Nonpolarizable Water Models Research Articles

Accuracy limit of non-polarizable four-point water models: TIP4P/2005 vs OPC. Should water models reproduce the experimental dielectric constant?

The last generation of four center non-polarizable models of water can be divided into two groups: those reproducing the dielectric constant of water, as OPC, and those significantly underestimating its value, as TIP4P/2005. To evaluate the global performance of OPC and TIP4P/2005, we shall follow the test proposed by Vega and Abascal in 2011 evaluating about 40 properties to fairly address this comparison. The liquid-vapor and liquid-solid equilibria are computed, as well as the heat capacities, isothermal compressibilities, surface tensions, densities of different ice polymorphs, the density maximum, equations of state at high pressures, and transport properties. General aspects of the phase diagram are considered by comparing the ratios of different temperatures (namely, the temperature of maximum density, the melting temperature of hexagonal ice, and the critical temperature). The final scores are 7.2 for TIP4P/2005 and 6.3 for OPC. The results of this work strongly suggest that we have reached the limit of what can be achieved with non-polarizable models of water and that the attempt to reproduce the experimental dielectric constant deteriorates the global performance of the water force field. The reason is that the dielectric constant depends on two surfaces (potential energy and dipole moment surfaces), whereas in the absence of an electric field, all properties can be determined simply from just one surface (the potential energy surface). The consequences of the choice of the water model in the modeling of electrolytes in water are also discussed.

Molecular Dynamics Simulation to Evaluate the Stability of Tetra-n-butyl Ammonium/Phosphonium Bromide Semiclathrate Hydrates in the Presence and Absence of Methane, Carbon Dioxide, Methanol, and Ethanol Molecules

Stability of tetra-n-butyl ammonium bromide (TBAB) and tetra-n-butyl phosphonium bromide (TBPB) semiclathrate hydrates with a hydration number of 38 is studied by the molecular dynamics (MD) simulation in the absence and presence of methane, carbon dioxide, methanol, and ethanol molecules. All of the simulation runs are performed under NVT (constant number of atoms, volume, and temperature) and NPT (constant number of atoms, pressure, and temperature) conditions using optimized potentials for liquid simulations-all-atom (OPLS-AA) force field with nonpolarizable water models (including SPC, TIP3P, TIP4P, and TIP4P/Ice), where the operating conditions include a temperature range of 250–350 K and pressures of 0.1 and 50 MPa. The potential energy and structural analysis, mean square displacement (MSD), diffusion coefficient, radial distribution function (RDF), lattice parameter, and the average number of hydrogen bonds between water–water molecules are evaluated by employing MD strategy. According to the potential energy results, the order for the water models in both TBAB and TBPB hydrate stabilities is as follows: TIP4P/Ice > TIP4P ≈ SPC > TIP3P. This order agrees well with the previous studies of gas hydrates and ices. In the absence and presence of methane and carbon dioxide guest molecules, the height of the peaks in the RDF of oxygen–oxygen atoms decreases with lowering pressure and increasing temperature; greater MSD, diffusion coefficient, and lattice parameter values are also achieved. Thus, in the absence and/or presence of guest gas molecules, the stability of TBAB and TBPB hydrate cages decreases with increasing temperature and reducing pressure. A good match is noticed between the results of MD simulation and previous experimental and theoretical studies, confirming the accuracy and validation of the simulation method. Reduction of the hydrogen bond balance between water molecules and formation of new hydrogen bonds between the water and the hydroxyl groups of methanol and/or ethanol molecules in the cages indicate that methanol and ethanol molecules have an inhibitory effect on TBAB and TBPB hydrates. Due to different hydrophilic versus hydrophobic behaviors of alcohols, the extent of disruption of hydrogen bonds between water–water molecules of TBAB and TBPB hydrates in the presence of methanol is larger than that in the presence of ethanol, which is consistent with the MD simulation results of clathrate hydrate. This study can help to further understand the semiclathrate hydrate stability or dissociation conditions at a molecular scale for better design and operation of corresponding processes.

