Wigner Momentum Estimation and Sampling with Local Modes: A Second-Moment Approximation to High-Frequency Momentum Marginals
Abstract
Instantaneous local Gaussian approximations assign nuclear momentum widths from the curvature of the potential at each sampled configuration. Strongly compressed bonds can consequently acquire large momentum widths even when their positions are drawn from an anharmonic path-integral ensemble. We estimate momentum covariances from pathintegral coordinates and forces in local modes that follow molecular deformations. These covariances define Gaussian approximations to high-frequency Wigner momentum marginals without evaluating a Hessian at each configuration. The resulting sampling recovers the Maxwell momentum distribution in the classical limit. A rotating bond model with harmonic stretching and periodic torsion agrees with an independent quantum reference within statistical uncertainty. For trans-azobenzene at 300 K with 32 beads, the most compressed C–H bond receives a mass-weighted momentum variance of 36.53 kJ mol−1 from LGA and 19.55 kJ mol−1 from the local covariance along the same physical stretch direction. Temporal holdout errors in C–H second moments are 7.2–7.6%, compared with 2.2–5.1% for LGA relative to the finite-bead reference; the demonstrated benefit concerns the suppression of local width spikes. The largest collective C–H width remains sensitive to estimator noise. These results support the method as an approximation to high-frequency momentum widths without a frequency cap. Position-conditioned quantum correlations, non-Gaussian tails, and the continuum-bead molecular limit remain outside the demonstrated accuracy.
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BibTeX
@misc{cheng2026wigner,
title = {{Wigner Momentum Estimation and Sampling with Local Modes: A Second-Moment Approximation to High-Frequency Momentum Marginals}},
author = {Jianxin Cheng},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010857/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010857/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Wigner Momentum Estimation and Sampling with Local Modes: A Second-Moment Approximation to High-Frequency Momentum Marginals
AU - Jianxin Cheng
PY - 2026
DA - 2026/10/22
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010857/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010857/v1
AB - Instantaneous local Gaussian approximations assign nuclear momentum widths from the curvature of the potential at each sampled configuration. Strongly compressed bonds can consequently acquire large momentum widths even when their positions are drawn from an anharmonic path-integral ensemble. We estimate momentum covariances from pathintegral coordinates and forces in local modes that follow molecular deformations. These covariances define Gaussian approximations to high-frequency Wigner momentum marginals without evaluating a Hessian at each configuration. The resulting sampling recovers the Maxwell momentum distribution in the classical limit. A rotating bond model with harmonic stretching and periodic torsion agrees with an independent quantum reference within statistical uncertainty. For trans-azobenzene at 300 K with 32 beads, the most compressed C–H bond receives a mass-weighted momentum variance of 36.53 kJ mol−1 from LGA and 19.55 kJ mol−1 from the local covariance along the same physical stretch direction. Temporal holdout errors in C–H second moments are 7.2–7.6%, compared with 2.2–5.1% for LGA relative to the finite-bead reference; the demonstrated benefit concerns the suppression of local width spikes. The largest collective C–H width remains sensitive to estimator noise. These results support the method as an approximation to high-frequency momentum widths without a frequency cap. Position-conditioned quantum correlations, non-Gaussian tails, and the continuum-bead molecular limit remain outside the demonstrated accuracy.
ER -