Hydration Numbers from Computer Simulations

An ND study of K+ hydration gives a Gk(/ ) that shows little structure (Fig. 4), a result in marked contrast to that for Li. Clearly the larger K+ ion coordinates water molecules relatively weakly and so forms a labile aquaion. One can show from Gk(t) that nKo is 5.5 0.5 in the range 2.3 r 3.4. However, such a value cannot be taken as a hydration number in the same sense as for a stable species. Indeed, the value from computer simulation of 10 for tiko can be equally useful (7). 

The hydration numbers of ions that were obtained from computer simulations are already described in Section 4.4.2 and in Table 4.8. The ability of ions to affect the... 

In sharp contrast to the large number of experimental and computer simulation studies reported in literature, there have been relatively few analytical or model dependent studies on the dynamics of protein hydration layer. A simple phenomenological model, proposed earlier by Nandi and Bagchi [4] explains the observed slow relaxation in the hydration layer in terms of a dynamic equilibrium between the bound and the free states of water molecules within the layer. The slow time scale is the inverse of the rate of bound to free transition. In this model, the transition between the free and bound states occurs by rotation. Recently Mukherjee and Bagchi [14] have numerically solved the space dependent reaction-diffusion model to obtain the probability distribution and the time dependent mean-square displacement (MSD). The model predicts a transition from sub-diffusive to super-diffusive translational behaviour, before it attains a diffusive nature in the long time. However, a microscopic theory of hydration layer dynamics is yet to be fully developed. 

Previous studies have shown that there is a correlation between the enthalpy of hydration of alkanes and their accessible surface area [30,31] or related magnitudes. Moreover, relationships between the hydration numbers calculated from discrete simulations for hydrocarbons and both the free energy and enthalpy of hydration of these molecules have also been reported [32] and have been often used to evaluate solvation enthalpies. Analysis of our results, illustrates the existence of a linear relationship between A//n eie and the surface of the van der Waals cavity,. SVw, defined in MST computations for the calculation of the non-electrostatic contributions (Figure 4-1). In contrast, no relationship was found for the electrostatic component of the hydration enthalpy (A//eie data not shown). Clearly, in a first approximation, one can assume that the electrostatic interactions between solute and solvent can be decoupled from the interactions formed between uncharged solutes and solvent molecules. 

Fig. 2.59. Ion-0 radial distribution functions in the ion-( 2 )199 cluster, (a) Na, (b) K. 1 Gj q (ordinate to the left). 2 Number of H2O molecules in the sphere of radius R (ordinate to the right). (Reprinted from G. G. Malenkov, Models for the structure of Hydrated Shells of Simple Ions Based on Crystal Structure Data and Computer Simulation, in The Chemical Physics of Solvation, Part A, R. R. Dogo-nadze, E. Kalman, A. A. Komyshev, and J. Ulstrup, eds., Elsevier, New York, 1985.)...

Figure 1(A) shows the ESR spectrum, at 77 K, that results from hydrated DNA (F = 12 2), /-irradiated, at 77 K, to a dose of 8.8 kGy the spectrum is a composite resulting from a number of radicals stabilized and trapped at 77 K An analysis of the composition of the underlying radicals is done by a least-square fitting of the appropriate individual radical benchmark spectra to the composite spectrum. An error parameter is calculated for each spectrum fit and a visual comparison of the computer simulated composite spectrum is done with the experimental spectrum to assure that deconvolutions are properly performed.

Spohr describes in detail the use of computer simulations in modeling the metal/ electrolyte interface, which is currently one of the main routes towards a microscopic understanding of the properties of aqueous solutions near a charged surface. After an extensive discussion of the relevant interaction potentials, results for the metal/water interface and for electrolytes containing non-specifically and specifically adsorbing ions, are presented. Ion density profiles and hydration numbers as a function of distance from the electrode surface reveal amazing details about the double layer structure. In turn, the influence of these phenomena on electrode kinetics is briefly addressed for simple interfacial reactions. 

The most expensive part of a simulation of a system with explicit solvent is the computation of the long-range interactions because this scales as Consequently, a model that represents the solvent properties implicitly will considerably reduce the number of degrees of freedom of the system and thus also the computational cost. A variety of implicit water models has been developed for molecular simulations [56-60]. Explicit solvent can be replaced by a dipole-lattice model representation [60] or a continuum Poisson-Boltzmann approach [61], or less accurately, by a generalised Bom (GB) method [62] or semi-empirical model based on solvent accessible surface area [59]. Thermodynamic properties can often be well represented by such models, but dynamic properties suffer from the implicit representation. The molecular nature of the first hydration shell is important for some systems, and consequently, mixed models have been proposed, in which the solute is immersed in an explicit solvent sphere or shell surrounded by an implicit solvent continuum. A boundary potential is added that takes into account the influence of the van der Waals and the electrostatic interactions [63-67]. 

Figure 12 Free energy surfaces for protein A computed with REMD simulations, (a) shows the surface as a function of RMSD and the number of native contacts below the folding transition temperature. The native state shows two basins corresponding to a hydrated nearly folded state and to the dry folded state, (b) shows the surface as a function of RMSD and the number of native contacts at the folding transition temperature. The unfolded and folded states are equally populated at this temperature. Taken with permission from Garcia and Onuchic. ...

We now consider a more realistic case. Let the saturated density of pure smectitic clay (for example, beidellite) be about 1.8[Mg/m ]. The crystal density of the beidellite determined from an MD simulation is found to be 2.901 [Mg/m ]. A stack is assumed to consist of nine minerals. The molecular formula of the hydrated beidellite is Nai/3Al2[Sin/3Ali/3]Oio(OH)2 nH20 where n is the number of water molecules in an interlayer space. We assume that n = 1, 3, 5, and the distance between two minerals (i.e., the interlayer distance) can be obtained from Fig. 8.4 from this, we can determine the volume of external water that exists on the outside of the stack. For each case of n = 1, 3, 5 we calculate the characteristic functions as shown in Fig. 8.10 (note that the scale is different in each case). Then we compute the C-permeability as shown in Fig. 8.11. Based on numerous experimental results, Pusch (1994) obtained the permeability characteristics of clays as a function of density as shown in Fig. 8.12. We recall that the permeability of the saturated smectitic clay is not only a function of the density but also of the ratio of interlayer water to the external water, which indicates that there exists a distribution of permeability for the same density. The range of permeability given in Fig. 8.12 with a saturated density of 1.8Mg/m corresponds well to our calculated results, which were obtained using the MD/HA procedure. 

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