Dynamics of supercooled water in configuration space.

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by mode-coupling theory. We find that the diffusion constant depends on the fraction of directions in configuration space connecting different local minima, supporting the hypothesis that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find a relation between the number of basins accessed in equilibrium and the connectivity between them.

In our previous study [Plankova et al., EPJWeb. Conf. 92 , 02071 (2015)], several molecular simulations of vapor-liquid phase interfaces for pure water were performed using the DL_POLY Classic software. The TIP4P/2005 molecular model was successfully used for the modeling of the density profile and the thickness of phase interfaces together with the temperature dependence of the surface tension. In the current study, the extended simple point charge (SPC/E) model for water was employed for the investigation of vapor-liquid phase interfaces over a wide temperature range from 250 K to 600 K. The TIP4P/2005 model was also used with the temperature step of 25 K to obtain more consistent data compared to our previous study. Results of the new simulations are in a good agreement with most of the literature data. TIP4P/2005 provides better results for the saturated liquid density with its maximum close to 275 K, while SPC/E predicts slightly better saturated vapor density. Both models give qualitatively correct representation for the surface tension of water. The maximum absolute deviation from the IAPWS standard for the surface tension of ordinary water is 10.4 mN · m−1 and 4.1 mN · m−1 over the temperature range from 275 K to 600 K in case of SPC/E and TIP4P/2005, respectively.

We investigate the properties of geometrically modified water models by performing molecular dynamics simulations of perturbations of the extended simple point charge (SPC/E) model of water over a wide range of temperatures at 1 bar. The geometric modification consists of altering the H-O-H angle in SPC/E. The dipole moment is held constant by altering the O-H bond length, while the electrostatic charges are left unchanged. We find that a H-O-H angle of at least 100 degrees is necessary for the appearance of density anomalies and of solubility extrema with respect to temperature for small apolar solutes. We observe the occurrence of two incompatible types of structural order in these models: Tetrahedral, with waterlike translational order for bent models with H-O-H angles in excess of 100 degrees ; and linear, with Lennard-Jones-like orientationally averaged translational order for smaller H-O-H angles. Increasing the H-O-H angle causes the density to increase, while at the same time shifting waterlike anomalies to progressively higher temperatures. For bent models with H-O-H angle greater than SPC/E's, we observe arrest of translational motion at 300 K (115 degrees) and 330 K (120 degrees).

Path integral molecular dynamics (PIMD) simulations of the extended simple point charge (SPC/E) model of liquid water (both H2O and D2O) have been performed in order to find the temperature at which the maximum liquid density is obtained. For comparison, purely classical SPC and SPC/E water have also been simulated over long periods (more than 200 ps). Structural properties and various temperature dependent quantities are reported. Special attention has been given to the fluctuations of pressure and volume in simulations run in the canonical (constant NVT) and isothermal–isobaric (constant NPT) ensembles, respectively. Although a density maximum is detected by monitoring energy–volume correlations as a function of temperature, the large statistical uncertainty in the correlations reduces the significance of this finding. The main conclusions of this work are threefold. First, the use of the energy–volume correlation moment to determine the density maximum appears to be a useful method, although a number of very long simulations of between 0.5–1.0 ns over a fairly wide temperature range are necessary to obtain accurate results. Second, neither the SPC nor the SPC/E water models are able to reproduce the density of cold water accurately. Finally, a quantum mechanical treatment of the water model is necessary to correctly represent the structure, energy, and fluctuations of the condensed phase.

A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.

On the Temperature and Pressure Dependence of a Range of Properties of a Type of Water Model Commonly Used in High-Temperature Protein Unfolding Simulations

Constant temperature and constant pressure molecular dynamics calculations have been performed on the extended simple point charge (SPC/E) model water to understand the effects of pressure on its structural and dynamical properties. The effect of pressure is to increase the presence of interstitial water molecules, which is shown to be responsible for the experimentally observed increase in the first x-ray diffraction peak and a broadening of the OOO∧ bond angle distribution. These structural changes lead to weaker hydrogen bonding and the observed minimum in the rotational correlation time as a function of pressure. The weak maximum in the measured translational diffusion coefficient at around 1.5 kbar was not reproduced. The temperature of the density maximum was estimated to occur at 245±4 K, which suggests that structural changes with increasing pressure and decreasing temperature are not quantitatively reproduced by the SPC/E model.

This paper discusses the computer simulation of the diffusion coefficients and structure of infinitely dilute aqueous ionic solutions at ambient (298 K, solvent density 0.997 g cm−3) and supercritical (683 K, solvent density 0.35 g cm−3) conditions using two different models for water. They are the extended simple point charge (SPC/E) and renormalized polarizability (RPOL) models in which the electronic polarizations of the water molecule are treated differently. The effect of polarizability is implicit in the SPC/E model and explicit in the RPOL model. The RPOL model shows slightly greater hydrogen bonding, at room temperature than the SPC/E model, but less hydrogen bonding at 683 K. It is concluded that the explicit neglect of electronic polarization of the solvent and ions in calculations based on the SPC/E model of water, has only a small effect on the diffusion coefficients of the ions. Both models predict diffusion coefficients of ions in supercritical water that are weakly dependent on their size in contrast to their behavior under ambient conditions discussed in previous work [S. Koneshan et al., J. Phys. Chem. 102, 4193 (1998)]. The simulations suggest that the mechanism of diffusion at the ambient and supercritical states of the solvent water is different.

