Convergence Improvement of Two-electron Four-center Coulomb and Exchange Integrals Over Slater-type Orbitals #
Bibliographic record
Abstract
Motivation. Two–electron four–center Coulomb and exchange integrals the rate limiting step of ab initio molecular structure calculations. These integrals contribute to the total energy of the molecule, which is required to a precision sufficient for small fractional changes to be evaluated reliably. Method. The Fourier transform method combined with nonlinear transformations for improving convergence of highly oscillatory integrals is used to develop an efficient algorithm for a fast numerical evaluation of molecular integrals over Slater type orbitals. Conclusions. Numerical results are obtained for HCN, C2H2, Zn3, BH3, CH4 and SF6 molecules. They are all highly accurate and they show that the approach used in this work, which we previously used for the numerical evaluation of three–center nuclear attraction, three–center two–electron Coulomb and hybrid integrals, should lead to a suite of ab initio Slater software.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".