Highest order rotation axis

If the object does not belong to the linear point groups, the polyhedral point groups, or the point groups C, C , Cl or S2 , then look for the highest order rotation axis. Call the highest order rotation axis C . 

Assign X, y, and z coordinates to the atoms, chosen for convenience. Experience is the best guide here. The general rule in all the examples in this book is that the highest order rotation axis of the molecule is chosen as the z axis of the central atom. In nonlinear molecules, the y axes of the outer atoms are chosen to point toward the central atom. 

For each of the following two-dimensional shapes, determine the highest order rotation axis of symmetry. 

The main part of the Schoenflies symbol is a capital letter. There is a capital C if there are no two-fold axes perpendicular to the principal rotation axis (the axis of largest value of n) or a capital D if there are such two-fold axes. There is a subscript that denotes the value of n for the highest-order rotation axis. A subscript v indicates the presence of vertical mirror plans, and a subscript h denotes the presence of a horizontal... 

Each of the irreducible representations could be labeled in a simple way, F, Fi,. . . , F , but there is a notation due to Mulliken, which is very useful. A and 6 refer to one-dimensional representations where A refers to a representation for which the character corresponding to the highest order rotation axis is +1 and B when it is I. and T refer to doubly and triply degenerate representations, respectively. From the definition of these characters, the entry in the character table for the identity operation, y,( ) defines the order of the representation. (I for A, 6 2 for 3 for T, etc.) If there is more than one representation with the same label, then they are distinguished by subscripts 1,2,. . ., and so on. 

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