Othmar Steinhauser

Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations

Recently a computer adapted theory suitable for evaluating the dielectric properties of polar systems has been proposed. It rests on the assumption that the system behaves like a macroscopic dielectric and that the modifications of dipolar interactions do not affect its dielectric constant. In the present paper these assumptions are tested, for a system of 512 Stockmayer particles with μ*2 = 3·0 and I* = 0·025 at ρ* = 0·822 and T* = 1·15, in a series of extensive simulations, in which the boundary conditions (spherical reaction field (RF) vs. lattice summation technique (LS)) have been varied in a systematic way. Within the limits of statistical accuracy all simulations give identical results for the static as well as for the frequency dependent dielectric constant, namely e(0) = 66 and a relaxation time of τD* ≃ 1·0 for the almost Debye-like behaviour of e(ω). For particle numbers of 256 and upward the system studied behaves like a macroscopic dielectric; the bulk dielectric constant is independent of N ...

Reaction field simulation of water

Two molecular dynamics simulations of 216 molecules interacting by the ST2 water potential were carried out. Apart from technical improvements, the first simulation was identical to that reported by Stillinger and Rahman [4]. In the second, however, the reaction field method was applied and the influence of long range interactions was carefully studied. 7500 time steps (= 7·5 ps) were generated. The temperature given by the average kinetic energy was 120°C. The atom-atom pair correlation functions and the average dipole energy are rather insensitive to the reaction field. The average cosine between two molecular dipoles, however, is strongly influenced and corresponding curves are of different sign in the second and third coordination shell. For the integral of the average cosine, namely the Kirkwood g-factor g K, the situation is even worse : Large errors occur if the long range interactions are neglected. On the other hand, a convergence of g K was achieved by the inclusion of the reaction field. The pr...

On the calculation of the dielectric constant using the Ewald-Kornfeld tensor

Abstract It is shown that the formula applied in calculations of the dielectric constant in computer simulations using the Ewald-Kornfeld summation corresponds to an idealized limiting case which cannot be realized in practice. For the deviations a quantitative relation is given that permits the correction of data already published.

The influence of boundary conditions used in machine simulations on the structure of polar systems

Studying generalized Onsager models the effect of boundary conditions (finite volume and potential cut-off), used in machine simulations, on the structure of polar systems is examined critically. It is found that deviations from the infinite-system structure stem primarily from the truncation of the potential, which is by no means equivalent to a finite volume, as assumed so far. Intended originally to model computer-generated R-dependent Kirkwood g-factors, continuum theory also predicts correctly the qualitative shape of h Δ- and hD -curves, reported in [10] for various geometries. The present analysis enables, for the first time, a physical understanding of the influence of the cut-off. It turns out that the mean electrostatic energy is only slightly affected and that the asymptotic value of Gk (R) profits from a cancellation of errors. An improved relation is given for the volume dependence of . Within the framework of our models one can also understand rigorously the origin of Barkers reaction ...

Rationalization of the dielectric properties of common three-site water models in terms of their force field parameters

The dielectric properties (static dielectric constant e0, Debye relaxation time τD and distance dependent Kirkwood G-factor Gk(R)) of commonly used three-site water models (the “simple point charge” models SPC and SPC/E, as well as the “transferable intermolecular potentials with three point charges” TIP3P and its CHARMM modified variant TIP3Pmod) were evaluated from 2 ns molecular dynamics simulations using the Ewald summation method to compute the electrostatic interactions. The results for SPC (e0=65±5, τD=7.6±0.8 ps) and SPC/E (e0=68±6, τD=12.1±1.3 ps) are in good agreement with the literature; for TIP3P (TIP3Pmod) we obtained a dielectric constant e0=97±7 (97±6) and a Debye relaxation time τD=7.3±0.7 ps (6.9±0.6 ps). The surprisingly large differences in e0 were rationalized by an investigation of the relationship between the force field parameters and the dielectric properties. Based on simulations of hybrid SPC/TIP3P models, the HOH bond angle was identified as the determining factor of the dielect...

