Determination of the effective dielectric constant from the accurate solution of the Poisson equation
Bibliographic record
Abstract
Constant dielectric (CD) and distance-dependent dielectric (DDD) functions are the most popular and widespread in the Molecular Mechanics simulations of large molecular systems. In this article, we present a simple procedure to derive an effective dielectric constant, epsilon (out,eff), for these two methods based on numerical solutions of the Poisson equation. It was found that because of the very approximate nature of the CD and DDD models there is no universal epsilon (out,eff), which will work equally well for all molecular systems. For example, different MD trajectories of the same molecule can produce different optimal epsilon (out,eff)s. The DDD function was found to yield better agreement with the numerical solutions of the Poisson equation than a CD model does. The reason is that a DDD function gives a better description of the electrostatic interactions at short distances between the atoms. Another interesting finding of this study is that under certain conditions epsilon (out,eff) can take negative values for a system of two atoms at a limited distance range. However, in principle, there is nothing to prevent the epsilon (out,eff) from taking negative values for specific conformations of some molecules.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 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) | 0.001 | 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".