Numerical integration of exchange-correlation energies and potentials using transformed sparse grids
Bibliographic record
Abstract
A new numerical integration procedure for exchange-correlation energies and potentials is proposed and "proof of principle" results are presented. The numerical integration grids are built from sparse-tensor product grids (constructed according to Smolyak's prescription [Dokl. Akad. Nauk. 4, 240 (1963)] ) on the unit cube. The grid on the unit cube is then transformed to a grid over real space with respect to a weight function, which we choose to be the promolecular density. This produces a "whole molecule" grid, in contrast to conventional integration methods in density-functional theory, which use atom-in-molecule grids. The integration scheme was implemented in a modified version of the DEMON2K density-functional theory program, where it is used to evaluate integrals of the exchange-correlation energy density and the exchange-correlation potential. Ground-state energies and molecular geometries are accurately computed. The biggest advantages of the grid are its flexibility (it is easy to change the number and distribution of grid points) and its whole molecule nature. The latter feature is potentially helpful for basis-set-free computational algorithms.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".