# Uncertainties in the Static Dielectric Constants computed from Molecular Dynamics Simulations

## TL;DR

This study compares methods for calculating dielectric constants in molecular dynamics simulations, analyzing uncertainties, system size effects, and sampling frequency, with water as a test case.

## Contribution

It introduces new uncertainty expressions for the external field method and compares them with the fluctuation method, highlighting differences and proposing alternatives.

## Key findings

- Significant differences in system size dependence between methods
- Best dielectric constant estimate for water: 70.46±0.31
- Sampling frequency impacts uncertainty estimates

## Abstract

In this work, the uncertainties in the dielectric constants of polar liquids, computed using molecular dynamics (MD) simulations, are compared for two different calculations schemes. Expressions of the uncertainty are derived for the external field method, and compared with those of the fluctuation method. Significant differences on their the system size dependence were found. In addition, alternative calculation procedures are proposed. The individual contributions of different parts of the system to the electric susceptibility, and their corresponding uncertainties, are also studied. Additionally, the effects of the sampling frequency on the uncertainties are analyzed. MD simulations of pure liquid water (SPC/E) at 298.15 K and 1 bar were performed in order to corroborate the obtained results. In such conditions, the best estimate of the dielectric constant obtained in this study is 70.46$\pm$0.31.