Finite Field Method for Nonlinear Optical Property Prediction Using Rational Function Approximants
Bibliographic record
Abstract
The finite field (FF) method is a quick, easy-to-implement tool for the prediction of nonlinear optical properties. Here, we present and explore a novel variant of the FF method, which uses a rational function to fit a molecule's energy with respect to an electric field. Similarly to previous FF methods, factors crucial for the method's accuracy were tuned. These factors include the number of terms in the function, the distribution of fields used to construct the approximation, and the initial field in the approximation. It was found that the approximant form that best fits the energy has four numerator terms and three denominator terms. To determine a reasonable field distribution, the common ratio of a geometric progression was optimized to √2. Finally, an algorithm for determining a good initial field guess was devised. The optimized FF method was used to compute the polarizability and second hyperpolarizability for a set of 121 molecules and the first hyperpolarizability for a set of 91 molecules. The results from this were compared to a previous polynomial-based FF method. It was found that using a rational function gives higher errors compared to the polynomial model. However, unlike the polynomial model, no subsequent refinement steps were needed to obtain usable results. An overall comparison of the behavior of the two methods also shows that the rational function is less sensitive to the chosen initial field, making it a good choice for new quantum chemistry codes.
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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 | 0.003 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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".