On the accurate calculation of the dielectric constant and the diffusion coefficient from molecular dynamics simulations: the case of SPC/E water

Abstract: The effect of the applied trajectory length on the convergence of the static dielectric constant and the self-diffusion coefficient were examined for the SPC/E water model in the NVT ensemble with different system size at 293 K. Very long simulation times of 6-8 ns were employed in order to track the convergence of these properties. Temperature dependence and isotope effects, via using D$_2$O instead of H$_2$O, were also investigated. A simulation for the polarizable SWM4-DP model was also carried out to compare the effect of different potential models. Radial distribution functions and the neutron weighted structure factor were also calculated; they were found to be insensitive to changing the system size in the range of 216-16000 molecules. On the other hand, the static dielectric constant and the diffusion coefficient are rather sensitive to the applied trajectory length, system size and the method of calculation. These latter properties are therefore not appropriate for assessing, and distinguishing between, potential models of water. It is clearly shown that trajectories shorter than about 6 ns are not sufficient for a sufficiently accurate determination of the dielectric constant of this water model.