Dual-basis self-consistent field methods: 6-31G<b>*</b> calculations with a minimal 6-4G primary basis
Bibliographic record
Abstract
The feasibility of the strongest possible dual-basis approximation to polarized valence double zeta Hartree–Fock and density functional theory calculations is explored. Specifically, to approximate 6-31G* and 6-31 + G* calculations, a minimal 6-4G basis is constructed from 6-31G exponents. The self-consistent field calculation is performed in this minimal basis, followed by a single diagonalization step in the target basis. Statistical errors in atomization energies, molecular structures, and harmonic frequencies approach those of the target basis for HF, B3LYP and EDF1, and are far superior to calculations that do not include polarization functions. Speedups of approximately 5–10 are obtained for the energy, with speedups of 2–3 for the gradient, using existing algorithms, with significant potential for future improvements.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".