Similarity, continued molecular, index

Molecular Similarity and QSAR. - In a first contribution on the design of a practical, fast and reliable molecular similarity index Popelier107 proposed a measure operating in an abstract space spanned by properties evaluated at BCPs, called BCP space. Molecules are believed to be represented compactly and reliably in BCP space, as this space extracts the relevant information from the molecular ab initio wave functions. Typical problems of continuous quantum similarity measures are hereby avoided. The practical use of this novel method is adequately illustrated via the Hammett equation for para- and me/a-substituted benzoic acids. On the basis of the author s definition of distances between molecules in BCP space, the experimental sequence of acidities determined by the well-known a constant of a set of substituted congeners is reproduced. Moreover, the approach points out where the common reactive centre of the molecules is. The generality and feasibility of this method will enable predictions in medically related Quantitative Structure Activity Relationships (QSAR). This contribution combines the historically disparate fields of molecular similarity and QSAR. 

For the comparison of analytical data, e.g. molecular spectra and/or chromatographic retention data, a similarity index in the form of a P-value, as used in hypothesis testing, has been developed. This similarity index requires that unknown and reference compounds be characterised by a set of continuous feature quantities qi... qj... q. In the case of mass spectra these may be the peak intensities at a certain number of selected masses, whereas for C-NMR spectra the chemical shifts could be used. 

Nevertheless, the connectivity index continues to be one of the most widely used molecular descriptors, and the degeneracy is not so important for structure-property correlations because there are also molecules having some of the same or very similar values for molecular properties. The degeneracy, however, is the critical factor if one wishes to discriminate among molecules as much as possible, which is our interest in this section. 

Wasserman et al [57] used similar moments to characterize molecular structure, but worked with the discrete rather than the continuous spectrum. They defined a relaxation spectrum index , or RSI, in terms of two moments of the discrete spectrum as follows ... 

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