On the application of Marcus–Hush theory to small polaron chemical dynamics in oxides: its relationship to the Holstein model and the importance of lattice–orbital symmetries
Bibliographic record
Abstract
The chemical dynamics of small polaron hopping within oxides is often interpreted through two-site variations on Marcus-Hush theory, while from a physics perspective small polaron hopping is more often approached from Holstein's solid-state formalism. Here we seek to provide a chemically oriented viewpoint, focusing on small polaron hopping in oxides, concerning these two phenomenological frameworks by employing both tight-binding modelling and first-principles calculations. First, within a semiclassical approach the Marcus-Hush relations are overviewed as a two-site reduction of Holstein's model. Within the single-band regime, similarities and differences between Holstein derived small polaron hopping and the Marcus-Hush model are also discussed. In this context the emergence of adiabaticity (or, conversely, diabaticity) is also explored within each framework both analytically and by directly evolving the system wavefunction. Then, through first-principles calculations of select oxides we explore how coupled lattice and orbital symmetries can impact on hopping properties - in a manner that is quite distinct typical chemical applications of Marcus-Hush theory. These results are then related back to the Holstein model to explore the relative applicability of the two frameworks towards interpreting small polaron hopping properties, where it is emphasized that the Holstein model offers an increasingly more appealing physicochemical interpretation of hopping processes as band and/or coupling interactions increase. Overall, this work aims to strengthen the physically oriented exploration of small polarons and their physicochemical properties in the growing oxide chemistry community.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".