Radial distribution functions calculations

Figure 2.9 Glucose-cation (solid line) and glucose-anion (dashed line) center-of-mass radial distribution functions calculated from molecular dynamics simulations of a single sugar molecule in [CjCjlm]Cl.

FIGURE 3.12 Methane-methane radial distribution functions calculated from successive 0.9 ns portions of the simulation, indicating ordering of the methane molecules during hydrate nucleation. (Reproduced from Moon, C., Taylor, P.C., Rodger, P.M., J. Am. Chem. Soc., 125, 4706 (2003). With permission from the American Chemical Society.)... 

An example of an Li-0 radial distribution function (calculated by MD) is shown in Fig. 2.56. From such calculations one can obtain relaxation features of the rotational and translational motion of the neighboring waters and find the effect of Li or F , for example. 

Figure 21. Radial distribution functions calculated using a Fourier transform of scattering patterns produced with a Debye equation. Top Cuboctahedron (cluster with both octahedral 111 and cnbe 100 faces) and icosahedron (multiply twinned hep structure) clusters of the same size. Center Cuboctahedra of different sizes. Bottom Experimental and simulated cluster RDF of a Pt colloid. The fit is a 90 10 mixture of 55 and 147 cuboctahedral clusters, respectively. After Casanove et al. (1997).

Figure 1. Radial distribution functions calculated for a Lennard-Jones KrAr binary mixture (left) and molten LiF alloy (right).

The radial distribution function of a liquid is intermediate between the solid and the gas, with a small number of peaks as short distances, superimposed on a steady decay to a constant value at longer distances. The radial distribution function calculated from a molecular dynamics simulation of liquid argon (shown in Figure 6.2) is typical. For short distances (less... 

Figure 1.11 Comparison between the radial distribution function, calculated with HS.EXE, for the Li-2s orbital and from the simple Slater function.

In the liquid, a first view of the structure was given by the radial distribution functions calculated from the centers of the ions. The simulations revealed a first... 

Comparison of the radial distribution function calculated tor the 5.1-residue helical configuration, with inclusion of a jS carbon atom per residue, and the experimental radial distribution function for carbonmonoxyhemo-globin, as calculated from the three-dimensional Patterson function given by Perutz. 

Fig. 16.3. (left) Reduced radial distribution function calculated from binary dense random packing hard sphere model (DRPHS) for GdjjCot, compared (right) to the X-ray experimental C(r). (Cargill and Kirkpatrick, 1976 Wagner et al., 1976). 

Figure 3.4.4 Radial distribution function calculated atJ = 2000 K at atmospheric pressure for the binary system silica-calcia at composition 1 1...

Figure 6 shows the radial distribution function calculated from the Percus-Yevick equation for the Lennard-Jones 6-12 potential... 

Figure 2 Ion-ion radial distribution function calculated from a 100 ps simulation of a l.O M aqueous NaCI solution. The simulation box contained 29 ion pairs and 1531 water molecules. Discontinuities at the 16 A cut-off limit are marked with an arrow...

Steinhauer and Gasteiger [30] developed a new 3D descriptor based on the idea of radial distribution functions (RDFs), which is well known in physics and physico-chemistry in general and in X-ray diffraction in particular [31], The radial distribution function code (RDF code) is closely related to the 3D-MoRSE code. The RDF code is calculated by Eq. (25), where/is a scaling factor, N is the number of atoms in the molecule, p/ and pj are properties of the atoms i and/ B is a smoothing parameter, and Tij is the distance between the atoms i and j g(r) is usually calculated at a number of discrete points within defined intervals [32, 33]. 

Topological descriptors and 3D descriptors calculated in distance space", such as 3D autocorrelation, surface autocorrelation, and radial distribution function... 

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... 

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. 

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. 

I All three radial distribution functions are calculated I within this loop k= 1,2,3 correspond to the functions (g-AA, g-AB,g-BB respectively. 

Radial distribution function, 79 computer program for calculating, 96-106 Rate constant, see Rate of reaction Rate of reaction ... 

Carbon Tetrachloride.—By the usual visual method and by other methods involving microphotometer records, we have assigned8 to the carbon tetrachloride molecule the value 1.760 0.005 A. for the C-Cl distance, a value supported by other recent work.9 The radial distribution function for this molecule calculated by Equation 6, using the ten terms for which data are given in Table I, is shown in Fig. 1. 

The intensity curves I, II, III, and IV of Fig. 4 are calculated for coplanar trans models with C-H = 1.06 A., the angle H - C=C = 115°, and the angle H—C—H = 109.5°. Although these hydrogen parameters are so chosen as to agree as well as possible with minor peaks of the radial distribution function, no great reliance can be placed on them, and indeed it is likely that for this molecule the C-H bond distance is 1.09 A. The models have the following additional parameters... 

Fig. 5.12 Normalized radial distribution function for the neutral Mn atom (3d 4s as calculated by the UHF method...

A straightforward Fourier transform of the EXAFS signal does not yield the true radial distribution function. First, the phase shift causes each coordination shell to peak at the incorrect distance second, due to the element-specific backscattering amplitude, the intensity may not be correct. The appropriate corrections can be made, however, when phase shift and amplitude functions are derived from reference samples or from theoretical calculations. The phase- and amplitude-corrected Fourier transform becomes ... 

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