Interrogating the Becke’05 density functional for non-locality information
Bibliographic record
Abstract
In two papers, Becke [J. Chem. Phys. 119, 2972 (2003) and J. Chem. Phys. 122, 064101 (2005)] introduced Kohn-Sham density-functional approximations for static and dynamical correlation to be partnered with 100 percent exactly computed exchange. Known as "B05," this was the first non-local correlation model designed to work with the full non-locality of exact (or Hartree-Fock) exchange. Non-locality issues, often referred to as the "delocalization" problem, are among the most vexing problems in density-functional theory today. How much exact exchange should be used in a hybrid functional? What value of the range parameter should be used in a long-range corrected functional? Questions such as these abound, and the answers are system dependent. The physics of non-locality is built into the B05 functional in a natural way, and one wonders, therefore, if B05 might provide a mechanism to answer such questions. Here we explore a variational procedure, "B05min," to do so. We compute dipole moments of 52 small molecules and find that B05min delivers better moments than parent hybrid and long-range corrected functionals. Furthermore, B05min provides a priori optimum exact-exchange mixing fractions and range parameters for the parent functionals, whose values agree with literature values fit to experimental data.
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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 | 0.004 | 0.006 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".