Augmented Lagrangian method for spin‐coupled wave function
Bibliographic record
Abstract
Abstract We applied augmented Lagrangian method coupled with derivative‐free methods to optimize molecular wave function based on non‐orthogonal orbitals, that is called spin‐coupled generalized valence bond (SCGVB), for its ground‐state energy. In contrast to the orthogonal‐orbital‐based electronic structure theory, the SCGVB includes spin eigenfunctions to satisfy the eigenstates as the operator of the square of the spin. To obtain the ground‐state energy of SCGVB, therefore, it is necessary to optimize the orbital and the spin‐coupling coefficients simultaneously. In this study, we validated feasibility of the derivative‐free augmented Lagrangian method for optimizing the spin‐coupling and the orbital coefficients with the constraint of normality of the wave function. We employed this SCGVB method to compute dissociative potential energy curves (PECs) of H 2 , , , and LiH. The obtained PECs by the SCGVB method are close to these by full configuration interaction theory. These results indicate that the augmented Lagrangian method is effective to optimize the wave function of SCGVB.
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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".