Determining the number of symmetries displayed by a compound can be done using various methods, but there are a few shortcut ways that can be employed. Here's a simplified approach to determine the number of symmetries:
Identify the point group: The first step is to determine the point group of the compound. The point group describes the symmetry elements present in the molecule, such as rotation axes, reflection planes, and improper rotation axes. Each point group has a specific set of symmetry operations associated with it.
Utilize character tables: Character tables are organized tables that provide information about the symmetry operations and their corresponding symmetry elements for different point groups. These tables also list the reducible representations (characters) associated with different molecular vibrations or electronic states.
Apply the shortcut rule: One shortcut rule is to count the number of symmetry operations associated with each symmetry element in the compound. For example, if a molecule has a C2 axis (rotation axis of order 2), it will have one symmetry operation associated with that axis. If it has a σh plane (horizontal reflection plane), it will have one symmetry operation associated with that plane.
Sum the symmetry operations: Add up the number of symmetry operations associated with all the symmetry elements present in the compound. This will give you the total number of symmetries displayed by the compound.
It's important to note that this shortcut method assumes that the compound has idealized symmetry without taking into account any distortions or deviations. For more complex molecules or cases involving distortions, a more detailed analysis and consideration of the molecular structure would be required.
It's recommended to consult appropriate references, such as group theory textbooks or online resources that provide character tables and detailed instructions for symmetry analysis, to ensure accurate determination of symmetries in a compound.