Ionic dynamics

An issue that has been explored is how the relative distribution of charge and mass affect the viscosity of an ionic liquid. Kobrak and Sandalow [183] pointed out that ionic dynamics are sensitive to the distance between the centers of charge and mass. Where these centers are separated, ionic rotation is coupled to Coulomb interactions with neighboring ions where the centers of charge and mass are the same, rotational motion is, in the lowest order description, decoupled from an applied electric field. This is significant, because the Kerr effect experiments and simulation studies noted in Section III. A imply a separation of time scales for ionic libration (fast) and translation (slow) in ILs. Ions in which charge and mass centers are displaced can respond rapidly to an applied electric field via libration. Time-dependent electric fields are generated by the motion of ions in the liquid... 

For the extended system of ions and particles C, the Lagrangian may be obtained by extension of the classical Lagrangian for ionic dynamics by means of a (fictitious) kinetic energy term due to the particles C ... 

The purpose of this chapter will be to review the fundamentals of ab initio MD. We will consider here Density Functional Theory based ab initio MD, in particular in its Car-Parrinello version. We will start by introducing the basics of Density Functional Theory and the Kohn-Sham method, as the method chosen to perform electronic structure calculation. This will be followed by a rapid discussion on plane wave basis sets to solve the Kohn-Sham equations, including pseudopotentials for the core electrons. Then we will discuss the critical point of ab initio MD, i.e. coupling the electronic structure calculation to the ionic dynamics, using either the Born-Oppenheimer or the Car-Parrinello schemes. Finally, we will extend this presentation to the calculation of some electronic properties, in particular polarization through the modern theory of polarization in periodic systems. 

In empirical force-fields calculations, the information about the electronic system is entirely contracted in the data of the ground state potential energy surface and forces acting on the nuclei. Model potentials and forces are then used to propagate the ionic dynamics, instead of performing an electronic structure calculation. This on the fly quantum calculation is the challenging part of first-principle Molecular Dynamics simulations. 

As most of the electronic structure simulation methods, we start with the Born-Oppenheimer approximation to decouple the ionic and electronic degrees of freedom. The ions are treated classically, while the electrons are described by quantum mechanics. The electronic wavefunctions are solved in the instantaneous potential created by the ions, and are assumed to evolve adiabatically during the ionic dynamics, so as to remain on the Born-Oppenheimer surface. Beyond this, the most basic approximations of the method concern the treatment of exchange and correlation (XC) and the use of pseudopotentials. XC is treated within Kohn-Sham DFT [3]. Both the local (spin) density approximation (LDA/LSDA) [16] and the generalized gradients approximation (GGA) [17] are implemented. The pseudopotentials are standard norm-conserving [18, 19], treated in the fully non-local form proposed by Kleinman and Bylander [20]. 

In this chapter we review a recently developed microscopic theory to study such collective excitations in molecular liquids based on the interaction-site representation. As an application we also present a molecular theory for dynamics of solvated ion, in which the ionic dynamics is described in terms of the response of the solvent collective excitations to the solute perturbation. But before embarking on the main subject, let us make a brief survey of the historical developments of the theory... 

The recent development of high-resolution experimental techniques allows for the structural analysis of protein channels with unprecedented detail. However, the fundamental problem of relating the structure of ion channels to their function is a formidable task. This chapter describes some of the most popular simulation approaches used to model channel systems. Particle-based approaches such as Brownian and molecular dynamics will continue to play a major role in the study of protein channels and in validating the results obtained with the extremely fast continuum models. Research in the area of atomistic simulations will focus mainly on the force-field schemes used in the ionic dynamics simulation engines. In particular, polar interactions between the various components of the system need to be computed with algorithms that are more accurate than those currently used. The effects of the local polarization fields need to be accounted for explicitly and, at the same time, efficiently. Continuum models will remain attractive for their efficiency in depicting the electrostatic landscape of protein channels. Both Poisson-Boltzmann and Poisson-Nemst-Plank solvers will continue to be used to... 

Donoso P, Gorecki W, Berthier C et al (1988) NMR, conductivity and neutron scattering investigation of ionic dynamics in the anhydrous polymer protonic conductor PE0(H3P04)x. Solid State Ionics 28 969-974... 

Honda H, Ishimaru S, Bceda R (1999) Ionic dynamics in LiN02 studied by 7Li and 15N solid NMR. Z Naturforsch A 54 519-523... 

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

Roberts J E and Schnitker J 1993 Ionic quadrupolar relaxation in aqueous solution—dynamics of the hydration sphered. Rhys. Chem. 97 5410-17... 

Many-body problems wnth RT potentials are notoriously difficult. It is well known that the Coulomb potential falls off so slowly with distance that mathematical difficulties can arise. The 4-k dependence of the integration volume element, combined with the RT dependence of the potential, produce ill-defined interaction integrals unless attractive and repulsive mteractions are properly combined. The classical or quantum treatment of ionic melts [17], many-body gravitational dynamics [18] and Madelung sums [19] for ionic crystals are all plagued by such difficulties. 

Straatsma, T.P, Berendsen, H.J.C. Free energy of ionic hydration Analysis of a thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations. J. Chem. Phys. 89 (1988) 5876-5886. 

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

Allan N L, G D Barrera, J A Purton, C E Sims and M B Taylor 2000. Ionic Solids at High Temperatures and Pressures Ah initio, Lattice Dynamics and Monte Carlo Studies. Physical Chemistry Chemical Physics 2 1099-1111. 

The concentration of salt in physiological systems is on the order of 150 mM, which corresponds to approximately 350 water molecules for each cation-anion pair. Eor this reason, investigations of salt effects in biological systems using detailed atomic models and molecular dynamic simulations become rapidly prohibitive, and mean-field treatments based on continuum electrostatics are advantageous. Such approximations, which were pioneered by Debye and Huckel [11], are valid at moderately low ionic concentration when core-core interactions between the mobile ions can be neglected. Briefly, the spatial density throughout the solvent is assumed to depend only on the local electrostatic poten-... 

The structure on the left is biradical, while the two others are ionic, corresponding to both electrons being at the same carbon. The simplest CASSCF wave function which qualitatively can describe this system has two electrons in two orbitals, giving the three configurations shown above. The dynamical correlation between die two active electrons will tend to keep them as far apart as possible, i.e. favouring the biradical structure. Now... 

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