We determined many functional representations of interparticle interactions between water molecules, all of which reproduce the experimentally measured density-temperature relation at 1 bar with an accuracy better than obtained by previous models. Numerous similar descriptions of pair interactions will be discovered increasingly in the coming years, which will help us to understand why solid water has polymorphic structures and why liquid water has a large number of anomalies. We used a self-consistent Ornstein-Zernike approximation (SCOZA) with a potential given by multi-Yukawa terms. Because any smooth potential function can be fitted by multi-Yukawa terms, the method can be applied to various types of fluids. We also present a new simple fitting technique that makes the application of the SCOZA to any type of liquid much easier compared to a conventional Yukawa fit. Our new SCOZA fitting technique is among the most useful methods for determining the pair interaction between molecules of any liquid, and the potential will be helpful in improving realistic models.

Although the density anomaly of liquid water has long been studied by many different authors, it is still not clear what thermodynamic mechanism induces the anomaly. The thermodynamic properties of substances are determined by interparticle interactions. We analyze what characteristics of the pair potential cause the density anomaly on the basis of statistical mechanics and thermodynamics using a thermodynamically self-consistent Ornstein-Zernike approximation. We consider a fluid of spherical particles with a pair potential given by a hard-core repulsion plus a soft-repulsion and an attraction. We show that the density anomaly occurs when the value of the soft-repulsive potential at hard-core contact is in some proper range, and that the range depends on the attraction. Furthermore, we show that the behavior of excess internal energy plays an essential role in the density anomaly, and that the behavior is mainly determined by the value of the soft-repulsive potential, especially near the hard-core contact. Our results show that most of the ideas put forward up to now do not explain the direct causes of the density anomaly of liquid water. It has been known for a long time that these ideas tell us nothing about what causes the negative thermal expansion at temperatures below 4 C.•

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The analytical solution of the Ornstein-Zernike equation with a Sogami-Ise type closure for a multicomponent fluid discussed in our previous work (Yasutomi and Ginoza 2000 J. Phys.: Condens. Matter 12 L605) is extended to a more general case that where cij(r) is the direct correlation function, r is the interparticle separation, Kij(n,τ) and zn are constants, σij is the distance at contact of the pair (i,j) of particles. Almost all of the interaction potentials between particles (such as a potential due to diffuse electric double layer, van der Waals potential, steric potential and so on) can be well approximated by the above closure. In this sense the present analytical solution will be applicable to a large variety of colloidal fluids under the mean-spherical-approximation (MSA).