On variational estimates for exchange‐correlation interaction obtained within super‐CI approach to MCSCF approximation
Bibliographic record
Abstract
Abstract Variation approximations for the exchange‐correlation interaction are considered which can be obtained when necessary conditions of the generalized Brillouin's theorem are fulfilled. It is done in the post‐Hartree–Fock approach to the electronic structure theories. The corresponding approximations appear within the two‐step Super‐CI self‐consistent procedure of the MCSCF one‐particle optimization. The basic formalism used is in close connection with the formalism of the extended Koopmans' theorem but here the extended Koopmans' matrix itself is calculated in a self‐consistent way. It is based on the singular value decomposition of the Koopmans' matrix. The final hermitian Koopmans' matrix satisfies the conditions of the generalized Brillouin's theorem. It commutes with the density matrix and equations for self‐consistent orbitals are transformed to the generalized Hartree–Fock equations with additional hermitian exchange correlation matrix. This matrix is interpreted as a matrix of the exchange‐correlation interaction. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".