Compounds with Achiral Ligands Only

Abstract

Enumeration of compounds in chemistry is one of the most important fields to which the Pólya-Redfield theorem^[1] has been applied. Ruch et al.^[2] and later Brocas^[3] have proved the concept of double coset to be very convenient for such compound-counting problems. Sheehan^[4] has applied the concept of table of marks (see Chapter 5) to enumeration of graphs under an automorphic group. More recently, Hässelbarth^[5] has developed a method that is also based on the concept of table of marks. This method is capable of enumerating compounds with respect to a given symmetry. Mead^[6] has discussed an alternative method that is a combination of table of marks and double cosets. These methods, however, have taken no account of intransitivity of a domain explicitly; hence, they have disregarded the restriction due to OMVs (obligatory minimum valencies).

This chapter is based on the article published in S. Fujita, Theor. Chim. Acta, 76, 247–268 (1989).