Average descriptor

The next step is to calculate the difference between each descriptor g ir) and the average descriptor g r). This value is defined by the average descriptor deviation 6g for an individual descriptor i with the components j,... 

The sum of all average descriptor deviations divided by the number of descriptors L leads to the average diversity A ... 

Average Descriptor Deviation is a statistical measure for the deviation between descriptors in a data set and the average descriptor. 

One way to characterize an individual descriptor within its data set is to calculate the average descriptor g(r) for a data set... 

Mixtures containing up to several thousand distinct chemical entities are often synthesized and tested in mix-and-split combinatorial chemistry. The descriptor representation of a mixture may be approximated as the descriptor average of its individual component molecules, e.g., using atom-pair and topological torsion descriptors. 

An extended set of physicochemical descriptors was used in this study, including, for example, partial atomic charge and effective polari2 ability of the protons, average of electronegativities of atoms two bonds away, or maximum, T-atomic charge of atoms two bonds away. 

Values for hydrocarbons other than alkynes and alkadienes can be predicted by the method of Suzuki et al. The best model includes the descriptors T, P, the parachor, the molecular surface area (which can be approximated by the van der Waals area), and the zero-order connectivity index. Excluding alkynes and alkadienes, a studv for 58 alkanes, aromatics, and cycloalkanes showed an average deviation from experimental values of about 30 K. 

When applied to QSAR studies, the activity of molecule u is calculated simply as the average activity of the K nearest neighbors of molecule u. An optimal K value is selected by the optimization through the classification of a test set of samples or by the leave-one-out cross-validation. Many variations of the kNN method have been proposed in the past, and new and fast algorithms have continued to appear in recent years. The automated variable selection kNN QSAR technique optimizes the selection of descriptors to obtain the best models [20]. 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

A quite different aspect of local kinetics is that having to do with changes of charge state, e.g., between H+ and H° or H° and H. Such changes require emission or absorption of electrons or holes. Since the mean free paths of these carriers are large compared with atomic dimensions, it is customary (see for example Lax, 1960) to use a velocity-averaged cross section a as the key descriptor of the rate of a capture reaction such as H+ + e— H°. Explicitly, we write, for this case,... 

Table 4.6. Geometries and NBO descriptors 0/MH2 and MH3 metal hydrides of the third transition series of various spin multiplicities (IS + I), illustrating the correlations of metal charge (Qu) with metal hybrid d character (%d, taken as the average of a and 3 hybrids for open-shell species), bond length (Ruw) and angle (9hmh)> and average absolute deviation (Dev. = average %mh — 90" ), from idealized covalent geometry...

Along the same line, the CFF for radical attack is defined as the average of fk and. Descriptors such as electrophilicity index and its local counterpart are also a useful quantity [15]. Several other reactivity descriptors have been proposed to explain the reactivity of chemical species [16,17]. 

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