手性异构体的片断染色计数

COLORATION AND ENUMERATION OF STEREOISOMERS

将配体取代看作对骨架点的染色,通过染色片断的对称性分类,直接计数取代手性和非手性异构体.列表示出典型结果.将Polya定理推广于陪集,与片断染色计数进行比较。

The enumeration of stereoisomers is performed by concerning the ligandsubstitution as coloring of vertices in the skeleton of a molecule. The coloredfragments are classified into species denoted by the symbol (α_1^(n1), α_2^(n2), …, α_f^(nf)) inwhich α_i(i=1, 2,…,f) being the number of vertices colored identically and n_istanding for its appearances. They satisfy: α_1>α_2>…>α_f and n_1α__1+n_2α_2+…+n_fα__f=Nwhere N is the total number of skeleton vertices. By means of symmetry and com-binatorial analysis, both the chiral and achiral isomers can be enumerased respectivelyfor each substitutional species. For example, species (I^N) means ligands differcompletely one another and the number of chiral isomers can be computed by usingthe following formula M_c=N_!/|G|where |G| representing the order of skeletal point group. Similarly, one has thecounting formula for species (α_1^(N-α_)) M_c=sum from j=1 to α(N-α)_!/|G_j(N-α)|if there are s non-planar fragments of species (I^(N-α) with point groups G_j(j=1,2,…, s) respectively. These formulas can be either used for enumerating achiralisomers provided planar fragments are considered. This analysis is easily extended toother cases. As illustrations, regular octahedron (e. g. B_6H_6^(2-)), cube (C_8H_8), ico-sahedron (B_(12)H_(12)^(2-)) and dodecahedron (C_(20)H_(20)) are discussed and tabulated. In this paper, Polya theorem has been proved applicable to the coset of thesecond point groups (C_s, C_(nv), D_(nd), D_(nh), T_d, O_h, I_h, etc). On combining these twomethods, a deeper insight into the significance of Polya theorem in dealing withisomer enumerations has been got.