Interpretation of the Kohn–Sham orbital energies as approximate vertical ionization potentials
Bibliographic record
Abstract
Theoretical analysis and results of calculations are put forward to interpret the energies −εk of the occupied Kohn–Sham (KS) orbitals as approximate but rather accurate relaxed vertical ionization potentials (VIPs) Ik. Exact relations between εk and Ik are established with a set of linear equations for the εk, which are expressed through Ik and the matrix elements εkresp of a component of the KS exchange-correlation (xc) potential vxc, the response potential vresp. Although −Ik will be a leading contribution to εk, other Ij≠k do enter through coupling terms which are determined by the overlaps between the densities of the KS orbitals as well as by overlaps between the KS and Dyson orbital densities. The orbital energies obtained with “exact” KS potentials are compared with the experimental VIPs of the molecules N2, CO, HF, and H2O. Very good agreement between the accurate −εk of the outer valence KS orbitals and the corresponding VIPs is established. The average difference, approaching 0.1 eV, is about an order of magnitude smaller than for HF orbital energies. The lower valence KS levels are a few eV higher than the corresponding −Ik, and the core levels some 20 eV, in agreement with the theoretically deduced upshift of the KS levels compared to −Ik by the response potential matrix elements. Calculations of 64 molecules are performed with the approximate vxc obtained with the statistical averaging of (model) orbitals potentials (SAOP) and the calculated εk are compared with 406 experimental VIPs. Reasonable agreement between the SAOP −εk and the outer valence VIPs is found with an average deviation of about 0.4 eV.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".