Further Descriptors

In addition to the descriptors mentioned above, grid-based methods have been frequently used in the field of quantitative structure-activity relationships (QSAR). In one of the most successful approaches, the comparative molecular field analysis (CoMFA), the molecule is placed in a box and the interaction energy values between this molecule 

Further commonly used molecular descriptors are for example, eigenvalue-based descriptors including 3D information, such as BCUT descriptors (Burden, CAS, University of Texas eigenvalues), EVA, and WHIM descriptors (weighted holistic invariant molecular descriptors). For more information about molecular descriptors, the reader is referred to a handbook by Todeschini and Consonni and a recent review by Xue and Bajorath.  

A comprehensive overview of spatial molecular descriptors is given by Todeschini and Consormi [15]. 

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Multilinear regression can be used where the investigated endpoint is correlated to a linear combination of independent variables (the descriptors). This technique assumes linearity over the whole data set with respect to the descriptors. In addition, normality of the data must be fulfilled, and the descriptors cannot be intercorrelated. Multilinear regression is widely used in (Q)SAR modeling and has the advantage that all numerical information is retained and the predicted endpoint may be better estimated. However, the model may eventually overfit the data, after which the addition of further descriptors causes a decrease in accuracy of the model however, this will typically be disclosed in the calibration step of development. 

Whereas the methods we have discussed so far focus on minimizing the total energy, Cheng and Fournier consider further descriptors (besides the total energy) of the structures. First, for each atom they calculate the number of neighbours, c, within a sphere of a pre-defined radius centered around atom k. From the N values they define an average... 

As two further descriptors, the largest and smallest values of ck are used,... 

In their study, Cheng et al.4S compared different Lennard-Jones clusters with 98 atoms using their proposed connectivity tables. The results for eight isomers are reproduced in Table 2. It is clear that all clusters have comparable total energies as well as number of nearest-neighbour pairs. Therefore, in order to clearly distinguish between the isomers, further descriptors are needed. Their connectivity tables are indeed one way of distinguishing, as the table clearly... 

Then, one no longer has to content oneself with requiring the co-occurrence of substance and substance attributes merely within a common document. Rather one can more specifically require the co-occurrence within a common segment with hardly any danger of information loss. If, for example, the vocabulary already contains the descriptor iron and also sheet metal , then no further descriptor is needed to express iron sheet , because this concept can be expressed justas precisely by a segment comprising the concepts iron and sheet metal. 

For drugs which are not simple bio-depressants, it is necessary to insert one or more further descriptors (such as an electronic and a steric constant) into the above equation to convert it to multiple regression analysis. This modification, due to Hansch (1968, 1971), is discussed in Chapter 16. 

Embedding a molecule in space yields further descriptors. Examples include the chirality of a molecule in 3D space, the symmetry group, the van der Waals volume, etc. As embeddings are local energy minima obtained via optimization, they do not describe ideal tetrahedra or other ideal geometric shapes but rue often somewhat deformed, such that calculation of descriptors of embeddings still has many unsolved problems. 

There is one further descriptor that can be used to characterize double bonds. This is bond ellipticity. Figure 10.48(a) and (b) show an uneven distribution of the electron density along the N=N bond in HN=NH. This is more apparent in Figure 10.51, which shows a plot of the electron density in a plane perpendicular to the AIL at the BCP. The plot is elhptical. In the standard valence-bond picture a double bond consists of a rotational symmetry of electron density about the line linking the two bonded nuclei) and a it bond of two overlapping p orbitals perpendicular to this line. The preferential accumulation of electronic charge, or the amount of deviation from a circular symmetric distribution of p(r), is called... 

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