Hartree–Fock method

E166679

ab initio method approximate quantum mechanical method electronic structure method mean-field approximation quantum chemistry 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.

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All labels observed (19)

Label	Occurrences
Hartree–Fock method canonical	5
Hartree–Fock	4
Hartree method	3
Hartree–Fock approximation	3
restricted Hartree–Fock	3
Hartree approximation	1
Hartree-Fock approximation	1
Hartree–Fock atomic orbitals	1
Hartree–Fock energy	1
Hartree–Fock equations	1
Hartree–Fock ground state	1
Hartree–Fock–Bogoliubov theory	1
Roothaan–Hall equations	1
generalized Hartree–Fock	1
restricted open-shell Hartree–Fock	1
self-consistent field method	1
the Hartree–Fock determinant is an eigenfunction of the Fock operator within the space of single excitations	1
time-dependent Hartree–Fock	1
unrestricted Hartree–Fock	1

How this entity was disambiguated

This entity first appeared as the object of triple T1462697 — 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: Hartree–Fock method
Context triple: [Pauli exclusion principle, usedIn, Hartree–Fock method]

A. 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.
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. 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.
D. Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
E. Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
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: Hartree–Fock method
Target entity description: 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.

A. 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.
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. 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.
D. Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
E. Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
F. None of above. chosen

Statements (59)

Predicate	Object
instanceOf	ab initio method ⓘ approximate quantum mechanical method ⓘ electronic structure method ⓘ mean-field approximation ⓘ quantum chemistry method ⓘ
accountsFor	exchange interaction ⓘ
appliesTo	atoms ⓘ molecules ⓘ solids ⓘ
approximates	many-electron wavefunction ⓘ
assumes	independent-particle model ⓘ
basedOn	Schrödinger equation ⓘ
computationalScaling	approximately O(N^4) with system size ⓘ
developedBy	Douglas Hartree ⓘ Vladimir Fock ⓘ
enforces	Pauli exclusion principle ⓘ
field	computational chemistry ⓘ condensed matter physics ⓘ quantum chemistry ⓘ
hasVariant	generalized Hartree–Fock ⓘ linked to: Hartree–Fock method multiconfigurational Hartree–Fock ⓘ relativistic Hartree–Fock ⓘ restricted Hartree–Fock ⓘ linked to: Hartree–Fock method restricted open-shell Hartree–Fock ⓘ time-dependent Hartree–Fock ⓘ linked to: Hartree–Fock method unrestricted Hartree–Fock ⓘ
historicalPrecursor	Hartree method ⓘ linked to: Hartree–Fock method
improvesUpon	Hartree method ⓘ linked to: Hartree–Fock method
input	basis set ⓘ nuclear charges ⓘ nuclear coordinates ⓘ
neglects	dynamic electron correlation ⓘ
output	electron density ⓘ molecular orbital coefficients ⓘ total electronic energy ⓘ
relatedTo	density functional theory ⓘ
solvedBy	Roothaan–Hall equations ⓘ linked to: Hartree–Fock method self-consistent field procedure ⓘ
solvesFor	molecular orbitals ⓘ orbital energies ⓘ total electronic energy ⓘ
typicalImplementation	Gaussian-type orbital basis sets ⓘ Slater-type orbital basis sets ⓘ
usedAsReferenceFor	Møller–Plesset perturbation theory ⓘ configuration interaction ⓘ coupled-cluster theory ⓘ post-Hartree–Fock methods ⓘ
usedFor	ground-state electronic structure calculations ⓘ molecular property calculations ⓘ potential energy surface generation ⓘ
usesApproximation	Born–Oppenheimer approximation ⓘ mean-field approximation ⓘ
usesConcept	Slater determinant ⓘ antisymmetry of fermionic wavefunctions ⓘ self-consistent field ⓘ single-particle orbitals ⓘ
yields	Fock matrix ⓘ Fock operator ⓘ Hartree–Fock energy ⓘ linked to: Hartree–Fock method

How these facts were elicited