Water radial distribution function

Figures 4.29 and 4.30 display the co-evolution of the formamide dipole moment and of the oxygen(formamide)-oxygen(water) radial distribution function during the polarization process [12]. As the dipole moment of the formamide increases, the position of the first peak of the RDF is shifted inward and its height increases. Once the dipole moment has reached its equilibrium value, it begins to fluctuate. Fluctuations are related to the statistical error associated with the finite length of the simulations. From Figures 4.29 and 4.30 it is clear that (1) ASEP/MD permits one to simultaneously equilibrate the...

Fig. 3.49. Comparison of the weighted Cf-water radial distribution function from an MD simulation of a 1.1 M MgCl2 solution (solid line) with results from neutron diffraction studies of a 5.32 /WNaCI(o), a3 /WNiCl2 (x), and a 9.95 MUCI ( ) solution (1 A = 0.1 nm). (Reprinted from P. Bopp, NATO ASI Series 206-. 237,1987.)...

For an understanding of protein-solvent interactions it is necessary to explore the modifications of the dynamics and structure of the surrounding water induced by the presence of the biopolymer. The theoretical methods best suited for this purpose are conventional molecular dynamics with periodic boundary conditions and stochastic boundary molecular dynamics techniques, both of which treat the solvent explicitly (Chapt. IV.B and C). We focus on the results of simulations concerned with the dynamics and structure of water in the vicinity of a protein both on a global level (i.e., averages over all solvation sites) and on a local level (i.e., the solvent dynamics and structure in the neighborhood of specific protein atoms). The methods of analysis are analogous to those commonly employed in the determination of the structure and dynamics of water around small solute molecules.163 In particular, we make use of the conditional protein solute -water radial distribution function,... 

An analysis of all the solvent cavities found in the liquid structure shows that the cavity to water radial distribution functions reproduce in detail those found in pure water (19). In a sample as large as ours, most cavities lie outside the second coordination shell. Our transition moment profile, however, contains an orbital overlap term that decreases exponentially with the distance of the cavity from the ion, effectively precluding transitions to cavities located outside the second shell. The cavities between the first and second shells have different structures from those in the bulk Uquid (i.e., those outside the second shell), with four water molecules spanning each cavity. The average kinetic energies of the electron and solvent shift are calculated to be 5.2 eV and 29.7 eV, respectively. 

An analysis of the structure of the dilute aqueous solution of methane was also developed in terms of quasicomponent distribution functions and stereographic views of significant molecular structures. The coordination number of methane in this system was calculated on the basis of 5.38, fixed at the first minimum In the methane-water radial distribution function. A plot of the mole fraction of methane molecules x (K) vs. their corresponding water coordination number is given in Figure 7. 

Figure 11. Calculated cation-water radial distribution function ui. center of mass separation R for the dilute aqueous solution of lithium at T = 25°C...

We have recently carried out Monte Carlo computer simulation of dilute aqueous solutions of the monatomic cations Li, Na and K and the monatomic anions F and Cl using the KPC-HF functions for the ion-water interaction and the MCY-CI potential for the water-water interaction. The temperature of the systems was taken to be 25° and the density chosen to be commensurate with the partial molar volumes as reported by Millero. - The calculated average quantities are based on from 600- 900K configurations after equilibration of the systems. The calculated ion-water radial distribution functions are given for the dilute aqueous solutions of Li", K" ", Na" ", F and Cl" in Figures 11-15, respectively. 

Fig. 4. Radial distribution functions between the centre of a test cavity and the (jxygen atom of the surrounding water. The curves correspond to the different barrier heights for the softcore interaction illustrated in Fig. 3...

FIGURE 3.1. The oxygen-oxygen radial distribution function of water. The dotted curve represents the experimental result and the other curves correspond to the results calculated with the different models considered in Ref. 10. 

After this computer experiment, a great number of papers followed. Some of them attempted to simulate with the ab-initio data the properties of the ion in solution at room temperature [76,77], others [78] attempted to determine, via Monte Carlo simulations, the free energy, enthalpy and entropy for the reaction (24). The discrepancy between experimental and simulated data was rationalized in terms of the inadequacy of a two-body potential to represent correctly the n-body system. In addition, the radial distribution function for the Li+(H20)6 cluster showed [78] only one maximum, pointing out that the six water molecules are in the first hydration shell of the ion. The Monte Carlo simulation [77] for the system Li+(H20)2oo predicted five water molecules in the first hydration shell. A subsequent MD simulation [79] of a system composed of one Li+ ion and 343 water molecules at T=298 K, with periodic boundary conditions, yielded... 

Thus, effects of the surfaces can be studied in detail, separately from effects of counterions or solutes. In addition, individual layers of interfacial water can be analyzed as a function of distance from the surface and directional anisotropy in various properties can be studied. Finally, one computer experiment can often yield information on several water properties, some of which would be time-consuming or even impossible to obtain by experimentation. Examples of interfacial water properties which can be computed via the MD simulations but not via experiment include the number of hydrogen bonds per molecule, velocity autocorrelation functions, and radial distribution functions. 

Fig. 55. Radial distribution function for liquid water synthesized as a mixture of ice I, ice II and ice III (from Ref. 75>)...

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. 

Figure 8. The structure of hydrated Na and CP ions at the water/Pt(IOO) interface (dotted lines) compared with the structure in bulk water (solid lines). In the two top panels are the oxygen ion radial distribution functions, and in the two bottom panels are the probability distribution functions for the angle between the water dipole and the oxygen-ion vector for water molecules in the first hydration shell. (Data adapted from Ref. 100.)...

These studies showed that sulfonate groups surrounding the hydronium ion at low X sterically hinder the hydration of fhe hydronium ion. The interfacial structure of sulfonafe pendanfs in fhe membrane was studied by analyzing structural and dynamical parameters such as density of the hydrated polymer radial distribution functions of wafer, ionomers, and protons water coordination numbers of side chains and diffusion coefficients of water and protons. The diffusion coefficienf of wafer agreed well with experimental data for hydronium ions, fhe diffusion coefficienf was found to be 6-10 times smaller than the value for bulk wafer. 

Site-site radial distribution functions for the CNWS system (C carbon P polymer backbones W water H cluster containing hydronium). (Reprinted from K. Malek et al. Journal of Physical Chemistry C 111 (2007) 13627. Copyright 2007, with permission from ACS.)... 

Fig. 2. The radial distribution function between F and the oxygen atom of water.

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