Incorporating Polarization and Charge Transfer into a Point-Charge Model for Water Using Machine Learning

Rigid nonpolarizable water models with fixed point charges have been widely employed in molecular dynamics simulations due to their efficiency and reasonable accuracy for the potential energy surface. However, the dipole moment surface of water is not necessarily well-described by the same fixed charges, leading to failure in reproducing dipole-related properties. Here, we developed a machine-learning model trained against electronic structure data to assign point charges for water, and the resulting dipole moment surface significantly improved the predictions of the dielectric constant and the low-frequency IR spectrum of liquid water. Our analysis reveals that within our atom-centered point-charge description of the dipole moment surface, the intermolecular charge transfer is the major source of the peak intensity at 200 cm-1, whereas the intramolecular polarization controls the enhancement of the dielectric constant. The effects of exact Hartree-Fock exchange in the hybrid density functional on these properties are also discussed.

Fast Polarizable Water Model for Atomistic Simulations.

Simulating water accurately has been a major challenge in atomistic simulations for decades. Inclusion of electronic polarizability effects holds considerable promise, yet existing approaches suffer from significant computational overheads compared to the widely used nonpolarizable water models. We have developed a globally optimal polarizable water model, OPC3-pol, that explicitly accounts for electronic polarizability with minimal impact on the computational efficiency. OPC3-pol reproduces five key bulk water properties at room temperature with an average relative error of 0.6%. In atomistic simulations, OPC3-pol's computational efficiency is in between that of 3- and 4-point nonpolarizable models; the model supports increased (4 fs) integration time step. OPC3-pol is tested in simulations of globular protein ubiquitin and a B-DNA dodecamer with several AMBER force fields, ff99SB, ff14SB, ff19SB, and OL15, demonstrating structure stability close to reference on multi-microsecond time scale. Simulation of an intrinsically disordered amyloid β-peptide yields an ensemble with the radius of gyration of a random coil. The proposed water model can be trivially adopted by any package that supports standard nonpolarizable force fields and water models; its intended use is in long classical atomistic simulations where water polarization effects are expected to be important.

Homogeneous ice nucleation rates for mW and TIP4P/ICE models through Lattice Mold calculations.

Freezing of water is the most common liquid-to-crystal phase transition on Earth; however, despite its critical implications on climate change and cryopreservation among other disciplines, its characterization through experimental and computational techniques remains elusive. In this work, we make use of computer simulations to measure the nucleation rate (J) of water at normal pressure under different supercooling conditions, ranging from 215 to 240K. We employ two different water models: mW, a coarse-grained potential for water, and TIP4P/ICE, an atomistic nonpolarizable water model that provides one of the most accurate representations of the different ice phases. To evaluate J, we apply the Lattice Mold technique, a computational method based on the use of molds to induce the nucleus formation from the metastable liquid under conditions at which observing spontaneous nucleation would be unfeasible. With this method, we obtain estimates of the nucleation rate for ice Ih and Ic and a stacking mixture of ice Ih/Ic, reaching consensus with most of the previously reported rates, although differing with some others. Furthermore, we confirm that the predicted nucleation rates obtained by the TIP4P/ICE model are in better agreement with experimental data than those obtained through the mW potential. Taken together, our study provides a reliable methodology to measure nucleation rates in a simple and computationally efficient manner that contributes to benchmarking the freezing behavior of two popular water models.

A Polarizable Cationic Dummy Metal Ion Model.

A novel locally polarizable multisite model based on the original cation dummy atom (CDA) model is described for molecular dynamics simulations of ions in condensed phases. Polarization effects are introduced by the electronegativity equalization model (EEM) method where charges on the metal ion and its dummy atoms can fluctuate to respond to the environment. This model includes explicit polarization and ion-induced interactions and can be coupled with nonpolarizable or polarizable water models, making it more transferable to simpler force fields. This approach allows us to enhance the original fixed charge CDA model where the charge distribution cannot adapt to the local solvent structure. To illustrate the new CDApol model, we examined properties of the Zn2+, Al3+, and Zr4+ ions in aqueous solution. The polarizable model and Lennard-Jones parameters were refined for octahedrally coordinated Zn2+, Al3+, and Zr4+ CDAs to reproduce thermodynamic and geometrical properties. Using this locally polarizable model, we were able to obtain the experimental hydration free energy, ion-oxygen distance, and coordination number coupled with the standard 12-6 Lennard-Jones model. This model can be used in myriad additional applications where local polarization and charge transfer is important.

