Solvents radial distribution function

For (Ar) interactions the collapsed state of the polymer is a tight globule from which solvent is excluded. Figure 15 shows the polymer bead and solvent radial distribution functions relative to the center of mass of the globule,... 

Note that the binary HMSA [60] scheme gives the solute-solvent radial distribution function only in a limited range of solute-solvent size ratio. It fails to provide a proper description for such a large variation in size. Thus, here the solute-solvent radial distribution function has been calculated by employing the well-known Weeks-Chandler-Anderson (WCA) perturbation scheme [118], which requires the solution of the Percus-Yevick equation for the binary mixtures [119]. 

It is found that as the solute size is increased, keeping all other parameters fixed, the peak in the solute-solvent radial distribution function slowly disappears and approaches the value 1. This implies that the probability of a solvent particle, provided that there is a solute at the origin, is same everywhere. The solute-solvent static structure factor Si2(q), which can be obtained from g 12(f), will also have no structure and will have a uniform value that is, Si2(q) = 1 for all wavenumbers. 

The MFA [1] introduces the perturbation due to the solvent effect in an averaged way. Specifically, the quantity that is introduced into the solute molecular Hamiltonian is the averaged value of the potential generated by the solvent in the volume occupied by the solute. In the past, this approximation has mainly been used with very simplified descriptions of the solvent, such as those provided by the dielectric continuum [2] or Langevin dipole models [3], A more detailed description of the solvent has been used by Ten-no et al. [4], who describe the solvent through atom-atom radial distribution functions obtained via an extended version of the interaction site method. Less attention has been paid, however, to the use of the MFA in conjunction with simulation calculations of liquids, although its theoretical bases are well known [5]. In this respect, we would refer to the papers of Sese and co-workers [6], where the solvent radial distribution functions obtained from MD [7] calculations and its perturbation are introduced a posteriori into the molecular Hamiltonian. 

We should hasten to note that these fundamental difficulties do not mean that this theory does not often work. The most common application of IBC theory points to its particularly simple prediction for the dependence of relaxation rates on the thermodynamic state of the solvent with the Enskog estimate of collision rates, the ratio of vibrational relaxation rates at two different liquid densities p and p2 is just the ratio of the local solvent densities [pigi(R)//02g2(R)], where g(r) is the solute-solvent radial distribution function and R defines the solute-solvent distance at... 

Figure 48. Solute-solvent radial distribution functions and running coordination numbers. The radial distribution (the solid line using the left scale) and the running coordination number (the dashed line using the right scale) are plotted versus distance in angstroms for the distribution of water oxygens around apolar atoms (o) Asp-48 Cs (b) Ser-72 O3 (c) Asn-46 C 3 and ((i) Gly-71 C .

In Figs.1.15 and 1.16 plotted are the solvent-solvent radial distribution function for water between 0-0 atoms and between O-H atoms, and the perturbation due to the existence of ions calculated from the RISM equation. The perturbation owed to ions or the density derivative of the PCF are calculated using the method developed by Yu, Roux,... 

Figure 2. Computed solute-solvent radial distribution function g(r) in hard disc system. Unit distance is solvent diameter a. Data points were tabulated over 100 intervals, equally spaced in r. ...

We recently proposed a new method referred to as RISM-SCF/MCSCF based on the ab initio electronic structure theory and the integral equation theory of molecular liquids (RISM). Ten-no et al. [12,13] proposed the original RISM-SCF method in 1993. The basic idea of the method is to replace the reaction field in the continuum models with a microscopic expression in terms of the site-site radial distribution functions between solute and solvent, which can be calculated from the RISM theory. Exploiting the microscopic reaction field, the Fock operator of a molecule in solution can be expressed by... 

The desired average is simply obtained by a time average of the given property. For example, one of the interesting properties of bulk solvents is the radial distribution function (rdf), which expresses the probability of finding a given atom type around a reference atom by... 

This subroutine calculates the three radial distribution functions for the solvent. The radial distribution functions provide information on the solvent structure. Specially, the function g-AB(r) is die average number of type B atoms within a spherical shell at a radius r centered on an aibitaiy type A atom, divided by the number of type B atoms that one would expect to find in the shell based cm the hulk solvent density. 

Figure 15. (a) Radial distribution functions gcM-b(i ) (solid line and short dashed line) and, cm -j (> ) (dotted line and long dashed line) versus r for Ni, = 60 and 200, respectively, (b) Collapsed polymer with A), = 60 and surrounding solvent molecules. 

The probability of cavity formation in bulk water, able to accommodate a solute molecule, by exclusion of a given number of solvent molecules, was inferred from easily available information about the solvent, such as the density of bulk water and the oxygen-oxygen radial distribution function [65,79]. 

PtSn-OM and PtSn-OM samples show a more complicated radial distribution function. At least two different scatterer atoms must be present to obtain such a result. Considering the way the catalysts are prepared, a Pt-C and a Pt-Pt shell were used to perform the fits. Before the reduction process, a solvent fraction remains adsorbed on the samples, so the appearance of C near the Pt atoms is natural. Results show that the coordination number for the Pt-Pt shell is smaller in both... 

Studies of solvent structure are usually carried out by analyzing radial distribution functions that are obtained by X-ray or neutron diffraction methods. Monte Carlo (MC) or molecular dynamics (MD) calculations are also used. Studies of the structure of lion-aqueous and mixed solvents are not extensive yet but some of the results have been reviewed. Pure and mixed solvents included in the reviews... 

Because the solvent molecules are usually of a similar size to the reactants, the assumption that reactants diffuse in a structureless and isotropic continuum is not very satisfactory. Liquids possess short-range order. Solvent molecules are several times more likely to be separated by a distance equal to their diameter than separated by about one and a half diameters. More details are revealed by the radial distribution function [see Figs. 38 (p. 216) and 44 (p. 235)]. This implies that there is an... 

Hynes [131] remarked that if the radial distribution function is used instead of the random distribution [eqn. (68)], the rate coefficient will be more sensitive to the details of the solvent structure if significant transfer occurs over distances of at most a few solvent diameters. Furthermore, marked deviations from the steady-state and especially time-dependent rate coefficients may be anticipated. 

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