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 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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".