Why Molecular-Scale Occupancy Fluctuations Appear Gaussian without Being Bulk-Like
- 1H. H. Wills Physics Laboratory
- 2University of Bristol
Abstract
Molecular-scale occupancy distributions in water and hard-sphere fluids can appear remarkably Gaussian. Using classical density functional theory with an external field conjugate to the occupancy, we calculate occupancy cumulants for spherical volumes in a hard-sphere fluid and reproduce the variance and small, oscillatory third moment reported previously in Monte Carlo simulations. This agreement shows that the density functional captures the correlations responsible for the phenomenon and allows the role of excluded-volume packing to be isolated. By comparison with the Poisson limit and by varying both observation-volume size and bulk density, we show that excluded-volume correlations strongly suppress the higher cumulants. The resulting skewness and excess kurtosis remain nonzero and oscillatory, but they become small as the observation volume increases. However, over the same molecular-scale range, the finite-volume variance remains strongly scale-dependent and does not attain the extensive scaling set by the bulk compressibility. The early onset of near-Gaussianity is therefore governed primarily by molecular packing: it does not demonstrate that the fluctuations have reached the thermodynamic Gaussian limit, nor does it support a distinct small-cavity regime governed by bulk-like Gaussian fluctuations.
Related
- Angular Momentum Fluctuations Induced by Phonon-Rotation Coupling Govern Nuclear Spin Relaxation in a Molecular Rotator Phase
- GPU implementation of mixed quantum-classical Liouville molecular dynamics without momentum jump
- Resistance without a detectable bindingenergy penalty: distinct dynamic defects of gatekeeper and molecular-brake mutations in FGFR1–erdafitinib recognition
- Reference Conventions and Structure Types, Rather Than 4f Occupancy, Shape Lanthanide Errors in Universal Machine-Learning Interatomic Potentials
- Tuning antibonding-orbital occupancy in pyrene-COFs via electron-donating phenolic −OH for boosted photocatalytic H2 evolution
BibTeX
@misc{wilding2026molecularscale,
title = {{Why Molecular-Scale Occupancy Fluctuations Appear Gaussian without Being Bulk-Like}},
author = {Nigel B. Wilding},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15009134/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009134/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Why Molecular-Scale Occupancy Fluctuations Appear Gaussian without Being Bulk-Like
AU - Nigel B. Wilding
PY - 2026
DA - 2026/09/21
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009134/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009134/v1
AB - Molecular-scale occupancy distributions in water and hard-sphere fluids can appear remarkably Gaussian. Using classical density functional theory with an external field conjugate to the occupancy, we calculate occupancy cumulants for spherical volumes in a hard-sphere fluid and reproduce the variance and small, oscillatory third moment reported previously in Monte Carlo simulations. This agreement shows that the density functional captures the correlations responsible for the phenomenon and allows the role of excluded-volume packing to be isolated. By comparison with the Poisson limit and by varying both observation-volume size and bulk density, we show that excluded-volume correlations strongly suppress the higher cumulants. The resulting skewness and excess kurtosis remain nonzero and oscillatory, but they become small as the observation volume increases. However, over the same molecular-scale range, the finite-volume variance remains strongly scale-dependent and does not attain the extensive scaling set by the bulk compressibility. The early onset of near-Gaussianity is therefore governed primarily by molecular packing: it does not demonstrate that the fluctuations have reached the thermodynamic Gaussian limit, nor does it support a distinct small-cavity regime governed by bulk-like Gaussian fluctuations.
ER -