Transport properties of bulk water at 243–550 K: a Comparative molecular dynamics simulation study using SPC/E,TIP4P,and TIP4P/2005 water models

ABSTRACT

Molecular dynamics simulations of various water models – SPC/E (extended simple point charge), TIP4P (transferable intermolecular potential 4 points), and TIP4P/2005 – have been carried out in the canonical (NVT fixed) ensemble over the range of temperatures 243–550?K with Ewald summation. The transport properties (self-diffusion coefficients D, viscosities η, and thermal conductivities λ) of SPC/E, TIP4P, and TIP4P/2005 water were evaluated at 243–550?K and compared with experimental data. The temperature dependence of transport properties of SPC/E, TIP4P and TIP4P/2005 water was discussed to determine how reliable the models are over this temperature range.     

A study of the structural and thermodynamic properties of water by the molecular dynamics method

The thermodynamic and structural properties of four rigid water models were studied by the molecular dynamics method over a wide temperature range. Two three-center (SPC/E and TIP3P) and two five-center (ST4 and TIP5P) models were considered. The results discussed include the boiling and condensation temperatures, VT phase transition diagrams, three-dimensional spatial distributions of atoms, the temperature dependences of the total energy, density, heat capacity, the number of H-bonds per molecule, the distribution of H-bonds over the ∠HOO angle, the self-diffusion coefficient, and the radial distribution functions. The boiling points of all the models did not correspond to 100°C and were noticeably different from each other. The condensation points were also different. The data on the structural parameters led us to conclude that the TIP5P model reproduced the local structure of water most correctly. However, if the reproduction of the local structure is not a necessary condition, less resource consuming three-center models can be used.     

Water and other tetrahedral liquids: order, anomalies and solvation

In order to understand the common features of tetrahedral liquids with water-like anomalies, the relationship between local order and anomalies has been studied using molecular dynamics simulations for three categories of such liquids: (a)?atomistic rigid-body models for water (TIP4P, TIP4P/2005, mTIP3P, SPC/E), (b)?ionic melts, BeF(2) (TRIM model) and SiO(2) (BKS potential) and (c)?Stillinger-Weber liquids parametrized to model water (mW) and silicon. Rigid-body, atomistic models for water and the Stillinger-Weber liquids show a strong correlation between tetrahedral and pair correlation order and the temperature for the onset of the density anomaly is close to the melting temperature. In contrast, the ionic melts show weaker and more variable degrees of correlation between tetrahedral and pair correlation metrics, and the onset temperature for the density anomaly is more than twice the melting temperature. In the case of water, the relationship between water-like anomalies and solvation is studied by examining the hydration of spherical solutes (Na(+), Cl(-), Ar) in water models with different temperature regimes of anomalies (SPC/E, TIP4P and mTIP3P). For both ionic and nonpolar solutes, the local structure and energy of water molecules is essentially the same as in bulk water beyond the second-neighbour shell. The local order and binding energy of water molecules are not perturbed by the presence of a hydrophobic solute. In the case of ionic solutes, the perturbation is largely localized within the first hydration shell. The binding energies for the ions are strongly dependent on the water models and clearly indicate that the geometry of the partial charge distributions, and the associated multipole moments, play an important role. However the anomalous behaviour of the water network has been found to be unimportant for polar solvation.     

Fragile to strong crossover and Widom line in supercooled water: A comparative study

The aim of this paper is to discuss the relationship between the dynamics and thermodynamics of water in the supercooled region. Reviewed case studies comprehend bulk water simulated with the SPC/E, TIP4P and TIP4P/2005 potentials, water at protein interfaces, and water in solution with electrolytes. Upon supercooling, the fragile to strong crossover in the α-relaxation of water is found to occur when the Widom line emanating from the liquid-liquid critical point is crossed. This appears to be a general characteristic of supercooled water, not depending on the applied interaction potential and/or different local environments.     

