Characterization of the TIP4P-Ew water model: vapor pressure and boiling point

The liquid-vapor-phase equilibrium properties of the previously developed TIP4P-Ew water model have been studied using thermodynamic integration free-energy simulation techniques in the temperature range of 274-400 K. We stress that free-energy results from simulations need to be corrected in order to be compared to the experiment. This is due to the fact that the thermodynamic end states accessible through simulations correspond to fictitious substances (classical rigid liquids and classical rigid ideal gases) while experiments operate on real substances (liquids and real gases, with quantum effects). After applying analytical corrections the vapor pressure curve obtained from simulated free-energy changes is in excellent agreement with the experimental vapor pressure curve. The boiling point of TIP4P-Ew water under ambient pressure is found to be at 370.3+/-1.9 K, about 7 K higher than the boiling point of TIP4P water (363.7+/-5.1 K; from simulations that employ finite range treatment of electrostatic and Lennard-Jones interactions). This is in contrast to the approximately +15 K by which the temperature of the density maximum and the melting temperature of TIP4P-Ew are shifted relative to TIP4P, indicating that the temperature range over which the liquid phase of TIP4P-Ew is stable is narrower than that of TIP4P and resembles more that of real water. The quality of the vapor pressure results highlights the success of TIP4P-Ew in describing the energetic and entropic aspects of intermolecular interactions in liquid water.     

Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew

A re-parameterization of the standard TIP4P water model for use with Ewald techniques is introduced, providing an overall global improvement in water properties relative to several popular nonpolarizable and polarizable water potentials. Using high precision simulations, and careful application of standard analytical corrections, we show that the new TIP4P-Ew potential has a density maximum at approximately 1 degrees C, and reproduces experimental bulk-densities and the enthalpy of vaporization, DeltaH(vap), from -37.5 to 127 degrees C at 1 atm with an absolute average error of less than 1%. Structural properties are in very good agreement with x-ray scattering intensities at temperatures between 0 and 77 degrees C and dynamical properties such as self-diffusion coefficient are in excellent agreement with experiment. The parameterization approach used can be easily generalized to rehabilitate any water force field using available experimental data over a range of thermodynamic points.     

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.     

Structural properties and thermodynamics of water clusters: a Wang-Landau study

The temperature dependence of structural properties and thermodynamic behavior of water clusters has been studied using Wang-Landau sampling. Four potential models, simple point charge/extended (SPC/E), transferable intermolecular potential 3 point (TIP3P), transferable intermolecular potential 4 point (TIP4P), and Gaussian charge polarizable (GCP), are compared for ground states and properties at finite temperatures. Although the hydrogen bond energy and the distance of the nearest-neighbor oxygen pair are significantly different for TIP4P and GCP models, they approach to similar ground state structures and melting transition temperatures in cluster sizes we considered. Comparing with TIP3P, SPC/E model provides properties closer to that of TIP4P and GCP.     

Vapor+liquid equilibrium of water, carbon dioxide, and the binary system, water+carbon dioxide, from molecular simulation

NVT- and NpT-Gibbs ensemble Monte Carlo (GEMC) simulations were applied to describe the vapor–liquid equilibrium of water (between 323 and 573 K), carbon dioxide (between 230 and 290 K) and their binary mixtures (between 348 and 393 K). The properties of supercritical carbon dioxide were determined between 310 and 520 K by NpT-MC simulations. Literature data for the effective pair potentials (for water: the SPC-, SPC/E-, and TIP4P potential models; for carbon dioxide: the EPM2 potential model) were used to describe the properties of the pure substances. The vapor pressures of water and carbon dioxide are calculated. For water, the SPC- and TIP4P models give superior results for the vapor pressure when compared to the SPC/E model. The vapor–liquid equilibrium of the binary mixture, carbon dioxide–water, was predicted using the SPC- as well as the TIP4P model for water and the EPM2 model for carbon dioxide. The interactions between carbon dioxide and water were estimated from the pair potentials of the pure components using common mixing rules without any adjustable binary parameter. Agreement of the predicted data for the compositions of the coexisting phases in vapor–liquid equilibrium and experimental results is observed within the statistical uncertainties of the simulation results in the investigated range of state, i.e. at pressures up to about 20 MPa.     

