where ε0 is the permittivity of free space, and V the system volume. Since the dielectric constant results from the cooperative motion and structure between water molecules, it is one of the most important properties a water model should reproduce. The results for the dielectric constant are presented in Figure . As with the other properties discussed so far, there is a general improvement in the reproduction of the dielectric constant as a function of publication year. One notable exception is the TIP5P-2018 model, which exhibits a 63% overestimate of the experimental value, despite being one of the most recent models published. Designed to improve the density and self-diffusion coefficient over a range of temperatures, the TIP5P-2018 model does represent an improvement for 5-point models in self-diffusion coefficient, density, surface tension, and other properties not examined in this study, but the authors report that in order to reproduce the dynamic properties of water, it was necessary to downscale the charges, which resulted in an anomalously high dielectric constant. In general, models published before 2006 reproduce the experimental dielectric constant poorly, with TIP3P, TIP5P, and Class II models overestimating and SPC and TIP4P models underestimating the dielectric constant. This is likely due to the fact that dielectric constant was generally not part of the target data in the force field parameterization process, rather than due to the use of PPPM for long-range electrostatics here. In fact, values for the dielectric constant for TIP4P and SPC/E calculated in the 1990s agree quite well with the values calculated in this work. On the other hand, values for TIP3P calculated in the 1990s varied from 73 to 82 using different methods, 136, 137 which while quite close to the experimental value differ significantly from the value calculated here. This further emphasizes the need for properties to be calculated within a consistent framework, using consistent methods. Three of the models in this study were specifically parameterized to reproduce the dielectric constant: TIP4P/ε, SPC/ε, and the flexible FBA/ε. As expected, all reproduce the experimental dielectric constant quite well, although for the SPC/ε and FBA/ε models it appears to come at the cost of the self-diffusion coefficient, which is discussed in the next section. For the SWM4-NDP polarizable model, the Drude induced dipole represents (in a very simplified manner) electronic degrees of freedom, and the polarization terms are expected to be relevant for the dielectric constant. It is therefore not surprising that it performs well for the reproduction of the experimental dielectric constant.