<i>Ab initio</i>evaluation of Coulomb and exchange parameters for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>DFT</mml:mi><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi></mml:mrow></mml:math>calculations
Bibliographic record
Abstract
Conventional density functional theory (DFT) fails for materials with strongly correlated electrons, such as late transition metal oxides. Large errors in the intra-atomic Coulomb and exchange interactions are the source of this failure. The $\mathrm{DFT}+\mathrm{U}$ method has provided a means, through empirical parameters, to correct these errors. Here, we present a systematic ab initio approach in evaluating the intra-atomic Coulomb and exchange terms, $U$ and $J$, respectively, in order to make the $\mathrm{DFT}+\mathrm{U}$ method a fully first-principles technique. The method is based on a relationship between these terms and the Coulomb and exchange integrals evaluated in the basis of unrestricted Hartree-Fock molecular orbitals that represent localized states of the extended system. We used this ab initio scheme to evaluate $U$ and $J$ for chromia $({\mathrm{Cr}}_{2}{\mathrm{O}}_{3})$. The resulting values are somewhat higher than those determined earlier either empirically or in constrained DFT calculations but have the advantage of originating from an ab initio theory containing exact exchange. Subsequent $\mathrm{DFT}+\mathrm{U}$ calculations on chromia using the ab initio derived $U$ and $J$ yield properties consistent with experiment, unlike conventional DFT. Overall, the technique developed and tested in this work holds promise in enabling accurate and fully predictive $\mathrm{DFT}+\mathrm{U}$ calculations of strongly correlated electron materials.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".