Symmetry breaking in spin-restricted Hartree–Fock solutions: the case of the C2 molecule and the N2+ and F2+ cations
Bibliographic record
Abstract
We examine a spin-preserving stability of restricted Hartree-Fock (RHF) and open-shell RHF (ROHF) solutions for homonuclear diatomic species, namely the molecule C(2) and the N(2)(+) and F(2)(+)cations, in the entire relevant range of internuclear separations. In the presence of respective singlet, doublet, or triplet 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. Since for homonuclear diatomic species the space symmetry of the nuclear framework cannot be broken, the only possible space symmetry breaking involves either the electron charge distribution or the rotational symmetry about the internuclear axis. Such BS solutions arise primarily due to the symmetry breaking of the valence, mostly frontier, molecular orbitals, which approach atomic-type orbitals in the dissociation limit. The resulting BS RHF or ROHF solutions yield much more realistic potential energy curves (PECs) than do the symmetry-adapted (SA) solutions. For the sake of comparison, we also generated corresponding PECs using the density functional theory (DFT). Finally, we examine the role of BS molecular orbitals in post-HF correlated approaches to the many-electron problem, specifically in the computation of equilibrium properties using the coupled-cluster method with singles and doubles (CCSD) and its perturbatively corrected version for triples, the CCSD(T) method.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".