Dynamics of TIP5P and TIP4P/ice potentials

The dynamics of a thin film of ice Ih deposited on MgO (001) is studied through molecular dynamics simulations performed with two new potential models of ice. This system is chosen because it is possible to compare the results of the simulations to incoherent neutron quasielastic scattering experiments performed few years ago and to previous molecular dynamics simulations using the TIP4P potential model. The present simulations are performed to determine the evolution of the translational and orientational order parameters of the ice film upon temperature increase in the 250-280 K range. They are also used to calculate the translational and orientational diffusion coefficients of the water molecules in the supported film as a function of the temperature. When using the TIP5P potential, the present results show a better agreement with experimental data than those calculated with the TIP4P potential, especially regarding the temperature above which significant changes are obtained in the dynamics of the water film. Similar conclusions are obtained when using the TIP4P/ice potential, although this latter potential clearly underestimates the translational diffusion coefficients.     

The low-temperature dynamic crossover phenomenon in protein hydration water: simulations vs experiments

A super-Arrhenius-to-Arrhenius dynamic crossover phenomenon has been observed in the translational alpha-relaxation time and in the inverse of the self-diffusion constant both experimentally and by simulations for lysozyme hydration water in the temperature range of TL = 223 +/- 2 K. MD simulations are based on a realistic hydrated powder model, which uses the TIP4P-Ew rigid molecular model for the hydration water. The convergence of neutron scattering, nuclear magnetic resonance and molecular dynamics simulations supports the interpretation that this crossover is a result of the gradual evolution of the structure of hydration water from a high-density liquid to a low-density liquid form upon crossing of the Widom line above the possible liquid-liquid critical point of water.     

Effects of water model and simulation box size on protein diffusional motions

We performed molecular dynamics simulations of ubiquitin with the distinct water models, TIP3P, SPC, SPC/E, and SPC/Fw, in different system sizes with different box shapes. The translational diffusion constants of pure water linearly depend on the effective box length, which is known as finite size effect, whereas the first and second rotational times of pure water are nearly constant. We then observed that both the overall translation and rotational motions of the protein are linearly correlated to the viscosity of pure water. As expected from the finite size effect in pure water, the translational diffusion of the protein is significantly affected by the system size, and rotational diffusion is nearly size-independent. After correction for the finite size effect, the SPC/E and SPC/Fw models reproduce both the translational and rotational motion of the protein relatively well. Thus, water models that reproduce the experimentally derived diffusional properties of pure water accurately are expected to also be suitable for simulating protein diffusion quantitatively.     

Dynamics of surface water in ZrO2 studied by quasielastic neutron scattering

A quasielastic neutron scattering experiment has revealed the dynamics of surface water in a high surface area zirconium oxide in the temperature range of 300-360 K. The characteristic times of the rotational (picoseconds) and translational (tens of picoseconds) components of diffusion motion are well separated. The rotational correlation time shows an Arrhenius-type behavior with an activation energy of 4.48 kJ/mol, which is lower compared to bulk water. The rotational diffusion at room temperature is slower by about a factor of 2 compared to bulk water, whereas the translational diffusion slows down by a factor of 40. In contrast to bulk water, the translational correlation time exhibits an Arrhenius-type temperature dependence with an activation energy of 11.38 kJ/mol. Comparison of different models for jump diffusion processes suggests that water molecules perform two-dimensional jumps at a well-defined, almost temperature-independent distance of 4.21-4.32 A. Such a large jump distance indicates a low molecular density of the layer of diffusing molecules. We argue that undissociated water molecules on an average form two hydrations layers on top of the surface layer of hydroxyl groups, and all the layers have similar molecular density. Quasielastic neutron scattering experiment assesses the dynamics of the outermost hydration layer, whereas slower motion of the water molecules in the inner hydration layer contributes to the elastic signal.     

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.     

Prediction of self-diffusion coefficient and shear viscosity of water and its binary mixtures with methanol and ethanol by molecular simulation

Density, self-diffusion coefficient, and shear viscosity of pure liquid water are predicted for temperatures between 280 and 373 K by molecular dynamics simulation and the Green-Kubo method. Four different rigid nonpolarizable water models are assessed: SPC, SPC/E, TIP4P, and TIP4P/2005. The pressure dependence of the self-diffusion coefficient and the shear viscosity for pure liquid water is also calculated and the anomalous behavior of these properties is qualitatively well predicted. Furthermore, transport properties as well as excess volume and excess enthalpy of aqueous binary mixtures containing methanol or ethanol, based on the SPC/E and TIP4P/2005 water models, are calculated. Under the tested conditions, the TIP4P/2005 model gives the best quantitative and qualitative agreement with experiments for the regarded transport properties. The deviations from experimental data are of 5% to 15% for pure liquid water and 5% to 20% for the water + alcohol mixtures. Moreover, the center of mass power spectrum of water as well as the investigated mixtures are analyzed and the hydrogen-bonding structure is discussed for different states.     

