Studies of the energy density functional approach. I. Kinetic energy
Bibliographic record
Abstract
The quantum kinetic energy density is defined and its properties discussed. Its limiting values, at the nucleus of an atom and at large distances from it, are both shown to be proportional to the corresponding values of the charge density. The properties of existing kinetic energy density functionals are analyzed with respect to their local behavior and compared with the quantum results at the Hartree-Fock level. Their local behavior is found to be unsatisfactory. It is shown that the higher-order terms in the general gradient expansion, which may be considered as the basis for these models, diverge in the long-range limit. In view of these findings, a model of the kinetic energy density functional is proposed which possesses the correct limiting values for an exact as well as for a Hartree-Fock charge density. Its local behavior is found to be in good agreement with the quantum results. Thus, the integrated values of this kinetic energy density functional are in excellent general agreement with Hartree-Fock values, the percentage error in the estimate for argon, for example, being 0.04%. The basis for this model is a partitioning of the charge density into corelike and valence components. The charge density itself is not modeled, as the proposed partitioning scheme may be applied to any density, including the exact one. Consequently, the present model should be useful in the energy density functional approach to the study of the physical properties of atoms, molecules, and solids.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| 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) | 0.004 | 0.001 |
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".