On the quantum mechanical potential of mean force. II. Constrained path integral molecular dynamics integrators
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Bibliographic record
Abstract
Building on Paper I of this series, which introduced path integral Monte Carlo (PIMC) estimators for the derivative of the potential of mean force (PMF), we propose two path integral molecular dynamics (PIMD) integrators that can make use of these estimators. These integrators, c-OBABO and c-BAOAB, are based on the path integral Langevin equation (PILE) integrator, which has seen widespread success in PIMD applications, but they include support for holonomic constraints. When the reaction coordinate is the distance between two centers of mass, we find that several exact expressions are accessible: the Fixman correction, the position constraint Lagrange multiplier, and various derivatives with respect to the reaction coordinate. It is observed that c-BAOAB tends to have a smaller time step error than c-OBABO, which is consistent with previous studies on integrator step ordering in molecular dynamics with holonomic constraints and in PIMD. Further, we show that both the PMF of a water dimer and its derivative may be obtained from PIMD simulations using c-BAOAB, yielding results in agreement with the path integral umbrella sampling method previously used for this system.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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 it