Hybrid density functionals with proper exact exchange
Bibliographic record
Abstract
Hybrid density functionals have the best overall performance among standard density func-tional approximations (DFA). According to their original design, hybrid DFAs are supposedto use the exact exchange (EXX). However, when hybrid functionals were originally intro-duced, there was no simple method to compute EXX, so all of their practical implementationsstarted using the Hartree–Fock exchange (HFX), which can be computed easily and is simi-lar to but distinct from EXX. Recent development of an efficient method for computing EXXmade it possible to implement hybrid functionals in line with their original definition. Weimplemented EXX in the PBE0 functional and compared its performance with that of HFX.We found that using EXX in PBE0 improves the standard enthalpies of formation, and thisimprovement increases with the size of the basis set and the size of the system. The max-imum improvement in standard enthalpies of formation of the G3-3 test set is 0.4 kcal/molwhen using 6-311++G(3df,3pd) basis set. For a hybrid density functional, the difference in theground-state energies computed using EXX and HFX depends quadratically on the percentageof EXX in the functional. We have also developed a method to generate the exact remainderexchange-correlation potential of the generalized Kohn–Sham DFT.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| 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".