Theoretical approaches to the temperature and zero‐point motion effects on the electronic band structure
Bibliographic record
Abstract
Abstract The modifications of the electronic band structure of solids due to electron‐phonon interactions (temperature and zero‐point motion effects) have been explored by Manuel Cardona from both the experimental and theoretical sides. In the present contribution, we focus on the theoretical approaches to such effects. Although the situation has improved since the seventies, the wish for a fully developed theory (and associated efficient implementations) is not yet fulfilled. We review noticeable semi‐empirical and first‐principle studies, with a special emphasis on the Allen‐Heine‐Cardona (AHC) approach. We then focus on the non‐diagonal Debye‐Waller contribution, appearing beyond the rigid‐ion approximation, in a Density‐Functional Theory (DFT) approach. A numerical study shows that they can be sizeable (10%–50%) for diatomic molecules. We also present the basic idea of a new formalism, based on Density‐Functional Perturbation Theory, that allows one to avoid the sums over a large number of empty states, and speed up the calculation by one order of magnitude, compared to the straightforward implementation of the AHC approach within DFT.
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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 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".