MO Diagram from Group Theory: Central Atom

In summary, the conversation discusses the use of group theory to determine the orbitals of a central atom in a molecule, using the example of CO3^-2 with a D3h point group. The p-orbitals of carbon are described by a1''+e' and the s-orbital by a1'. The speaker is unsure of how these symbols were obtained and is looking for further resources to understand them better.
  • #1
mrshappy0
99
0

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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  • #2
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?
 

1. What is a MO diagram from group theory?

A MO (molecular orbital) diagram from group theory is a visual representation of the molecular orbitals of a molecule, specifically focusing on the central atom and its interactions with surrounding atoms. Group theory is used to predict the symmetry of these molecular orbitals.

2. How does group theory relate to MO diagrams?

Group theory is used to determine the symmetry of molecular orbitals, which is crucial in constructing a MO diagram. The symmetry determines the possible combinations and interactions between atomic orbitals, resulting in the formation of molecular orbitals.

3. What information can be obtained from a MO diagram from group theory?

A MO diagram from group theory can provide information about the energy levels and stability of molecular orbitals, as well as the bonding and antibonding nature of these orbitals. It can also show the number of bonding and antibonding orbitals, which can determine the overall stability of the molecule.

4. How does the central atom affect the MO diagram?

The central atom plays a crucial role in determining the symmetry and energy levels of the molecular orbitals in a MO diagram. Its interactions with surrounding atoms can result in different combinations of atomic orbitals, leading to the formation of unique molecular orbitals.

5. Can MO diagrams from group theory be used for all molecules?

Yes, MO diagrams from group theory can be used for all molecules. However, the accuracy and complexity of the diagram may vary depending on the molecule's size and complexity. Simple molecules with few atoms may have simpler MO diagrams, while larger and more complex molecules may have more intricate diagrams.

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