An initial value representation semiclassical approach for the study of molecular systems with geometric constraints
Bibliographic record
Abstract
We present an approach for the inclusion of geometric constraints in quantum dynamics calculations based on the semiclassical initial value representation. An important feature of the method is that a Cartesian coordinate system is used throughout, resulting in a general approach that does not require the definition of new coordinates. The Herman–Kluk [M. F. Herman and E. Kluk, Chem. Phys. 91, 27 (1984)] coherent state formulation is used. The required (constrained) classical trajectories are calculated using the standard techniques of molecular dynamics and initial conditions are sampled from a distribution that obeys the constraints. An approximate form of the Herman–Kluk prefactor is used and its evaluation requires the construction of a projected Hessian matrix. In its present form, the approach allows the calculation of energy levels from the Fourier transform of the autocorrelation function. The approach is tested on a model problem consisting of two particles in a harmonic trap and constrained to remain at a fixed distance from one another. The approach yields exact results for this simplified case when compared to the exact quantum mechanical formulation. The method is then applied to a real molecular system consisting of a water molecule with fixed OH bonds and yields accurate results when compared to exact quantum mechanical results. The accuracy of the method is comparable to that of the usual semiclassical implementation where the problem is written in a new set of coordinates. The approach can be extended to more complex cases in a straightforward manner.
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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 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".