Recent progress in the accurate and rapid evaluation of all Coulomb integrals over slater‐type orbitals
Bibliographic record
Abstract
Abstract One of the main objectives in ab initio Slater research is rapid and accurate evaluation of the two‐, three‐, and four‐center Coulomb integrals. General expressions for these integrals were obtained and evaluated for the first time using the single center strategy and requisite orbital translations. The alternative strategy using the Fourier transform of the B functions basis has been thoroughly explored by the Steinborn group. The analytical expressions of these integrals have been shown to be adapted to the use of nonlinear transformations to accelerate their convergence. A complete study of D‐ (due to Levin and Sidi) and \documentclass{article}\pagestyle{empty}\begin{document}$\bar{D}$\end{document} ‐transformations (due to Sidi) for all these integrals has led to the improved HD and \documentclass{article}\pagestyle{empty}\begin{document}$H\bar{D}$\end{document} methods, which greatly simplified the application of the above nonlinear transformations. The results presented show that the \documentclass{article}\pagestyle{empty}\begin{document}$H\bar{D}$\end{document} method gives unprecedented accuracy with speedup by a factor of 5 over the \documentclass{article}\pagestyle{empty}\begin{document}$\bar{D}$\end{document} approach and over 70 over the initial STOP method for four center terms. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".