Do independent-particle-model broken-symmetry solutions contain more physics than the symmetry-adapted ones? The case of homonuclear diatomics
Bibliographic record
Abstract
We explore spin-preserving, singlet stability of restricted Hartree-Fock (RHF) solutions for a number of closed-shell, homonuclear diatomics in the entire relevant range of internuclear separations. In the presence of such instabilities we explore the implied broken-symmetry (bs) solutions and check their stability. We also address the occurrence of vanishing roots rendered by the stability problem in the case of bs solutions. The RHF bs solutions arise primarily due to the symmetry breaking of the relevant, mostly frontier, molecular orbitals, which approach atomic-type orbitals in the dissociation limit. The resulting bs RHF solutions yield more realistic potential energy curves (PECs) than do the symmetry adapted (sa) solutions. These PECs are shown to be very similar to those rendered by the density functional theory (DFT). Moreover, the sa DFT solutions are found to be stable in a much wider range of internuclear separations than are the RHF solutions, and their bs analogs differ very little from the sa ones. Finally, we examine a possible usefulness of bs RHF solutions in post-HF correlated approaches to the many-electron problem, specifically in the limited configuration interaction and coupled-cluster methods.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".