Soft sticky dipole-quadrupole-octupole potential energy function for liquid water: an approximate moment expansion

A new, efficient potential energy function for liquid water is presented here. The new model, which is referred here as the soft sticky dipole-quadrupole-octupole (SSDQO) model, describes a water molecule as a Lennard-Jones sphere with point dipole, quadrupole, and octupole moments. It is a single-point model and resembles the hard-sphere sticky dipole potential model for water by Bratko et al. [J. Chem. Phys. 83, 6367 (1985)] and the soft sticky dipole model by Ichiye and Liu [J. Phys. Chem. 100, 2723 (1996)] except now the sticky potential consists of an approximate moment expansion for the dimer interaction potential, which is much faster than the true moment expansion. The object here is to demonstrate that the SSDQO potential energy function can accurately mimic the potential energy function of a multipoint model using the moments of that model. First, the SSDQO potential energy function using the dipole, quadruple, and octupole moments from SPC/E, TIP3P, or TIP5P is shown to reproduce the dimer potential energy functions of the respective multipoint model. In addition, in Monte Carlo simulations of the pure liquid at room temperature, SSDQO reproduces radial distribution functions of the respective model. However, the Monte Carlo simulations using the SSDQO model are about three times faster than those using the three-point models and the long-range interactions decay faster for SSDQO (1/r(3) and faster) than for multipoint models (1/r). Moreover, the contribution of each moment to the energetics and other properties can be determined. Overall, the simplicity, efficiency, and accuracy of the SSDQO potential energy function make it potentially very useful for studies of aqueous solvation by computer simulations.     

Study of multipole contributions to the structure of water around ions in solution using the soft sticky dipole-quadrupole-octupole (SSDQO) model of water

The solvation of ions in the soft sticky dipole-quadrupole-octupole (SSDQO) model for liquid water is presented here. This new potential energy function for liquid water describes water-water interactions by a Lennard-Jones term plus a sticky potential consisting of an approximate moment expansion with point dipole, quadrupole, and octupole moments. The SSDQO potential energy function using the moments from extended simple point charge (SPC/E), TIP3P, or TIP5P reproduces the pair potential energy functions and radial distribution functions of the respective multipoint model but it is much faster than even the three-point models. Here, the solvation of ions in SSDQO water is studied using ion-water potential energy functions consisting of moment expansions up to the charge-quadrupole term, up to the charge-octupole term, and up to an approximate charge-hexadecapole term using the moments of SPC/E water. The radial distributions from Monte Carlo simulations show the best agreement with the results for ions in SPC/E water for the expansion up to the charge-hexadecapole term. Thus, the best results are obtained when the water-water and ion-water potentials are exact up to the 1r(4) term and also contain an approximate 1r(5) term. Overall, the simplicity, efficiency, and accuracy of the SSDQO potential make it potentially very useful for computer simulations of aqueous solvation.     

UNDERSTANDING STRUCTURAL EFFECTS OF MULTIPOLE MOMENTS ON AQUEOUS SOLVATION OF IONS USING THE SOFT-STICKY DIPOLE-QUADRUPOLE-OCTUPOLE WATER MODEL

The effects of water multipole moments on the aqueous solvation of ions were determined in Monte Carlo simulations using soft-sticky dipole-quadrupole-octupole (SSDQO) water. Water molecules formed linear hydrogen bonds to Cl(-) using the new SSDQO1 parameters, similar to multi-site models. However, the dipole vector was tilted rather than parallel to the oxygen-Na(+) internuclear vector as in most multi-site model, while experiment and ab initio molecular dynamics simulations generally indicate a range of values between tilted and parallel. By varying the multipoles in SSDQO, the octupole was found to determine the orientation around Na(+). Moreover, analysis of the multipoles of more conventional models is predictive of their performance as solvents.     

