Adapting hybrid density functionals with machine learning
Bibliographic record
Abstract
Exact exchange contributions significantly affect electronic states, influencing covalent bond formation and breaking. Hybrid density functional approximations, which average exact exchange admixtures empirically, have achieved success but fall short of high-level quantum chemistry accuracy due to delocalization errors. We propose adaptive hybrid functionals, generating optimal exact exchange admixture ratios on the fly using data-efficient quantum machine learning models with negligible overhead. The adaptive Perdew-Burke-Ernzerhof hybrid density functional (aPBE0) improves energetics, electron densities, and HOMO-LUMO gaps in QM9, QM7b, and GMTKN55 benchmark datasets. A model uncertainty-based constraint reduces the method smoothly to PBE0 in extrapolative regimes, ensuring general applicability with limited training. By tuning exact exchange fractions for different spin states, aPBE0 effectively addresses the spin gap problem in open-shell systems such as carbenes. We also present a revised QM9 (revQM9) dataset with more accurate quantum properties, including stronger covalent binding, larger bandgaps, more localized electron densities, and larger dipole moments.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".