Dependence of the virial exciton model on basis set and exact-exchange fraction
Bibliographic record
Abstract
The exchange-only (uncorrelated) singlet-triplet energy difference in one-electron excited configurations is 2Kif, where Kif is the Coulomb self-energy of the product of the transition orbitals. A nonempirical, virial-theorem argument was presented by Becke [J. Chem. Phys. 148, 044112 (2018)] that the correlated singlet-triplet energy difference should be half of this, namely, Kif. This incredibly simple result gave HOMO-LUMO singlet excitation energies in small-molecule benchmark sets as good as the popular TD-B3LYP time-dependent approach to excited states. In a subsequent application to long-chain polyenes approaching the polyacetylene limit [A. D. Becke, J. Chem. Phys. 149, 081102 (2018)], we found a dramatic dependence of the optical gap on the amount of exact exchange in the density functionals used to generate the orbitals. Here, we assess the effect of the exact-exchange fraction in standard small-molecule tests. Also, we assess two basis-set extremes: the highly practical cc-pVDZ basis set and the higher-quality aug-cc-pVTZ.
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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 | 0.005 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".