MO Diagram from Group Theory: Central Atom

AI Thread Summary
Determining the central atom's orbitals in a molecule like CO3^-2 involves using point group character tables from group theory. For the D3h point group, the carbon atom's p-orbitals are represented by the symmetry labels a1'' and e', while the s-orbital is labeled as a1'. The process of obtaining these labels is primarily based on interpreting the character table, particularly the right side. However, there is a noted lack of resources that explain this process in detail. Understanding the Mulliken symmetry symbols, such as "a1" and "t1," is essential for this analysis.
mrshappy0
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Homework Statement


I am wondering how for determine the central atom's orbitals from the point group character tables described by group theory.

For example CO3^-2 (D3h)
Carbon's (central atom) p-orbitals are described by a1''+e'. The s-orbital is a1'


Homework Equations





The Attempt at a Solution



I'm not entirely sure how this was obtained.
I'm certain that they are found from just reading the right side of the character table but I am unable to find any resources describing it any further.
 
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mrshappy0 said:

Homework Statement


I am wondering how for determine the central atom's orbitals from the point group character tables described by group theory.

For example CO3^-2 (D3h)
Carbon's (central atom) p-orbitals are described by a1''+e'. The s-orbital is a1'

Homework Equations


The Attempt at a Solution



I'm not entirely sure how this was obtained.
I'm certain that they are found from just reading the right side of the character table but I am unable to find any resources describing it any further.

Are you having problems understanding what the Mulliken symmetry symbols "a1" or "t1" mean?
 
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