Direct iterative solution of the generalized Bloch equation. II. A general formalism for many-electron systems
Bibliographic record
Abstract
A general nonperturbative formulation of the recently proposed [H. Meißner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997); Part I] quadratic iterative scheme for the wave function expansion coefficients (WECs), enabling a direct solution of the generalized Bloch equation, is given for the ab initio electronic Hamiltonians, thus enabling the computation of the molecular electronic structure. The method exploits the concepts of a multidimensional reference or model space, a (non-Hermitian) effective Hamiltonian, and the generalized Bloch equation. The formulation in terms of WECs provides a considerable freedom in the design of various approximation schemes by combining direct iterations on WECs with their approximation by disconnected cluster components based on the exponential cluster ansatz for the wave operator. The resulting formalism is capable of handling a rather large class of both ground and excited states. While the general formulation represents a multiconfigurational, multireference scheme, a special attention is paid to its two-dimensional state selective or state specific version.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".