Description of Aqueous Systems

The gradient-corrected Becke, Lee, Yang, and Parr (BLYP) [30,31] exchange correlation functional has been shown to give a good description of aqueous systems [32-34] it was employed in our present simulation. 

The Marcus-Hush theory was adapted to calculation of the volumes of activation for self-exchange [Co(en)3] + 2+, [Co(sep)]3+/2+, [Co(diAMsar)]3+/2+ [Co(diAMHsar)]5+/4+ [CoD3(BR)2]3+ 2+ and [Co([9]aneS3)2] + + reactions [301, 333, 342, 355]. A plot of the calculated and observed mean volumes of activation for these reactions in aqueous solution is shown in Fig. 57. The Marcus-Hush theory is quantitatively successful in the description of aqueous systems for a variety of self-exchange reactions including the... 

Despite their catalytic (preparative) efficiency similar colloidal systems will be only occasionally included into the present description of aqueous organometalHc catalysis although it should be kept in mind that in aqueous systems they can be formed easily. Catalysis by colloids is a fast growing, important field in its own right, and special interest is turned recently to nanosized colloidal catalysts [62-64]. This, however, is outside the scope of this book. 

Figure 17. An empirical model was developed to describe the extraction process, taking account of the observation that [U02(DBP)2(HDBP)2] was the predominant uranyl species in the organic phase at aqueous phase acidities of less than 2 M, while [U02(N03)2(HDBP)2] predominated at higher acidities. The curves derived from this model, and a revised model which took into account the presence of other organic phase species such as H[U02(N03)3] (HDBP), are shown in Figure 18. The latter model gave a good description of the system in the aqueous phase acidity range 1 -7 M.

Molecular dynamics (MD) simulations provide a detailed description of complex systems in a wide range of time and spatial scales.138 Simulations involve a statistical uncertainty component as the result of the finite length of the simulation.139 143 MD methods generate a series of time-correlated points in phase space by propagating a suitable starting set of coordinates and velocities according to Newton s second equation. This kind of computational simulations are useful in studies of time evolution of a variety of systems biological molecules, polymers, or catalytic materials, and in a variety of states crystal, aqueous solutions, or in the gas phase. 

Quantization enters the wave mechanical description of the particle in a box via the boundary conditions. Boundary conditions arise from the physical requirements of natural systems. That is, we must insist that our descriptions of natural systems make physical sense. For example, assume that in describing an aqueous solution containing an acid, we arrive at the expression H + ]2 = 4.0 X 10 s M2. The solutions to this expression are... 

With the development of GGA functionals, description of molecular systems with the Kohn-Sham method reached a precision similar to other quantum theory methods. It was quickly shown that the GGA s could also well reproduce the hydrogen bond properties. Short after, liquid water at ambient condition was first simulated by Car-Parrinello MD, with a sample of 32 water molecules with periodic boundary conditions [31]. Since then, many simulations of liquid water at different temperatures and pressures and of water solutions have been performed [32-39]. Nowadays, Car-Parrinello MD has become a major tool for the study of aqueous solutions [40-64]. 

The redox status of an aqueous system is described by the concentrations of the oxidized and reduced species of all system components. Redox systems, generally not at equilibrium as the result of kinetically slow redox reactions, are poorly characterized by intensity factors (Ej or pE) alone. Capacity factors, which reflect the total concentration of relevant species, are conservative parameters that can be meaningful guides to the redox status of aqueous systems. Oxidative capacity (OXC) is defined as a conservative quantity that incorporates a comprehensive chemical analysis of the redox couples of an aqueous system into a single descriptive parameter. OXC classifies aqueous systems in terms of well-defined geochemical and microbial parameters (e.g., oxic, sulfidic). Examples of model and actual groundwater systems are discussed to illustrate the concept. A redox titration model is another tool that is useful in describing a redox system as it approaches an equilibrium state. 

The pair potential functions for the description of the intermolecular interactions used in molecular simulations of aqueous systems can be grouped into two broad classes as far as their origin is concerned empirical and quantum mechanical potentials. In the first case, all parameters of a model are adjusted to fit experimental data for water from different sources, and thus necessarily incorporate effects of many-body interactions in some implicit average way. The second class of potentials, obtained from ab initio quantum mechanical calculations, represent purely the pair energy of the water dimer and they do not take into account any many-body effects. However, such potentials can be regarded as the first term in a systematic many-body expansion of the total quantum mechanical potential (dementi 1985 Famulari et al. 1998 Stem et al. 1999). 

Water molecules are represented by three- or four-center models with fixed values of point charges. These models have been thoroughly tested in simulations of bulk water and aqueous solutions. So far, no attempts have been made to study water-membrane systems using polarizable models of water and lipid molecules. Since interfacial molecules experience an anisotropic environment very different from the bulk liquid, it may be expected that including polarization will yield an improved description of these systems. The extent to which this is the case remains to be explored. 

Two conceptual models were tested in this study and were implemented in the programs PRECIP (Noy 1990) and CHEQMATE (Haworth Smith 1994). The main difference between these models was whether the dissolu-tion/precipitation processes occurred fast enough for the aqueous phase to be considered to be in equilibrium with the primary and secondary minerals (as implemented in CHEQMATE), or whether a kinetic description of the system was necessary (as implemented in PRECIP). 

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