Simulation studies of ionic liquids: Orientational correlations and static dielectric properties

The ionic liquids BMIM+I-, BMIM+BF4-, and BMIM+PF6- were simulated by means of the molecular dynamics method over a time period of more than 100 ns. Besides the common structural analysis, e.g., radial distribution functions and three dimensional occupancy plots, a more sophisticated orientational analysis was performed. The angular correlation functions g(00)110(r) and g(00)101(r) are the first distance dependent coefficients of the pairwise orientational distribution function g(rij,Omega1,Omega2,Omega12). These functions help to interpret the three dimensional plot and reveal interesting insights into the local structure of the analyzed ionic liquids. Furthermore, the collective network of ionic liquids can be characterized by the Kirkwood factor Gkappa(r) [J. Chem. Phys. 7, 911 (1939)]. The short-range behavior (r<10 A) of this factor may be suitable to predict the water miscibility of the ionic liquid. The long-range limit of Gkinfinity is below 1 which demonstrates the strongly coupled nature of the ionic liquid networks. In addition, this factor relates the orientational structure and the dielectric properties of the ionic liquids. The static dielectric constant epsilon(omega=0) for the simulated system is 8.9-9.5. Since in ionic liquids the very same molecule contributes to the total dipole moment as well as carries a net charge, a small, but significant contribution of the cross term between the total dipole moment and the electric current to epsilon(omega=0) is observed.

The influence of a protein on water dynamics in its vicinity investigated by molecular dynamics simulation

A system containing the globular protein ubiquitin and 4,197 water molecules has been used for the analysis of the influence exerted by a protein on solvent dynamics in its vicinity. Using Voronoi polyhedra, the solvent has been divided into three subsets, i.e., the first and second hydration shell, and the remaining bulk, which is hardly affected by the protein. Translational motion in the first shell is retarded by a factor of 3 in comparison to bulk. Several molecules in the first shell do not reach the diffusive regime within 100 ps. Shell‐averaged orientational autocorrelation functions, which are also subject to a retardation effect, cannot be modeled by a single exponential time law, but are instead well‐described by a Kohlrausch‐Williams‐Watts (KWW) function. The underlying distribution of single‐molecule rotational correlation times is both obtained directly from the simulation and derived theoretically. The temperature dependence of reorientation is characterized by a strongly varying correlation time, but a virtually temperature‐independent KWW exponent. Thus, the coupling of water structure relaxation with the respective environment, which is characteristic of each solvation shell, is hardly affected by temperature. In other words, the functional form of the distributions of single‐molecule rotational correlation times is not subject to a temperature effect. On average, a correlation between reorientation and lifetimes of neighborhood relations is observed.

On the collective network of ionic liquid/water mixtures. I. Orientational structure

In this work, the collective structure of aqueous solutions of ionic liquids was studied by means of molecular dynamics simulations. Various concentrations of 1-butyl-3-methyl-imidazolium tetrafluoroborate and TIP3P water were simulated at the very same size of the simulation box. For the analysis, the ternary system cation/anion/water was subdivided into binary networks. The local structure of each of these six networks is investigated by atom-atom radial distribution functions as well as by the so-called g coefficients, which reveal the mutual orientation of the network constituting partners. Furthermore, the collective structure of the whole samples was characterized by the contribution of each species to the static dielectric constant epsilon(omega=0) and to the Kirkwood G(K) factor. The combination of the analysis tools mentioned above provides knowledge about the cross-linking of the ionic species with the dipolar water. Thereby, the interplay between charge-charge and hydrogen bond networks is analyzed in detail.

On the calculation of the frequency-dependent dielectric constant in computer simulations

Abstract An equation is derived which relates, for all boundary conditions currently used, the dipole moment fluctuations observed in computer simulations of polar systems to the frequency-dependent dielectric constant. Provided that the modified dipolar interactions do not explicitly depend upon time, the resulting formula is of a generalized Glarum type.

Computer simulation and the dielectric constant of polarizable polar systems

Abstract A theory presented recently, allowing the static and frequency-dependent dielectric constant of polar systems to be calculated in computer simulations with arbitrary boundary conditions, is extended to the polarizable case. For modified dipolar interactions not explicitly depending upon time, the resulting equations are found to be of the generalized Frohlich-Glarum type.