Local RDF Descriptors

The resulting descriptor can be regarded as isolated from the molecular RDF that contains the sum of N possible descriptors. Thus, every Af-atomic molecule can have N local RDF descriptors. However, local descriptors can cover the entire molecule, depending on the predehned maximum distance of the function their center is just localized on a single atom. 

In particular, local RDF descriptors are useful for characterizing the chemical environment of an atom and can be applied, for example, to represent the environment of protons in H-NMR spectrum-structure correlations and for the evaluation of steric hindrance at a reaction center. 

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Geometric descriptors were based on local RDF descriptors (see Eq, (16 ) for the proton j. 

Local, or atomic, RDF descriptors are snitable to characterize an individual atom in its chemical environment. They are nsnally not appropriate for investigations of diverse data sets, since each A-atomic molecnle can have N local descriptors. A typical application of local descriptors is the characterization of steric hindrance at reaction centers. This can be performed nsing a conseqnent numbering of the atoms of the reactants. In the following experiment, the Rnthenium atom of each conformer shown in Figure 5.8 was the first atom in the data file, and the local RDF descriptors for atom 1 (Ru) were calculated. Figures 5.10a through 5.10c show the results for the Cartesian RDF descriptors. 

The discussions in this section briefly described the use of local descriptors. Another application of local descriptors is the characterization of atoms in nuclear magnetic resonance (NMR) spectroscopy. This is described later with an application for the prediction of chemical shifts in H-NMR spectroscopy, where protons were represented by their local RDF descriptors. 

Special geometric descriptors for proton NMR spectroscopy based on a local RDF descriptors for a proton. 

The prediction of chemical shifts in H-NMR spectroscopy is usually more problematic than in C-NMR. Experimental conditions can have an influence on the chemical shifts in H-NMR spectroscopy and structural effects are difficult to estimate. In particular, stereochemistry and 3D effects have been addressed in the context of empirical H-NMR chemical shift prediction only in a few specific situations [81,82]. Most of the available databases lack stereochemical labeling, assignments for diastereo-topic protons, and suitable representations for the 3D environment of hydrogen nuclei [83]. This is the point where local RDF descriptors seemed to be a promising tool. 

FIGURE 6.17 Example for a local RDF descriptor for proton 6 used in the prediction of chemical shifts and distances (S = 20 A ). 

Local RDF Descriptor is a geometric descriptor based on radial distribution functions and designed for the characterization of individual atoms in a molecule in their chemical environment. 

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... 

FROM THE VIEW OF AN ATOM — LOCAL AND RESTRICTED RDF DESCRIPTORS... 

The local Cartesian RDF descriptors of the stereoisomers are generally more similar among each other than the molecnlar ones. They exhibit particularly two patterns that describe the different ligand sphere of the stereoisomers in the distance... 

FIGURE 5.10 (a) Local Cartesian RDF descriptors calculated on the Ruthenium atom in the... 

The Cartesian RDF seems to represent the biological activity of the Ruthenium complex. In any case, the descriptor is qnite complex and cannot be compared easily with other molecnles of similar ligand arrangement and with similar biologic potency. Another approach is based on a local descriptor that specifies the chemical environment of the reaction center the Rntheninm atom. 

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