Accuracy of expectation values of one‐electron operators obtained from Hartree–Fock wavefunctions expanded using Lambda functions
Bibliographic record
Abstract
Abstract The accuracy of the expectation values () of one‐electron operators is examined using Hartree–Fock wavefunctions expanded using functions. In this expansion, 150 terms, then 149, 148, and 147 terms are used for the s‐, p‐, d‐, and f‐symmetries, respectively. The systems investigated are He–Ne and the Group 18 atoms of Ar–Og. The one‐electron properties investigated are the cusp condition (CC), the electron density at the nucleus (), and (). Convergence of is examined by increasing the number of expansion terms () up to the given limit (150). The number of significant figures (SF) of is counted by comparing the calculated value at =150 () with the extrapolated value . For He, the SF of CC is found to be 26. For the atoms under consideration, the SF of CC is approximately half that of the total energy (TE). The SFs of expectation values of the other properties are also smaller than for the TE.
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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 | 0.005 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 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".