Assessment of the Tao-Mo nonempirical semilocal density functional in applications to solids and surfaces
Bibliographic record
Abstract
Recently, Tao and Mo developed a semilocal exchange-correlation density functional. The exchange part of this functional is derived from a density-matrix expansion corrected to reproduce the fourth-order gradient expansion of the exchange energy in the slowly-varying-density limit, while the correlation part is based on the Tao-Perdew-Staroverov-Scuseria (TPSS) correlation functional, with a modification for the low-density limit. In the present paper, the Tao-Mo (TM) functional is assessed by computing various properties of solids and jellium surfaces. This includes 22 lattice constants and bulk moduli, 30 band gaps, seven cohesive energies, and jellium surface exchange and correlation energies for the density parameter ${r}_{s}$ in the range from 2 to 3 bohr. Our calculations show that the TM approximation can yield consistently high accuracy for most properties considered here, with mean absolute errors (MAEs) of 0.025 \AA{} for lattice constants, 7.0 GPa for bulk moduli, 0.08 eV/atom for cohesive energies, and $35\phantom{\rule{0.16em}{0ex}}\mathrm{erg}/\mathrm{c}{\mathrm{m}}^{2}$ for surface exchange-correlation energies. The MAE in band gaps is larger than that of TPSS, but slightly smaller than the errors of the local spin-density approximation, Perdew-Burke-Ernzerhof generalized gradient approximation, and revised TPSS. However, band gaps are still underestimated, particularly for large-gap semiconductors, compared to the Heyd-Scuseria-Ernzerhof nonlocal screened hybrid functional.
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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 | 0.003 | 0.003 |
| 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 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".