Kappa-shape descriptors

Simultaneous with the work from Kier and Hall, Zefirov et al. developed a similar technique with the count of paths. The QSARs they used were given for three Kappa-shape descriptors and they considered three functional groups, namely, alkanes, alcohols, and small oxygen-containing compounds. 

The data containing 324 descriptor values of 88 molecules was given as an input to VSMP program, to build models based on three and four descriptors, keeping the interdescriptor correlation below 0.75. The best three-descriptors model, Eq. 80, was based on descriptors 254 (atomic type E-state index), 311 (AlogP98), and 320 (2D Van der Waals surface area) with a correlation coefficient, r, of 0.8425, and the cross-validated correlation coefficient, q, of 0.8239. The correlation coefficients of the other two VSMP models, Eqs. 81 and 82 were 0.8411 and 0.8329, respectively. Significantly, the descriptors 254 and 311 were selected in all the best three-descriptors models of VSMP. The three descriptors, in the models 80, 81, and 82 were 320, 144 (Kappa shape index of order 1), and 30 (topological Xu index), respectively. 

Traditional 2D-QSAR descriptors are generally considered to be the characteristics of a molecule, as a chemist would perceive the molecules. The molecules are described by their physical properties, subdivided surface area (86), atom counts and bonds, Kier and Hall connectivity and kappa shape indices... 

Fig. 5. The r2 correlation coefficients for linear models of traditional descriptors as a function of the 32 VSA descriptors. Notes (a) connectivity and kappa shape indices (4) (b) van der Waals surface area, volume, and density ...

The kappa shape indexes are relatively new descriptors, and few studies have been reported to date. It is expected that the kappa indexes will generally be used along with other topological indexes in QSAR equations rather than by themselves as in most of the examples above. Shape is not the sole determinant... 

Based on the use of chemical graph theory as described above, various indexes of molecular structure have been developed. These indexes may all be termed topological indexes. In the molecular connectivity method, indexes have been developed to characterize various aspects of molecular structure. The kappa shape indexes were developed so that shape measures could be directly entered in QSAR analyses. Each of these indexes characterizes the whole molecule with respect to one or more aspects of structure. In chemistry it is also of interest to characterize the skeletal atoms. In this final section we review briefly an investigation of the skeletal atoms as vertexes in the molecular graph as a basis for an atom descriptor. 

Z eb index, Wiener index. Balaban J index, connectivity indices chi (x), kappa (k) shape indices, molecular walk counts, BCUT descriptors, 2D autocorrelation vector... 

MolConn-Z descriptors include valence, path, cluster, path/cluster, and chain molecular connectivity indices, kappa molecular shape indices, topological and electrotopological state indices, differential cormectivity indices, Wiener and Platt indices, information... 

Kier, L.B. and Hall, L.H. (1999d) The kappa indices for modeling molecular shape and flexibility, in Topological Indices and Rdated Descriptors in QSAR and QSPR (eds J. Devillers and A.T. Balaban), Gordon and Breach Science Publishers, Amsterdam, The Netherlands, pp. 455-489. 

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