MO Diagram from Group Theory: Central Atom

[mrshappy0]

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.

 

[chemisttree]

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?