Bond-Path RDF

The bond-path RDF is calculated using the sum of the bond lengths along the shortest bond path b j (instead of r j) between two atoms i and j  

One can imagine this type of function as a representation of a molecule flatted along the individual atom pair that is actually calculated. Therefore, these functions are independent of conformational changes in a molecule. Again, the unit of the smoothing parameter B is A-.  

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Although binary pattern descriptors exclusively contain information about the presence or absence of distances, frequency pattern descriptors additionally contain the frequency of distances. Frequency pattern descriptors are valuable for direct comparison of structural similarities. For instance, a substructure can be assumed to exist if the frequencies in a substructure pattern occur in the query descriptor. Bond patterns can be used in a similar pattern search approach to determine structural similarities. In this case bond-path RDF descriptors are used. 

The topological-path RDF is derived from the bond-path RDF. This type simply uses the number of bonds (instead of r j) between the atom pairs along the shortest path. 

The statement that the bond-path RDF is independent of conformational changes relies on the precision of the Cartesian coordinates of the atoms and the accuracy of calculation. In practice, the bond-path functions of two conformers are extremely similar but seldom coincidental. 

FIGURE 5.7 Comparison of Cartesian and bond-path RDF descriptor (256 components each) of a cyclohexanedione derivative. The bond-path descriptor exhibits sharper peaks in particular single bond-distance patterns and is generally larger than the corresponding Cartesian descriptor. 

The correlation coefficients between the individual RDF descriptors and the ASD (Figure 5.15) show no signihcant difference between the compounds 7-14 because of the high diversity in the data set. In addition, the compounds 2 and 3 as well as compounds 19 and 20 are indicated as similar within the data set. One major difference between the compounds 6-14 (ethyl ester) and 15 (methyl ester) is only indicated by the bond-path RDF descriptor that reacts sensitively to the additional carbonyl group of compound 15. 

We have seen before that different types of matrices can be used for characterizing a molecule. Depending on which matrix is used, the distance r j in a radial function can represent either the Cartesian distance, a bond-path distance, or simply the number of bonds between two atoms. Consequently, we yield three groups of RDF descriptors. 

Some of the effects previously described are valuable for automatic RDF interpretation. In fact, this sensitivity is an elementary prerequisite in a rule base for descriptor interpretation. However, since many molecular properties are independent of the conformation, the sensitivity of RDF descriptors can be an undesired effect. Conformational changes occur through several effects, such as rotation, inversion, configuration interchange, or pseudo-rotation, and almost all of these effects occur more or less intensely in Cartesian RDF descriptors. If a descriptor needs to be insensitive to changes in the conformation of the molecule, bond-path descriptors or topological bond-path descriptors are more appropriate candidates. Figure 5.7 shows a comparison of the Cartesian and bond-path descriptors. 

A typical feature of Cartesian RDF descriptors is a (at least virtual) decrease in characteristic information with increasing distance. The influence of the short distance range (in particular, the bond information) dominates the shape of a Cartesian RDF. In contrast to that, the bond-path descriptor is generally simpler it exhibits... 

In addition, three distance modes — Cartesian, bond-path, and topological-path distances — are compared. Cartesian RDF descriptors are usually quite sensitive to small constitntional changes in the molecule. The bond-path descriptors exhibit less sensitivity, whereas topological bond-path descriptors only indicate extreme changes in the entire molecnle or in the size of the molecule. 

Whereas the skewness of Cartesian RDF descriptors reacts qnite insensitively to changes in the dataset (except in hydrazine, 14), significant changes occnr in bond-path descriptors when the molecnle becomes more compact (e.g., the sequence 2-1-3-4) and when the freqnency of side chains changes (e.g., 7, 9 and 8, 10). 

RDF. The distance mode dehnes the mode for distance calculation available modes are Cartesian distances, bond-path distances, and topological distances. Descriptors may be calculated on particular atoms. Exclusive mode restricts the calculation to the atom type, and with ignore mode the selected atom type is ignored when calculating the descriptor. In partial-atom mode an atom number has to be given instead of the atom type. The second atom property is available if 2D RDF is selected as code method. 

RDF descriptors may be used in any combination to fit the required task. For instance, it is possible to calculate a multidimensional descriptor based on bond-path distances and restricted to nonhydrogen atoms in the shape of a frequency pattern. Consequently, more than 1,400 different descriptors are available. A final summary of RDF descriptor types, their properties, and applications is given in Table 5.1. This section summarizes typical applications, some of which are described in detail in the next chapter. 

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