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.