Elements of Electron Density Shape Analysis

The complete, three-dimensional shape of fuzzy electron densities can be described in detail using the Shape Group Methods, (SGM), reviewed in detail in a recent monograph [27], Here, only a brief summary of this method will be given. 

The next step involves a truncation of MIDCO surfaces according to the various curvature domains identified on them. For each (a,b) pair of values, all curvature domains D fb) of a specified type p (usually, the type p = 2) are 

The results of the shape group analysis can be summarized using the Betti numbers. The distribution of various values of Betti numbers bPp(a,b) as a 

Shape similarity between two molecules or molecular regions A and B can be expressed using the following shape-similarity measure  

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