Counting descriptors

Liang and Gallagher found that the inclusion of counting descriptors for OH, C = O, NH, COOH, NO2, and CN groups improved somewhat the correlation as expressed in Eq. [32]. 

The negative signs are physically reasonable because these additional parameters would be expected to be associated with increased intramolecular attractions. The authors provided no measure of intercorrelation indeed, one might expect some correlation of a, the average molecular polarizability, with the presence of C=0, COOH, NO2, and CN groups. The counting descriptors are not QM quantities their inclusion is not philosophically satisfying, but they do improve the fit. 

The most common constitutional descriptors are number of atoms atom number), number of bonds (- bond number), absolute and relative numbers of specific atom types count descriptors), absolute and relative numbers of single, double, tri-... 

These are simple molecular descriptors based on counting the defined elements of a compound. The most common chemical count descriptors are atom number A, bond number B, cyclomatic number C, -> hydrogen-bond acceptor number and -> hydrogen-bond donor number, -> distance-counting descriptors, -> path counts, walk counts. 

Count descriptors give local chemical information, are insensitive to isomers and to conformational changes and show a high level of degeneracy. However, due to their immediate availability, they are among the most used descriptors. 

The final distance-counting descriptor is obtained by chaining in an arbitrary but constant way all of the calculated SE-vectors, such as... 

The HBi parameter is a count descriptor based on atoms in a group which possess the ability to form hydrogen bonds. This includes both H-bond acceptors and H-bond donors. The rules for HBi are ... 

A simple empirical index related to hydrophilicity of compounds based on - count descriptors [Todeschini et al, 1997b]. It is defined as ... 

However, the assumptions needed to facilitate calculation and numerical approximation are themselves associated with an inherent error, although in most cases the direction, but not the magnitude, of the error is known. Moreover, within a series of related compounds the error term is usually considered to be approximately constant. All kinds of error are absent only for the most simple theoretical descriptors such as count descriptors or for descriptors directly derived from exact mathematical theories such as graph invariants. 

Referring to the subgraph order, rth order indices can be defined as -+ count descriptors, i.e. the number of rth order subgraphs in the graph The zero order index is simply the - atom number A, i.e. the number of graph vertices 1 order index is the -> bond number B, i.e. the number of graph edges 2" order index is the... 

The simplest descriptors of the degree of unsaturation of a molecule are -> count descriptors based on the presence of double bonds, triple bonds, and aromatic bonds they are the double-bond count, the triple-bond count n= and the aromatic-bond count The MCB index was proposed as the number of multiple C-C bonds in the molecule accounting for double, triple, and aromatic bonds [Bakken and Jurs, 1999b]. Another simple global multiple bond count is defined as ... 

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