Molecular dynamics simulation study on the transient response of solvation structure during the translational diffusion of solute

Coupling between Translational Diffusion of a Solute and Dynamics of the Heterogeneous Structure: Higher Alcohols and Ionic Liquids

Translational diffusion of nonpolar monoatomic solutes in a room-temperature ionic liquid and 1-octanol was studied by molecular dynamics simulation. The diffusion coefficient was evaluated in two different ways: (1) from the mean-square displacement of a freely diffusing solute and (2) from the time correlation function of force acting on a fixed solute. The diffusion of the free solute is much greater than the prediction of the Stokes-Einstein (SE) relation when the size of the solute is small, as has been reported by many experimental works. In contrast, the friction on fixed small solutes follows the SE relation. The mechanism of the solute diffusion in both solvents was then analyzed based on the coupling between the translational motion of the solute and the collective dynamics of the heterogeneous intermediate-range structure characteristic to these solvents. Analysis revealed that the coupling is present in all systems, but the relaxation is fast in the cases of free and small solutes. This suggests that the coupling can relax through the motion of the solute when the solute is free and small, while the relaxation of the heterogeneous structure itself is required for large or fixed solutes. The difference in the relaxation dynamics of the friction on the solute and the shear viscosity is explained as the coupling with different dynamic modes of the solvent. Therefore, the validity of the SE relation may not be a good criterion to judge whether the mechanisms of the diffusion and the viscosity are the same or not.

Analysis of shear viscosity and viscoelastic relaxation of liquid methanol based on molecular dynamics simulation and mode-coupling theory

The role of the prepeak structure of liquid methanol in determining its shear viscosity was studied by means of molecular dynamics (MD) simulation and mode-coupling theory (MCT). The autocorrelation function of the shear stress and the intermediate scattering functions at both the prepeak and the main peak were calculated from the MD trajectories. Their comparison based on MCT suggests that the viscoelastic relaxation in the ps regime is affected by the slow structural dynamics at the prepeak. On the other hand, the MCT for molecular liquids based on the interaction-site model (site-site MCT) fails to describe the coupling between the prepeak dynamics and shear stress. The direct evaluation of the coupling between the two-body density and the shear stress reveals that the viscoelastic relaxation is actually affected by the prepeak dynamics, although the coupling is not captured by the site-site MCT. The site-site MCT works well for a model methanol without partial charges, suggesting that the failure of the site-site MCT originates from the existence of a hydrogen-bonding network structure.

Microscopic flow around a diffusing particle

We report here on the computation of the microscopic flow induced by the motion of a small tagged particle in a fluid from molecular dynamic simulations. It is found that the hydrodynamical Stokes solution with slip boundary conditions is recovered at only a few diameters away from the tagged particle. However, fluctuations of the diffusing particle itself induce a renormalization of the bath viscosity and, more strikingly, an apparent violation of the non-penetrability of the particles in the laboratory frame. The expected zero normal velocity at contact is satisfied only in the particle frame, or for heavy particles. Further evidence of this generalized boundary condition is given by the evaluation of the flow in a granular gas using data from particle tracking experiments.

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.

Two algorithms to compute projected correlation functions in molecular dynamics simulations

An explicit derivation of the Mori-Zwanzig orthogonal dynamics of observables is presented and leads to two practical algorithms to compute exactly projected observables (e.g., random noise) and projected correlation function (e.g., memory kernel) from a molecular dynamics trajectory. The algorithms are then applied to study the diffusive dynamics of a tagged particle in a Lennard-Jones fluid, the properties of the associated random noise, and a decomposition of the corresponding memory kernel.

Generator estimation of Markov jump processes based on incomplete observations nonequidistant in time

Markov jump processes can be used to model the effective dynamics of observables in applications ranging from molecular dynamics to finance. In this paper we present a different method which allows the inverse modeling of Markov jump processes based on incomplete observations in time: We consider the case of a given time series of the discretely observed jump process. We show how to compute efficiently the maximum likelihood estimator of its infinitesimal generator and demonstrate in detail that the method allows us to handle observations nonequidistant in time. The method is based on the work of and Bladt and Sørensen [J. R. Stat. Soc. Ser. B (Stat. Methodol.) 67, 395 (2005)] but scales much more favorably than it with the length of the time series and the dimension and size of the state space of the jump process. We illustrate its performance on a toy problem as well as on data arising from simulations of biochemical kinetics of a genetic toggle switch.

Data-based parameter estimation of generalized multidimensional Langevin processes

The generalized Langevin equation is useful for modeling a wide range of physical processes. Unfortunately its parameters, especially the memory function, are difficult to determine for nontrivial processes. We establish relations between a time-discrete generalized Langevin model and discrete multivariate autoregressive (AR) or autoregressive moving average models (ARMA). This allows a wide range of discrete linear methods known from time series analysis to be applied. In particular, the determination of the memory function via the order of the respective AR or ARMA model is addressed. The method is illustrated on a one-dimensional test system and subsequently applied to the molecular dynamics time series of a biomolecule that exhibits an interesting relationship between the solvent method used, the respective molecular conformation, and the depth of the memory.

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.

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.