Contributions Per Atom in MO diagram

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To find contributions per atom for calculating reducible parts in a molecular orbital (MO) diagram, one must refer to the character tables associated with the molecule's point group, in this case, D3h for CO3-2. The contributions per atom can be derived from the coefficients in the character table and the symmetry operations. The specific contributions for CO3-2 are 3, 0, -1, 1, -2, 1, which align with the symmetry representations. Understanding how to interpret the character table and apply symmetry operations is crucial for solving these types of problems. Mastery of these concepts is essential for accurate calculations in molecular symmetry.
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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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