Atomic shell structure from an orbital-free-related density-functional-theory Pauli potential
Bibliographic record
Abstract
Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modeled as Gaussian threads with ring-polymer architecture in a four-dimensional thermal space, and a Pauli potential is postulated based on classical excluded volume implemented in the thermal space using Edwards--Flory-Huggins interactions in a mean-field approximation. Other approximations include a Fermi-Amaldi correction for electron-electron self-interactions, a spherical averaging approximation to reduce the dimensionality of the problem, and the neglect of correlations. Polymer scaling theory is used to show that the excluded volume form of Pauli potential reduces to the known Thomas-Fermi energy density in the uniform limit. Self-consistent equations are solved using a bilinear Fourier expansion, with radial basis functions, for the first 18 elements of the periodic table. Radial electron densities show correct shell structure, and the errors on the total binding energies compared to known binding energies are less than $9%$ for the lightest elements and drop to $3%$ or less for atoms heavier than nitrogen. More generally, it is suggested that only two postulates are needed within classical statistical mechanics to achieve equivalency of predictions with static, nonrelativistic quantum mechanics: First, quantum particles are modeled as Gaussian threads in four-dimensional thermal space and, second, pairs of threads (allowing for spin) are subject to classical excluded volume in the thermal space. It is shown that these two postulates in thermal space become the same as the Heisenberg uncertainty principle and the Pauli exclusion principle in three-dimensional space.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".