Triple
T7150561
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hartree–Fock method |
E166679
|
entity |
| Predicate | solvedBy |
P8791
|
FINISHED |
| Object |
Roothaan–Hall equations
The Roothaan–Hall equations are a set of matrix equations that recast the Hartree–Fock approximation into an algebraic form suitable for computational determination of molecular orbitals and electronic structure.
|
E166679
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Roothaan–Hall equations | Statement: [Hartree–Fock method, solvedBy, Roothaan–Hall equations]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Roothaan–Hall equations Context triple: [Hartree–Fock method, solvedBy, Roothaan–Hall equations]
-
A.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
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.
Lippmann–Schwinger equation
The Lippmann–Schwinger equation is an integral equation in quantum scattering theory that reformulates the Schrödinger equation to describe how incoming waves are transformed into scattered waves by a potential.
-
D.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
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.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Roothaan–Hall equations Triple: [Hartree–Fock method, solvedBy, Roothaan–Hall equations]
Generated description
The Roothaan–Hall equations are a set of matrix equations that recast the Hartree–Fock approximation into an algebraic form suitable for computational determination of molecular orbitals and electronic structure.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Roothaan–Hall equations Target entity description: The Roothaan–Hall equations are a set of matrix equations that recast the Hartree–Fock approximation into an algebraic form suitable for computational determination of molecular orbitals and electronic structure.
-
A.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
B.
Hartree–Fock method
chosen
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.
Lippmann–Schwinger equation
The Lippmann–Schwinger equation is an integral equation in quantum scattering theory that reformulates the Schrödinger equation to describe how incoming waves are transformed into scattered waves by a potential.
-
D.
Wigner–Eckart theorem
The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
-
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.
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69c68886779c8190a8e3fbabffe68253 |
completed | March 27, 2026, 1:39 p.m. |
| NER | Named-entity recognition | batch_69c6e7f28b188190b1732ca711666531 |
completed | March 27, 2026, 8:26 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7ada940e08190b16e97e363801e75 |
completed | March 28, 2026, 10:30 a.m. |
| NEDg | Description generation | batch_69c7ae5767408190860c1c7bc3a769fa |
completed | March 28, 2026, 10:32 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7aeb68c3481909c6dff8ee51349ab |
completed | March 28, 2026, 10:34 a.m. |
Created at: March 27, 2026, 2:46 p.m.