On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods
Bibliographic record
Abstract
The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabaticdynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabaticdynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: (1) nuclei have kinetic energy lower than DBOC and (2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically.
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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 | 0.002 | 0.006 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".