How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2
Bibliographic record
Abstract
Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".