On the origins of spontaneous spherical symmetry-breaking in open-shell atoms through polymer self-consistent field theory
Bibliographic record
Abstract
An alternative approach to density functional theory based on self-consistent field theory for ring polymers is applied to neutral atoms hydrogen to neon in their ground-states. The spontaneous emergence of an atomic shell structure and spherical symmetry-breaking of the total electron density are predicted by the model using the ideas of polymer excluded-volume between pairs of electrons to enforce the Pauli-exclusion principle and an exact electron self-interaction correction. The Pauli potential is approximated by neglecting inter-atomic correlations along with other types of correlations, and comparisons to Hartree-Fock theory are made, which also ignores correlations. The model shows excellent agreement with Hartree-Fock theory to within the standards of orbital-free density functional theory for the atomic binding energies and density profiles of the first six elements, providing exact matches for the elements hydrogen and helium. The predicted shell structure starts to deviate significantly past the element neon, and spherical symmetry-breaking is first predicted to occur at carbon instead of boron. The self-consistent field theory energy functional that describes the model is decomposed into thermodynamic components to trace the origin of spherical symmetry-breaking. It is found to arise from the electron density approaching closer to the nucleus in non-spherical distributions, which lowers the energy despite resulting in frustration between the quantum kinetic energy, electron-electron interaction, and the Pauli exclusion interaction. The symmetry-breaking effect is found to have a minimal impact on the binding energies, which suggests that the spherical-averaging approximation used in previous work is physically reasonable when investigating atomic systems. The pair density contour plots display behavior similar to polymer macro-phase separation, where individual electron pairs occupy single lobe structures that together form a dumbbell shape analogous to the 2p orbital shape. It is further shown that the predicted densities satisfy known constraints and produce the same total electronic density profile that is predicted by other formulations of quantum mechanics.
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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 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".