Modeling thermodiffusion in aqueous sodium chloride solutions-Which water model is best?

Thermodiffusion is the migration of a species due to a temperature gradient and is the driving phenomenon in many applications ranging from early cancer detection to uranium enrichment. Molecular dynamics (MD) simulations can be a useful tool for exploring the rather complex thermodiffusive behavior of species, such as proteins and ions. However, current MD models of thermodiffusion in aqueous ionic solutions struggle to quantitatively predict the Soret coefficient, which indicates the magnitude and direction of species migration under a temperature gradient. In this work, we aim to improve the accuracy of MD thermodiffusion models by assessing how well different water models can recreate thermodiffusion in a benchmark aqueous NaCl solution. We tested four of the best available rigid non-polarizable water models (TIP3P-FB, TIP4P-FB, OPC3, and OPC) and the commonly used TIP3P and SPC/E water models for their ability to predict the inversion temperature and Soret coefficient in 0.5, 2, and 4M aqueous NaCl solutions. Each water model predicted a noticeably different ion distribution yielding different inversion temperatures and magnitudes of the Soret coefficient. By comparing the modeled Soret coefficients to published experimental values, we determine TIP3P-FB to be the water model that best recreates thermodiffusion in aqueous NaCl solutions. Our findings can aid future works in selecting the most accurate rigid non-polarizable water model, including water and ion parameters for investigating thermodiffusion through MD simulations.

Optical Kerr Effect and Structural Tetrahedrality of Supercooled Water at Ambient Pressure

The correlation between the optical Kerr effect (OKE) spectroscopy of supercooled water at ambient pressure and its structural tetrahedrality was investigated by contrasting simulation results of two non-polarizable water models modified with the same collective polarizability, which involves intrinsic molecular polarizability and induced polarizability arising from interactions between molecular dipoles. The tetrahedrality of water structure was typified with the second-peak maximum in the pair distribution function of oxygens and the fraction of molecules, which and their neighbours up to the second hydration shell all have four H-bond coordinators. Our results indicate that the intermolecular vibrational band in the OKE spectrum of supercooled water is considerably correlated to its structural tetrahedrality.

Dielectric Profile and Electromelting of a Monolayer of Water Confined in Graphene Slit Pore.

A monolayer of water confined between two parallel graphene sheets exists in many different phases and exhibits fascinating dielectric properties that have been studied in experiments. In this work, we use molecular dynamics simulations to study how the dielectric properties of a confined monolayer of water is affected by its structure. We consider six of the popular nonpolarizable water models-SPC/E, SPC/Fw, TIP3P, TIP3P_M (modified), TIP4P-2005, and TIP4P-2005f-and find that the in-plane structure of the water molecules at ambient temperature and pressure is strongly dependent on the water model: all the 3-point water models considered here show square ice formation, whereas no such structural ordering is observed for the 4-point water models. This allows us to investigate the role of the in-plane structure of the water monolayer on its dielectric profile. Our simulations show an anomalous perpendicular dielectric constant compared to the bulk, and the models that do not exhibit ice formation show very different dielectric response along the channel width compared to models that exhibit square ice formation. We also demonstrate the occurrence of electromelting of the in-plane ordered water under the application of a perpendicular electric field and find that the critical field for electromelting strongly depends on the water model. Together, we have shown the dependence of confined water properties on the different water structures that it may take when sandwiched between bilayer graphene. These remarkable properties of confined water can be exploited in various nanofluidic devices, artificial ion channels, and molecular sieving.

