Correlated double-proton transfer. I. Theory
Bibliographic record
Abstract
The dynamics of double-proton transfer reactions is studied on a model of transfer along two identical hydrogen bonds represented by quartic double-minimum potentials. Correlation between the proton motions is introduced by a coupling term that is bilinear in the two proton coordinates; it is shown that this form properly accounts for the polarity and symmetry of the interaction and correctly reproduces the observed transfer behavior in the strong- and weak-coupling limits. The model allows a universal description of double-proton transfer mechanisms in symmetric systems in terms of the variation of a single parameter, the (dimensionless) coupling between the two hydrogen bonds. The corresponding two-dimensional (2D) transfer potential has up to nine stationary points, depending on the coupling strength. The resulting dynamics and its dependence on temperature and isotopic substitution are studied analytically by instanton techniques for the full range of the correlation parameter whereby the potential has multiple saddle points. For any coupling, the dynamics at high temperatures is dominated by classical transitions over the saddle point of lowest barrier. Strong coupling leads exclusively to synchronous transfer along a single collective coordinate, weak coupling to competition between this synchronous transfer, and stepwise transfer along local coordinates, the relative contributions of these mechanisms being governed by the temperature. Below a certain crossover temperature, transfer dynamics is dominated by the instanton, i.e., the trajectory with maximum tunneling probability. Two types of instanton are found on the 2D potential. The well-known one-dimensional instanton, corresponding to synchronous motion, exists for any coupling. It dominates at low temperatures and is responsible for any observed tunneling splittings, independent of the number of saddle points of the symmetric potential. An alternative 2D instanton, corresponding to asynchronous motion, exists for weak coupling. It is shown that under conditions where 2D tunneling dominates, it is much slower than stepwise transfer. Therefore 2D tunneling trajectories do not contribute significantly to the rate of transfer and can be ignored. The favorable quantitative aspects of the model are illustrated by an application to double-proton rate constants in porphine, which have been measured in a wide range of temperatures.
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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 | 0.000 | 0.001 |
| 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 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".