Correlation effects in the low-lying excited states of the PPP models of alternant hydrocarbons. II. State correlation diagrams
Bibliographic record
Abstract
It is shown how to construct highly realistic state correlation diagrams for alternant hydrocarbons in the π-electron approximation based on the Pariser-Parr-Pople (PPP) Hamiltonian. These diagrams display the dependence of the N-electron eigenenergies of the PPP Hamiltonian on the coupling constant, which is chosen conveniently as the reciprocal value of the resonance integral β. These diagrams are easily constructed, using a minimum of calculations, since (a) the exact eigenstates and energies of the PPP Hamiltonian are easily found in both fully correlated and uncorrelated limits, (b) the states in both limits may be interrelated using the spin, space, and alternancy symmetry classification as well as the assumption of the noncrossing rule, and (c) the slopes of the eigenenergy dependence on the coupling constant is easily available in both limits. The resulting correlation diagrams give a good approximation to the low-lying exact eigenvalues of the PPP Hamiltonian for the whole range of the coupling constant and yield the correct sequences of the low-lying excited states for physically plausible values of the resonance integral.
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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 | 0.002 |
| 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) | 0.004 | 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".