Force-field dependence on the interfacial structure of oil–water interfaces

We investigate the performance of different force-fields for alkanes, united (TraPPE) and all atom (OPLS-AA) models, and water (SPC/E and TIP4P-2005), in the prediction of the interfacial structure of alkane (n-octane, and n-dodecane)–water interfaces. We report an extensive comparison of the interfacial thermodynamic properties as well as the interfacial structure (translational and orientational). We use the recently introduced intrinsic sampling method, which removes the averaging effect of the interfacial capillary waves and provides a clear view of the interface structure. The alkane interfacial structure is sensitive to the environment, i.e. alkane–vapour or alkane–water interfaces, showing a stronger structure when it is in contact with the water phase. We find that this structure is fairly independent of the level of detail, full or united atom, employed to describe the alkane phase. The water surface properties show a small dependence on the water model. The dipole moment of the SPC/E model shows asymmetric fluctuations, with a tendency to point both towards the alkane and water phases. On the other hand the dipole moment of the TIP4P-2005 model shows a tendency to point towards the water phase only. Analysis of the intrinsic electrostatic field indicates that the surface water potential is confined to an interfacial region of about 8 Å. Overall we find that the intrinsic structure of alkane–water interfaces is a robust interfacial property, which is independent of the details of the force-field employed. Hence, it should provide a good reference to interpret experimental data.     

Molecular dynamics computation of the work of ion solvation: comparison of two models of water

Clusters of the TIP4P water model with 125 and 256 molecules and with the K⁺ or K^? ions were simulated by the molecular dynamics method. The radial profiles of local density, energy, normal pressure and molecular orientation were obtained. The work of cluster formation was calculated from the normal pressure profile. The results for the TIP4P and SPC/E model of water are discussed in comparison with each other. A divergence in behaviour of water molecules in the two models was discovered.     

Hydration of apolar solutes of varying size: a systematic study

We report results of a systematic and extensive study on the orientational structure of water molecules in the vicinity of apolar solutes of varying size in infinitely diluted aqueous solutions at ambient conditions. A wide range of sizes of the solute, modelled as a Lennard–Jones particle, has been considered including also the limiting case of a smooth planar wall (i.e. a solute of an infinite diameter). Both the bivariate and monovariate angle distributions are used to describe the orientation of water molecules. It is demonstrated that the commonly used latter method may lead to misleading or even erroneous conclusions. It is found that all three considered models of water, SPC/E, TIP4P and TIP5P, exhibit, unlike some simplified models, qualitatively the same behaviour, i.e. with increasing size of the solute only the water molecules in closest proximity of the solute adopt orientations which sacrifice a possible hydrogen bond, whereas the preferred orientation of water molecules farther from the surface, but yet belonging to the first solvation shell, is independent of the solute size.     

Comparative atomistic and coarse-grained study of water: What do we lose by coarse-graining?

We employ the inverse Boltzmann method to coarse-grain three commonly used three-site water models (TIP3P, SPC and SPC/E) where one molecule is replaced with one coarse-grained particle with isotropic two-body interactions only. The shape of the coarse-grained potentials is dominated by the ratio of two lengths, which can be rationalized by the geometric constraints of the water clusters. It is shown that for simple two-body potentials either the radial distribution function or the geometrical packing can be optimized. In a similar way, as needed for multiscale methods, either the pressure or the compressibility can be fitted to the all atom liquid. In total, a speed-up by a factor of about 50 in computational time can be reached by this coarse-graining procedure.     

Direct correlation functions for three-site and four-site water models

ABSTRACT

Direct correlation functions (DCFs) play a pivotal role in modern liquid-state theories and are virtually indispensable for non-mean-field implementation of the classical density functional theory (cDFT). Whereas analytical expressions have been derived for the DCFs of simple fluids and electrolytes, DCFs for molecular systems are attainable only through numerical solution of the integral-equation theories in combination with molecular simulation or an approximate closure. Unlike radial distribution functions, DCFs reflect the variational of the local chemical potential of individual atoms/interaction sites with the density-profile fluctuations, which are difficult to be sampled from the simulation trajectory. This article presents an improved numerical procedure to calculate the DCFs of three-site (SPC/E and TIP3P) and four-site (TIP4P-Ew) water models based on the reference interaction site model and molecular dynamics simulations. In combination with the modified fundamental measure theory for the bridge functionals, the DCFs have been utilised to predict the hydration free energies of 504 small organic molecules. The theoretical predictions yield an average unsigned error of 0.66 kcal/mol in comparison with the simulation data, better than that (～1 kcal/mol) reported in previous cDFT calculations.     

