July 15, 2024, 01:42:31 PM
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Topic: ML5 complex: Point Group D3h Proving the Reducible Representations  (Read 9321 times)

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Offline ncdavids

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I was told to find the reducible and irreducible representations of an ML5 complex (i.e. such as PF5 or SF5).I was able to visually find the reducible representation of

E    2C3 3C2 sigma h  2S3 3sigma v

18     0    -2      4        -2     4

(note: I am finding translational, rotational, and vibrational modes that is why E is 18. 3 modes per atom or 3x6=18).

Now I need help proving these reducible representations via matrices showing how I came up with these numbers. My question is how do I do that? I read in my textbook that axis of C3 use trigonometric functions and that they can't be block diagonalized. Instead a 2x2 and 1x1 matrix is used for each operation.

Can anyone help me or offer ANY suggestions.



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