Symmetry and Group Theory. Chapter 4. Symmetry and Group Theory. The symmetry properties of molecules can be useful in predicting infrared spectra, describing the types of orbitals used in bonding, predicting optical activity, and interpreting electronic spectra (to name a few).
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Several objects for examples
Note: The principal axes is usually chosen as the z-axis.
S2 i (preferred)
It will help to build these molecules with your model kits (especially in the beginning).
Website for software:
Examine Figure 4-7.
Vertical planes contain the highest order Cn axis. In the Dnd case, the planes are dihedral because they are between the C2 axes.
Purely rotation groups of Ih, Oh, and Td are I, O, and T, respectively (only other symmetry operation is E). These are rare.
The Th point group is derived by adding inversion symmetry to the T point group. These are rare.
Understand each property.
Let’s do a few matrix multiplications.
Let’s examine the symmetry operations of a C2v point group (e.g. H2O). All the symmetry operations of this point group can be represented by transformation matrices.
Note: The row under each symmetry operation corresponds to the result of the operation on that particular dimension.
Explanation of labels on page 97.
Go over properties of character of IRs in point groups on page 98 (with relation to the C2v point group).
Where did the A2 representation come from? Property 3. Using property 6 of orthogonality the characters of this representation can be determined.
Go over Table 4-7 with this point group.