Radial distribution function proton

A combination of physicochemical, topological, and geometric information is used to encode the environment of a proton, The geometric information is based on (local) proton radial distribution function (RDF) descriptors and characterizes the 3D environment of the proton. Counterpropagation neural networks established the relationship between protons and their h NMR chemical shifts (for details of neural networks, see Section 9,5). Four different types of protons were... 

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. 

Fig. 17. Gd-aqueous proton radial distribution function for the aqueous solution of the Gd(III)(DOTP) complex (after Borel, A. Helm, L. Merbach, A.E. Chemistry - A European Journal 2001, 7, 600-610).

The MD simulations show that second shell water molecules exist and are distinct from freely diffusing bulk water. Freed s analytical force-free model can only be applied to water molecules without interacting force relative to the Gd-complex, it should therefore be restricted to water molecules without hydrogen bonds formed. Freed s general model [91,92] allows the calculation of NMRD profiles if the radial distribution function g(r) is known and if the fluctuation of the water-proton - Gd vector can be described by a translational motion. The potential of mean force in Eq. 24 is obtained from U(r) = -kBT In [g(r)] and the spectral density functions have to be calculated numerically [91,97]. 

Figure 8.22 Radial distribution functions associated with the distinguished acid proton H and its closest oxygen O. The darker lines show decomposition according to the distance-order of the contributing atoms, i.e., the solid line is the contribution from the nearest-neighbor O atom in each case, the dark dashed curve is the contribution of the second-nearest neighbor, and so on.

Fig. 5. FT[x(k) k] at the Cl K-edge of PdY-4.0 (left) and protonated HPdY-2.2 (right) during reaction with chlorobenzene. For comparison the radial distribution functions of chlorobenzene and PdCl2 are included.

A. A. Barker (1965) Monte Carlo calculations of the radial distribution functions for a proton-electron plasma. Aust. J. Phys., 18, p. 119... 

Secondly, the proton chemical shifts decrease with increasing temperature. These results clearly demonstrate the capability of the theory to predict experimental results. Analysis on the radial distribution function provides molecular level information on solvation structure and its relation to NMR chemical shifts. 

Solvent potential. The averaged solvent electrostatic field, , is important for inhomogeneous media, such as enzymes, membranes, miscelles and crystalline environments systems. Due to the existence of strong correlations, such a field does not cancel out. This factor becomes an important contribution to solvent effects at a microscopic level. In a study of non-rigid molecules in solution, Sese et al. [25] constructed a by using the solute-solvent atom-atom radial distribution function. Electrostatic interactions in three-dimensional solids were treated by Angyan and Silvi [26] in their self-consistent Madelung potential approach such a procedure can be traced back to a calculation of . An earlier application of the ISCRF theory to the study of proton mechanisms in crystals of hydronium perchlorate both [Pg.441]

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