type-itemized enumeration of rs-stereoisomers of octahedral complexes

stereoisograms of octahedral complexes are classified into five types (type i--typev) 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 o_h 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 ofoctahedral 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.