Compounds with Rotatable Ligands

Pólya[1] has already mentioned the enumeration of non-rigid molecules in terms of “coronas”, which are equivalent to wreath products. The counting of non-rigid cyclohexane isomers was discussed by introducing a ring-flip-rotation operator along with usual symmetry operations.[2] Isomers derived from a non-rigid ethane were enumerated by means of the concept of covering groups.[3] A generalized wreath product method has been presented for enumerating stereo- and positional isomers.[4] However, systematic enumeration of non-rigid isomers that takes into account the spacial symmetries of isomers is open to further investigation. As a continuation of our studies on USCIs,[5] the present chapter will deal with this type of enumeration by using 2,2-diphenyl- and 2,2-dimethylpropane as examples. In particular, we discuss a general case in which a non-rigid molecule involves chiral ligands as well as achiral ones.