A potential model intended to be a general purpose model for the condensed phases of water is presented. TIP4P/2005 is a rigid four site model which consists of three fixed point charges and one Lennard-Jones center. The parametrization has been based on a fit of the temperature of maximum density (indirectly estimated from the melting point of hexagonal ice), the stability of several ice polymorphs and other commonly used target quantities. The calculated properties include a variety of thermodynamic properties of the liquid and solid phases, the phase diagram involving condensed phases, properties at melting and vaporization, dielectric constant, pair distribution function, and self-diffusion coefficient. These properties cover a temperature range from 123 to 573 K and pressures up to 40,000 bar. The model gives an impressive performance for this variety of properties and thermodynamic conditions. For example, it gives excellent predictions for the densities at 1 bar with a maximum density at 278 K and an averaged difference with experiment of 7 x 10(-4) g/cm3.

The ability of several water models to predict the properties of ices is discussed. The emphasis is put on the results for the densities and the coexistence curves between the different ice forms. It is concluded that none of the most commonly used rigid models is satisfactory. A new model specifically designed to cope with solid-phase properties is proposed. The parameters have been obtained by fitting the equation of state and selected points of the melting lines and of the coexistence lines involving different ice forms. The phase diagram is then calculated for the new potential. The predicted melting temperature of hexagonal ice (Ih) at 1 bar is 272.2 K. This excellent value does not imply a deterioration of the rest of the properties. In fact, the predictions for both the densities and the coexistence curves are better than for TIP4P, which previously yielded the best estimations of the ice properties.

Over the last forty years many computer simulations of water have been performed using rigid non-polarizable models. Since these models describe water interactions in an approximate way it is evident that they cannot reproduce all of the properties of water. By now many properties for these kinds of models have been determined and it seems useful to compile some of these results and provide a critical view of the successes and failures. In this paper a test is proposed in which 17 properties of water, from the vapour and liquid to the solid phases, are taken into account to evaluate the performance of a water model. A certain number of points between zero (bad agreement) and ten (good agreement) are given for the predictions of each model and property. We applied the test to five rigid non-polarizable models, TIP3P, TIP5P, TIP4P, SPC/E and TIP4P/2005, obtaining an average score of 2.7, 3.7, 4.7, 5.1, and 7.2 respectively. Thus although no model reproduces all properties, some models perform better than others. It is clear that there are limitations for rigid non-polarizable models. Neglecting polarizability prevents an accurate description of virial coefficients, vapour pressures, critical pressure and dielectric constant. Neglecting nuclear quantum effects prevents an accurate description of the structure, the properties of water below 120 K and the heat capacity. It is likely that for rigid non-polarizable models it may not be possible to increase the score in the test proposed here beyond 7.6. To get closer to experiment, incorporating polarization and nuclear quantum effects is absolutely required even though a substantial increase in computer time should be expected. The test proposed here, being quantitative and selecting properties from all phases of water can be useful in the future to identify progress in the modelling of water.

Abstract. In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The methodology to compute the free energy of solid phases will be discussed. In particular, the Einstein crystal and Einstein molecule methodologies are described in a comprehensive way. It is shown that both methodologies yield the same free energies and that free energies of solid phases present noticeable finite size effects. In fact this is the case for hard spheres in the solid phase. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices) will be described in detail. The free energies of ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4P models of water. Initial coexistence points leading to the determination of the phase diagram of water for these two models will be provided. Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from free energy calculations, direct coexistence simulations and free surface simulations, agree within their statistical uncertainty. Phase diagram calculations can indeed help to improve potential models of molecular fluids. For instance, for water, the potential model TIP4P/2005 can be regarded as an improved version of TIP4P. Here we will review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe the behaviour of charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites (patchy sites).

The performance of several popular water models (TIP3P, TIP4P, TIP5P and TIP4P/2005) is analyzed. For that purpose the predictions for ten different properties of water are investigated, namely: 1. vapour-liquid equilibria (VLE) and critical temperature; 2. surface tension; 3. densities of the different solid structures of water (ices); 4. phase diagram; 5. melting-point properties; 6. maximum in the density of water at room pressure and thermal coefficients alpha and KT; 7. structure of liquid water and ice; 8. equation of state at high pressures; 9. self-diffusion coefficient; 10. dielectric constant. For each property, the performance of each model is analyzed in detail with a critical discussion of the possible reason of the success or failure of the model. A final judgement on the quality of these models is provided. TIP4P/2005 provides the best description of almost all properties of the list, the only exception being the dielectric constant. In second position, TIP5P and TIP4P yield a similar performance overall, and the last place with the poorest description of the water properties is provided by TIP3P. The ideas leading to the proposal and design of the TIP4P/2005 are also discussed in detail. TIP4P/2005 is probably close to the best description of water that can be achieved with a non-polarizable model described by a single Lennard-Jones (LJ) site and three charges.