Evaluation of site-site bridge diagrams for molecular fluids
Bibliographic record
Abstract
The presence of bridge functions in formally exact integral equation theories is the primary obstacle preventing the extraction of exact fluid structure from these theories. The bridge functions are typically neglected but in many fluids their impact may be significant. Each bridge function can be subdivided into bridge diagrams, which are well defined but difficult to evaluate. The calculation of bridge diagrams for the Chandler-Silbey-Ladanyi (CSL) integral equation theory is the subject of this paper. In particular, we evaluate the diagrams required to yield an exact theory up to the first power in density [O(rho(1))] and provide algorithms that remain feasible for any molecule. Further, the bridge diagrams are evaluated and compared with the f-bond and h-bond formulations. Exact bridge diagrams are numerically evaluated for several chiral molecules, for two polar dimers, and for SPC/E water. The quality of the diagrams is assessed in two ways: First, the predicted interatomic distributions are compared with those obtained from Monte Carlo simulations. Second, the connectivity constraints are evaluated and the errors in satisfying these exact relationships are compared for the f-bond and h-bond formulations. For apolar fluids, a clear improvement in CSL theory is evident with the inclusion of O(rho(0)) and O(rho(1)) diagrams. In contrast, for polar fluids, the inclusion of bridge diagrams does not lead to improvement in the structural predictions.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| 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) | 0.003 | 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".