Optimization of nonlinear parameters in trial wave functions with a very large number of terms
Bibliographic record
Abstract
A procedure is proposed to construct highly accurate variational wave functions with large and very large numbers of basis functions. The procedure has a number of advantages in actual computations on parallel computer clusters. In particular, by using this procedure we have determined very accurate numerical values of the ground-state energies in the positronium ion ${\mathrm{Ps}}^{\ensuremath{-}}$ (or ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}}$) $(E=\ensuremath{-}0.262\phantom{\rule{0.2em}{0ex}}005\phantom{\rule{0.2em}{0ex}}070\phantom{\rule{0.2em}{0ex}}232\phantom{\rule{0.2em}{0ex}}980\phantom{\rule{0.2em}{0ex}}107\phantom{\rule{0.2em}{0ex}}770\phantom{\rule{0.2em}{0ex}}375\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ and hydrogen ion $^{\ensuremath{\infty}}\mathrm{H}^{\ensuremath{-}}$ $(E=\ensuremath{-}0.527\phantom{\rule{0.2em}{0ex}}751\phantom{\rule{0.2em}{0ex}}016\phantom{\rule{0.2em}{0ex}}544\phantom{\rule{0.2em}{0ex}}377\phantom{\rule{0.2em}{0ex}}196\phantom{\rule{0.2em}{0ex}}589\phantom{\rule{0.2em}{0ex}}759\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ The variational energies of the negative hydrogenlike ions (or ${\mathrm{H}}^{\ensuremath{-}}$-like ions) with the finite nuclear masses (${\mathrm{T}}^{\ensuremath{-}}$, ${\mathrm{D}}^{\ensuremath{-}}$, $^{1}\mathrm{H}^{\ensuremath{-}}$, and ${\mathrm{Mu}}^{\ensuremath{-}}$) are also presented. These energies are the best variational ground-state energies ever obtained for these ions.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| 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 | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".