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
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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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it