
mathematicalForm	⟨Φ₀\|H\|Φᵢᵃ⟩ = 0 for all single excitations \|Φᵢᵃ⟩ from the Hartree–Fock determinant \|Φ₀⟩ ⓘ
namedAfter	Léon Brillouin ⓘ
relatesTo	Brillouin condition ⓘ linked to: Brillouin theorem Fock operator ⓘ linked to: Fock matrix Slater determinants ⓘ linked to: Slater determinant orbital rotations ⓘ
states	single excitations do not lower the Hartree–Fock ground-state energy to first order ⓘ single excitations from a Hartree–Fock ground state do not mix with the ground state to first order ⓘ
usedIn	Møller–Plesset perturbation theory ⓘ analysis of orbital optimization conditions ⓘ configuration interaction theory ⓘ coupled-cluster theory ⓘ derivation of post-Hartree–Fock methods ⓘ
yearProposed	1930s ⓘ

How these facts were elicited

Referenced by (3)

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

Léon Brillouin → notableConcept → Brillouin theorem ⓘ

Brillouin theorem → relatesTo → Brillouin condition ⓘ

linked to: Brillouin theorem

Brillouin theorem → alsoKnownAs → Brillouin condition ⓘ