Fast and accurate evaluation of three‐center, two‐electron Coulomb, hybrid, and three‐center nuclear attraction integrals over Slater‐type orbitals using the <i>SD</i> transformation
Bibliographic record
Abstract
Abstract In this work, Slater‐type atomic orbitals (STOs) are expanded over B functions to exploit the compact Fourier transform of these functions. The analytic representations of three‐center nuclear attraction integrals and multicenter bielectronic integrals over B functions involve semiinfinite highly oscillatory integrals, which can be transformed into infinite series. These integrals must be evaluated precisely and quickly. This work describes an efficient method for the evaluation of these integrals based on the nonlinear SD transformation, recently developed by Safouhi. The SD method was applied to multicenter integrals over B functions, and it is shown that this method is highly efficient compared with alternatives previously used. The SD approach should lead to a definitive suite of ab initio Slater software. The convergence properties were analyzed and they showed that the approximations obtained using the SD approach converge to the exact values of the semiinfinite integrals without any constraint. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".