Combinatorial enumeration of nonrigid isomers with given ligand symmetries on the basis of promolecules with a subsymmetry of D infinity h
To enumerate nonrigid isomers with given ligand symmetries on the basis of a D infinity h skeleton, the concept of extended partial cycle indices (extended PCIs) proposed newly has been combined with the concept of promolecules proposed previously. The infinite nature of the D infinity h-group is concealed by adopting the factor group of finite order, D infinity h/C infinity (= K). Thus, the partial cycle indices with chirality fittingness (PCI-CFs) for the factor group K are calculated and combined with the PCIs for ligand symmetries so as to give the extended PCIs for various itemized enumurations. This method has been successfully applied to the enumeration of ethane derivatives, where the full enumeration based on K has been compared with partial enumerations based on K as well as with those based on the factor group C infinity h/C infinity (= K3 [symbol: see text] K). Each term of the resulting generating functions has been factorized into a pair of factors to represent ligand constitutions. Thereby, the depiction of resulting molecules can be conducted systematically so as to provide the maps of ethane derivatives corresponding to all of the substitution types.
Fujita
S
Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Japan.