Brillouin theorem
E675971
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| 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]
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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.
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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.
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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.
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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.
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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 NERFINISHED ⓘ |
| appliesTo |
Hartree–Fock ground state
NERFINISHED
ⓘ
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 NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
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 NERFINISHED ⓘ |
| mathematicalForm | ⟨Φ₀|H|Φᵢᵃ⟩ = 0 for all single excitations |Φᵢᵃ⟩ from the Hartree–Fock determinant |Φ₀⟩ ⓘ |
| namedAfter | Léon Brillouin NERFINISHED ⓘ |
| relatesTo |
Brillouin condition
NERFINISHED
ⓘ
Fock operator NERFINISHED ⓘ Slater determinants NERFINISHED ⓘ 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
NERFINISHED
ⓘ
analysis of orbital optimization conditions ⓘ configuration interaction theory NERFINISHED ⓘ coupled-cluster theory ⓘ derivation of post-Hartree–Fock methods ⓘ |
| yearProposed | 1930s ⓘ |
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Input
Subject: Brillouin theorem Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.