Periphery Codes

A molecular descriptor that was proposed to discriminate between a chiral molecule and its mirror image it is restricted to molecules embedded in 2D space, such as ben-zenoids, and is based on - periphery codes [Randic, 1998a]. 

However, when molecular descriptors are derived from molecular graphs, cis/trans isomerism is not usually recognized and some molecular descriptors were proposed in order to discriminate between cis/trans isomers, such as the - corrected electron charge density connectivity index, and - periphery codes. - Weighted matrices were also devised for obtaining the -> geometric modification number that is added to any topological index in order to discriminate cis/trans isomers. 

Periphery codes can be used to evaluate - similarity/diversity based on molecular shape among several compounds [Randic and Razinger, 1995b]. Moreover, periphery codes can also be used to distinguish between cis- and trans- isomers [Oth and Gilles, 1968 Balaban, 1969 Balaban, 1997a] and to recognize whether a shape is chiral or... 

Several shape descriptors are defined within more general approaches to - molecular descriptors. This is the case of - Kier shape descriptors, -> shape profiles, -> shadow indices, -> WHIM shape descriptors, - Sterimol shape parameters L/Bj and B1/B5, molecular - periphery codes, and -> centric indices. Other approaches to the study of molecular surface and shape are Mezey 3D shape analysis and Hopfinger - molecular shape analysis. -> Triangular descriptors have also been used to characterize molecular shape to search for similarities among molecules. 

Figure 5. Six configurations of [22]annulene possessing three mutually onhogonal symmetry axes with inscribed index (boldface) which is the sum of all individual squared geometrical distance sums d, and w ith Randic and Razinger s periphery code under each structure.

Different characterizations will reflect different aspects of the similarity among objects. We will consider here how the similarity is reflected when benzenoids are characterized by their binary periphery codes. Consider the 19 achiral shapes of Figure 33 having periphery P = 22 labeled as A-S. Their binary codes are hsted in Table 29. We will use the Hamming distance as the index ofsimilarity/dissimilarity. A Hamming... 

Table 30. The Hamming Distance for the Periphery Codes of Table 28...

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