Theoretical Chemistry Accounts

, Volume 113, Issue 2, pp 80–86 | Cite as

Graphs to chemical structures 2. Extended sphericity indices of cycles for stereochemical extension of Pólya’s coronas

  • Shinsaku FujitaEmail author


In order to enumerate nonrigid isomers, we have proposed the proligand approach, where extended sphericity indices of k-cycles have been defined according to the enantiospheric, homospheric, or hemispheric nature of each k-cycle. Then, cycle indices with chirality fittingness have been defined so as to enumerate nonrigid stereoisomers with chiral and achiral ligands. Results of the proligand approach using tetramethylmethane as an example have been compared with those based on Pólya’s corona. Thereby, Pólya’s corona is concluded to be concerned with graphs, but not with chemical structures, where it is incapable of treating chiral ligands properly.


Cycle index Chirality fittingness Sphericity index Pólya’s corona 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Chemistry and Materials TechnologyKyoto Institute of TechnologyKyotoJapan

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