[ncdavids]

Hello,

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.

Sincerley,

ncdavids