Theoretical study of the molecular motion of liquid water under high pressure

Diffusion theory of molecular liquids in the energy representation and application to solvation dynamics

The generalized Langevin equation (GLE) formalism is a useful theoretical fundament for analyzing dynamical phenomena rigorously. Despite the systematic formulation of dynamics theories with practical approximations, however, the applicability of GLE-based methods is still limited to simple polyatomic liquids due to the approximate treatment of molecular orientations involved in the static molecular liquid theory. Here, we propose an exact framework of dynamics based on the GLE formalism incorporating the energy representation theory of solution, an alternative static molecular liquid theory. A fundamental idea is the projection of the relative positions and orientations of solvents around a solute onto the solute-solvent interaction, namely the energy coordinate, enabling us to describe the dynamics on a one-dimensional coordinate. Introducing systematic approximations, such as the overdamped limit, leads to the molecular diffusion equation in the energy representation that is described in terms of the distribution function of solvents on the energy coordinate and the diffusion coefficients. The present theory is applied to the solvation dynamics triggered by the photoexcitation of benzonitrile. The long-time behavior of the solvation time correlation function is in good agreement with that obtained by the molecular dynamics simulation.

Coupling between Structural and Dielectric Relaxations of Methanol and Ethanol Studied by Molecular Dynamics Simulation

The microscopic origin of the fast dielectric relaxation modes and the integrated dielectric relaxation times of methanol and ethanol was investigated by means of cross-correlation analysis of molecular dynamics simulation. Random force on the fluctuation of collective dipole moment was correlated with the two-body density mode in both real and reciprocal spaces. A strong coupling was observed with the OH alternation mode at 30 nm^-1, suggesting that alternating switching of the hydrogen bond within a hydrogen-bonding chain is the principal origin of the retarded friction on the collective dipole moment. The relaxation of the coupling was much slower than that of the partial intermediate scattering functions at the corresponding wavenumber, which suggests the breakdown of the factorization approximation employed in the mode-coupling theory. Although the prepeak structure is strongly coupled to the viscoelastic relaxation, its coupling with the dielectric relaxation is relatively weak. The difference between the viscoelastic and the dielectric relaxations was discussed in terms of the different symmetries of the shear stress tensor and the collective dipole moment.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

Mode-coupling theoretical study on the roles of heterogeneous structure in rheology of ionic liquids

Theoretical calculations of the rheological properties of coarse-grained model ionic liquids were performed using mode-coupling theory. The nonpolar part of the cation was systematically increased in order to clarify the effects of the heterogeneous structure on shear viscosity. The shear viscosity showed a minimum as the function of the size of the nonpolar part, as had been reported in literatures. The minimum was ascribed to the interplay between the increase in the shear relaxation time and the decrease in the high-frequency shear modulus with increasing the size of the nonpolar part of the cation. The ionic liquids with symmetric charge distribution of cations were less viscous than those with asymmetric cations, which is also in harmony with experiments. The theoretical analysis demonstrated that there are two mechanisms for the higher viscosity of the asymmetric model. The first one is the direct coupling between the domain dynamics and the shear stress. The second one is that the microscopic dynamics within the polar domain is retarded due to the nonlinear coupling with the heterogeneous structure.

Study on the temperature-dependent coupling among viscosity, conductivity and structural relaxation of ionic liquids

The frequency-dependent viscosity and conductivity of three imidazolium-based ionic liquids were measured at several temperatures in the MHz region, and the results are compared with the intermediate scattering functions determined by neutron spin echo spectroscopy.

Transport coefficients of the TIP4P-2005 water model

A detailed understanding of the dynamics of liquid water at molecular level is of fundamental importance as well as have applications in many branches of science and technology. In this work, the diffusion of the TIP4P-2005 model of water is systematically investigated in liquid phase in the temperature range 210-310 K. The translational and rotational diffusions, as well as correlations between them, are examined. The effects of system size and shape are also probed in this study. The results suggest the presence of a temperature of dynamical arrest of molecular translations in the range of 150-180 K and of molecular rotations in the range of 80-130 K, depending on specific direction. A substantial change in the preferred directions of translations and rotations relative to the molecular coordinate system is observed slightly below (≈15 K) the melting temperature of the model. It is shown that there is a correlation between translational and rotational molecular motions essential for diffusion in the liquid. The presence of hydrodynamic size effects is confirmed and quantified; it is also shown that using a non-cubic simulation box for a liquid system leads to an anisotropic splitting in the diffusion tensor. The findings of this study enhance our general understanding of models of water, specifically the TIP4P-2005 model, as well as provide evidences of the direct connection between thermodynamics of liquid water and dynamics of its molecules.

