Triple points and coexistence properties of the dense phases of water calculated using computer simulationw Jose L. F. Abascal,* Eduardo Sanz and Carlos Vega Received 25th July 2008, Accepted 19th September 2008 First published as an Advance Article on the web 6th November 2008 DOI: 10.1039/b812832d In recent years our group has performed a thorough study of the dense region of the phase diagram of water. In this paper we report the numerical results for the triple points and for the change in volume, Dv, and enthalpy, DH, along the coexistence lines involving liquid water and/or ices ih (hexagonal), II, III, V and VI for several simple water models. The predictions for Dv using the TIP4P/2005 model are in excellent agreement with the experimental values. As to DH for the same model, the computer simulation results are also satisfactory although there are small but significant differences between simulation and experiment. I. Introduction Water exhibits a rich variety of crystalline phases. 1 In fact, the phase diagram of water presents (at least) fifteen different solid phases 2–6 with the last ones discovered in recent years. 7–9 Despite the great number of studies of water and amorphous water by computer simulation, 10–18 the crystalline solids have received less attention. In recent years there is a clear increase in the interest to study solid phases of water by computer simula- tion 19–36 and in the determination of the relative stability of the different ices between them or with respect to the liquid. 19,37–52 Most of the studies have focused on the investigation of the melting temperature of hexagonal ice (Ih). For this reason, we undertook the task of calculating the complete phase diagram of water for two of the simplest and more popular water models: SPC/E, 53 and TIP4P. 54,55 As a result we were able to present the overall appearance of the dense region of the water phase for these models. 56 That work resulted in a number of important conclusions. Firstly, it became apparent that the coexistence lines invol- ving the liquid and any of the relatively low density ices (Ih, III, V, and VI) exhibited a reentrant behaviour. As the reentrants lie in the metastable region, this behaviour has not yet been seen in real experiments. The only experimental support comes from the fact that the liquid–ice Ih coexistence line has a negative slope (in the p-T plane) with the absolute value of the slope increasing with temperature. Because of this, the existence of the reentrant was already suggested some time ago 57 based exclusively on experimental results. Our results confirmed that, and thus, the part of the liquid-Ih line exhibiting a negative slope is simply the upper branch of the reentrant. Moreover, other ices also exhibited similar beha- viour. Another important conclusion of our former work was that the phase diagram is a stringent test of water models. Although both models perform similarly for many liquid properties, their predicted phase diagrams are significantly different: that of TIP4P is in qualitative agreement with experiment while SPC/E shows significant departures. For SPC/E, ice II takes over most of the low to medium pressures range of the phase diagram so that ices Ih, III, and V become metastable phases. This fact triggered new studies trying to explain the observed behaviour. The conclusions pointed towards the important effect of the quadrupolar interactions in water. 58–61 From a more practical point of view it was concluded that the superio- rity of TIP4P is a consequence of a more appropriate distribu- tion of the charges, with the negative charge shifted from the oxygen atom. 56,58–60 It became clear that this information could be used to improve the water potential model and some effort was made in that direction. Two reparametrisations of TIP4P were proposed: TIP4P/Ice 62 and TIP4P/2005. 63 The first model was designed to reproduce the melting temperature of ice Ih while the second one was parametrised to produce a general purpose model for the condensed phases of water. The interest of these studies eclipsed other questions involved in the phase diagram of water. But some properties fully deserve a report. The case of the enthalpy change at melting is paradigmatic, especially when compared with the importance attributed to the enthalpy of vaporisation which has been the basis (together with the density at ambient conditions) of most of the parametrisation schemes for water models. In fact, it seems interesting to investigate the change in the more relevant quantities (volume, entropy and enthalpy changes) along the coexistence lines. On the other hand, the great effort done in the calculation of the phase diagram of SPC/E and TIP4P (later extended to TIP4P/Ice and TIP4P/ 2005) may help other researchers to do similar work for other water models. The condition for this to be fulfilled is to make available the numerical values of the coexistence temperatures and pressures of the different coexisting phases and of thermo- dynamic quantities at the triple points. In this way, the aim of this work is twofold. Firstly, we want to provide the numerical values of the coexistence lines and triple points reported previously in a graphical manner. On the other hand, in this Departamento de Quı´mica Fı´sica, Facultad de Ciencias Quı´micas, Universidad Complutense, Madrid, 28040, Spain. E-mail: abascal@quim.ucm.es w Electronic supplementary information (ESI) available: Coexistence temperatures and pressures; internal energies and densities of the coexisting phases. See DOI: 10.1039/b812832d 556 | Phys. Chem. Chem. Phys., 2009, 11, 556–562 This journal is  c the Owner Societies 2009 PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics