Let us consider octahedral complexes.We shall represent the ligands by smallcase letters a,b,c etc. and the metal by M. Let the first example be Mabcdef, in which all the ligands are different.We shall write the trans pairs of ligands in brackets in alphabetical order. In each isomer there will be three trans pairs. Ligands that are not within the same bracket are cis to each other.
The geometrical isomers of Mabcdef areas follows.
Mabcdef
M(ab)(cd)(ef), M(ab)(ce)(df), M(ab)(cf)(de)
M(ac)(bd)(ef), M(ac)(be)(df), M(ac)(bf)(de)
M(ad)(bc)(ef), M(ad)(be)(cf), M(ad)(bf)(ce)
M(ae)(bc)(df), M(ae)(bd)(cf), M(ae)(bf)(cd)
M(af)(bc)(de), M(af)(bd)(ce), M(af)(be)(cd)
Note that in writing the isomers we have always followed the alphabetical order. (ac) comes before (bd) because even if c comes after b, a comes before both b and d.
2. Maabcde
M(aa)(bc)(de),M(aa)(bd)(ce), M(aa)(be)(cd)
M(ab)(ac)(de), M(ab)(ad)(ce), M(ab)(ae)(cd)
M(ac)(ad)(be), M(ac)(ae)(bd)
M(ad)(ae)(bc)
3. Maaabcd
M(aa)(ab)(cd), M(aa)(ac)(bd), M(aa)(ad)(bc)
M(ab)(ac)(ad)
4. Maabbcd
M(aa)(bb)(cd), M(aa)(bc)(bd)
M(ab)(ab)(cd), M(ab)(ac)(bd), M(ab)(ad)(bc)
M(ac)(ad)(bb)
5. Maabbcc
M(aa)(bb)(cc), M(aa)(bc)(bc)
M(ab)(ab)(cc), M(ab)(ac)(bc)
M(ac)(ac)(bb)
Remember, the ligands within a bracket are trans to each other. In an octahedral complex there are three trans pairs of ligands. In enumerating the geometrical isomers note that alphabetical order has been maintained. Each succeeding trans pair is either equivalent to the preceding as in (ab)(ab) or alphabetically comes later as in (ab)(cd) or
(ac)(bd). This ensures that there is no duplication of isomers.
For practice use this technique to enumerate the geometrical isomers in square planar complexes. There , of course, will be only two trans pairs of ligands in sq pl complexes.
We have considered examples of only monodentate ligands but this method can be applied to bidentate ligands as well if you keep it in mind that the two donor atoms of a bidentate ligand cannot be trans to each other.
Let us represent the donor atoms of a bidentate ligand by upper case letters. For example, ethylenediamine by AA. Let us enumerate the geometrical isomers of the complex M AAbcde.
6. M AAbcde
M(Ab)(Ac)(de), M(Ab)(Ad)(ce), M(Ab)(Ae)(cd)
M(Ac)(Ad)(be), M(Ac)(Ae)(bd)
M(Ad)(Ae)(bc)
This enumeration technique also helps in identifying the isomer which is not optically active. Any isomer in which the same letters are within a bracket is optically inactive. For example, M(aa)(bc)(de) is optically inactive. For identifying the optically active isomers you will have to draw the structure and check whether the mirror image is superimposable or not.
Hope this helps.Let us consider octahedral complexes.We shall represent the ligands by smallcase letters a,b,c etc. and the metal by M. Let the first example be Mabcdef, in which all the ligands are different.We shall write the trans pairs of ligands in brackets in alphabetical order. In each isomer there will be three trans pairs. Ligands that are not within the same bracket are cis to each other.
The geometrical isomers of Mabcdef areas follows.
Mabcdef
M(ab)(cd)(ef), M(ab)(ce)(df), M(ab)(cf)(de)
M(ac)(bd)(ef), M(ac)(be)(df), M(ac)(bf)(de)
M(ad)(bc)(ef), M(ad)(be)(cf), M(ad)(bf)(ce)
M(ae)(bc)(df), M(ae)(bd)(cf), M(ae)(bf)(cd)
M(af)(bc)(de), M(af)(bd)(ce), M(af)(be)(cd)
Note that in writing the isomers we have always followed the alphabetical order. (ac) comes before (bd) because even if c comes after b, a comes before both b and d.
2. Maabcde
M(aa)(bc)(de),M(aa)(bd)(ce), M(aa)(be)(cd)
M(ab)(ac)(de), M(ab)(ad)(ce), M(ab)(ae)(cd)
M(ac)(ad)(be), M(ac)(ae)(bd)
M(ad)(ae)(bc)
3. Maaabcd
M(aa)(ab)(cd), M(aa)(ac)(bd), M(aa)(ad)(bc)
M(ab)(ac)(ad)
4. Maabbcd
M(aa)(bb)(cd), M(aa)(bc)(bd)
M(ab)(ab)(cd), M(ab)(ac)(bd), M(ab)(ad)(bc)
M(ac)(ad)(bb)
5. Maabbcc
M(aa)(bb)(cc), M(aa)(bc)(bc)
M(ab)(ab)(cc), M(ab)(ac)(bc)
M(ac)(ac)(bb)
Remember, the ligands within a bracket are trans to each other. In an octahedral complex there are three trans pairs of ligands. In enumerating the geometrical isomers note that alphabetical order has been maintained. Each succeeding trans pair is either equivalent to the preceding as in (ab)(ab) or alphabetically comes later as in (ab)(cd) or
(ac)(bd). This ensures that there is no duplication of isomers.
For practice use this technique to enumerate the geometrical isomers in square planar complexes. There , of course, will be only two trans pairs of ligands in sq pl complexes.
We have considered examples of only monodentate ligands but this method can be applied to bidentate ligands as well if you keep it in mind that the two donor atoms of a bidentate ligand cannot be trans to each other.
Let us represent the donor atoms of a bidentate ligand by upper case letters. For example, ethylenediamine by AA. Let us enumerate the geometrical isomers of the complex M AAbcde.
6. M AAbcde
M(Ab)(Ac)(de), M(Ab)(Ad)(ce), M(Ab)(Ae)(cd)
M(Ac)(Ad)(be), M(Ac)(Ae)(bd)
M(Ad)(Ae)(bc)