Mode-coupling theoretical analysis of transport and relaxation properties of liquid dimethylimidazolium chloride

The mode-coupling theory for molecular liquids based on the interaction-site model is applied to a representative molecular ionic liquid, dimethylimidazolium chloride, and dynamic properties such as shear viscosity, self-diffusion coefficients, reorientational relaxation time, electric conductivity, and dielectric relaxation spectrum are analyzed. Molecular dynamics (MD) simulation is also performed on the same system for comparison. The theory captures the characteristics of the dynamics of the ionic liquid qualitatively, although theoretical relaxation times are several times larger than those from the MD simulation. Large relaxations are found in the 100 MHz region in the dispersion of the shear viscosity and the dielectric relaxation, in harmony with various experiments. The relaxations of the self-diffusion coefficients are also found in the same frequency region. The dielectric relaxation spectrum is divided into the contributions of the translational and reorientational modes, and it is demonstrated that the relaxation in the 100 MHz region mainly stems from the translational modes. The zero-frequency electric conductivity is close to the value predicted by the Nernst-Einstein equation in both MD simulation and theoretical calculation. However, the frequency dependence of the electric conductivity is different from those of self-diffusion coefficients in that the former is smaller than the latter in the gigahertz-terahertz region, which is compensated by the smaller dispersion of the former in the 100 MHz region. The analysis of the theoretical calculation shows that the difference in their frequency dependence is due to the different contribution of the short- and long-range liquid structures.

Site-site memory equation approach in study of density/pressure dependence of translational diffusion coefficient and rotational relaxation time of polar molecular solutions: acetonitrile in water, methanol in water, and methanol in acetonitrile

We present results of the theoretical study and numerical calculation of the dynamics of molecular liquids based on the combination of the memory equation formalism and the reference interaction site model (RISM). Memory equations for the site-site intermediate scattering functions are studied in the mode-coupling approximation for the first-order memory kernels, while equilibrium properties such as site-site static structure factors are deduced from RISM. The results include the temperature-density (pressure) dependence of translational diffusion coefficients D and orientational relaxation times tau for acetonitrile in water, methanol in water, and methanol in acetonitrile--all in the limit of infinite dilution. Calculations are performed over the range of temperatures and densities employing the extended simple point charge model for water and optimized site-site potentials for acetonitrile and methanol. The theory is able to reproduce qualitatively all main features of temperature and density dependences of D and tau observed in real and computer experiments. In particular, anomalous behavior, i.e, the increase in mobility with density, is observed for D and tau of methanol in water, while acetonitrile in water and methanol in acetonitrile do not show deviations from the ordinary behavior. The variety exhibited by the different solute-solvent systems in the density dependence of the mobility is interpreted in terms of the two competing origins of friction, which interplay with each other as density increases: the collisional and dielectric frictions which, respectively, increase and decrease with increasing density.

Protein under pressure: Molecular dynamics simulation of the arc repressor

Experimental nuclear magnetic resonance results for the Arc Repressor have shown that this dimeric protein dissociates into a molten globule at high pressure. This structural change is accompanied by a modification of the hydrogen-bonding pattern of the intermolecular beta-sheet: it changes its character from intermolecular to intramolecular with respect to the two monomers. Molecular dynamics simulations of the Arc Repressor, as a monomer and a dimer, at elevated pressure have been performed with the aim to study this hypothesis and to identify the major structural and dynamical changes of the protein under such conditions. The monomer appears less stable than the dimer. However, the complete dissociation has not been seen because of the long timescale needed to observe this phenomenon. In fact, the protein structure altered very little when increasing the pressure. It became slightly compressed and the dynamics of the side-chains and the unfolding process slowed down. Increasing both, temperature and pressure, a tendency of conversion of intermolecular into intramolecular hydrogen bonds in the beta-sheet region has been detected, supporting the mentioned hypothesis. Also, the onset of denaturation of the separated chains was observed.

