Augmented Lagrangian Method for Optimizing Non-Orthogonal Orbitals
Bibliographic record
Abstract
We applied augmented Lagrangian method to optimize molecular wave function based on non-orthogonal orbitals (Spin coupled wave function; SCWF) for its grand-state energy. In contrast to the orthogonal-orbital-based electronic structure theory, SCWF includes spin eigenfunctions to satisfy the eigen states as the operator of the square of the spin. To obtain the ground-state energy of SCWF, therefore, it is necessary to optimize the orbital and the spin-coupling coefficients simultaneously. In this study, the spin-coupling and the orbital coefficients are optimized with the augmented Lagrangian method under the constrain of normality of the wave function. We employed this SCWF method to compute dissociative potential energy surfaces (PESs) of H2, H2-, He2+, and HLi. The obtained PESs by the SCWF method are close to these by full configuration interaction theory. These results indicate that the augmented Lagrangian method is effective to optimize SCWF.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 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".