Anomalous thermodynamic properties of water: What is wrong and/or missing in SAFT equations?

This work is motivated by a simple question: why have none of the Statistical Association Fluid Theory (SAFT)-type equations of state proposed for water so far-perturbation-like models with several adjustable parameters-been able to reproduce water's thermodynamic properties over a broad range of conditions, even at a qualitative level? We examine two theoretical, analytically treatable water models of different character, i.e., models that provide genuine predictions without being parameterized to experimental thermodynamic data. The first is an extremely simple toy model designed to capture the essential physics of association. The second is a short-range model derived from the realistic TIP4P force field and intended for the same purpose. For both models, we compute the isobaric temperature dependence of the density and three response functions: the isothermal compressibility, the isobaric expansivity, and the isobaric heat capacity over a wide range of thermodynamic conditions. The results are compared with experimental data and with predictions from the best-performing SAFT equation identified in our earlier work. We show that the short-range models correctly capture the characteristic behavior of the density and the isothermal compressibility, as well as the critical compressibility factor and the universal expansivity point (the crossing point) of the isobaric expansivity-features that are generally missing in SAFT-type equations. However, these short-range models fail to reproduce the heat capacity, which is an expected consequence of missing long-range electrostatic contributions. We argue that the shortcomings of existing SAFT equations for water stem from (i) the arbitrariness in defining the reference system, (ii) neglecting the van der Waals interaction in the reference completely, (iii) the ambiguity of the correction terms, and (iv) the subsequent parameter-estimation strategy.