Bond-path descriptor

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... 

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. 

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). 

Molecule indices describe structural features of entire molecules. The molecular connectivity index (also called %-index) encodes total size, branching, unsaturation, heteroatom content and cyclicity in only one descriptor for a given bond path length [56, 57]. 

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. 

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. 

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. 

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. 

Topological Representation and Topology), geometrical, electronic, and physicochemical. Topological de.scriptors are derived directly from the connection table repre.sentation of the structure and include atom and bond counts,. substructure counts, molecular connectivity indices (see Topological Indices), kappa indices, substructure environments, path descriptors, distance-sum connectivity, and molecular symmetry. Substructure-ba.sed descriptors are topological de.scriptors which allow the tailoring of the descriptor set to. specific user-defined substructures contained in the molecules of the data set. 

Table 6.3. Sample molecules acetone and isobutene described by atom pair (ap) descriptors.

FIGURE 23.5 Profiles of different local reactivity descriptors (electrophilic attack) along the path of the gas phase SN2 substitution F + CH3—Fb —> Fa—CH3 + Fb. Profiles of energy and bond order are also shown. (Reprinted from Chattaraj, P.K. and Roy, D.R., J. Phys. Chem. A, 110, 11401, 2006. With permission.)... 

At the low end of the hierarchy are the TS descriptors. This is the simplest of the four classes molecular structure is viewed only in terms of atom connectivity, not as a chemical entity, and thus no chemical information is encoded. Examples include path length descriptors [13], path or cluster connectivity indices [13,14], and number of circuits. The TC descriptors are more complex in that they encode chemical information, such as atom and bond type, in addition to encoding information about how the atoms are connected within the molecule. Examples of TC descriptors include neighborhood complexity indices [23], valence path connectivity indices [13], and electrotopological state indices [17]. The TS and TC are two-dimensional descriptors which are collectively referred to as TIs (Section 31.2.1). They are straightforward in their derivation, uncomplicated by conformational assumptions, and can be calculated very quickly and inexpensively. The 3-D descriptors encode 3-D aspects of molecular structure. At the upper end of the hierarchy are the QC descriptors, which encode electronic aspects of chemical structure. As was mentioned previously, QC descriptors may be obtained using either semiempirical or ab initio calculation methods. The latter can be prohibitive in terms of the time required for calculation, especially for large molecules. 

Figure 6.15 Examples of topological descriptors calculated on backbone and R groups of three bidentate ligands. The broken arrows on the left indicate the minimum Pn-P2 connectivity path (Dt) and the second Pn-P2 path (D2). The dotted arrows indicate freely rotating bonds. The R group descriptor SAMR<3 pertains to the sum of the mass units of atoms that are connected within three bonds of the ligating P atoms.

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