Slater-type orbital basis sets
E645113
Slater-type orbital basis sets are mathematical functions used in quantum chemistry to approximate atomic orbitals with realistic radial behavior, particularly in early and conceptual implementations of electronic structure methods.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Slater-type orbitals | 2 |
| Slater-type orbital | 1 |
| Slater-type orbital basis sets canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7150575 — 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: Slater-type orbital basis sets Context triple: [Hartree–Fock method, typicalImplementation, Slater-type orbital basis sets]
-
A.
Electronic Structures of Molecules
Electronic Structures of Molecules is a foundational scientific work by Robert S. Mulliken that systematically develops molecular orbital theory and its application to understanding the electronic properties and bonding of molecules.
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B.
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.
-
C.
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.
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D.
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.
-
E.
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.
- 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: Slater-type orbital basis sets Target entity description: Slater-type orbital basis sets are mathematical functions used in quantum chemistry to approximate atomic orbitals with realistic radial behavior, particularly in early and conceptual implementations of electronic structure methods.
-
A.
Electronic Structures of Molecules
Electronic Structures of Molecules is a foundational scientific work by Robert S. Mulliken that systematically develops molecular orbital theory and its application to understanding the electronic properties and bonding of molecules.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
basis set in quantum chemistry
ⓘ
mathematical function set ⓘ |
| approximates |
Hartree–Fock atomic orbitals
ⓘ
linked to:
Hartree–Fock method
hydrogen-like atomic orbitals ⓘ |
| assumes | central field approximation for atoms ⓘ |
| basedOn |
Slater-type orbital
ⓘ
linked to:
Slater-type orbital basis sets
|
| canBeOptimizedBy | energy minimization ⓘ |
| canBeOptimizedBy | fitting to Hartree–Fock orbitals ⓘ |
| comparedWith | Gaussian-type orbital basis set ⓘ |
| contrastsWith | Gaussian orbitals lacking nuclear cusp ⓘ |
| domain |
computational chemistry
ⓘ
theoretical chemistry ⓘ |
| hasAdvantage |
compact representation of atomic orbitals
ⓘ
correct electron–nucleus cusp ⓘ physically realistic radial behavior ⓘ |
| hasAngularPart | spherical harmonic Y_l^m(θ,φ) ⓘ |
| hasComponent |
radial function
ⓘ
spherical harmonic angular function ⓘ |
| hasCuspCondition | finite derivative at r = 0 proportional to nuclear charge ⓘ |
| hasDisadvantage |
computationally expensive multi-center integrals
ⓘ
two-electron integrals lack simple analytic solutions ⓘ |
| hasGeneralForm | R_{n,l}(r) = N r^{n-1} e^{-\zeta r} ⓘ |
| hasNormalization | N chosen to satisfy orbital normalization condition ⓘ |
| hasParameter |
orbital angular momentum quantum number l
ⓘ
principal quantum number n ⓘ screening constant zeta ⓘ |
| hasRadialBehavior |
correct exponential decay at large distance
ⓘ
realistic near-nuclear cusp ⓘ |
| hasRadialNodeCount | n-l-1 ⓘ |
| hasRadialPart | exponential function of r ⓘ |
| hasVariant | STO-nG contracted Gaussian approximation ⓘ |
| influencedDevelopmentOf | Gaussian contracted basis sets ⓘ |
| lessCommonThan | Gaussian-type orbital basis set in modern quantum chemistry ⓘ |
| namedAfter | John C. Slater ⓘ |
| usedFor |
approximation of atomic orbitals
ⓘ
atomic structure calculations ⓘ conceptual and pedagogical studies ⓘ model calculations ⓘ |
| usedIn |
LCAO (linear combination of atomic orbitals) methods
ⓘ
Slater–Condon rules applications ⓘ atomic spectral calculations ⓘ configuration interaction with STOs ⓘ early Hartree–Fock calculations ⓘ early ab initio molecular calculations ⓘ electronic structure theory ⓘ molecular orbital theory ⓘ quantum chemistry ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Slater-type orbital basis sets Description of subject: Slater-type orbital basis sets are mathematical functions used in quantum chemistry to approximate atomic orbitals with realistic radial behavior, particularly in early and conceptual implementations of electronic structure methods.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Slater-type orbital basis sets
linked to: Slater-type orbital basis sets
subject linked to:
Slater-type orbital basis sets
linked to: Slater-type orbital basis sets