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Dipolar versions of two qualitatively different types of simple short range model fluids which exhibit the phenomenon of hydrogen bonding and which could thus serve as a reference in equations of state for associating fluids have been considered: the primitive model of water descending from the TIP4P model and the fluid of hard tetrahedra. The hydrogen bonding structure exhibited by the latter model results from purely repulsive interactions whereas in the first model the “hydrogen bonding interaction” is explicitly incorporated in the model. Since the water molecules bear a strong dipole moment, the effect of the added dipole-dipole interaction on the structure of the two short-range models is therefore examined considering them both in the full and screened dipole-dipole modifications. It is found that the hydrogen bonding structure in the primitive model resulting from the site-site interactions is so strong that the additional dipole-dipole interaction has only a marginal effect on its structure and contributes thus only to the internal energy. On the contrary, even only a weak dipole-dipole interaction destroys the original hydrogen bonding structure of the hard tetrahedron fluid; to preserve it, a screened dipole-dipole interaction has to be used in the equation of state development.

An alternative way of utilizing the thermodynamic perturbation theory of Wertheim for the development of equations of state for associating fluid models is presented and detailed for water. The approach makes use of general features of the parameter of non-saturation to avoid the necessary solution of an algebraic equation and unbinds the results from a tight dependence on details of the simple reference fluid model used in the perturbation theory.

The papers in this special issue of ``Condensed Matter Physics'' have been submitted with the dedication to Professor Dr. Yuriy Kalyuzhnyi on the occasion of his 70th birthday.

We argue that recently proposed [Melnyk et al., Fluid Phase Equilibr., 2009, 279, 1] a criterion to split the pair interaction potential into two parts, one of which is forced to be responsible for excluded volume in the system, results in the expressions for virial coefficients that improve the performance of the virial equation of state in general, and at subcritical temperatures, in particular. As an example, application to the Lennard-Jones-like hard-core attractive Yukawa fluid is discussed.

Molecular dynamics simulations have been performed on pure liquid water, aqueous solutions of sodium chloride, and polymer solutions exposed to a strong external electric field with the goal to gain molecular insight into the structural response to the field. Several simulation methodologies have been used to elucidate the molecular mechanisms of the processes leading to the formation of liquid bridges and jets (in the production of nanofibers). It is shown that in the established nanoscale structures, the molecules form a chain with their dipole moments oriented parallel to the applied field throughout the entire sample volume. The presence of ions may disturb this structure leading to its ultimate disintegration into droplets; the concentration dependence of the threshold field required to stabilize a liquid column has been determined. Conformational changes of the polymer in the jetting process have also been observed.

The idea of this special issue was derived a year ago. The year 2014 was a significant anniversary both generally and personally. Personally, it was 80 years since the oldest of us, Douglas Henderson, was born. More generally, it was a hundred years since another important paper in the theory of liquids by Ornstein and Zernike appeared. With this in mind, we felt it is timely for a collection of expert contributions to fill at least some of the gaps on the way to answer that magic question What is "liquid"? We are thankful for all colleagues who joined us in this project.

The problem of a physical relevance (meaning) of percolation in supercritical fluids is addressed considering a primitive model of water. Two different criteria, physical and configurational, are used for the cluster definition in Monte Carlo simulations over a range of pressures to determine the percolation line and skewness, and a theoretical analytic equation of state is used to evaluate response functions. It is found that both criteria yield practically the same percolation line. However, unlike the findings for simple fluids, the loci of the response function extrema exhibit density/pressure dependence quite different from that of the percolation line. The only potential coincidence between the loci of the extrema of a thermodynamic property and a detectable structural change is found for the coefficient of isothermal compressibility and Voronoi neighbors distribution skewness maximum.

