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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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 ⓘ

Referenced by (1)

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

Léon Brillouin → notableConcept → Brillouin theorem ⓘ