Atomic radial correlation energy density components
Bibliographic record
Abstract
The components of the radial correlation energy density are calculated and analyzed for the atoms from He to Ar. The components include the nucleus-electron potential correlation energy density, the kinetic correlation energy density and the electron–electron potential correlation energy density. The necessary correlated one and two-electron density matrices are obtained from the Extrapolated-Full-Configuration-Interaction (exFCI) wave function where the reference wave function is restricted Hartree–Fock (RHF) or restricted open-shell Hartree–Fock (ROHF) depending on whether the atom is closed or open-shell. The accuracy associated with integrating the HF and exFCI energy density components, and the correlation energy density components, is evaluated on the SG-1 and SG-2 atomic grids. The SG-1 grid provides atomic energies that are accurate to about 1 kJ mol −1 , with the exception of the kinetic energy. The SG-2 grid is required for the analysis of atomic kinetic energies and more subtle energetic effects. There is also a significant amount of integration error cancellation in the correlation energy densities. The radial correlation energy densities display notable shell structure, and there is a substantial difference between the α and β -electron correlation energy densities for the open-shell atoms. • For analysis of atomic kinetic energies or subtle energetic effects the SG-2 grid is required. • Calculation of the one and two-electron density matrices allows for analysis of the one and two-electron correlation energy components. • Effects of correlation can vary widely depending on the spin of the electrons.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.023 | 0.008 |
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".