<i>Ansatz</i> for the evaluation of the relativistic contributions to core ionization energies in complex molecules involving heavy atoms
Bibliographic record
Abstract
Abstract On the basis of numerical, ab initio ΔDF and ΔHF computations of 1s‐core, 2s‐core, and 2p‐core ionization energies of atoms, from Li through Xe, an allometric empirical formula that was proposed for evaluating relativistic corrections (including QED effects) to nonrelativistic values is assessed for homogeneous sets of elements in the periodic table. The two coefficients involved in this formula are precisely determined for 1s‐core ionization in the sets of atoms Be‐Ne, Mg‐Ar, Zn‐Kr, and Cd‐Xe; 2s‐core ionization in the sets of atoms Mg‐Ar, Zn‐Kr, and Cd‐Xe; and 2p‐core ionization in the set Mg‐Ar. It is shown that the medium relative error on the results obtained using this formula, with respect to those directly computed, decreases from a few percent to a few hundredths of 1% when the depth of the ionized level increases. This formula could be used to include relativistic (and QED) corrections to results yielded by simpler, nonrelativistic calculations on complex molecules involving heavy atoms. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".