A perturbation approach based on the first-order mean spherical approximation (FMSA) is proposed. It consists in adopting a hard-sphere plus short-range attractive Yukawa fluid as the novel reference system, over which the perturbative solution of the Ornstein-Zernike equation is performed. A choice of the optimal range of the reference attraction is discussed. The results are compared against conventional FMSA/HS theory and Monte-Carlo simulation data for compressibility factor and vapor-liquid phase diagrams of the medium-ranged Yukawa fluid. Proposed theory keeps the same level of simplicity and transparency, as the conventional FMSA/HS approach does, but shows to be more accurate.

Monte Carlo simulation studies are performed for the Lennard-Jones like two Yukawa (LJ2Y) potential to show how properties of this model fluid depend on the replacement of the soft repulsion by the hard-core repulsion. Different distances for the positioning of hard core have been explored. We have found, that for temperatures that are slightly lower and slightly higher of the critical point temperature for the Lennard-Jones fluid, placing the hard core at distances that are shorter than zero-potential energy is well justified by thermodynamic properties that are practically the same as in original LJ2Y model without hard core. However, going to extreme conditions with the high temperature one should be careful since presence of the hard core provokes changes in the properties of the system. The later is extremely important when the mean spherical approximation (MSA) theory is applied to treat the Lennard-Jones-like fluid.

Recent systematic and extensive computer simulations on realistic models of polar and associating fluids have shown that the long-range interactions have only marginal effect on the properties of these fluids. This finding leads to short-range models upon which a perturbation theory may be developed. An attempt to develop a methodology to construct such models (called primitive models) directly from the parent realistic models without resorting to (or reducing at least to minimum) ad hoc adjustments is presented and exemplified by constructing models of methanol, water, and carbon dioxide. It is shown that the structural properties of the primitive model fluids obtained by means of purely theoretical considerations compare well with those of their realistic counterparts. [ABSTRACT FROM AUTHOR]

The two-dimensional Mercedes-Benz model of water has been studied by molecular simulations over a wide range of thermodynamic conditions as an attempt to locate the supercooled region where a liquid-liquid separation and, potentially, also other structures may occur. Both the correlation functions and a number of local structure factors have been used to identify different structural arrangements. These include, in addition to the hexatic phase, also the hexagon, pentagon, and quadruplet arrangements. All these structures result from the competition between the hydrogen bonding and Lennard-Jones interactions and their effect at different temperatures and pressures. Based on the obtained results, an attempt is made to sketch a (rather complex) phase diagram of the model., Competing Interests: Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Thermodynamic properties and structure of binary mixtures of patchy and spherical colloids are studied using a recently developed theory [Y. V. Kalyuzhnyi, et al., Soft Matter, 2020, 16, 3456]. The theory is based on a solution of the multidensity Ornstein-Zernike equation and provides completely analytical expressions for the structure factors of these systems and for all their major thermodynamical quantities. The considered mixtures are made up of particles of different size and with a different number of patches. A set of molecular simulation data has been generated to enable a systematic comparison and to access thus accuracy of the theoretical predictions. In general, the predictions of the theory appear to be in good agreement with computer simulation data. For the models with a lower number of patches (n p = 1, 2) the theoretical results show very good accuracy. Less accurate are the predictions for the four-patch versions of the model. While theoretical results for the radial distribution functions are, generally, relatively accurate for all the models, results for thermodynamics deteriorate with increasing concentration of the spherical colloids. Possible ways to improve the theory are briefly outlined.

An analytic theory for the structure and thermodynamics of two-component mixtures of patchy and spherical colloids is developed. The theory is based on an analytical solution of the multidensity Ornstein-Zernike equation supplemented by the associative Percus-Yevick closure relations. We derive closed-form analytic expressions for the partial structure factors and thermodynamic properties using the energy route for the model with arbitrary number of patches and any hard-sphere size ratio of the particles. To assess the accuracy of the theoretical predictions we compare them against existing and newly generated set of computer simulation data. In our numerical calculations we consider the model with equal hard-sphere sizes and one patch. Very good agreement between results of the theory and simulation for the pair correlation functions, excess internal energy and pressure is observed for almost all values of the system density, temperature and composition studied. Only in the region of low concentrations of spherical colloids the theoretical results become less accurate.