Dynamical properties of the soft sticky dipole-quadrupole-octupole water model: a molecular dynamics study

The dynamical properties of the soft sticky dipole-quadrupole-octupole (SSDQO) water model using SPC/E moments are calculated utilizing molecular dynamics simulations. This new potential for liquid water describes the water-water interactions by a Lennard-Jones term and a sticky potential, which is an approximate moment expansion with point dipole, quadrupole, and octupole moments, and reproduces radial distribution functions of pure liquid water using the moments of SPC/E [Ichiye and Tan, J. Chem. Phys. 124, 134504 (2006)]. The forces and torques of SSDQO water for the dipole-quadrupole, quadrupole-quadrupole, and dipole-octupole interactions are derived here. The simulations are carried out at 298 K in the microcanonical ensemble employing the Ewald method for the long-range dipole-dipole interactions. Here, various dynamical properties associated with translational and rotational motions of SSDQO water using the moments of SPC/E (SSDQO:SPC/E) water are compared with the results from SPC/E and also experiment. The self-diffusion coefficient of SSDQO:SPC/E water is found to be in excellent agreement with both SPC/E and experiment whereas the single particle orientational relaxation time for dipole vector is better than SPC/E water but it is somewhat smaller than experiment. The dielectric constant of SSDQO:SPC/E is essentially identical to SPC/E, and both are slightly lower than experiment. Also, molecular dynamics simulations of the SSDQO water model are found to be about twice as fast as three-site models such as SPC/E.     

Molecular dynamics simulations of the aqueous interface with the [BMI][PF6] ionic liquid: Comparison of different solvent models

We report a Molecular Dynamics (MD) study of the interface between water and the hygroscopic room temperature Ionic Liquid "IL" [BMI][PF6] (1-butyl-3-methyl-imidazolium hexafluorophosphate), comparing the TIP3P, SPC/E and TIP5P models for water and two IL models where the ions are +/-1 or +/-0.9 charged. A recent MD study (A. Chaumont, R. Schurhammer and G. Wipff, J. Phys. Chem. B, 2005, 109, 18964) showed that using TIP3P water in conjunction with the IL(+/-1) model led to water-IL mixing without forming an interface, whereas a biphasic system could be obtained with the IL(+/-0.9) model. With the TIP5P and SPC/E models, the juxtaposed aqueous and IL phases are found to remain distinct for at least 20 ns. The resulting IL humidity, exaggerated with the IL(+/-1) model, is in better agreement with experiment using the IL(+/-0.9) model. We also report demixing simulations on the "randomly mixed" liquids, using the IL(+/-0.9) model for the ionic liquid. With the three tested water models, the phases separate very slowly ( approximately 20 ns or more) compared to "classical" chloroform-water mixtures (less than 1 ns), leading to biphasic systems similar to those obtained after equilibration of the juxtaposed liquids. The characteristics of the interface (size, polarity, ion orientation, electrostatic potential) are compared with the different models. Possible reasons why, among the three tested water models, the widely-used TIP3P model exaggerates the inter-solvent mixing, are analyzed. The difficulty in computationally and experimentally equilibrating water-IL mixtures is attributed to the slow dynamics and micro-heterogeneity of the IL and to the different states of water in the IL phase.     

Correlations in liquid water for the TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP models

Water is one of the simplest molecules in existence, but also one of the most important in biological and engineered systems. However, understanding the structure and dynamics of liquid water remains a major scientific challenge. Molecular dynamics simulations of liquid water were performed using the water models TIP3P-Ewald, TIP4P-2005, TIP5P-Ewald, and SWM4-NDP to calculate the radial distribution functions (RDFs), the relative angular distributions, and the excess enthalpies, entropies, and free energies. In addition, lower-order approximations to the entropy were considered, identifying the fourth-order approximation as an excellent estimate of the full entropy. The second-order and third-order approximations are ~20% larger and smaller than the true entropy, respectively. All four models perform very well in predicting the radial distribution functions, with the TIP5P-Ewald model providing the best match to the experimental data. The models also perform well in predicting the excess entropy, enthalpy, and free energy of liquid water. The TIP4P-2005 and SWM4-NDP models are more accurate than the TIP3P-Ewald and TIP5P-Ewald models in this respect. However, the relative angular distribution functions of the four water models reveal notable differences. The TIP5P-Ewald model demonstrates an increased preference for water molecules to act both as tetrahedral hydrogen bond donors and acceptors, whereas the SWM4-NDP model demonstrates an increased preference for water molecules to act as planar hydrogen bond acceptors. These differences are not uncovered by analysis of the RDFs or the commonly employed tetrahedral order parameter. However, they are expected to be very important when considering water molecules around solutes and are thus a key consideration in modelling solvent entropy.     

