List of topological charge indices calculated by DRAGON

 

Topological charge descriptors are derived from an unsymmetric matrix CT, whose single elements are defined as:

 

 

where di is the vertex degree of the ith atom, i.e. the number of connected atoms in the H-depleted molecular graph, and mij are elements of the matrix obtained by multiplying the adjacency matrix by the reciprocal square distance matrix [J. Gálvez, R. Garcěa, M.T. Salabert, R. Soler, J.Chem.Inf.Comput.Sci. 1994, 34, 520-525]. The diagonal entries of the CT matrix represent the topological valence of the atoms; the off-diagonal entries CTij represent a measure of the net charge transferred from the atom j to the atom i.

 

For each path of length k, a topological charge index GGIk is defined as the half-sum of all charge terms CTij (absolute values) corresponding to pair of vertices with topological distance equal to k. The maximum number of GGIk terms in a molecule is equal to the maximum topological distance in the corresponding molecular graph; however, to obtain uniform length descriptors for a set of molecules, DRAGON calculates topological charge indices from order 1 to order 10 for all the molecules.

 

A mean topological charge index JGIk is obtained by dividing the corresponding topological charge index GGIk by the total number of summation terms in GGIk.

 

Moreover, a global topological charge index JGT is defined as the sum of the mean topological charge indices (from order 1 to order 10 in DRAGON).