Analytic expressions for the three- and four-particle correlation functions of the hard disk fluid in terms of geometric functionals have been derived using the combined geometric/thermodynamic idea of Boublik [Fluid Phase Equilib. 316, 1 (2012)]. To assess the approximate result, extensive Monte Carlo simulations were performed to obtain the triplet correlation function, g 3 , over a wide range of densities. We then focussed on the rolling contact configurations that are required in the second-order thermodynamic perturbation theory of patchy colloid models. The analytic approximation is shown to perform very well, and the simulation data have therefore been parametrized using Boublik's functional form for their subsequent use.

A general and direct computational scheme to locate the surface separating arbitrarily shaped domains made up of molecules (or any other particles) has been developed and is described and illustrated for several, both artificial and physical examples. The proposed scheme consists of two modules: (i) triangulation and (ii) assignment of simplices to domains. Three different triangulation methods are employed, viz., the Delaunay triangulation, regular triangulation, and quasi-triangulation. In the triangulated system, the assignment step is carried out in two different ways, one based on the characteristic metric of a particular triangulation procedure and the other on the concept of a touching sphere. Some of the combinations of the triangulation and assignment steps lead to methods already used by others to find interfacial or surface molecules, namely the alpha-shape-based method of Usabiaga nad Duque [Phys. Rev. E 79 (2009) 046709] and GITIM of Sega et al. [J. Chem. Phys. 138 (2013) 044110]. The resulting surface is defined not only as a discrete set of particles, but it is build up of facets of the triangulation forming a broken line in two dimensions or a polyhedral surface in three dimensions. Individual molecular layers are identified in a very straightforward manner, starting with the interfacial layer itself and proceeding into the interior of the phase. The proposed scheme is illustrated first by identifying border molecules of pre-sampled domains of several shapes in a plane and then applied to five physically meaningful examples: thin films, near critical water, liquid water slab in an electric field, liquid water at a solid wall, and water at condition of electric-field-induced jetting. Performance of the considered methods is critically assessed. Treatment of domains forming percolating clusters through periodic boundary conditions is also described along with the determination of their periodicity and dimensionality., (Copyright © 2017 Elsevier Inc. All rights reserved.)

The calculation of caloric properties such as heat capacity, Joule-Thomson coefficients, and the speed of sound by classical force-field-based molecular simulation methodology has received scant attention in the literature, particularly for systems composed of complex molecules whose force fields (FFs) are characterized by a combination of intramolecular and intermolecular terms. The calculation of a thermodynamic property for a system whose molecules are described by such a FF involves the calculation of the residual property prior to its addition to the corresponding ideal-gas property, the latter of which is separately calculated, either using thermochemical compilations or nowadays accurate quantum mechanical calculations. Although the simulation of a volumetric residual property proceeds by simply replacing the intermolecular FF in the rigid molecule case by the total (intramolecular plus intermolecular) FF, this is not the case for a caloric property. We describe the correct methodology required to perform such calculations and illustrate it in this paper for the case of the internal energy and the enthalpy and their corresponding molar heat capacities. We provide numerical results for c P , one of the most important caloric properties. We also consider approximations to the correct calculation procedure previously used in the literature and illustrate their consequences for the examples of the relatively simple molecule 2-propanol, CH 3 CH(OH)CH 3 , and for the more complex molecule monoethanolamine, HO(CH 2 ) 2 NH 2 , an important fluid used in carbon capture.

Supersaturated steam modeled by the Gaussian charge polarizable model [P. Paricaud, M. Předota, and A. A. Chialvo, J. Chem. Phys. 122, 244511 (2005)] and BK3 model [P. Kiss and A. Baranyai, J. Chem. Phys. 138, 204507 (2013)] has been simulated at conditions occurring in steam turbines using the multiple-particle-move Monte Carlo for both the homogeneous phase and also implemented for the Gibbs ensemble Monte Carlo molecular simulation methods. Because of these thermodynamic conditions, a specific simulation algorithm has been developed to bypass common simulation problems resulting from very low densities of steam and cluster formation therein. In addition to pressure-temperature-density and orthobaric data, the distribution of clusters has also been evaluated. The obtained extensive data of high precision should serve as a basis for development of reliable molecular-based equations for properties of metastable steam.

