Contributions Per Atom in MO diagram

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SUMMARY

The discussion focuses on calculating contributions per atom for the carbonate ion (CO32-) using its point group D3h. The character table for D3h reveals the first row as 3,0,1,3,0,1 and the coefficients as 1,2,3,1,2,3. The definitive contributions per atom are determined to be 3,0,-1,1,-2,1, derived from symmetry operations and character tables.

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Homework Statement


How do you find the contributions per atom for calculating the reducible parts?

For example CO3-2 has pt. grp: D3h.

From the character tables-- the first row (unshifted atoms) is: 3,0,1,3,0,1. Second row (coefficients): 1,2,3,1,2,3 Third Row (contributions per atom): ?,?,?,?,?,?

Homework Equations


The Attempt at a Solution



I know the answer is 3,0,-1,1,-2,1 but I can't find any hints as to how this was obtained. Is it from the character tables or from the symmetry operations?
 
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