Dnd point groups

A Dnd point group contains a C axis, an S2n axis, n C2 axes perpendicular to C and at equal angles to each other and n ad planes bisecting the angles between the C2 axes. For n odd the point group contains a centre of inversion i. It also contains other elements which may be generated from these. 

The point group Dld is the same as C2v. Molecules belonging to other Dnd point groups can be visualized as consisting of two identical fragments of Cnv symmetry back to back with one staggered at an angle of n/n to the other. 

Apart from these two important examples molecules belonging to Dnd point groups are rare. 

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Type 3. One n-fold axis and n twofold axes point groups Dn, Dnh, Dnd. 

Particular care should be taken to check for two-fold axes perpendicular to the principal axis. Overlooking these is probably the commonest error made in identifying point groups. Note also that the group that results from the product of a centre of inversion with Dn is Dnh when n is even but Dnd when n is odd. 

Table 3.2 a,jc,S representations on the distinct orbits of the molecnlar point gronps Dn, Dnh Dnd Sn, up to n = 6 Oj is the orbit of order i and m is the number of times it occurs in a particular molecule as explained in the text. For each group the regular representation direct sum is given explicitly as the a representation for the largest orbit, but otherwise is abbreviated as r ulari in column 1 identifies a group in which a central Oj orbit can be present. For this orbit the a, n and 8 analysis does not apply. 

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