Water rotational relaxation and diffusion in hydrated lysozyme

This paper is concerned with the dynamics of water around a small globular protein. Dipolar second-rank relaxation time and diffusion properties of surface water were computed by extensive molecular dynamics simulations of lysozyme in water which lasted a total of 28 ns. Our results indicate that the rotational relaxation of water in the vicinity of lysozyme is 3-7 times slower than that in the bulk depending on how the hydration shell is defined in the calculation. We have also verified that the dynamics of water translational diffusion in the vicinity of lysozyme have retardations similar to rotational relaxation. This is a common assumption in nuclear magnetic relaxation dispersion (NMRD) studies to derive residence times. In contrast to bulk water dynamics, surface water is in a dispersive diffusion regime or subdiffusion. Very good agreement of dipolar second-rank relaxation time with NMRD estimates is obtained by using appropriate dimensions of the hydration shell. Although our computed second-rank dipolar retardations are independent of the water model, SPC/E describes more realistically the time scale of the water dynamics around lysozyme than does TIP3P.     

Molecular dynamics of n-hexane: a quasi-elastic neutron scattering study on the bulk and spatially nanochannel-confined liquid

We present incoherent quasi-elastic neutron scattering measurements in a wave vector transfer range from 0.4 A?(-1) to 1.6A? (-1) on liquid n-hexane confined in cylindrical, parallel-aligned nanochannels of 6 nm mean diameter and 260 μm length in monolithic, mesoporous silicon. They are complemented with, and compared to, measurements on the bulk system in a temperature range from 50 K to 250 K. The time-of-flight spectra of the bulk liquid (BL) can be modeled by microscopic translational as well as fast localized rotational, thermally excited, stochastic motions of the molecules. In the nano-confined state of the liquid, which was prepared by vapor condensation, we find two molecular populations with distinct dynamics, a fraction which is immobile on the time scale of 1 ps to 100 ps probed in our experiments and a second component with a self-diffusion dynamics slightly slower than observed for the bulk liquid. No hints of an anisotropy of the translational diffusion with regard to the orientation of the channels' long axes have been found. The immobile fraction amounts to about 5% at 250 K, gradually increases upon cooling and exhibits an abrupt increase at 160 K (20 K below bulk crystallization), which indicates pore freezing.     

Kinetic aspects of the thermostatted growth of ice from supercooled water in simulations

In experiments, the growth rate of ice from supercooled water is seen to increase with the degree of supercooling, that is, the lower the temperature, the faster the crystallization takes place. In molecular dynamics simulations of the freezing process, however, the temperature is usually kept constant by means of a thermostat that artificially removes the heat released during the crystallization by scaling the velocities of the particles. This direct removal of energy from the system replaces a more realistic heat-conduction mechanism and is believed to be responsible for the curious observation that the thermostatted ice growth proceeds fastest near the melting point and more slowly at lower temperatures, which is exactly opposite to the experimental findings [M. A. Carignano, P. B. Shepson, and I. Szleifer, Mol. Phys. 103, 2957 (2005)]. This trend is explained by the diffusion and the reorientation of molecules in the liquid becoming the rate-determining steps for the crystal growth, both of which are slower at low temperatures. Yet, for a different set of simulations, a kinetic behavior analogous to the experimental finding has been reported [H. Nada and Y. Furukawa, J. Crystal Growth 283, 242 (2005)]. To clarify this apparent contradiction, we perform relatively long simulations of the TIP4P/Ice model in an extended range of temperatures. The temperature dependence of the thermostatted ice growth is seen to be more complex than was previously reported: The crystallization process is very slow close to the melting point at 270 K, where the thermodynamic driving force for the phase transition is weak. On lowering the temperature, the growth rate initially increases, but displays a maximum near 260 K. At even lower temperatures, the freezing process slows down again due to the reduced diffusivity in the liquid. The velocity of the thermostatted melting process, in contrast, shows a monotonic increase upon raising the temperature beyond the normal melting point. In this case, the effects of the increasing thermodynamic driving force and the faster diffusion at higher temperatures reinforce each other. In the context of this study, we also report data for the diffusion coefficient as a function of temperature for the water models TIP4P/Ice and TIP4P/2005.     