Structural properties of water: comparison of the SPC, SPCE, TIP4P, and TIP5P models of water

Molecular-dynamics simulations were carried out for the SPC, SPCE, TIP4P, and TIP5P models of water at 298 K. From these results we determine the following quantities: the absolute entropy using the two-particle approximation, the mean lifetime of the hydrogen bond, the mean number of hydrogen bonds per molecule, and the mean energy of the hydrogen bond. From the entropy calculations we find that nearly all contributions to the total entropy originates from the orientation effects. Moreover, we determine the contributions to the total entropy which originate from the first, second, and higher solvation shells. It is interesting that the limits between solvation shells are clearly visible. The first solvation shell (0.22 < r < 0.36 nm) contributes approximately 43 J mol K to the total entropy; the second solvation shell (0.36 < r < 0.60 nm) contributes approximately 12 J mol K, while contributions from the third and other solvation shells are very small, approximately 2 J mol K in summary. This indicates that water molecules are strongly ordered up to 0.55-0.6 nm around the central water molecule, and beyond this limit the ordering diminishes. The results of calculations (entropy and hydrogen bonds) are compared with the experimental data for the choosing of the best water model. We find that the SPC and TIP4P models reproduce the best experimental values, and we recommend these models for computer simulations of the aqueous solution of biomolecules.     

Relation between the melting temperature and the temperature of maximum density for the most common models of water

Water exhibits a maximum in density at normal pressure at 4 degrees above its melting point. The reproduction of this maximum is a stringent test for potential models used commonly in simulations of water. The relation between the melting temperature and the temperature of maximum density for these potential models is unknown mainly due to our ignorance about the melting temperature of these models. Recently we have determined the melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P). In this work we locate the temperature of maximum density for these models. In this way the relative location of the temperature of maximum density with respect to the melting temperature is established. For SPC, SPC/E, TIP3P, TIP4P, and TIP4P/Ew the maximum in density occurs at about 21-37 K above the melting temperature. In all these models the negative charge is located either on the oxygen itself or on a point along the H-O-H bisector. For the TIP5P and TIP5P-E models the maximum in density occurs at about 11 K above the melting temperature. The location of the negative charge appears as a geometrical crucial factor to the relative position of the temperature of maximum density with respect to the melting temperature.     

Computer simulation of two new solid phases of water: Ice XIII and ice XIV

NpT Monte Carlo simulations have been performed for two recently discovered solid phases of water which have been denoted as ice XIII and ice XIV C. G. Salzmann et al. [Science311, 1758 (2006)]. Several potential models of water were considered, namely, the traditional SPC/E, TIP4P, and TIP5P and the more recent TIP5P-E, TIP4P-Ew, TIP4P/Ice, and TIP4P/2005 models. Significant differences in density and oxygen-oxygen radial distribution functions are found between the predictions of the SPC/E, TIP5P, and the models of the TIP4P family. The models TIP4P/Ice and TIP4P/2005 provide the best estimates of the density.     

The importance of polarizability in the modeling of solubility: quantifying the effect of solute polarizability on the solubility of small nonpolar solutes in popular models of water

In recent work by Paschek [J. Chem. Phys. 120, 6674 (2004)] and others [see H. Docherty et al., J. Chem. Phys. 125, 074510 (2006) for a review] it has been suggested that, when coupled to a simple Lennard-Jones model for various small nonpolar solute molecules, the most common models of water (e.g., SPC/E and TIP4P) fail to reproduce quantitatively the solubility of small nonpolar solute molecules in water due in part to failing to account for polarization of the solute molecule. Given the importance of such systems as test-case prototype models of the solubility of proteins and biomolecules, in this work, we investigate the impact of using a polarizable solute model with the SPC/E, TIP3P, TIP4P, TIP4P-Ew, and TIP4P/2005 rigid water models. Specifically we consider Ne, Ar, Kr, Xe, and methane as solutes. In all cases we observe that the use of a polarizable solute improves agreement between experiment and simulations, with the best agreement seen for the largest solutes, Kr, CH(4), and Xe and the modern reparametrizations of the TIP4P model, i.e., the TIP4P-Ew and TIP4P/2005 models.     

