Nonspectral Methods for Solving the Schrödinger Equation for Electronic and Vibrational Problems
Bibliographic record
Abstract
To compute molecular and material properties, one must solve the electronic and/or vibrational Schrödinger equation. This Perspective briefly presents nonspectral (pseudospectral and grid) methods to solve the Schrödinger equation and their recent and promising applications to vibrational and electronic problems. Pseudospectral and grid methods facilitate parallelization, which is of critical importance for modern material modeling applications. By obviating the need to choose basis functions for which exact integrals are possible, they also enable one to use smaller basis sets. For the vibrational problem, pseudospectral and grid methods, in principle, make it possible to compute a vibrational spectrum without a potential surface, simply from values of the potential at points. This is possible if optimized basis functions are used. Iterative eigensolvers are very advantageous when simpler basis functions are used because matrix–vector products can be evaluated efficiently.
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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) | 0.000 | 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 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
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".