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.     

Evaluating rotational diffusion from protein MD simulations

It is now feasible to carry out molecular dynamics simulations of proteins in water that are long compared to the overall tumbling of the molecule. Here, we examine rotational diffusion in four small, globular proteins (ubiquitin, binase, lysozyme, and fragment B3 of protein G) with the TIP3P, TIP4P/EW, and SPC/E water models, in simulations that are 6 to 60 times as long as the mean rotational tumbling time. We describe a method for extracting diffusion tensors from such simulations and compare the results to experimental values extracted from NMR relaxation measurements. The simulation results accurately follow a diffusion equation, even for spherical harmonic correlation functions with l as large as 8. However, the best-fit tensors are significantly different from experiment, especially for the commonly used TIP3P water model. Simulations that are 20 to 100 times longer than the rotational tumbling times are needed for good statistics. A number of residues exhibit internal motions on the nanosecond time scale, but in all cases examined here, a product of internal and overall time-correlation functions matches the total time-correlation function well.     

Quantum effects in liquid water and ice: model dependence

This paper explores the influence of choice of potential model on the quantum effects observed in liquid water and ice. This study utilizes standard rigid models and a more formal context for the rigid-body centroid molecular dynamics methodology used to perform the quantum simulations is provided. Quantum and classical molecular dynamics simulations are carried out for liquid water and ice Ih at 298 and 220 K, respectively, with the simple point charge/extended and TIP4P-Ew water models. The results obtained for equilibrium and dynamical properties are compared with those recently reported on TIP4P [L. Hernandez de la Pena and P. G. Kusalik, J. Chem. Phys. 121, 5992 (2004); L. Hernandez de la Pena et al., J. Chem. Phys 123, 144506 (2005)]. For the liquid, an energy shift of about 8% and an average molecular uncertainty of about 11 degrees were found independently of the water model. The self-diffusion coefficient consistently increases by more than 50% when going from the classical to the quantum system and quantum dynamics are found to reproduce the experimental isotopic shifts with the models examined. The ice results compare remarkably well with those previously reported for the TIP4P water model; they confirm that quantum effects are considerable and that the quantum mechanical uncertainty and the energy shifts due to quantization are smaller in ice than in liquid water. The relevance of these findings in the context of the construction of water models is briefly discussed.     

Dynamic arrest in a liquid of symmetric dumbbells: reorientational hopping for small molecular elongations

We present extensive equilibrium and out-of-equilibrium molecular-dynamics simulations of a liquid of symmetric dumbbell molecules, for constant packing fraction, as a function of temperature and molecular elongation. We compute diffusion constants as well as odd and even orientational correlators. The notations odd and even refer to the parity of the order l of the corresponding Legendre l polynomial, evaluated for the orientation of the molecular axis relative to its initial position. Rotational degrees of freedom of order l are arrested if, in the long-time limit, the corresponding orientational l correlator does not decay to zero. It is found that for large elongations translational and rotational degrees of freedom freeze at the same temperature. For small elongations only the even rotational degrees of freedom remain coupled to translational motions and arrest at a finite common temperature. On the contrary, the odd rotational degrees of freedom remain ergodic at all investigated temperatures. Hence, in the translationally arrested state, each molecule remains trapped in the cage formed by its neighboring molecules, but is able to perform 180 degrees rotations, which lead to relaxation only for the odd orientational correlators. The temperature dependence of the characteristic time of these residual rotations is well described by an Arrhenius law. Finally, we discuss the evidence in favor of the presence of the type-A transition for the odd rotational degrees of freedom, as predicted by mode-coupling theory for small molecular elongations. This transition is distinct from the type-B transition, associated with the arrest of the translational and even rotational degrees of freedom for small elongations, and with all degrees of freedom for large elongations. Odd orientational correlators are computed for small elongations at very low temperatures in the translationally arrested state. The obtained results suggest that hopping events restore the ergodicity of the odd rotational degrees of freedom at temperatures far below the A transition.     

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.     

