2.8. Derivation of C2v Character Table

[@enkoyamian8146]

thank you Mr. Barile , this video helps a lot, it really save my final exam

[@sandipan15]

Very much helpful. Thank you sir .

[@alecat9990]

thank you this is super clear! I was very confused on what conjugacy classes are but splitting them into 'a transform on the x/y/z' vector makes sense.
I am trying to do this for the octahedral group, and I guess I am still a little confused on how we group these things (for example I know xy, yz, xz is one class, but I have trouble justifying it)? I don't know if I am being clear.

[@alecat9990]

I think I also always thought of it as connecting to the trace of a matrix in that class, but maybe thats wrong

[@christopherbarile2539]

Glad this helps. When you see (xy, yz ,xz) together, it means that all three functions transform together under a single irreducible representation. That is not the case for any of the irreducible representations in C2v in which all of the vectors are one dimensional. Check out my other derivation videos. I have not done one for Oh point group, but I have one on Td character table, which is mathematically similar and also has those three functions transforming together.

[@christopherbarile2539]

The trace of the transformation matrices are where the characters in the character table come from.

[@savvasnicolaou8843]

Thanks.

[@christopherbarile2539]

You're welcome

[@와우와우와우-v1z]

thank you sir

[@akashsarkar8888]

in higher study hit and trial method get more importance😒😒