Radial distribution functions solvation

The structure of the adsorbed ion coordination shell is determined by the competition between the water-ion and the metal-ion interactions, and by the constraints imposed on the water by the metal surface. This structure can be characterized by water-ion radial distribution functions and water-ion orientational probability distribution functions. Much is known about this structure from X-ray and neutron scattering measurements performed in bulk solutions, and these are generally in agreement with computer simulations. The goal of molecular dynamics simulations of ions at the metal/water interface has been to examine to what degree the structure of the ion solvation shell is modified at the interface. 

The gas-phase model would then be tested on condensed phases. In the case of the carbonate ion, the parameters can be used to examine the structure of C02(aq), C032-(aq), and HC03 (aq) as well as the structure of, for example, siderite FeC03 and nahcolite Na(HC03). For the aqueous species, the most instructive comparisons are with the results of ab initio molecular dynamics studies of solvated ions, where the radial distribution functions can be used to check the extent of solvation. Fig. 2, for... 

In short, our S-MC/QM methodology uses structures generated by MC simulation to perform QM supermolecular calculations of the solute and all the solvent molecules up to a certain solvation shell. As the wave-function is properly anti-symmetrized over the entire system, CIS calculations include the dispersive interaction[35]. The solvation shells are obtained from the MC simulation using the radial distribution function. This has been used to treat solvatochromic shifts of several systems, such as benzene in CCI4, cyclohexane, water and liquid benzene[29, 37] formaldehyde in water(28, 38] pyrimidine in water and in CCl4(31] acetone in water[39] methyl-acetamide in water[40] etc. 

Figure 10. Solvation of twelve 18C6 crowns "diluted" in dry versus humid [BMI][PF6] solutions. Typical snapshots of die "first shell" solvent molecules and radial distribution functions "RDFs" around the center of the crown 18C6 BMI (bold), 18C6 F (dotted), 18C6 P (plain) and Sr OH2 (inversed ordinate).

The solvation structure around a molecule is commonly described by a pair correlation function (PCF) or radial distribution function g(r). This function represents the probability of finding a specific particle (atom) at a distance r from the atom being studied. Figure 4.32 shows the PCF of oxygen-oxygen and hydrogen-oxygen in liquid water. 

The structure of liquids can be analyzed by the calculated radial distribution function (RDF), which defines the solvation shells. In Fig. 16.1, the calculated RDF of the liquid Aris shown, and in Table 16.1, the structure is compared with the experimental results. Four solvation shells are well defined. The spherical integration of these peaks defines the coordination number, or the number of atoms in each solvation shell. The first shell that starts at 3.20A has a maximum at 3.75A, and ends at 5.35 A, has an average of 13 Ar atoms. Therefore, in the first solvation shell, there is a reference Ar atom surrounded by other neighboring 13 Ar atoms. All the maxima of the RDF, shown in Table 16.1, are in good agreement with the experimental results obtained by Eisenstein and Gingrich [29], using X-ray diffraction in the liquid Ar in the same condition of temperature and pressure. The calculated... 

Fig. 26. Comparison between radial distribution functions for 3 M silver(I) nitrate in aqueous and in DMSO solutions. Intramolecular interactions of the solvent molecules have been removed. The derived structures for the solvated silver(I) ion in the two solvents are shown.

Figure 11-10 Solvation of the oxygen atoms of poly(vinyl alcohol), (a) Partial radial distribution functions of PVA oxygen with solvent oxygen and (b) solvent carbon atoms. The figure is taken from Miiller-Plathe and van Gunsteren [79]...

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.)...

In cluster calculations, an element essential in solution calculations is missing. Thus, intrinsically, gas-phase cluster calculations cannot allow for ionic movement. Such calculations can give rise to average coordination numbers and radial distribution functions, but cannot account for the effect of ions jumping from place to place. Since one important aspect of solvation phenomena is the solvation number (which is intrinsically dependent on ions moving), this is a serious weakness. 

Furthermore, the explicit-water simulations do include the CDS terms to the extent that dispersion and hydrogen bonding are well represented by the force field. Finally, by virtue of the solvent being explicitly part of the system, it is possible to derive many useful non-entropy-based properties "" (radial distribution functions, average numbers of hydrogen bonds, size and stability of the first solvation shell, time-dependent correlation functions, etc.). Since many of these properties are experimentally observable, it is often possible to identify and correct at least some deficiencies in the simulation. Simulation is thus an extremely powerful tool for studying solvation, especially when focused on the response of the solvent to the solute. 

In the case of a single test particle B in a fluid of molecules M, the effective one-dimensional potential f (R) is — fcrln[R gBM(f )]. where 0bm( ) is th radial distribution function of the solvent molecules around the test particle. In this chapter it will be assumed that 0bm( )> equilibrium property, is a known quantity and the aim is to develop a theory of diffusion of B in which the only input is bm( )> particle masses, temp>erature, and solvent density Pm- The friction of the particles M and B will be taken to be frequency indep>endent, and this should restrict the model to the case where > Wm, although the results will be tested in Section III B for self-diffusion. Instead of using a temporal cutoff of the force correlation function as did Kirkwood, a spatial cutoff of the forces arising from pair interactions will be invoked at the transition state Rj of i (R). While this is a natural choice because the mean effective force is zero at Rj, it will preclude contributions from beyond the first solvation shell. For a stationary stochastic process Eq. (3.1) can then be... 

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