The melting temperature of the most common models of water

The melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E,TIP3P,TIP4P, TIP4P/Ew, and TIP5P) is obtained from computer simulations at p = 1 bar. Since the melting temperature of ice I(h) for the TIP4P model is now known [E. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, Phys. Rev. Lett. 92, 255701 (2004)], it is possible to use the Gibbs-Duhem methodology [D. Kofke, J. Chem. Phys. 98, 4149 (1993)] to evaluate the melting temperature of ice I(h) for other potential models of water. We have found that the melting temperatures of ice I(h) for SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P models are T = 190 K, 215 K, 146 K, 232 K, 245 K, and 274 K, respectively. The relative stability of ice I(h) with respect to ice II for these models has also been considered. It turns out that for SPC, SPC/E, TIP3P, and TIP5P the stable phase at the normal melting point is ice II (so that ice I(h) is not a thermodynamically stable phase for these models). For TIP4P and TIP4P/Ew, ice I(h) is the stable solid phase at the standard melting point. The location of the negative charge along the H-O-H bisector appears as a critical factor in the determination of the relative stability between the I(h) and II ice forms. The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters.     

A comparison of the value of viscosity for several water models using Poiseuille flow in a nano-channel

The viscosity-temperature relation is determined for the water models SPC/E, TIP4P, TIP4P/Ew, and TIP4P/2005 by considering Poiseuille flow inside a nano-channel using molecular dynamics. The viscosity is determined by fitting the resulting velocity profile (away from the walls) to the continuum solution for a Newtonian fluid and then compared to experimental values. The results show that the TIP4P/2005 model gives the best prediction of the viscosity for the complete range of temperatures for liquid water, and thus it is the preferred water model of these considered here for simulations where the magnitude of viscosity is crucial. On the other hand, with the TIP4P model, the viscosity is severely underpredicted, and overall the model performed worst, whereas the SPC/E and TIP4P/Ew models perform moderately.     

Capillary waves at the liquid-vapor interface and the surface tension of water

Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at the liquid-vapor interface, is compared for a number of standard three- and four-point water models. We study four three-point models (SPC/E, TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and TIP4P-Ew). All of the models examined underestimate the surface tension; the TIP4P-Ew model comes closest to reproducing the experimental data. The surface tension can also be determined from the amplitude of capillary waves at the liquid-vapor interface by varying the surface area of the interface. The surface tensions determined from the amplitude of the logarithmic divergence of the capillary interfacial width and from the traditional thermodynamic method agree only if the density profile is fitted to an error function instead of a hyperbolic tangent function.     

Melting temperature of ice Ih calculated from coexisting solid-liquid phases

We carried out molecular-dynamics simulations by using the two-phase coexistence method with the constant pressure, particle number, and enthalpy ensemble to compute the melting temperature of proton-disordered hexagonal ice I(h) at 1-bar pressure. Four models of water were considered, including the widely used TIP4P [W. L. Jorgensen, J. Chandrasekha, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys.79, 926 (1983)] and TIP5P [M. W. Mahoney and W. L. Jorgensen J. Chem. Phys.112, 8910 (2000)] models, as well as recently improved TIP4P and TIP5P models for use with Ewald techniques-the TIP4P-Ew [W. Horn, W. C. Swope, J. W. Pitera, J. C. Madura, T. J. Dick, G. L. Hura, and T. Head-Gordon, J. Chem. Phys.120, 9665 (2004)] and TIP5P-Ew [S. W. Rick, J. Chem. Phys.120, 6085 (2004)] models. The calculated melting temperature at 1 bar is T(m) = 229 +/- 1 K for the TIP4P and T(m) = 272.0 +/- 0.6 K for the TIP5P ice I(h), both are consistent with previous simulations based on free-energy methods. For the TIP4P-Ew and TIP5P-Ew models, the calculated melting temperature is T(m) = 257.0 +/- 1.1 K and T(m) = 253.9 +/- 1.1 K, respectively.     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.