We developed the Gaussian charge-on-spring (GCOS) version of the original self-consistent field implementation of the Gaussian Charge Polarizable water model and test its accuracy to represent the polarization behavior of the original model involving smeared charges and induced dipole moments. For that purpose we adapted the recently proposed multiple-particle-move (MPM) within the Gibbs and isochoric-isothermal ensembles Monte Carlo methods for the efficient simulation of polarizable fluids. We assessed the accuracy of the GCOS representation by a direct comparison of the resulting vapor-liquid phase envelope, microstructure, and relevant microscopic descriptors of water polarization along the orthobaric curve against the corresponding quantities from the actual GCP water model.

We describe a computationally efficient molecular simulation methodology for calculating the concentration dependence of the chemical potentials of both solute and solvent in aqueous electrolyte solutions, based on simulations of the salt chemical potential alone. We use our approach to study the predictions for aqueous NaCl solutions at ambient conditions of these properties by the recently developed polarizable force fields (FFs) AH/BK3 of Kiss and Baranyai (J. Chem. Phys. 2013, 138, 204507) and AH/SWM4-DP of Lamoureux and Roux (J. Phys. Chem. B 2006, 110, 3308 - 3322) and by the nonpolarizable JC FF of Joung and Cheatham tailored to SPC/E water (J. Phys. Chem. B 2008, 112, 9020 - 9041). We also consider their predictions of the concentration dependence of the electrolyte activity coefficient, the crystalline solid chemical potential, the electrolyte solubility, and the solution specific volume. We first highlight the disagreement in the literature concerning calculations of solubility by means of molecular simulation in the case of the JC FF and provide strong evidence of the correctness of our methodology based on recent independently obtained results for this important test case. We then compare the predictions of the three FFs with each other and with experiment and draw conclusions concerning their relative merits, with particular emphasis on the salt chemical potential and activity coefficient vs concentration curves and their derivatives. The latter curves have only previously been available from Kirkwood-Buff integrals, which require approximate numerical integrations over system pair correlation functions at each concentration. Unlike the case of the other FFs, the AH/BK3 curves are nearly parallel to the corresponding experimental curves at moderate and higher concentrations. This leads to an excellent prediction of the water chemical potential via the Gibbs-Duhem equation and enables the activity coefficient curve to be brought into excellent agreement with experiment by incorporating an appropriate value of the standard state chemical potential in the Henry Law convention.

We evaluate the ability of selected classical molecular models to describe the thermodynamic and structural aspects of gas-phase hydration of alkali metal halide ions and the formation of small water clusters. To understand the effect of many-body interactions (polarization) and charge penetration effects on the accuracy of a force field, we perform Monte Carlo simulations with three rigid water models using different functional forms to account for these effects: (i) point charge nonpolarizable SPC/E, (ii) Drude point charge polarizable SWM4-DP, and (iii) Drude Gaussian charge polarizable BK3. Model predictions are compared with experimental Gibbs free energies and enthalpies of ion hydration, and with microscopic structural properties obtained from quantum DFT calculations. We find that all three models provide comparable predictions for pure water clusters and cation hydration but differ significantly in their description of anion hydration. None of the investigated classical force fields can consistently and quantitatively reproduce the experimental gas-phase hydration thermodynamics. The outcome of this study highlights the relation between the functional form that describes the effective intermolecular interactions and the accuracy of the resulting ion hydration properties.

