Bibliographic record
Abstract
Abstract The problem of the numerical determination of the atomic orbitals used in the construction of molecular orbitals in MO‐LCAO calculations is studied. This gives rise to a two‐fold optimization problem; the Roothaan–Hall Hartree–Fock problem of minimizing the energy with respect to the molecular orbital expansion coefficients and the variational problem of optimizing the atomic orbitals. The variational equations for the atomic orbitals are derived and the methods of solution described. The methods of computing the required multicenter integrals for numerical orbitals using Fourier transform methods are also reviewed. The calculation of energy gradients within this framework is discussed. Results are presented for a number of small molecules. Possible advantages of this approach are smaller basis sets are required and the wave functions at the nuclei can be much better approximated than with Gaussian‐type orbitals. As well, the fact that orbitals are better approximated implies that basis set superposition errors for dissociation energies calculated in the Hartree–Fock approximation will be reduced. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".