Molecular dynamics simulations of liquid water using various long-range electrostatics techniques

Water is one of the most extensively studied molecules, owing to its crucial role in biological processes. The water molecule is both highly polar and highly polarizable. Properties of water computed from molecular simulations are therefore critically dependent on both the intermolecular potential and the method for computing long-range electrostatic corrections. In this paper, the effects of the potential and the long-range electrostatic corrections are quantified for liquid water from 260 to 400?K. Simulations were carried out for a system of 256 molecules in the NVT ensemble. Thermodynamic, structural, dynamical, hydrogen bonding and dielectric properties have been computed for the flexible SPC and rigid SPC, SPC/E, TIP4P, TIP4P-Ew and TIP4P-FQ potentials, using the Lekner, Ewald and reaction field techniques to handle long-range electrostatics. The Lekner method gave the best overall agreement with experimental data, while the reaction field approach produced poorer results. Some measurable differences were found between the Lekner and Ewald techniques. For dielectric properties, the performance of the TIP4P-FQ model was superior relative to other potentials. For 256 molecules, the computational speeds of the Ewald and reaction field methods were found to be 2.5 to 3 times and 3.5 to 5 times faster than the Lekner technique, respectively.     

GROMOS polarisable model for acetone

A polarisable model for acetone, COS/A, is proposed that is based on the charge-on-spring (COS) polarisation model and is compatible with the polarisable COS/D2 and COS/G2 models for liquid water. A series of acetone-water mixtures at different acetone mole fractions was simulated using the new model in conjunction with the mentioned polarisable and the non-polarisable SPC and SPC/E water models. The model was parameterised to reproduce the following liquid acetone properties: density, heat of vaporisation, surface tension, dielectric permittivity, self diffusion and heat capacity and subsequently tested in mixtures with water using different water models. For pure liquid acetone the polarisable COS/A model agrees better with experimental data than the non-polarisable Kirkwood-Buff derived force field (KBFF) model, which was parameterised using experimental data for a 0.5 mole fraction acetone-water mixture. For such mixtures the polarisable models yield better agreement with experiment than the non-polarisable models for the heat of vaporisation and dielectric permittivity, while worse agreement for diffusion. The computational cost of simulating the polarisable acetone-water mixtures is a factor of 3 to 4 higher compared with the non-polarisable models due to the increased number of interaction sites and the multiple iterations required to evaluate self-consistently the positions of the COS sites at every simulation step. The COS/A acetone model can be used in biomolecular simulations in conjunction with the mentioned polarisable water models to solvate biomolecules.     

The Adam–Gibbs relation and the TIP4P/2005 model of water

ABSTRACT

We report a numerical test of the Adam–Gibbs relation for the TIP4P/2005 model of water. The configurational entropy is here evaluated as the logarithm of the number of different basins in the potential energy landscape sampled in equilibrium conditions. Despite the non-monotonic behaviour which characterise the density dependence of the diffusion coefficient, the Adam–Gibbs relation is satisfied within the numerical precision in a wide range of densities and temperatures. We also show that expressions based on the excess entropy (the logarithm of the number of sampled microstates in phase space) fail in the region of densities where a tetrahedral hydrogen bond network develops.     

Temperature dependent anomalous fluctuations in water: shift of ≈1 kbar between experiment and classical force field simulations

Here we report on the temperature dependence of the anomalous behaviour of water in terms of (i) its growth in tetrahedral structures, (ii) instantaneous spatial correlations from small angle x-ray scattering (SAXS) data, (iii) estimates of thermodynamic response functions of isothermal compressibility and (iv) thermal expansion coefficient. Water’s thermal expansion coefficient is estimated for the first time at supercooled conditions from liquid water’s structure factor. We used previously published data from classical force-fields of TIP4P/2005 and iAMOEBA to compare experimental data with molecular dynamics simulations and observe that these force-fields underestimate water’s anomalous behaviour but perform better upon increasing pressure. We demonstrate that the molecular dynamics simulations can describe better the temperature dependent anomalous behaviour of ambient pressure water if simulated at 1?kbar. The deviation in anomalous fluctuations in the simulations is not restricted to ≈228?K but extends all the way to ambient temperatures.     