Electronic continuum correction without scaled charges

In recent years the “Pandora's box” of charges used in classical simulations of nonpolarizable molecular models, especially for aqueous solutions and ionic liquids, has been opened. Particularly we refer to the Electronic continuum correction (ECC) model that suggests applying scaled down charges of ions and tearing down the ‘dogma’ of identical charges used to describe the potential energy surfaces (PES) and dipole moment surface (DMS). We elaborate on both ideas and integrate them into a consistent description of ‘real’ atomic charges of water and ions, which does not necessarily need to violate the ‘dogma’. We promote ECCε approach directly incorporating the electronic polarizability into screening of electrostatic interactions, avoiding the use of scaled charges, which perplex the comparison with experiment, ab initio or polarizable models and are cumbersome for interactions with external electric or magnetic fields. We conclude that none of the existing nonpolarizable water models is fully consistent with the continuum electronic polarizability and stimulate a quest for a better model implementing ECCε ideas.

Three-site and five-site fixed-charge water models compatible with AMOEBA force field.

In a typical biomolecular simulation using Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field, the vast majority molecules in the simulation box consist of water, and these water molecules consume the most CPU power due to the explicit mutual induction effect. To improve the computational efficiency, we here develop two new nonpolarizable water models (with flexible bonds and fixed charges) that are compatible with AMOEBA solute: the 3-site AW3C and 5-site AW5C. To derive the force-field parameters for AW3C and AW5C, we fit to six experimental liquid thermodynamic properties: liquid density, enthalpy of vaporization, dielectric constant, isobaric heat capacity, isothermal compressibility and thermal expansion coefficient, at a broad range of temperatures from 261.15 to 353.15 K under 1.0 atm pressure. We further validate our AW3C and AW5C water models by showing that they can well reproduce the radial distribution function g(r), self-diffusion constant D, and hydration free energy from the AMOEBA03 water model and the experimental observations. Furthermore, we show that our AW3C and AW5C water models can greatly accelerate (>5 times) the bulk water as well as biomolecular simulations when compared to AMOEBA water. Specifically, we demonstrate that the applications of AW3C and AW5C water models to simulate a DNA duplex lead to a threefold acceleration, and in the meanwhile well maintain the structural properties as the fully polarizable AMOEBA water. We expect that our AW3C and AW5C water models hold great promise to be widely applied to simulate complex bio-molecules using the AMOEBA force field.

Temperature-dependence of the dielectric relaxation of water using non-polarizable water models.

Key physical and chemical properties of aqueous fluids are determined by the structure and dynamics of the hydrogen bond network of water but we lack adequate models for the linkages between hydrogen bonding and aqueous chemistry, particularly in non-ambient conditions or in confinement. Dielectric relaxation spectroscopy (DRS) provides a sensitive approach for probing water dynamics but sound interpretation of DRS data requires molecular simulation and associated computational methods capable of accurately representing aqueous fluids and their frequency dependent, complex permittivity. Here, we test the accuracy of dielectric spectra of bulk liquid water calculated from molecular dynamics simulations using 19 non-polarizable water models at 298 K. In contrast to prior studies, the simulation size, time-step and duration allow calculation of the dielectric function from 107-1012 Hz without assuming an analytical form. The accuracy of the prediction of the low-frequency (static) dielectric constant at room temperature is related to the water molecule dipole moment, specifically models with μ ≥ 2.4 D give ε(0) with a relative error lower than 5%. However, no water model tested can fully reproduce the complex dielectric spectra of water. For a subset of models, calculations of the dielectric response from -5 to 60 °C reproduces the experimental trend in water dynamics with temperature but the characteristic relaxation time is always underestimated. The calculated water dipole relaxation time and hydrogen-bond lifetime are both exponentially decaying functions of temperature, and exhibit a linear correlation very close to equality. The comparison provides new computational support for the concept that the Debye relaxation of liquid water is determined by the dynamics of the hydrogen-bond network, and that both are ensemble properties.

Seven-Site Effective Pair Potential for Simulating Liquid Water.

