Self-interaction correction scheme for approximate Kohn-Sham potentials
Bibliographic record
Abstract
Recently [Phys. Rev. Lett. 108, 253005 (2012)], we observed that approximate Hartree-exchange-correlation potentials constructed from electron densities depleted at the highest-occupied molecular orbital (HOMO) level mimic the exact potential at intermediate distances from the nuclei; we then used this fact to obtain accurate Rydberg excitation energies of atoms and molecules within time-dependent density-functional linear-response theory employing standard semilocal approximations. Here we reinterpret this method as a form of self-interaction correction for Kohn-Sham potentials. We show that the greatest improvement in HOMO eigenvalues occurs when the charge removed from the HOMO level is about $\frac{1}{2}$ electron, which explains why the Slater transition-state method works well for predicting ionization energies. The greatest improvement in Kohn-Sham orbital gaps, however, is achieved when about $\frac{1}{4}$ electron is removed, which is why smaller HOMO depopulations are required for obtaining accurate excitation energies. The relationship between our self-interaction correction scheme, Slater's transition-state technique, and the $X\ensuremath{\alpha}$ method is also clarified.
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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".