The Groups Dnh

Group D. Tf the horizontal plane containing the twofold axes of Dn is also a plane of symmetry, then n vertical planes containing the main axis of symmetry and a twofold axis are necessarily also planes of symmetry. This system of axes and planes of symmetry gives rise to the group Dnh which, in addition to the elements of... 

When to the above is added a reflection perpendicular to the principal axis, 6h, one obtains the group Dnh generated by Cn, C2 and 6h. Again, as for Cnh, for n even we can instead generate the point group from the operators C, Q and I. 

The group Dnd (a principal axis C , n vertical planes of symmetry Sd and n C2 axes perpendicular to C bisecting each angle between two adjacent Sd planes and the identity E) -The group Dnh (a principal axis Cn, n C2 axes perpendicular to n planes of symmetry and a plane of symmetry Sh and the identity E)... 

The second expression is simply a list of the six /s, in numerical order, each multiplied by the character for one of the six operations, in the conventional order , CA, Cl,..., C. This must be true for each and every representation. Hence, the sets of characters of the group are the coefficients of the LCAO-MOs. The argument is obviously a general one and applies to all cyclic (CH) systems belonging to the point groups Dnh, each of which has a uniaxial pure rotation subgroup, C . 

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. 

Dnh. ADnh, group will also, necessarily, contain n vertical planes these planes contain the C2 axes. If there is no oh but there is a set of n vertical planes which pass between the C2 axes, the group is Dnd. 

There is another set of groups Dnh, which contain the elements... 

When the symmetry of a given molecule has been determined, electronic transitions fall into the following three categories i a. electric allowed — magnetic forbidden b. magnetic allowed — electric forbidden [Groups C, Cnh, Dnh (n 2), S2n (n, odd), Oh, Td]... 

Other carbocyclic systems of the type (CH) , belonging to the point groups ) l/l, which are of interest are those with n equal to 3, 4, 5, 7, and 8. In some cases the actual systems (which may be cations, neutral molecules, or anions) are not necessarily of Dnh symmetry, but there is usually some purpose in... 

A Dnh point group contains a Cn axis, n C2 axes perpendicular to C and at equal angles to each other, a ah plane and n other a planes. For n even the point group contains a centre of inversion i. It also contains other elements which may be generated from these. 

A Dnh point group is related to the corresponding Cnv point group by the inclusion of a ah plane. 

In any case the search is for the highest order C axis. Then it is ascertained whether there are n C2 axes present perpendicular to the C axis. If such C2 axes are present, then there is D symmetry. If in addition to D symmetry there is a a plane, the point group is Dnh, while if there are n symmetry planes (arf) bisecting the twofold axes,... 

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