Unified treatment of electronic attraction, electric field, and electric-field gradient multicenter integrals of reened and nonscreened Coulomb potentials using overlap integrals for Slater orbitals
Bibliographic record
Abstract
A unified treatment of multicenter electronic attraction (EA), electric field (EF), and electric-field gradient (EFG) integrals of Yukawa-like screened and nonscreened Coulomb potentials with Slater-type orbitals (STOs) is described. Using different sets of series expansion formulas of two-center distributions for STOs in terms of STOs at a displaced center the EA, EF, and EFG integrals over STOs are expressed through the overlap integrals between potentials or their derivatives and STOs. These two-center overlap integrals are evaluated by the use of rotational transformation for overlap integrals established by the author. The final results expressed through the overlap integrals of STOs with the same screening constants are valid for the arbitrary parameters of STOs and potentials. PACS No.: 31.15.p
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".