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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".