Highly accurate numerical results for three‐center nuclear attraction and two‐electron Coulomb and exchange integrals over Slater‐type functions
Bibliographic record
Abstract
Abstract The present work focuses on the recent progress in nonlinear transformation methods for improving the convergence of highly oscillatory integrals and in their applications for an efficient and rapid numerical evaluation of molecular electronic integrals over Slater‐type functions (STFs). The nonlinear D transformation, which is probably the most effective general approach for increasing the rate of convergence of semi‐infinite oscillatory integrals, is presented. Molecular integrals over STFs are expressed as finite linear combinations of integrals over B functions. The basis set of B functions is suitable to apply the Fourier transform method, which led to analytic expressions, involving highly oscillatory functions, for molecular integrals. Efficient algorithms based on the D transformation are now developed for a numerical evaluation of molecular integrals over STFs. Numerical results that we obtained with linear and nonlinear molecules, and which are in agreement with those obtained using existing codes (Alchemy, STOP, and ADGGSTNGINT), show that the algorithms described in this work are relevant. © 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 | 0.002 | 0.006 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".