It is known that none of the available simple molecular interaction models of aqueous electrolytes based on SPC/E water and their associated force fields are able to reproduce the concentration dependence of important thermodynamic properties of even the simplest electrolyte, NaCl, at ambient conditions over the entire experimentally accessible concentration range [ Mouc̆ka , F. ; Nezbeda , I. ; Smith , W. R. J. Chem. Phys. 2013 , 138 , 154102 ]. This paper explores the possibility of improving their performance by incorporating concentration-dependent experimental data for the total ionic chemical potential and the density into the fitting procedure, in addition to experimental values of solubility and solid chemical potential. We describe a general parameter estimation methodology for a studied class of models that incorporates the aforementioned experimental data. When the entire concentration range is considered, although the resulting force field is a slight improvement over others currently available in the literature, overall quantitative agreement with the experimental data over this range remains unsatisfactory. This indicates an inherent limitation of such simple molecular interaction models and strongly suggests that more complex mathematical forms of such models are required to quantitatively predict the properties of aqueous electrolyte solutions when the entire concentration range is of interest. Our parameter estimation methodology is also applicable to such cases.

This paper deals with molecular simulation of the chemical potentials in aqueous electrolyte solutions for the water solvent and its relationship to chemical potential simulation results for the electrolyte solute. We use the Gibbs-Duhem equation linking the concentration dependence of these quantities to test the thermodynamic consistency of separate calculations of each quantity. We consider aqueous NaCl solutions at ambient conditions, using the standard SPC/E force field for water and the Joung-Cheatham force field for the electrolyte. We calculate the water chemical potential using the osmotic ensemble Monte Carlo algorithm by varying the number of water molecules at a constant amount of solute. We demonstrate numerical consistency of these results in terms of the Gibbs-Duhem equation in conjunction with our previous calculations of the electrolyte chemical potential. We present the chemical potential vs molality curves for both solvent and solute in the form of appropriately chosen analytical equations fitted to the simulation data. As a byproduct, in the context of the force fields considered, we also obtain values for the Henry convention standard molar chemical potential for aqueous NaCl using molality as the concentration variable and for the chemical potential of pure SPC/E water. These values are in reasonable agreement with the experimental values.

Thirteen of the most common aqueous NaCl solution force fields based on the SPC/E water solvent are examined with respect to their prediction at ambient conditions of the concentration dependence of the total electrolyte chemical potential and the solution density. We also calculate the salt solubility and the chemical potential and density of the NaCl crystalline solid. We obtain the solution chemical potential in a computationally efficient manner using our recently developed Osmotic Ensemble Monte Carlo method [F. Moučka, M. Lísal, and W. R. Smith, J. Phys. Chem. B 116, 5468 (2012)]. We find that the results of the force fields considered are scattered over a wide range of values, and none is capable of producing quantitatively accurate results over the entire concentration range, with only two of them deemed to be acceptable. Our results indicate that several force fields exhibit precipitation at concentrations below the experimental solubility limit, thus limiting their usefulness. This has important implications, both in general and for their use in biomolecular simulations carried out in the presence of counter-ions. We conclude that either different parameter fitting techniques taking high-concentration properties into account must be used when determining force field model parameters, or that the class of models considered here is intrinsically incapable of the task and more sophisticated mathematical forms must be used.

Different ways of molecular modeling of water are analyzed and their similarities and differences identified. An up-to-date summary of achievements of a general approach to common rigid site-site interaction models of molecular fluids applied to water and aqueous solutions is then presented and discussed. The method is based on considering only a short-range part of a total realistic potential (such as SPC/E or TIPxP) which determines the structure of water (and fluids in general). A simplification of the interactions at short intermolecular separations leads then to simple models, called primitive models. Quite accurate results in an analytic form for the thermodynamic properties of the models are obtained using the thermodynamic perturbation theory. It is shown that the properly constructed primitive models reproduce, qualitatively, anomalies of pure water and basic characteristics of hydrophobic hydration. The concept of an extended excluded volume, based on pseudo-hard bodies, is introduced and exemplified by considering the partial molar volume of apolar solutes. Potential future development towards a theory of water based on the primitive models as a reference with the long-range contributions added as a perturbation is discussed.