Influence of water-protein hydrogen bonding on the stability of Trp-cage miniprotein. A comparison between the TIP3P and TIP4P-Ew water models

We report extensive replica exchange molecular dynamics (REMD) simulations on the folding/unfolding equilibrium of Trp-cage miniprotein using the Amber ff99SB all atom forcefield and TIP3P and TIP4P-Ew explicit water solvent models. REMD simulation-lengths in the 500 ns to the microsecond regime per replica are required to adequately sample the folding/unfolding equilibrium. We observe that this equilibrium is significantly affected by the choice of the water model. Compared with experimental data, simulations using the TIP3P solvent describe the stability of the Trp-cage quite realistically, providing a melting point which is just a few Kelvins above the experimental transition temperature of 317 K. The TIP4P-Ew model shifts the equilibrium towards the unfolded state and lowers the free energy of unfolding by about 3 kJ mol(-1) at 280 K, demonstrating the need to fine-tune the protein-forcefield depending on the chosen water model. We report evidence that the main difference between the two water models is mostly due to the different solvation of polar groups of the peptide. The unfolded state of the Trp-cage is stabilized by an increasing number of hydrogen bonds, destabilizing the α-helical part of the molecule and opening the R-D salt bridge. By reweighting the strength of solvent-peptide hydrogen bonds by adding a hydrogen bond square well potential, we can fully recover the effect of the different water models and estimate the shift in population as due to a difference in hydrogen bond-strength of about 0.4 kJ mol(-1) per hydrogen bond.     

Thermodynamic transferability of coarse-grained potentials for polymer-additive systems

In this work we study the transferability of systematically coarse-grained (CG) potentials for polymer-additive systems. The CG nonbonded potentials between the polymer (atactic polystyrene) and three different additives (ethylbenzene, methane and neopentane) are derived using the Conditional Reversible Work (CRW) method, recently proposed by us [Brini et al., Phys. Chem. Chem. Phys., 2011, 13, 10468-10474]. A CRW-based effective pair potential corresponds to the interaction free energy between the two atom groups of an atomistic parent model that represent the coarse-grained interaction sites. Since the CRW coarse-graining procedure does not involve any form of parameterisation, thermodynamic and structural properties of the condensed phase are predictions of the model. We show in this work that CRW-based CG models of polymer-additive systems are capable of predicting the correct structural correlations in the mixture. Furthermore, the excess chemical potentials of the additives obtained with the CRW-based CG models and the united-atom parent models are in satisfactory agreement and the CRW-based CG models show a good temperature transferability. The temperature transferability of the model is discussed by analysing the entropic and enthalpic contributions to the excess chemical potentials. We find that CRW-based CG models provide good predictions of the excess entropies, while discrepancies are observed in the excess enthalpies. Overall, we show that the CRW CG potentials are suitable to model structural and thermodynamic properties of polymer-penetrant systems.     

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.     

Hydration thermodynamic properties of amino acid analogues: a systematic comparison of biomolecular force fields and water models

We present an extensive study on hydration thermodynamic properties of analogues of 13 amino acid side chains at 298 K and 1 atm. The hydration free energies DeltaG, entropies DeltaS, enthalpies DeltaH, and heat capacities Deltac(P)() were determined for 10 combinations of force fields and water models. The statistical sampling was extended such that precisions of 0.3, 0.8, 0.8 kJ/mol and 25 J/(mol K) were reached for DeltaG, TDeltaS, DeltaH, and Deltac(P)(), respectively. The three force fields used in this study are AMBER99, GROMOS 53A6, and OPLS-AA; the five water models are SPC, SPC/E, TIP3P, TIP4P, and TIP4P-Ew. We found that the choice of water model strongly influences the accuracy of the calculated hydration entropies, enthalpies, and heat capacities, while differences in accuracy between the force fields are small. On the basis of an analysis of the hydrophobic analogues of the amino acid side chains, we discuss what properties of the water models are responsible for the observed discrepancies between computed and experimental values. The SPC/E water model performs best with all three biomolecular force fields.     

Spectral characterization of hydrogen bond network dynamics in water

Some computational aspects of the characterization of the complex hydrogen bond network dynamics using power spectral analysis are discussed. In the case of hydrogen-bonded liquids, the tagged molecule potential energy is shown to be a useful quantity for capturing the behavior of the networked liquid on different lengths and time scales. The computation of the tagged potential energy for rigid-body effective pair potentials, such as the TIP5P-E and SPC-E models, is discussed. The more structured nature of the TIP5P-E potential, compared to the SPC/E potential, shows up as differences in the high-frequency librational band of the power spectra of the tagged molecule potential energies. The static distributions of the tagged molecule potential energies are also more structured in the case of TIP5P-E, rather than SPC/E, water. The overall behavior of the key power spectral features remains the same in both the models. The possibility of detailed characterization of the power spectrum, and therefore of the underlying dynamics, using a model-based parametric fitting procedure for the power spectra is also discussed. We show that a parametric fitting can allow one to test alternative models of the dynamics underlying the liquid state dynamics.     