Mode-coupling study on the dynamics of hydrophobic hydration

The molecular motion of water in water-hydrophobic solute mixtures was investigated by the mode-coupling theory for molecular liquids based on the interaction-site description. When the model Lennard-Jones solute was mixed with water, both the translational and reorientational motions of solvent water become slower, in harmony with various experiments and molecular dynamics simulations. We compared the mechanism of the slowing down with that of the pressure dependence of the molecular motion of neat water [T. Yamaguchi, S.-H. Chong, and F. Hirata, J. Chem. Phys. 119, 1021 (2003)]. We found that the decrease in the solvent mobility caused by the solute can essentially be elucidated by the same mechanism: That is, the fluctuation of the number density of solvent due to the cavity formation by the solute strengthens the friction on the collective polarization through the dielectric friction mechanism: We also employed the solute molecule that is the same as solvent water except for the amount of partial charges, in order to alter the strength of the solute-solvent interaction continuously. The mobility of the solvent water was reduced both by the hydrophobic and strongly hydrophilic solutes, but it was enhanced in the intermediate case. Such a behavior was discussed in connection with the concept of positive and negative hydrations.

Quasielastic neutron scattering investigation of the pressure dependence of molecular motions in liquid water

We report on a high-resolution, high-statistics, quasielastic neutron scattering (QENS) experiment on liquid water, aimed at accurately measuring the pressure dependence of the single-particle dynamic response function at low wave vector transfers, namely, from 0.26 to 1.32 A(-1). High-pressure QENS data were collected along the T = 268 K isothermal path over the rather extended pressure range of 80 up to 350 MPa, a thermodynamic region so far unexplored by this microscopic technique. The analysis of the measured line shapes enabled us to draw a consistent picture of the wave vector and pressure dependences of the diffusion mechanisms in liquid water, against which the most recent models for water dynamics can be checked. In close similarity with the case of supercooled water, the relaxing-cage model was found to provide a quantitatively more accurate description of the molecular motions and their pressure evolution in liquid water.

Mode-coupling study on the dynamics of hydrophobic hydration II: Aqueous solutions of benzene and rare gases

The dynamic properties of both the solute and solvent of the aqueous solution of benzene, xenon and neon are calculated by the mode-coupling theory for molecular liquids based on the interaction-site model. The B-coefficients of the reorientational relaxation and the translational diffusion of the solvent are evaluated from their dependence on the concentration of the solute, and the reorientational relaxation time of water within the hydration shell is estimated based on the two-state model. The reorientational relaxation times of water in the bulk and within the hydration shell, that of solute, and the translational diffusion coefficients of solute and solvent, are calculated at 0-30 degrees C. The temperature dependence of these dynamic properties is in qualitative agreement with that of NMR experiment reported by Nakahara et al. (M. Nakahara, C. Wakai, Y. Yoshimoto and N. Matubayasi, J. Phys. Chem., 1996, 100, 1345-1349, ref. 36), although the agreement of the absolute values is not so good. The B-coefficients of the reorientational relaxation times for benzene, xenon and neon solution are correlated with the hydration number and the partial molar volume of the solute. The proportionality with the latter is better than that with the former. These results support the mechanism that the retardation of the mobility of water is caused by the cavity formation of the solute, as previously suggested by us (T. Yamaguchi, T. Matsuoka and S. Koda, J. Chem. Phys., 2004, 120, 7590-7601, ref. 34), rather than the conventional one that the rigid hydration structure formed around the hydrophobic solute reduces the mobility of water.

Molecular multivalent electrolytes: microstructure and screening lengths

We study small rod-like molecular electrolytes solutions with their corresponding atomic counterions. The asymptotic length scales (decay length and wavelength) of the structural correlations are analyzed using the formalism of the dressed interaction site theory (DIST). The correlation functions are determined using the reference interaction site model equation complemented with a mixed approach in which the hypernetted-chain closure is used for the repulsive interactions, and the mean spherical approximation is used for the attractive interactions. The results from this scheme are in good agreement with the Monte Carlo computer simulations reported here. The asymptotic properties of the correlation functions of this molecular system are compared against those corresponding to two related simple (atomic) electrolyte models. The main conclusion is that the molecular structure of the ions lowers by two orders of magnitude the concentration at which the transition from monotonic to oscillatory decay occurs.