Constant pressure simulations were carried out to construct a new rigid nonpolarizable seven-site water model (TIP7P), which is an effective and efficient version of flexible seven-fluctuating-charge water model. In this model, the positive charges are located on three nuclei and the negative charges disperse on two bond sites at the geometric center of each OH bond and two lone-pair sites along the tetrahedral direction away from the oxygen atom. Our new model performs better than other models in properties, such as radial distribution function, liquid density, thermal expansion coefficient, isothermal compressibility, vaporization enthalpy, isobaric heat capacity, static dielectric constant, self-diffusion coefficient, critical temperature, and density. This model reproduces liquid density and static dielectric constant over the temperatures from 253 to 373 K at 1 atm with the standard deviation of 0.0010 g/cm3 and 1.37 to the experimental data, respectively. The maximum density is 1.0006 g/cm3 at 277 K. The calculated isobaric compressibility presents a minimum at about 310 K close to the experimental value of 319 K. The self-diffusion coefficient agrees the experimental data with the standard deviation of 0.55 × 10-5 cm2/s, although it is not the target property for parameterization. Liquid-vapor phase equilibrium was examined in slab simulations. The evaluated critical temperature and density are 633 K and 0.337 g/cm3 close to the experimental values of 647.096 K and 0.322 g/cm3. This model also presents reasonable vaporization enthalpy and isobaric heat capacity. Based upon good performances mentioned, our new model is a good choice for more accurate investigation to large molecular systems.

Anisotropic structure and dynamics of water under static electric fields.

We study the structure and dynamics of water subject to a range of static external electric fields, using molecular dynamics simulations. In particular, we monitor the changes in hydrogen bond kinetics, reorientation dynamics, and translational motions of water molecules. We find that water molecules translate and rotate slower in electric fields because the tendency to reinstate the aligned orientation reduces the probability of finding a new hydrogen bond partner and hence increases the probability of reforming already ruptured bonds. Furthermore, dipolar alignment of water molecules with the field results in structural and dynamic anisotropies even though the angularly averaged metrics indicate only minor structural changes. Through comparison of selected nonpolarizable and polarizable water models, we find that the electric field effects are stronger in polarizable water models, where field-enhanced dipole moments and thus more stable hydrogen bonds lead to slower switching of hydrogen bond partners and reduced translational mobility, compared to a nonpolarizable water model.

Polarization Corrections and the Hydration Free Energy of Water.

Classical nonpolarizable water models play a crucial role in computer simulations due to their simplicity and computational efficiency. However, the neglect of explicit polarization can jeopardize their accuracy and predictive capabilities, particularly for properties that involve a change in electrostatic environment (e.g., phase changes). In order to mitigate this intrinsic shortcoming, highly simplified analytical polarization corrections describing the distortion of the molecular dipole are commonly applied in force field development and validation. In this paper, we perform molecular dynamics simulations and thermodynamic integration to show that applying the current state-of-the-art polarization corrections leads to a systematic inability of current nonpolarizable water models to simultaneously predict the experimental enthalpy of vaporization and hydration free energy. We go on to extend existing theories of polarization and combine them with data from recent ab initio molecular dynamics simulations to obtain a better estimate of the real contribution of polarization to phase-change energies and free energies. Our results show that for strongly polar molecules like water, the overall polarization correction is close to zero, resulting from a cancellation of multipole distortion and purely electronic polarization effects. In light of these findings, we suggest that parametrization of classical nonpolarizable models of water should be revisited in an attempt to simultaneously describe phase-change energetics and other thermodynamic and structural properties of the liquid.

Dynamic and Electronic Polarization Corrections to the Dielectric Constant of Water.

The standard approach to calculating the dielectric constant from molecular dynamics (MD) simulations employs a variant of the Kirkwood-Fröhlich methodology. Many popular nonpolarizable models of water, such as TIPnP, give a reasonable agreement with the experimental value of 78. However, it has been argued in the literature that the dipole moments of these models are effective, being smaller than the real dipole of a liquid water molecule by about a factor of [Formula: see text], or roughly [Formula: see text]. If the total or corrected dipole moment is used in calculations, the dielectric constant comes out nearly twice as large, i.e., in the range of 160, which is twice as high as the experimental value. Here we discuss possible reasons for such a discrepancy. One approach takes into account dynamic corrections due to the dependence of the dielectric response of the medium producing the reaction field on the time scale of dipole fluctuations computed in the Kirkwood-Fröhlich method. When dynamic corrections are incorporated into the computational scheme, a much better agreement with the experimental value of the dielectric constant is found when the corrected (real) dipole moment of liquid water is used. However, a formal analysis indicates that the static properties, such as dielectric constant, should not depend on dynamics. We discuss the resulting conundrum and related issues of simulations of electrostatic interactions using periodic boundary conditions in the context of our findings.

