Dual-basis self-consistent field methods: 6-31G<b>*</b> calculations with a minimal 6-4G primary basis
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Bibliographic record
Abstract
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. Keywords: Dual-basisDensity functional theoryHartree–FockSelf-consistent field theoryGeometry optimization6-31G*B3LYPEDF1Minimal basisHarmonic frequencies Acknowledgements Funding for this work has been provided by the National Science Foundation under Grant No. CHE-0535710. RPS thanks Robert A. DiStasio Jr for providing the glycine chain structures. MH-G is a part owner of Q-Chem.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it