Bibliographic record
Abstract
Abstract We propose a new density functional for the evaluation of the total electronic energy by subtracting the Roothaan energy, i.e. the Hartree energy of the density residual, from the Hohenberg–Kohn–Sham (HKS) functional, which is normally used in self‐consistent Kohn–Sham (KS) density functional theory (DFT) calculations. Because of the positive semi‐definite nature of the Roothaan energy, the resulting Wang–Zhou (WZ) functional always produces a total energy lower than that from the HKS functional and usually converges to the exact total energy from below. Following the same spirit of the Zhou–Wang‐λ (ZWλ) functional in the recently proposed orbital‐corrected orbital‐free (OO) DFT method (Zhou and Wang, J Chem Phys 2006, 124, 081107), we linearly mix the WZ functional with the HKS functional to allow further systematic error cancellations. The resulting Wang–Zhou‐α (WZα) functional is compared with the ZWλ functional in OO‐DFT calculations for systems within different chemical environment. We find that the optimal value of α for the WZα functional is more stable than that of λ for the ZWλ functional. This is because the WZ functional remedies the oscillatory convergence behavior of the Harris functional and renders the direct evaluation of α for the WZα functional more plausible in the application of the linear‐scaling OO‐DFT method for large systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
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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) | 0.001 | 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 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".