Published: January 20, 2011 r2011 American Chemical Society 1045 dx.doi.org/10.1021/jp109976p | J. Phys. Chem. B 2011, 115, 1045–1055 ARTICLE pubs.acs.org/JPCB Using Solvent Binding and Dielectric Friction To Interpret the Hydration Behavior of Complex Anions Richard P. Matthews, Gerhard A. Venter, and Kevin J. Naidoo* Scientific Computing Research Unit and Department of Chemistry, University of Cape Town, Rondebosch 7701, South Africa b S Supporting Information ABSTRACT: We investigate the hydration structure and water/ion dynamics about complex anions using a revised platinum group metal chloro-anion force field. Nanosecond atomistic molecular dynamics simulations were performed for the plati- num group metal chloro-anion complexes. This investigation makes the first attempt at describing diffusion trends of polyatomic complex anions with counterions such as these using both hydrodynamic and dielectric friction properties of the anion solution. The transition metal anion complex diffusion rates are shown to be correlated to their first solvent shell radial distribution function peaks, their mean water residence times, and their solvation volumes as calculated by Voronoi tessellation of the simulation cell. The general trend is for slower diffusion rates to result from larger hydration shell volumes. This diffusion rate trend calculated from Stokes’ law is best described using the solventberg approach with well-chosen effective solvated radii. However, to improve the diffusion constant estimates when they are compared with those calculated from computer simulations, the dielectric friction is required. 1. INTRODUCTION The translational self-diffusion behavior of ions is a complex property that depends on the nature of the ion and the solvent. Moreover, the relationship between diffusion coefficients for cations and anions has been shown to be different in the same solvent. 1 This is most obvious in plots of the mobilities of simple monovalent ions against their atomic crystallographic radii where different maxima for anions and cations are observed. In the case of halides the fastest diffusing ion in water is Br - while for alkali metals the fastest diffusing ion is Rb þ . 2,3 Several theories have been invoked to understand the origin of this anomaly. First, the solventberg model 4 was used. Here solvent molecules immediately adjacent to an ion are found to be rigidly bound and so contribute to a larger effective ion size. The ion and bound water sheath are therefore more bulky compared to a bare ion, which results in a reduced ion mobility. The solventberg theory is routinely used to explain the well-known lower than expected mobility of Li þ compared to Na þ and larger alkali metals 2 but fails in explaining anion mobility trends. A dielectric friction theory was initially developed by Born using a continuum model. In this approach the ionic field of a solute is coupled with the bulk polarization of a solvent. 5 The ionic motion disturbs the equi- librium polarization of the solvent and the relaxation of the perturbed polarization to equilibrium dissipates energy, thereby enhancing the friction on the ion. In this model the total friction experienced by an ion moving through a viscous continuum is given as ξ ¼ ξ 0 þ ξ DF ð1Þ where ξ 0 is the hydrodynamic or mechanical friction arising from Stokes’ law due to the shear viscosity of the solvent, and ξ DF is the dielectric friction. Assuming slip boundary conditions, the hydro- dynamic friction coefficient is given by ξ 0 ¼ 4πη 0 R i ð2Þ where η 0 is the solvent bulk viscosity and R i is the ion radius. In later years Fouss, 6 Boyd, 7 and Zwanzig 8 further developed Born’ s continuum model. Zwanzig’ s revised theory of dielectric fric- tion on a moving ion 8 expressed the dielectric friction coefficient as ξ DF ¼ 3q 2 ðε - ε ¥ Þ 4R i 3 εð1 þ 2εÞ τ d ð3Þ where τ d is the Debye relaxation time of the solvent, ε and ε ¥ are static and high-frequency dielectric constants of the solvent, and q is the charge on the ion. It must be noted that the solvent relaxation time is described by a single relaxation time and that the charge appears as a quadratic contribution; as such, the dielectric friction is symmetrical for both cations and anions of the same size. In an attempt to correctly reproduce the experimental mobilities and improve on the poor treatment of the electrohydrodynamic effects in the dielectric friction models, Hubbard and Onsager studied the ionic mobility problem in great detail within the frame- work of the continuum picture. 9 Wolynes and Hubbard further proposed that the friction coefficient can be written as 1 ξ ¼ Z ¥ r ion dr 4πr 2 ηðrÞ ð4Þ Received: March 4, 2010 Revised: December 18, 2010