Löwdin partitioning
E668826
effective Hamiltonian method
mathematical method
perturbation theory method
quantum mechanical technique
Löwdin partitioning is a quantum mechanical technique that reduces complex many-level systems to effective Hamiltonians acting in a smaller subspace, simplifying the analysis of electronic structure and interactions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Löwdin partitioning canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7491957 — 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: Löwdin partitioning Context triple: [Feshbach projection formalism, relatedTo, Löwdin partitioning]
-
A.
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.
-
B.
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.
-
C.
Kohn–Sham equations
The Kohn–Sham equations are a set of self-consistent single-particle equations in density functional theory that map an interacting many-electron system onto a fictitious non-interacting system with the same electron density.
-
D.
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.
-
E.
Longuet-Higgins theorem in molecular symmetry
The Longuet-Higgins theorem in molecular symmetry is a fundamental result in theoretical chemistry that relates molecular symmetry properties to electronic state degeneracies and the occurrence of phenomena such as the Jahn–Teller effect.
- 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: Löwdin partitioning Target entity description: Löwdin partitioning is a quantum mechanical technique that reduces complex many-level systems to effective Hamiltonians acting in a smaller subspace, simplifying the analysis of electronic structure and interactions.
-
A.
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.
-
B.
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.
-
C.
Kohn–Sham equations
The Kohn–Sham equations are a set of self-consistent single-particle equations in density functional theory that map an interacting many-electron system onto a fictitious non-interacting system with the same electron density.
-
D.
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.
-
E.
Longuet-Higgins theorem in molecular symmetry
The Longuet-Higgins theorem in molecular symmetry is a fundamental result in theoretical chemistry that relates molecular symmetry properties to electronic state degeneracies and the occurrence of phenomena such as the Jahn–Teller effect.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
effective Hamiltonian method
ⓘ
mathematical method ⓘ perturbation theory method ⓘ quantum mechanical technique ⓘ |
| advantage |
provides systematic corrections to effective Hamiltonians
ⓘ
reduces dimensionality of the eigenvalue problem ⓘ retains exact eigenvalues within the model space when treated formally ⓘ |
| appliesTo |
electronic structure problems
ⓘ
many-level quantum systems ⓘ molecular systems ⓘ solid-state systems ⓘ |
| assumes |
separation between model space and outer space
ⓘ
weak coupling between subspaces for perturbative expansions ⓘ |
| basedOn |
block matrix representation of the Hamiltonian
ⓘ
partitioning of the Hilbert space into model and complementary subspaces ⓘ |
| category |
electronic structure method
ⓘ
quantum mechanical approximation method ⓘ |
| field |
condensed matter physics
ⓘ
quantum chemistry ⓘ quantum mechanics ⓘ |
| hasPurpose |
derive effective Hamiltonians in a smaller subspace
ⓘ
reduce many-level quantum systems to effective few-level descriptions ⓘ simplify analysis of electronic structure ⓘ simplify analysis of interactions between electronic states ⓘ |
| introducedBy | Per-Olov Löwdin ⓘ |
| involvesOperation |
construction of an effective operator acting in the model space
ⓘ
elimination of outer-space components ⓘ |
| mathematicalForm | block-partitioned Schrödinger equation ⓘ |
| namedAfter | Per-Olov Löwdin ⓘ |
| produces |
effective Hamiltonian
ⓘ
energy-dependent effective Hamiltonian ⓘ renormalized interaction parameters ⓘ |
| relatedTo |
Brillouin–Wigner perturbation theory
ⓘ
Feshbach projection formalism ⓘ Schrieffer–Wolff transformation ⓘ downfolding techniques ⓘ |
| usedFor |
constructing tight-binding effective Hamiltonians
ⓘ
deriving low-energy effective models ⓘ eliminating high-energy degrees of freedom ⓘ treating quasi-degenerate states ⓘ |
| usedIn |
band structure calculations
ⓘ
model Hamiltonian derivations in strongly correlated systems ⓘ molecular orbital theory ⓘ spin Hamiltonian derivations ⓘ |
| usesConcept |
Hamiltonian operator
ⓘ
Hilbert space partitioning ⓘ perturbation expansion ⓘ projection operators ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Löwdin partitioning Description of subject: Löwdin partitioning is a quantum mechanical technique that reduces complex many-level systems to effective Hamiltonians acting in a smaller subspace, simplifying the analysis of electronic structure and interactions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.