RDF code

The RDF code discussed in Chapter VIll, Sections 2 and 3 of the Handbook) also can be used to this end. 

D MoRSE desaiptor, radial distribution function (RDF code), WHIM descriptors, GETAWAY descriptors,... 

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]. 

Figure 8-5. Procedure of encoding a structure with an RDF code,...

The length or dimension of the RDF code is independent of the number of atoms and the size of a molecule, unambiguous regarding the three-dimensional arrangement of the atoms, and invariant against translation and rotation of the entire molecule. 

Both regioisomers and different conformations can be distinguished with the RDF code. (Figures 8-6 and 8-7). 

Figure 8-7, Comparison of tlie RDF code for aromatic compounds with different subslilulic patterns (hydrogen atoms are not considered).

The compounds were described by a set of 32 radial distribution function (RDF) code values [27] representing the 3D structure of a molecule and eight additional descriptors. The 3D coordinates were obtained using the 3D structure generator GORINA [33]. 

By including characteristic atomic properties, A. of atoms i andj, the RDF code can be used in different tasks to fit the requirements of the information to be represented. The exponential term contains the distance r j between the atoms i andj and the smoothing parameter fl, which defines the probability distribution of the individual distances. The function g(r) was calculated at a number of discrete points with defined intervals. 

Figure 10.2-9. Application of a counterpropagation neural network as a look-up table for IR spectra sinnulation, The winning neuron which contains the RDF code in the upper layer of the network points to the simulated IR spectrum in the lower layer.

The right-hand side of the form gives the network map in the upper part and to its right the simulated IR spectrum is plotted, which can be downloaded as a JCAMP File (cf. Section 2,4.5, Section 4,2,4.2). By clicking on tbe neurons in the map one obtains the RDF code and the spectrum of the corresponding structure in the lower part of the form and compared with those of the winning neuron,... 

Several methods have been developed for establishing correlations between IR vibrational bands and substructure fragments. Counterpropagation neural networks were used to make predictions of the full spectra from RDF codes of the molecules. 

These descriptors are based on the distance distribution in the - geometrical representation of a molecule and constitute a radial distribution function code (RDF code) that shows certain characteristics in common with the - 3D-MoRSE code. 

Formally, the radial distribution function of an ensemble of A atoms can be interpreted as the probability distribution of finding an atom in a spherical volume of radius R. The general form of the radial distribution function code (RDF code) is represented by ... 

The radial distribution Wction in this form meets all the requirements for a 3D structure descriptor it is independent of the number of atoms, i.e., the size of a molecule, it is unique regarding the three-dimensional arrangement of the atoms, and it is invariant against translation and rotation of the entire molecule. Additionally, the RDF code can be restricted to specific atom types or distance ranges to represent specific information in a certain three-dimensional structure space, e.g., to describe steric hindrance or structure/activity properties of a molecule. 

The RDF descriptor is interpretable by using simple rule sets, and thus it provides a possibility for conversion of the code back into the corresponding 3D structure. Besides information about interatomic distances in the entire molecule, the RDF code provides further valuable information, e.g., about bond distances, ring types, planar and non-planar systems and atom types. This fact is a most valuable consideration for a computer-assisted code elucidation. 

A slight modification of the general form of an RDF leads to a molecular descriptor, the radial distribution function (RDF) code, which includes atom properties that address characteristic atom features in the molecular environment. Fields of application for RDF codes are the simulation of infrared spectra and deriving molecular structure information from infrared spectra [40,41]. 

All of the RDF functions presented already can be calculated including properties p of the individual atoms. These properties can be inserted in a preexponential term as a product leading to the property-weighted RDF descriptor, sometimes called RDF code ... 

Selection of Data Set with Most Similar RDF Code... 

To account for stereochemistry of molecules, the —> Chirality Code was proposed as a modification of the RDF code [Aires-de-Sousa and Gasteiger, 2001]. 

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