Why good quality water models have a surprisingly wide range of dielectric constants

Simple water models with fixed partial charges, particularly 4-site models such as TIP4P/2005, TIP4P-FB, and OPC, have proven to be highly accurate in reproducing many experimental properties of liquid water. It is intriguing that dielectric constants of these models, together with those of popular 3-site models, such as SPC/E and TIP3P, cover a wide range of values, often very far from the experimental one. Here, we address the issue of the surprising insensitivity of the quality of a water model to its dielectric constant. We build upon our recently developed machine learning-assisted methodology for water model development to construct and analyze a large set of high-quality water models with dielectric constants varying from ∼45 to ∼75. We confirm the weak sensitivity of the water model quality on the dielectric constant in this broad range, with optimal values for classical 4-site fixed charge water models lying between 55 and 70. We also identified a set of correlations between parameters of high quality water models at a given value of the dielectric constant.