We present a new and computationally efficient methodology using osmotic ensemble Monte Carlo (OEMC) simulation to calculate chemical potential-concentration curves and the solubility of aqueous electrolytes. The method avoids calculations for the solid phase, incorporating readily available data from thermochemical tables that are based on well-defined reference states. It performs simulations of the aqueous solution at a fixed number of water molecules, pressure, temperature, and specified overall electrolyte chemical potential. Insertion/deletion of ions to/from the system is implemented using fractional ions, which are coupled to the system via a coupling parameter λ that varies between 0 (no interaction between the fractional ions and the other particles in the system) and 1 (full interaction between the fractional ions and the other particles of the system). Transitions between λ-states are accepted with a probability following from the osmotic ensemble partition function. Biasing weights associated with the λ-states are used in order to efficiently realize transitions between them; these are determined by means of the Wang-Landau method. We also propose a novel scaling procedure for λ, which can be used for both nonpolarizable and polarizable models of aqueous electrolyte systems. The approach is readily extended to involve other solvents, multiple electrolytes, and species complexation reactions. The method is illustrated for NaCl, using SPC/E water and several force field models for NaCl from the literature, and the results are compared with experiment at ambient conditions. Good agreement is obtained for the chemical potential-concentration curve and the solubility prediction is reasonable. Future improvements to the predictions will require improved force field models.

A two-Yukawa representation of the EXP6 fluids at supercritical temperatures and high pressures has been developed and examined using molecular simulations. A uniquely defined mapping of the repulsive part of the EXP6 potential curve onto the two-Yukawa potential is used. Two ranges of temperatures, one encountered in geochemical applications (T(geo) range) and the other at conditions of detonations (T(det) range), are considered and it is shown that the local structures of both fluids are practically identical. Deviations between the EXP6 and two-Yukawa potential functions at intermediate separations lead to differences in the thermodynamic properties of the two fluids at lower temperatures of the T(geo) range; at higher temperatures and in the high T(det) temperature range both the structural and thermodynamic properties of the EXP6 and two-Yukawa fluids are practically identical.

The liquid-vapor phase diagram and surface tension for the Sutherland fluids with a variable range of interaction have been determined by canonical Monte Carlo simulations and compared with the augmented van der Waals analytic theory. The theory, based on a short-range Yukawa reference, performs well for medium-range models but its accuracy deteriorates with the shortening range due to deteriorating accuracy of the underlined analytic mean spherical approximation solution for the reference Yukawa potential. The simulation results are also analyzed from the point of the extended principle of corresponding states and it is shown that the surface tension and also, to a certain degree of accuracy, the vapor-liquid coexistence curve satisfy the principle.

Extensive Monte Carlo simulations on three qualitatively different model supercritical fluids (square-well fluid, Lennard-Jonesium, and primitive water) have been performed to examine percolation threshold parameters for continuum (correlated) models and their relation to general results valid for random lattice models; random-site percolation simple-cubic lattice has therefore been considered as well. Two different bond criteria, the configurational and self-bound ones, defining a cluster have been used. In addition to the percolation threshold occupation probability pc and the percolation threshold fluid density rhoc, the correlation length exponent nu and the wrapping probability at the percolation threshold Rw,c have also been evaluated. It is found that parameters nu and Rw,c exhibit not only strong temperature dependence but also, unlike the case of lattice systems, dependence on the nature of the system considered and the employed definition of the cluster.

Starting from a realistic Hamiltonian and making use of recent findings that the properties of associating fluids are determined primarily by short-ranged interactions, this methodology has been implemented using statistical mechanical approaches and thermodynamic perturbation theory for the TIP4P model of water. We focus on the short-range reference system for which an analytic expression for the Helmholtz free energy is derived. It is found that the model (reference system) exhibits, in addition to a faithful representation of the structure of water, the same features that are characteristic for real water, namely, (i) the temperature of the density maximum and its pressure dependence, including the inflection point at high pressures and (ii) the temperature minima of the constant pressure heat capacity and the coefficient of isothermal compressibility.

