General-model-space state-universal coupled-cluster theory: Connectivity conditions and explicit equations
Bibliographic record
Abstract
We present a new version of the state-universal (SU), multireference, coupled-cluster (CC) theory that is capable of handling completely general, incomplete model spaces. This is achieved by exploiting the concept of “locality” for the active molecular spin orbitals and by introducing the constraining conditions (C conditions) on cluster amplitudes that are associated with the internal excitations transforming one reference configuration into another one. These C conditions make it possible to represent the exact (i.e., full configuration interaction) wave function via the SU CC cluster ansatz based on an arbitrary model space. The C conditions are then taken into account together with the standard SU CC equations for the external amplitudes, thus enabling us to reach the exact result in the limit, while preserving the connectivity property and thus the size extensivity. We also present compact expressions for the matrix elements of the effective Hamiltonian as well as the explicit expressions for the most important coupling coefficients that are required at the single and double excitation level. All other expressions are the same as in the single reference CC formalism.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| 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".