Acta Phys. -Chim. Sin. ›› 1990, Vol. 6 ›› Issue (01): 8-16.doi: 10.3866/PKU.WHXB19900103

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Coloration and Enumeration of Stereoisomers

Liang Cheng-Zhi;Jiang Yuan-Sheng   

  1. Institute of Theoretical Chemistry,Jilin University
  • Received:1988-03-24 Revised:1988-12-06 Published:1990-02-15
  • Contact: 江元生

Abstract: The enumeration of stereoisomers is performed by concerning the ligand substitution as coloring of vertices in the skeleton of a molecule. The colored fragments are classified into species denoted by the symbol (α_1~(n1), α_2~(n2), …, α_f~(nf)) in which α_i(i=1, 2,…,f) being the number of vertices colored identically and n_i standing for its appearances. They satisfy: α_1>α_2>…>α_f and
n_1α__1+n_2α_2+…+n_fα__f=N
where N is the total number of skeleton vertices. By means of symmetry and com-binatorial analysis, both total number of skeleton vertices. By means of symmetry and combinatorial analysis, both the chiral and achiral isomers can be enumerased respectively for each substitutional species. For example, species (1~N) means ligands differ completely one another and the number of chiral isomers can be computed by using the following formula
M_c=N!/|G|...