Fast computation of DFT nuclear gradient with multiresolution*<i>This article is dedicated to Dr. Russell J. Boyd for his distinguished career in chemical research</i>.
Bibliographic record
Abstract
We present an efficient algorithm for evaluating the exchange-correlation contribution to the nuclear gradients of density-functional theory calculation within the local spin-density approximation. The algorithm is an extension of the multiresolution exchange-correlation (mrXC) method, which treats smooth and compact parts of the electron density separately. The nuclear gradient of the smooth density is calculated on the even-spaced grid while the compact part of the density is handled on the normal atom-centered grid (ACG). The overall formulism is still formally based on the ACG, and thus does not change the results of the existing ACG-based algorithms for all-electron density-functional theory (DFT) calculations. The variation of the positions and weights of ACG owing to the nuclear perturbation is also handled rigorously. Benchmark calculations with different basis sets and sizes of ACG show that mrXC reduces the computational cost by several times without loss of accuracy. It also lessens the impact on the CPU time when the size of the ACG is increased.
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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 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".