Type-atemized Enumeration of RS-stereoisomers of Octahedral Complexes

Stereoisograms of octahedral complexes are classified into five types (type i– type v) under the action of the corresponding rs-stereoisomeric group. their enumeration is accomplished in a type-itemized fashion, where fujita’s proligand method developed originally for combinatorial enumeration under point groups (s. fujita, theor. chem. acc., 113, 73–79 (2005)) is extended to meet the requirement of fujita’s stereoisogram approach. the cycle index with chirality fittingness (ci-cf) of the point group oh is modulated by taking account of the ci-cf for calculating type-v quadruplets contained in stereoisograms. the modulated ci-cf is combined with a ci-cf of the maximum chiral point group (o), a ci-cf of the maximum rs-permutation group, a ci-cf of the maximum ligand-reflection group, and a ci-cf of the rs-stereoisomeric group, so as to generate ci-cfs for evaluating type-i to type-v quadruplets. by introducing ligand-inventory functions into the ci-cfs, the numbers of quadruplets of octahedral complexes are obtained and shown in tabular forms. several stereoisograms for typical complexes are depicted. their configuration indices and c/a-descriptors are discussed on the basis of fujita’s stereoisogram approach.