An investigation of the kohn-sham and slater approximations to the hartree-fock exchange potential
Bibliographic record
Abstract
The self-consistent-field equations for the ground state of the argon atom have been solved for a range of values of the parameter C in the local approximation: to the Hartree-Fock exchange potential. The orbital solutions with and without the Latter tail modification are used to investigate the relative merits of the Slater (C = 1) and Kohn-Sham (C = 2/3) local exchange potentials. To do this various expectation values are calculated. Total and one-electron binding energies are calculated as the expectation value of the Slater determinant built up from the orbitals and by using the statistical approximation to that expression. It is this statistical approximation for the total energy which Kohn-Sham varied to obtain their local exchange potential. When computing one-electron binding energies for frozen orbitals in the statistical approximation, it is only in the Slater case (C = 1) that the eigen-values of the self-consistent-field equations may be so interpreted. The role of the virial theorem and the improvements yielded by scaling are discussed. The Kohn-Sham model compares better with Hartree-Fock than the Slater model with regard to total energy, one-electron binding energies and the virial theorem. Other choices for C, according to various criteria, are discussed with the view towards a better statistical approximation to the Hartree-Fock exchange potential.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.001 | 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".