Geometrical Similarity as Topological Equivalence

The GSTE Principle Geometrical Similarity as Topological Equivalence... 

The above treatment of similarity is the basis of the GSTE Principle treating Geometrical Similarity as Topological Equivalence [108]. 

The GSTE Principle Geometrical Similarity as Topological Equivalence is a general principle for similarity analysis [108]. 

ADMA = adjustable density matrix assembler AFDF = additive fiizzy density fragmentation GSTE = geometrical similarity as topological equivalence MEDLA = molecular electron density loge assembler MEP = molecular electrostatic potential RBSM = resolution-based similarity measures SGM = shape group methods VDWS = van der Waals surface ID, 2D, 3D = one, two, and three dimensions. 

Furthermore, the two inner carbon atoms (C2, C4 ) in 222 exhibit similar electron densities as the central atom in allene (11). The carbon atoms considered in the preceding hydrocarbons which seem to be electronically equivalent all have the same neighbor-atom topology. However, as the example of 11 and 222 shows, electronically equivalent atoms of molecules need not be geometrically equivalent. This remark concerns the central atoms in 11 and 222,... 

The shape group method (SGM), reviewed in ref. [2], has been proposed for the analysis of three-dimensional shape properties of formal molecular bodies. For example, by choosing the electronic charge isodensity contours G(a) (of various density values a) as the physical property P for shape representation, and by taking the family of Betti numbers b as the topological tool for shape description [2], the similarity of the geometrical shapes of two molecules, A and B, is transformed into an equivalence of their topological shape, expressed as... 

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