Molecular dynamics study of anisotropic translational and rotational diffusion in liquid benzene

Equilibrium NPT and NVT molecular dynamics simulations were performed on liquid benzene over an extended range of temperature (from 260 to 360 K) using the COMPASS force field. Densities and enthalpies of vaporization (from cohesive energy densities) were within 1% of experiment at all temperatures. tumbling and spinning rotational diffusion coefficients, D(perpendicular) and D(parallel), computed as a function of temperature, agreed qualitatively with the results of earlier reported experimental and computational investigations. Generally, it was found that D(parallel)/D(perpendicular) approximately 1.4-2.5 and the activation energy for tumbling was significantly greater than for spinning about the C6 axis [Ea(D(perpendicular)) = 8.1 kJ mol(-1) and Ea(D(parallel)) = 4.5 kJ mol(-1)]. Calculated translational diffusion coefficients were found to be in quantitative agreement with experimental values at all temperatures [deviations were less than the scatter between different reported measurements]. In addition, translational diffusion coefficients were computed in the molecule-fixed frame to yield values for Dxy (diffusion in the plane of the molecule) and Dz (diffusion perpendicular to the plane). It was found that the ratio Dxy/Dz approximately 2.0, and that the two coefficients have roughly equal activation energies. This represents the first atomistic molecular dynamics study of translational diffusion in the molecular frame.     

Molecular dynamics simulation of the nematic liquid crystal phase in the presence of an intense magnetic field

The influence of an intense external field on the dynamics of the nematic liquid crystal phase is investigated using a molecular dynamics simulation for the Gay-Berne nematogen under isobaric-isothermal conditions. The molecular dynamics as a function of the second-rank orientational order parameter P<2> for a system consisting of a nematic liquid crystal in the presence of an intense magnetic field is compared with that of a similar system without the field. The translational motion of molecules is determined as a function of the translational diffusion coefficient tensor and the anisotropy and compared with the values predicted theoretically. The rotational dynamics of molecules is analyzed using the first- and the second-rank orientational time correlation functions. The translational diffusion coefficient parallel with respect to the director is constrained by the intense field, although the perpendicular one is decreased as the P<2> is increased, just as it is in the system without the field. However, no essential effect of the strong magnetic field is observed in the rotational molecular dynamics. Further, the rotational diffusion coefficient parallel with respect to the director obtained from the first-rank orientational time correlation function in the simulation is qualitatively in agreement with that in the real nematic liquid crystalline molecules. The P<2> dependence of the rotational diffusion coefficient for the system with the intense magnetic field shows a tendency similar to that for the system without the field.     

Molecular dynamics study of translational and rotational diffusion in liquid ortho-terphenyl

NVT molecular dynamics simulations were performed on liquid o-terphenyl as a function of temperature in the range 320-480 K. Computed translational diffusion coefficients displayed the non-Arrhenius behavior expected of a fragile glass-forming liquid and were in good, semiquantitative agreement with experimental results. Rotational correlation functions calculated for various vectors within the molecule exhibited a very short time (0-1 ps) initial decay, followed by a reversal, which corresponds to free reorientation within the "solvent" cage prior to collision with a wall. Rotational correlation times of three orthogonal vectors fixed on the central benzene were close to equal at all temperatures, indicating nearly isotropic overall molecular reorientation. The average correlation times exhibited a non-Arrhenius temperature dependence and were in very good agreement with experimental values derived from 2D and 1H NMR relaxation times. Correlation times of vectors located on the lateral phenyl rings were used to calculate the "spinning" internal rotation diffusion coefficients, which were approximately twice as great as the overall rotational diffusion constants, indicating rapid internal rotation of the phenyl side groups over wide ranges of angle in the liquid.     

Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations

Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision (17)O and (2)H NMR relaxation data for H(2)O and D(2)O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τ(R) is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ～48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τ(R)?D(T) at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τ(R) to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.     

Quantum effects in light and heavy liquid water: A rigid-body centroid molecular dynamics study

The centroid molecular dynamics (CMD) method is applied to the study of liquid water in the context of the rigid-body approximation. This rigid-body CMD technique, which is significantly more efficient than the standard CMD method, is implemented on the TIP4P model for water and used to examine isotopic effects in the equilibrium and dynamical properties of liquid H(2)O and D(2)O. The results obtained with this approach compare remarkably well with those determined previously with path integrals simulations as well as those obtained from the standard CMD method employing flexible models. In addition, an examination of the impact of quantization on the rotational and librational motion of the water molecule is also reported.