ANALYTICAL DEVELOPMENT OF MULTICENTER OVERLAP-LIKE QUANTUM SIMILARITY INTEGRALS OVER SLATER TYPE ORBITALS AND NUMERICAL EVALUATION
Bibliographic record
Abstract
Molecular overlap-like quantum similarity measurements imply the evaluation of overlap integrals of two molecular electronic densities related by the Dirac delta function. When the electronic densities are expanded over atomic orbitals using the usual LCAO (Linear Combination of Atomic Orbitals) scheme, overlap-like quantum similarity integrals could be expressed as a linear combination of four-center overlap integrals. In previous works, we showed that the one-center two-range expansion method leads to very complicated analytic expressions for three- and four-center terms. This is why its use has been prevented even for two-center integrals. We also showed that the use of the Fourier transform approach, combined with the so-called B functions, leads to great simplifications in both analytical and numerical development of overlap-like quantum similarity integrals over Slater type functions. In this work, a unified analytical treatment of multicenter overlap-like quantum similarity integrals over Slater type functions is described. The Fourier transform and nonlinear transformation methods are used. The numerical results section shows that the approach described in the present work can be applied to two-, three- and four-center integrals whatever nucleus positions might be.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".