Topological Autocorrelation and Cross-correlation Coefficients

Autocorrelation coefficients are used to transform a pattern of atom properties into a representation that allows comparison of molecules without needing to find the correct atom-by-atom superposition [60, 61]. Any atom property P (atomic charge, Hpophilicity parameter, topological or electrotopological index, etc.) can be used as input 

The autocorrelation coefficient A describes the correlation of any atomic property of atom pairs (a,h) vdth a distance of i bonds ((a,h),d = i). The products of the properties of all atom pairs with the same distance i are summarized and result in one autocorrelation coefficient  

The set of all computed A values is a descriptor with the ability to identify typical patterns of properties in a molecule, e.g., the. distance of two polar functional groups or the distance of lipophilic groups. Due to the importance of functional groups as interaction sites of drag molecules, the autocorrelation coefficients are very helpful in classifying or describing drugs. 

Because the autocorrelation function uses the number of bonds to describe the distance between two atoms in a molecule, autocorrelation coefficients are topological descriptors. In addition to the topology information, however, they include the atom properties considered. 

The same procedure is used to compute cross-correlation coefficients C, which correlate two different properties, e.g., electrostatic and lipophilic single atom parameters. Every C value describes typical distances of regions in a molecule with 

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