Fock matrix

E645111

matrix one-electron Hamiltonian operator quantum chemistry concept

The Fock matrix is the effective one-electron Hamiltonian used in Hartree–Fock calculations to determine molecular orbitals and approximate electronic structure.

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All labels observed (2)

Label	Occurrences
Fock operator	3
Fock matrix canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T7150544 — 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: Fock matrix
Context triple: [Hartree–Fock method, yields, Fock matrix]

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. Extended Hückel method
The Extended Hückel method is a semi-empirical quantum chemistry approach developed by Roald Hoffmann to approximate molecular electronic structure and bonding using simplified orbital interactions.
C. Fock
Fock is a Swedish surname associated with several notable historical figures and families in Sweden.
D. Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
E. Clebsch–Gordan coefficients
Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
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: Fock matrix
Target entity description: The Fock matrix is the effective one-electron Hamiltonian used in Hartree–Fock calculations to determine molecular orbitals and approximate electronic structure.

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. Extended Hückel method
The Extended Hückel method is a semi-empirical quantum chemistry approach developed by Roald Hoffmann to approximate molecular electronic structure and bonding using simplified orbital interactions.
C. Fock
Fock is a Swedish surname associated with several notable historical figures and families in Sweden.
D. Huang–Rhys factor
The Huang–Rhys factor is a dimensionless parameter in solid-state and molecular spectroscopy that quantifies the strength of electron–phonon (vibronic) coupling during electronic transitions.
E. Clebsch–Gordan coefficients
Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
F. None of above. chosen

Statements (49)

Predicate	Object
instanceOf	matrix ⓘ one-electron Hamiltonian ⓘ operator ⓘ quantum chemistry concept ⓘ
actsOn	molecular orbitals ⓘ spin orbitals ⓘ
appearsIn	Hartree–Fock secular equation ⓘ linked to: Roothaan equations generalized eigenvalue problem F C = S C ε ⓘ
approximates	electronic Hamiltonian ⓘ
componentOf	Fock operator ⓘ linked to: Fock matrix
definedIn	Hartree–Fock equations ⓘ linked to: Hartree–Fock method
dependsOn	density matrix ⓘ one-electron integrals ⓘ two-electron integrals ⓘ
domain	Hilbert space of spin orbitals ⓘ
elementDependsOn	density matrix elements ⓘ electron–electron repulsion integrals ⓘ overlap matrix ⓘ
expressedIn	atomic orbital basis ⓘ molecular orbital basis ⓘ
generalizedBy	Kohn–Sham matrix ⓘ linked to: Kohn–Sham equations
hasElementType	Fock matrix element ⓘ
hasProperty	Hermitian ⓘ nonlinear functional of the orbitals ⓘ real (for real basis functions) ⓘ
hasRole	effective one-electron Hamiltonian ⓘ generator of molecular orbitals ⓘ
includesContributionFrom	Coulomb operator ⓘ core Hamiltonian ⓘ exchange operator ⓘ
namedAfter	Vladimir Fock ⓘ
range	Hilbert space of spin orbitals ⓘ
relatedTo	Kohn–Sham operator ⓘ linked to: Kohn–Sham equations Pople–Nesbet equations ⓘ Roothaan equations ⓘ
usedFor	approximating electronic structure ⓘ computing total electronic energy ⓘ determining molecular orbitals ⓘ determining orbital energies ⓘ iterative self-consistent field optimization ⓘ
usedIn	Hartree–Fock method ⓘ ab initio quantum chemistry ⓘ electronic structure calculations ⓘ molecular orbital theory ⓘ restricted Hartree–Fock ⓘ linked to: Hartree–Fock method restricted open-shell Hartree–Fock ⓘ linked to: Hartree–Fock method self-consistent field method ⓘ linked to: Hartree–Fock method semiempirical molecular orbital methods ⓘ unrestricted Hartree–Fock ⓘ linked to: Hartree–Fock method

How these facts were elicited

Referenced by (4)

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

Hartree–Fock method → yields → Fock matrix ⓘ

Fock matrix → componentOf → Fock operator ⓘ

linked to: Fock matrix

Vladimir Fock → notableWork → Fock operator ⓘ

linked to: Fock matrix

Brillouin theorem → relatesTo → Fock operator ⓘ

linked to: Fock matrix

All labels observed (2)

How this entity was disambiguated Show

Statements (49)

How these facts were elicited Show

Referenced by (4)

How this entity was disambiguated

How these facts were elicited