The model also presents a minimum in the isothermal compressibility close to 310K. We have also investigated the atmospheric pressure isobar for three other water models; the SPC/E and TIP4P models also present a minimum in the isothermal compressibility, although at a considerably lower temperature than the experimental one. For the temperature range considered no such minimum is found for the TIP5P model.

The melting point of ice I h for the TIP3P, SPC, SPC/E, TIP4P, TIP4P/Ew and TIP5P models has been determined by computer simulation. It has been found that the melting points of ice I h for these models are 146, 190, 215, 232, 245 and 274 K respectively. Thus from the models of water available so far only TIP5P reproduces the experimental melting point of water. The relative stability of ice II with respect to ice I h at the normal melting point has also been considered. Ice II is more stable than ice I h for the TIP3P, SPC, SPC/E and TIP5P models. Only for the TIP4P and TIP4P/Ew models is ice I h more stable than ice II at low pressures. The complete phase diagram for the SPC/E, TIP4P and TIP5P models has been computed. It has been found that SPC/E and TIP5P do not correctly describe the phase diagram of water. However, TIP4P provides a qualitatively correct description of the phase diagram of water. A slight modification of the parameters of the TIP4P model yields a new model, denoted as TIP4P/ice, which reproduces the experimental melting point of water and provides an excellent description of the densities of all ice phases.

With a view to a better understanding of the influence of atomic quantum delocalisation effects on the phase behaviour of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model, in conjunction with the rigid rotor propagator proposed by Müser and Berne [Phys. Rev. Lett. 77, 2638]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example densities, structure and relative stabilities.

Monte Carlo computer simulation studies have been undertaken for virtually all of the ice phases as well as for liquid water for three of the most popular model potentials; namely SPC/E, TIP4P and TIP5P. Densities have been calculated for specific thermodynamic state points and compared to experimental results. The SPC/E and TIP4P models overestimate the solid densities by about 2%. The TIP5P model overestimates the solid densities by about 5-10%. The structural pair correlation functions between oxygen-oxygen, hydrogen-hydrogen and oxygen-hydrogen atoms were also obtained from the simulations. (These are available as ESIt). It has been found that SPC/E and TIP4P structural predictions are rather similar, with the only exception of ice II for which differences are visible between these two models. Predictions from the TIP5P are clearly different from those of the other models, especially for ices Ih and II. For the higher density ices structural differences between the models are rather small. Experimental data would be highly desirable to test the structural predictions of the different models of water. This is especially true for ice II. We have also found that the oxygen-oxygen correlation function of high density amorphous (HDA) water presents the same broad features as those exhibited by ice XII.

In this note we present results for the heat capacity at constant pressure for the TIP4PQ/2005 model, as obtained from path integral simulations. The model does a rather good job of describing both the heat capacity of ice I h and of liquid water. Classical simulations using the TIP4P/2005, TIP3P, TIP4P, TIP4P-Ew, SPC/E and TIP5P models are unable to reproduce the heat capacity of water. Given that classical simulations do not satisfy the third law of thermodynamics, one would expect such a failure at low temperatures. However, it seems that for water, nuclear quantum effects influence the heat capacities all the way up to room temperature. The failure of classical simulations to reproduce C p points to the the necessity of incorporating nuclear quantum effects to describe this property accurately.