Sir i need help for understanding symmetry elements which is the basis of group theory.i have read many books containing this subject , however i can't imagine these elements.please help me.thanking you?
1 Answer
Many good group theory texts should have images... but this website is great for additional visualization practice. Bookmark it! You can perform the operations by clicking the button next to the symmetry element.
Also, you will find this website useful later; it'll help you check your reduced reducible representations, so keep this website in mind as well. For instance,
Symmetry operations can be categorized in general as:
- Identity,
#hatE# , symmetry element =#E# (nothing) - Rotation,
#hatC_n# , symmetry element =#C_n# (an axis) - Reflection,
#hatsigma# , symmetry element =#sigma# (a plane) - Inversion,
#hati# , symmetry element =#i# (a dot)
We can use
Note:
IDENTITY
The identity operation
There really is no point in identifying what the symmetry element
ROTATION
The rotation operation,
For example,
When you rotate
From this angle, it is more noticeable that you can rotate
REFLECTION
The reflection operation,
#sigma_v# is colinear with the principal#C_n# axis (of the highest#n# ), and lines up with an outer atom.#sigma_h# is perpendicular to the principal#C_n# axis.#sigma_d# bisects two outer atoms, crossing through the center of the molecule, and is in between two#sigma_v# planes. It must not directly line up with an outer atom (otherwise it is#sigma_v# ).
Cyclobutane (
ROTATION-REFLECTION (IMPROPER ROTATION)
This is its own operation,
For example,
You should convince yourself though that
INVERSION
The inversion operation
The easiest way I can think of to describe it is that it takes the coordinates
Here's an example of inversion with a molecule that doesn't have inversion symmetry, like
This is hard to visualize for molecules with inversion symmetry, because it looks like it does nothing. Practice with this one.