Solvation of Glucose, Trehalose, and Sucrose by the Soft Sticky Dipole-Quadrupole-Octupole Water Model

Water structure around sugars modeled by partial charges is compared for soft-sticky dipole-quadrupole-octupole (SSDQO), a fast single-site multipole model, and commonly used multi-site models in Monte Carlo simulations. Radial distribution functions and coordination numbers of all the models indicate similar hydration by hydrogen-bond donor and acceptor waters. However, the new optimized SSDQO1 parameters as well as TIP4P-Ew and TIP5P predict a "lone-pair" orientation for the water accepting the sugar hydroxyl hydrogen bond that is more consistent with the limited experimental data than the "dipole" orientation in SPC/E, which has important implications for studies of the cryoprotectant properties of sugars.     

Long-range Lennard-Jones and electrostatic interactions in interfaces: application of the isotropic periodic sum method

Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields.     

岩盐结构氧化锌物态方程的分子动力学模拟

The equation of state of ZnO with rocksalt phase under high pressure and high temperature was calculated by using the molecular dynamics method with effective pair potentials which consist of the Coulomb, dispersion, and repulsion interaction. It was shown that molecular dynamics simulation is very successful in accurately reproducing the measured molar volumes of the rocksalt phase of ZnO over a wide range of temperatures and pressures. The simulated P-V -T data matched experimental results up to 10.4 GPa and 1273 K. In addition, the linear thermal expansion coe±cient, isothermal bulk modulus and its pressure derivative were also calculated and compared with available experimental data and the latest theoretical results at ambient condition. At extended temperature and pressure ranges, the P-V -T relationship, linear thermal expansion coe±cient, and isothermal bulk modulus were predicted up to 2273 K and 50 GPa. The detailed knowledge of thermodynamic behavior and equations of state at extreme conditions are of fundamental importance to the understanding of the physical properties of ZnO.     

Solvation free energies of amino acid side chain analogs for common molecular mechanics water models

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). In order to examine the accuracy of a range of common water models used for protein simulation for their solute/solvent properties, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from the OPLS-AA parameter set with the TIP3P, TIP4P, SPC, SPC/E, TIP3P-MOD, and TIP4P-Ew water models. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02-0.06 kcal/mol, equivalent to that obtained in experimental hydration free energy measurements of the same molecules. We find that TIP3P-MOD, a model designed to give improved free energy of hydration for methane, gives uniformly the closest match to experiment; we also find that the ability to accurately model pure water properties does not necessarily predict ability to predict solute/solvent behavior. We also evaluate the free energies of a number of novel modifications of TIP3P designed as a proof of concept that it is possible to obtain much better solute/solvent free energetic behavior without substantially negatively affecting pure water properties. We decrease the average error to zero while reducing the root mean square error below that of any of the published water models, with measured liquid water properties remaining almost constant with respect to our perturbations. This demonstrates there is still both room for improvement within current fixed-charge biomolecular force fields and significant parameter flexibility to make these improvements. Recent research in computational efficiency of free energy methods allows us to perform simulations on a local cluster that previously required large scale distributed computing, performing four times as much computational work in approximately a tenth of the computer time as a similar study a year ago.     

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.     

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.     

Consistent and transferable coarse-grained model for semidilute polymer solutions in good solvent

We present a coarse-grained model for linear polymers with a tunable number of effective atoms (blobs) per chain interacting by intra- and intermolecular potentials obtained at zero density. We show how this model is able to accurately reproduce the universal properties of the underlying solution of athermal linear chains at various levels of coarse-graining and in a range of chain densities which can be widened by increasing the spatial resolution of the multiblob representation, i.e., the number of blobs per chain. The present model is unique in its ability to quantitatively predict thermodynamic and large scale structural properties of polymer solutions deep in the semidilute regime with a very limited computational effort, overcoming most of the problems related to the simulations of semidilute polymer solutions in good solvent conditions.     

Coarse-graining in interaction space: a systematic approach for replacing long-range electrostatics with short-range potentials

A short-range effective potential for long-range electrostatic interactions in homogeneously disordered condensed phase systems has been determined with a novel approach to coarse-graining in interaction space. As opposed to coarse-graining the system resolution, this approach "coarsens" the system's interactions by mapping multiple configurations of an accurate long-range atomistic potential onto a more efficient, short-range effective potential with a force-matching (FM) method. Developing an empirical potential in this manner is fundamentally different from existing strategies because it utilizes condensed-phase (as opposed to gas-phase) atomistic interactions to determine general pair potentials defined on distance meshes (as opposed to fitting predetermined functional forms). The resulting short-range ( approximately 10 A) effective potential reproduces structural, dynamical, and many thermodynamic properties of liquid water, ions in water, and hydrophobes in water, with unprecedented accuracy. The effective potential is also shown to be transferable to a nonaqueous molten salt system. With continued development, such effective potentials may provide an accurate and highly efficient alternative to Ewald-based long-range electrostatics methods.