We examine different spanning probability functions (wrapping and crossing) near the percolation threshold of a supercritical square-well fluid and determine the threshold values of these probabilities, which may be universal for all fluids. It is shown that for a continuous system, over a wide range of system size, the wrapping probabilities can be described by universal scaling functions, whereas the crossing probabilities do not show such universal behavior over the same range of system size. The obtained universal functions for the wrapping probabilities can be used for an estimation of the percolation threshold in fluids in general. The results for the crossing probabilities allow us then to characterize large clusters in real fluids.

A novel perturbation approach for the structure factor S(k) of the Lennard-Jones-type Yukawa fluid with z=1.8 is presented. An approach is based on a new reference system, that is, the short-range Yukawa model with z0>z=1.8. By choosing for the reference system the value z0=6, it is shown that (i) the proposed approach for S(k) performs much better than the traditional hard-sphere reference perturbation method does; (ii) the use of an approximate mean spherical (MSA) description of the reference structure factor provides the results for S(k) that are more accurate as those obtained from the direct MSA computations; and (iii) the results obtained for S(k) tend to reproduce "exact" simulation results when accurate simulation data for the reference system are used.

A novel Monte Carlo simulation scheme based on biased simultaneous displacements of all particles of the system has been developed. The method is particularly suited for systems with nonadditive interactions and its efficiency is demonstrated by its implementation for the polarizable Stockmayer fluid. Performance of the method is compared with both the standard one-particle move method and an unbiased multiparticle scheme by computing the mean squared displacements, rotation relaxation, and the speed of equilibration (translational order parameter). It is shown that the proposed biased method is about a factor of 10 faster, for the system considered, when compared with the other schemes.

The vapor-liquid equilibria of three recently proposed water models have been computed using Gibbs-Duhem simulations. These models are TIP4P/Ew, TIP4P/2005, and TIP4P/ice and can be considered as modified versions of the TIP4P model. By design TIP4P reproduces the vaporization enthalpy of water at room temperature, whereas TIP4P/Ew and TIP4P/2005 match the temperature of maximum density and TIP4P/ice the melting temperature of water. Recently, the melting point for each of these models has been computed, making it possible for the first time to compute the complete vapor-liquid equilibria curve from the triple point to the critical point. From the coexistence results at high temperature, it is possible to estimate the critical properties of these models. None of them is capable of reproducing accurately the critical pressure or the vapor pressures and densities. Additionally, in the cases of TIP4P and TIP4P/ice the critical temperatures are too low and too high, respectively, compared to the experimental value. However, models accounting for the density maximum of water, such as TIP4P/Ew and TIP4P/2005 provide a better estimate of the critical temperature. In particular, TIP4P/2005 provides a critical temperature just 7 K below the experimental result as well as an extraordinarily good description of the liquid densities from the triple point to the critical point. All TIP4P-like models present a ratio of the triple point temperature to the critical point temperature of about 0.39, compared with the experimental value of 0.42. As is the case for any effective potential neglecting many body forces, TIP4P/2005 fails in describing simultaneously the vapor and the liquid phases of water. However, it can be considered as one of the best effective potentials of water for describing condensed phases, both liquid and solid. In fact, it provides a completely coherent view of the phase diagram of water including fluid-solid, solid-solid, and vapor-liquid equilibria.

A parallelized sampling version of the Gibbs Ensemble (Mol. Phys. 2000, 98, 1887) has been implemented to predict low-temperature vapor-liquid equilibria of 1- and 2-methylnaphthalene modeled by anisotropic united atom potentials. The simulation were performed at the low temperature of 364.2 K at which common direct simulation methods fail due to particle transfer problems. The simulation results are compared with published results obtained from the Gibbs-Duhem integration method and with experimental data. Both methods are compared and discussed in terms of computational efficiency and with respect to their future use at other thermodynamic conditions.