Density and bond-orientational relaxations in supercooled water

ABSTRACT

Recent computational studies have reported evidence of a metastable liquid–liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artefacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artefacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behaviour in the coarse-grained mW model of water. Our findings, therefore, challenge the key physical assumption underlying the competing hypothesis.     

System size and trajectory length dependence of the static structure factor and the diffusion coefficient as calculated from molecular dynamics simulations: The case of SPC/E water

The effect of the applied trajectory length on the convergence of the self-diffusion coefficient was examined for the SPC/E water model in the NVT ensemble with different system sizes at 293 K. Temperature dependence and isotope effects, via using D₂O instead of H₂O, were also investigated. A simulation for the polarizable SWM4-DP model was also carried out to compare the effect of different potential models. Radial distribution functions and the neutron weighted structure factor were also calculated; they were found to be insensitive to changing the system size in the range of 216 to 16,000 molecules. On the other hand, the diffusion coefficient is rather sensitive to the applied trajectory length, system size and the method of calculation. The diffusion coefficient is therefore not appropriate for assessing, and distinguishing between, potential models of water, whereas the structure factor could serve as a more stable measure.     

A molecular dynamics study of carbon dioxide in water: diffusion,structure and thermodynamics

Atomistic simulations are reported of a model of CO₂ in water. CO₂ is modelled by partial charges and Lennard-Jones interaction sites on each atom; the SPC/E model for water is used. Good agreement with experiment is found for the translational diffusion constants. The variation of the dynamics with the potential parameter was investigated. As expected, the orientational correlation times increase as the magnitude of the quadrupole moment is increased, but the translational diffusion constants are found to be surprisingly insensitive to the magnitude of the CO₂ quadrupole moment. The translational friction coefficient was resolved into electrostatic, Lennard-Jones and cross-terms; the Lennard-Jones contribution is found to be the largest. Varying the Lennard-Jones size parameter affects both translational and reorientational motion. In order to try to understand these results further, the variation of solvation free energy was investigated and the solvent structure around carbon dioxide was examined as the electrostatic and Lennard-Jones parameters were changed. The temperature dependence of the self-diffusion constant of pure SPC/E water was determined.     

Surface tension calculations of the cationic (CTAB) and the zwitterionic (SB3-12) surfactants using new force field models: a computational study

Actual CTAB and SB3-12 surfactant force field models fail to reproduce one of the most important thermodynamic property of those molecules, the surface tension. Molecular dynamics simulations were conducted to construct new force fields of the cationic surfactant, Cetyl Trimethyl Ammonium Bromide (CTAB), and the non-ionic, cocoamidopropyl betaine, surfactants using united atom models. By scaling the Lennard Jones parameters, the well depth potential (ε) and the intermolecular distance (σ), we constructed an united atom model of the cationic and the betaine surfactants. The new models were tested with actual experiments reported in the literature. With the correct parameters, surface tensions of both surfactants were calculated at different temperatures and different areas per molecule. Electrostatic properties and micelle structures were also calculated with the new set of parameters and radius of gyrations, i.e. micelle radius, were evaluated showing good affinity with experimental data. The new force fields were proved with two different water models, TIP4P/ε and SPC/E, having good agreement with actual experiments     

Phase diagrams and surface properties of modified water models

The surface properties and phase diagrams are examined for a number of modified water models. In the ‘bent’ family of models where the bond angle is decreased and the network structure is lost the surface tension is lower than in SPC/E water and the critical temperature is lower. In the ‘hybrid’ family of models which are hybrids between SPC/E water and a Lennard–Jones liquid the surface tension and the critical temperature are higher that in SPC/E water. These properties correlate well with the varying ability of the liquids to dissolve hard spheres. The surface potential, on the other hand, is slightly smaller in magnitude in the hybrid models than in SPC/E water because there is slightly less alignment of the dipoles in the surface layer. The degree of molecular alignment in the surface and the consequent surface potential drop is much lower in magnitude in the bent models than in SPC/E water.