Sent to CCL by: nagams [nagams]=[rpi.edu]Be careful not to confuse symmetry elements, symmetry operations that constitute a group and representations (reducible or irreducible) of that group. A reflection plane, a rotation axis, an inversion center, etc. are symmetry elements. Reflection in the plane, rotations about the axis are symmetry operations. A single rotation axis can generate multiple symmetry operations (e.g. C3 generates C3, C3^2 and the identity, while C_inf generates an infinite number of rotations) which may fall into the same class or into multiple classes. Representations of a group are an entirely different matter. In an n-dimensional representation of a group, each symmetry operation is represented by an nxn transformation matrix.
In D_infh the symmetry elements are the C_inf rotation axis, the inversion center, reflection planes and C2 axes. The symmetry operations are the infinite C_inf rotations, the infinite S_inf rotations, the infinite C2 rotations, the infinite reflections, inversion and the identity. These are properties of the D_infh group, irrespective of any representation thereof.
SukumarOn 2014-10-16 17:39, Sergio Manzetti sergio.manzetti%a%outlook.com wrote:
Sent to CCL by: "Sergio Manzetti" [sergio.manzetti|-|outlook.com] Hello, one can for instance classify C_3 as one symmetry representation, composed of 1 unique operation, C_3^2, because C_3^3 is not unique as it is equal to E. In other words, E and C_3 encompass together 2 unique operations, E and C_3^2 for a given group C_3. Conversely in relation to O2 molecule, belonging to the point group D_inf_h, it has these representations: E C2 1 x sigma_v 1 x sigma_h 1 x sigma_d 1 x i However, the cyclic representation C_inf is not added here, on purpose, as I wonder if it is a representation for this particular group (as inf is infinite)?Thanks> To recover the email address of the author of the message, please change