Finite-Size Effects and Convergence of Dielectric Fluctuations in Molecular Dynamics Simulations of Water
ORAL
Abstract
The dielectric constant of water governs electrostatic interactions in chemistry, biology, and materials science, yet its microscopic origin remains incompletely resolved. Classical fluctuation formulas estimate the static dielectric constant (εw) from dipole moment correlations, but reported SPC/E values vary between 68 and 75, with discrepancies far exceeding statistical uncertainties. Here in our study, we present a theoretical and computational study of the longitudinal dielectric function εl(k), which approaches εw in the k → 0 limit. Explicit expressions for finite-size and cut-off errors are derived and applied to extensive molecular dynamics simulations of SPC/E water using HOOMD-blue, spanning up to 400 ns and 4000 molecules.
We demonstrate that the slow convergence of εw is not a numerical artifact but a manifestation of long-lived dipole autocorrelations and metastable polarization states. Even with hundreds of nanoseconds of sampling, εw exhibits persistent finite-time bias, explaining the broad spread of values reported in prior literature. By resolving εl(k) across wavevectors, we obtain high-precision fits to the Stillinger–Lovett relation and locate the poles and zeros that control the short-range form of the Coulomb potential, introducing oscillatory corrections to 1/r interactions at nanometer distances.
Our analysis yields a consistent value of εw = 71.0 ± 2.3 (at 300 K and 1 bar pressure) and provides a quantitative framework for evaluating dielectric convergence in atomistic simulations. The results clarify the physical origin of slow dielectric relaxation, establish finite-size scaling relations, and extend the applicability of fluctuation formulas to other rigid and polarizable liquid models.
We demonstrate that the slow convergence of εw is not a numerical artifact but a manifestation of long-lived dipole autocorrelations and metastable polarization states. Even with hundreds of nanoseconds of sampling, εw exhibits persistent finite-time bias, explaining the broad spread of values reported in prior literature. By resolving εl(k) across wavevectors, we obtain high-precision fits to the Stillinger–Lovett relation and locate the poles and zeros that control the short-range form of the Coulomb potential, introducing oscillatory corrections to 1/r interactions at nanometer distances.
Our analysis yields a consistent value of εw = 71.0 ± 2.3 (at 300 K and 1 bar pressure) and provides a quantitative framework for evaluating dielectric convergence in atomistic simulations. The results clarify the physical origin of slow dielectric relaxation, establish finite-size scaling relations, and extend the applicability of fluctuation formulas to other rigid and polarizable liquid models.
*Research was supported by the U.S. Department of Energy (U.S. DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Ames National Laboratory is operated for the U.S. DOE by Iowa State University under Contract DE-AC02-07CH11358.
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Publication: 1) Water Dielectric Function at Finite Wavelength and the Convergence of its Large Wavelength Limit (Static Dielectric) by Fluctuation Formulas (only in SPC/E model).
2) Water Dielectric Function at Finite Wavelength and the Convergence of its Large Wavelength Limit (Static Dielectric) by Fluctuation Formulas in TIP3P and TIP4P (Planned paper)
Presenters
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Prapti Kakkar
- Iowa State University