Alchemical insights into approximately quadratic energies of iso-electronic atoms
Bibliographic record
Abstract
Accurate quantum mechanics based predictions of property trends are so important for materials design and discovery that even inexpensive approximate methods are valuable. We use the Alchemical Integral Transform (AIT) to study multi-electron atoms, and to gain a better understanding of the approximately quadratic behavior of energy differences between iso-electronic atoms in their nuclear charges. Based on this, we arrive at the following simple analytical estimate of energy differences between any two iso-electronic atoms, $ΔE \approx -(1 + 2γ\sqrt{N_e-1})\,ΔZ\, \bar{Z}$. Here, $γ\approx 0.3766 \pm 0.0020$ Ha corresponds to an empirical constant, and $N_e$, $ΔZ$, and $\bar{Z}$ respectively to electron number, and nuclear charge difference and average. We compare the formula's predictive accuracy using experimental numbers and non-relativistic, numerical results obtained via DFT (pbe0) for the entire periodic table up to Radon. A detailed discussion of the atomic Helium-series is included.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".