Monte Carlo Simulations of Fluid Phase Equilibria and Interfacial Properties for Water/Alkane Mixtures: An Assessment of Nonpolarizable Water Models and of Departures from the Lorentz–Berthelot Combining Rules

Monte Carlo simulations in the Gibbs ensemble were carried out to determine the mutual solubilities for water/n-alkane mixtures over a wide range of temperatures, pressures, and alkane chain length...

Building better water models using the shape of the charge distribution of a water molecule.

The unique properties of liquid water apparently arise from more than just the tetrahedral bond angle between the nuclei of a water molecule since simple three-site models of water are poor at mimicking these properties in computer simulations. Four- and five-site models add partial charges on dummy sites and are better at modeling these properties, which suggests that the shape of charge distribution is important. Since a multipole expansion of the electrostatic potential describes a charge distribution in an orthogonal basis set that is exact in the limit of infinite order, multipoles may be an even better way to model the charge distribution. In particular, molecular multipoles up to the octupole centered on the oxygen appear to describe the electrostatic potential from electronic structure calculations better than four- and five-site models, and molecular multipole models give better agreement with the temperature and pressure dependence of many liquid state properties of water while retaining the computational efficiency of three-site models. Here, the influence of the shape of the molecular charge distribution on liquid state properties is examined by correlating multipoles of non-polarizable water models with their liquid state properties in computer simulations. This will aid in the development of accurate water models for classical simulations as well as in determining the accuracy needed in quantum mechanical/molecular mechanical studies and ab initio molecular dynamics simulations of water. More fundamentally, this will lead to a greater understanding of how the charge distribution of a water molecule leads to the unique properties of liquid water. In particular, these studies indicate that p-orbital charge out of the molecular plane is important.

Solvation free energies and partition coefficients with the coarse-grained and hybrid all-atom/coarse-grained MARTINI models

We present the estimation of solvation free energies of small solutes in water, n-octanol and hexane using molecular dynamics simulations with two MARTINI models at different resolutions, viz. the coarse-grained (CG) and the hybrid all-atom/coarse-grained (AA/CG) models. From these estimates, we also calculate the water/hexane and water/octanol partition coefficients. More than 150 small, organic molecules were selected from the Minnesota solvation database and parameterized in a semi-automatic fashion. Using either the CG or hybrid AA/CG models, we find considerable deviations between the estimated and experimental solvation free energies in all solvents with mean absolute deviations larger than 10 kJ/mol, although the correlation coefficient is between 0.55 and 0.75 and significant. There is also no difference between the results when using the non-polarizable and polarizable water model, although we identify some improvements when using the polarizable model with the AA/CG solutes. In contrast to the estimated solvation energies, the estimated partition coefficients are generally excellent with both the CG and hybrid AA/CG models, giving mean absolute deviations between 0.67 and 0.90 log units and correlation coefficients larger than 0.85. We analyze the error distribution further and suggest avenues for improvements.

Protein simulation using coarse-grained two-bead multipole force field with polarizable water models.

A recently developed two-bead multipole force field (TMFF) is employed in coarse-grained (CG) molecular dynamics (MD) simulation of proteins in combination with polarizable CG water models, the Martini polarizable water model, and modified big multipole water model. Significant improvement in simulated structures and dynamics of proteins is observed in terms of both the root-mean-square deviations (RMSDs) of the structures and residue root-mean-square fluctuations (RMSFs) from the native ones in the present simulation compared with the simulation result with Martini's non-polarizable water model. Our result shows that TMFF simulation using CG water models gives much stable secondary structures of proteins without the need for adding extra interaction potentials to constrain the secondary structures. Our result also shows that by increasing the MD time step from 2 fs to 6 fs, the RMSD and RMSF results are still in excellent agreement with those from all-atom simulations. The current study demonstrated clearly that the application of TMFF together with a polarizable CG water model significantly improves the accuracy and efficiency for CG simulation of proteins.