Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots
Bibliographic record
Abstract
Koopmans' theorem implies that the Hartree-Fock quasiparticle gap in a closed-shell system is equal to its single-particle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closed-shell graphene system within the Hubbard model is equal to its tight-binding single-particle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interaction, and thus, both become small when only on-site Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and single-particle gaps of the graphene systems.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.013 | 0.003 |
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".