The formalism of the dynamical theory of diffusion is shown to be strictly analogous to that of the reaction-rate theory in the sense that expressions for the jump rate and related quantities can be written in the same form as the corresponding expressions of rate theory. However, the physical meaning of corresponding quantities is different. For example, the role of the saddle-point configuration in rate theory is taken by a dynamical state in the dynamical theory. The reaction coordinate is shown to measure the extent to which lattice reaction forces barring the jump have been overcome by thermal fluctuations. Geometric considerations indicate that for vacancy diffusion, the factor $\ensuremath{\Delta}K$ should have a lower limit on the order of 0.5 in the fcc lattice and an upper limit of the same order for the bcc lattice. In general, $\ensuremath{\Delta}K$ measures the mass dependence of the rms velocity of the system along the jump direction in configuration space. The mass dependence of the isotope effect for impurity diffusion is developed, and a double-isotope-effect experiment involving the simultaneous diffusion of three solute isotopes is proposed to determine impurity correlation factors.

The ice/water interface is investigated using the simple point charge (SPC) model for water. Molecular dynamics simulations at constant NVE demonstrate that the model interface is stable on the time scale of at least 300 ps. The density profile and mean square displacement of molecules are measured, and the results are nearly identical to those obtained earlier using the TIP4P model for water. This is additional evidence that the properties measured in the simulation are intrinsic to the ice/water interface and do not depend on the particular model potentials employed.

We present a Monte Carlo simulation study of adsorption and desorption for two molecular models of water in activated carbon, focusing on the temperature range for which the system exhibits hysteresis. The activated carbon is modeled using an adaptation of the platelet model developed by Segarra and Glandt (Chem. Eng. Sci. 1994, 49 (17), 2953−2965). The active sites in the carbon are modeled by placing interaction sites at the periphery of the platelets. To model water we have used two model potentials: the simple point charge (SPC) model and adaptation of the primitive model of water developed by Kolafa and Nezbeda (Mol. Phys. 1987, 61 (1), 161−175). We find that both models considered yield quite good qualitative agreement with the experimental data for water in BPL carbon obtained by Levan and co-workers (Ind. Eng. Chem. Res. 1992, 31 (4), 1122−1130). In particular both the shape of the hysteresis loops and their temperature dependence are correctly described by the simulation results. The sensitivity of the results to changes in the model parameters is investigated.

We investigate structural order in glassy water by performing classical molecular dynamics simulations using the extended simple point charge (SPC/E) model of water. We perform isochoric cooling simulations across the glass transition temperature at different cooling rates and densities. We quantify structural order by orientational and translational order metrics. Upon cooling the liquid into the glassy state, both the orientational order parameter Q and translational order parameter tau increase. At T=0 K, the glasses fall on a line in the Q-tau plane or order map. The position of this line depends only on density and coincides with the location in the order map of the inherent structures (IS) sampled upon cooling. We evaluate the energy of the IS, eIS(T), and find that both order parameters for the IS are proportional to eIS. We also study the structural order during the transformation of low-density amorphous ice (LDA) to high-density amorphous ice (HDA) upon isothermal compression and are able to identify distinct regions in the order map corresponding to these glasses. Comparison of the order parameters for LDA and HDA with those obtained upon isochoric cooling indicates major structural differences between glasses obtained by cooling and glasses obtained by compression. These structural differences are only weakly reflected in the pair correlation function. We also characterize the evolution of structural order upon isobaric annealing, leading at high pressure to very-high density amorphous ice (VHDA).

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.

Improved SPC force field of water based on the dielectric constant: SPC/[formula omitted

Water is a notoriously difficult substance to model both accurately and efficiently. Here, we focus on descriptions with a single coarse-grained particle per molecule using the so-called approximate non-conformal and generalized Stockmayer potentials as the starting points. They are fitted using the radial distribution function and the liquid-gas density profile of the atomistic extended simple point charge (SPC/E) model by downhill simplex optimization. We compare the results with monatomic water (mW), ELBA, and direct iterative Boltzmann inversion of SPC/E. The results show that symmetrical potentials result in non-transferable models, that is, they need to be reparametrized for new state points. This indicates that transferability may require more complex models. Furthermore, the results also show that the addition of a point dipole is not sufficient to make the potentials accurate and transferable to different temperatures (300 K-500 K) and pressures without an appropriate choice of properties as targets during model optimization.